%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO194+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.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 02:52:33 EDT 2022
% Result : Theorem 0.73s 1.11s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO194+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n024.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 06:42:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.73/1.11 *** allocated 10000 integers for termspace/termends
% 0.73/1.11 *** allocated 10000 integers for clauses
% 0.73/1.11 *** allocated 10000 integers for justifications
% 0.73/1.11 Bliksem 1.12
% 0.73/1.11
% 0.73/1.11
% 0.73/1.11 Automatic Strategy Selection
% 0.73/1.11
% 0.73/1.11
% 0.73/1.11 Clauses:
% 0.73/1.11
% 0.73/1.11 { ! distinct_points( X, X ) }.
% 0.73/1.11 { ! distinct_lines( X, X ) }.
% 0.73/1.11 { ! convergent_lines( X, X ) }.
% 0.73/1.11 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.73/1.11 ) }.
% 0.73/1.11 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.73/1.11 }.
% 0.73/1.11 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.73/1.11 , Z ) }.
% 0.73/1.11 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.73/1.11 , Y ) ) }.
% 0.73/1.11 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.73/1.11 , Y ) ) }.
% 0.73/1.11 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.73/1.11 , Y ), X ) }.
% 0.73/1.11 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.73/1.11 , Y ), Y ) }.
% 0.73/1.11 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.73/1.11 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 0.73/1.11 apart_point_and_line( Y, T ) }.
% 0.73/1.11 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 0.73/1.11 apart_point_and_line( Z, Y ) }.
% 0.73/1.11 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 0.73/1.11 apart_point_and_line( X, Z ) }.
% 0.73/1.11 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 0.73/1.11 Z ) }.
% 0.73/1.11 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.73/1.11 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.73/1.11 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.73/1.11 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.73/1.11 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.73/1.11 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.73/1.11 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.73/1.11 , convergent_lines( Y, Z ) }.
% 0.73/1.11 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.73/1.11 , unorthogonal_lines( Y, Z ) }.
% 0.73/1.11 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.73/1.11 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.73/1.11 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.73/1.11 }.
% 0.73/1.11 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.73/1.11 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.73/1.11 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.73/1.11 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 0.73/1.11 unorthogonal_lines( Y, T ) }.
% 0.73/1.11 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.73/1.11 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.73/1.11 unorthogonal_lines( X, Y ) }.
% 0.73/1.11 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.73/1.11 unorthogonal_lines( X, Y ) }.
% 0.73/1.11 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.73/1.11 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.73/1.11 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.73/1.11 }.
% 0.73/1.11 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 0.73/1.11 convergent_lines( X, Y ) }.
% 0.73/1.11 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.73/1.11 line_connecting( X, Y ) ) }.
% 0.73/1.11 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 0.73/1.11 intersection_point( X, Y ) ) }.
% 0.73/1.11 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.73/1.11 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.73/1.11 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.73/1.11 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.73/1.11 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.73/1.11 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.73/1.11 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.73/1.11 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.73/1.11 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.73/1.11 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.73/1.11 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.73/1.11 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.73/1.11 { convergent_lines( skol1, skol2 ) }.
% 0.73/1.11 { convergent_lines( skol3, skol2 ) }.
% 0.73/1.11 { convergent_lines( skol1, skol3 ) }.
% 0.73/1.11 { apart_point_and_line( intersection_point( skol1, skol2 ), skol3 ) }.
% 0.73/1.11 { ! apart_point_and_line( intersection_point( skol1, skol3 ), skol2 ) }.
