%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO194+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.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 24.71s 25.12s
% Output : Refutation 24.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : GEO194+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.09 % Command : bliksem %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % DateTime : Sat Jun 18 00:43:46 EDT 2022
% 0.09/0.28 % CPUTime :
% 24.71/25.12 *** allocated 10000 integers for termspace/termends
% 24.71/25.12 *** allocated 10000 integers for clauses
% 24.71/25.12 *** allocated 10000 integers for justifications
% 24.71/25.12 Bliksem 1.12
% 24.71/25.12
% 24.71/25.12
% 24.71/25.12 Automatic Strategy Selection
% 24.71/25.12
% 24.71/25.12
% 24.71/25.12 Clauses:
% 24.71/25.12
% 24.71/25.12 { ! distinct_points( X, X ) }.
% 24.71/25.12 { ! distinct_lines( X, X ) }.
% 24.71/25.12 { ! convergent_lines( X, X ) }.
% 24.71/25.12 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 24.71/25.12 ) }.
% 24.71/25.12 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 24.71/25.12 }.
% 24.71/25.12 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 24.71/25.12 , Z ) }.
% 24.71/25.12 { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 24.71/25.12 , Y ) ), distinct_points( Z, X ) }.
% 24.71/25.12 { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 24.71/25.12 , Y ) ), distinct_points( Z, Y ) }.
% 24.71/25.12 { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, X ),
% 24.71/25.12 distinct_points( Z, intersection_point( X, Y ) ) }.
% 24.71/25.12 { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, Y ),
% 24.71/25.12 distinct_points( Z, intersection_point( X, Y ) ) }.
% 24.71/25.12 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 24.71/25.12 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 24.71/25.12 apart_point_and_line( Y, T ) }.
% 24.71/25.12 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 24.71/25.12 apart_point_and_line( Z, Y ) }.
% 24.71/25.12 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 24.71/25.12 apart_point_and_line( X, Z ) }.
% 24.71/25.12 { ! convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 24.71/25.12 { convergent_lines( skol1, skol2 ) }.
% 24.71/25.12 { convergent_lines( skol3, skol2 ) }.
% 24.71/25.12 { convergent_lines( skol1, skol3 ) }.
% 24.71/25.12 { apart_point_and_line( intersection_point( skol1, skol2 ), skol3 ) }.
% 24.71/25.12 { ! apart_point_and_line( intersection_point( skol1, skol3 ), skol2 ) }.
% 24.71/25.12
% 24.71/25.12 percentage equality = 0.000000, percentage horn = 0.684211
% 24.71/25.12 This a non-horn, non-equality problem
% 24.71/25.12
% 24.71/25.12
% 24.71/25.12 Options Used:
% 24.71/25.12
% 24.71/25.12 useres = 1
% 24.71/25.12 useparamod = 0
% 24.71/25.12 useeqrefl = 0
% 24.71/25.12 useeqfact = 0
% 24.71/25.12 usefactor = 1
% 24.71/25.12 usesimpsplitting = 0
% 24.71/25.12 usesimpdemod = 0
% 24.71/25.12 usesimpres = 3
% 24.71/25.12
% 24.71/25.12 resimpinuse = 1000
% 24.71/25.12 resimpclauses = 20000
% 24.71/25.12 substype = standard
% 24.71/25.12 backwardsubs = 1
% 24.71/25.12 selectoldest = 5
% 24.71/25.12
