%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO210+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 : 0s
% DateTime : Sat Jul 16 02:52:47 EDT 2022
% Result : Theorem 14.87s 15.23s
% Output : Refutation 14.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO210+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sat Jun 18 04:48:47 EDT 2022
% 0.13/0.35 % CPUTime :
% 14.87/15.23 *** allocated 10000 integers for termspace/termends
% 14.87/15.23 *** allocated 10000 integers for clauses
% 14.87/15.23 *** allocated 10000 integers for justifications
% 14.87/15.23 Bliksem 1.12
% 14.87/15.23
% 14.87/15.23
% 14.87/15.23 Automatic Strategy Selection
% 14.87/15.23
% 14.87/15.23
% 14.87/15.23 Clauses:
% 14.87/15.23
% 14.87/15.23 { ! distinct_points( X, X ) }.
% 14.87/15.23 { ! distinct_lines( X, X ) }.
% 14.87/15.23 { ! convergent_lines( X, X ) }.
% 14.87/15.23 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 14.87/15.23 ) }.
% 14.87/15.23 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 14.87/15.23 }.
% 14.87/15.23 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 14.87/15.23 , Z ) }.
% 14.87/15.23 { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 14.87/15.23 , Y ) ), distinct_points( Z, X ) }.
% 14.87/15.23 { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 14.87/15.23 , Y ) ), distinct_points( Z, Y ) }.
% 14.87/15.23 { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, X ),
% 14.87/15.23 distinct_points( Z, intersection_point( X, Y ) ) }.
% 14.87/15.23 { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, Y ),
% 14.87/15.23 distinct_points( Z, intersection_point( X, Y ) ) }.
% 14.87/15.23 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 14.87/15.23 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 14.87/15.23 apart_point_and_line( Y, T ) }.
% 14.87/15.23 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 14.87/15.23 apart_point_and_line( Z, Y ) }.
% 14.87/15.23 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 14.87/15.23 apart_point_and_line( X, Z ) }.
% 14.87/15.23 { ! convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 14.87/15.23 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 14.87/15.23 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 14.87/15.23 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 14.87/15.23 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 14.87/15.23 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 14.87/15.23 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 14.87/15.23 , convergent_lines( Y, Z ) }.
% 14.87/15.23 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 14.87/15.23 , unorthogonal_lines( Y, Z ) }.
% 14.87/15.23 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 14.87/15.23 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 14.87/15.23 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 14.87/15.23 }.
% 14.87/15.23 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 14.87/15.23 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 14.87/15.23 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 14.87/15.23 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 14.87/15.23 unorthogonal_lines( Y, T ) }.
% 14.87/15.23 { ! apart_point_and_line( skol1, skol2 ) }.
% 14.87/15.23 { ! unorthogonal_lines( skol2, skol3 ) }.
% 14.87/15.23 { distinct_lines( skol2, orthogonal_through_point( skol3, skol1 ) ) }.
% 14.87/15.23
% 14.87/15.23 percentage equality = 0.000000, percentage horn = 0.620690
% 14.87/15.23 This a non-horn, non-equality problem
% 14.87/15.23
% 14.87/15.23
% 14.87/15.23 Options Used:
% 14.87/15.23
% 14.87/15.23 useres = 1
% 14.87/15.23 useparamod = 0
% 14.87/15.23 useeqrefl = 0
% 14.87/15.23 useeqfact = 0
% 14.87/15.23 usefactor = 1
% 14.87/15.23 usesimpsplitting = 0
% 14.87/15.23 usesimpdemod = 0
% 14.87/15.23 usesimpres = 3
% 14.87/15.23
% 14.87/15.23 resimpinuse = 1000
% 14.87/15.23 resimpclauses = 20000
