TSTP Solution File: GEO182+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO182+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.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 03:48:19 EDT 2022
% Result : Theorem 5.46s 2.05s
% Output : Proof 11.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO182+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n019.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 : Sat Jun 18 02:35:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.62/0.61 ____ _
% 0.62/0.61 ___ / __ \_____(_)___ ________ __________
% 0.62/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.62/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.62/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.62/0.61
% 0.62/0.62 A Theorem Prover for First-Order Logic
% 0.62/0.62 (ePrincess v.1.0)
% 0.62/0.62
% 0.62/0.62 (c) Philipp Rümmer, 2009-2015
% 0.62/0.62 (c) Peter Backeman, 2014-2015
% 0.62/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.62/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.62/0.62 Bug reports to peter@backeman.se
% 0.62/0.62
% 0.62/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.62/0.62
% 0.62/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.78/1.00 Prover 0: Preprocessing ...
% 1.95/1.13 Prover 0: Warning: ignoring some quantifiers
% 1.95/1.16 Prover 0: Constructing countermodel ...
% 2.75/1.35 Prover 0: gave up
% 2.75/1.35 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.75/1.37 Prover 1: Preprocessing ...
% 3.23/1.47 Prover 1: Constructing countermodel ...
% 3.36/1.52 Prover 1: gave up
% 3.36/1.52 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.36/1.54 Prover 2: Preprocessing ...
% 3.89/1.66 Prover 2: Warning: ignoring some quantifiers
% 3.89/1.67 Prover 2: Constructing countermodel ...
% 5.46/2.05 Prover 2: proved (536ms)
% 5.46/2.05
% 5.46/2.05 No countermodel exists, formula is valid
% 5.46/2.05 % SZS status Theorem for theBenchmark
% 5.46/2.05
% 5.46/2.05 Generating proof ... Warning: ignoring some quantifiers
% 11.21/3.32 found it (size 167)
% 11.21/3.32
% 11.21/3.32 % SZS output start Proof for theBenchmark
% 11.21/3.32 Assumed formulas after preprocessing and simplification:
% 11.21/3.32 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v1, v0) = v4 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v4) = v5 & apart_point_and_line(v2, v3) = 0 & distinct_points(v0, v1) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v7, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v6, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v6, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v8, v7) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = v10) | ~ (distinct_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v7, v8) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v8, v7) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v7, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v6, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v7, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v6, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (apart_point_and_line(v9, v8) = v7) | ~ (apart_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (convergent_lines(v9, v8) = v7) | ~ (convergent_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_lines(v9, v8) = v7) | ~ (distinct_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_points(v9, v8) = v7) | ~ (distinct_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | ~ (distinct_points(v6, v7) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v7, v9) = 0) | (v10 = 0 & apart_point_and_line(v7, v8) = 0) | (v10 = 0 & apart_point_and_line(v6, v9) = 0) | (v10 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v7) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v7) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v6) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v7, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0) & ? [v6] : ? [v7] : ? [v8] : intersection_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : line_connecting(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : apart_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : convergent_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_points(v7, v6) = v8)
% 11.21/3.37 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 11.21/3.37 | (1) ~ (all_0_0_0 = 0) & line_connecting(all_0_4_4, all_0_5_5) = all_0_1_1 & line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2 & apart_point_and_line(all_0_3_3, all_0_1_1) = all_0_0_0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0 & distinct_points(all_0_5_5, all_0_4_4) = 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
% 11.21/3.38 |
% 11.21/3.38 | Applying alpha-rule on (1) yields:
% 11.21/3.38 | (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)))
% 11.21/3.38 | (3) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 11.21/3.38 | (4) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 11.21/3.38 | (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)))
% 11.68/3.38 | (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))
% 11.68/3.38 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 11.68/3.38 | (8) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 11.68/3.38 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 11.68/3.38 | (10) ! [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)))
% 11.68/3.38 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 11.68/3.38 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 11.68/3.38 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 11.68/3.39 | (14) ! [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)))
% 11.68/3.39 | (15) ! [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)
% 11.68/3.39 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 11.68/3.39 | (17) ! [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)
% 11.68/3.39 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 11.68/3.39 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 11.68/3.39 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 11.68/3.39 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 11.68/3.39 | (22) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 11.68/3.39 | (23) ! [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)))
