TSTP Solution File: GEO176+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO176+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 03:48:12 EDT 2022
% Result : Theorem 18.95s 5.55s
% Output : Proof 20.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GEO176+3 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Fri Jun 17 22:46:28 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.59/0.62 ____ _
% 0.59/0.62 ___ / __ \_____(_)___ ________ __________
% 0.59/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.62
% 0.59/0.62 A Theorem Prover for First-Order Logic
% 0.59/0.63 (ePrincess v.1.0)
% 0.59/0.63
% 0.59/0.63 (c) Philipp Rümmer, 2009-2015
% 0.59/0.63 (c) Peter Backeman, 2014-2015
% 0.59/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.63 Bug reports to peter@backeman.se
% 0.59/0.63
% 0.59/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.63
% 0.59/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.96/1.04 Prover 0: Preprocessing ...
% 2.66/1.32 Prover 0: Warning: ignoring some quantifiers
% 2.66/1.35 Prover 0: Constructing countermodel ...
% 18.14/5.32 Prover 0: gave up
% 18.14/5.32 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.14/5.37 Prover 1: Preprocessing ...
% 18.95/5.50 Prover 1: Constructing countermodel ...
% 18.95/5.55 Prover 1: proved (225ms)
% 18.95/5.55
% 18.95/5.55 No countermodel exists, formula is valid
% 18.95/5.55 % SZS status Theorem for theBenchmark
% 18.95/5.55
% 18.95/5.55 Generating proof ... found it (size 36)
% 20.41/5.86
% 20.41/5.86 % SZS output start Proof for theBenchmark
% 20.41/5.86 Assumed formulas after preprocessing and simplification:
% 20.41/5.86 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & intersection_point(v2, v3) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & convergent_lines(v2, v3) = 0 & distinct_points(v0, v6) = v7 & distinct_points(v0, v1) = 0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (unorthogonal_lines(v9, v11) = v13) | ~ (apart_point_and_line(v8, v9) = v12) | ~ (distinct_lines(v9, v10) = 0) | ? [v14] : ? [v15] : (unorthogonal_lines(v10, v11) = v15 & apart_point_and_line(v8, v10) = v14 & (v15 = 0 | v14 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (unorthogonal_lines(v8, v10) = v12) | ~ (unorthogonal_lines(v8, v9) = v11) | ? [v13] : ( ~ (v13 = 0) & convergent_lines(v9, v10) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (unorthogonal_lines(v8, v10) = v12) | ~ (unorthogonal_lines(v8, v9) = v11) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (unorthogonal_lines(v9, v10) = v16 & convergent_lines(v9, v10) = v15 & convergent_lines(v8, v10) = v14 & convergent_lines(v8, v9) = v13 & ( ~ (v16 = 0) | ~ (v15 = 0) | (v14 = 0 & v12 = 0) | (v13 = 0 & v11 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v9) = v11) | ~ (distinct_lines(v9, v10) = 0) | ? [v12] : ? [v13] : (apart_point_and_line(v8, v10) = v12 & convergent_lines(v9, v10) = v13 & (v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v9) = 0) | ~ (distinct_lines(v9, v10) = v11) | apart_point_and_line(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v9) = 0) | ~ (distinct_points(v8, v10) = v11) | apart_point_and_line(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (convergent_lines(v8, v10) = v11) | ~ (convergent_lines(v8, v9) = 0) | convergent_lines(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (convergent_lines(v8, v9) = 0) | ~ (distinct_lines(v9, v10) = v11) | convergent_lines(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (distinct_lines(v8, v10) = v11) | ~ (distinct_lines(v8, v9) = 0) | distinct_lines(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (distinct_points(v8, v10) = v11) | ~ (distinct_points(v8, v9) = 0) | distinct_points(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (orthogonal_lines(v11, v10) = v9) | ~ (orthogonal_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (incident_point_and_line(v11, v10) = v9) | ~ (incident_point_and_line(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (parallel_lines(v11, v10) = v9) | ~ (parallel_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (equal_lines(v11, v10) = v9) | ~ (equal_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (equal_points(v11, v10) = v9) | ~ (equal_points(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (orthogonal_through_point(v11, v10) = v9) | ~ (orthogonal_through_point(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unorthogonal_lines(v11, v10) = v9) | ~ (unorthogonal_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (parallel_through_point(v11, v10) = v9) | ~ (parallel_through_point(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (intersection_point(v11, v10) = v9) | ~ (intersection_point(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (line_connecting(v11, v10) = v9) | ~ (line_connecting(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (apart_point_and_line(v11, v10) = v9) | ~ (apart_point_and_line(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (convergent_lines(v11, v10) = v9) | ~ (convergent_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (distinct_lines(v11, v10) = v9) | ~ (distinct_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (distinct_points(v11, v10) = v9) | ~ (distinct_points(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v8, v10) = v11) | ~ (unorthogonal_lines(v8, v9) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (unorthogonal_lines(v9, v10) = v15 & convergent_lines(v9, v10) = v14 & convergent_lines(v8, v10) = v13 & convergent_lines(v8, v9) = v12 & ( ~ (v12 = 0) | (v15 = 0 & v14 = 0) | (v13 = 0 & v11 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (distinct_lines(v10, v11) = 0) | ~ (distinct_points(v8, v9) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (apart_point_and_line(v9, v11) = v15 & apart_point_and_line(v9, v10) = v14 & apart_point_and_line(v8, v11) = v13 & apart_point_and_line(v8, v10) = v12 & (v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (orthogonal_lines(v8, v9) = v10) | unorthogonal_lines(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (incident_point_and_line(v8, v9) = v10) | apart_point_and_line(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (parallel_lines(v8, v9) = v10) | convergent_lines(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equal_lines(v8, v9) = v10) | distinct_lines(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equal_points(v8, v9) = v10) | distinct_points(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unorthogonal_lines(v8, v9) = v10) | convergent_lines(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (point(v10) = v9) | ~ (point(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (line(v10) = v9) | ~ (line(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (orthogonal_through_point(v9, v8) = v10) | ~ (unorthogonal_lines(v10, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (orthogonal_through_point(v9, v8) = v10) | ~ (apart_point_and_line(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (orthogonal_through_point(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (point(v9) = v12 & line(v10) = v13 & line(v8) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | v13 = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (parallel_through_point(v9, v8) = v10) | ~ (apart_point_and_line(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (parallel_through_point(v9, v8) = v10) | ~ (convergent_lines(v10, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (parallel_through_point(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (point(v9) = v12 & line(v10) = v13 & line(v8) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | v13 = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection_point(v8, v9) = v10) | ~ (apart_point_and_line(v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection_point(v8, v9) = v10) | ~ (apart_point_and_line(v10, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection_point(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (point(v10) = v14 & line(v9) = v12 & line(v8) = v11 & convergent_lines(v8, v9) = v13 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | v14 = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v8, v9) = v10) | ~ (apart_point_and_line(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v8, v9) = v10) | ~ (apart_point_and_line(v8, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (point(v9) = v12 & point(v8) = v11 & line(v10) = v14 & distinct_points(v8, v9) = v13 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | v14 = 0))) & ! [v8] : ! [v9] : ( ~ (orthogonal_lines(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & unorthogonal_lines(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (incident_point_and_line(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (parallel_lines(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (equal_lines(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & distinct_lines(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (equal_points(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & distinct_points(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | convergent_lines(v8, v9) = 0) & ! [v8] : ~ (convergent_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_points(v8, v8) = 0) & (v5 = 0 | v4 = 0))
% 20.88/5.91 | 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, all_0_7_7 yields:
% 20.88/5.91 | (1) ~ (all_0_0_0 = 0) & intersection_point(all_0_5_5, all_0_4_4) = all_0_1_1 & apart_point_and_line(all_0_7_7, all_0_4_4) = all_0_2_2 & apart_point_and_line(all_0_7_7, all_0_5_5) = all_0_3_3 & convergent_lines(all_0_5_5, all_0_4_4) = 0 & distinct_points(all_0_7_7, all_0_1_1) = all_0_0_0 & distinct_points(all_0_7_7, all_0_6_6) = 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_2_2 = 0 | all_0_3_3 = 0)
% 20.88/5.92 |
% 20.88/5.92 | Applying alpha-rule on (1) yields:
% 20.88/5.92 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 20.88/5.92 | (3) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 20.88/5.92 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0))
% 20.88/5.92 | (5) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 20.88/5.92 | (6) intersection_point(all_0_5_5, all_0_4_4) = all_0_1_1
% 20.88/5.92 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 20.88/5.93 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 20.88/5.93 | (9) distinct_points(all_0_7_7, all_0_1_1) = all_0_0_0
% 20.88/5.93 | (10) ! [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))))
% 20.88/5.93 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0))
% 20.88/5.93 | (12) ! [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))))
% 20.88/5.93 | (13) ! [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)))
% 20.88/5.93 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 20.88/5.93 | (15) ! [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))
% 20.88/5.93 | (16) ! [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)
% 20.88/5.93 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 20.88/5.93 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 20.88/5.93 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 20.88/5.93 | (20) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 20.88/5.93 | (21) apart_point_and_line(all_0_7_7, all_0_4_4) = all_0_2_2
% 20.88/5.93 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 20.88/5.93 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 20.88/5.93 | (24) ! [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)))
% 20.88/5.93 | (25) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 20.88/5.93 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 20.88/5.93 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 20.88/5.93 | (28) distinct_points(all_0_7_7, all_0_6_6) = 0
% 20.88/5.93 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 20.88/5.93 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 20.88/5.93 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 20.88/5.93 | (32) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 20.88/5.93 | (33) ! [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)))
% 20.88/5.94 | (34) ~ (all_0_0_0 = 0)
% 20.88/5.94 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0))
% 20.88/5.94 | (36) all_0_2_2 = 0 | all_0_3_3 = 0
% 20.88/5.94 | (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)))
% 20.88/5.94 | (38) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 20.88/5.94 | (39) apart_point_and_line(all_0_7_7, all_0_5_5) = all_0_3_3
% 20.88/5.94 | (40) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 20.88/5.94 | (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)))
% 20.88/5.94 | (42) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 20.88/5.94 | (43) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 20.88/5.94 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 20.88/5.94 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0))