% 14.87/15.23 substype = standard
% 14.87/15.23 backwardsubs = 1
% 14.87/15.23 selectoldest = 5
% 14.87/15.23
% 14.87/15.23 litorderings [0] = split
% 14.87/15.23 litorderings [1] = liftord
% 14.87/15.23
% 14.87/15.23 termordering = none
% 14.87/15.23
% 14.87/15.23 litapriori = 1
% 14.87/15.23 termapriori = 0
% 14.87/15.23 litaposteriori = 0
% 14.87/15.23 termaposteriori = 0
% 14.87/15.23 demodaposteriori = 0
% 14.87/15.23 ordereqreflfact = 0
% 14.87/15.23
% 14.87/15.23 litselect = none
% 14.87/15.23
% 14.87/15.23 maxweight = 15
% 14.87/15.23 maxdepth = 30000
% 14.87/15.23 maxlength = 115
% 14.87/15.23 maxnrvars = 195
% 14.87/15.23 excuselevel = 1
% 14.87/15.23 increasemaxweight = 1
% 14.87/15.23
% 14.87/15.23 maxselected = 10000000
% 14.87/15.23 maxnrclauses = 10000000
% 14.87/15.23
% 14.87/15.23 showgenerated = 0
% 14.87/15.23 showkept = 0
% 14.87/15.23 showselected = 0
% 14.87/15.23 showdeleted = 0
% 14.87/15.23 showresimp = 1
% 14.87/15.23 showstatus = 2000
% 14.87/15.23
% 14.87/15.23 prologoutput = 0
% 14.87/15.23 nrgoals = 5000000
% 14.87/15.23 totalproof = 1
% 14.87/15.23
% 14.87/15.23 Symbols occurring in the translation:
% 14.87/15.23
% 14.87/15.23 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 14.87/15.23 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 14.87/15.23 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 14.87/15.23 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 14.87/15.23 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 14.87/15.23 distinct_points [36, 2] (w:1, o:48, a:1, s:1, b:0),
% 14.87/15.23 distinct_lines [37, 2] (w:1, o:49, a:1, s:1, b:0),
% 14.87/15.23 convergent_lines [38, 2] (w:1, o:47, a:1, s:1, b:0),
% 14.87/15.23 line_connecting [41, 2] (w:1, o:50, a:1, s:1, b:0),
% 14.87/15.23 apart_point_and_line [42, 2] (w:1, o:51, a:1, s:1, b:0),
% 14.87/15.23 intersection_point [43, 2] (w:1, o:52, a:1, s:1, b:0),
% 14.87/15.23 parallel_through_point [46, 2] (w:1, o:54, a:1, s:1, b:0),
% 14.87/15.23 unorthogonal_lines [49, 2] (w:1, o:55, a:1, s:1, b:0),
% 14.87/15.23 orthogonal_through_point [52, 2] (w:1, o:53, a:1, s:1, b:0),
% 14.87/15.23 alpha1 [53, 2] (w:1, o:56, a:1, s:1, b:0),
% 14.87/15.23 skol1 [54, 0] (w:1, o:15, a:1, s:1, b:0),
% 14.87/15.23 skol2 [55, 0] (w:1, o:16, a:1, s:1, b:0),
% 14.87/15.23 skol3 [56, 0] (w:1, o:17, a:1, s:1, b:0).
% 14.87/15.23
% 14.87/15.23
% 14.87/15.23 Starting Search:
% 14.87/15.23
% 14.87/15.23 *** allocated 15000 integers for clauses
% 14.87/15.23 *** allocated 22500 integers for clauses
% 14.87/15.23 *** allocated 33750 integers for clauses
% 14.87/15.23 *** allocated 15000 integers for termspace/termends
% 14.87/15.23 *** allocated 50625 integers for clauses
% 14.87/15.23 Resimplifying inuse:
% 14.87/15.23 Done
% 14.87/15.23
% 14.87/15.23 *** allocated 22500 integers for termspace/termends
% 14.87/15.23 *** allocated 75937 integers for clauses
% 14.87/15.23 *** allocated 33750 integers for termspace/termends
% 14.87/15.23 *** allocated 113905 integers for clauses
% 14.87/15.23
% 14.87/15.23 Intermediate Status:
% 14.87/15.23 Generated: 14670
% 14.87/15.23 Kept: 2019
% 14.87/15.23 Inuse: 299
% 14.87/15.23 Deleted: 0
% 14.87/15.23 Deletedinuse: 0
% 14.87/15.23
% 14.87/15.23 Resimplifying inuse:
% 14.87/15.23 Done
% 14.87/15.23
% 14.87/15.23 *** allocated 50625 integers for termspace/termends
% 14.87/15.23 *** allocated 170857 integers for clauses
% 14.87/15.23 Resimplifying inuse:
% 14.87/15.23 Done
% 14.87/15.23
% 14.87/15.23 *** allocated 75937 integers for termspace/termends
% 14.87/15.23
% 14.87/15.23 Intermediate Status:
% 14.87/15.23 Generated: 64358
% 14.87/15.23 Kept: 4021
% 14.87/15.23 Inuse: 658
% 14.87/15.23 Deleted: 7
% 14.87/15.23 Deletedinuse: 0
% 14.87/15.23
% 14.87/15.23 Resimplifying inuse:
% 14.87/15.23 Done
% 14.87/15.23
% 14.87/15.23 *** allocated 256285 integers for clauses
% 14.87/15.23 Resimplifying inuse:
% 14.87/15.23 Done
% 14.87/15.23
