TSTP Solution File: GEO179+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO179+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.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 03:48:16 EDT 2022
% Result : Theorem 14.29s 3.98s
% Output : Proof 16.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO179+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n015.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 : Fri Jun 17 19:32:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.88/0.93 Prover 0: Preprocessing ...
% 2.26/1.14 Prover 0: Warning: ignoring some quantifiers
% 2.26/1.17 Prover 0: Constructing countermodel ...
% 13.29/3.75 Prover 0: gave up
% 13.29/3.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 13.29/3.79 Prover 1: Preprocessing ...
% 14.29/3.92 Prover 1: Constructing countermodel ...
% 14.29/3.98 Prover 1: proved (229ms)
% 14.29/3.98
% 14.29/3.98 No countermodel exists, formula is valid
% 14.29/3.98 % SZS status Theorem for theBenchmark
% 14.29/3.98
% 14.29/3.98 Generating proof ... found it (size 62)
% 16.13/4.31
% 16.13/4.31 % SZS output start Proof for theBenchmark
% 16.13/4.31 Assumed formulas after preprocessing and simplification:
% 16.13/4.31 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (line_connecting(v2, v1) = v6 & line_connecting(v2, v0) = v4 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = 0 & distinct_lines(v3, v6) = v7 & distinct_lines(v3, v4) = v5 & 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] : ( ~ (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] : ( ~ (point(v9) = 0) | ~ (point(v8) = 0) | ? [v10] : ? [v11] : ? [v12] : (line(v11) = v12 & line_connecting(v8, v9) = v11 & distinct_points(v8, v9) = v10 & ( ~ (v10 = 0) | v12 = 0))) & ! [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) & ( ~ (v7 = 0) | ~ (v5 = 0)))
% 16.13/4.36 | 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:
% 16.13/4.36 | (1) line_connecting(all_0_5_5, all_0_6_6) = all_0_1_1 & line_connecting(all_0_5_5, all_0_7_7) = all_0_3_3 & line_connecting(all_0_7_7, all_0_6_6) = all_0_4_4 & apart_point_and_line(all_0_5_5, all_0_4_4) = 0 & distinct_lines(all_0_4_4, all_0_1_1) = all_0_0_0 & distinct_lines(all_0_4_4, all_0_3_3) = all_0_2_2 & 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] : ( ~ (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] : ( ~ (point(v1) = 0) | ~ (point(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (line(v3) = v4 & line_connecting(v0, v1) = v3 & distinct_points(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0))) & ! [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_2_2 = 0))
% 16.42/4.37 |
% 16.42/4.37 | Applying alpha-rule on (1) yields:
% 16.42/4.37 | (2) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 16.42/4.37 | (3) ! [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)))
% 16.42/4.37 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 16.42/4.37 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 16.42/4.37 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 16.42/4.37 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 16.42/4.37 | (8) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 16.42/4.38 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 16.42/4.38 | (10) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 16.42/4.38 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 16.42/4.38 | (12) ! [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)))
% 16.42/4.38 | (13) apart_point_and_line(all_0_5_5, all_0_4_4) = 0
% 16.42/4.38 | (14) ! [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))))
% 16.42/4.38 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 16.42/4.38 | (16) ~ (all_0_0_0 = 0) | ~ (all_0_2_2 = 0)
% 16.42/4.38 | (17) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 16.42/4.38 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0))
% 16.42/4.38 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 16.42/4.38 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 16.42/4.38 | (21) ! [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))))
% 16.42/4.38 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 16.42/4.38 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 16.42/4.38 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 16.42/4.38 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 16.42/4.38 | (26) line_connecting(all_0_7_7, all_0_6_6) = all_0_4_4
% 16.42/4.38 | (27) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 16.42/4.38 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 16.42/4.38 | (29) distinct_lines(all_0_4_4, all_0_1_1) = all_0_0_0