% 20.88/5.94 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 20.88/5.94 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 20.88/5.94 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 20.88/5.94 | (49) ! [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)))
% 20.88/5.94 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 20.88/5.94 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 20.88/5.94 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 20.88/5.94 | (53) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 20.88/5.94 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 20.88/5.94 | (55) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 20.88/5.94 | (56) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 20.88/5.94 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 20.88/5.94 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 20.88/5.94 | (59) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 20.88/5.94 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 20.88/5.94 | (61) ! [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)))
% 20.88/5.94 | (62) ! [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)
% 20.88/5.94 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 20.88/5.94 | (64) convergent_lines(all_0_5_5, all_0_4_4) = 0
% 20.88/5.94 |
% 20.88/5.94 | Instantiating formula (49) with all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_1_1, yields:
% 20.88/5.94 | (65) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_0_1_1) = v3 & line(all_0_4_4) = v1 & line(all_0_5_5) = v0 & convergent_lines(all_0_5_5, all_0_4_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 20.88/5.94 |
% 20.88/5.94 | Instantiating formula (16) with all_0_0_0, all_0_1_1, all_0_4_4, all_0_7_7 and discharging atoms distinct_points(all_0_7_7, all_0_1_1) = all_0_0_0, yields:
% 20.88/5.95 | (66) all_0_0_0 = 0 | ~ (apart_point_and_line(all_0_7_7, all_0_4_4) = 0) | apart_point_and_line(all_0_1_1, all_0_4_4) = 0
% 20.88/5.95 |
% 20.88/5.95 | Instantiating formula (16) with all_0_0_0, all_0_1_1, all_0_5_5, all_0_7_7 and discharging atoms distinct_points(all_0_7_7, all_0_1_1) = all_0_0_0, yields:
% 20.88/5.95 | (67) all_0_0_0 = 0 | ~ (apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | apart_point_and_line(all_0_1_1, all_0_5_5) = 0
% 20.88/5.95 |
% 20.88/5.95 | Instantiating (65) with all_16_0_8, all_16_1_9, all_16_2_10, all_16_3_11 yields:
% 20.88/5.95 | (68) point(all_0_1_1) = all_16_0_8 & line(all_0_4_4) = all_16_2_10 & line(all_0_5_5) = all_16_3_11 & convergent_lines(all_0_5_5, all_0_4_4) = all_16_1_9 & ( ~ (all_16_1_9 = 0) | ~ (all_16_2_10 = 0) | ~ (all_16_3_11 = 0) | all_16_0_8 = 0)
% 20.88/5.95 |
% 20.88/5.95 | Applying alpha-rule on (68) yields:
% 20.88/5.95 | (69) ~ (all_16_1_9 = 0) | ~ (all_16_2_10 = 0) | ~ (all_16_3_11 = 0) | all_16_0_8 = 0
% 20.88/5.95 | (70) line(all_0_4_4) = all_16_2_10
% 20.88/5.95 | (71) point(all_0_1_1) = all_16_0_8
% 20.88/5.95 | (72) line(all_0_5_5) = all_16_3_11
% 20.88/5.95 | (73) convergent_lines(all_0_5_5, all_0_4_4) = all_16_1_9
% 20.88/5.95 |
% 20.88/5.95 | Instantiating formula (50) with all_0_5_5, all_0_4_4, all_16_1_9, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = all_16_1_9, convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 20.88/5.95 | (74) all_16_1_9 = 0
% 20.88/5.95 |
% 20.88/5.95 | From (74) and (73) follows:
% 20.88/5.95 | (64) convergent_lines(all_0_5_5, all_0_4_4) = 0
% 20.88/5.95 |
% 20.88/5.95 +-Applying beta-rule and splitting (36), into two cases.
% 20.88/5.95 |-Branch one:
% 20.88/5.95 | (76) all_0_2_2 = 0
% 20.88/5.95 |
% 20.88/5.95 | From (76) and (21) follows:
% 20.88/5.95 | (77) apart_point_and_line(all_0_7_7, all_0_4_4) = 0
% 20.88/5.95 |
% 20.88/5.95 +-Applying beta-rule and splitting (66), into two cases.
% 20.88/5.95 |-Branch one:
% 20.88/5.95 | (78) ~ (apart_point_and_line(all_0_7_7, all_0_4_4) = 0)
% 20.88/5.95 |
% 20.88/5.95 | Using (77) and (78) yields:
% 20.88/5.95 | (79) $false
% 20.88/5.95 |
% 20.88/5.95 |-The branch is then unsatisfiable
% 20.88/5.95 |-Branch two:
% 20.88/5.95 | (77) apart_point_and_line(all_0_7_7, all_0_4_4) = 0
% 20.88/5.95 | (81) all_0_0_0 = 0 | apart_point_and_line(all_0_1_1, all_0_4_4) = 0
% 20.88/5.95 |
% 20.88/5.95 +-Applying beta-rule and splitting (81), into two cases.
