TSTP Solution File: GEO210+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO210+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 03:48:45 EDT 2022
% Result : Theorem 3.96s 1.60s
% Output : Proof 5.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : GEO210+1 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n025.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 06:00:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.59 ____ _
% 0.18/0.59 ___ / __ \_____(_)___ ________ __________
% 0.18/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.59
% 0.18/0.59 A Theorem Prover for First-Order Logic
% 0.18/0.59 (ePrincess v.1.0)
% 0.18/0.59
% 0.18/0.59 (c) Philipp Rümmer, 2009-2015
% 0.18/0.59 (c) Peter Backeman, 2014-2015
% 0.18/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.59 Bug reports to peter@backeman.se
% 0.18/0.59
% 0.18/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.77/0.96 Prover 0: Preprocessing ...
% 2.19/1.12 Prover 0: Warning: ignoring some quantifiers
% 2.19/1.14 Prover 0: Constructing countermodel ...
% 3.41/1.41 Prover 0: gave up
% 3.41/1.41 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.41/1.44 Prover 1: Preprocessing ...
% 3.96/1.56 Prover 1: Constructing countermodel ...
% 3.96/1.60 Prover 1: proved (194ms)
% 3.96/1.60
% 3.96/1.60 No countermodel exists, formula is valid
% 3.96/1.60 % SZS status Theorem for theBenchmark
% 3.96/1.60
% 3.96/1.60 Generating proof ... found it (size 29)
% 5.32/1.82
% 5.32/1.82 % SZS output start Proof for theBenchmark
% 5.32/1.82 Assumed formulas after preprocessing and simplification:
% 5.32/1.82 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v4 = 0) & ~ (v3 = 0) & orthogonal_through_point(v2, v0) = v5 & unorthogonal_lines(v1, v2) = v4 & apart_point_and_line(v0, v1) = v3 & distinct_lines(v1, v5) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (apart_point_and_line(v6, v7) = v10) | ~ (distinct_lines(v7, v8) = 0) | ? [v12] : ? [v13] : (unorthogonal_lines(v8, v9) = v13 & apart_point_and_line(v6, v8) = v12 & (v13 = 0 | v12 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v10] : ? [v11] : (apart_point_and_line(v6, v8) = v10 & convergent_lines(v7, v8) = v11 & (v11 = 0 | v10 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v6, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v6, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (orthogonal_through_point(v9, v8) = v7) | ~ (orthogonal_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (unorthogonal_lines(v9, v8) = v7) | ~ (unorthogonal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_through_point(v9, v8) = v7) | ~ (parallel_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (apart_point_and_line(v9, v8) = v7) | ~ (apart_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (convergent_lines(v9, v8) = v7) | ~ (convergent_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_lines(v9, v8) = v7) | ~ (distinct_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_points(v9, v8) = v7) | ~ (distinct_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (unorthogonal_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (unorthogonal_lines(v7, v8) = v13 & convergent_lines(v7, v8) = v12 & convergent_lines(v6, v8) = v11 & convergent_lines(v6, v7) = v10 & ( ~ (v10 = 0) | (v13 = 0 & v12 = 0) | (v11 = 0 & v9 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | ~ (distinct_points(v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (apart_point_and_line(v7, v9) = v13 & apart_point_and_line(v7, v8) = v12 & apart_point_and_line(v6, v9) = v11 & apart_point_and_line(v6, v8) = v10 & (v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ~ (unorthogonal_lines(v8, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ~ (apart_point_and_line(v6, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ~ (apart_point_and_line(v6, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ~ (convergent_lines(v8, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ~ (apart_point_and_line(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ~ (apart_point_and_line(v8, v6) = 0) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ~ (apart_point_and_line(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & distinct_points(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ~ (apart_point_and_line(v6, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & distinct_points(v6, v7) = v9)) & ! [v6] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0))
% 5.35/1.86 | 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 yields:
% 5.35/1.86 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0) & orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_0_0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1 & apart_point_and_line(all_0_5_5, all_0_4_4) = all_0_2_2 & distinct_lines(all_0_4_4, all_0_0_0) = 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] : (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_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 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [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] : ( ~ (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] : ( ~ (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] : ( ~ (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] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 5.35/1.87 |
