TSTP Solution File: GEO184+3 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO184+3 : TPTP v8.1.0. Released v4.0.0.
% 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 02:52:24 EDT 2022
% Result : Theorem 1.70s 2.10s
% Output : Refutation 1.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO184+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.32 % Computer : n018.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Sat Jun 18 15:27:18 EDT 2022
% 0.12/0.32 % CPUTime :
% 1.70/2.10 *** allocated 10000 integers for termspace/termends
% 1.70/2.10 *** allocated 10000 integers for clauses
% 1.70/2.10 *** allocated 10000 integers for justifications
% 1.70/2.10 Bliksem 1.12
% 1.70/2.10
% 1.70/2.10
% 1.70/2.10 Automatic Strategy Selection
% 1.70/2.10
% 1.70/2.10
% 1.70/2.10 Clauses:
% 1.70/2.10
% 1.70/2.10 { ! distinct_points( X, X ) }.
% 1.70/2.10 { ! distinct_lines( X, X ) }.
% 1.70/2.10 { ! convergent_lines( X, X ) }.
% 1.70/2.10 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 1.70/2.10 ) }.
% 1.70/2.10 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.70/2.10 }.
% 1.70/2.10 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 1.70/2.10 , Z ) }.
% 1.70/2.10 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 1.70/2.10 , Y ) ) }.
% 1.70/2.10 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 1.70/2.10 , Y ) ) }.
% 1.70/2.10 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.70/2.10 , Y ), X ) }.
% 1.70/2.10 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.70/2.10 , Y ), Y ) }.
% 1.70/2.10 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 1.70/2.10 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 1.70/2.10 apart_point_and_line( Y, T ) }.
% 1.70/2.10 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 1.70/2.10 apart_point_and_line( Z, Y ) }.
% 1.70/2.10 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 1.70/2.10 apart_point_and_line( X, Z ) }.
% 1.70/2.10 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 1.70/2.10 Z ) }.
% 1.70/2.10 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 1.70/2.10 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 1.70/2.10 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 1.70/2.10 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 1.70/2.10 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 1.70/2.10 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.70/2.10 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.70/2.10 , convergent_lines( Y, Z ) }.
% 1.70/2.10 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.70/2.10 , unorthogonal_lines( Y, Z ) }.
% 1.70/2.10 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 1.70/2.10 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.70/2.10 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 1.70/2.10 }.
% 1.70/2.10 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 1.70/2.10 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 1.70/2.10 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 1.70/2.10 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 1.70/2.10 unorthogonal_lines( Y, T ) }.
% 1.70/2.10 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.70/2.10 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 1.70/2.10 unorthogonal_lines( X, Y ) }.
% 1.70/2.10 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 1.70/2.10 unorthogonal_lines( X, Y ) }.
% 1.70/2.10 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 1.70/2.10 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 1.70/2.10 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 1.70/2.10 }.
% 1.70/2.10 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 1.70/2.10 convergent_lines( X, Y ) }.
% 1.70/2.10 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 1.70/2.10 line_connecting( X, Y ) ) }.
% 1.70/2.10 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 1.70/2.10 intersection_point( X, Y ) ) }.
% 1.70/2.10 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 1.70/2.10 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 1.70/2.10 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 1.70/2.10 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 1.70/2.10 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 1.70/2.10 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 1.70/2.10 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 1.70/2.10 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 1.70/2.10 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 1.70/2.10 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 1.70/2.10 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.70/2.10 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 1.70/2.10 { distinct_points( skol1, skol2 ) }.
% 1.70/2.10 { convergent_lines( skol3, skol4 ) }.
% 1.70/2.10 { incident_point_and_line( skol1, skol3 ) }.
% 1.70/2.10 { incident_point_and_line( skol2, skol3 ) }.