% 24.71/25.12 litorderings [0] = split
% 24.71/25.12 litorderings [1] = liftord
% 24.71/25.12
% 24.71/25.12 termordering = none
% 24.71/25.12
% 24.71/25.12 litapriori = 1
% 24.71/25.12 termapriori = 0
% 24.71/25.12 litaposteriori = 0
% 24.71/25.12 termaposteriori = 0
% 24.71/25.12 demodaposteriori = 0
% 24.71/25.12 ordereqreflfact = 0
% 24.71/25.12
% 24.71/25.12 litselect = none
% 24.71/25.12
% 24.71/25.12 maxweight = 15
% 24.71/25.12 maxdepth = 30000
% 24.71/25.12 maxlength = 115
% 24.71/25.12 maxnrvars = 195
% 24.71/25.12 excuselevel = 1
% 24.71/25.12 increasemaxweight = 1
% 24.71/25.12
% 24.71/25.12 maxselected = 10000000
% 24.71/25.12 maxnrclauses = 10000000
% 24.71/25.12
% 24.71/25.12 showgenerated = 0
% 24.71/25.12 showkept = 0
% 24.71/25.12 showselected = 0
% 24.71/25.12 showdeleted = 0
% 24.71/25.12 showresimp = 1
% 24.71/25.12 showstatus = 2000
% 24.71/25.12
% 24.71/25.12 prologoutput = 0
% 24.71/25.12 nrgoals = 5000000
% 24.71/25.12 totalproof = 1
% 24.71/25.12
% 24.71/25.12 Symbols occurring in the translation:
% 24.71/25.12
% 24.71/25.12 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 24.71/25.12 . [1, 2] (w:1, o:19, a:1, s:1, b:0),
% 24.71/25.12 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 24.71/25.12 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 24.71/25.12 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 24.71/25.12 distinct_points [36, 2] (w:1, o:44, a:1, s:1, b:0),
% 24.71/25.12 distinct_lines [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 24.71/25.12 convergent_lines [38, 2] (w:1, o:43, a:1, s:1, b:0),
% 24.71/25.12 line_connecting [41, 2] (w:1, o:46, a:1, s:1, b:0),
% 24.71/25.12 apart_point_and_line [42, 2] (w:1, o:47, a:1, s:1, b:0),
% 24.71/25.12 intersection_point [43, 2] (w:1, o:48, a:1, s:1, b:0),
% 24.71/25.12 skol1 [46, 0] (w:1, o:11, a:1, s:1, b:0),
% 24.71/25.12 skol2 [47, 0] (w:1, o:12, a:1, s:1, b:0),
% 24.71/25.12 skol3 [48, 0] (w:1, o:13, a:1, s:1, b:0).
% 24.71/25.12
% 24.71/25.12
% 24.71/25.12 Starting Search:
% 24.71/25.12
% 24.71/25.12 *** allocated 15000 integers for clauses
% 24.71/25.12 *** allocated 22500 integers for clauses
% 24.71/25.12 *** allocated 33750 integers for clauses
% 24.71/25.12 *** allocated 15000 integers for termspace/termends
% 24.71/25.12 Resimplifying inuse:
% 24.71/25.12 Done
% 24.71/25.12
% 24.71/25.12 Failed to find proof!
% 24.71/25.12 maxweight = 15
% 24.71/25.12 maxnrclauses = 10000000
% 24.71/25.12 Generated: 121534
% 24.71/25.12 Kept: 885
% 24.71/25.12
% 24.71/25.12
% 24.71/25.12 The strategy used was not complete!
% 24.71/25.12
% 24.71/25.12 Increased maxweight to 16
% 24.71/25.12
% 24.71/25.12 Starting Search:
% 24.71/25.12
% 24.71/25.12 *** allocated 50625 integers for clauses
% 24.71/25.12 Resimplifying inuse:
% 24.71/25.12 Done
% 24.71/25.12
% 24.71/25.12 *** allocated 22500 integers for termspace/termends
% 24.71/25.12 Resimplifying inuse:
% 24.71/25.12 Done
% 24.71/25.12
% 24.71/25.12 Failed to find proof!
% 24.71/25.12 maxweight = 16
% 24.71/25.12 maxnrclauses = 10000000
% 24.71/25.12 Generated: 396916
% 24.71/25.12 Kept: 1241
% 24.71/25.12
% 24.71/25.12
% 24.71/25.12 The strategy used was not complete!