% 14.87/15.23 *** allocated 113905 integers for termspace/termends
% 14.87/15.23
% 14.87/15.23 Intermediate Status:
% 14.87/15.23 Generated: 519621
% 14.87/15.23 Kept: 6120
% 14.87/15.23 Inuse: 1612
% 14.87/15.23 Deleted: 56
% 14.87/15.23 Deletedinuse: 11
% 14.87/15.23
% 14.87/15.23 *** allocated 384427 integers for clauses
% 14.87/15.23 Resimplifying inuse:
% 14.87/15.23 Done
% 14.87/15.23
% 14.87/15.23 Resimplifying inuse:
% 14.87/15.23 Done
% 14.87/15.23
% 14.87/15.23 *** allocated 170857 integers for termspace/termends
% 14.87/15.23
% 14.87/15.23 Intermediate Status:
% 14.87/15.23 Generated: 576584
% 14.87/15.23 Kept: 8172
% 14.87/15.23 Inuse: 1677
% 14.87/15.23 Deleted: 58
% 14.87/15.23 Deletedinuse: 11
% 14.87/15.23
% 14.87/15.23 Resimplifying inuse:
% 14.87/15.23 Done
% 14.87/15.23
% 14.87/15.23 *** allocated 576640 integers for clauses
% 14.87/15.23 Resimplifying inuse:
% 14.87/15.23 Done
% 14.87/15.23
% 14.87/15.23
% 14.87/15.23 Intermediate Status:
% 14.87/15.23 Generated: 1042389
% 14.87/15.23 Kept: 10173
% 14.87/15.23 Inuse: 2214
% 14.87/15.23 Deleted: 96
% 14.87/15.23 Deletedinuse: 11
% 14.87/15.23
% 14.87/15.23 Resimplifying inuse:
% 14.87/15.23 Done
% 14.87/15.23
% 14.87/15.23
% 14.87/15.23 Bliksems!, er is een bewijs:
% 14.87/15.23 % SZS status Theorem
% 14.87/15.23 % SZS output start Refutation
% 14.87/15.23
% 14.87/15.23 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 14.87/15.23 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 14.87/15.23 , ! distinct_lines( X, Y ) }.
% 14.87/15.23 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 14.87/15.23 X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.87/15.23 (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 14.87/15.23 ( Y, X ), Y ) }.
% 14.87/15.23 (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 14.87/15.23 orthogonal_through_point( Y, X ) ) }.
% 14.87/15.23 (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ),
% 14.87/15.23 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 14.87/15.23 unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 14.87/15.23 (26) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1, skol2 ) }.
% 14.87/15.23 (27) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2, skol3 ) }.
% 14.87/15.23 (28) {G0,W5,D3,L1,V0,M1} I { distinct_lines( skol2,
% 14.87/15.23 orthogonal_through_point( skol3, skol1 ) ) }.
% 14.87/15.23 (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 14.87/15.23 ( X, Y ) }.
% 14.87/15.23 (36) {G2,W5,D3,L1,V0,M1} R(34,28) { distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.87/15.23 (131) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 14.87/15.23 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 14.87/15.23 apart_point_and_line( Z, X ) }.
% 14.87/15.23 (145) {G1,W6,D2,L2,V1,M1} R(12,26) { distinct_lines( X, skol2 ), !
% 14.87/15.23 apart_point_and_line( skol1, X ) }.
% 14.87/15.23 (146) {G2,W9,D2,L3,V2,M1} R(145,12) { distinct_lines( X, skol2 ),
% 14.87/15.23 distinct_lines( Y, X ), ! apart_point_and_line( skol1, Y ) }.
% 14.87/15.23 (277) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 14.87/15.23 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 14.87/15.23 unorthogonal_lines( Z, X ) }.
% 14.87/15.23 (2604) {G3,W15,D2,L5,V4,M1} R(131,146) { distinct_lines( X, Y ),
% 14.87/15.23 distinct_lines( Y, Z ), distinct_lines( T, skol2 ), distinct_lines( Z, T
% 14.87/15.23 ), ! apart_point_and_line( skol1, X ) }.
% 14.87/15.23 (2618) {G4,W9,D2,L3,V2,M1} F(2604);r(34) { distinct_lines( Y, X ),
% 14.87/15.23 distinct_lines( Y, skol2 ), ! apart_point_and_line( skol1, X ) }.
% 14.87/15.23 (3731) {G2,W13,D3,L3,V2,M1} R(277,27) { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( Y,
% 14.87/15.23 skol2 ), apart_point_and_line( Y, orthogonal_through_point( skol3, X ) )
% 14.87/15.23 }.
% 14.87/15.23 (10818) {G3,W8,D3,L2,V1,M1} R(3731,24) { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X,
% 14.87/15.23 skol2 ) }.