% 0.73/1.11
% 0.73/1.11 percentage equality = 0.000000, percentage horn = 0.627451
% 0.73/1.11 This a non-horn, non-equality problem
% 0.73/1.11
% 0.73/1.11
% 0.73/1.11 Options Used:
% 0.73/1.11
% 0.73/1.11 useres = 1
% 0.73/1.11 useparamod = 0
% 0.73/1.11 useeqrefl = 0
% 0.73/1.11 useeqfact = 0
% 0.73/1.11 usefactor = 1
% 0.73/1.11 usesimpsplitting = 0
% 0.73/1.11 usesimpdemod = 0
% 0.73/1.11 usesimpres = 3
% 0.73/1.11
% 0.73/1.11 resimpinuse = 1000
% 0.73/1.11 resimpclauses = 20000
% 0.73/1.11 substype = standard
% 0.73/1.11 backwardsubs = 1
% 0.73/1.11 selectoldest = 5
% 0.73/1.11
% 0.73/1.11 litorderings [0] = split
% 0.73/1.11 litorderings [1] = liftord
% 0.73/1.11
% 0.73/1.11 termordering = none
% 0.73/1.11
% 0.73/1.11 litapriori = 1
% 0.73/1.11 termapriori = 0
% 0.73/1.11 litaposteriori = 0
% 0.73/1.11 termaposteriori = 0
% 0.73/1.11 demodaposteriori = 0
% 0.73/1.11 ordereqreflfact = 0
% 0.73/1.11
% 0.73/1.11 litselect = none
% 0.73/1.11
% 0.73/1.11 maxweight = 15
% 0.73/1.11 maxdepth = 30000
% 0.73/1.11 maxlength = 115
% 0.73/1.11 maxnrvars = 195
% 0.73/1.11 excuselevel = 1
% 0.73/1.11 increasemaxweight = 1
% 0.73/1.11
% 0.73/1.11 maxselected = 10000000
% 0.73/1.11 maxnrclauses = 10000000
% 0.73/1.11
% 0.73/1.11 showgenerated = 0
% 0.73/1.11 showkept = 0
% 0.73/1.11 showselected = 0
% 0.73/1.11 showdeleted = 0
% 0.73/1.11 showresimp = 1
% 0.73/1.11 showstatus = 2000
% 0.73/1.11
% 0.73/1.11 prologoutput = 0
% 0.73/1.11 nrgoals = 5000000
% 0.73/1.11 totalproof = 1
% 0.73/1.11
% 0.73/1.11 Symbols occurring in the translation:
% 0.73/1.11
% 0.73/1.11 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.73/1.11 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 0.73/1.11 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 0.73/1.11 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.11 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.11 distinct_points [36, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.73/1.11 distinct_lines [37, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.73/1.11 convergent_lines [38, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.73/1.11 line_connecting [41, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.73/1.11 apart_point_and_line [42, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.73/1.11 intersection_point [43, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.73/1.11 parallel_through_point [46, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.73/1.11 unorthogonal_lines [49, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.73/1.11 orthogonal_through_point [52, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.73/1.11 point [54, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.73/1.11 line [55, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.73/1.11 equal_points [56, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.73/1.11 equal_lines [57, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.73/1.11 parallel_lines [58, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.73/1.11 incident_point_and_line [59, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.73/1.11 orthogonal_lines [60, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.73/1.11 alpha1 [61, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.73/1.11 alpha2 [62, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.73/1.11 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.73/1.11 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.73/1.11 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0).
% 0.73/1.11
% 0.73/1.11
% 0.73/1.11 Starting Search:
% 0.73/1.11
% 0.73/1.11
% 0.73/1.11 Bliksems!, er is een bewijs:
% 0.73/1.11 % SZS status Theorem
% 0.73/1.11 % SZS output start Refutation
% 0.73/1.11
% 0.73/1.11 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.73/1.11 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.73/1.11 , ! distinct_lines( X, Y ) }.
% 0.73/1.11 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 0.73/1.11 X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.73/1.11 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 0.73/1.11 , Y ) }.
% 0.73/1.11 (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 0.73/1.11 , X ), Y ) }.
% 0.73/1.11 (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.73/1.11 parallel_through_point( Y, X ) ) }.
% 0.73/1.11 (49) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( intersection_point(
% 0.73/1.11 skol1, skol2 ), skol3 ) }.
% 0.73/1.11 (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 0.73/1.11 ( X, Y ) }.