% 24.71/25.12
% 24.71/25.12 Increased maxweight to 17
% 24.71/25.12
% 24.71/25.12 Starting Search:
% 24.71/25.12
% 24.71/25.12 Resimplifying inuse:
% 24.71/25.12 Done
% 24.71/25.12
% 24.71/25.12 *** allocated 75937 integers for clauses
% 24.71/25.12 *** allocated 33750 integers for termspace/termends
% 24.71/25.12 Resimplifying inuse:
% 24.71/25.12 Done
% 24.71/25.12
% 24.71/25.12 Failed to find proof!
% 24.71/25.12 maxweight = 17
% 24.71/25.12 maxnrclauses = 10000000
% 24.71/25.12 Generated: 513084
% 24.71/25.12 Kept: 1597
% 24.71/25.12
% 24.71/25.12
% 24.71/25.12 The strategy used was not complete!
% 24.71/25.12
% 24.71/25.12 Increased maxweight to 18
% 24.71/25.12
% 24.71/25.12 Starting Search:
% 24.71/25.12
% 24.71/25.12 Resimplifying inuse:
% 24.71/25.12 Done
% 24.71/25.12
% 24.71/25.12
% 24.71/25.12 Intermediate Status:
% 24.71/25.12 Generated: 126064
% 24.71/25.12 Kept: 2051
% 24.71/25.12 Inuse: 823
% 24.71/25.12 Deleted: 2
% 24.71/25.12 Deletedinuse: 0
% 24.71/25.12
% 24.71/25.12 Resimplifying inuse:
% 24.71/25.12 Done
% 24.71/25.12
% 24.71/25.12 *** allocated 50625 integers for termspace/termends
% 24.71/25.12 *** allocated 113905 integers for clauses
% 24.71/25.12
% 24.71/25.12 Bliksems!, er is een bewijs:
% 24.71/25.12 % SZS status Theorem
% 24.71/25.12 % SZS output start Refutation
% 24.71/25.12
% 24.71/25.12 (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 24.71/25.12 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 24.71/25.12 (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), distinct_points( Y, Z
% 24.71/25.12 ), ! distinct_points( X, Y ) }.
% 24.71/25.12 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 24.71/25.12 , ! distinct_lines( X, Y ) }.
% 24.71/25.12 (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), distinct_points( Z
% 24.71/25.12 , intersection_point( X, Y ) ), ! apart_point_and_line( Z, X ) }.
% 24.71/25.12 (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), distinct_points( Z
% 24.71/25.12 , intersection_point( X, Y ) ), ! apart_point_and_line( Z, Y ) }.
% 24.71/25.12 (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines(
% 24.71/25.12 Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 24.71/25.12 apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 24.71/25.12 (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), apart_point_and_line
% 24.71/25.12 ( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 24.71/25.12 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 24.71/25.12 X, Z ), ! apart_point_and_line( X, Y ) }.
% 24.71/25.12 (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), distinct_lines( X
% 24.71/25.12 , Y ) }.
% 24.71/25.12 (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 ) }.
% 24.71/25.12 (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol2 ) }.
% 24.71/25.12 (16) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol3 ) }.
% 24.71/25.12 (17) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( intersection_point(
% 24.71/25.12 skol1, skol2 ), skol3 ) }.
% 24.71/25.12 (18) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( intersection_point(
% 24.71/25.12 skol1, skol3 ), skol2 ) }.
% 24.71/25.12 (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 24.71/25.12 distinct_points( X, Y ) }.
% 24.71/25.12 (22) {G2,W9,D2,L3,V3,M3} R(21,3) { distinct_points( Z, X ), !
% 24.71/25.12 distinct_points( Y, Z ), distinct_points( X, Y ) }.
% 24.71/25.12 (26) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 24.71/25.12 ( X, Y ) }.