% 11.68/3.39 | (24) ! [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)))
% 11.68/3.39 | (25) line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2
% 11.68/3.39 | (26) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 11.68/3.39 | (27) line_connecting(all_0_4_4, all_0_5_5) = all_0_1_1
% 11.68/3.39 | (28) ~ (all_0_0_0 = 0)
% 11.68/3.39 | (29) ! [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)
% 11.68/3.39 | (30) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 11.68/3.39 | (31) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 11.68/3.39 | (32) ! [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)))
% 11.68/3.39 | (33) distinct_points(all_0_5_5, all_0_4_4) = 0
% 11.68/3.39 | (34) ! [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))
% 11.68/3.39 | (35) apart_point_and_line(all_0_3_3, all_0_1_1) = all_0_0_0
% 11.68/3.39 | (36) ! [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)))
% 11.68/3.39 | (37) ! [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))
% 11.68/3.39 | (38) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 11.68/3.39 | (39) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 11.68/3.39 | (40) ! [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))
% 11.68/3.39 | (41) apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 11.68/3.39 | (42) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 11.68/3.40 | (43) ! [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)))
% 11.68/3.40 | (44) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 11.68/3.40 | (45) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 11.68/3.40 | (46) ! [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))
% 11.76/3.40 | (47) ! [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)
% 11.76/3.40 | (48) ! [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))
% 11.76/3.40 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 11.76/3.40 | (50) ! [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)))
% 11.76/3.40 | (51) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 11.76/3.40 | (52) ! [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)))
% 11.76/3.40 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 11.76/3.40 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 11.76/3.40 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 11.76/3.40 |
% 11.76/3.40 | Instantiating formula (50) with all_0_1_1, all_0_5_5, all_0_4_4 and discharging atoms line_connecting(all_0_4_4, all_0_5_5) = all_0_1_1, yields:
% 11.76/3.40 | (56) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 11.76/3.40 |
% 11.76/3.40 | Instantiating formula (2) with all_0_1_1, all_0_5_5, all_0_4_4 and discharging atoms line_connecting(all_0_4_4, all_0_5_5) = all_0_1_1, yields:
% 11.76/3.40 | (57) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 11.76/3.40 |
% 11.76/3.40 | Instantiating formula (50) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 11.76/3.40 | (58) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 11.76/3.40 |
% 11.76/3.40 | Instantiating formula (2) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 11.76/3.40 | (59) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 11.76/3.40 |
% 11.76/3.40 | Instantiating formula (15) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_3_3, all_0_2_2) = 0, yields:
% 11.76/3.40 | (60) all_0_0_0 = 0 | distinct_lines(all_0_2_2, all_0_1_1) = 0
% 11.76/3.40 |
% 11.76/3.40 | Instantiating formula (8) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 11.76/3.40 | (61) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(all_0_4_4, v0) = v1)
% 11.76/3.40 |
% 11.76/3.40 | Instantiating formula (51) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 11.76/3.40 | (62) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(all_0_5_5, v0) = v1)
% 11.76/3.40 |
% 11.76/3.40 | Instantiating (62) with all_20_0_24, all_20_1_25 yields:
% 11.76/3.40 | (63) ~ (all_20_0_24 = 0) & line_connecting(all_0_5_5, all_0_4_4) = all_20_1_25 & apart_point_and_line(all_0_5_5, all_20_1_25) = all_20_0_24
% 11.76/3.40 |
% 11.76/3.40 | Applying alpha-rule on (63) yields:
% 11.76/3.40 | (64) ~ (all_20_0_24 = 0)
% 11.76/3.40 | (65) line_connecting(all_0_5_5, all_0_4_4) = all_20_1_25
% 11.76/3.40 | (66) apart_point_and_line(all_0_5_5, all_20_1_25) = all_20_0_24
% 11.76/3.40 |
% 11.76/3.40 | Instantiating (61) with all_22_0_26, all_22_1_27 yields:
% 11.76/3.40 | (67) ~ (all_22_0_26 = 0) & line_connecting(all_0_5_5, all_0_4_4) = all_22_1_27 & apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26
% 11.76/3.40 |
% 11.76/3.41 | Applying alpha-rule on (67) yields:
% 11.76/3.41 | (68) ~ (all_22_0_26 = 0)
% 11.76/3.41 | (69) line_connecting(all_0_5_5, all_0_4_4) = all_22_1_27
% 11.76/3.41 | (70) apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26
% 11.76/3.41 |
% 11.76/3.41 | Instantiating (59) with all_24_0_28 yields:
% 11.76/3.41 | (71) ( ~ (all_24_0_28 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_24_0_28) | ( ~ (all_24_0_28 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_24_0_28)
% 11.76/3.41 |
% 11.76/3.41 | Instantiating (58) with all_25_0_29 yields:
% 11.76/3.41 | (72) ( ~ (all_25_0_29 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_25_0_29) | ( ~ (all_25_0_29 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_25_0_29)
% 11.76/3.41 |
% 11.76/3.41 | Instantiating (57) with all_26_0_30 yields:
% 11.76/3.41 | (73) ( ~ (all_26_0_30 = 0) & apart_point_and_line(all_0_4_4, all_0_1_1) = all_26_0_30) | ( ~ (all_26_0_30 = 0) & distinct_points(all_0_4_4, all_0_5_5) = all_26_0_30)
% 11.76/3.41 |
% 11.76/3.41 | Instantiating (56) with all_27_0_31 yields:
% 11.76/3.41 | (74) ( ~ (all_27_0_31 = 0) & apart_point_and_line(all_0_5_5, all_0_1_1) = all_27_0_31) | ( ~ (all_27_0_31 = 0) & distinct_points(all_0_4_4, all_0_5_5) = all_27_0_31)
% 11.76/3.41 |
% 11.76/3.41 +-Applying beta-rule and splitting (71), into two cases.
% 11.76/3.41 |-Branch one:
% 11.76/3.41 | (75) ~ (all_24_0_28 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_24_0_28
% 11.76/3.41 |
% 11.76/3.41 | Applying alpha-rule on (75) yields:
% 11.76/3.41 | (76) ~ (all_24_0_28 = 0)
% 11.76/3.41 | (77) apart_point_and_line(all_0_5_5, all_0_2_2) = all_24_0_28
% 11.76/3.41 |
% 11.76/3.41 +-Applying beta-rule and splitting (60), into two cases.