% 14.87/15.23 (10869) {G5,W3,D2,L1,V1,M1} R(10818,2618);f;r(36) { distinct_lines( X,
% 14.87/15.23 skol2 ) }.
% 14.87/15.23 (10887) {G6,W0,D0,L0,V0,M0} R(10818,26);r(10869) { }.
% 14.87/15.23
% 14.87/15.23
% 14.87/15.23 % SZS output end Refutation
% 14.87/15.23 found a proof!
% 14.87/15.23
% 14.87/15.23
% 14.87/15.23 Unprocessed initial clauses:
% 14.87/15.23
% 14.87/15.23 (10889) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 14.87/15.23 (10890) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 14.87/15.23 (10891) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 14.87/15.23 (10892) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points(
% 14.87/15.23 X, Z ), distinct_points( Y, Z ) }.
% 14.87/15.23 (10893) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X
% 14.87/15.23 , Z ), distinct_lines( Y, Z ) }.
% 14.87/15.23 (10894) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 14.87/15.23 ( X, Z ), convergent_lines( Y, Z ) }.
% 14.87/15.23 (10895) {G0,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ), !
% 14.87/15.23 apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, X
% 14.87/15.23 ) }.
% 14.87/15.23 (10896) {G0,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ), !
% 14.87/15.23 apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, Y
% 14.87/15.23 ) }.
% 14.87/15.23 (10897) {G0,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ), !
% 14.87/15.23 apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X,
% 14.87/15.23 Y ) ) }.
% 14.87/15.23 (10898) {G0,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ), !
% 14.87/15.23 apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X,
% 14.87/15.23 Y ) ) }.
% 14.87/15.23 (10899) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 14.87/15.23 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 14.87/15.23 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 14.87/15.23 (10900) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 14.87/15.23 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 14.87/15.23 (10901) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 14.87/15.23 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 14.87/15.23 (10902) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ), distinct_lines(
% 14.87/15.23 X, Y ) }.
% 14.87/15.23 (10903) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point(
% 14.87/15.23 Y, X ), Y ) }.
% 14.87/15.23 (10904) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 14.87/15.23 parallel_through_point( Y, X ) ) }.
% 14.87/15.23 (10905) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 14.87/15.23 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 14.87/15.23 convergent_lines( X, Y ) }.
% 14.87/15.23 (10906) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 14.87/15.23 ( X, Y ) }.
% 14.87/15.23 (10907) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 14.87/15.23 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 14.87/15.23 (10908) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 14.87/15.23 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 14.87/15.23 }.
% 14.87/15.23 (10909) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 14.87/15.23 }.
% 14.87/15.23 (10910) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 14.87/15.23 }.
% 14.87/15.23 (10911) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 14.87/15.23 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 14.87/15.23 (10912) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 14.87/15.23 orthogonal_through_point( Y, X ), Y ) }.
% 14.87/15.23 (10913) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 14.87/15.23 orthogonal_through_point( Y, X ) ) }.
% 14.87/15.23 (10914) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 14.87/15.23 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 14.87/15.23 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 14.87/15.23 (10915) {G0,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1, skol2 ) }.
% 14.87/15.23 (10916) {G0,W3,D2,L1,V0,M1} { ! unorthogonal_lines( skol2, skol3 ) }.
% 14.87/15.23 (10917) {G0,W5,D3,L1,V0,M1} { distinct_lines( skol2,
% 14.87/15.23 orthogonal_through_point( skol3, skol1 ) ) }.
% 14.87/15.23
% 14.87/15.23
% 14.87/15.23 Total Proof:
% 14.87/15.23
% 14.87/15.23 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 14.87/15.23 parent0: (10890) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 0
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 14.87/15.23 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 14.87/15.23 parent0: (10893) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 14.87/15.23 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 Y := Y
% 14.87/15.23 Z := Z
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 2
% 14.87/15.23 1 ==> 0
% 14.87/15.23 2 ==> 1
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 14.87/15.23 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.87/15.23 parent0: (10901) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 14.87/15.23 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 Y := Y
% 14.87/15.23 Z := Z
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 2
% 14.87/15.23 1 ==> 0
% 14.87/15.23 2 ==> 1
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 14.87/15.23 orthogonal_through_point( Y, X ), Y ) }.
% 14.87/15.23 parent0: (10912) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 14.87/15.23 orthogonal_through_point( Y, X ), Y ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 Y := Y
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 0
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 14.87/15.23 orthogonal_through_point( Y, X ) ) }.
