TSTP Solution File: GEO220+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO220+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 03:48:53 EDT 2022
% Result : Theorem 12.59s 3.65s
% Output : Proof 14.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO220+3 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 : Fri Jun 17 19:54:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.61/0.61 ____ _
% 0.61/0.61 ___ / __ \_____(_)___ ________ __________
% 0.61/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.61/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.61/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.61/0.61
% 0.61/0.61 A Theorem Prover for First-Order Logic
% 0.61/0.61 (ePrincess v.1.0)
% 0.61/0.61
% 0.61/0.61 (c) Philipp Rümmer, 2009-2015
% 0.61/0.61 (c) Peter Backeman, 2014-2015
% 0.61/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.61 Bug reports to peter@backeman.se
% 0.61/0.61
% 0.61/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.61
% 0.61/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.89/1.03 Prover 0: Preprocessing ...
% 2.43/1.24 Prover 0: Warning: ignoring some quantifiers
% 2.43/1.26 Prover 0: Constructing countermodel ...
% 11.53/3.46 Prover 0: gave up
% 11.53/3.46 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 12.04/3.50 Prover 1: Preprocessing ...
% 12.59/3.61 Prover 1: Constructing countermodel ...
% 12.59/3.65 Prover 1: proved (184ms)
% 12.59/3.65
% 12.59/3.65 No countermodel exists, formula is valid
% 12.59/3.65 % SZS status Theorem for theBenchmark
% 12.59/3.65
% 12.59/3.65 Generating proof ... found it (size 28)
% 14.07/3.98
% 14.07/3.98 % SZS output start Proof for theBenchmark
% 14.07/3.98 Assumed formulas after preprocessing and simplification:
% 14.07/3.98 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & orthogonal_lines(v0, v2) = 0 & orthogonal_lines(v0, v1) = 0 & parallel_lines(v1, v2) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (unorthogonal_lines(v5, v7) = v9) | ~ (apart_point_and_line(v4, v5) = v8) | ~ (distinct_lines(v5, v6) = 0) | ? [v10] : ? [v11] : (unorthogonal_lines(v6, v7) = v11 & apart_point_and_line(v4, v6) = v10 & (v11 = 0 | v10 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (unorthogonal_lines(v4, v6) = v8) | ~ (unorthogonal_lines(v4, v5) = v7) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v4, v6) = v8) | ~ (unorthogonal_lines(v4, v5) = v7) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (unorthogonal_lines(v5, v6) = v12 & convergent_lines(v5, v6) = v11 & convergent_lines(v4, v6) = v10 & convergent_lines(v4, v5) = v9 & ( ~ (v12 = 0) | ~ (v11 = 0) | (v10 = 0 & v8 = 0) | (v9 = 0 & v7 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v4, v5) = v7) | ~ (distinct_lines(v5, v6) = 0) | ? [v8] : ? [v9] : (apart_point_and_line(v4, v6) = v8 & convergent_lines(v5, v6) = v9 & (v9 = 0 | v8 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v4, v5) = 0) | ~ (distinct_lines(v5, v6) = v7) | apart_point_and_line(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v4, v5) = 0) | ~ (distinct_points(v4, v6) = v7) | apart_point_and_line(v6, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v4, v6) = v7) | ~ (convergent_lines(v4, v5) = 0) | convergent_lines(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v4, v5) = 0) | ~ (distinct_lines(v5, v6) = v7) | convergent_lines(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_lines(v4, v6) = v7) | ~ (distinct_lines(v4, v5) = 0) | distinct_lines(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_points(v4, v6) = v7) | ~ (distinct_points(v4, v5) = 0) | distinct_points(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (orthogonal_lines(v7, v6) = v5) | ~ (orthogonal_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (incident_point_and_line(v7, v6) = v5) | ~ (incident_point_and_line(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (parallel_lines(v7, v6) = v5) | ~ (parallel_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (equal_lines(v7, v6) = v5) | ~ (equal_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (equal_points(v7, v6) = v5) | ~ (equal_points(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (orthogonal_through_point(v7, v6) = v5) | ~ (orthogonal_through_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (unorthogonal_lines(v7, v6) = v5) | ~ (unorthogonal_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (parallel_through_point(v7, v6) = v5) | ~ (parallel_through_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (intersection_point(v7, v6) = v5) | ~ (intersection_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (line_connecting(v7, v6) = v5) | ~ (line_connecting(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (apart_point_and_line(v7, v6) = v5) | ~ (apart_point_and_line(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (convergent_lines(v7, v6) = v5) | ~ (convergent_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (distinct_lines(v7, v6) = v5) | ~ (distinct_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (distinct_points(v7, v6) = v5) | ~ (distinct_points(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v4, v6) = v7) | ~ (unorthogonal_lines(v4, v5) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (unorthogonal_lines(v5, v6) = v11 & convergent_lines(v5, v6) = v10 & convergent_lines(v4, v6) = v9 & convergent_lines(v4, v5) = v8 & ( ~ (v8 = 0) | (v11 = 0 & v10 = 0) | (v9 = 0 & v7 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | ~ (distinct_points(v4, v5) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (apart_point_and_line(v5, v7) = v11 & apart_point_and_line(v5, v6) = v10 & apart_point_and_line(v4, v7) = v9 & apart_point_and_line(v4, v6) = v8 & (v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (orthogonal_lines(v4, v5) = v6) | unorthogonal_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (incident_point_and_line(v4, v5) = v6) | apart_point_and_line(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (parallel_lines(v4, v5) = v6) | convergent_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (equal_lines(v4, v5) = v6) | distinct_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (equal_points(v4, v5) = v6) | distinct_points(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unorthogonal_lines(v4, v5) = v6) | convergent_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (point(v6) = v5) | ~ (point(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (line(v6) = v5) | ~ (line(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (orthogonal_through_point(v5, v4) = v6) | ~ (unorthogonal_lines(v6, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (orthogonal_through_point(v5, v4) = v6) | ~ (apart_point_and_line(v4, v6) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (orthogonal_through_point(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : (point(v5) = v8 & line(v6) = v9 & line(v4) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | v9 = 0))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (parallel_through_point(v5, v4) = v6) | ~ (apart_point_and_line(v4, v6) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (parallel_through_point(v5, v4) = v6) | ~ (convergent_lines(v6, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (parallel_through_point(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : (point(v5) = v8 & line(v6) = v9 & line(v4) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | v9 = 0))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection_point(v4, v5) = v6) | ~ (apart_point_and_line(v6, v5) = 0) | ? [v7] : ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection_point(v4, v5) = v6) | ~ (apart_point_and_line(v6, v4) = 0) | ? [v7] : ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection_point(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (point(v6) = v10 & line(v5) = v8 & line(v4) = v7 & convergent_lines(v4, v5) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v10 = 0))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ~ (apart_point_and_line(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & distinct_points(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ~ (apart_point_and_line(v4, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & distinct_points(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (point(v5) = v8 & point(v4) = v7 & line(v6) = v10 & distinct_points(v4, v5) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v10 = 0))) & ! [v4] : ! [v5] : ( ~ (orthogonal_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & unorthogonal_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (incident_point_and_line(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & apart_point_and_line(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (parallel_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & convergent_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (equal_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & distinct_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (equal_points(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & distinct_points(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (distinct_lines(v4, v5) = 0) | convergent_lines(v4, v5) = 0) & ! [v4] : ~ (convergent_lines(v4, v4) = 0) & ! [v4] : ~ (distinct_lines(v4, v4) = 0) & ! [v4] : ~ (distinct_points(v4, v4) = 0))
% 14.44/4.02 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 14.44/4.02 | (1) ~ (all_0_0_0 = 0) & orthogonal_lines(all_0_3_3, all_0_1_1) = 0 & orthogonal_lines(all_0_3_3, all_0_2_2) = 0 & parallel_lines(all_0_2_2, all_0_1_1) = all_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] : ! [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)
% 14.44/4.03 |
% 14.44/4.03 | Applying alpha-rule on (1) yields:
% 14.44/4.03 | (2) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 14.44/4.03 | (3) ! [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)))
% 14.44/4.03 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 14.44/4.03 | (5) ! [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)))
% 14.44/4.03 | (6) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 14.44/4.03 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 14.44/4.04 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 14.44/4.04 | (9) ! [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)
