TSTP Solution File: GEO201+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO201+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n006.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 03:48:37 EDT 2022
% Result : Theorem 5.62s 2.05s
% Output : Proof 14.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO201+1 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jun 17 15:48:41 EDT 2022
% 0.20/0.35 % CPUTime :
% 0.56/0.60 ____ _
% 0.56/0.60 ___ / __ \_____(_)___ ________ __________
% 0.56/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.60
% 0.56/0.60 A Theorem Prover for First-Order Logic
% 0.56/0.60 (ePrincess v.1.0)
% 0.56/0.60
% 0.56/0.60 (c) Philipp Rümmer, 2009-2015
% 0.56/0.60 (c) Peter Backeman, 2014-2015
% 0.56/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.60 Bug reports to peter@backeman.se
% 0.56/0.60
% 0.56/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.60
% 0.56/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.79/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.74/0.96 Prover 0: Preprocessing ...
% 2.02/1.09 Prover 0: Warning: ignoring some quantifiers
% 2.02/1.11 Prover 0: Constructing countermodel ...
% 3.01/1.38 Prover 0: gave up
% 3.01/1.38 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.01/1.41 Prover 1: Preprocessing ...
% 3.31/1.49 Prover 1: Constructing countermodel ...
% 3.42/1.52 Prover 1: gave up
% 3.42/1.52 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.58/1.54 Prover 2: Preprocessing ...
% 3.97/1.65 Prover 2: Warning: ignoring some quantifiers
% 3.97/1.65 Prover 2: Constructing countermodel ...
% 5.62/2.05 Prover 2: proved (531ms)
% 5.62/2.05
% 5.62/2.05 No countermodel exists, formula is valid
% 5.62/2.05 % SZS status Theorem for theBenchmark
% 5.62/2.05
% 5.62/2.05 Generating proof ... Warning: ignoring some quantifiers
% 14.34/4.03 found it (size 179)
% 14.34/4.03
% 14.34/4.03 % SZS output start Proof for theBenchmark
% 14.34/4.03 Assumed formulas after preprocessing and simplification:
% 14.34/4.03 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (intersection_point(v1, v0) = v3 & intersection_point(v0, v1) = v2 & convergent_lines(v0, v1) = 0 & distinct_points(v2, v3) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v9) | ~ (apart_point_and_line(v5, v6) = v8) | ~ (distinct_points(v4, v5) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v4, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v9) | ~ (apart_point_and_line(v4, v7) = v8) | ~ (distinct_lines(v6, v7) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v6) = 0) | (v10 = 0 & apart_point_and_line(v4, v6) = 0) | ( ~ (v10 = 0) & distinct_points(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v9) | ~ (apart_point_and_line(v4, v6) = v8) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v6) = 0) | (v10 = 0 & apart_point_and_line(v4, v7) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10) | ( ~ (v10 = 0) & distinct_points(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v6) = v9) | ~ (apart_point_and_line(v4, v7) = v8) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10) | ( ~ (v10 = 0) & distinct_points(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v6) = v9) | ~ (apart_point_and_line(v4, v6) = v8) | ~ (distinct_lines(v6, v7) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v7) = 0) | ( ~ (v10 = 0) & distinct_points(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v4, v7) = v9) | ~ (apart_point_and_line(v4, v6) = v8) | ~ (distinct_points(v4, v5) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v7) = 0) | (v10 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (apart_point_and_line(v6, v5) = v8) | ~ (distinct_points(v4, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (apart_point_and_line(v4, v6) = v8) | ~ (distinct_lines(v5, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (convergent_lines(v5, v6) = v8) | ~ (convergent_lines(v4, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (convergent_lines(v4, v6) = v8) | ~ (distinct_lines(v5, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (distinct_lines(v5, v6) = v8) | ~ (distinct_lines(v4, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & distinct_lines(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (distinct_points(v5, v6) = v8) | ~ (distinct_points(v4, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & distinct_points(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v6, v5) = v7) | ~ (apart_point_and_line(v4, v5) = 0) | distinct_points(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v4, v6) = v7) | ~ (apart_point_and_line(v4, v5) = 0) | distinct_lines(v5, v6) = 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(v5, v6) = v7) | ~ (convergent_lines(v4, v5) = 0) | convergent_lines(v4, v6) = 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, v6) = v7) | ~ (convergent_lines(v4, v5) = 0) | distinct_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(v5, v6) = v7) | ~ (distinct_lines(v4, v5) = 0) | distinct_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(v5, v6) = v7) | ~ (distinct_points(v4, v5) = 0) | distinct_points(v4, 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 | ~ (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] : ( ~ (distinct_lines(v6, v7) = 0) | ~ (distinct_points(v4, v5) = 0) | ? [v8] : ((v8 = 0 & apart_point_and_line(v5, v7) = 0) | (v8 = 0 & apart_point_and_line(v5, v6) = 0) | (v8 = 0 & apart_point_and_line(v4, v7) = 0) | (v8 = 0 & apart_point_and_line(v4, v6) = 0))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection_point(v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & apart_point_and_line(v6, v5) = v7) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection_point(v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & apart_point_and_line(v6, v4) = v7) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & apart_point_and_line(v5, v6) = v7) | ( ~ (v7 = 0) & distinct_points(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & apart_point_and_line(v4, v6) = v7) | ( ~ (v7 = 0) & distinct_points(v4, v5) = v7))) & ! [v4] : ! [v5] : ( ~ (convergent_lines(v4, v5) = 0) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & intersection_point(v4, v5) = v6 & apart_point_and_line(v6, v5) = v7)) & ! [v4] : ! [v5] : ( ~ (convergent_lines(v4, v5) = 0) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & intersection_point(v4, v5) = v6 & apart_point_and_line(v6, v4) = v7)) & ! [v4] : ! [v5] : ( ~ (distinct_points(v4, v5) = 0) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & line_connecting(v4, v5) = v6 & apart_point_and_line(v5, v6) = v7)) & ! [v4] : ! [v5] : ( ~ (distinct_points(v4, v5) = 0) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & line_connecting(v4, v5) = v6 & apart_point_and_line(v4, v6) = v7)) & ! [v4] : ~ (convergent_lines(v4, v4) = 0) & ! [v4] : ~ (distinct_lines(v4, v4) = 0) & ! [v4] : ~ (distinct_points(v4, v4) = 0) & ? [v4] : ? [v5] : ? [v6] : intersection_point(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : line_connecting(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : apart_point_and_line(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : convergent_lines(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : distinct_lines(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : distinct_points(v5, v4) = v6)
% 14.47/4.11 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 14.47/4.11 | (1) intersection_point(all_0_2_2, all_0_3_3) = all_0_0_0 & intersection_point(all_0_3_3, all_0_2_2) = all_0_1_1 & convergent_lines(all_0_3_3, all_0_2_2) = 0 & distinct_points(all_0_1_1, all_0_0_0) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 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(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 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, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_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(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_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(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, 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 | ~ (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] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 14.70/4.13 |
% 14.70/4.13 | Applying alpha-rule on (1) yields:
% 14.70/4.13 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 14.70/4.13 | (3) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 14.70/4.13 | (4) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 14.70/4.13 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 14.70/4.13 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 14.70/4.13 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 14.70/4.13 | (8) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 14.70/4.13 | (9) intersection_point(all_0_3_3, all_0_2_2) = all_0_1_1
% 14.70/4.13 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 14.70/4.13 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 14.70/4.13 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 14.70/4.13 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 14.70/4.13 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 14.70/4.13 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 14.70/4.14 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 14.70/4.14 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 14.70/4.14 | (18) ! [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)
% 14.70/4.14 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 14.70/4.14 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 14.70/4.14 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 14.70/4.14 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 14.70/4.14 | (23) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 14.70/4.14 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 14.70/4.14 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 14.70/4.14 | (26) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 14.70/4.14 | (27) ! [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)
% 14.70/4.14 | (28) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 14.70/4.14 | (29) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 14.70/4.14 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 14.70/4.14 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 14.70/4.14 | (32) intersection_point(all_0_2_2, all_0_3_3) = all_0_0_0
% 14.70/4.14 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 14.70/4.14 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5))
% 14.70/4.14 | (35) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 14.70/4.14 | (36) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 14.70/4.14 | (37) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 14.70/4.14 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5))
% 14.70/4.14 | (39) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 14.70/4.15 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 14.70/4.15 | (41) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 14.70/4.15 | (42) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 14.70/4.15 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 14.70/4.15 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 14.70/4.15 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 14.70/4.15 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 14.70/4.15 | (47) distinct_points(all_0_1_1, all_0_0_0) = 0
% 14.70/4.15 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 14.70/4.15 | (49) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 14.70/4.15 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 14.70/4.15 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 14.70/4.15 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 14.70/4.15 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 14.70/4.15 |
% 14.70/4.15 | Instantiating formula (24) with all_0_0_0, all_0_3_3, all_0_2_2 and discharging atoms intersection_point(all_0_2_2, all_0_3_3) = all_0_0_0, yields:
% 14.70/4.15 | (54) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_0_0, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = v0))
% 14.70/4.15 |
% 14.70/4.15 | Instantiating formula (50) with all_0_0_0, all_0_3_3, all_0_2_2 and discharging atoms intersection_point(all_0_2_2, all_0_3_3) = all_0_0_0, yields:
% 14.70/4.15 | (55) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = v0))
% 14.70/4.15 |
% 14.70/4.15 | Instantiating formula (24) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 14.70/4.15 | (56) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0))
% 14.70/4.15 |
% 14.70/4.15 | Instantiating formula (50) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 14.70/4.15 | (57) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0))
% 14.70/4.15 |
% 14.70/4.15 | Instantiating formula (39) with all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 14.70/4.15 | (58) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_2_2) = v0 & apart_point_and_line(v0, all_0_2_2) = v1)
% 14.70/4.15 |
% 14.70/4.15 | Instantiating formula (35) with all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 14.70/4.15 | (59) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_2_2) = v0 & apart_point_and_line(v0, all_0_3_3) = v1)
% 14.70/4.16 |
% 14.70/4.16 | Instantiating formula (8) with all_0_0_0, all_0_1_1 and discharging atoms distinct_points(all_0_1_1, all_0_0_0) = 0, yields:
% 14.70/4.16 | (60) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_1_1, all_0_0_0) = v0 & apart_point_and_line(all_0_0_0, v0) = v1)
% 14.70/4.16 |
% 14.70/4.16 | Instantiating formula (49) with all_0_0_0, all_0_1_1 and discharging atoms distinct_points(all_0_1_1, all_0_0_0) = 0, yields:
% 14.70/4.16 | (61) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_1_1, all_0_0_0) = v0 & apart_point_and_line(all_0_1_1, v0) = v1)
% 14.70/4.16 |
% 14.70/4.16 | Instantiating (61) with all_20_0_22, all_20_1_23 yields:
% 14.70/4.16 | (62) ~ (all_20_0_22 = 0) & line_connecting(all_0_1_1, all_0_0_0) = all_20_1_23 & apart_point_and_line(all_0_1_1, all_20_1_23) = all_20_0_22
% 14.70/4.16 |
% 14.70/4.16 | Applying alpha-rule on (62) yields:
% 14.70/4.16 | (63) ~ (all_20_0_22 = 0)
% 14.70/4.16 | (64) line_connecting(all_0_1_1, all_0_0_0) = all_20_1_23
% 14.70/4.16 | (65) apart_point_and_line(all_0_1_1, all_20_1_23) = all_20_0_22
% 14.70/4.16 |
% 14.70/4.16 | Instantiating (60) with all_22_0_24, all_22_1_25 yields:
% 14.70/4.16 | (66) ~ (all_22_0_24 = 0) & line_connecting(all_0_1_1, all_0_0_0) = all_22_1_25 & apart_point_and_line(all_0_0_0, all_22_1_25) = all_22_0_24
% 14.70/4.16 |
% 14.70/4.16 | Applying alpha-rule on (66) yields:
% 14.70/4.16 | (67) ~ (all_22_0_24 = 0)
% 14.70/4.16 | (68) line_connecting(all_0_1_1, all_0_0_0) = all_22_1_25
% 14.70/4.16 | (69) apart_point_and_line(all_0_0_0, all_22_1_25) = all_22_0_24
% 14.70/4.16 |
% 14.70/4.16 | Instantiating (59) with all_24_0_26, all_24_1_27 yields:
% 14.70/4.16 | (70) ~ (all_24_0_26 = 0) & intersection_point(all_0_3_3, all_0_2_2) = all_24_1_27 & apart_point_and_line(all_24_1_27, all_0_3_3) = all_24_0_26
% 14.70/4.16 |
% 14.70/4.16 | Applying alpha-rule on (70) yields:
% 14.70/4.16 | (71) ~ (all_24_0_26 = 0)
% 14.70/4.16 | (72) intersection_point(all_0_3_3, all_0_2_2) = all_24_1_27
% 14.70/4.16 | (73) apart_point_and_line(all_24_1_27, all_0_3_3) = all_24_0_26
% 14.70/4.16 |
% 14.70/4.16 | Instantiating (58) with all_26_0_28, all_26_1_29 yields:
% 14.70/4.16 | (74) ~ (all_26_0_28 = 0) & intersection_point(all_0_3_3, all_0_2_2) = all_26_1_29 & apart_point_and_line(all_26_1_29, all_0_2_2) = all_26_0_28
% 14.70/4.16 |
% 14.70/4.16 | Applying alpha-rule on (74) yields:
% 14.70/4.16 | (75) ~ (all_26_0_28 = 0)
% 14.70/4.16 | (76) intersection_point(all_0_3_3, all_0_2_2) = all_26_1_29
% 14.70/4.16 | (77) apart_point_and_line(all_26_1_29, all_0_2_2) = all_26_0_28
% 14.70/4.16 |
% 14.70/4.16 | Instantiating (57) with all_28_0_30 yields:
% 14.70/4.16 | (78) ( ~ (all_28_0_30 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_28_0_30) | ( ~ (all_28_0_30 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_28_0_30)
% 14.70/4.16 |
% 14.70/4.16 | Instantiating (56) with all_29_0_31 yields:
% 14.70/4.16 | (79) ( ~ (all_29_0_31 = 0) & apart_point_and_line(all_0_1_1, all_0_2_2) = all_29_0_31) | ( ~ (all_29_0_31 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_29_0_31)
% 14.70/4.16 |
% 14.70/4.16 | Instantiating (55) with all_30_0_32 yields:
% 14.70/4.16 | (80) ( ~ (all_30_0_32 = 0) & apart_point_and_line(all_0_0_0, all_0_2_2) = all_30_0_32) | ( ~ (all_30_0_32 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = all_30_0_32)
% 14.70/4.16 |
% 14.70/4.16 | Instantiating (54) with all_31_0_33 yields:
% 14.70/4.16 | (81) ( ~ (all_31_0_33 = 0) & apart_point_and_line(all_0_0_0, all_0_3_3) = all_31_0_33) | ( ~ (all_31_0_33 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = all_31_0_33)
% 14.70/4.16 |
% 14.70/4.16 +-Applying beta-rule and splitting (79), into two cases.