% 14.87/15.23 parent0: (10913) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 14.87/15.23 orthogonal_through_point( Y, X ) ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 Y := Y
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 0
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ),
% 14.87/15.23 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 14.87/15.23 unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 14.87/15.23 parent0: (10914) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 14.87/15.23 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 14.87/15.23 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 Y := Y
% 14.87/15.23 Z := Z
% 14.87/15.23 T := T
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 0
% 14.87/15.23 1 ==> 1
% 14.87/15.23 2 ==> 2
% 14.87/15.23 3 ==> 4
% 14.87/15.23 4 ==> 3
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (26) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1,
% 14.87/15.23 skol2 ) }.
% 14.87/15.23 parent0: (10915) {G0,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1,
% 14.87/15.23 skol2 ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 0
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (27) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2,
% 14.87/15.23 skol3 ) }.
% 14.87/15.23 parent0: (10916) {G0,W3,D2,L1,V0,M1} { ! unorthogonal_lines( skol2, skol3
% 14.87/15.23 ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 0
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (28) {G0,W5,D3,L1,V0,M1} I { distinct_lines( skol2,
% 14.87/15.23 orthogonal_through_point( skol3, skol1 ) ) }.
% 14.87/15.23 parent0: (10917) {G0,W5,D3,L1,V0,M1} { distinct_lines( skol2,
% 14.87/15.23 orthogonal_through_point( skol3, skol1 ) ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 0
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 resolution: (10997) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 14.87/15.23 distinct_lines( X, Y ) }.
% 14.87/15.23 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 14.87/15.23 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 14.87/15.23 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 end
% 14.87/15.23 substitution1:
% 14.87/15.23 X := X
% 14.87/15.23 Y := Y
% 14.87/15.23 Z := X
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 14.87/15.23 distinct_lines( X, Y ) }.
% 14.87/15.23 parent0: (10997) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 14.87/15.23 distinct_lines( X, Y ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := Y
% 14.87/15.23 Y := X
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 1
% 14.87/15.23 1 ==> 0
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 resolution: (10999) {G1,W5,D3,L1,V0,M1} { distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.87/15.23 parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 14.87/15.23 distinct_lines( X, Y ) }.
% 14.87/15.23 parent1[0]: (28) {G0,W5,D3,L1,V0,M1} I { distinct_lines( skol2,
% 14.87/15.23 orthogonal_through_point( skol3, skol1 ) ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := orthogonal_through_point( skol3, skol1 )
% 14.87/15.23 Y := skol2
% 14.87/15.23 end
% 14.87/15.23 substitution1:
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (36) {G2,W5,D3,L1,V0,M1} R(34,28) { distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.87/15.23 parent0: (10999) {G1,W5,D3,L1,V0,M1} { distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 0
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 resolution: (11000) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 14.87/15.23 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 14.87/15.23 apart_point_and_line( Z, T ) }.
% 14.87/15.23 parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 14.87/15.23 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.87/15.23 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 14.87/15.23 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := Z
% 14.87/15.23 Y := X
% 14.87/15.23 Z := Y
% 14.87/15.23 end
% 14.87/15.23 substitution1:
% 14.87/15.23 X := Z
% 14.87/15.23 Y := T
% 14.87/15.23 Z := X
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (131) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 14.87/15.23 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 14.87/15.23 apart_point_and_line( Z, X ) }.
% 14.87/15.23 parent0: (11000) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 14.87/15.23 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 14.87/15.23 apart_point_and_line( Z, T ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := Y
% 14.87/15.23 Y := T
% 14.87/15.23 Z := Z
% 14.87/15.23 T := X
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 1
% 14.87/15.23 1 ==> 2
% 14.87/15.23 2 ==> 0
% 14.87/15.23 3 ==> 3
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 resolution: (11002) {G1,W6,D2,L2,V1,M2} { distinct_lines( X, skol2 ), !
% 14.87/15.23 apart_point_and_line( skol1, X ) }.
% 14.87/15.23 parent0[0]: (26) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1,
% 14.87/15.23 skol2 ) }.
% 14.87/15.23 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 14.87/15.23 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 end
% 14.87/15.23 substitution1:
% 14.87/15.23 X := skol1
% 14.87/15.23 Y := X
% 14.87/15.23 Z := skol2
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (145) {G1,W6,D2,L2,V1,M1} R(12,26) { distinct_lines( X, skol2
% 14.87/15.23 ), ! apart_point_and_line( skol1, X ) }.
% 14.87/15.23 parent0: (11002) {G1,W6,D2,L2,V1,M2} { distinct_lines( X, skol2 ), !
% 14.87/15.23 apart_point_and_line( skol1, X ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 0
% 14.87/15.23 1 ==> 1
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 resolution: (11003) {G1,W9,D2,L3,V2,M3} { distinct_lines( X, skol2 ),
% 14.87/15.23 distinct_lines( Y, X ), ! apart_point_and_line( skol1, Y ) }.