% 16.42/4.38 | (30) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 16.42/4.38 | (31) ! [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)))
% 16.42/4.38 | (32) ! [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)))
% 16.42/4.38 | (33) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 16.42/4.38 | (34) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 16.42/4.38 | (35) line_connecting(all_0_5_5, all_0_7_7) = all_0_3_3
% 16.42/4.38 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0))
% 16.42/4.39 | (37) ! [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)
% 16.42/4.39 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0))
% 16.42/4.39 | (39) ! [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)
% 16.42/4.39 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 16.42/4.39 | (41) ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (point(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (line(v3) = v4 & line_connecting(v0, v1) = v3 & distinct_points(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0)))
% 16.42/4.39 | (42) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 16.42/4.39 | (43) distinct_lines(all_0_4_4, all_0_3_3) = all_0_2_2
% 16.42/4.39 | (44) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 16.42/4.39 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 16.42/4.39 | (46) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 16.42/4.39 | (47) ! [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)))
% 16.42/4.39 | (48) ! [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))
% 16.42/4.39 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 16.42/4.39 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 16.42/4.39 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 16.42/4.39 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 16.42/4.39 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 16.42/4.39 | (54) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 16.42/4.39 | (55) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 16.42/4.39 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0))
% 16.42/4.39 | (57) line_connecting(all_0_5_5, all_0_6_6) = all_0_1_1
% 16.42/4.39 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 16.42/4.39 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 16.42/4.39 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 16.42/4.39 | (61) ! [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)))
% 16.42/4.39 | (62) distinct_points(all_0_7_7, all_0_6_6) = 0
% 16.42/4.39 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 16.42/4.39 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 16.42/4.39 |
% 16.42/4.39 | Instantiating formula (63) with all_0_4_4, all_0_3_3, all_0_2_2, all_0_0_0 and discharging atoms distinct_lines(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 16.42/4.39 | (65) all_0_0_0 = all_0_2_2 | ~ (distinct_lines(all_0_4_4, all_0_3_3) = all_0_0_0)
% 16.42/4.39 |
% 16.42/4.39 | Instantiating formula (58) with all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_4_4, yields:
% 16.42/4.39 | (66) ~ (apart_point_and_line(all_0_6_6, all_0_4_4) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)
% 16.42/4.39 |
% 16.42/4.39 | Instantiating formula (6) with all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_4_4, yields:
% 16.42/4.39 | (67) ~ (apart_point_and_line(all_0_7_7, all_0_4_4) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)
% 16.42/4.39 |
% 16.42/4.39 | Instantiating formula (37) with all_0_0_0, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_4_4) = 0, distinct_lines(all_0_4_4, all_0_1_1) = all_0_0_0, yields:
% 16.42/4.39 | (68) all_0_0_0 = 0 | apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 16.42/4.39 |
% 16.42/4.39 | Instantiating formula (37) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_4_4) = 0, distinct_lines(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 16.42/4.40 | (69) all_0_2_2 = 0 | apart_point_and_line(all_0_5_5, all_0_3_3) = 0
% 16.42/4.40 |
% 16.42/4.40 +-Applying beta-rule and splitting (65), into two cases.
% 16.42/4.40 |-Branch one:
% 16.42/4.40 | (70) ~ (distinct_lines(all_0_4_4, all_0_3_3) = all_0_0_0)
% 16.42/4.40 |
% 16.42/4.40 +-Applying beta-rule and splitting (67), into two cases.
% 16.42/4.40 |-Branch one:
% 16.42/4.40 | (71) ~ (apart_point_and_line(all_0_7_7, all_0_4_4) = 0)
% 16.42/4.40 |
% 16.42/4.40 +-Applying beta-rule and splitting (66), into two cases.
% 16.42/4.40 |-Branch one:
% 16.42/4.40 | (72) ~ (apart_point_and_line(all_0_6_6, all_0_4_4) = 0)
% 16.42/4.40 |
% 16.42/4.40 | Using (43) and (70) yields:
% 16.42/4.40 | (73) ~ (all_0_0_0 = all_0_2_2)
% 16.42/4.40 |
% 16.42/4.40 +-Applying beta-rule and splitting (16), into two cases.