% 1.70/2.10 { ! equal_lines( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10
% 1.70/2.10 percentage equality = 0.000000, percentage horn = 0.627451
% 1.70/2.10 This a non-horn, non-equality problem
% 1.70/2.10
% 1.70/2.10
% 1.70/2.10 Options Used:
% 1.70/2.10
% 1.70/2.10 useres = 1
% 1.70/2.10 useparamod = 0
% 1.70/2.10 useeqrefl = 0
% 1.70/2.10 useeqfact = 0
% 1.70/2.10 usefactor = 1
% 1.70/2.10 usesimpsplitting = 0
% 1.70/2.10 usesimpdemod = 0
% 1.70/2.10 usesimpres = 3
% 1.70/2.10
% 1.70/2.10 resimpinuse = 1000
% 1.70/2.10 resimpclauses = 20000
% 1.70/2.10 substype = standard
% 1.70/2.10 backwardsubs = 1
% 1.70/2.10 selectoldest = 5
% 1.70/2.10
% 1.70/2.10 litorderings [0] = split
% 1.70/2.10 litorderings [1] = liftord
% 1.70/2.10
% 1.70/2.10 termordering = none
% 1.70/2.10
% 1.70/2.10 litapriori = 1
% 1.70/2.10 termapriori = 0
% 1.70/2.10 litaposteriori = 0
% 1.70/2.10 termaposteriori = 0
% 1.70/2.10 demodaposteriori = 0
% 1.70/2.10 ordereqreflfact = 0
% 1.70/2.10
% 1.70/2.10 litselect = none
% 1.70/2.10
% 1.70/2.10 maxweight = 15
% 1.70/2.10 maxdepth = 30000
% 1.70/2.10 maxlength = 115
% 1.70/2.10 maxnrvars = 195
% 1.70/2.10 excuselevel = 1
% 1.70/2.10 increasemaxweight = 1
% 1.70/2.10
% 1.70/2.10 maxselected = 10000000
% 1.70/2.10 maxnrclauses = 10000000
% 1.70/2.10
% 1.70/2.10 showgenerated = 0
% 1.70/2.10 showkept = 0
% 1.70/2.10 showselected = 0
% 1.70/2.10 showdeleted = 0
% 1.70/2.10 showresimp = 1
% 1.70/2.10 showstatus = 2000
% 1.70/2.10
% 1.70/2.10 prologoutput = 0
% 1.70/2.10 nrgoals = 5000000
% 1.70/2.10 totalproof = 1
% 1.70/2.10
% 1.70/2.10 Symbols occurring in the translation:
% 1.70/2.10
% 1.70/2.10 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.70/2.10 . [1, 2] (w:1, o:27, a:1, s:1, b:0),
% 1.70/2.10 ! [4, 1] (w:0, o:20, a:1, s:1, b:0),
% 1.70/2.10 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.70/2.10 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.70/2.10 distinct_points [36, 2] (w:1, o:52, a:1, s:1, b:0),
% 1.70/2.10 distinct_lines [37, 2] (w:1, o:53, a:1, s:1, b:0),
% 1.70/2.10 convergent_lines [38, 2] (w:1, o:51, a:1, s:1, b:0),
% 1.70/2.10 line_connecting [41, 2] (w:1, o:54, a:1, s:1, b:0),
% 1.70/2.10 apart_point_and_line [42, 2] (w:1, o:55, a:1, s:1, b:0),
% 1.70/2.10 intersection_point [43, 2] (w:1, o:56, a:1, s:1, b:0),
% 1.70/2.10 parallel_through_point [46, 2] (w:1, o:59, a:1, s:1, b:0),
% 1.70/2.10 unorthogonal_lines [49, 2] (w:1, o:60, a:1, s:1, b:0),
% 1.70/2.10 orthogonal_through_point [52, 2] (w:1, o:57, a:1, s:1, b:0),
% 1.70/2.10 point [54, 1] (w:1, o:25, a:1, s:1, b:0),
% 1.70/2.10 line [55, 1] (w:1, o:26, a:1, s:1, b:0),
% 1.70/2.10 equal_points [56, 2] (w:1, o:61, a:1, s:1, b:0),
% 1.70/2.10 equal_lines [57, 2] (w:1, o:62, a:1, s:1, b:0),
% 1.70/2.10 parallel_lines [58, 2] (w:1, o:63, a:1, s:1, b:0),
% 1.70/2.10 incident_point_and_line [59, 2] (w:1, o:64, a:1, s:1, b:0),
% 1.70/2.10 orthogonal_lines [60, 2] (w:1, o:58, a:1, s:1, b:0),
% 1.70/2.10 alpha1 [61, 2] (w:1, o:65, a:1, s:1, b:0),
% 1.70/2.10 alpha2 [62, 2] (w:1, o:66, a:1, s:1, b:0),
% 1.70/2.10 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 1.70/2.10 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 1.70/2.10 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0),
% 1.70/2.10 skol4 [66, 0] (w:1, o:19, a:1, s:1, b:0).
