TSTP Solution File: GEO181+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO181+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 03:48:18 EDT 2022
% Result : Theorem 6.19s 2.18s
% Output : Proof 12.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO181+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.32 % Computer : n025.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Sat Jun 18 12:48:13 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.17/0.56 ____ _
% 0.17/0.56 ___ / __ \_____(_)___ ________ __________
% 0.17/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.17/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.17/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.17/0.56
% 0.17/0.56 A Theorem Prover for First-Order Logic
% 0.17/0.56 (ePrincess v.1.0)
% 0.17/0.56
% 0.17/0.56 (c) Philipp Rümmer, 2009-2015
% 0.17/0.56 (c) Peter Backeman, 2014-2015
% 0.17/0.56 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.17/0.56 Free software under GNU Lesser General Public License (LGPL).
% 0.17/0.56 Bug reports to peter@backeman.se
% 0.17/0.56
% 0.17/0.56 For more information, visit http://user.uu.se/~petba168/breu/
% 0.17/0.56
% 0.17/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.66/0.94 Prover 0: Preprocessing ...
% 1.83/1.07 Prover 0: Warning: ignoring some quantifiers
% 2.00/1.10 Prover 0: Constructing countermodel ...
% 2.52/1.29 Prover 0: gave up
% 2.52/1.29 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.85/1.32 Prover 1: Preprocessing ...
% 3.09/1.41 Prover 1: Constructing countermodel ...
% 3.09/1.46 Prover 1: gave up
% 3.09/1.46 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.39/1.48 Prover 2: Preprocessing ...
% 3.60/1.61 Prover 2: Warning: ignoring some quantifiers
% 3.60/1.62 Prover 2: Constructing countermodel ...
% 6.19/2.17 Prover 2: proved (711ms)
% 6.19/2.18
% 6.19/2.18 No countermodel exists, formula is valid
% 6.19/2.18 % SZS status Theorem for theBenchmark
% 6.19/2.18
% 6.19/2.18 Generating proof ... Warning: ignoring some quantifiers
% 11.68/3.48 found it (size 185)
% 11.68/3.48
% 11.68/3.48 % SZS output start Proof for theBenchmark
% 11.68/3.48 Assumed formulas after preprocessing and simplification:
% 11.68/3.48 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v0, v2) = v4 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = 0 & apart_point_and_line(v1, v4) = v5 & 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)
% 12.29/3.52 | 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:
% 12.29/3.52 | (1) ~ (all_0_0_0 = 0) & line_connecting(all_0_5_5, all_0_3_3) = 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_2_2) = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = all_0_0_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
% 12.39/3.54 |
% 12.39/3.54 | Applying alpha-rule on (1) yields:
% 12.39/3.54 | (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)))
% 12.39/3.54 | (3) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 12.39/3.54 | (4) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 12.39/3.54 | (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)))
% 12.39/3.54 | (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))
% 12.39/3.54 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 12.39/3.54 | (8) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 12.39/3.54 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 12.39/3.54 | (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)))
% 12.39/3.54 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 12.39/3.54 | (12) line_connecting(all_0_5_5, all_0_3_3) = all_0_1_1
% 12.39/3.54 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 12.39/3.54 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 12.39/3.54 | (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)))
% 12.39/3.54 | (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)
% 12.39/3.54 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 12.39/3.54 | (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)
% 12.39/3.55 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 12.39/3.55 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 12.39/3.55 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 12.39/3.55 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 12.39/3.55 | (23) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 12.39/3.55 | (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)))
% 12.39/3.55 | (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)))
% 12.39/3.55 | (26) line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2
% 12.39/3.55 | (27) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 12.39/3.55 | (28) ~ (all_0_0_0 = 0)
% 12.39/3.55 | (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)
% 12.39/3.55 | (30) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 12.39/3.55 | (31) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 12.39/3.55 | (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)))
% 12.39/3.55 | (33) distinct_points(all_0_5_5, all_0_4_4) = 0
% 12.39/3.55 | (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))
% 12.39/3.55 | (35) apart_point_and_line(all_0_4_4, all_0_1_1) = all_0_0_0
% 12.39/3.55 | (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)))
% 12.39/3.55 | (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))
% 12.39/3.55 | (38) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 12.39/3.55 | (39) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 12.39/3.55 | (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))
% 12.39/3.55 | (41) apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 12.39/3.55 | (42) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 12.39/3.55 | (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)))