% 16.42/4.40 |-Branch one:
% 16.42/4.40 | (74) ~ (all_0_0_0 = 0)
% 16.42/4.40 |
% 16.42/4.40 +-Applying beta-rule and splitting (68), into two cases.
% 16.42/4.40 |-Branch one:
% 16.42/4.40 | (75) apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 16.42/4.40 |
% 16.42/4.40 | Instantiating formula (6) with all_0_1_1, all_0_6_6, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_6_6) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_1_1) = 0, yields:
% 16.42/4.40 | (76) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0)
% 16.42/4.40 |
% 16.42/4.40 | Instantiating (76) with all_46_0_8 yields:
% 16.42/4.40 | (77) ~ (all_46_0_8 = 0) & distinct_points(all_0_5_5, all_0_6_6) = all_46_0_8
% 16.42/4.40 |
% 16.42/4.40 | Applying alpha-rule on (77) yields:
% 16.42/4.40 | (78) ~ (all_46_0_8 = 0)
% 16.42/4.40 | (79) distinct_points(all_0_5_5, all_0_6_6) = all_46_0_8
% 16.42/4.40 |
% 16.42/4.40 | Instantiating formula (39) with all_46_0_8, all_0_6_6, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_4_4) = 0, distinct_points(all_0_5_5, all_0_6_6) = all_46_0_8, ~ (apart_point_and_line(all_0_6_6, all_0_4_4) = 0), yields:
% 16.42/4.40 | (80) all_46_0_8 = 0
% 16.42/4.40 |
% 16.42/4.40 | Equations (80) can reduce 78 to:
% 16.42/4.40 | (81) $false
% 16.42/4.40 |
% 16.42/4.40 |-The branch is then unsatisfiable
% 16.42/4.40 |-Branch two:
% 16.42/4.40 | (82) ~ (apart_point_and_line(all_0_5_5, all_0_1_1) = 0)
% 16.42/4.40 | (83) all_0_0_0 = 0
% 16.42/4.40 |
% 16.42/4.40 | Equations (83) can reduce 74 to:
% 16.42/4.40 | (81) $false
% 16.42/4.40 |
% 16.42/4.40 |-The branch is then unsatisfiable
% 16.42/4.40 |-Branch two:
% 16.42/4.40 | (83) all_0_0_0 = 0
% 16.42/4.40 | (86) ~ (all_0_2_2 = 0)
% 16.42/4.40 |
% 16.42/4.40 | Equations (83) can reduce 73 to:
% 16.42/4.40 | (87) ~ (all_0_2_2 = 0)
% 16.42/4.40 |
% 16.42/4.40 | Simplifying 87 yields:
% 16.42/4.40 | (86) ~ (all_0_2_2 = 0)
% 16.42/4.40 |
% 16.42/4.40 +-Applying beta-rule and splitting (69), into two cases.
% 16.42/4.40 |-Branch one:
% 16.42/4.40 | (89) apart_point_and_line(all_0_5_5, all_0_3_3) = 0
% 16.42/4.40 |
% 16.42/4.40 | Instantiating formula (6) with all_0_3_3, all_0_7_7, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_7_7) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_3_3) = 0, yields:
% 16.42/4.40 | (90) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0)
% 16.42/4.40 |
% 16.42/4.40 | Instantiating (90) with all_67_0_17 yields:
% 16.42/4.40 | (91) ~ (all_67_0_17 = 0) & distinct_points(all_0_5_5, all_0_7_7) = all_67_0_17
% 16.42/4.40 |
% 16.42/4.40 | Applying alpha-rule on (91) yields:
% 16.42/4.40 | (92) ~ (all_67_0_17 = 0)
% 16.42/4.40 | (93) distinct_points(all_0_5_5, all_0_7_7) = all_67_0_17
% 16.42/4.40 |
% 16.42/4.40 | Instantiating formula (39) with all_67_0_17, all_0_7_7, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_4_4) = 0, distinct_points(all_0_5_5, all_0_7_7) = all_67_0_17, ~ (apart_point_and_line(all_0_7_7, all_0_4_4) = 0), yields:
% 16.42/4.40 | (94) all_67_0_17 = 0
% 16.42/4.40 |
% 16.42/4.40 | Equations (94) can reduce 92 to:
% 16.42/4.40 | (81) $false
% 16.42/4.40 |
% 16.42/4.40 |-The branch is then unsatisfiable
% 16.42/4.40 |-Branch two:
% 16.42/4.40 | (96) ~ (apart_point_and_line(all_0_5_5, all_0_3_3) = 0)
% 16.42/4.40 | (97) all_0_2_2 = 0
% 16.42/4.40 |
% 16.42/4.40 | Equations (97) can reduce 86 to:
% 16.42/4.40 | (81) $false
% 16.42/4.40 |
% 16.42/4.40 |-The branch is then unsatisfiable
% 16.42/4.40 |-Branch two:
% 16.42/4.40 | (99) apart_point_and_line(all_0_6_6, all_0_4_4) = 0
% 16.42/4.40 | (100) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)
% 16.42/4.40 |
% 16.42/4.40 | Instantiating (100) with all_26_0_18 yields:
% 16.42/4.40 | (101) ~ (all_26_0_18 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_26_0_18
% 16.42/4.40 |
% 16.42/4.40 | Applying alpha-rule on (101) yields:
% 16.42/4.40 | (102) ~ (all_26_0_18 = 0)
% 16.42/4.40 | (103) distinct_points(all_0_7_7, all_0_6_6) = all_26_0_18
% 16.42/4.40 |
% 16.42/4.40 | Instantiating formula (52) with all_0_7_7, all_0_6_6, all_26_0_18, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_26_0_18, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 16.42/4.40 | (104) all_26_0_18 = 0
% 16.42/4.40 |
% 16.42/4.40 | Equations (104) can reduce 102 to:
% 16.42/4.40 | (81) $false
% 16.42/4.40 |
% 16.42/4.40 |-The branch is then unsatisfiable
% 16.42/4.40 |-Branch two:
% 16.42/4.40 | (106) apart_point_and_line(all_0_7_7, all_0_4_4) = 0
% 16.42/4.40 | (100) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)
% 16.42/4.40 |
% 16.42/4.40 | Instantiating (100) with all_22_0_19 yields:
% 16.42/4.40 | (108) ~ (all_22_0_19 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_22_0_19
% 16.42/4.40 |
% 16.42/4.40 | Applying alpha-rule on (108) yields:
% 16.42/4.40 | (109) ~ (all_22_0_19 = 0)
% 16.42/4.40 | (110) distinct_points(all_0_7_7, all_0_6_6) = all_22_0_19
% 16.42/4.40 |
% 16.42/4.40 | Instantiating formula (52) with all_0_7_7, all_0_6_6, all_22_0_19, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_22_0_19, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 16.42/4.40 | (111) all_22_0_19 = 0
% 16.42/4.40 |
% 16.42/4.40 | Equations (111) can reduce 109 to:
% 16.42/4.40 | (81) $false
% 16.42/4.40 |
% 16.42/4.40 |-The branch is then unsatisfiable
% 16.42/4.40 |-Branch two:
% 16.42/4.40 | (113) distinct_lines(all_0_4_4, all_0_3_3) = all_0_0_0
% 16.42/4.40 | (114) all_0_0_0 = all_0_2_2
% 16.42/4.40 |
% 16.42/4.40 +-Applying beta-rule and splitting (16), into two cases.
% 16.42/4.40 |-Branch one:
% 16.42/4.40 | (74) ~ (all_0_0_0 = 0)
% 16.42/4.40 |
% 16.42/4.40 | Equations (114) can reduce 74 to:
% 16.42/4.40 | (86) ~ (all_0_2_2 = 0)
% 16.42/4.40 |
% 16.42/4.40 +-Applying beta-rule and splitting (69), into two cases.
% 16.42/4.40 |-Branch one:
% 16.42/4.40 | (89) apart_point_and_line(all_0_5_5, all_0_3_3) = 0
% 16.42/4.40 |
% 16.42/4.40 +-Applying beta-rule and splitting (67), into two cases.