% 20.88/5.95 |-Branch one:
% 20.88/5.95 | (82) apart_point_and_line(all_0_1_1, all_0_4_4) = 0
% 20.88/5.95 |
% 20.88/5.95 | Instantiating formula (17) with all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_1_1, apart_point_and_line(all_0_1_1, all_0_4_4) = 0, yields:
% 20.88/5.95 | (83) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = v0)
% 20.88/5.95 |
% 20.88/5.95 | Instantiating (83) with all_61_0_12 yields:
% 20.88/5.95 | (84) ~ (all_61_0_12 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_61_0_12
% 20.88/5.95 |
% 20.88/5.95 | Applying alpha-rule on (84) yields:
% 20.88/5.95 | (85) ~ (all_61_0_12 = 0)
% 20.88/5.95 | (86) convergent_lines(all_0_5_5, all_0_4_4) = all_61_0_12
% 20.88/5.95 |
% 20.88/5.95 | Instantiating formula (50) with all_0_5_5, all_0_4_4, all_61_0_12, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = all_61_0_12, convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 20.88/5.95 | (87) all_61_0_12 = 0
% 20.88/5.95 |
% 20.88/5.95 | Equations (87) can reduce 85 to:
% 20.88/5.95 | (88) $false
% 20.88/5.95 |
% 20.88/5.95 |-The branch is then unsatisfiable
% 20.88/5.95 |-Branch two:
% 20.88/5.95 | (89) ~ (apart_point_and_line(all_0_1_1, all_0_4_4) = 0)
% 20.88/5.95 | (90) all_0_0_0 = 0
% 20.88/5.95 |
% 20.88/5.95 | Equations (90) can reduce 34 to:
% 20.88/5.95 | (88) $false
% 20.88/5.95 |
% 20.88/5.95 |-The branch is then unsatisfiable
% 20.88/5.95 |-Branch two:
% 20.88/5.95 | (92) ~ (all_0_2_2 = 0)
% 20.88/5.95 | (93) all_0_3_3 = 0
% 20.88/5.95 |
% 20.88/5.95 | From (93) and (39) follows:
% 20.88/5.95 | (94) apart_point_and_line(all_0_7_7, all_0_5_5) = 0
% 20.88/5.95 |
% 20.88/5.95 +-Applying beta-rule and splitting (67), into two cases.
% 20.88/5.95 |-Branch one:
% 20.88/5.95 | (95) ~ (apart_point_and_line(all_0_7_7, all_0_5_5) = 0)
% 20.88/5.95 |
% 20.88/5.95 | Using (94) and (95) yields:
% 20.88/5.95 | (79) $false
% 20.88/5.95 |
% 20.88/5.95 |-The branch is then unsatisfiable
% 20.88/5.95 |-Branch two:
% 20.88/5.95 | (94) apart_point_and_line(all_0_7_7, all_0_5_5) = 0
% 20.88/5.95 | (98) all_0_0_0 = 0 | apart_point_and_line(all_0_1_1, all_0_5_5) = 0
% 20.88/5.95 |
% 20.88/5.95 +-Applying beta-rule and splitting (98), into two cases.
% 20.88/5.95 |-Branch one:
% 20.88/5.95 | (99) apart_point_and_line(all_0_1_1, all_0_5_5) = 0
% 20.88/5.95 |
% 20.88/5.95 | Instantiating formula (58) with all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_1_1, apart_point_and_line(all_0_1_1, all_0_5_5) = 0, yields:
% 20.88/5.95 | (83) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = v0)
% 20.88/5.95 |
% 20.88/5.95 | Instantiating (83) with all_61_0_13 yields:
% 20.88/5.95 | (101) ~ (all_61_0_13 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_61_0_13
% 20.88/5.95 |
% 20.88/5.95 | Applying alpha-rule on (101) yields:
% 20.88/5.95 | (102) ~ (all_61_0_13 = 0)
% 20.88/5.95 | (103) convergent_lines(all_0_5_5, all_0_4_4) = all_61_0_13
% 20.88/5.95 |
% 20.88/5.95 | Instantiating formula (50) with all_0_5_5, all_0_4_4, all_61_0_13, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = all_61_0_13, convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 20.88/5.95 | (104) all_61_0_13 = 0
% 20.88/5.95 |
% 20.88/5.95 | Equations (104) can reduce 102 to:
% 20.88/5.95 | (88) $false
% 20.88/5.95 |
% 20.88/5.95 |-The branch is then unsatisfiable
% 20.88/5.95 |-Branch two:
% 20.88/5.95 | (106) ~ (apart_point_and_line(all_0_1_1, all_0_5_5) = 0)
% 20.88/5.95 | (90) all_0_0_0 = 0
% 20.88/5.95 |
% 20.88/5.95 | Equations (90) can reduce 34 to:
% 20.88/5.95 | (88) $false
% 20.88/5.95 |
% 20.88/5.95 |-The branch is then unsatisfiable
% 20.88/5.95 % SZS output end Proof for theBenchmark
% 20.88/5.95
% 20.88/5.95 5319ms
%------------------------------------------------------------------------------