% 1.70/2.10
% 1.70/2.10
% 1.70/2.10 Starting Search:
% 1.70/2.10
% 1.70/2.10 *** allocated 15000 integers for clauses
% 1.70/2.10 *** allocated 22500 integers for clauses
% 1.70/2.10 *** allocated 33750 integers for clauses
% 1.70/2.10 *** allocated 15000 integers for termspace/termends
% 1.70/2.10 *** allocated 50625 integers for clauses
% 1.70/2.10 Resimplifying inuse:
% 1.70/2.10 Done
% 1.70/2.10
% 1.70/2.10 *** allocated 22500 integers for termspace/termends
% 1.70/2.10 *** allocated 75937 integers for clauses
% 1.70/2.10 *** allocated 33750 integers for termspace/termends
% 1.70/2.10 *** allocated 113905 integers for clauses
% 1.70/2.10
% 1.70/2.10 Intermediate Status:
% 1.70/2.10 Generated: 13862
% 1.70/2.10 Kept: 2007
% 1.70/2.10 Inuse: 348
% 1.70/2.10 Deleted: 2
% 1.70/2.10 Deletedinuse: 1
% 1.70/2.10
% 1.70/2.10 Resimplifying inuse:
% 1.70/2.10 Done
% 1.70/2.10
% 1.70/2.10 *** allocated 50625 integers for termspace/termends
% 1.70/2.10 *** allocated 170857 integers for clauses
% 1.70/2.10 Resimplifying inuse:
% 1.70/2.10 Done
% 1.70/2.10
% 1.70/2.10 *** allocated 75937 integers for termspace/termends
% 1.70/2.10 *** allocated 256285 integers for clauses
% 1.70/2.10
% 1.70/2.10 Intermediate Status:
% 1.70/2.10 Generated: 29015
% 1.70/2.10 Kept: 4084
% 1.70/2.10 Inuse: 540
% 1.70/2.10 Deleted: 5
% 1.70/2.10 Deletedinuse: 1
% 1.70/2.10
% 1.70/2.10 Resimplifying inuse:
% 1.70/2.10 Done
% 1.70/2.10
% 1.70/2.10 Resimplifying inuse:
% 1.70/2.10 Done
% 1.70/2.10
% 1.70/2.10 *** allocated 113905 integers for termspace/termends
% 1.70/2.10 *** allocated 384427 integers for clauses
% 1.70/2.10
% 1.70/2.10 Intermediate Status:
% 1.70/2.10 Generated: 37494
% 1.70/2.10 Kept: 6145
% 1.70/2.10 Inuse: 588
% 1.70/2.10 Deleted: 6
% 1.70/2.10 Deletedinuse: 2
% 1.70/2.10
% 1.70/2.10 Resimplifying inuse:
% 1.70/2.10 Done
% 1.70/2.10
% 1.70/2.10 Resimplifying inuse:
% 1.70/2.10 Done
% 1.70/2.10
% 1.70/2.10 *** allocated 170857 integers for termspace/termends
% 1.70/2.10
% 1.70/2.10 Intermediate Status:
% 1.70/2.10 Generated: 57803
% 1.70/2.10 Kept: 8159
% 1.70/2.10 Inuse: 684
% 1.70/2.10 Deleted: 6
% 1.70/2.10 Deletedinuse: 2
% 1.70/2.10
% 1.70/2.10 Resimplifying inuse:
% 1.70/2.10 Done
% 1.70/2.10
% 1.70/2.10 Resimplifying inuse:
% 1.70/2.10 Done
% 1.70/2.10
% 1.70/2.10
% 1.70/2.10 Bliksems!, er is een bewijs:
% 1.70/2.10 % SZS status Theorem
% 1.70/2.10 % SZS output start Refutation
% 1.70/2.10
% 1.70/2.10 (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), !
% 1.70/2.10 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.70/2.10 (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), !
% 1.70/2.10 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.70/2.10 (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines(
% 1.70/2.10 Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 1.70/2.10 apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 1.70/2.10 (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ), equal_lines( X, Y )
% 1.70/2.10 }.
% 1.70/2.10 (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 1.70/2.10 incident_point_and_line( X, Y ) }.
% 1.70/2.10 (46) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 ) }.
% 1.70/2.10 (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1, skol3 ) }.
% 1.70/2.10 (49) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol2, skol3 ) }.