% 12.39/3.55 | (44) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 12.39/3.55 | (45) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 12.39/3.55 | (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))
% 12.39/3.55 | (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)
% 12.39/3.55 | (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))
% 12.39/3.56 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 12.39/3.56 | (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)))
% 12.39/3.56 | (51) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 12.39/3.56 | (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)))
% 12.39/3.56 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 12.39/3.56 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 12.39/3.56 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 12.39/3.56 |
% 12.39/3.56 | Instantiating formula (50) with all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_3_3) = all_0_1_1, yields:
% 12.39/3.56 | (56) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 12.39/3.56 |
% 12.39/3.56 | Instantiating formula (2) with all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_3_3) = all_0_1_1, yields:
% 12.39/3.56 | (57) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 12.39/3.56 |
% 12.39/3.56 | 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:
% 12.39/3.56 | (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))
% 12.39/3.56 |
% 12.39/3.56 | 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:
% 12.39/3.56 | (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))
% 12.39/3.56 |
% 12.39/3.56 | Instantiating formula (15) with all_0_0_0, all_0_0_0, all_0_1_1, all_0_1_1, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_0_0_0, yields:
% 12.39/3.56 | (60) all_0_0_0 = 0 | ? [v0] : ((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_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 12.39/3.56 |
% 12.39/3.56 | Instantiating formula (10) with all_0_0_0, all_0_0_0, all_0_1_1, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_0_0_0, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 12.39/3.56 | (61) all_0_0_0 = 0 | ? [v0] : ((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_1_1) = v0))
% 12.39/3.56 |
% 12.39/3.56 | 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:
% 12.39/3.56 | (62) ? [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)
% 12.39/3.56 |
% 12.39/3.56 | 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:
% 12.39/3.56 | (63) ? [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)
% 12.39/3.56 |
% 12.39/3.56 | Instantiating (63) with all_20_0_24, all_20_1_25 yields:
% 12.39/3.56 | (64) ~ (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
% 12.39/3.56 |
% 12.39/3.56 | Applying alpha-rule on (64) yields:
% 12.39/3.56 | (65) ~ (all_20_0_24 = 0)
% 12.39/3.56 | (66) line_connecting(all_0_5_5, all_0_4_4) = all_20_1_25
% 12.39/3.56 | (67) apart_point_and_line(all_0_5_5, all_20_1_25) = all_20_0_24
% 12.39/3.56 |
% 12.39/3.56 | Instantiating (62) with all_22_0_26, all_22_1_27 yields:
% 12.39/3.56 | (68) ~ (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
% 12.39/3.56 |
% 12.39/3.56 | Applying alpha-rule on (68) yields:
% 12.39/3.56 | (69) ~ (all_22_0_26 = 0)
% 12.39/3.56 | (70) line_connecting(all_0_5_5, all_0_4_4) = all_22_1_27
% 12.39/3.56 | (71) apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26
% 12.39/3.56 |
% 12.39/3.56 | Instantiating (59) with all_24_0_28 yields:
% 12.39/3.56 | (72) ( ~ (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)
% 12.39/3.56 |
% 12.39/3.56 | Instantiating (58) with all_25_0_29 yields:
% 12.39/3.56 | (73) ( ~ (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)
% 12.39/3.57 |
% 12.39/3.57 | Instantiating (57) with all_26_0_30 yields:
% 12.39/3.57 | (74) ( ~ (all_26_0_30 = 0) & apart_point_and_line(all_0_5_5, all_0_1_1) = all_26_0_30) | ( ~ (all_26_0_30 = 0) & distinct_points(all_0_5_5, all_0_3_3) = all_26_0_30)
% 12.39/3.57 |
% 12.39/3.57 | Instantiating (56) with all_27_0_31 yields:
% 12.39/3.57 | (75) ( ~ (all_27_0_31 = 0) & apart_point_and_line(all_0_3_3, all_0_1_1) = all_27_0_31) | ( ~ (all_27_0_31 = 0) & distinct_points(all_0_5_5, all_0_3_3) = all_27_0_31)
% 12.39/3.57 |
% 12.39/3.57 +-Applying beta-rule and splitting (72), into two cases.
% 12.39/3.57 |-Branch one:
% 12.39/3.57 | (76) ~ (all_24_0_28 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_24_0_28
% 12.39/3.57 |
% 12.39/3.57 | Applying alpha-rule on (76) yields:
% 12.39/3.57 | (77) ~ (all_24_0_28 = 0)
% 12.39/3.57 | (78) apart_point_and_line(all_0_5_5, all_0_2_2) = all_24_0_28
% 12.39/3.57 |
% 12.39/3.57 +-Applying beta-rule and splitting (73), into two cases.
% 12.39/3.57 |-Branch one:
% 12.39/3.57 | (79) ~ (all_25_0_29 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_25_0_29
% 12.39/3.57 |
% 12.39/3.57 | Applying alpha-rule on (79) yields:
% 12.39/3.57 | (80) ~ (all_25_0_29 = 0)
% 12.39/3.57 | (81) apart_point_and_line(all_0_4_4, all_0_2_2) = all_25_0_29
% 12.39/3.57 |
% 12.39/3.57 +-Applying beta-rule and splitting (60), into two cases.
% 12.39/3.57 |-Branch one:
% 12.39/3.57 | (82) all_0_0_0 = 0
% 12.39/3.57 |
% 12.39/3.57 | Equations (82) can reduce 28 to:
% 12.39/3.57 | (83) $false
% 12.39/3.57 |
% 12.39/3.57 |-The branch is then unsatisfiable
% 12.39/3.57 |-Branch two:
% 12.39/3.57 | (28) ~ (all_0_0_0 = 0)
% 12.39/3.57 | (85) ? [v0] : ((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_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 12.39/3.57 |
% 12.39/3.57 +-Applying beta-rule and splitting (61), into two cases.