% 5.35/1.87 | Applying alpha-rule on (1) yields:
% 5.35/1.87 | (2) ! [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)))
% 5.35/1.87 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 5.35/1.87 | (4) ! [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))))
% 5.35/1.87 | (5) ~ (all_0_2_2 = 0)
% 5.35/1.87 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 5.35/1.87 | (7) ~ (all_0_1_1 = 0)
% 5.35/1.87 | (8) ! [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)
% 5.35/1.87 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 5.35/1.87 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 5.35/1.88 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 5.35/1.88 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0))
% 5.35/1.88 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 5.35/1.88 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 5.35/1.88 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 5.35/1.88 | (16) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 5.35/1.88 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 5.35/1.88 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 5.35/1.88 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0))
% 5.35/1.88 | (20) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 5.35/1.88 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 5.35/1.88 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 5.35/1.88 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ? [v7] : (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = 0 | v6 = 0)))
% 5.35/1.88 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 5.35/1.88 | (25) orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_0_0
% 5.35/1.88 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 5.35/1.88 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 5.35/1.88 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 5.35/1.88 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 5.35/1.88 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0))
% 5.35/1.88 | (31) ! [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)
% 5.35/1.88 | (32) apart_point_and_line(all_0_5_5, all_0_4_4) = all_0_2_2
% 5.35/1.88 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0))
% 5.35/1.88 | (34) distinct_lines(all_0_4_4, all_0_0_0) = 0
% 5.35/1.88 | (35) ! [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)))
% 5.35/1.88 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 5.35/1.88 | (37) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 5.35/1.88 | (38) unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1
% 5.35/1.88 |
% 5.35/1.88 | Instantiating formula (23) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_4_4) = all_0_2_2, distinct_lines(all_0_4_4, all_0_0_0) = 0, yields:
% 5.35/1.88 | (39) all_0_1_1 = 0 | all_0_2_2 = 0 | ? [v0] : ? [v1] : (unorthogonal_lines(all_0_0_0, all_0_3_3) = v1 & apart_point_and_line(all_0_5_5, all_0_0_0) = v0 & (v1 = 0 | v0 = 0))
% 5.35/1.88 |
% 5.35/1.88 | Instantiating formula (35) with all_0_2_2, all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_4_4) = all_0_2_2, distinct_lines(all_0_4_4, all_0_0_0) = 0, yields:
% 5.35/1.89 | (40) all_0_2_2 = 0 | ? [v0] : ? [v1] : (apart_point_and_line(all_0_5_5, all_0_0_0) = v0 & convergent_lines(all_0_4_4, all_0_0_0) = v1 & (v1 = 0 | v0 = 0))
% 5.35/1.89 |
% 5.35/1.89 +-Applying beta-rule and splitting (40), into two cases.
% 5.35/1.89 |-Branch one:
% 5.35/1.89 | (41) all_0_2_2 = 0
% 5.35/1.89 |
% 5.35/1.89 | Equations (41) can reduce 5 to:
% 5.35/1.89 | (42) $false
% 5.35/1.89 |
% 5.35/1.89 |-The branch is then unsatisfiable
% 5.35/1.89 |-Branch two:
% 5.35/1.89 | (5) ~ (all_0_2_2 = 0)
% 5.35/1.89 | (44) ? [v0] : ? [v1] : (apart_point_and_line(all_0_5_5, all_0_0_0) = v0 & convergent_lines(all_0_4_4, all_0_0_0) = v1 & (v1 = 0 | v0 = 0))
% 5.35/1.89 |
% 5.35/1.89 | Instantiating (44) with all_22_0_6, all_22_1_7 yields:
% 5.35/1.89 | (45) apart_point_and_line(all_0_5_5, all_0_0_0) = all_22_1_7 & convergent_lines(all_0_4_4, all_0_0_0) = all_22_0_6 & (all_22_0_6 = 0 | all_22_1_7 = 0)
% 5.35/1.89 |
% 5.35/1.89 | Applying alpha-rule on (45) yields:
% 5.35/1.89 | (46) apart_point_and_line(all_0_5_5, all_0_0_0) = all_22_1_7
% 5.35/1.89 | (47) convergent_lines(all_0_4_4, all_0_0_0) = all_22_0_6
% 5.35/1.89 | (48) all_22_0_6 = 0 | all_22_1_7 = 0
% 5.35/1.89 |
% 5.35/1.89 +-Applying beta-rule and splitting (39), into two cases.
% 5.35/1.89 |-Branch one:
% 5.35/1.89 | (49) all_0_1_1 = 0
% 5.35/1.89 |
% 5.35/1.89 | Equations (49) can reduce 7 to:
% 5.35/1.89 | (42) $false
% 5.35/1.89 |
% 5.35/1.89 |-The branch is then unsatisfiable
% 5.35/1.89 |-Branch two:
% 5.35/1.89 | (7) ~ (all_0_1_1 = 0)
% 5.35/1.89 | (52) all_0_2_2 = 0 | ? [v0] : ? [v1] : (unorthogonal_lines(all_0_0_0, all_0_3_3) = v1 & apart_point_and_line(all_0_5_5, all_0_0_0) = v0 & (v1 = 0 | v0 = 0))
% 5.35/1.89 |
% 5.35/1.89 +-Applying beta-rule and splitting (52), into two cases.