% 1.70/2.10 (50) {G0,W5,D3,L1,V0,M1} I { ! equal_lines( skol3, line_connecting( skol1,
% 1.70/2.10 skol2 ) ) }.
% 1.70/2.10 (76) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line( skol1, skol3 )
% 1.70/2.10 }.
% 1.70/2.10 (77) {G1,W3,D2,L1,V0,M1} R(42,49) { ! apart_point_and_line( skol2, skol3 )
% 1.70/2.10 }.
% 1.70/2.10 (78) {G1,W5,D3,L1,V0,M1} R(39,50) { distinct_lines( skol3, line_connecting
% 1.70/2.10 ( skol1, skol2 ) ) }.
% 1.70/2.10 (101) {G1,W22,D3,L6,V4,M3} R(10,6) { ! distinct_points( X, Y ), !
% 1.70/2.10 distinct_lines( Z, line_connecting( X, T ) ), ! distinct_points( X, T ),
% 1.70/2.10 apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ),
% 1.70/2.10 apart_point_and_line( Y, line_connecting( X, T ) ) }.
% 1.70/2.10 (114) {G2,W14,D3,L4,V3,M2} F(101);r(7) { ! distinct_points( X, Y ), !
% 1.70/2.10 distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( Y, Z
% 1.70/2.10 ), apart_point_and_line( X, Z ) }.
% 1.70/2.10 (1989) {G3,W11,D3,L3,V1,M1} R(114,77) { ! distinct_points( X, skol2 ), !
% 1.70/2.10 distinct_lines( skol3, line_connecting( X, skol2 ) ),
% 1.70/2.10 apart_point_and_line( X, skol3 ) }.
% 1.70/2.10 (9258) {G4,W5,D3,L1,V0,M1} R(1989,76);r(46) { ! distinct_lines( skol3,
% 1.70/2.10 line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10 (9259) {G5,W0,D0,L0,V0,M0} S(9258);r(78) { }.
% 1.70/2.10
% 1.70/2.10
% 1.70/2.10 % SZS output end Refutation
% 1.70/2.10 found a proof!
% 1.70/2.10
% 1.70/2.10
% 1.70/2.10 Unprocessed initial clauses:
% 1.70/2.10
% 1.70/2.10 (9261) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 1.70/2.10 (9262) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 1.70/2.10 (9263) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 1.70/2.10 (9264) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 1.70/2.10 , Z ), distinct_points( Y, Z ) }.
% 1.70/2.10 (9265) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 1.70/2.10 Z ), distinct_lines( Y, Z ) }.
% 1.70/2.10 (9266) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 1.70/2.10 ( X, Z ), convergent_lines( Y, Z ) }.
% 1.70/2.10 (9267) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.70/2.10 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.70/2.10 (9268) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.70/2.10 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.70/2.10 (9269) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 1.70/2.10 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 1.70/2.10 (9270) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 1.70/2.10 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 1.70/2.10 (9271) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 1.70/2.10 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 1.70/2.10 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 1.70/2.10 (9272) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.70/2.10 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 1.70/2.10 (9273) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.70/2.10 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.70/2.10 (9274) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 1.70/2.10 , Z ), convergent_lines( X, Z ) }.
% 1.70/2.10 (9275) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 1.70/2.10 , Y ) }.
% 1.70/2.10 (9276) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 1.70/2.10 , X ), Y ) }.
% 1.70/2.10 (9277) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 1.70/2.10 parallel_through_point( Y, X ) ) }.
% 1.70/2.10 (9278) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 1.70/2.10 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 1.70/2.10 convergent_lines( X, Y ) }.
% 1.70/2.10 (9279) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 1.70/2.10 ( X, Y ) }.
% 1.70/2.10 (9280) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 1.70/2.10 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 1.70/2.10 (9281) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 1.70/2.10 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 1.70/2.10 }.
% 1.70/2.10 (9282) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 1.70/2.10 }.
% 1.70/2.10 (9283) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 1.70/2.10 }.
% 1.70/2.10 (9284) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 1.70/2.10 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 1.70/2.10 (9285) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 1.70/2.10 orthogonal_through_point( Y, X ), Y ) }.
% 1.70/2.10 (9286) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 1.70/2.10 orthogonal_through_point( Y, X ) ) }.
% 1.70/2.10 (9287) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 1.70/2.10 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 1.70/2.10 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 1.70/2.10 (9288) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 1.70/2.10 ( X, Y ) }.