% 11.76/3.41 |-Branch one:
% 11.76/3.41 | (78) distinct_lines(all_0_2_2, all_0_1_1) = 0
% 11.76/3.41 |
% 11.76/3.41 +-Applying beta-rule and splitting (72), into two cases.
% 11.76/3.41 |-Branch one:
% 11.76/3.41 | (79) ~ (all_25_0_29 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_25_0_29
% 11.76/3.41 |
% 11.76/3.41 | Applying alpha-rule on (79) yields:
% 11.76/3.41 | (80) ~ (all_25_0_29 = 0)
% 11.76/3.41 | (81) apart_point_and_line(all_0_4_4, all_0_2_2) = all_25_0_29
% 11.76/3.41 |
% 11.76/3.41 | Instantiating formula (20) with all_0_5_5, all_0_4_4, all_22_1_27, all_0_2_2 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_22_1_27, line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 11.76/3.41 | (82) all_22_1_27 = all_0_2_2
% 11.76/3.41 |
% 11.76/3.41 | Instantiating formula (20) with all_0_5_5, all_0_4_4, all_20_1_25, all_22_1_27 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_22_1_27, line_connecting(all_0_5_5, all_0_4_4) = all_20_1_25, yields:
% 11.76/3.41 | (83) all_22_1_27 = all_20_1_25
% 11.76/3.41 |
% 11.76/3.41 | Combining equations (82,83) yields a new equation:
% 11.76/3.41 | (84) all_20_1_25 = all_0_2_2
% 11.76/3.41 |
% 11.76/3.41 | Combining equations (84,83) yields a new equation:
% 11.76/3.41 | (82) all_22_1_27 = all_0_2_2
% 11.76/3.41 |
% 11.76/3.41 | From (82) and (70) follows:
% 11.76/3.41 | (86) apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26
% 11.76/3.41 |
% 11.76/3.41 | From (84) and (66) follows:
% 11.76/3.41 | (87) apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24
% 11.76/3.41 |
% 11.76/3.41 | Instantiating formula (21) with all_0_4_4, all_0_2_2, all_22_0_26, all_25_0_29 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_25_0_29, apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, yields:
% 11.76/3.41 | (88) all_25_0_29 = all_22_0_26
% 11.76/3.41 |
% 11.76/3.41 | Instantiating formula (21) with all_0_5_5, all_0_2_2, all_20_0_24, all_24_0_28 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_24_0_28, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 11.76/3.41 | (89) all_24_0_28 = all_20_0_24
% 11.76/3.41 |
% 11.76/3.41 | Equations (88) can reduce 80 to:
% 11.76/3.41 | (68) ~ (all_22_0_26 = 0)
% 11.83/3.41 |
% 11.83/3.41 | Equations (89) can reduce 76 to:
% 11.83/3.41 | (64) ~ (all_20_0_24 = 0)
% 11.83/3.41 |
% 11.83/3.41 | From (88) and (81) follows:
% 11.83/3.41 | (86) apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26
% 11.83/3.41 |
% 11.83/3.41 | From (89) and (77) follows:
% 11.83/3.41 | (87) apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24
% 11.83/3.41 |
% 11.83/3.41 | Instantiating formula (14) with all_22_0_26, all_0_0_0, all_0_2_2, all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, yields:
% 11.83/3.41 | (94) all_22_0_26 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 11.83/3.41 |
% 11.83/3.41 | Instantiating formula (14) with all_0_0_0, all_22_0_26, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, yields:
% 11.83/3.41 | (95) all_22_0_26 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 11.83/3.41 |
% 11.83/3.41 | Instantiating formula (36) with all_22_0_26, all_0_0_0, all_0_1_1, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, yields:
% 11.83/3.41 | (96) all_22_0_26 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 11.83/3.42 |
% 11.83/3.42 | Instantiating formula (36) with all_0_0_0, all_22_0_26, all_0_2_2, all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, yields:
% 11.83/3.42 | (97) all_22_0_26 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 11.83/3.42 |
% 11.83/3.42 | Instantiating formula (10) with all_22_0_26, all_22_0_26, all_0_2_2, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 11.83/3.42 | (98) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 11.83/3.42 |
% 11.83/3.42 | Instantiating formula (14) with all_22_0_26, all_22_0_26, all_0_2_2, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, yields:
% 11.83/3.42 | (99) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 11.83/3.42 |
% 11.83/3.42 | Instantiating formula (14) with all_20_0_24, all_0_0_0, all_0_2_2, all_0_1_1, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 11.83/3.42 | (100) all_20_0_24 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 11.83/3.42 |
% 11.83/3.42 | Instantiating formula (14) with all_0_0_0, all_20_0_24, all_0_1_1, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 11.83/3.42 | (101) all_20_0_24 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 11.83/3.42 |
% 11.83/3.42 | Instantiating formula (36) with all_0_0_0, all_20_0_24, all_0_2_2, all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 11.83/3.42 | (102) all_20_0_24 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 11.83/3.42 |
% 11.83/3.42 | Instantiating formula (14) with all_20_0_24, all_22_0_26, all_0_2_2, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 11.83/3.42 | (103) all_22_0_26 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 11.83/3.42 |