% 12.39/3.57 |-Branch one:
% 12.39/3.57 | (82) all_0_0_0 = 0
% 12.39/3.57 |
% 12.39/3.57 | Equations (82) can reduce 28 to:
% 12.39/3.57 | (83) $false
% 12.39/3.57 |
% 12.39/3.57 |-The branch is then unsatisfiable
% 12.39/3.57 |-Branch two:
% 12.39/3.57 | (28) ~ (all_0_0_0 = 0)
% 12.39/3.57 | (89) ? [v0] : ((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_1_1) = v0))
% 12.39/3.57 |
% 12.39/3.57 | Instantiating formula (21) 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:
% 12.39/3.57 | (90) all_22_1_27 = all_0_2_2
% 12.39/3.57 |
% 12.39/3.57 | Instantiating formula (21) 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:
% 12.39/3.57 | (91) all_22_1_27 = all_20_1_25
% 12.39/3.57 |
% 12.39/3.57 | Combining equations (90,91) yields a new equation:
% 12.39/3.57 | (92) all_20_1_25 = all_0_2_2
% 12.39/3.57 |
% 12.39/3.57 | Combining equations (92,91) yields a new equation:
% 12.39/3.57 | (90) all_22_1_27 = all_0_2_2
% 12.39/3.57 |
% 12.39/3.57 | From (90) and (71) follows:
% 12.39/3.57 | (94) apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26
% 12.39/3.57 |
% 12.39/3.57 | From (92) and (67) follows:
% 12.39/3.57 | (95) apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24
% 12.39/3.57 |
% 12.39/3.57 | Instantiating formula (22) 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:
% 12.39/3.57 | (96) all_25_0_29 = all_22_0_26
% 12.39/3.57 |
% 12.39/3.57 | Instantiating formula (22) 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:
% 12.39/3.57 | (97) all_24_0_28 = all_20_0_24
% 12.39/3.57 |
% 12.39/3.57 | Equations (96) can reduce 80 to:
% 12.39/3.57 | (69) ~ (all_22_0_26 = 0)
% 12.39/3.57 |
% 12.39/3.57 | Equations (97) can reduce 77 to:
% 12.39/3.57 | (65) ~ (all_20_0_24 = 0)
% 12.39/3.57 |
% 12.39/3.57 | From (96) and (81) follows:
% 12.39/3.57 | (94) apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26
% 12.39/3.57 |
% 12.39/3.57 | From (97) and (78) follows:
% 12.39/3.57 | (95) apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24
% 12.39/3.57 |
% 12.39/3.57 | Instantiating formula (10) with all_0_0_0, all_22_0_26, 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_1_1) = all_0_0_0, 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:
% 12.39/3.57 | (102) all_22_0_26 = 0 | all_0_0_0 = 0 | ? [v0] : ((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) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 12.39/3.57 |
% 12.39/3.57 | Instantiating formula (15) with all_22_0_26, all_0_0_0, all_0_2_2, all_0_1_1, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, 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:
% 12.39/3.57 | (103) all_22_0_26 = 0 | all_0_0_0 = 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_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 12.39/3.57 |
% 12.39/3.57 | Instantiating formula (15) with all_0_0_0, 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_1_1) = all_0_0_0, apart_point_and_line(all_0_4_4, all_0_2_2) = all_22_0_26, yields:
% 12.39/3.57 | (104) all_22_0_26 = 0 | all_0_0_0 = 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_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 12.39/3.58 |
% 12.39/3.58 | 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:
% 12.39/3.58 | (105) 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))
% 12.39/3.58 |
% 12.39/3.58 | Instantiating formula (15) 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:
% 12.39/3.58 | (106) 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))
% 12.39/3.58 |
% 12.39/3.58 | Instantiating formula (47) with all_20_0_24, all_0_5_5, all_0_2_2, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = 0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 12.39/3.58 | (107) all_20_0_24 = 0 | distinct_points(all_0_3_3, all_0_5_5) = 0
% 12.39/3.58 |
% 12.39/3.58 | Instantiating formula (15) with all_20_0_24, all_0_0_0, all_0_2_2, all_0_1_1, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, 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:
% 12.39/3.58 | (108) all_20_0_24 = 0 | all_0_0_0 = 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_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_5_5) = v0))
% 12.39/3.58 |
% 12.39/3.58 | Instantiating formula (15) with all_0_0_0, 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_1_1) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 12.39/3.58 | (109) all_20_0_24 = 0 | all_0_0_0 = 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_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_4_4) = v0))
% 12.39/3.58 |
% 12.39/3.58 | Instantiating formula (36) with all_20_0_24, all_0_0_0, 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_1_1) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 12.39/3.58 | (110) all_20_0_24 = 0 | all_0_0_0 = 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_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_5_5) = v0))
% 12.39/3.58 |
% 12.39/3.58 | Instantiating formula (36) with all_0_0_0, all_20_0_24, all_0_2_2, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, 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:
% 12.39/3.58 | (111) all_20_0_24 = 0 | all_0_0_0 = 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_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_4_4) = v0))
% 12.39/3.58 |
% 12.39/3.58 | Instantiating formula (15) 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:
% 12.39/3.58 | (112) 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))
% 12.39/3.58 |
% 12.39/3.58 | Instantiating formula (15) 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:
% 12.39/3.58 | (113) 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))
% 12.39/3.58 |
% 12.39/3.58 | 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:
% 12.39/3.58 | (114) 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))
% 12.39/3.58 |
% 12.39/3.58 | Instantiating formula (15) 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:
% 12.39/3.58 | (115) 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))
% 12.39/3.58 |
% 12.39/3.58 +-Applying beta-rule and splitting (74), into two cases.
% 12.39/3.58 |-Branch one:
% 12.39/3.58 | (116) ~ (all_26_0_30 = 0) & apart_point_and_line(all_0_5_5, all_0_1_1) = all_26_0_30
% 12.39/3.58 |
% 12.39/3.58 | Applying alpha-rule on (116) yields:
% 12.39/3.58 | (117) ~ (all_26_0_30 = 0)
% 12.39/3.58 | (118) apart_point_and_line(all_0_5_5, all_0_1_1) = all_26_0_30
% 12.39/3.58 |
% 12.39/3.58 +-Applying beta-rule and splitting (107), into two cases.
% 12.39/3.58 |-Branch one:
% 12.39/3.58 | (119) distinct_points(all_0_3_3, all_0_5_5) = 0
% 12.39/3.58 |
% 12.39/3.58 +-Applying beta-rule and splitting (105), into two cases.
% 12.39/3.58 |-Branch one:
% 12.39/3.58 | (120) all_22_0_26 = 0
% 12.39/3.58 |
% 12.39/3.58 | Equations (120) can reduce 69 to:
% 12.39/3.58 | (83) $false
% 12.39/3.58 |
% 12.39/3.58 |-The branch is then unsatisfiable
% 12.39/3.58 |-Branch two:
% 12.39/3.58 | (69) ~ (all_22_0_26 = 0)
% 12.39/3.58 | (123) ? [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))
% 12.39/3.59 |
% 12.39/3.59 +-Applying beta-rule and splitting (106), into two cases.