% 1.70/2.10 (9289) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 1.70/2.10 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.70/2.10 (9290) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ),
% 1.70/2.10 ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.70/2.10 (9291) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X )
% 1.70/2.10 }.
% 1.70/2.10 (9292) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 1.70/2.10 }.
% 1.70/2.10 (9293) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 1.70/2.10 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 1.70/2.10 (9294) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 1.70/2.10 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 1.70/2.10 (9295) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), !
% 1.70/2.10 distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 1.70/2.10 (9296) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 1.70/2.10 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 1.70/2.10 (9297) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 1.70/2.10 parallel_through_point( X, Y ) ) }.
% 1.70/2.10 (9298) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 1.70/2.10 orthogonal_through_point( X, Y ) ) }.
% 1.70/2.10 (9299) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X
% 1.70/2.10 , Y ) }.
% 1.70/2.10 (9300) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 1.70/2.10 }.
% 1.70/2.10 (9301) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 1.70/2.10 ) }.
% 1.70/2.10 (9302) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 1.70/2.10 }.
% 1.70/2.10 (9303) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines
% 1.70/2.10 ( X, Y ) }.
% 1.70/2.10 (9304) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X,
% 1.70/2.10 Y ) }.
% 1.70/2.10 (9305) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 1.70/2.10 apart_point_and_line( X, Y ) }.
% 1.70/2.10 (9306) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 1.70/2.10 incident_point_and_line( X, Y ) }.
% 1.70/2.10 (9307) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 1.70/2.10 unorthogonal_lines( X, Y ) }.
% 1.70/2.10 (9308) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines
% 1.70/2.10 ( X, Y ) }.
% 1.70/2.10 (9309) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 1.70/2.10 (9310) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol4 ) }.
% 1.70/2.10 (9311) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol1, skol3 ) }.
% 1.70/2.10 (9312) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol2, skol3 ) }.
% 1.70/2.10 (9313) {G0,W5,D3,L1,V0,M1} { ! equal_lines( skol3, line_connecting( skol1
% 1.70/2.10 , skol2 ) ) }.
% 1.70/2.10
% 1.70/2.10
% 1.70/2.10 Total Proof:
% 1.70/2.10
% 1.70/2.10 subsumption: (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), !
% 1.70/2.10 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.70/2.10 parent0: (9267) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.70/2.10 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 X := X
% 1.70/2.10 Y := Y
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 0 ==> 0
% 1.70/2.10 1 ==> 1
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 subsumption: (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), !
% 1.70/2.10 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.70/2.10 parent0: (9268) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.70/2.10 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 X := X
% 1.70/2.10 Y := Y
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 0 ==> 0
% 1.70/2.10 1 ==> 1
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 1.70/2.10 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 1.70/2.10 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 1.70/2.10 apart_point_and_line( X, Z ) }.
% 1.70/2.10 parent0: (9271) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), !
% 1.70/2.10 distinct_lines( Z, T ), apart_point_and_line( X, Z ),
% 1.70/2.10 apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 1.70/2.10 apart_point_and_line( Y, T ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 X := X
% 1.70/2.10 Y := Y
% 1.70/2.10 Z := Z
% 1.70/2.10 T := T
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 0 ==> 0
% 1.70/2.10 1 ==> 1
% 1.70/2.10 2 ==> 5
% 1.70/2.10 3 ==> 2
% 1.70/2.10 4 ==> 3
% 1.70/2.10 5 ==> 4
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 subsumption: (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ),
% 1.70/2.10 equal_lines( X, Y ) }.
% 1.70/2.10 parent0: (9302) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines
% 1.70/2.10 ( X, Y ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 X := X
% 1.70/2.10 Y := Y
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 0 ==> 0
% 1.70/2.10 1 ==> 1
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 subsumption: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 1.70/2.10 incident_point_and_line( X, Y ) }.
% 1.70/2.10 parent0: (9305) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 1.70/2.10 apart_point_and_line( X, Y ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 X := X
% 1.70/2.10 Y := Y
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 0 ==> 1
% 1.70/2.10 1 ==> 0
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 subsumption: (46) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.70/2.10 }.
% 1.70/2.10 parent0: (9309) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 0 ==> 0
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 subsumption: (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1,
% 1.70/2.10 skol3 ) }.