% 11.83/3.42 | Instantiating formula (14) with all_22_0_26, all_20_0_24, all_0_2_2, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 11.83/3.42 | (104) all_22_0_26 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 11.83/3.42 |
% 11.83/3.42 | Instantiating formula (32) with all_20_0_24, all_20_0_24, all_0_2_2, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 11.83/3.42 | (105) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 11.83/3.42 |
% 11.83/3.42 | Instantiating formula (14) with all_20_0_24, all_20_0_24, all_0_2_2, all_0_2_2, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 11.83/3.42 | (106) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 11.83/3.42 |
% 11.83/3.42 | Instantiating formula (43) with all_22_0_26, all_22_0_26, all_0_1_1, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, distinct_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 11.83/3.42 | (107) all_22_0_26 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 11.83/3.42 |
% 11.83/3.42 | Instantiating formula (43) with all_22_0_26, all_20_0_24, all_0_1_1, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 11.83/3.42 | (108) all_22_0_26 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 11.83/3.42 |
% 11.83/3.42 | Instantiating formula (43) with all_20_0_24, all_22_0_26, all_0_1_1, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 11.83/3.42 | (109) all_22_0_26 = 0 | all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 11.83/3.42 |
% 11.83/3.42 | Instantiating formula (43) with all_20_0_24, all_20_0_24, all_0_1_1, all_0_2_2, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 11.83/3.42 | (110) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 11.83/3.43 |
% 11.83/3.43 | Instantiating formula (24) with all_0_1_1, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms distinct_lines(all_0_2_2, all_0_1_1) = 0, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 11.83/3.43 | (111) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0))
% 11.83/3.43 |
% 11.83/3.43 | Instantiating (111) with all_57_0_33 yields:
% 11.83/3.43 | (112) (all_57_0_33 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (all_57_0_33 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (all_57_0_33 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (all_57_0_33 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0)
% 11.83/3.43 |
% 11.83/3.43 +-Applying beta-rule and splitting (73), into two cases.
% 11.83/3.43 |-Branch one:
% 11.83/3.43 | (113) ~ (all_26_0_30 = 0) & apart_point_and_line(all_0_4_4, all_0_1_1) = all_26_0_30
% 11.83/3.43 |
% 11.83/3.43 | Applying alpha-rule on (113) yields:
% 11.83/3.43 | (114) ~ (all_26_0_30 = 0)
% 11.83/3.43 | (115) apart_point_and_line(all_0_4_4, all_0_1_1) = all_26_0_30
% 11.83/3.43 |
% 11.83/3.43 +-Applying beta-rule and splitting (108), into two cases.
% 11.83/3.43 |-Branch one:
% 11.83/3.43 | (116) all_22_0_26 = 0
% 11.83/3.43 |
% 11.83/3.43 | Equations (116) can reduce 68 to:
% 11.83/3.43 | (117) $false
% 11.83/3.43 |
% 11.83/3.43 |-The branch is then unsatisfiable
% 11.83/3.43 |-Branch two:
% 11.83/3.43 | (68) ~ (all_22_0_26 = 0)
% 11.83/3.43 | (119) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 11.83/3.43 |
% 11.83/3.43 +-Applying beta-rule and splitting (107), into two cases.
% 11.83/3.43 |-Branch one:
% 11.83/3.43 | (116) all_22_0_26 = 0
% 11.83/3.43 |
% 11.83/3.43 | Equations (116) can reduce 68 to:
% 11.83/3.43 | (117) $false
% 11.83/3.43 |
% 11.83/3.43 |-The branch is then unsatisfiable
% 11.83/3.43 |-Branch two:
% 11.83/3.43 | (68) ~ (all_22_0_26 = 0)
% 11.83/3.43 | (123) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 11.83/3.43 |
% 11.83/3.43 +-Applying beta-rule and splitting (109), into two cases.
% 11.83/3.43 |-Branch one:
% 11.83/3.43 | (116) all_22_0_26 = 0
% 11.83/3.43 |
% 11.83/3.43 | Equations (116) can reduce 68 to:
% 11.83/3.43 | (117) $false
% 11.83/3.43 |
% 11.83/3.43 |-The branch is then unsatisfiable
% 11.83/3.43 |-Branch two:
% 11.83/3.43 | (68) ~ (all_22_0_26 = 0)
% 11.83/3.43 | (127) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 11.83/3.43 |
% 11.83/3.43 +-Applying beta-rule and splitting (119), into two cases.
% 11.83/3.43 |-Branch one:
% 11.83/3.43 | (128) all_20_0_24 = 0
% 11.83/3.43 |
% 11.83/3.43 | Equations (128) can reduce 64 to:
% 11.83/3.43 | (117) $false
% 11.83/3.43 |
% 11.83/3.43 |-The branch is then unsatisfiable
% 11.83/3.43 |-Branch two:
% 11.83/3.43 | (64) ~ (all_20_0_24 = 0)
% 11.83/3.43 | (131) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 11.83/3.43 |
% 11.83/3.43 +-Applying beta-rule and splitting (98), into two cases.
% 11.83/3.43 |-Branch one:
% 11.83/3.43 | (116) all_22_0_26 = 0
% 11.83/3.43 |
% 11.83/3.43 | Equations (116) can reduce 68 to:
% 11.83/3.43 | (117) $false
% 11.83/3.43 |
% 11.83/3.43 |-The branch is then unsatisfiable
% 11.83/3.43 |-Branch two:
% 11.83/3.43 | (68) ~ (all_22_0_26 = 0)
% 11.83/3.43 | (135) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 11.83/3.43 |
% 11.83/3.43 +-Applying beta-rule and splitting (99), into two cases.