% 12.39/3.59 |-Branch one:
% 12.39/3.59 | (120) all_22_0_26 = 0
% 12.39/3.59 |
% 12.39/3.59 | Equations (120) can reduce 69 to:
% 12.39/3.59 | (83) $false
% 12.39/3.59 |
% 12.39/3.59 |-The branch is then unsatisfiable
% 12.39/3.59 |-Branch two:
% 12.39/3.59 | (69) ~ (all_22_0_26 = 0)
% 12.39/3.59 | (127) ? [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))
% 12.39/3.59 |
% 12.39/3.59 +-Applying beta-rule and splitting (104), into two cases.
% 12.39/3.59 |-Branch one:
% 12.39/3.59 | (120) all_22_0_26 = 0
% 12.39/3.59 |
% 12.39/3.59 | Equations (120) can reduce 69 to:
% 12.39/3.59 | (83) $false
% 12.39/3.59 |
% 12.39/3.59 |-The branch is then unsatisfiable
% 12.39/3.59 |-Branch two:
% 12.39/3.59 | (69) ~ (all_22_0_26 = 0)
% 12.39/3.59 | (131) all_0_0_0 = 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_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 12.39/3.59 |
% 12.39/3.59 +-Applying beta-rule and splitting (110), into two cases.
% 12.39/3.59 |-Branch one:
% 12.39/3.59 | (132) all_20_0_24 = 0
% 12.39/3.59 |
% 12.39/3.59 | Equations (132) can reduce 65 to:
% 12.39/3.59 | (83) $false
% 12.39/3.59 |
% 12.39/3.59 |-The branch is then unsatisfiable
% 12.39/3.59 |-Branch two:
% 12.39/3.59 | (65) ~ (all_20_0_24 = 0)
% 12.39/3.59 | (135) all_0_0_0 = 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_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_5_5) = v0))
% 12.39/3.59 |
% 12.39/3.59 +-Applying beta-rule and splitting (108), into two cases.
% 12.39/3.59 |-Branch one:
% 12.39/3.59 | (132) all_20_0_24 = 0
% 12.39/3.59 |
% 12.39/3.59 | Equations (132) can reduce 65 to:
% 12.39/3.59 | (83) $false
% 12.39/3.59 |
% 12.39/3.59 |-The branch is then unsatisfiable
% 12.39/3.59 |-Branch two:
% 12.39/3.59 | (65) ~ (all_20_0_24 = 0)
% 12.39/3.59 | (139) all_0_0_0 = 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_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_5_5) = v0))
% 12.39/3.59 |
% 12.39/3.59 +-Applying beta-rule and splitting (109), into two cases.
% 12.39/3.59 |-Branch one:
% 12.39/3.59 | (132) all_20_0_24 = 0
% 12.39/3.59 |
% 12.39/3.59 | Equations (132) can reduce 65 to:
% 12.39/3.59 | (83) $false
% 12.39/3.59 |
% 12.39/3.59 |-The branch is then unsatisfiable
% 12.39/3.59 |-Branch two:
% 12.39/3.59 | (65) ~ (all_20_0_24 = 0)
% 12.39/3.59 | (143) all_0_0_0 = 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_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_4_4) = v0))
% 12.39/3.59 |
% 12.39/3.59 +-Applying beta-rule and splitting (111), into two cases.
% 12.39/3.59 |-Branch one:
% 12.39/3.59 | (132) all_20_0_24 = 0
% 12.39/3.59 |
% 12.39/3.59 | Equations (132) can reduce 65 to:
% 12.39/3.59 | (83) $false
% 12.39/3.59 |
% 12.39/3.59 |-The branch is then unsatisfiable
% 12.39/3.59 |-Branch two:
% 12.39/3.59 | (65) ~ (all_20_0_24 = 0)
% 12.39/3.59 | (147) all_0_0_0 = 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_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_4_4) = v0))
% 12.39/3.59 |
% 12.39/3.59 +-Applying beta-rule and splitting (131), into two cases.
% 12.39/3.59 |-Branch one:
% 12.39/3.59 | (82) all_0_0_0 = 0
% 12.39/3.59 |
% 12.39/3.59 | Equations (82) can reduce 28 to:
% 12.39/3.59 | (83) $false
% 12.39/3.59 |
% 12.39/3.59 |-The branch is then unsatisfiable
% 12.39/3.59 |-Branch two:
% 12.39/3.59 | (28) ~ (all_0_0_0 = 0)
% 12.39/3.59 | (151) ? [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) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 12.39/3.59 |
% 12.39/3.59 +-Applying beta-rule and splitting (114), into two cases.
% 12.39/3.59 |-Branch one:
% 12.39/3.59 | (132) all_20_0_24 = 0
% 12.39/3.59 |
% 12.39/3.59 | Equations (132) can reduce 65 to:
% 12.39/3.59 | (83) $false
% 12.39/3.59 |
% 12.39/3.59 |-The branch is then unsatisfiable
% 12.39/3.59 |-Branch two:
% 12.39/3.59 | (65) ~ (all_20_0_24 = 0)
% 12.39/3.59 | (155) ? [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))
% 12.39/3.59 |
% 12.39/3.59 +-Applying beta-rule and splitting (115), into two cases.
% 12.39/3.59 |-Branch one:
% 12.39/3.59 | (132) all_20_0_24 = 0
% 12.39/3.59 |
% 12.39/3.59 | Equations (132) can reduce 65 to:
% 12.39/3.59 | (83) $false
% 12.39/3.59 |
% 12.39/3.59 |-The branch is then unsatisfiable
% 12.39/3.59 |-Branch two:
% 12.39/3.59 | (65) ~ (all_20_0_24 = 0)
% 12.39/3.59 | (159) ? [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))
% 12.39/3.59 |
% 12.39/3.59 +-Applying beta-rule and splitting (112), into two cases.