% 1.70/2.10 parent0: (9311) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol1,
% 1.70/2.10 skol3 ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 0 ==> 0
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 subsumption: (49) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol2,
% 1.70/2.10 skol3 ) }.
% 1.70/2.10 parent0: (9312) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol2,
% 1.70/2.10 skol3 ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 0 ==> 0
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 subsumption: (50) {G0,W5,D3,L1,V0,M1} I { ! equal_lines( skol3,
% 1.70/2.10 line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10 parent0: (9313) {G0,W5,D3,L1,V0,M1} { ! equal_lines( skol3,
% 1.70/2.10 line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 0 ==> 0
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 resolution: (9419) {G1,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1,
% 1.70/2.10 skol3 ) }.
% 1.70/2.10 parent0[1]: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 1.70/2.10 incident_point_and_line( X, Y ) }.
% 1.70/2.10 parent1[0]: (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1,
% 1.70/2.10 skol3 ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 X := skol1
% 1.70/2.10 Y := skol3
% 1.70/2.10 end
% 1.70/2.10 substitution1:
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 subsumption: (76) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line(
% 1.70/2.10 skol1, skol3 ) }.
% 1.70/2.10 parent0: (9419) {G1,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1, skol3
% 1.70/2.10 ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 0 ==> 0
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 resolution: (9420) {G1,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol2,
% 1.70/2.10 skol3 ) }.
% 1.70/2.10 parent0[1]: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 1.70/2.10 incident_point_and_line( X, Y ) }.
% 1.70/2.10 parent1[0]: (49) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol2,
% 1.70/2.10 skol3 ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 X := skol2
% 1.70/2.10 Y := skol3
% 1.70/2.10 end
% 1.70/2.10 substitution1:
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 subsumption: (77) {G1,W3,D2,L1,V0,M1} R(42,49) { ! apart_point_and_line(
% 1.70/2.10 skol2, skol3 ) }.
% 1.70/2.10 parent0: (9420) {G1,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol2, skol3
% 1.70/2.10 ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 0 ==> 0
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 resolution: (9421) {G1,W5,D3,L1,V0,M1} { distinct_lines( skol3,
% 1.70/2.10 line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10 parent0[0]: (50) {G0,W5,D3,L1,V0,M1} I { ! equal_lines( skol3,
% 1.70/2.10 line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10 parent1[1]: (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ),
% 1.70/2.10 equal_lines( X, Y ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 end
% 1.70/2.10 substitution1:
% 1.70/2.10 X := skol3
% 1.70/2.10 Y := line_connecting( skol1, skol2 )
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 subsumption: (78) {G1,W5,D3,L1,V0,M1} R(39,50) { distinct_lines( skol3,
% 1.70/2.10 line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10 parent0: (9421) {G1,W5,D3,L1,V0,M1} { distinct_lines( skol3,
% 1.70/2.10 line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 0 ==> 0
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 resolution: (9422) {G1,W22,D3,L6,V4,M6} { ! distinct_points( X, Y ), !
% 1.70/2.10 distinct_points( X, Z ), ! distinct_lines( T, line_connecting( X, Y ) ),
% 1.70/2.10 apart_point_and_line( Z, T ), apart_point_and_line( Z, line_connecting( X
% 1.70/2.10 , Y ) ), apart_point_and_line( X, T ) }.
% 1.70/2.10 parent0[1]: (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), !
% 1.70/2.10 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.70/2.10 parent1[2]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 1.70/2.10 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 1.70/2.10 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 1.70/2.10 apart_point_and_line( X, Z ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 X := X
% 1.70/2.10 Y := Y
% 1.70/2.10 end
% 1.70/2.10 substitution1:
% 1.70/2.10 X := X
% 1.70/2.10 Y := Z
% 1.70/2.10 Z := T
% 1.70/2.10 T := line_connecting( X, Y )
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 subsumption: (101) {G1,W22,D3,L6,V4,M3} R(10,6) { ! distinct_points( X, Y )
% 1.70/2.10 , ! distinct_lines( Z, line_connecting( X, T ) ), ! distinct_points( X, T
% 1.70/2.10 ), apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ),
% 1.70/2.10 apart_point_and_line( Y, line_connecting( X, T ) ) }.
% 1.70/2.10 parent0: (9422) {G1,W22,D3,L6,V4,M6} { ! distinct_points( X, Y ), !