% 5.35/1.89 |-Branch one:
% 5.35/1.89 | (41) all_0_2_2 = 0
% 5.35/1.89 |
% 5.35/1.89 | Equations (41) can reduce 5 to:
% 5.35/1.89 | (42) $false
% 5.35/1.89 |
% 5.35/1.89 |-The branch is then unsatisfiable
% 5.35/1.89 |-Branch two:
% 5.35/1.89 | (5) ~ (all_0_2_2 = 0)
% 5.35/1.89 | (56) ? [v0] : ? [v1] : (unorthogonal_lines(all_0_0_0, all_0_3_3) = v1 & apart_point_and_line(all_0_5_5, all_0_0_0) = v0 & (v1 = 0 | v0 = 0))
% 5.35/1.89 |
% 5.35/1.89 | Instantiating (56) with all_31_0_8, all_31_1_9 yields:
% 5.35/1.89 | (57) unorthogonal_lines(all_0_0_0, all_0_3_3) = all_31_0_8 & apart_point_and_line(all_0_5_5, all_0_0_0) = all_31_1_9 & (all_31_0_8 = 0 | all_31_1_9 = 0)
% 5.35/1.89 |
% 5.35/1.89 | Applying alpha-rule on (57) yields:
% 5.35/1.89 | (58) unorthogonal_lines(all_0_0_0, all_0_3_3) = all_31_0_8
% 5.35/1.89 | (59) apart_point_and_line(all_0_5_5, all_0_0_0) = all_31_1_9
% 5.35/1.89 | (60) all_31_0_8 = 0 | all_31_1_9 = 0
% 5.35/1.89 |
% 5.35/1.89 | Instantiating formula (12) with all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_0_0, yields:
% 5.35/1.89 | (61) ~ (unorthogonal_lines(all_0_0_0, all_0_3_3) = 0)
% 5.35/1.89 |
% 5.35/1.89 | Instantiating formula (19) with all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_0_0, yields:
% 5.35/1.89 | (62) ~ (apart_point_and_line(all_0_5_5, all_0_0_0) = 0)
% 5.35/1.89 |
% 5.35/1.89 | Instantiating formula (6) with all_0_5_5, all_0_0_0, all_22_1_7, all_31_1_9 and discharging atoms apart_point_and_line(all_0_5_5, all_0_0_0) = all_31_1_9, apart_point_and_line(all_0_5_5, all_0_0_0) = all_22_1_7, yields:
% 5.35/1.89 | (63) all_31_1_9 = all_22_1_7
% 5.35/1.89 |
% 5.35/1.89 | From (63) and (59) follows:
% 5.35/1.89 | (46) apart_point_and_line(all_0_5_5, all_0_0_0) = all_22_1_7
% 5.35/1.89 |
% 5.35/1.89 | Using (58) and (61) yields:
% 5.35/1.89 | (65) ~ (all_31_0_8 = 0)
% 5.35/1.89 |
% 5.35/1.89 | Using (46) and (62) yields:
% 5.35/1.89 | (66) ~ (all_22_1_7 = 0)
% 5.35/1.89 |
% 5.35/1.89 +-Applying beta-rule and splitting (60), into two cases.
% 5.35/1.89 |-Branch one:
% 5.35/1.89 | (67) all_31_0_8 = 0
% 5.35/1.89 |
% 5.35/1.89 | Equations (67) can reduce 65 to:
% 5.35/1.89 | (42) $false
% 5.35/1.89 |
% 5.35/1.89 |-The branch is then unsatisfiable
% 5.35/1.89 |-Branch two:
% 5.35/1.89 | (65) ~ (all_31_0_8 = 0)
% 5.35/1.89 | (70) all_31_1_9 = 0
% 5.35/1.89 |
% 5.35/1.89 | Combining equations (70,63) yields a new equation:
% 5.35/1.89 | (71) all_22_1_7 = 0
% 5.35/1.89 |
% 5.35/1.89 | Equations (71) can reduce 66 to:
% 5.35/1.89 | (42) $false
% 5.35/1.89 |
% 5.35/1.89 |-The branch is then unsatisfiable
% 5.35/1.89 % SZS output end Proof for theBenchmark
% 5.35/1.89
% 5.35/1.89 1294ms
%------------------------------------------------------------------------------