% 24.71/25.12 (29) {G2,W6,D2,L2,V2,M1} R(13,26) { ! convergent_lines( X, Y ),
% 24.71/25.12 distinct_lines( Y, X ) }.
% 24.71/25.12 (60) {G1,W10,D3,L2,V1,M1} R(8,17) { ! convergent_lines( skol3, X ),
% 24.71/25.12 distinct_points( intersection_point( skol1, skol2 ), intersection_point(
% 24.71/25.12 skol3, X ) ) }.
% 24.71/25.12 (106) {G1,W19,D3,L5,V2,M3} R(10,18) { ! distinct_points( intersection_point
% 24.71/25.12 ( skol1, skol3 ), X ), ! distinct_lines( Y, skol2 ), apart_point_and_line
% 24.71/25.12 ( X, skol2 ), apart_point_and_line( intersection_point( skol1, skol3 ), Y
% 24.71/25.12 ), apart_point_and_line( X, Y ) }.
% 24.71/25.12 (109) {G1,W19,D3,L5,V2,M3} R(10,18) { ! distinct_points( intersection_point
% 24.71/25.12 ( skol1, skol3 ), X ), ! distinct_lines( skol2, Y ), apart_point_and_line
% 24.71/25.12 ( X, skol2 ), apart_point_and_line( X, Y ), apart_point_and_line(
% 24.71/25.12 intersection_point( skol1, skol3 ), Y ) }.
% 24.71/25.12 (127) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y ), !
% 24.71/25.12 convergent_lines( T, Z ), distinct_points( Y, intersection_point( T, Z )
% 24.71/25.12 ), ! apart_point_and_line( X, Z ) }.
% 24.71/25.12 (128) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y ), !
% 24.71/25.12 convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z, T )
% 24.71/25.12 ), ! apart_point_and_line( X, Z ) }.
% 24.71/25.12 (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X, Y ), !
% 24.71/25.12 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.71/25.12 (136) {G2,W8,D3,L2,V2,M1} F(127);r(0) { ! convergent_lines( X, Y ), !
% 24.71/25.12 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.71/25.12 (151) {G1,W8,D3,L2,V1,M1} R(12,17) { distinct_lines( skol3, X ),
% 24.71/25.12 apart_point_and_line( intersection_point( skol1, skol2 ), X ) }.
% 24.71/25.12 (157) {G3,W3,D2,L1,V0,M1} R(151,136);r(14) { distinct_lines( skol3, skol2 )
% 24.71/25.12 }.
% 24.71/25.12 (211) {G3,W9,D2,L3,V3,M3} R(22,21) { distinct_points( Z, X ),
% 24.71/25.12 distinct_points( Z, Y ), ! distinct_points( X, Y ) }.
% 24.71/25.12 (468) {G4,W13,D3,L3,V2,M2} R(60,211) { ! convergent_lines( skol3, X ),
% 24.71/25.12 distinct_points( Y, intersection_point( skol3, X ) ), distinct_points( Y
% 24.71/25.12 , intersection_point( skol1, skol2 ) ) }.
% 24.71/25.12 (1458) {G4,W14,D3,L4,V1,M1} R(106,136);r(157) { ! distinct_points(
% 24.71/25.12 intersection_point( skol1, skol3 ), X ), apart_point_and_line( X, skol2 )
% 24.71/25.12 , ! convergent_lines( skol1, skol3 ), apart_point_and_line( X, skol3 )
% 24.71/25.12 }.
% 24.71/25.12 (1506) {G3,W14,D3,L4,V1,M1} R(109,135);r(16) { ! distinct_points(
% 24.71/25.12 intersection_point( skol1, skol3 ), X ), ! distinct_lines( skol2, skol1 )
% 24.71/25.12 , apart_point_and_line( X, skol1 ), apart_point_and_line( X, skol2 ) }.