% 0.73/1.11 (125) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ), !
% 0.73/1.11 distinct_lines( Y, X ) }.
% 0.73/1.11 (145) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.73/1.11 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.73/1.11 (194) {G2,W7,D4,L1,V1,M1} R(145,49) { distinct_lines( skol3,
% 0.73/1.11 parallel_through_point( X, intersection_point( skol1, skol2 ) ) ) }.
% 0.73/1.11 (197) {G3,W7,D4,L1,V1,M1} R(194,125) { convergent_lines(
% 0.73/1.11 parallel_through_point( X, intersection_point( skol1, skol2 ) ), skol3 )
% 0.73/1.11 }.
% 0.73/1.11 (202) {G4,W0,D0,L0,V0,M0} R(197,15) { }.
% 0.73/1.11
% 0.73/1.11
% 0.73/1.11 % SZS output end Refutation
% 0.73/1.11 found a proof!
% 0.73/1.11
% 0.73/1.11 *** allocated 15000 integers for clauses
% 0.73/1.11
% 0.73/1.11 Unprocessed initial clauses:
% 0.73/1.11
% 0.73/1.11 (204) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.73/1.11 (205) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.73/1.11 (206) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.73/1.11 (207) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.73/1.11 , Z ), distinct_points( Y, Z ) }.
% 0.73/1.11 (208) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.73/1.11 ), distinct_lines( Y, Z ) }.
% 0.73/1.11 (209) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines(
% 0.73/1.11 X, Z ), convergent_lines( Y, Z ) }.
% 0.73/1.11 (210) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.73/1.11 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.73/1.11 (211) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.73/1.11 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.73/1.11 (212) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.73/1.11 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.73/1.11 (213) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.73/1.11 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.73/1.11 (214) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines(
% 0.73/1.11 Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 0.73/1.11 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.73/1.11 (215) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.73/1.11 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.73/1.11 (216) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ), distinct_lines
% 0.73/1.11 ( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.73/1.11 (217) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.73/1.11 , Z ), convergent_lines( X, Z ) }.
% 0.73/1.11 (218) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 0.73/1.11 , Y ) }.
% 0.73/1.11 (219) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 0.73/1.11 , X ), Y ) }.
% 0.73/1.11 (220) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.73/1.11 parallel_through_point( Y, X ) ) }.
% 0.73/1.11 (221) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 0.73/1.11 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.73/1.11 convergent_lines( X, Y ) }.
% 0.73/1.11 (222) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.73/1.11 X, Y ) }.
% 0.73/1.11 (223) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.73/1.11 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.73/1.11 (224) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.73/1.11 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.73/1.11 }.
% 0.73/1.11 (225) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.73/1.11 (226) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.73/1.11 }.
% 0.73/1.11 (227) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 0.73/1.11 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.73/1.11 (228) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines( orthogonal_through_point
% 0.73/1.11 ( Y, X ), Y ) }.
% 0.73/1.11 (229) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.73/1.11 orthogonal_through_point( Y, X ) ) }.
% 0.73/1.11 (230) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 0.73/1.11 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.73/1.11 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.73/1.11 (231) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.73/1.11 X, Y ) }.
% 0.73/1.11 (232) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 0.73/1.11 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.73/1.11 (233) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ), !
% 0.73/1.11 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.73/1.11 (234) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.73/1.11 (235) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.73/1.11 }.
% 0.73/1.11 (236) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 0.73/1.11 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.73/1.11 (237) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ), unorthogonal_lines
% 0.73/1.11 ( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.73/1.11 (238) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.73/1.11 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.73/1.11 (239) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 0.73/1.11 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.73/1.11 (240) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.73/1.11 parallel_through_point( X, Y ) ) }.
% 0.73/1.11 (241) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.73/1.11 orthogonal_through_point( X, Y ) ) }.
% 0.73/1.11 (242) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X,
% 0.73/1.11 Y ) }.
% 0.73/1.11 (243) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 0.73/1.11 }.