% 16.42/4.40 |-Branch one:
% 16.42/4.40 | (71) ~ (apart_point_and_line(all_0_7_7, all_0_4_4) = 0)
% 16.42/4.40 |
% 16.42/4.40 | Instantiating formula (6) with all_0_3_3, all_0_7_7, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_7_7) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_3_3) = 0, yields:
% 16.42/4.40 | (90) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0)
% 16.42/4.40 |
% 16.42/4.40 | Instantiating (90) with all_47_0_20 yields:
% 16.42/4.40 | (120) ~ (all_47_0_20 = 0) & distinct_points(all_0_5_5, all_0_7_7) = all_47_0_20
% 16.42/4.40 |
% 16.42/4.40 | Applying alpha-rule on (120) yields:
% 16.42/4.40 | (121) ~ (all_47_0_20 = 0)
% 16.42/4.40 | (122) distinct_points(all_0_5_5, all_0_7_7) = all_47_0_20
% 16.42/4.40 |
% 16.42/4.40 | Instantiating formula (39) with all_47_0_20, all_0_7_7, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_4_4) = 0, distinct_points(all_0_5_5, all_0_7_7) = all_47_0_20, ~ (apart_point_and_line(all_0_7_7, all_0_4_4) = 0), yields:
% 16.42/4.40 | (123) all_47_0_20 = 0
% 16.42/4.40 |
% 16.42/4.40 | Equations (123) can reduce 121 to:
% 16.42/4.40 | (81) $false
% 16.42/4.40 |
% 16.42/4.40 |-The branch is then unsatisfiable
% 16.42/4.40 |-Branch two:
% 16.42/4.40 | (106) apart_point_and_line(all_0_7_7, all_0_4_4) = 0
% 16.42/4.40 | (100) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)
% 16.42/4.40 |
% 16.42/4.40 | Instantiating (100) with all_34_0_22 yields:
% 16.42/4.40 | (127) ~ (all_34_0_22 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_34_0_22
% 16.42/4.40 |
% 16.42/4.40 | Applying alpha-rule on (127) yields:
% 16.42/4.40 | (128) ~ (all_34_0_22 = 0)
% 16.42/4.40 | (129) distinct_points(all_0_7_7, all_0_6_6) = all_34_0_22
% 16.42/4.40 |
% 16.42/4.40 | Instantiating formula (52) with all_0_7_7, all_0_6_6, all_34_0_22, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_34_0_22, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 16.42/4.41 | (130) all_34_0_22 = 0
% 16.42/4.41 |
% 16.42/4.41 | Equations (130) can reduce 128 to:
% 16.42/4.41 | (81) $false
% 16.42/4.41 |
% 16.42/4.41 |-The branch is then unsatisfiable
% 16.42/4.41 |-Branch two:
% 16.42/4.41 | (96) ~ (apart_point_and_line(all_0_5_5, all_0_3_3) = 0)
% 16.42/4.41 | (97) all_0_2_2 = 0
% 16.42/4.41 |
% 16.42/4.41 | Equations (97) can reduce 86 to:
% 16.42/4.41 | (81) $false
% 16.42/4.41 |
% 16.42/4.41 |-The branch is then unsatisfiable
% 16.42/4.41 |-Branch two:
% 16.42/4.41 | (83) all_0_0_0 = 0
% 16.42/4.41 | (86) ~ (all_0_2_2 = 0)
% 16.42/4.41 |
% 16.42/4.41 | Combining equations (83,114) yields a new equation:
% 16.42/4.41 | (97) all_0_2_2 = 0
% 16.42/4.41 |
% 16.42/4.41 | Equations (97) can reduce 86 to:
% 16.42/4.41 | (81) $false
% 16.42/4.41 |
% 16.42/4.41 |-The branch is then unsatisfiable
% 16.42/4.41 % SZS output end Proof for theBenchmark
% 16.42/4.41
% 16.42/4.41 3815ms
%------------------------------------------------------------------------------