% 14.70/4.16 |-Branch one:
% 14.70/4.16 | (82) ~ (all_29_0_31 = 0) & apart_point_and_line(all_0_1_1, all_0_2_2) = all_29_0_31
% 14.70/4.16 |
% 14.70/4.16 | Applying alpha-rule on (82) yields:
% 14.70/4.16 | (83) ~ (all_29_0_31 = 0)
% 14.70/4.16 | (84) apart_point_and_line(all_0_1_1, all_0_2_2) = all_29_0_31
% 14.70/4.16 |
% 14.70/4.16 +-Applying beta-rule and splitting (78), into two cases.
% 14.70/4.16 |-Branch one:
% 14.70/4.16 | (85) ~ (all_28_0_30 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_28_0_30
% 14.70/4.16 |
% 14.70/4.16 | Applying alpha-rule on (85) yields:
% 14.70/4.16 | (86) ~ (all_28_0_30 = 0)
% 14.70/4.16 | (87) apart_point_and_line(all_0_1_1, all_0_3_3) = all_28_0_30
% 14.70/4.16 |
% 14.70/4.16 | Instantiating formula (14) with all_0_3_3, all_0_2_2, all_26_1_29, all_0_1_1 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_26_1_29, intersection_point(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 14.70/4.16 | (88) all_26_1_29 = all_0_1_1
% 14.70/4.16 |
% 14.70/4.16 | Instantiating formula (14) with all_0_3_3, all_0_2_2, all_24_1_27, all_26_1_29 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_26_1_29, intersection_point(all_0_3_3, all_0_2_2) = all_24_1_27, yields:
% 14.70/4.16 | (89) all_26_1_29 = all_24_1_27
% 14.70/4.16 |
% 14.70/4.16 | Instantiating formula (21) with all_0_1_1, all_0_0_0, all_20_1_23, all_22_1_25 and discharging atoms line_connecting(all_0_1_1, all_0_0_0) = all_22_1_25, line_connecting(all_0_1_1, all_0_0_0) = all_20_1_23, yields:
% 14.70/4.16 | (90) all_22_1_25 = all_20_1_23
% 14.70/4.16 |
% 14.70/4.16 | Combining equations (88,89) yields a new equation:
% 14.70/4.16 | (91) all_24_1_27 = all_0_1_1
% 14.70/4.16 |
% 14.70/4.16 | Combining equations (91,89) yields a new equation:
% 14.70/4.16 | (88) all_26_1_29 = all_0_1_1
% 14.70/4.16 |
% 14.70/4.16 | From (88) and (77) follows:
% 14.70/4.16 | (93) apart_point_and_line(all_0_1_1, all_0_2_2) = all_26_0_28
% 14.70/4.16 |
% 14.70/4.16 | From (91) and (73) follows:
% 14.70/4.16 | (94) apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26
% 14.70/4.17 |
% 14.70/4.17 | From (90) and (69) follows:
% 14.70/4.17 | (95) apart_point_and_line(all_0_0_0, all_20_1_23) = all_22_0_24
% 14.70/4.17 |
% 14.70/4.17 | Instantiating formula (22) with all_0_1_1, all_0_2_2, all_26_0_28, all_29_0_31 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_29_0_31, apart_point_and_line(all_0_1_1, all_0_2_2) = all_26_0_28, yields:
% 14.70/4.17 | (96) all_29_0_31 = all_26_0_28
% 14.70/4.17 |
% 14.70/4.17 | Instantiating formula (22) with all_0_1_1, all_0_3_3, all_24_0_26, all_28_0_30 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_28_0_30, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26, yields:
% 14.70/4.17 | (97) all_28_0_30 = all_24_0_26
% 14.70/4.17 |
% 14.70/4.17 | Equations (96) can reduce 83 to:
% 14.70/4.17 | (75) ~ (all_26_0_28 = 0)
% 14.70/4.17 |
% 14.70/4.17 | Equations (97) can reduce 86 to:
% 14.70/4.17 | (71) ~ (all_24_0_26 = 0)
% 14.70/4.17 |
% 14.70/4.17 | From (96) and (84) follows:
% 14.70/4.17 | (93) apart_point_and_line(all_0_1_1, all_0_2_2) = all_26_0_28
% 14.70/4.17 |
% 14.70/4.17 | From (97) and (87) follows:
% 14.70/4.17 | (94) apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26
% 14.70/4.17 |
% 14.70/4.17 | Instantiating formula (30) with all_26_0_28, all_26_0_28, all_0_2_2, all_0_2_2, all_0_0_0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_26_0_28, distinct_points(all_0_1_1, all_0_0_0) = 0, yields:
% 14.70/4.17 | (102) all_26_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 14.70/4.17 |
% 14.70/4.17 | Instantiating formula (15) with all_26_0_28, all_26_0_28, all_0_2_2, all_0_2_2, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_26_0_28, yields:
% 14.91/4.17 | (103) all_26_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 14.91/4.17 |
% 14.91/4.17 | Instantiating formula (15) with all_24_0_26, all_22_0_24, all_0_3_3, all_20_1_23, all_0_1_1, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_20_1_23) = all_22_0_24, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26, yields:
% 14.91/4.17 | (104) all_24_0_26 = 0 | all_22_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_20_1_23) = 0) | ( ~ (v0 = 0) & distinct_lines(all_20_1_23, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0))
% 14.91/4.17 |
% 14.91/4.17 | Instantiating formula (15) with all_22_0_24, all_24_0_26, all_20_1_23, all_0_3_3, all_0_0_0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_0_0, all_20_1_23) = all_22_0_24, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26, yields:
% 14.91/4.17 | (105) all_24_0_26 = 0 | all_22_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_20_1_23) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_20_1_23) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_0_0) = v0))
% 14.91/4.17 |
% 14.91/4.17 | Instantiating formula (33) with all_24_0_26, all_22_0_24, all_20_1_23, all_0_3_3, all_0_1_1, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_20_1_23) = all_22_0_24, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26, yields:
% 14.91/4.17 | (106) all_24_0_26 = 0 | all_22_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_20_1_23) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_20_1_23) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0))
% 14.91/4.17 |
% 14.91/4.17 | Instantiating formula (33) with all_22_0_24, all_24_0_26, all_0_3_3, all_20_1_23, all_0_0_0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_0_0, all_20_1_23) = all_22_0_24, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26, yields:
% 14.91/4.17 | (107) all_24_0_26 = 0 | all_22_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_20_1_23) = 0) | ( ~ (v0 = 0) & distinct_lines(all_20_1_23, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_0_0) = v0))
% 14.91/4.17 |
% 14.91/4.17 | Instantiating formula (30) with all_24_0_26, all_20_0_22, all_0_3_3, all_20_1_23, all_0_0_0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_20_1_23) = all_20_0_22, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26, distinct_points(all_0_1_1, all_0_0_0) = 0, yields:
% 14.91/4.17 | (108) all_24_0_26 = 0 | all_20_0_22 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_20_1_23) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_20_1_23, all_0_3_3) = v0))
% 14.91/4.17 |
% 14.91/4.17 | Instantiating formula (30) with all_20_0_22, all_24_0_26, all_20_1_23, all_0_3_3, all_0_0_0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_20_1_23) = all_20_0_22, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26, distinct_points(all_0_1_1, all_0_0_0) = 0, yields:
% 14.91/4.17 | (109) all_24_0_26 = 0 | all_20_0_22 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_20_1_23) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_20_1_23) = v0))
% 14.91/4.17 |
% 14.91/4.17 | Instantiating formula (15) with all_24_0_26, all_20_0_22, all_0_3_3, all_20_1_23, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_20_1_23) = all_20_0_22, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26, yields:
% 14.91/4.17 | (110) all_24_0_26 = 0 | all_20_0_22 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_20_1_23) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_20_1_23, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 14.91/4.18 |
% 14.91/4.18 | Instantiating formula (15) with all_20_0_22, all_24_0_26, all_20_1_23, all_0_3_3, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_20_1_23) = all_20_0_22, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26, yields:
% 14.91/4.18 | (111) all_24_0_26 = 0 | all_20_0_22 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_20_1_23) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_20_1_23) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 14.91/4.18 |
% 14.91/4.18 | Instantiating formula (30) with all_24_0_26, all_26_0_28, all_0_3_3, all_0_2_2, all_0_0_0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_26_0_28, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26, distinct_points(all_0_1_1, all_0_0_0) = 0, yields:
% 14.91/4.18 | (112) all_26_0_28 = 0 | all_24_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 14.91/4.18 |
% 14.91/4.18 | Instantiating formula (30) with all_24_0_26, all_24_0_26, all_0_3_3, all_0_3_3, all_0_0_0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26, distinct_points(all_0_1_1, all_0_0_0) = 0, yields:
% 14.91/4.18 | (113) all_24_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 14.91/4.18 |
% 14.91/4.18 | Instantiating formula (15) with all_24_0_26, all_24_0_26, all_0_3_3, all_0_3_3, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26, yields:
% 14.91/4.18 | (114) all_24_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 14.91/4.18 |
% 14.91/4.18 +-Applying beta-rule and splitting (80), into two cases.
% 14.91/4.18 |-Branch one:
% 14.91/4.18 | (115) ~ (all_30_0_32 = 0) & apart_point_and_line(all_0_0_0, all_0_2_2) = all_30_0_32
% 14.91/4.18 |
% 14.91/4.18 | Applying alpha-rule on (115) yields:
% 14.91/4.18 | (116) ~ (all_30_0_32 = 0)
% 14.91/4.18 | (117) apart_point_and_line(all_0_0_0, all_0_2_2) = all_30_0_32
% 14.91/4.18 |
% 14.91/4.18 +-Applying beta-rule and splitting (102), into two cases.
% 14.91/4.18 |-Branch one:
% 14.91/4.18 | (118) all_26_0_28 = 0
% 14.91/4.18 |
% 14.91/4.18 | Equations (118) can reduce 75 to:
% 14.91/4.18 | (119) $false
% 14.91/4.18 |
% 14.91/4.18 |-The branch is then unsatisfiable
% 14.91/4.18 |-Branch two:
% 14.91/4.18 | (75) ~ (all_26_0_28 = 0)
% 14.91/4.18 | (121) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 14.91/4.18 |
% 14.91/4.18 +-Applying beta-rule and splitting (103), into two cases.
% 14.91/4.18 |-Branch one:
% 14.91/4.18 | (118) all_26_0_28 = 0
% 14.91/4.18 |
% 14.91/4.18 | Equations (118) can reduce 75 to:
% 14.91/4.18 | (119) $false
% 14.91/4.18 |
% 14.91/4.18 |-The branch is then unsatisfiable
% 14.91/4.18 |-Branch two:
% 14.91/4.18 | (75) ~ (all_26_0_28 = 0)
% 14.91/4.18 | (125) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 14.91/4.18 |
% 14.91/4.18 +-Applying beta-rule and splitting (113), into two cases.
% 14.91/4.18 |-Branch one:
% 14.91/4.18 | (126) all_24_0_26 = 0
% 14.91/4.18 |
% 14.91/4.18 | Equations (126) can reduce 71 to:
% 14.91/4.18 | (119) $false
% 14.91/4.18 |
% 14.91/4.18 |-The branch is then unsatisfiable
% 14.91/4.18 |-Branch two:
% 14.91/4.18 | (71) ~ (all_24_0_26 = 0)
% 14.91/4.18 | (129) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 14.91/4.18 |
% 14.91/4.18 +-Applying beta-rule and splitting (114), into two cases.
% 14.91/4.18 |-Branch one:
% 14.91/4.18 | (126) all_24_0_26 = 0
% 14.91/4.18 |
% 14.91/4.18 | Equations (126) can reduce 71 to:
% 14.91/4.18 | (119) $false
% 14.91/4.18 |
% 14.91/4.18 |-The branch is then unsatisfiable
% 14.91/4.18 |-Branch two:
% 14.91/4.18 | (71) ~ (all_24_0_26 = 0)
% 14.91/4.18 | (133) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 14.91/4.18 |
% 14.91/4.18 +-Applying beta-rule and splitting (110), into two cases.