% 0.73/1.11 (244) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.73/1.11 ) }.
% 0.73/1.11 (245) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.73/1.11 }.
% 0.73/1.11 (246) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines(
% 0.73/1.11 X, Y ) }.
% 0.73/1.11 (247) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X, Y
% 0.73/1.11 ) }.
% 0.73/1.11 (248) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 0.73/1.11 apart_point_and_line( X, Y ) }.
% 0.73/1.11 (249) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.73/1.11 incident_point_and_line( X, Y ) }.
% 0.73/1.11 (250) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.73/1.11 unorthogonal_lines( X, Y ) }.
% 0.73/1.11 (251) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines(
% 0.73/1.11 X, Y ) }.
% 0.73/1.11 (252) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 0.73/1.11 (253) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol2 ) }.
% 0.73/1.11 (254) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol3 ) }.
% 0.73/1.11 (255) {G0,W5,D3,L1,V0,M1} { apart_point_and_line( intersection_point(
% 0.73/1.11 skol1, skol2 ), skol3 ) }.
% 0.73/1.11 (256) {G0,W5,D3,L1,V0,M1} { ! apart_point_and_line( intersection_point(
% 0.73/1.11 skol1, skol3 ), skol2 ) }.
% 0.73/1.11
% 0.73/1.11
% 0.73/1.11 Total Proof:
% 0.73/1.11
% 0.73/1.11 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.73/1.11 parent0: (205) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.73/1.11 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.73/1.11 parent0: (208) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 0.73/1.11 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 Z := Z
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 2
% 0.73/1.11 1 ==> 0
% 0.73/1.11 2 ==> 1
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.73/1.11 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.73/1.11 parent0: (216) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.73/1.11 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 Z := Z
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 2
% 0.73/1.11 1 ==> 0
% 0.73/1.11 2 ==> 1
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.73/1.11 distinct_lines( X, Y ) }.
% 0.73/1.11 parent0: (218) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 0.73/1.11 convergent_lines( X, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 1
% 0.73/1.11 1 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.73/1.11 parallel_through_point( Y, X ), Y ) }.
% 0.73/1.11 parent0: (219) {G0,W5,D3,L1,V2,M1} { ! convergent_lines(
% 0.73/1.11 parallel_through_point( Y, X ), Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.73/1.11 parallel_through_point( Y, X ) ) }.
% 0.73/1.11 parent0: (220) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.73/1.11 parallel_through_point( Y, X ) ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (49) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line(
% 0.73/1.11 intersection_point( skol1, skol2 ), skol3 ) }.
% 0.73/1.11 parent0: (255) {G0,W5,D3,L1,V0,M1} { apart_point_and_line(
% 0.73/1.11 intersection_point( skol1, skol2 ), skol3 ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (310) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.73/1.11 distinct_lines( X, Y ) }.
% 0.73/1.11 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.73/1.11 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.73/1.11 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 Z := X
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.73/1.11 distinct_lines( X, Y ) }.
% 0.73/1.11 parent0: (310) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.73/1.11 distinct_lines( X, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := Y
% 0.73/1.11 Y := X
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 1
% 0.73/1.11 1 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (312) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.73/1.11 distinct_lines( Y, X ) }.
% 0.73/1.11 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.73/1.11 distinct_lines( X, Y ) }.
% 0.73/1.11 parent1[1]: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.73/1.11 distinct_lines( X, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (125) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y )
% 0.73/1.11 , ! distinct_lines( Y, X ) }.
% 0.73/1.11 parent0: (312) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.73/1.11 distinct_lines( Y, X ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 1 ==> 1
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (313) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.73/1.11 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.73/1.11 parent0[0]: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.73/1.11 parallel_through_point( Y, X ) ) }.