% 24.71/25.12 (1647) {G4,W18,D3,L4,V1,M1} R(1506,136) { ! distinct_points(
% 24.71/25.12 intersection_point( skol1, skol3 ), intersection_point( X, skol2 ) ), !
% 24.71/25.12 distinct_lines( skol2, skol1 ), ! convergent_lines( X, skol2 ),
% 24.71/25.12 apart_point_and_line( intersection_point( X, skol2 ), skol1 ) }.
% 24.71/25.12 (1712) {G5,W11,D3,L3,V1,M1} S(1458);r(16) { ! distinct_points(
% 24.71/25.12 intersection_point( skol1, skol3 ), X ), apart_point_and_line( X, skol2 )
% 24.71/25.12 , apart_point_and_line( X, skol3 ) }.
% 24.71/25.12 (1738) {G6,W15,D3,L3,V1,M1} R(1712,135) { ! distinct_points(
% 24.71/25.12 intersection_point( skol1, skol3 ), intersection_point( skol3, X ) ), !
% 24.71/25.12 convergent_lines( skol3, X ), apart_point_and_line( intersection_point(
% 24.71/25.12 skol3, X ), skol2 ) }.
% 24.71/25.12 (1766) {G7,W7,D3,L1,V0,M1} R(1738,136);f;r(15) { ! distinct_points(
% 24.71/25.12 intersection_point( skol1, skol3 ), intersection_point( skol3, skol2 ) )
% 24.71/25.12 }.
% 24.71/25.12 (1835) {G8,W7,D3,L1,V0,M1} R(1766,468);r(15) { distinct_points(
% 24.71/25.12 intersection_point( skol1, skol3 ), intersection_point( skol1, skol2 ) )
% 24.71/25.12 }.
% 24.71/25.12 (2481) {G9,W6,D2,L2,V0,M1} R(1647,135);f;r(1835) { ! convergent_lines(
% 24.71/25.12 skol1, skol2 ), ! distinct_lines( skol2, skol1 ) }.
% 24.71/25.12 (2482) {G10,W3,D2,L1,V0,M1} S(2481);r(14) { ! distinct_lines( skol2, skol1
% 24.71/25.12 ) }.
% 24.71/25.12 (3005) {G11,W0,D0,L0,V0,M0} R(2482,29);r(14) { }.
% 24.71/25.12
% 24.71/25.12
% 24.71/25.12 % SZS output end Refutation
% 24.71/25.12 found a proof!
% 24.71/25.12
% 24.71/25.12
% 24.71/25.12 Unprocessed initial clauses:
% 24.71/25.12
% 24.71/25.12 (3007) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 24.71/25.12 (3008) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 24.71/25.12 (3009) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 24.71/25.12 (3010) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 24.71/25.12 , Z ), distinct_points( Y, Z ) }.
% 24.71/25.12 (3011) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 24.71/25.12 Z ), distinct_lines( Y, Z ) }.
% 24.71/25.12 (3012) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 24.71/25.12 ( X, Z ), convergent_lines( Y, Z ) }.
% 24.71/25.12 (3013) {G0,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ), !
% 24.71/25.12 apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, X
% 24.71/25.12 ) }.
% 24.71/25.12 (3014) {G0,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ), !
% 24.71/25.12 apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, Y
% 24.71/25.12 ) }.
% 24.71/25.12 (3015) {G0,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ), !
% 24.71/25.12 apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X,
% 24.71/25.12 Y ) ) }.
% 24.71/25.12 (3016) {G0,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ), !
% 24.71/25.12 apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X,
% 24.71/25.12 Y ) ) }.
% 24.71/25.12 (3017) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 24.71/25.12 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 24.71/25.12 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 24.71/25.12 (3018) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 24.71/25.12 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 24.71/25.12 (3019) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 24.71/25.12 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 24.71/25.12 (3020) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ), distinct_lines( X
% 24.71/25.12 , Y ) }.
% 24.71/25.12 (3021) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 24.71/25.12 (3022) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol2 ) }.