% 11.83/3.43 |-Branch one:
% 11.83/3.43 | (116) all_22_0_26 = 0
% 11.83/3.43 |
% 11.83/3.43 | Equations (116) can reduce 68 to:
% 11.83/3.43 | (117) $false
% 11.83/3.43 |
% 11.83/3.43 |-The branch is then unsatisfiable
% 11.83/3.43 |-Branch two:
% 11.83/3.43 | (68) ~ (all_22_0_26 = 0)
% 11.83/3.43 | (139) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 11.83/3.43 |
% 11.83/3.43 +-Applying beta-rule and splitting (105), into two cases.
% 11.83/3.43 |-Branch one:
% 11.83/3.43 | (128) all_20_0_24 = 0
% 11.83/3.43 |
% 11.83/3.43 | Equations (128) can reduce 64 to:
% 11.83/3.43 | (117) $false
% 11.83/3.43 |
% 11.83/3.43 |-The branch is then unsatisfiable
% 11.83/3.43 |-Branch two:
% 11.83/3.43 | (64) ~ (all_20_0_24 = 0)
% 11.83/3.43 | (143) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 11.83/3.43 |
% 11.83/3.43 +-Applying beta-rule and splitting (106), into two cases.
% 11.83/3.43 |-Branch one:
% 11.83/3.43 | (128) all_20_0_24 = 0
% 11.83/3.43 |
% 11.83/3.43 | Equations (128) can reduce 64 to:
% 11.83/3.43 | (117) $false
% 11.83/3.43 |
% 11.83/3.43 |-The branch is then unsatisfiable
% 11.83/3.43 |-Branch two:
% 11.83/3.43 | (64) ~ (all_20_0_24 = 0)
% 11.83/3.43 | (147) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 11.83/3.43 |
% 11.83/3.43 +-Applying beta-rule and splitting (94), into two cases.
% 11.83/3.43 |-Branch one:
% 11.83/3.43 | (116) all_22_0_26 = 0
% 11.83/3.43 |
% 11.83/3.43 | Equations (116) can reduce 68 to:
% 11.83/3.43 | (117) $false
% 11.83/3.43 |
% 11.83/3.43 |-The branch is then unsatisfiable
% 11.83/3.43 |-Branch two:
% 11.83/3.43 | (68) ~ (all_22_0_26 = 0)
% 11.83/3.44 | (151) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 11.83/3.44 |
% 11.83/3.44 +-Applying beta-rule and splitting (103), into two cases.
% 11.83/3.44 |-Branch one:
% 11.83/3.44 | (116) all_22_0_26 = 0
% 11.83/3.44 |
% 11.83/3.44 | Equations (116) can reduce 68 to:
% 11.83/3.44 | (117) $false
% 11.83/3.44 |
% 11.83/3.44 |-The branch is then unsatisfiable
% 11.83/3.44 |-Branch two:
% 11.83/3.44 | (68) ~ (all_22_0_26 = 0)
% 11.83/3.44 | (155) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 11.83/3.44 |
% 11.83/3.44 +-Applying beta-rule and splitting (95), into two cases.
% 11.83/3.44 |-Branch one:
% 11.83/3.44 | (116) all_22_0_26 = 0
% 11.83/3.44 |
% 11.83/3.44 | Equations (116) can reduce 68 to:
% 11.83/3.44 | (117) $false
% 11.83/3.44 |
% 11.83/3.44 |-The branch is then unsatisfiable
% 11.83/3.44 |-Branch two:
% 11.83/3.44 | (68) ~ (all_22_0_26 = 0)
% 11.83/3.44 | (159) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 11.83/3.44 |
% 11.83/3.44 +-Applying beta-rule and splitting (96), into two cases.
% 11.83/3.44 |-Branch one:
% 11.83/3.44 | (116) all_22_0_26 = 0
% 11.83/3.44 |
% 11.83/3.44 | Equations (116) can reduce 68 to:
% 11.83/3.44 | (117) $false
% 11.83/3.44 |
% 11.83/3.44 |-The branch is then unsatisfiable
% 11.83/3.44 |-Branch two:
% 11.83/3.44 | (68) ~ (all_22_0_26 = 0)
% 11.83/3.44 | (163) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 11.83/3.44 |
% 11.83/3.44 +-Applying beta-rule and splitting (97), into two cases.
% 11.83/3.44 |-Branch one:
% 11.83/3.44 | (116) all_22_0_26 = 0
% 11.83/3.44 |
% 11.83/3.44 | Equations (116) can reduce 68 to:
% 11.83/3.44 | (117) $false
% 11.83/3.44 |
% 11.83/3.44 |-The branch is then unsatisfiable
% 11.83/3.44 |-Branch two:
% 11.83/3.44 | (68) ~ (all_22_0_26 = 0)
% 11.83/3.44 | (167) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 11.83/3.44 |
% 11.83/3.44 +-Applying beta-rule and splitting (104), into two cases.
% 11.83/3.44 |-Branch one:
% 11.83/3.44 | (116) all_22_0_26 = 0
% 11.83/3.44 |
% 11.83/3.44 | Equations (116) can reduce 68 to:
% 11.83/3.44 | (117) $false
% 11.83/3.44 |
% 11.83/3.44 |-The branch is then unsatisfiable
% 11.83/3.44 |-Branch two:
% 11.83/3.44 | (68) ~ (all_22_0_26 = 0)
% 11.83/3.44 | (171) all_20_0_24 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 11.83/3.44 |
% 11.83/3.44 +-Applying beta-rule and splitting (171), into two cases.