% 12.39/3.59 |-Branch one:
% 12.39/3.59 | (120) all_22_0_26 = 0
% 12.39/3.59 |
% 12.39/3.59 | Equations (120) can reduce 69 to:
% 12.39/3.59 | (83) $false
% 12.39/3.59 |
% 12.39/3.59 |-The branch is then unsatisfiable
% 12.39/3.59 |-Branch two:
% 12.39/3.59 | (69) ~ (all_22_0_26 = 0)
% 12.39/3.59 | (163) 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))
% 12.39/3.59 |
% 12.39/3.59 +-Applying beta-rule and splitting (113), into two cases.
% 12.39/3.59 |-Branch one:
% 12.39/3.59 | (120) all_22_0_26 = 0
% 12.39/3.59 |
% 12.39/3.59 | Equations (120) can reduce 69 to:
% 12.39/3.59 | (83) $false
% 12.39/3.59 |
% 12.39/3.59 |-The branch is then unsatisfiable
% 12.39/3.59 |-Branch two:
% 12.39/3.59 | (69) ~ (all_22_0_26 = 0)
% 12.39/3.59 | (167) 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))
% 12.39/3.59 |
% 12.39/3.59 +-Applying beta-rule and splitting (139), into two cases.
% 12.39/3.59 |-Branch one:
% 12.39/3.59 | (82) all_0_0_0 = 0
% 12.39/3.59 |
% 12.39/3.59 | Equations (82) can reduce 28 to:
% 12.39/3.59 | (83) $false
% 12.39/3.59 |
% 12.39/3.59 |-The branch is then unsatisfiable
% 12.39/3.59 |-Branch two:
% 12.39/3.59 | (28) ~ (all_0_0_0 = 0)
% 12.39/3.59 | (171) ? [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_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_5_5) = v0))
% 12.39/3.59 |
% 12.39/3.59 +-Applying beta-rule and splitting (147), into two cases.
% 12.39/3.59 |-Branch one:
% 12.39/3.59 | (82) all_0_0_0 = 0
% 12.39/3.60 |
% 12.39/3.60 | Equations (82) can reduce 28 to:
% 12.39/3.60 | (83) $false
% 12.39/3.60 |
% 12.39/3.60 |-The branch is then unsatisfiable
% 12.39/3.60 |-Branch two:
% 12.39/3.60 | (28) ~ (all_0_0_0 = 0)
% 12.39/3.60 | (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_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_4_4) = v0))
% 12.39/3.60 |
% 12.39/3.60 +-Applying beta-rule and splitting (102), into two cases.
% 12.39/3.60 |-Branch one:
% 12.39/3.60 | (120) all_22_0_26 = 0
% 12.39/3.60 |
% 12.39/3.60 | Equations (120) can reduce 69 to:
% 12.39/3.60 | (83) $false
% 12.39/3.60 |
% 12.39/3.60 |-The branch is then unsatisfiable
% 12.39/3.60 |-Branch two:
% 12.39/3.60 | (69) ~ (all_22_0_26 = 0)
% 12.39/3.60 | (179) all_0_0_0 = 0 | ? [v0] : ((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) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 12.39/3.60 |
% 12.39/3.60 +-Applying beta-rule and splitting (103), into two cases.
% 12.39/3.60 |-Branch one:
% 12.39/3.60 | (120) all_22_0_26 = 0
% 12.39/3.60 |
% 12.39/3.60 | Equations (120) can reduce 69 to:
% 12.39/3.60 | (83) $false
% 12.39/3.60 |
% 12.39/3.60 |-The branch is then unsatisfiable
% 12.39/3.60 |-Branch two:
% 12.39/3.60 | (69) ~ (all_22_0_26 = 0)
% 12.39/3.60 | (183) all_0_0_0 = 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_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 12.39/3.60 |
% 12.39/3.60 +-Applying beta-rule and splitting (135), into two cases.
% 12.39/3.60 |-Branch one:
% 12.39/3.60 | (82) all_0_0_0 = 0
% 12.39/3.60 |
% 12.39/3.60 | Equations (82) can reduce 28 to:
% 12.39/3.60 | (83) $false
% 12.39/3.60 |
% 12.39/3.60 |-The branch is then unsatisfiable
% 12.39/3.60 |-Branch two:
% 12.39/3.60 | (28) ~ (all_0_0_0 = 0)
% 12.39/3.60 | (187) ? [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_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_5_5) = v0))
% 12.39/3.60 |
% 12.39/3.60 +-Applying beta-rule and splitting (143), into two cases.
% 12.39/3.60 |-Branch one:
% 12.39/3.60 | (82) all_0_0_0 = 0
% 12.39/3.60 |
% 12.39/3.60 | Equations (82) can reduce 28 to:
% 12.39/3.60 | (83) $false
% 12.39/3.60 |
% 12.39/3.60 |-The branch is then unsatisfiable
% 12.39/3.60 |-Branch two:
% 12.39/3.60 | (28) ~ (all_0_0_0 = 0)
% 12.39/3.60 | (191) ? [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_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_4_4) = v0))
% 12.39/3.60 |
% 12.39/3.60 | Instantiating (191) with all_146_0_113 yields:
% 12.39/3.60 | (192) (all_146_0_113 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (all_146_0_113 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (all_146_0_113 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = all_146_0_113) | ( ~ (all_146_0_113 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_146_0_113)
% 12.39/3.60 |
% 12.39/3.60 +-Applying beta-rule and splitting (163), into two cases.