% 14.44/4.04 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 14.44/4.04 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 14.44/4.04 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 14.44/4.04 | (13) ! [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))))
% 14.44/4.04 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 14.44/4.04 | (15) ! [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)))
% 14.44/4.04 | (16) ! [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)))
% 14.44/4.04 | (17) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 14.44/4.04 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 14.44/4.04 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 14.44/4.04 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 14.44/4.04 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 14.44/4.04 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 14.44/4.04 | (23) orthogonal_lines(all_0_3_3, all_0_1_1) = 0
% 14.44/4.04 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 14.44/4.04 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 14.44/4.04 | (26) ! [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)))
% 14.44/4.04 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 14.44/4.04 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 14.44/4.04 | (29) ~ (all_0_0_0 = 0)
% 14.44/4.04 | (30) ! [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)
% 14.44/4.04 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 14.44/4.04 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 14.44/4.04 | (33) ! [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)))
% 14.44/4.05 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 14.44/4.05 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 14.44/4.05 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0))
% 14.44/4.05 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 14.44/4.05 | (38) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 14.44/4.05 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 14.44/4.05 | (40) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 14.44/4.05 | (41) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 14.44/4.05 | (42) parallel_lines(all_0_2_2, all_0_1_1) = all_0_0_0
% 14.44/4.05 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 14.44/4.05 | (44) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 14.44/4.05 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 14.44/4.05 | (46) orthogonal_lines(all_0_3_3, all_0_2_2) = 0
% 14.44/4.05 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0))
% 14.44/4.05 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0))
% 14.44/4.05 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 14.44/4.05 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 14.44/4.05 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 14.44/4.05 | (52) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 14.44/4.05 | (53) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 14.44/4.05 | (54) ! [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))
% 14.44/4.05 | (55) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 14.44/4.05 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 14.44/4.05 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0))
% 14.44/4.05 | (58) ! [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))))
% 14.44/4.05 | (59) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 14.44/4.05 | (60) ! [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)))
% 14.44/4.05 |
% 14.44/4.05 | Instantiating formula (44) with all_0_1_1, all_0_3_3 and discharging atoms orthogonal_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 14.44/4.05 | (61) ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_1_1) = v0)
% 14.44/4.05 |
% 14.44/4.05 | Instantiating formula (44) with all_0_2_2, all_0_3_3 and discharging atoms orthogonal_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 14.44/4.05 | (62) ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = v0)
% 14.44/4.05 |
% 14.44/4.05 | Instantiating formula (41) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms parallel_lines(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 14.44/4.05 | (63) all_0_0_0 = 0 | convergent_lines(all_0_2_2, all_0_1_1) = 0
% 14.44/4.05 |
% 14.44/4.05 | Instantiating (62) with all_8_0_4 yields:
% 14.44/4.05 | (64) ~ (all_8_0_4 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_8_0_4
% 14.44/4.05 |
% 14.44/4.05 | Applying alpha-rule on (64) yields:
% 14.44/4.05 | (65) ~ (all_8_0_4 = 0)
% 14.44/4.05 | (66) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_8_0_4
% 14.44/4.05 |
% 14.44/4.05 | Instantiating (61) with all_10_0_5 yields:
% 14.44/4.05 | (67) ~ (all_10_0_5 = 0) & unorthogonal_lines(all_0_3_3, all_0_1_1) = all_10_0_5
% 14.44/4.05 |
% 14.44/4.05 | Applying alpha-rule on (67) yields:
% 14.44/4.05 | (68) ~ (all_10_0_5 = 0)
% 14.44/4.05 | (69) unorthogonal_lines(all_0_3_3, all_0_1_1) = all_10_0_5
% 14.44/4.05 |
% 14.44/4.05 +-Applying beta-rule and splitting (63), into two cases.