% 1.70/2.10 distinct_points( X, Z ), ! distinct_lines( T, line_connecting( X, Y ) ),
% 1.70/2.10 apart_point_and_line( Z, T ), apart_point_and_line( Z, line_connecting( X
% 1.70/2.10 , Y ) ), apart_point_and_line( X, T ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 X := X
% 1.70/2.10 Y := T
% 1.70/2.10 Z := Y
% 1.70/2.10 T := Z
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 0 ==> 2
% 1.70/2.10 1 ==> 0
% 1.70/2.10 2 ==> 1
% 1.70/2.10 3 ==> 4
% 1.70/2.10 4 ==> 5
% 1.70/2.10 5 ==> 3
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 factor: (9438) {G1,W19,D3,L5,V3,M5} { ! distinct_points( X, Y ), !
% 1.70/2.10 distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.70/2.10 ), apart_point_and_line( Y, Z ), apart_point_and_line( Y,
% 1.70/2.10 line_connecting( X, Y ) ) }.
% 1.70/2.10 parent0[0, 2]: (101) {G1,W22,D3,L6,V4,M3} R(10,6) { ! distinct_points( X, Y
% 1.70/2.10 ), ! distinct_lines( Z, line_connecting( X, T ) ), ! distinct_points( X
% 1.70/2.10 , T ), apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ),
% 1.70/2.10 apart_point_and_line( Y, line_connecting( X, T ) ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 X := X
% 1.70/2.10 Y := Y
% 1.70/2.10 Z := Z
% 1.70/2.10 T := Y
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 resolution: (9445) {G1,W17,D3,L5,V3,M5} { ! distinct_points( X, Y ), !
% 1.70/2.10 distinct_points( X, Y ), ! distinct_lines( Z, line_connecting( X, Y ) ),
% 1.70/2.10 apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ) }.
% 1.70/2.10 parent0[1]: (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), !
% 1.70/2.10 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.70/2.10 parent1[4]: (9438) {G1,W19,D3,L5,V3,M5} { ! distinct_points( X, Y ), !
% 1.70/2.10 distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.70/2.10 ), apart_point_and_line( Y, Z ), apart_point_and_line( Y,
% 1.70/2.10 line_connecting( X, Y ) ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 X := X
% 1.70/2.10 Y := Y
% 1.70/2.10 end
% 1.70/2.10 substitution1:
% 1.70/2.10 X := X
% 1.70/2.10 Y := Y
% 1.70/2.10 Z := Z
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 factor: (9446) {G1,W14,D3,L4,V3,M4} { ! distinct_points( X, Y ), !
% 1.70/2.10 distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.70/2.10 ), apart_point_and_line( Y, Z ) }.
% 1.70/2.10 parent0[0, 1]: (9445) {G1,W17,D3,L5,V3,M5} { ! distinct_points( X, Y ), !
% 1.70/2.10 distinct_points( X, Y ), ! distinct_lines( Z, line_connecting( X, Y ) ),
% 1.70/2.10 apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 X := X
% 1.70/2.10 Y := Y
% 1.70/2.10 Z := Z
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 subsumption: (114) {G2,W14,D3,L4,V3,M2} F(101);r(7) { ! distinct_points( X
% 1.70/2.10 , Y ), ! distinct_lines( Z, line_connecting( X, Y ) ),
% 1.70/2.10 apart_point_and_line( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.70/2.10 parent0: (9446) {G1,W14,D3,L4,V3,M4} { ! distinct_points( X, Y ), !
% 1.70/2.10 distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.70/2.10 ), apart_point_and_line( Y, Z ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 X := X
% 1.70/2.10 Y := Y
% 1.70/2.10 Z := Z
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 0 ==> 0
% 1.70/2.10 1 ==> 1
% 1.70/2.10 2 ==> 3
% 1.70/2.10 3 ==> 2
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 resolution: (9448) {G2,W11,D3,L3,V1,M3} { ! distinct_points( X, skol2 ), !
% 1.70/2.10 distinct_lines( skol3, line_connecting( X, skol2 ) ),
% 1.70/2.10 apart_point_and_line( X, skol3 ) }.
% 1.70/2.10 parent0[0]: (77) {G1,W3,D2,L1,V0,M1} R(42,49) { ! apart_point_and_line(
% 1.70/2.10 skol2, skol3 ) }.