% 14.87/15.23 parent0[1]: (145) {G1,W6,D2,L2,V1,M1} R(12,26) { distinct_lines( X, skol2 )
% 14.87/15.23 , ! apart_point_and_line( skol1, X ) }.
% 14.87/15.23 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 14.87/15.23 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 end
% 14.87/15.23 substitution1:
% 14.87/15.23 X := skol1
% 14.87/15.23 Y := Y
% 14.87/15.23 Z := X
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (146) {G2,W9,D2,L3,V2,M1} R(145,12) { distinct_lines( X, skol2
% 14.87/15.23 ), distinct_lines( Y, X ), ! apart_point_and_line( skol1, Y ) }.
% 14.87/15.23 parent0: (11003) {G1,W9,D2,L3,V2,M3} { distinct_lines( X, skol2 ),
% 14.87/15.23 distinct_lines( Y, X ), ! apart_point_and_line( skol1, Y ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 Y := Y
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 0
% 14.87/15.23 1 ==> 1
% 14.87/15.23 2 ==> 2
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 resolution: (11006) {G1,W16,D3,L4,V4,M4} { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 14.87/15.23 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 14.87/15.23 unorthogonal_lines( Z, X ) }.
% 14.87/15.23 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 14.87/15.23 orthogonal_through_point( Y, X ), Y ) }.
% 14.87/15.23 parent1[4]: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ),
% 14.87/15.23 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 14.87/15.23 unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := Y
% 14.87/15.23 Y := X
% 14.87/15.23 end
% 14.87/15.23 substitution1:
% 14.87/15.23 X := orthogonal_through_point( X, Y )
% 14.87/15.23 Y := Z
% 14.87/15.23 Z := T
% 14.87/15.23 T := X
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (277) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 14.87/15.23 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 14.87/15.23 unorthogonal_lines( Z, X ) }.
% 14.87/15.23 parent0: (11006) {G1,W16,D3,L4,V4,M4} { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 14.87/15.23 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 14.87/15.23 unorthogonal_lines( Z, X ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 Y := Y
% 14.87/15.23 Z := Z
% 14.87/15.23 T := T
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 0
% 14.87/15.23 1 ==> 1
% 14.87/15.23 2 ==> 2
% 14.87/15.23 3 ==> 3
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 resolution: (11008) {G2,W15,D2,L5,V4,M5} { distinct_lines( X, skol2 ),
% 14.87/15.23 distinct_lines( Y, X ), distinct_lines( Z, T ), distinct_lines( T, Y ), !
% 14.87/15.23 apart_point_and_line( skol1, Z ) }.
% 14.87/15.23 parent0[2]: (146) {G2,W9,D2,L3,V2,M1} R(145,12) { distinct_lines( X, skol2
% 14.87/15.23 ), distinct_lines( Y, X ), ! apart_point_and_line( skol1, Y ) }.
% 14.87/15.23 parent1[2]: (131) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 14.87/15.23 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 14.87/15.23 apart_point_and_line( Z, X ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 Y := Y
% 14.87/15.23 end
% 14.87/15.23 substitution1:
% 14.87/15.23 X := Z
% 14.87/15.23 Y := T
% 14.87/15.23 Z := skol1
% 14.87/15.23 T := Y
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (2604) {G3,W15,D2,L5,V4,M1} R(131,146) { distinct_lines( X, Y
% 14.87/15.23 ), distinct_lines( Y, Z ), distinct_lines( T, skol2 ), distinct_lines( Z
% 14.87/15.23 , T ), ! apart_point_and_line( skol1, X ) }.
% 14.87/15.23 parent0: (11008) {G2,W15,D2,L5,V4,M5} { distinct_lines( X, skol2 ),
% 14.87/15.23 distinct_lines( Y, X ), distinct_lines( Z, T ), distinct_lines( T, Y ), !
% 14.87/15.23 apart_point_and_line( skol1, Z ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := T
% 14.87/15.23 Y := Z
% 14.87/15.23 Z := X
% 14.87/15.23 T := Y
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 2
% 14.87/15.23 1 ==> 3
% 14.87/15.23 2 ==> 0
% 14.87/15.23 3 ==> 1
% 14.87/15.23 4 ==> 4
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 factor: (11022) {G3,W12,D2,L4,V2,M4} { distinct_lines( X, Y ),
% 14.87/15.23 distinct_lines( Y, X ), distinct_lines( Y, skol2 ), !
% 14.87/15.23 apart_point_and_line( skol1, X ) }.