% 14.44/4.05 |-Branch one:
% 14.44/4.05 | (70) convergent_lines(all_0_2_2, all_0_1_1) = 0
% 14.44/4.06 |
% 14.44/4.06 | Instantiating formula (54) with all_10_0_5, all_8_0_4, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_1_1) = all_10_0_5, unorthogonal_lines(all_0_3_3, all_0_2_2) = all_8_0_4, yields:
% 14.44/4.06 | (71) all_10_0_5 = 0 | all_8_0_4 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = v0)
% 14.44/4.06 |
% 14.44/4.06 | Instantiating formula (54) with all_8_0_4, all_8_0_4, all_0_2_2, all_0_2_2, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_8_0_4, yields:
% 14.44/4.06 | (72) all_8_0_4 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = v0)
% 14.44/4.06 |
% 14.44/4.06 +-Applying beta-rule and splitting (72), into two cases.
% 14.44/4.06 |-Branch one:
% 14.44/4.06 | (73) all_8_0_4 = 0
% 14.44/4.06 |
% 14.44/4.06 | Equations (73) can reduce 65 to:
% 14.44/4.06 | (74) $false
% 14.44/4.06 |
% 14.44/4.06 |-The branch is then unsatisfiable
% 14.44/4.06 |-Branch two:
% 14.44/4.06 | (65) ~ (all_8_0_4 = 0)
% 14.44/4.06 | (76) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = v0)
% 14.44/4.06 |
% 14.44/4.06 +-Applying beta-rule and splitting (71), into two cases.
% 14.44/4.06 |-Branch one:
% 14.44/4.06 | (77) all_10_0_5 = 0
% 14.44/4.06 |
% 14.44/4.06 | Equations (77) can reduce 68 to:
% 14.44/4.06 | (74) $false
% 14.44/4.06 |
% 14.44/4.06 |-The branch is then unsatisfiable
% 14.44/4.06 |-Branch two:
% 14.44/4.06 | (68) ~ (all_10_0_5 = 0)
% 14.44/4.06 | (80) all_8_0_4 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = v0)
% 14.44/4.06 |
% 14.44/4.06 +-Applying beta-rule and splitting (80), into two cases.
% 14.44/4.06 |-Branch one:
% 14.44/4.06 | (73) all_8_0_4 = 0
% 14.44/4.06 |
% 14.44/4.06 | Equations (73) can reduce 65 to:
% 14.44/4.06 | (74) $false
% 14.44/4.06 |
% 14.44/4.06 |-The branch is then unsatisfiable
% 14.44/4.06 |-Branch two:
% 14.44/4.06 | (65) ~ (all_8_0_4 = 0)
% 14.44/4.06 | (84) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = v0)
% 14.44/4.06 |
% 14.44/4.06 | Instantiating (84) with all_55_0_23 yields:
% 14.44/4.06 | (85) ~ (all_55_0_23 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_55_0_23
% 14.44/4.06 |
% 14.44/4.06 | Applying alpha-rule on (85) yields:
% 14.44/4.06 | (86) ~ (all_55_0_23 = 0)
% 14.44/4.06 | (87) convergent_lines(all_0_2_2, all_0_1_1) = all_55_0_23
% 14.44/4.06 |
% 14.44/4.06 | Instantiating formula (31) with all_0_2_2, all_0_1_1, all_55_0_23, 0 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_55_0_23, convergent_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 14.44/4.06 | (88) all_55_0_23 = 0
% 14.44/4.06 |
% 14.44/4.06 | Equations (88) can reduce 86 to:
% 14.44/4.06 | (74) $false
% 14.44/4.06 |
% 14.44/4.06 |-The branch is then unsatisfiable
% 14.44/4.06 |-Branch two:
% 14.44/4.06 | (90) ~ (convergent_lines(all_0_2_2, all_0_1_1) = 0)
% 14.44/4.06 | (91) all_0_0_0 = 0
% 14.44/4.06 |
% 14.44/4.06 | Equations (91) can reduce 29 to:
% 14.44/4.06 | (74) $false
% 14.44/4.06 |
% 14.44/4.06 |-The branch is then unsatisfiable
% 14.44/4.06 % SZS output end Proof for theBenchmark
% 14.44/4.06
% 14.44/4.06 3432ms
%------------------------------------------------------------------------------