% 14.91/4.18 |-Branch one:
% 14.91/4.18 | (126) all_24_0_26 = 0
% 14.91/4.18 |
% 14.91/4.18 | Equations (126) can reduce 71 to:
% 14.91/4.18 | (119) $false
% 14.91/4.18 |
% 14.91/4.18 |-The branch is then unsatisfiable
% 14.91/4.18 |-Branch two:
% 14.91/4.18 | (71) ~ (all_24_0_26 = 0)
% 14.91/4.18 | (137) all_20_0_22 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_20_1_23) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_20_1_23, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 14.91/4.18 |
% 14.91/4.18 +-Applying beta-rule and splitting (112), into two cases.
% 14.91/4.18 |-Branch one:
% 14.91/4.18 | (118) all_26_0_28 = 0
% 14.91/4.18 |
% 14.91/4.18 | Equations (118) can reduce 75 to:
% 14.91/4.18 | (119) $false
% 14.91/4.18 |
% 14.91/4.18 |-The branch is then unsatisfiable
% 14.91/4.18 |-Branch two:
% 14.91/4.18 | (75) ~ (all_26_0_28 = 0)
% 14.91/4.19 | (141) all_24_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 14.91/4.19 |
% 14.91/4.19 +-Applying beta-rule and splitting (111), into two cases.
% 14.91/4.19 |-Branch one:
% 14.91/4.19 | (126) all_24_0_26 = 0
% 14.91/4.19 |
% 14.91/4.19 | Equations (126) can reduce 71 to:
% 14.91/4.19 | (119) $false
% 14.91/4.19 |
% 14.91/4.19 |-The branch is then unsatisfiable
% 14.91/4.19 |-Branch two:
% 14.91/4.19 | (71) ~ (all_24_0_26 = 0)
% 14.91/4.19 | (145) all_20_0_22 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_20_1_23) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_20_1_23) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 14.91/4.19 |
% 14.91/4.19 +-Applying beta-rule and splitting (104), into two cases.
% 14.91/4.19 |-Branch one:
% 14.91/4.19 | (126) all_24_0_26 = 0
% 14.91/4.19 |
% 14.91/4.19 | Equations (126) can reduce 71 to:
% 14.91/4.19 | (119) $false
% 14.91/4.19 |
% 14.91/4.19 |-The branch is then unsatisfiable
% 14.91/4.19 |-Branch two:
% 14.91/4.19 | (71) ~ (all_24_0_26 = 0)
% 14.91/4.19 | (149) all_22_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_20_1_23) = 0) | ( ~ (v0 = 0) & distinct_lines(all_20_1_23, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0))
% 14.91/4.19 |
% 14.91/4.19 +-Applying beta-rule and splitting (108), into two cases.
% 14.91/4.19 |-Branch one:
% 14.91/4.19 | (126) all_24_0_26 = 0
% 14.91/4.19 |
% 14.91/4.19 | Equations (126) can reduce 71 to:
% 14.91/4.19 | (119) $false
% 14.91/4.19 |
% 14.91/4.19 |-The branch is then unsatisfiable
% 14.91/4.19 |-Branch two:
% 14.91/4.19 | (71) ~ (all_24_0_26 = 0)
% 14.91/4.19 | (153) all_20_0_22 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_20_1_23) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_20_1_23, all_0_3_3) = v0))
% 14.91/4.19 |
% 14.91/4.19 +-Applying beta-rule and splitting (105), into two cases.
% 14.91/4.19 |-Branch one:
% 14.91/4.19 | (126) all_24_0_26 = 0
% 14.91/4.19 |
% 14.91/4.19 | Equations (126) can reduce 71 to:
% 14.91/4.19 | (119) $false
% 14.91/4.19 |
% 14.91/4.19 |-The branch is then unsatisfiable
% 14.91/4.19 |-Branch two:
% 14.91/4.19 | (71) ~ (all_24_0_26 = 0)
% 14.91/4.19 | (157) all_22_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_20_1_23) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_20_1_23) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_0_0) = v0))
% 14.91/4.19 |
% 14.91/4.19 +-Applying beta-rule and splitting (106), into two cases.
% 14.91/4.19 |-Branch one:
% 14.91/4.19 | (126) all_24_0_26 = 0
% 14.91/4.19 |
% 14.91/4.19 | Equations (126) can reduce 71 to:
% 14.91/4.19 | (119) $false
% 14.91/4.19 |
% 14.91/4.19 |-The branch is then unsatisfiable
% 14.91/4.19 |-Branch two:
% 14.91/4.19 | (71) ~ (all_24_0_26 = 0)
% 14.91/4.19 | (161) all_22_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_20_1_23) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_20_1_23) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0))
% 14.91/4.19 |
% 14.91/4.19 +-Applying beta-rule and splitting (107), into two cases.
% 14.91/4.19 |-Branch one:
% 14.91/4.19 | (126) all_24_0_26 = 0
% 14.91/4.19 |
% 14.91/4.19 | Equations (126) can reduce 71 to:
% 14.91/4.19 | (119) $false
% 14.91/4.19 |
% 14.91/4.19 |-The branch is then unsatisfiable
% 14.91/4.19 |-Branch two:
% 14.91/4.19 | (71) ~ (all_24_0_26 = 0)
% 14.91/4.19 | (165) all_22_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_20_1_23) = 0) | ( ~ (v0 = 0) & distinct_lines(all_20_1_23, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_0_0) = v0))
% 14.91/4.19 |
% 14.91/4.19 +-Applying beta-rule and splitting (109), into two cases.
% 14.91/4.19 |-Branch one:
% 14.91/4.19 | (126) all_24_0_26 = 0
% 14.91/4.19 |
% 14.91/4.19 | Equations (126) can reduce 71 to:
% 14.91/4.19 | (119) $false
% 14.91/4.19 |
% 14.91/4.19 |-The branch is then unsatisfiable
% 14.91/4.19 |-Branch two:
% 14.91/4.19 | (71) ~ (all_24_0_26 = 0)
% 14.91/4.19 | (169) all_20_0_22 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_20_1_23) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_20_1_23) = v0))
% 14.91/4.19 |
% 14.91/4.19 +-Applying beta-rule and splitting (141), into two cases.