% 14.87/15.23 parent0[0, 3]: (2604) {G3,W15,D2,L5,V4,M1} R(131,146) { distinct_lines( X,
% 14.87/15.23 Y ), distinct_lines( Y, Z ), distinct_lines( T, skol2 ), distinct_lines(
% 14.87/15.23 Z, T ), ! apart_point_and_line( skol1, X ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 Y := Y
% 14.87/15.23 Z := X
% 14.87/15.23 T := Y
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 resolution: (11046) {G2,W12,D2,L4,V2,M4} { distinct_lines( Y, X ),
% 14.87/15.23 distinct_lines( Y, X ), distinct_lines( Y, skol2 ), !
% 14.87/15.23 apart_point_and_line( skol1, X ) }.
% 14.87/15.23 parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 14.87/15.23 distinct_lines( X, Y ) }.
% 14.87/15.23 parent1[0]: (11022) {G3,W12,D2,L4,V2,M4} { distinct_lines( X, Y ),
% 14.87/15.23 distinct_lines( Y, X ), distinct_lines( Y, skol2 ), !
% 14.87/15.23 apart_point_and_line( skol1, X ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := Y
% 14.87/15.23 Y := X
% 14.87/15.23 end
% 14.87/15.23 substitution1:
% 14.87/15.23 X := X
% 14.87/15.23 Y := Y
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 factor: (11049) {G2,W9,D2,L3,V2,M3} { distinct_lines( X, Y ),
% 14.87/15.23 distinct_lines( X, skol2 ), ! apart_point_and_line( skol1, Y ) }.
% 14.87/15.23 parent0[0, 1]: (11046) {G2,W12,D2,L4,V2,M4} { distinct_lines( Y, X ),
% 14.87/15.23 distinct_lines( Y, X ), distinct_lines( Y, skol2 ), !
% 14.87/15.23 apart_point_and_line( skol1, X ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := Y
% 14.87/15.23 Y := X
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (2618) {G4,W9,D2,L3,V2,M1} F(2604);r(34) { distinct_lines( Y,
% 14.87/15.23 X ), distinct_lines( Y, skol2 ), ! apart_point_and_line( skol1, X ) }.
% 14.87/15.23 parent0: (11049) {G2,W9,D2,L3,V2,M3} { distinct_lines( X, Y ),
% 14.87/15.23 distinct_lines( X, skol2 ), ! apart_point_and_line( skol1, Y ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := Y
% 14.87/15.23 Y := X
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 0
% 14.87/15.23 1 ==> 1
% 14.87/15.23 2 ==> 2
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 resolution: (11053) {G1,W13,D3,L3,V2,M3} { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( Y,
% 14.87/15.23 orthogonal_through_point( skol3, X ) ), apart_point_and_line( Y, skol2 )
% 14.87/15.23 }.
% 14.87/15.23 parent0[0]: (27) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2, skol3
% 14.87/15.23 ) }.
% 14.87/15.23 parent1[3]: (277) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 14.87/15.23 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 14.87/15.23 unorthogonal_lines( Z, X ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 end
% 14.87/15.23 substitution1:
% 14.87/15.23 X := skol3
% 14.87/15.23 Y := X
% 14.87/15.23 Z := skol2
% 14.87/15.23 T := Y
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (3731) {G2,W13,D3,L3,V2,M1} R(277,27) { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( Y,
% 14.87/15.23 skol2 ), apart_point_and_line( Y, orthogonal_through_point( skol3, X ) )
% 14.87/15.23 }.
% 14.87/15.23 parent0: (11053) {G1,W13,D3,L3,V2,M3} { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( Y,
% 14.87/15.23 orthogonal_through_point( skol3, X ) ), apart_point_and_line( Y, skol2 )
% 14.87/15.23 }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 Y := Y
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 0
% 14.87/15.23 1 ==> 2
% 14.87/15.23 2 ==> 1
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 resolution: (11054) {G1,W8,D3,L2,V1,M2} { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X,
% 14.87/15.23 skol2 ) }.
% 14.87/15.23 parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 14.87/15.23 orthogonal_through_point( Y, X ) ) }.
% 14.87/15.23 parent1[2]: (3731) {G2,W13,D3,L3,V2,M1} R(277,27) { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( Y,
% 14.87/15.23 skol2 ), apart_point_and_line( Y, orthogonal_through_point( skol3, X ) )
% 14.87/15.23 }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 Y := skol3
% 14.87/15.23 end
% 14.87/15.23 substitution1:
% 14.87/15.23 X := X
% 14.87/15.23 Y := X
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (10818) {G3,W8,D3,L2,V1,M1} R(3731,24) { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X,
% 14.87/15.23 skol2 ) }.