% 24.71/25.12 (3023) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol3 ) }.
% 24.71/25.12 (3024) {G0,W5,D3,L1,V0,M1} { apart_point_and_line( intersection_point(
% 24.71/25.12 skol1, skol2 ), skol3 ) }.
% 24.71/25.12 (3025) {G0,W5,D3,L1,V0,M1} { ! apart_point_and_line( intersection_point(
% 24.71/25.12 skol1, skol3 ), skol2 ) }.
% 24.71/25.12
% 24.71/25.12
% 24.71/25.12 Total Proof:
% 24.71/25.12
% 24.71/25.12 subsumption: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 24.71/25.12 parent0: (3007) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := X
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 0
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 24.71/25.12 parent0: (3008) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := X
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 0
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ),
% 24.71/25.12 distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 24.71/25.12 parent0: (3010) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ),
% 24.71/25.12 distinct_points( X, Z ), distinct_points( Y, Z ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := X
% 24.71/25.12 Y := Y
% 24.71/25.12 Z := Z
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 2
% 24.71/25.12 1 ==> 0
% 24.71/25.12 2 ==> 1
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 24.71/25.12 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 24.71/25.12 parent0: (3011) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 24.71/25.12 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := X
% 24.71/25.12 Y := Y
% 24.71/25.12 Z := Z
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 2
% 24.71/25.12 1 ==> 0
% 24.71/25.12 2 ==> 1
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 24.71/25.12 distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 24.71/25.12 ( Z, X ) }.
% 24.71/25.12 parent0: (3015) {G0,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ), !
% 24.71/25.12 apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X,
% 24.71/25.12 Y ) ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := X
% 24.71/25.12 Y := Y
% 24.71/25.12 Z := Z
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 0
% 24.71/25.12 1 ==> 2
% 24.71/25.12 2 ==> 1
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 24.71/25.12 distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 24.71/25.12 ( Z, Y ) }.
% 24.71/25.12 parent0: (3016) {G0,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ), !
% 24.71/25.12 apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X,
% 24.71/25.12 Y ) ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := X
% 24.71/25.12 Y := Y
% 24.71/25.12 Z := Z
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 0
% 24.71/25.12 1 ==> 2
% 24.71/25.12 2 ==> 1
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 24.71/25.12 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 24.71/25.12 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 24.71/25.12 apart_point_and_line( X, Z ) }.
% 24.71/25.12 parent0: (3017) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), !
% 24.71/25.12 distinct_lines( Z, T ), apart_point_and_line( X, Z ),
% 24.71/25.12 apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 24.71/25.12 apart_point_and_line( Y, T ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := X
% 24.71/25.12 Y := Y
% 24.71/25.12 Z := Z
% 24.71/25.12 T := T
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 0
% 24.71/25.12 1 ==> 1
% 24.71/25.12 2 ==> 5
% 24.71/25.12 3 ==> 2
% 24.71/25.12 4 ==> 3
% 24.71/25.12 5 ==> 4
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 24.71/25.12 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 24.71/25.12 parent0: (3018) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 24.71/25.12 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := X
% 24.71/25.12 Y := Y
% 24.71/25.12 Z := Z
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 2
% 24.71/25.12 1 ==> 0
% 24.71/25.12 2 ==> 1
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 24.71/25.12 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 24.71/25.12 parent0: (3019) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 24.71/25.12 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := X
% 24.71/25.12 Y := Y
% 24.71/25.12 Z := Z
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 2
% 24.71/25.12 1 ==> 0
% 24.71/25.12 2 ==> 1
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ),
% 24.71/25.12 distinct_lines( X, Y ) }.
% 24.71/25.12 parent0: (3020) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 24.71/25.12 distinct_lines( X, Y ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := X
% 24.71/25.12 Y := Y
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 0
% 24.71/25.12 1 ==> 1
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 24.71/25.12 }.