% 14.91/4.19 |-Branch one:
% 14.91/4.19 | (126) all_24_0_26 = 0
% 14.91/4.19 |
% 14.91/4.19 | Equations (126) can reduce 71 to:
% 14.91/4.19 | (119) $false
% 14.91/4.19 |
% 14.91/4.19 |-The branch is then unsatisfiable
% 14.91/4.19 |-Branch two:
% 14.91/4.19 | (71) ~ (all_24_0_26 = 0)
% 14.91/4.19 | (173) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 14.91/4.19 |
% 14.91/4.19 | Instantiating (173) with all_234_0_361 yields:
% 14.91/4.19 | (174) (all_234_0_361 = 0 & apart_point_and_line(all_0_0_0, all_0_2_2) = 0) | (all_234_0_361 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (all_234_0_361 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_234_0_361)
% 14.91/4.19 |
% 14.91/4.20 | Instantiating formula (15) with all_30_0_32, all_22_0_24, all_0_2_2, all_20_1_23, all_0_0_0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_20_1_23) = all_22_0_24, apart_point_and_line(all_0_0_0, all_0_2_2) = all_30_0_32, yields:
% 14.91/4.20 | (175) all_30_0_32 = 0 | all_22_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_20_1_23) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_20_1_23, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0))
% 14.91/4.20 |
% 14.91/4.20 | Instantiating formula (15) with all_22_0_24, all_30_0_32, all_20_1_23, all_0_2_2, all_0_0_0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_20_1_23) = all_22_0_24, apart_point_and_line(all_0_0_0, all_0_2_2) = all_30_0_32, yields:
% 14.91/4.20 | (176) all_30_0_32 = 0 | all_22_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_20_1_23) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_20_1_23) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0))
% 14.91/4.20 |
% 14.91/4.20 | Instantiating formula (15) with all_20_0_22, all_30_0_32, all_20_1_23, all_0_2_2, all_0_1_1, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_2_2) = all_30_0_32, apart_point_and_line(all_0_1_1, all_20_1_23) = all_20_0_22, yields:
% 14.91/4.20 | (177) all_30_0_32 = 0 | all_20_0_22 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_20_1_23) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_20_1_23) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0))
% 14.91/4.20 |
% 14.91/4.20 | Instantiating formula (33) with all_20_0_22, all_30_0_32, all_0_2_2, all_20_1_23, all_0_1_1, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_2_2) = all_30_0_32, apart_point_and_line(all_0_1_1, all_20_1_23) = all_20_0_22, yields:
% 14.91/4.20 | (178) all_30_0_32 = 0 | all_20_0_22 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_20_1_23) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_20_1_23, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0))
% 14.91/4.20 |
% 14.91/4.20 | Instantiating formula (15) with all_26_0_28, all_30_0_32, all_0_2_2, all_0_2_2, all_0_1_1, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_2_2) = all_30_0_32, apart_point_and_line(all_0_1_1, all_0_2_2) = all_26_0_28, yields:
% 14.91/4.20 | (179) all_30_0_32 = 0 | all_26_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0))
% 14.91/4.20 |
% 14.91/4.20 | Instantiating formula (15) with all_30_0_32, all_24_0_26, all_0_2_2, all_0_3_3, all_0_0_0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_0_0, all_0_2_2) = all_30_0_32, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26, yields:
% 14.91/4.20 | (180) all_30_0_32 = 0 | all_24_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_0_0) = v0))
% 14.91/4.20 |
% 14.91/4.20 | Instantiating formula (15) with all_24_0_26, all_30_0_32, all_0_3_3, all_0_2_2, all_0_1_1, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_2_2) = all_30_0_32, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26, yields:
% 14.91/4.20 | (181) all_30_0_32 = 0 | all_24_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0))
% 14.91/4.20 |
% 14.91/4.20 | Instantiating formula (33) with all_30_0_32, all_24_0_26, all_0_3_3, all_0_2_2, all_0_0_0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_0_0, all_0_2_2) = all_30_0_32, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26, yields:
% 14.91/4.20 | (182) all_30_0_32 = 0 | all_24_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_0_0) = v0))
% 14.91/4.20 |
% 14.91/4.20 | Instantiating formula (33) with all_24_0_26, all_30_0_32, all_0_2_2, all_0_3_3, all_0_1_1, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_2_2) = all_30_0_32, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_26, yields:
% 14.91/4.20 | (183) all_30_0_32 = 0 | all_24_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0))
% 14.91/4.20 |
% 14.91/4.20 | Instantiating formula (15) with all_30_0_32, all_30_0_32, all_0_2_2, all_0_2_2, all_0_0_0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_2_2) = all_30_0_32, yields:
% 14.91/4.20 | (184) all_30_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0))
% 14.91/4.20 |
% 14.91/4.20 +-Applying beta-rule and splitting (81), into two cases.
% 14.91/4.20 |-Branch one:
% 14.91/4.20 | (185) ~ (all_31_0_33 = 0) & apart_point_and_line(all_0_0_0, all_0_3_3) = all_31_0_33
% 14.91/4.20 |
% 14.91/4.20 | Applying alpha-rule on (185) yields:
% 14.91/4.20 | (186) ~ (all_31_0_33 = 0)
% 14.91/4.20 | (187) apart_point_and_line(all_0_0_0, all_0_3_3) = all_31_0_33
% 14.91/4.20 |
% 14.91/4.20 +-Applying beta-rule and splitting (184), into two cases.
% 14.91/4.20 |-Branch one:
% 14.91/4.20 | (188) all_30_0_32 = 0
% 14.91/4.20 |
% 14.91/4.20 | Equations (188) can reduce 116 to:
% 14.91/4.20 | (119) $false
% 14.91/4.20 |
% 14.91/4.20 |-The branch is then unsatisfiable
% 14.91/4.20 |-Branch two:
% 14.91/4.20 | (116) ~ (all_30_0_32 = 0)
% 14.91/4.20 | (191) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0))
% 14.91/4.20 |
% 14.91/4.20 +-Applying beta-rule and splitting (174), into two cases.
% 14.91/4.20 |-Branch one:
% 14.91/4.20 | (192) (all_234_0_361 = 0 & apart_point_and_line(all_0_0_0, all_0_2_2) = 0) | (all_234_0_361 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0)
% 14.91/4.20 |
% 14.91/4.20 +-Applying beta-rule and splitting (192), into two cases.
% 14.91/4.20 |-Branch one:
% 14.91/4.20 | (193) all_234_0_361 = 0 & apart_point_and_line(all_0_0_0, all_0_2_2) = 0
% 14.91/4.20 |
% 14.91/4.20 | Applying alpha-rule on (193) yields:
% 14.91/4.20 | (194) all_234_0_361 = 0
% 14.91/4.20 | (195) apart_point_and_line(all_0_0_0, all_0_2_2) = 0
% 14.91/4.20 |
% 14.91/4.20 +-Applying beta-rule and splitting (175), into two cases.
% 14.91/4.20 |-Branch one:
% 14.91/4.21 | (188) all_30_0_32 = 0
% 14.91/4.21 |
% 14.91/4.21 | Equations (188) can reduce 116 to:
% 14.91/4.21 | (119) $false
% 14.91/4.21 |
% 14.91/4.21 |-The branch is then unsatisfiable
% 14.91/4.21 |-Branch two:
% 14.91/4.21 | (116) ~ (all_30_0_32 = 0)
% 14.91/4.21 | (199) all_22_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_20_1_23) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_20_1_23, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0))
% 14.91/4.21 |
% 14.91/4.21 +-Applying beta-rule and splitting (176), into two cases.