% 1.70/2.10 parent1[2]: (114) {G2,W14,D3,L4,V3,M2} F(101);r(7) { ! distinct_points( X,
% 1.70/2.10 Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line
% 1.70/2.10 ( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 end
% 1.70/2.10 substitution1:
% 1.70/2.10 X := X
% 1.70/2.10 Y := skol2
% 1.70/2.10 Z := skol3
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 subsumption: (1989) {G3,W11,D3,L3,V1,M1} R(114,77) { ! distinct_points( X,
% 1.70/2.10 skol2 ), ! distinct_lines( skol3, line_connecting( X, skol2 ) ),
% 1.70/2.10 apart_point_and_line( X, skol3 ) }.
% 1.70/2.10 parent0: (9448) {G2,W11,D3,L3,V1,M3} { ! distinct_points( X, skol2 ), !
% 1.70/2.10 distinct_lines( skol3, line_connecting( X, skol2 ) ),
% 1.70/2.10 apart_point_and_line( X, skol3 ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 X := X
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 0 ==> 0
% 1.70/2.10 1 ==> 1
% 1.70/2.10 2 ==> 2
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 resolution: (9450) {G2,W8,D3,L2,V0,M2} { ! distinct_points( skol1, skol2 )
% 1.70/2.10 , ! distinct_lines( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10 parent0[0]: (76) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line(
% 1.70/2.10 skol1, skol3 ) }.
% 1.70/2.10 parent1[2]: (1989) {G3,W11,D3,L3,V1,M1} R(114,77) { ! distinct_points( X,
% 1.70/2.10 skol2 ), ! distinct_lines( skol3, line_connecting( X, skol2 ) ),
% 1.70/2.10 apart_point_and_line( X, skol3 ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 end
% 1.70/2.10 substitution1:
% 1.70/2.10 X := skol1
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 resolution: (9451) {G1,W5,D3,L1,V0,M1} { ! distinct_lines( skol3,
% 1.70/2.10 line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10 parent0[0]: (9450) {G2,W8,D3,L2,V0,M2} { ! distinct_points( skol1, skol2 )
% 1.70/2.10 , ! distinct_lines( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10 parent1[0]: (46) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.70/2.10 }.
% 1.70/2.10 substitution0:
% 1.70/2.10 end
% 1.70/2.10 substitution1:
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 subsumption: (9258) {G4,W5,D3,L1,V0,M1} R(1989,76);r(46) { ! distinct_lines
% 1.70/2.10 ( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10 parent0: (9451) {G1,W5,D3,L1,V0,M1} { ! distinct_lines( skol3,
% 1.70/2.10 line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 0 ==> 0
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 resolution: (9452) {G2,W0,D0,L0,V0,M0} { }.
% 1.70/2.10 parent0[0]: (9258) {G4,W5,D3,L1,V0,M1} R(1989,76);r(46) { ! distinct_lines
% 1.70/2.10 ( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10 parent1[0]: (78) {G1,W5,D3,L1,V0,M1} R(39,50) { distinct_lines( skol3,
% 1.70/2.10 line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10 substitution0:
% 1.70/2.10 end
% 1.70/2.10 substitution1:
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 subsumption: (9259) {G5,W0,D0,L0,V0,M0} S(9258);r(78) { }.
% 1.70/2.10 parent0: (9452) {G2,W0,D0,L0,V0,M0} { }.
% 1.70/2.10 substitution0:
% 1.70/2.10 end
% 1.70/2.10 permutation0:
% 1.70/2.10 end
% 1.70/2.10
% 1.70/2.10 Proof check complete!
% 1.70/2.10
% 1.70/2.10 Memory use:
% 1.70/2.10
% 1.70/2.10 space for terms: 131361
% 1.70/2.10 space for clauses: 379646
% 1.70/2.10
% 1.70/2.10
% 1.70/2.10 clauses generated: 83057
% 1.70/2.10 clauses kept: 9260
% 1.70/2.10 clauses selected: 855
% 1.70/2.10 clauses deleted: 7
% 1.70/2.10 clauses inuse deleted: 2
% 1.70/2.10
% 1.70/2.10 subsentry: 1778350
% 1.70/2.10 literals s-matched: 686979
% 1.70/2.10 literals matched: 686482
% 1.70/2.10 full subsumption: 396802
% 1.70/2.10
% 1.70/2.10 checksum: 1262685345
% 1.70/2.10
% 1.70/2.10
% 1.70/2.10 Bliksem ended
%------------------------------------------------------------------------------