% 14.87/15.23 parent0: (11054) {G1,W8,D3,L2,V1,M2} { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X,
% 14.87/15.23 skol2 ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 0
% 14.87/15.23 1 ==> 1
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 resolution: (11057) {G4,W11,D3,L3,V1,M3} { distinct_lines( X, skol2 ),
% 14.87/15.23 distinct_lines( X, skol2 ), ! distinct_lines( orthogonal_through_point(
% 14.87/15.23 skol3, skol1 ), skol2 ) }.
% 14.87/15.23 parent0[2]: (2618) {G4,W9,D2,L3,V2,M1} F(2604);r(34) { distinct_lines( Y, X
% 14.87/15.23 ), distinct_lines( Y, skol2 ), ! apart_point_and_line( skol1, X ) }.
% 14.87/15.23 parent1[1]: (10818) {G3,W8,D3,L2,V1,M1} R(3731,24) { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X,
% 14.87/15.23 skol2 ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := skol2
% 14.87/15.23 Y := X
% 14.87/15.23 end
% 14.87/15.23 substitution1:
% 14.87/15.23 X := skol1
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 resolution: (11059) {G3,W6,D2,L2,V1,M2} { distinct_lines( X, skol2 ),
% 14.87/15.23 distinct_lines( X, skol2 ) }.
% 14.87/15.23 parent0[2]: (11057) {G4,W11,D3,L3,V1,M3} { distinct_lines( X, skol2 ),
% 14.87/15.23 distinct_lines( X, skol2 ), ! distinct_lines( orthogonal_through_point(
% 14.87/15.23 skol3, skol1 ), skol2 ) }.
% 14.87/15.23 parent1[0]: (36) {G2,W5,D3,L1,V0,M1} R(34,28) { distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 end
% 14.87/15.23 substitution1:
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 factor: (11060) {G3,W3,D2,L1,V1,M1} { distinct_lines( X, skol2 ) }.
% 14.87/15.23 parent0[0, 1]: (11059) {G3,W6,D2,L2,V1,M2} { distinct_lines( X, skol2 ),
% 14.87/15.23 distinct_lines( X, skol2 ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (10869) {G5,W3,D2,L1,V1,M1} R(10818,2618);f;r(36) {
% 14.87/15.23 distinct_lines( X, skol2 ) }.
% 14.87/15.23 parent0: (11060) {G3,W3,D2,L1,V1,M1} { distinct_lines( X, skol2 ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 X := X
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 0 ==> 0
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 resolution: (11061) {G1,W5,D3,L1,V0,M1} { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.87/15.23 parent0[0]: (26) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1,
% 14.87/15.23 skol2 ) }.
% 14.87/15.23 parent1[1]: (10818) {G3,W8,D3,L2,V1,M1} R(3731,24) { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X,
% 14.87/15.23 skol2 ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 end
% 14.87/15.23 substitution1:
% 14.87/15.23 X := skol1
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 resolution: (11062) {G2,W0,D0,L0,V0,M0} { }.
% 14.87/15.23 parent0[0]: (11061) {G1,W5,D3,L1,V0,M1} { ! distinct_lines(
% 14.87/15.23 orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.87/15.23 parent1[0]: (10869) {G5,W3,D2,L1,V1,M1} R(10818,2618);f;r(36) {
% 14.87/15.23 distinct_lines( X, skol2 ) }.
% 14.87/15.23 substitution0:
% 14.87/15.23 end
% 14.87/15.23 substitution1:
% 14.87/15.23 X := orthogonal_through_point( skol3, skol1 )
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 subsumption: (10887) {G6,W0,D0,L0,V0,M0} R(10818,26);r(10869) { }.
% 14.87/15.23 parent0: (11062) {G2,W0,D0,L0,V0,M0} { }.
% 14.87/15.23 substitution0:
% 14.87/15.23 end
% 14.87/15.23 permutation0:
% 14.87/15.23 end
% 14.87/15.23
% 14.87/15.23 Proof check complete!
% 14.87/15.23
% 14.87/15.23 Memory use:
% 14.87/15.23
% 14.87/15.23 space for terms: 159052
% 14.87/15.23 space for clauses: 458864
% 14.87/15.23
% 14.87/15.23
% 14.87/15.23 clauses generated: 1247334
% 14.87/15.23 clauses kept: 10888
% 14.87/15.23 clauses selected: 2721
% 14.87/15.23 clauses deleted: 98
% 14.87/15.23 clauses inuse deleted: 11
% 14.87/15.23
% 14.87/15.23 subsentry: 8835628
% 14.87/15.23 literals s-matched: 2681661
% 14.87/15.23 literals matched: 2681604
% 14.87/15.23 full subsumption: 1505153
% 14.87/15.23
% 14.87/15.23 checksum: -392797102
% 14.87/15.23
% 14.87/15.23
% 14.87/15.23 Bliksem ended
%------------------------------------------------------------------------------