% 11.83/3.44 |-Branch one:
% 11.83/3.44 | (128) all_20_0_24 = 0
% 11.83/3.44 |
% 11.83/3.44 | Equations (128) can reduce 64 to:
% 11.83/3.44 | (117) $false
% 11.83/3.44 |
% 11.83/3.44 |-The branch is then unsatisfiable
% 11.83/3.44 |-Branch two:
% 11.83/3.44 | (64) ~ (all_20_0_24 = 0)
% 11.83/3.44 | (175) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 11.83/3.44 |
% 11.83/3.44 +-Applying beta-rule and splitting (110), into two cases.
% 11.83/3.44 |-Branch one:
% 11.83/3.44 | (128) all_20_0_24 = 0
% 11.83/3.44 |
% 11.83/3.44 | Equations (128) can reduce 64 to:
% 11.83/3.44 | (117) $false
% 11.83/3.44 |
% 11.83/3.44 |-The branch is then unsatisfiable
% 11.83/3.44 |-Branch two:
% 11.83/3.44 | (64) ~ (all_20_0_24 = 0)
% 11.83/3.44 | (179) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 11.83/3.44 |
% 11.83/3.44 +-Applying beta-rule and splitting (100), into two cases.
% 11.83/3.44 |-Branch one:
% 11.83/3.44 | (128) all_20_0_24 = 0
% 11.83/3.44 |
% 11.83/3.44 | Equations (128) can reduce 64 to:
% 11.83/3.44 | (117) $false
% 11.83/3.44 |
% 11.83/3.44 |-The branch is then unsatisfiable
% 11.83/3.44 |-Branch two:
% 11.83/3.44 | (64) ~ (all_20_0_24 = 0)
% 11.83/3.44 | (183) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 11.83/3.44 |
% 11.83/3.44 +-Applying beta-rule and splitting (102), into two cases.
% 11.83/3.44 |-Branch one:
% 11.83/3.44 | (128) all_20_0_24 = 0
% 11.83/3.44 |
% 11.83/3.44 | Equations (128) can reduce 64 to:
% 11.83/3.44 | (117) $false
% 11.83/3.44 |
% 11.83/3.44 |-The branch is then unsatisfiable
% 11.83/3.44 |-Branch two:
% 11.83/3.44 | (64) ~ (all_20_0_24 = 0)
% 11.83/3.44 | (187) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 11.83/3.44 |
% 11.83/3.44 +-Applying beta-rule and splitting (127), into two cases.
% 11.83/3.44 |-Branch one:
% 11.83/3.44 | (128) all_20_0_24 = 0
% 11.83/3.44 |
% 11.83/3.44 | Equations (128) can reduce 64 to:
% 11.83/3.44 | (117) $false
% 11.83/3.44 |
% 11.83/3.44 |-The branch is then unsatisfiable
% 11.83/3.44 |-Branch two:
% 11.83/3.44 | (64) ~ (all_20_0_24 = 0)
% 11.83/3.44 | (191) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 11.83/3.44 |
% 11.83/3.44 +-Applying beta-rule and splitting (74), into two cases.
% 11.83/3.44 |-Branch one:
% 11.83/3.44 | (192) ~ (all_27_0_31 = 0) & apart_point_and_line(all_0_5_5, all_0_1_1) = all_27_0_31
% 11.83/3.44 |
% 11.83/3.44 | Applying alpha-rule on (192) yields:
% 11.83/3.44 | (193) ~ (all_27_0_31 = 0)
% 11.83/3.44 | (194) apart_point_and_line(all_0_5_5, all_0_1_1) = all_27_0_31
% 11.83/3.44 |
% 11.83/3.44 +-Applying beta-rule and splitting (112), into two cases.
% 11.83/3.44 |-Branch one:
% 11.83/3.44 | (195) (all_57_0_33 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (all_57_0_33 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (all_57_0_33 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0)
% 11.83/3.44 |
% 11.83/3.44 +-Applying beta-rule and splitting (195), into two cases.
% 11.83/3.44 |-Branch one:
% 11.83/3.45 | (196) (all_57_0_33 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (all_57_0_33 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0)
% 11.83/3.45 |
% 11.83/3.45 +-Applying beta-rule and splitting (196), into two cases.