% 0.73/1.11 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.73/1.11 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Z
% 0.73/1.11 Z := parallel_through_point( Y, X )
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (145) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.73/1.11 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.73/1.11 parent0: (313) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.73/1.11 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := Z
% 0.73/1.11 Y := Y
% 0.73/1.11 Z := X
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 1 ==> 1
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (314) {G1,W7,D4,L1,V1,M1} { distinct_lines( skol3,
% 0.73/1.11 parallel_through_point( X, intersection_point( skol1, skol2 ) ) ) }.
% 0.73/1.11 parent0[1]: (145) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.73/1.11 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.73/1.11 parent1[0]: (49) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line(
% 0.73/1.11 intersection_point( skol1, skol2 ), skol3 ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := skol3
% 0.73/1.11 Y := X
% 0.73/1.11 Z := intersection_point( skol1, skol2 )
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (194) {G2,W7,D4,L1,V1,M1} R(145,49) { distinct_lines( skol3,
% 0.73/1.11 parallel_through_point( X, intersection_point( skol1, skol2 ) ) ) }.
% 0.73/1.11 parent0: (314) {G1,W7,D4,L1,V1,M1} { distinct_lines( skol3,
% 0.73/1.11 parallel_through_point( X, intersection_point( skol1, skol2 ) ) ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (315) {G3,W7,D4,L1,V1,M1} { convergent_lines(
% 0.73/1.11 parallel_through_point( X, intersection_point( skol1, skol2 ) ), skol3 )
% 0.73/1.11 }.
% 0.73/1.11 parent0[1]: (125) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ),
% 0.73/1.11 ! distinct_lines( Y, X ) }.
% 0.73/1.11 parent1[0]: (194) {G2,W7,D4,L1,V1,M1} R(145,49) { distinct_lines( skol3,
% 0.73/1.11 parallel_through_point( X, intersection_point( skol1, skol2 ) ) ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := parallel_through_point( X, intersection_point( skol1, skol2 ) )
% 0.73/1.11 Y := skol3
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := X
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (197) {G3,W7,D4,L1,V1,M1} R(194,125) { convergent_lines(
% 0.73/1.11 parallel_through_point( X, intersection_point( skol1, skol2 ) ), skol3 )
% 0.73/1.11 }.
% 0.73/1.11 parent0: (315) {G3,W7,D4,L1,V1,M1} { convergent_lines(
% 0.73/1.11 parallel_through_point( X, intersection_point( skol1, skol2 ) ), skol3 )
% 0.73/1.11 }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (316) {G1,W0,D0,L0,V0,M0} { }.
% 0.73/1.11 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.73/1.11 parallel_through_point( Y, X ), Y ) }.
% 0.73/1.11 parent1[0]: (197) {G3,W7,D4,L1,V1,M1} R(194,125) { convergent_lines(
% 0.73/1.11 parallel_through_point( X, intersection_point( skol1, skol2 ) ), skol3 )
% 0.73/1.11 }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := intersection_point( skol1, skol2 )
% 0.73/1.11 Y := skol3
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := skol3
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (202) {G4,W0,D0,L0,V0,M0} R(197,15) { }.
% 0.73/1.11 parent0: (316) {G1,W0,D0,L0,V0,M0} { }.
% 0.73/1.11 substitution0:
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 Proof check complete!
% 0.73/1.11
% 0.73/1.11 Memory use:
% 0.73/1.11
% 0.73/1.11 space for terms: 3535
% 0.73/1.11 space for clauses: 9316
% 0.73/1.11
% 0.73/1.11
% 0.73/1.11 clauses generated: 531
% 0.73/1.11 clauses kept: 203
% 0.73/1.11 clauses selected: 83
% 0.73/1.11 clauses deleted: 0
% 0.73/1.11 clauses inuse deleted: 0
% 0.73/1.11
% 0.73/1.11 subsentry: 840
% 0.73/1.11 literals s-matched: 662
% 0.73/1.11 literals matched: 637
% 0.73/1.11 full subsumption: 176
% 0.73/1.11
% 0.73/1.11 checksum: 2084928953
% 0.73/1.11
% 0.73/1.11
% 0.73/1.11 Bliksem ended
%------------------------------------------------------------------------------