% 12.39/3.60 |-Branch one:
% 12.39/3.60 | (132) all_20_0_24 = 0
% 12.39/3.60 |
% 12.39/3.60 | Equations (132) can reduce 65 to:
% 12.39/3.60 | (83) $false
% 12.39/3.60 |
% 12.39/3.60 |-The branch is then unsatisfiable
% 12.39/3.60 |-Branch two:
% 12.39/3.60 | (65) ~ (all_20_0_24 = 0)
% 12.39/3.60 | (196) ? [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))
% 12.39/3.60 |
% 12.39/3.60 +-Applying beta-rule and splitting (179), into two cases.
% 12.39/3.60 |-Branch one:
% 12.39/3.60 | (82) all_0_0_0 = 0
% 12.39/3.60 |
% 12.39/3.60 | Equations (82) can reduce 28 to:
% 12.39/3.60 | (83) $false
% 12.39/3.60 |
% 12.39/3.60 |-The branch is then unsatisfiable
% 12.39/3.60 |-Branch two:
% 12.39/3.60 | (28) ~ (all_0_0_0 = 0)
% 12.39/3.60 | (200) ? [v0] : ((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) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 12.39/3.60 |
% 12.39/3.60 | Instantiating (200) with all_154_0_115 yields:
% 12.39/3.60 | (201) (all_154_0_115 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (all_154_0_115 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (all_154_0_115 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = all_154_0_115)
% 12.39/3.60 |
% 12.39/3.60 +-Applying beta-rule and splitting (192), into two cases.
% 12.39/3.60 |-Branch one:
% 12.39/3.60 | (202) (all_146_0_113 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (all_146_0_113 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (all_146_0_113 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = all_146_0_113)
% 12.39/3.60 |
% 12.39/3.60 +-Applying beta-rule and splitting (202), into two cases.
% 12.39/3.60 |-Branch one:
% 12.39/3.60 | (203) (all_146_0_113 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (all_146_0_113 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0)
% 12.39/3.60 |
% 12.39/3.60 +-Applying beta-rule and splitting (203), into two cases.
% 12.39/3.60 |-Branch one:
% 12.39/3.60 | (204) all_146_0_113 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 12.39/3.60 |
% 12.39/3.60 | Applying alpha-rule on (204) yields:
% 12.39/3.60 | (205) all_146_0_113 = 0
% 12.39/3.60 | (206) apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 12.39/3.60 |
% 12.39/3.60 | Instantiating formula (22) 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:
% 12.39/3.60 | (120) all_22_0_26 = 0
% 12.39/3.60 |
% 12.39/3.60 | Equations (120) can reduce 69 to:
% 12.39/3.60 | (83) $false
% 12.39/3.60 |
% 12.39/3.60 |-The branch is then unsatisfiable
% 12.39/3.60 |-Branch two:
% 12.39/3.60 | (209) all_146_0_113 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 12.39/3.60 |
% 12.39/3.60 | Applying alpha-rule on (209) yields:
% 12.39/3.60 | (205) all_146_0_113 = 0
% 12.39/3.60 | (211) apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 12.39/3.60 |
% 12.39/3.60 | Instantiating formula (22) with all_0_5_5, all_0_1_1, 0, all_26_0_30 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_26_0_30, apart_point_and_line(all_0_5_5, all_0_1_1) = 0, yields:
% 12.39/3.60 | (212) all_26_0_30 = 0
% 12.39/3.60 |
% 12.39/3.60 | Equations (212) can reduce 117 to:
% 12.39/3.60 | (83) $false
% 12.39/3.60 |
% 12.39/3.60 |-The branch is then unsatisfiable
% 12.39/3.60 |-Branch two:
% 12.39/3.60 | (214) ~ (all_146_0_113 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = all_146_0_113
% 12.39/3.60 |
% 12.39/3.60 | Applying alpha-rule on (214) yields:
% 12.39/3.60 | (215) ~ (all_146_0_113 = 0)
% 12.39/3.60 | (216) distinct_lines(all_0_2_2, all_0_1_1) = all_146_0_113
% 12.39/3.60 |
% 12.39/3.60 +-Applying beta-rule and splitting (201), into two cases.
% 12.39/3.60 |-Branch one:
% 12.39/3.60 | (217) (all_154_0_115 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (all_154_0_115 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0)
% 12.39/3.60 |
% 12.39/3.60 +-Applying beta-rule and splitting (217), into two cases.