% 11.83/3.45 |-Branch one:
% 11.83/3.45 | (197) all_57_0_33 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0
% 11.83/3.45 |
% 11.83/3.45 | Applying alpha-rule on (197) yields:
% 11.83/3.45 | (198) all_57_0_33 = 0
% 11.83/3.45 | (199) apart_point_and_line(all_0_4_4, all_0_1_1) = 0
% 11.83/3.45 |
% 11.83/3.45 | Instantiating formula (21) with all_0_4_4, all_0_1_1, 0, all_26_0_30 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_26_0_30, apart_point_and_line(all_0_4_4, all_0_1_1) = 0, yields:
% 11.83/3.45 | (200) all_26_0_30 = 0
% 11.83/3.45 |
% 11.83/3.45 | Equations (200) can reduce 114 to:
% 11.83/3.45 | (117) $false
% 11.83/3.45 |
% 11.83/3.45 |-The branch is then unsatisfiable
% 11.83/3.45 |-Branch two:
% 11.83/3.45 | (202) all_57_0_33 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 11.83/3.45 |
% 11.83/3.45 | Applying alpha-rule on (202) yields:
% 11.83/3.45 | (198) all_57_0_33 = 0
% 11.83/3.45 | (204) apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 11.83/3.45 |
% 11.83/3.45 | Instantiating formula (21) with all_0_4_4, all_0_2_2, 0, all_22_0_26 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, apart_point_and_line(all_0_4_4, all_0_2_2) = 0, yields:
% 11.83/3.45 | (116) all_22_0_26 = 0
% 11.83/3.45 |
% 11.83/3.45 | Equations (116) can reduce 68 to:
% 11.83/3.45 | (117) $false
% 11.83/3.45 |
% 11.83/3.45 |-The branch is then unsatisfiable
% 11.83/3.45 |-Branch two:
% 11.83/3.45 | (207) all_57_0_33 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 11.83/3.45 |
% 11.83/3.45 | Applying alpha-rule on (207) yields:
% 11.83/3.45 | (198) all_57_0_33 = 0
% 11.83/3.45 | (209) apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 11.83/3.45 |
% 11.83/3.45 | Instantiating formula (21) with all_0_5_5, all_0_1_1, 0, all_27_0_31 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_27_0_31, apart_point_and_line(all_0_5_5, all_0_1_1) = 0, yields:
% 11.83/3.45 | (210) all_27_0_31 = 0
% 11.83/3.45 |
% 11.83/3.45 | Equations (210) can reduce 193 to:
% 11.83/3.45 | (117) $false
% 11.83/3.45 |
% 11.83/3.45 |-The branch is then unsatisfiable
% 11.83/3.45 |-Branch two:
% 11.83/3.45 | (212) all_57_0_33 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 11.83/3.45 |
% 11.83/3.45 | Applying alpha-rule on (212) yields:
% 11.83/3.45 | (198) all_57_0_33 = 0
% 11.83/3.45 | (214) apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 11.83/3.45 |
% 11.83/3.45 +-Applying beta-rule and splitting (101), into two cases.
% 11.83/3.45 |-Branch one:
% 11.83/3.45 | (128) all_20_0_24 = 0
% 11.83/3.45 |
% 11.83/3.45 | Equations (128) can reduce 64 to:
% 11.83/3.45 | (117) $false
% 11.83/3.45 |
% 11.83/3.45 |-The branch is then unsatisfiable
% 11.83/3.45 |-Branch two:
% 11.83/3.45 | (64) ~ (all_20_0_24 = 0)
% 11.83/3.45 | (218) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 11.83/3.45 |
% 11.83/3.45 +-Applying beta-rule and splitting (155), into two cases.
% 11.83/3.45 |-Branch one:
% 11.83/3.45 | (128) all_20_0_24 = 0
% 11.83/3.45 |
% 11.83/3.45 | Equations (128) can reduce 64 to:
% 11.83/3.45 | (117) $false
% 11.83/3.45 |
% 11.83/3.45 |-The branch is then unsatisfiable
% 11.83/3.45 |-Branch two:
% 11.83/3.45 | (64) ~ (all_20_0_24 = 0)
% 11.83/3.45 | (222) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 11.83/3.45 |
% 11.83/3.45 | Instantiating formula (21) with all_0_5_5, all_0_2_2, 0, all_20_0_24 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, apart_point_and_line(all_0_5_5, all_0_2_2) = 0, yields:
% 11.83/3.45 | (128) all_20_0_24 = 0
% 11.83/3.45 |
% 11.83/3.45 | Equations (128) can reduce 64 to:
% 11.83/3.45 | (117) $false
% 11.83/3.45 |
% 11.83/3.45 |-The branch is then unsatisfiable
% 11.83/3.45 |-Branch two:
% 11.83/3.45 | (225) ~ (all_27_0_31 = 0) & distinct_points(all_0_4_4, all_0_5_5) = all_27_0_31
% 11.83/3.45 |
% 11.83/3.45 | Applying alpha-rule on (225) yields:
% 11.83/3.45 | (193) ~ (all_27_0_31 = 0)
% 11.83/3.45 | (227) distinct_points(all_0_4_4, all_0_5_5) = all_27_0_31
% 11.83/3.45 |
% 11.83/3.45 | Instantiating formula (16) with all_27_0_31, all_0_5_5, all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_4_4, all_0_5_5) = all_27_0_31, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 11.83/3.45 | (228) all_27_0_31 = 0 | distinct_points(all_0_5_5, all_0_5_5) = 0
% 11.83/3.45 |
% 11.83/3.45 +-Applying beta-rule and splitting (228), into two cases.