% 14.91/4.21 |-Branch one:
% 14.91/4.21 | (188) all_30_0_32 = 0
% 14.91/4.21 |
% 14.91/4.21 | Equations (188) can reduce 116 to:
% 14.91/4.21 | (119) $false
% 14.91/4.21 |
% 14.91/4.21 |-The branch is then unsatisfiable
% 14.91/4.21 |-Branch two:
% 14.91/4.21 | (116) ~ (all_30_0_32 = 0)
% 14.91/4.21 | (203) all_22_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_20_1_23) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_20_1_23) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0))
% 14.91/4.21 |
% 14.91/4.21 +-Applying beta-rule and splitting (177), into two cases.
% 14.91/4.21 |-Branch one:
% 14.91/4.21 | (188) all_30_0_32 = 0
% 14.91/4.21 |
% 14.91/4.21 | Equations (188) can reduce 116 to:
% 14.91/4.21 | (119) $false
% 14.91/4.21 |
% 14.91/4.21 |-The branch is then unsatisfiable
% 14.91/4.21 |-Branch two:
% 14.91/4.21 | (116) ~ (all_30_0_32 = 0)
% 14.91/4.21 | (207) all_20_0_22 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_20_1_23) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_20_1_23) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0))
% 14.91/4.21 |
% 14.91/4.21 +-Applying beta-rule and splitting (178), into two cases.
% 14.91/4.21 |-Branch one:
% 14.91/4.21 | (188) all_30_0_32 = 0
% 14.91/4.21 |
% 14.91/4.21 | Equations (188) can reduce 116 to:
% 14.91/4.21 | (119) $false
% 14.91/4.21 |
% 14.91/4.21 |-The branch is then unsatisfiable
% 14.91/4.21 |-Branch two:
% 14.91/4.21 | (116) ~ (all_30_0_32 = 0)
% 14.91/4.21 | (211) all_20_0_22 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_20_1_23) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_20_1_23, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0))
% 14.91/4.21 |
% 14.91/4.21 +-Applying beta-rule and splitting (181), into two cases.
% 14.91/4.21 |-Branch one:
% 14.91/4.21 | (188) all_30_0_32 = 0
% 14.91/4.21 |
% 14.91/4.21 | Equations (188) can reduce 116 to:
% 14.91/4.21 | (119) $false
% 14.91/4.21 |
% 14.91/4.21 |-The branch is then unsatisfiable
% 14.91/4.21 |-Branch two:
% 14.91/4.21 | (116) ~ (all_30_0_32 = 0)
% 14.91/4.21 | (215) all_24_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0))
% 14.91/4.21 |
% 14.91/4.21 +-Applying beta-rule and splitting (179), into two cases.
% 14.91/4.21 |-Branch one:
% 14.91/4.21 | (188) all_30_0_32 = 0
% 14.91/4.21 |
% 14.91/4.21 | Equations (188) can reduce 116 to:
% 14.91/4.21 | (119) $false
% 14.91/4.21 |
% 14.91/4.21 |-The branch is then unsatisfiable
% 14.91/4.21 |-Branch two:
% 14.91/4.21 | (116) ~ (all_30_0_32 = 0)
% 14.91/4.21 | (219) all_26_0_28 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0))
% 14.91/4.21 |
% 14.91/4.21 +-Applying beta-rule and splitting (180), into two cases.
% 14.91/4.21 |-Branch one:
% 14.91/4.21 | (188) all_30_0_32 = 0
% 14.91/4.21 |
% 14.91/4.21 | Equations (188) can reduce 116 to:
% 14.91/4.21 | (119) $false
% 14.91/4.21 |
% 14.91/4.21 |-The branch is then unsatisfiable
% 14.91/4.21 |-Branch two:
% 14.91/4.21 | (116) ~ (all_30_0_32 = 0)
% 14.91/4.21 | (223) all_24_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_0_0) = v0))
% 14.91/4.21 |
% 14.91/4.21 +-Applying beta-rule and splitting (182), into two cases.
% 14.91/4.21 |-Branch one:
% 14.91/4.21 | (188) all_30_0_32 = 0
% 14.91/4.21 |
% 14.91/4.21 | Equations (188) can reduce 116 to:
% 14.91/4.21 | (119) $false
% 14.91/4.21 |
% 14.91/4.21 |-The branch is then unsatisfiable
% 14.91/4.21 |-Branch two:
% 14.91/4.21 | (116) ~ (all_30_0_32 = 0)
% 14.91/4.21 | (227) all_24_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_0_0) = v0))
% 14.91/4.21 |
% 14.91/4.21 +-Applying beta-rule and splitting (183), into two cases.
% 14.91/4.21 |-Branch one:
% 14.91/4.21 | (188) all_30_0_32 = 0
% 14.91/4.21 |
% 14.91/4.21 | Equations (188) can reduce 116 to:
% 14.91/4.21 | (119) $false
% 14.91/4.21 |
% 14.91/4.21 |-The branch is then unsatisfiable
% 14.91/4.21 |-Branch two:
% 14.91/4.21 | (116) ~ (all_30_0_32 = 0)
% 14.91/4.21 | (231) all_24_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_1_1) = v0))
% 14.91/4.21 |
% 14.91/4.21 | Instantiating formula (22) with all_0_0_0, all_0_2_2, 0, all_30_0_32 and discharging atoms apart_point_and_line(all_0_0_0, all_0_2_2) = all_30_0_32, apart_point_and_line(all_0_0_0, all_0_2_2) = 0, yields:
% 14.91/4.21 | (188) all_30_0_32 = 0
% 14.91/4.21 |
% 14.91/4.21 | Equations (188) can reduce 116 to:
% 14.91/4.21 | (119) $false
% 14.91/4.21 |
% 14.91/4.21 |-The branch is then unsatisfiable
% 14.91/4.21 |-Branch two:
% 14.91/4.21 | (234) all_234_0_361 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0
% 14.91/4.21 |
% 14.91/4.21 | Applying alpha-rule on (234) yields:
% 14.91/4.21 | (194) all_234_0_361 = 0
% 14.91/4.21 | (236) apart_point_and_line(all_0_0_0, all_0_3_3) = 0
% 14.91/4.21 |
% 14.91/4.21 | Instantiating formula (22) with all_0_0_0, all_0_3_3, 0, all_31_0_33 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_31_0_33, apart_point_and_line(all_0_0_0, all_0_3_3) = 0, yields:
% 14.91/4.21 | (237) all_31_0_33 = 0
% 14.91/4.21 |
% 14.91/4.21 | Equations (237) can reduce 186 to:
% 14.91/4.21 | (119) $false
% 14.91/4.21 |
% 14.91/4.21 |-The branch is then unsatisfiable
% 14.91/4.21 |-Branch two:
% 14.91/4.21 | (239) ~ (all_234_0_361 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_234_0_361
% 14.91/4.21 |
% 14.91/4.21 | Applying alpha-rule on (239) yields:
% 14.91/4.21 | (240) ~ (all_234_0_361 = 0)
% 14.91/4.21 | (241) distinct_lines(all_0_2_2, all_0_3_3) = all_234_0_361
% 14.91/4.21 |
% 14.91/4.21 | Instantiating formula (13) with all_234_0_361, all_0_3_3, all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, distinct_lines(all_0_2_2, all_0_3_3) = all_234_0_361, yields:
% 14.91/4.21 | (242) all_234_0_361 = 0 | convergent_lines(all_0_3_3, all_0_3_3) = 0
% 14.91/4.21 |
% 14.91/4.21 +-Applying beta-rule and splitting (242), into two cases.