% 12.39/3.60 |-Branch one:
% 12.39/3.60 | (218) all_154_0_115 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 12.39/3.60 |
% 12.39/3.60 | Applying alpha-rule on (218) yields:
% 12.39/3.60 | (219) all_154_0_115 = 0
% 12.39/3.60 | (211) apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 12.39/3.60 |
% 12.39/3.60 | Instantiating formula (22) with all_0_5_5, all_0_1_1, 0, all_26_0_30 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_26_0_30, apart_point_and_line(all_0_5_5, all_0_1_1) = 0, yields:
% 12.39/3.60 | (212) all_26_0_30 = 0
% 12.39/3.60 |
% 12.39/3.60 | Equations (212) can reduce 117 to:
% 12.39/3.60 | (83) $false
% 12.39/3.60 |
% 12.39/3.60 |-The branch is then unsatisfiable
% 12.39/3.60 |-Branch two:
% 12.39/3.60 | (223) all_154_0_115 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 12.39/3.60 |
% 12.39/3.60 | Applying alpha-rule on (223) yields:
% 12.39/3.60 | (219) all_154_0_115 = 0
% 12.39/3.60 | (225) apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 12.39/3.60 |
% 12.39/3.60 | Instantiating formula (22) 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:
% 12.39/3.61 | (132) all_20_0_24 = 0
% 12.39/3.61 |
% 12.39/3.61 | Equations (132) can reduce 65 to:
% 12.39/3.61 | (83) $false
% 12.39/3.61 |
% 12.39/3.61 |-The branch is then unsatisfiable
% 12.39/3.61 |-Branch two:
% 12.39/3.61 | (228) ~ (all_154_0_115 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = all_154_0_115
% 12.39/3.61 |
% 12.39/3.61 | Applying alpha-rule on (228) yields:
% 12.39/3.61 | (229) ~ (all_154_0_115 = 0)
% 12.39/3.61 | (230) distinct_lines(all_0_2_2, all_0_1_1) = all_154_0_115
% 12.39/3.61 |
% 12.39/3.61 | Instantiating formula (55) with all_0_2_2, all_0_1_1, all_146_0_113, all_154_0_115 and discharging atoms distinct_lines(all_0_2_2, all_0_1_1) = all_154_0_115, distinct_lines(all_0_2_2, all_0_1_1) = all_146_0_113, yields:
% 12.39/3.61 | (231) all_154_0_115 = all_146_0_113
% 12.39/3.61 |
% 12.39/3.61 | Equations (231) can reduce 229 to:
% 12.39/3.61 | (215) ~ (all_146_0_113 = 0)
% 12.39/3.61 |
% 12.39/3.61 | From (231) and (230) follows:
% 12.39/3.61 | (216) distinct_lines(all_0_2_2, all_0_1_1) = all_146_0_113
% 12.39/3.61 |
% 12.39/3.61 | Instantiating formula (18) with all_146_0_113, 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_2_2) = 0, distinct_lines(all_0_2_2, all_0_1_1) = all_146_0_113, yields:
% 12.39/3.61 | (234) all_146_0_113 = 0 | apart_point_and_line(all_0_3_3, all_0_1_1) = 0
% 12.39/3.61 |
% 12.39/3.61 +-Applying beta-rule and splitting (234), into two cases.
% 12.39/3.61 |-Branch one:
% 12.39/3.61 | (235) apart_point_and_line(all_0_3_3, all_0_1_1) = 0
% 12.39/3.61 |
% 12.39/3.61 +-Applying beta-rule and splitting (75), into two cases.
% 12.39/3.61 |-Branch one:
% 12.39/3.61 | (236) ~ (all_27_0_31 = 0) & apart_point_and_line(all_0_3_3, all_0_1_1) = all_27_0_31
% 12.39/3.61 |
% 12.39/3.61 | Applying alpha-rule on (236) yields:
% 12.39/3.61 | (237) ~ (all_27_0_31 = 0)
% 12.39/3.61 | (238) apart_point_and_line(all_0_3_3, all_0_1_1) = all_27_0_31
% 12.39/3.61 |
% 12.39/3.61 | Instantiating formula (22) with all_0_3_3, all_0_1_1, 0, all_27_0_31 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_27_0_31, apart_point_and_line(all_0_3_3, all_0_1_1) = 0, yields:
% 12.39/3.61 | (239) all_27_0_31 = 0
% 12.39/3.61 |
% 12.39/3.61 | Equations (239) can reduce 237 to:
% 12.39/3.61 | (83) $false
% 12.39/3.61 |
% 12.39/3.61 |-The branch is then unsatisfiable
% 12.39/3.61 |-Branch two:
% 12.39/3.61 | (241) ~ (all_27_0_31 = 0) & distinct_points(all_0_5_5, all_0_3_3) = all_27_0_31
% 12.39/3.61 |
% 12.39/3.61 | Applying alpha-rule on (241) yields:
% 12.39/3.61 | (237) ~ (all_27_0_31 = 0)
% 12.39/3.61 | (243) distinct_points(all_0_5_5, all_0_3_3) = all_27_0_31
% 12.39/3.61 |
% 12.39/3.61 | Instantiating formula (17) with all_27_0_31, all_0_3_3, all_0_5_5, all_0_3_3 and discharging atoms distinct_points(all_0_3_3, all_0_5_5) = 0, distinct_points(all_0_5_5, all_0_3_3) = all_27_0_31, yields:
% 12.39/3.61 | (244) all_27_0_31 = 0 | distinct_points(all_0_3_3, all_0_3_3) = 0
% 12.39/3.61 |
% 12.39/3.61 +-Applying beta-rule and splitting (244), into two cases.