% 11.83/3.45 |-Branch one:
% 11.83/3.45 | (229) distinct_points(all_0_5_5, all_0_5_5) = 0
% 11.83/3.45 |
% 11.83/3.45 | Instantiating formula (3) with all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_5_5) = 0, yields:
% 11.83/3.45 | (230) $false
% 11.83/3.45 |
% 11.83/3.45 |-The branch is then unsatisfiable
% 11.83/3.45 |-Branch two:
% 11.83/3.45 | (231) ~ (distinct_points(all_0_5_5, all_0_5_5) = 0)
% 11.83/3.45 | (210) all_27_0_31 = 0
% 11.83/3.45 |
% 11.83/3.45 | Equations (210) can reduce 193 to:
% 11.83/3.45 | (117) $false
% 11.83/3.45 |
% 11.83/3.45 |-The branch is then unsatisfiable
% 11.83/3.45 |-Branch two:
% 11.83/3.45 | (234) ~ (all_26_0_30 = 0) & distinct_points(all_0_4_4, all_0_5_5) = all_26_0_30
% 11.83/3.45 |
% 11.83/3.45 | Applying alpha-rule on (234) yields:
% 11.83/3.45 | (114) ~ (all_26_0_30 = 0)
% 11.83/3.45 | (236) distinct_points(all_0_4_4, all_0_5_5) = all_26_0_30
% 11.83/3.45 |
% 11.83/3.45 | Instantiating formula (16) with all_26_0_30, all_0_5_5, all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_4_4, all_0_5_5) = all_26_0_30, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 11.83/3.45 | (237) all_26_0_30 = 0 | distinct_points(all_0_5_5, all_0_5_5) = 0
% 11.83/3.45 |
% 11.83/3.45 | Instantiating formula (37) with all_26_0_30, all_26_0_30, all_0_5_5, all_0_4_4, all_0_4_4 and discharging atoms distinct_points(all_0_4_4, all_0_5_5) = all_26_0_30, yields:
% 11.83/3.45 | (238) all_26_0_30 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0)
% 11.83/3.45 |
% 11.83/3.45 +-Applying beta-rule and splitting (238), into two cases.
% 11.83/3.45 |-Branch one:
% 11.83/3.45 | (200) all_26_0_30 = 0
% 11.83/3.45 |
% 11.83/3.45 | Equations (200) can reduce 114 to:
% 11.83/3.45 | (117) $false
% 11.83/3.45 |
% 11.83/3.45 |-The branch is then unsatisfiable
% 11.83/3.45 |-Branch two:
% 11.83/3.45 | (114) ~ (all_26_0_30 = 0)
% 11.83/3.45 | (242) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0)
% 11.83/3.45 |
% 11.83/3.45 +-Applying beta-rule and splitting (237), into two cases.
% 11.83/3.45 |-Branch one:
% 11.83/3.45 | (229) distinct_points(all_0_5_5, all_0_5_5) = 0
% 11.83/3.45 |
% 11.83/3.45 | Instantiating formula (3) with all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_5_5) = 0, yields:
% 11.83/3.45 | (230) $false
% 11.83/3.45 |
% 11.83/3.45 |-The branch is then unsatisfiable
% 11.83/3.45 |-Branch two:
% 11.83/3.45 | (231) ~ (distinct_points(all_0_5_5, all_0_5_5) = 0)
% 11.83/3.45 | (200) all_26_0_30 = 0
% 11.83/3.45 |
% 11.83/3.46 | Equations (200) can reduce 114 to:
% 11.83/3.46 | (117) $false
% 11.83/3.46 |
% 11.83/3.46 |-The branch is then unsatisfiable
% 11.83/3.46 |-Branch two:
% 11.83/3.46 | (248) ~ (all_25_0_29 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_25_0_29
% 11.83/3.46 |
% 11.83/3.46 | Applying alpha-rule on (248) yields:
% 11.83/3.46 | (80) ~ (all_25_0_29 = 0)
% 11.83/3.46 | (250) distinct_points(all_0_5_5, all_0_4_4) = all_25_0_29
% 11.83/3.46 |
% 11.83/3.46 | Instantiating formula (11) with all_0_5_5, all_0_4_4, all_25_0_29, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_25_0_29, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 11.83/3.46 | (251) all_25_0_29 = 0
% 11.83/3.46 |
% 11.83/3.46 | Equations (251) can reduce 80 to:
% 11.83/3.46 | (117) $false
% 11.83/3.46 |
% 11.83/3.46 |-The branch is then unsatisfiable
% 11.83/3.46 |-Branch two:
% 11.83/3.46 | (253) ~ (distinct_lines(all_0_2_2, all_0_1_1) = 0)
% 11.83/3.46 | (254) all_0_0_0 = 0
% 11.83/3.46 |
% 11.83/3.46 | Equations (254) can reduce 28 to:
% 11.83/3.46 | (117) $false
% 11.83/3.46 |
% 11.83/3.46 |-The branch is then unsatisfiable
% 11.83/3.46 |-Branch two:
% 11.83/3.46 | (256) ~ (all_24_0_28 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_24_0_28
% 11.83/3.46 |
% 11.83/3.46 | Applying alpha-rule on (256) yields:
% 11.83/3.46 | (76) ~ (all_24_0_28 = 0)
% 11.83/3.46 | (258) distinct_points(all_0_5_5, all_0_4_4) = all_24_0_28
% 11.83/3.46 |
% 11.83/3.46 | Instantiating formula (11) with all_0_5_5, all_0_4_4, all_24_0_28, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_24_0_28, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 11.83/3.46 | (259) all_24_0_28 = 0
% 11.83/3.46 |
% 11.83/3.46 | Equations (259) can reduce 76 to:
% 11.83/3.46 | (117) $false
% 11.83/3.46 |
% 11.83/3.46 |-The branch is then unsatisfiable
% 11.83/3.46 % SZS output end Proof for theBenchmark
% 11.83/3.46
% 11.83/3.46 2822ms
%------------------------------------------------------------------------------