% 14.91/4.21 |-Branch one:
% 14.91/4.21 | (243) convergent_lines(all_0_3_3, all_0_3_3) = 0
% 14.91/4.21 |
% 14.91/4.21 | Instantiating formula (42) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 14.91/4.21 | (244) $false
% 14.91/4.21 |
% 14.91/4.21 |-The branch is then unsatisfiable
% 14.91/4.21 |-Branch two:
% 14.91/4.21 | (245) ~ (convergent_lines(all_0_3_3, all_0_3_3) = 0)
% 14.91/4.21 | (194) all_234_0_361 = 0
% 14.91/4.21 |
% 14.91/4.21 | Equations (194) can reduce 240 to:
% 14.91/4.21 | (119) $false
% 14.91/4.21 |
% 14.91/4.21 |-The branch is then unsatisfiable
% 14.91/4.21 |-Branch two:
% 14.91/4.21 | (248) ~ (all_31_0_33 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = all_31_0_33
% 14.91/4.21 |
% 14.91/4.21 | Applying alpha-rule on (248) yields:
% 14.91/4.21 | (186) ~ (all_31_0_33 = 0)
% 14.91/4.21 | (250) convergent_lines(all_0_2_2, all_0_3_3) = all_31_0_33
% 14.91/4.21 |
% 14.91/4.21 | Instantiating formula (10) with all_31_0_33, all_0_3_3, all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_2_2, all_0_3_3) = all_31_0_33, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 14.91/4.21 | (251) all_31_0_33 = 0 | convergent_lines(all_0_3_3, all_0_3_3) = 0
% 14.91/4.21 |
% 14.91/4.21 +-Applying beta-rule and splitting (251), into two cases.
% 14.91/4.21 |-Branch one:
% 14.91/4.22 | (243) convergent_lines(all_0_3_3, all_0_3_3) = 0
% 14.91/4.22 |
% 14.91/4.22 | Instantiating formula (42) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 14.91/4.22 | (244) $false
% 14.91/4.22 |
% 14.91/4.22 |-The branch is then unsatisfiable
% 14.91/4.22 |-Branch two:
% 14.91/4.22 | (245) ~ (convergent_lines(all_0_3_3, all_0_3_3) = 0)
% 14.91/4.22 | (237) all_31_0_33 = 0
% 14.91/4.22 |
% 14.91/4.22 | Equations (237) can reduce 186 to:
% 14.91/4.22 | (119) $false
% 14.91/4.22 |
% 14.91/4.22 |-The branch is then unsatisfiable
% 14.91/4.22 |-Branch two:
% 14.91/4.22 | (257) ~ (all_30_0_32 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = all_30_0_32
% 14.91/4.22 |
% 14.91/4.22 | Applying alpha-rule on (257) yields:
% 14.91/4.22 | (116) ~ (all_30_0_32 = 0)
% 14.91/4.22 | (259) convergent_lines(all_0_2_2, all_0_3_3) = all_30_0_32
% 14.91/4.22 |
% 14.91/4.22 | Instantiating formula (10) with all_30_0_32, all_0_3_3, all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_2_2, all_0_3_3) = all_30_0_32, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 14.91/4.22 | (260) all_30_0_32 = 0 | convergent_lines(all_0_3_3, all_0_3_3) = 0
% 14.91/4.22 |
% 14.91/4.22 +-Applying beta-rule and splitting (260), into two cases.
% 14.91/4.22 |-Branch one:
% 14.91/4.22 | (243) convergent_lines(all_0_3_3, all_0_3_3) = 0
% 14.91/4.22 |
% 14.91/4.22 | Instantiating formula (42) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 14.91/4.22 | (244) $false
% 14.91/4.22 |
% 14.91/4.22 |-The branch is then unsatisfiable
% 14.91/4.22 |-Branch two:
% 14.91/4.22 | (245) ~ (convergent_lines(all_0_3_3, all_0_3_3) = 0)
% 14.91/4.22 | (188) all_30_0_32 = 0
% 14.91/4.22 |
% 14.91/4.22 | Equations (188) can reduce 116 to:
% 14.91/4.22 | (119) $false
% 14.91/4.22 |
% 14.91/4.22 |-The branch is then unsatisfiable
% 14.91/4.22 |-Branch two:
% 14.91/4.22 | (266) ~ (all_28_0_30 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_28_0_30
% 14.91/4.22 |
% 14.91/4.22 | Applying alpha-rule on (266) yields:
% 14.91/4.22 | (86) ~ (all_28_0_30 = 0)
% 14.91/4.22 | (268) convergent_lines(all_0_3_3, all_0_2_2) = all_28_0_30
% 14.91/4.22 |
% 14.91/4.22 | Instantiating formula (7) with all_0_3_3, all_0_2_2, all_28_0_30, 0 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_28_0_30, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 14.91/4.22 | (269) all_28_0_30 = 0
% 14.91/4.22 |
% 14.91/4.22 | Equations (269) can reduce 86 to:
% 14.91/4.22 | (119) $false
% 14.91/4.22 |
% 14.91/4.22 |-The branch is then unsatisfiable
% 14.91/4.22 |-Branch two:
% 14.91/4.22 | (271) ~ (all_29_0_31 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_29_0_31
% 14.91/4.22 |
% 14.91/4.22 | Applying alpha-rule on (271) yields:
% 14.91/4.22 | (83) ~ (all_29_0_31 = 0)
% 14.91/4.22 | (273) convergent_lines(all_0_3_3, all_0_2_2) = all_29_0_31
% 14.91/4.22 |
% 14.91/4.22 | Instantiating formula (7) with all_0_3_3, all_0_2_2, all_29_0_31, 0 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_29_0_31, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 14.91/4.22 | (274) all_29_0_31 = 0
% 14.91/4.22 |
% 14.91/4.22 | Equations (274) can reduce 83 to:
% 14.91/4.22 | (119) $false
% 14.91/4.22 |
% 14.91/4.22 |-The branch is then unsatisfiable
% 14.91/4.22 % SZS output end Proof for theBenchmark
% 14.91/4.22
% 14.91/4.22 3604ms
%------------------------------------------------------------------------------