% 12.39/3.61 |-Branch one:
% 12.39/3.61 | (245) distinct_points(all_0_3_3, all_0_3_3) = 0
% 12.39/3.61 |
% 12.39/3.61 | Instantiating formula (3) with all_0_3_3 and discharging atoms distinct_points(all_0_3_3, all_0_3_3) = 0, yields:
% 12.39/3.61 | (246) $false
% 12.39/3.61 |
% 12.39/3.61 |-The branch is then unsatisfiable
% 12.39/3.61 |-Branch two:
% 12.39/3.61 | (247) ~ (distinct_points(all_0_3_3, all_0_3_3) = 0)
% 12.39/3.61 | (239) all_27_0_31 = 0
% 12.39/3.61 |
% 12.39/3.61 | Equations (239) can reduce 237 to:
% 12.39/3.61 | (83) $false
% 12.39/3.61 |
% 12.39/3.61 |-The branch is then unsatisfiable
% 12.39/3.61 |-Branch two:
% 12.39/3.61 | (250) ~ (apart_point_and_line(all_0_3_3, all_0_1_1) = 0)
% 12.39/3.61 | (205) all_146_0_113 = 0
% 12.39/3.61 |
% 12.39/3.61 | Equations (205) can reduce 215 to:
% 12.39/3.61 | (83) $false
% 12.39/3.61 |
% 12.39/3.61 |-The branch is then unsatisfiable
% 12.39/3.61 |-Branch two:
% 12.39/3.61 | (253) ~ (all_146_0_113 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_146_0_113
% 12.39/3.61 |
% 12.39/3.61 | Applying alpha-rule on (253) yields:
% 12.39/3.61 | (215) ~ (all_146_0_113 = 0)
% 12.39/3.61 | (255) distinct_points(all_0_5_5, all_0_4_4) = all_146_0_113
% 12.39/3.61 |
% 12.39/3.61 | Instantiating formula (11) with all_0_5_5, all_0_4_4, all_146_0_113, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_146_0_113, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 12.39/3.61 | (205) all_146_0_113 = 0
% 12.39/3.61 |
% 12.39/3.61 | Equations (205) can reduce 215 to:
% 12.39/3.61 | (83) $false
% 12.39/3.61 |
% 12.39/3.61 |-The branch is then unsatisfiable
% 12.39/3.61 |-Branch two:
% 12.39/3.61 | (258) ~ (distinct_points(all_0_3_3, all_0_5_5) = 0)
% 12.39/3.61 | (132) all_20_0_24 = 0
% 12.39/3.61 |
% 12.39/3.61 | Equations (132) can reduce 65 to:
% 12.39/3.61 | (83) $false
% 12.39/3.61 |
% 12.39/3.61 |-The branch is then unsatisfiable
% 12.39/3.61 |-Branch two:
% 12.39/3.61 | (261) ~ (all_26_0_30 = 0) & distinct_points(all_0_5_5, all_0_3_3) = all_26_0_30
% 12.39/3.61 |
% 12.39/3.61 | Applying alpha-rule on (261) yields:
% 12.39/3.61 | (117) ~ (all_26_0_30 = 0)
% 12.39/3.61 | (263) distinct_points(all_0_5_5, all_0_3_3) = all_26_0_30
% 12.39/3.61 |
% 12.39/3.61 +-Applying beta-rule and splitting (107), into two cases.
% 12.39/3.61 |-Branch one:
% 12.39/3.61 | (119) distinct_points(all_0_3_3, all_0_5_5) = 0
% 12.39/3.61 |
% 12.39/3.61 | Instantiating formula (17) with all_26_0_30, all_0_3_3, all_0_5_5, all_0_3_3 and discharging atoms distinct_points(all_0_3_3, all_0_5_5) = 0, distinct_points(all_0_5_5, all_0_3_3) = all_26_0_30, yields:
% 12.39/3.61 | (265) all_26_0_30 = 0 | distinct_points(all_0_3_3, all_0_3_3) = 0
% 12.39/3.61 |
% 12.39/3.61 +-Applying beta-rule and splitting (265), into two cases.
% 12.39/3.61 |-Branch one:
% 12.39/3.61 | (245) distinct_points(all_0_3_3, all_0_3_3) = 0
% 12.39/3.61 |
% 12.39/3.61 | Instantiating formula (3) with all_0_3_3 and discharging atoms distinct_points(all_0_3_3, all_0_3_3) = 0, yields:
% 12.39/3.62 | (246) $false
% 12.39/3.62 |
% 12.39/3.62 |-The branch is then unsatisfiable
% 12.39/3.62 |-Branch two:
% 12.39/3.62 | (247) ~ (distinct_points(all_0_3_3, all_0_3_3) = 0)
% 12.39/3.62 | (212) all_26_0_30 = 0
% 12.39/3.62 |
% 12.39/3.62 | Equations (212) can reduce 117 to:
% 12.39/3.62 | (83) $false
% 12.39/3.62 |
% 12.39/3.62 |-The branch is then unsatisfiable
% 12.39/3.62 |-Branch two:
% 12.39/3.62 | (258) ~ (distinct_points(all_0_3_3, all_0_5_5) = 0)
% 12.39/3.62 | (132) all_20_0_24 = 0
% 12.39/3.62 |
% 12.39/3.62 | Equations (132) can reduce 65 to:
% 12.39/3.62 | (83) $false
% 12.39/3.62 |
% 12.39/3.62 |-The branch is then unsatisfiable
% 12.39/3.62 |-Branch two:
% 12.39/3.62 | (274) ~ (all_25_0_29 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_25_0_29
% 12.39/3.62 |
% 12.39/3.62 | Applying alpha-rule on (274) yields:
% 12.39/3.62 | (80) ~ (all_25_0_29 = 0)
% 12.39/3.62 | (276) distinct_points(all_0_5_5, all_0_4_4) = all_25_0_29
% 12.39/3.62 |
% 12.39/3.62 | 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:
% 12.39/3.62 | (277) all_25_0_29 = 0
% 12.39/3.62 |
% 12.39/3.62 | Equations (277) can reduce 80 to:
% 12.39/3.62 | (83) $false
% 12.39/3.62 |
% 12.39/3.62 |-The branch is then unsatisfiable
% 12.39/3.62 |-Branch two:
% 12.39/3.62 | (279) ~ (all_24_0_28 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_24_0_28
% 12.39/3.62 |
% 12.39/3.62 | Applying alpha-rule on (279) yields:
% 12.39/3.62 | (77) ~ (all_24_0_28 = 0)
% 12.39/3.62 | (281) distinct_points(all_0_5_5, all_0_4_4) = all_24_0_28
% 12.39/3.62 |
% 12.39/3.62 | 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:
% 12.39/3.62 | (282) all_24_0_28 = 0
% 12.39/3.62 |
% 12.39/3.62 | Equations (282) can reduce 77 to:
% 12.39/3.62 | (83) $false
% 12.39/3.62 |
% 12.39/3.62 |-The branch is then unsatisfiable
% 12.39/3.62 % SZS output end Proof for theBenchmark
% 12.39/3.62
% 12.39/3.62 3036ms
%------------------------------------------------------------------------------