% 24.71/25.12 parent0: (3021) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 0
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol2 )
% 24.71/25.12 }.
% 24.71/25.12 parent0: (3022) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol2 ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 0
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (16) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol3 )
% 24.71/25.12 }.
% 24.71/25.12 parent0: (3023) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol3 ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 0
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (17) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line(
% 24.71/25.12 intersection_point( skol1, skol2 ), skol3 ) }.
% 24.71/25.12 parent0: (3024) {G0,W5,D3,L1,V0,M1} { apart_point_and_line(
% 24.71/25.12 intersection_point( skol1, skol2 ), skol3 ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 0
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (18) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line(
% 24.71/25.12 intersection_point( skol1, skol3 ), skol2 ) }.
% 24.71/25.12 parent0: (3025) {G0,W5,D3,L1,V0,M1} { ! apart_point_and_line(
% 24.71/25.12 intersection_point( skol1, skol3 ), skol2 ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 0
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 resolution: (3116) {G1,W6,D2,L2,V2,M2} { distinct_points( Y, X ), !
% 24.71/25.12 distinct_points( X, Y ) }.
% 24.71/25.12 parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 24.71/25.12 parent1[0]: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ),
% 24.71/25.12 distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := X
% 24.71/25.12 end
% 24.71/25.12 substitution1:
% 24.71/25.12 X := X
% 24.71/25.12 Y := Y
% 24.71/25.12 Z := X
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 24.71/25.12 distinct_points( X, Y ) }.
% 24.71/25.12 parent0: (3116) {G1,W6,D2,L2,V2,M2} { distinct_points( Y, X ), !
% 24.71/25.12 distinct_points( X, Y ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := Y
% 24.71/25.12 Y := X
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 1
% 24.71/25.12 1 ==> 0
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 resolution: (3118) {G1,W9,D2,L3,V3,M3} { distinct_points( Y, X ),
% 24.71/25.12 distinct_points( Z, Y ), ! distinct_points( X, Z ) }.
% 24.71/25.12 parent0[0]: (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 24.71/25.12 distinct_points( X, Y ) }.
% 24.71/25.12 parent1[0]: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ),
% 24.71/25.12 distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := Y
% 24.71/25.12 Y := X
% 24.71/25.12 end
% 24.71/25.12 substitution1:
% 24.71/25.12 X := X
% 24.71/25.12 Y := Z
% 24.71/25.12 Z := Y
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (22) {G2,W9,D2,L3,V3,M3} R(21,3) { distinct_points( Z, X ), !
% 24.71/25.12 distinct_points( Y, Z ), distinct_points( X, Y ) }.
% 24.71/25.12 parent0: (3118) {G1,W9,D2,L3,V3,M3} { distinct_points( Y, X ),
% 24.71/25.12 distinct_points( Z, Y ), ! distinct_points( X, Z ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := Y
% 24.71/25.12 Y := X
% 24.71/25.12 Z := Z
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 2
% 24.71/25.12 1 ==> 0
% 24.71/25.12 2 ==> 1
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 resolution: (3121) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 24.71/25.12 distinct_lines( X, Y ) }.
% 24.71/25.12 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 24.71/25.12 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 24.71/25.12 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := X
% 24.71/25.12 end
% 24.71/25.12 substitution1:
% 24.71/25.12 X := X
% 24.71/25.12 Y := Y
% 24.71/25.12 Z := X
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (26) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 24.71/25.12 distinct_lines( X, Y ) }.
% 24.71/25.12 parent0: (3121) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 24.71/25.12 distinct_lines( X, Y ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := Y
% 24.71/25.12 Y := X
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 1
% 24.71/25.12 1 ==> 0
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 resolution: (3123) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 24.71/25.12 convergent_lines( X, Y ) }.
% 24.71/25.12 parent0[0]: (26) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 24.71/25.12 distinct_lines( X, Y ) }.
% 24.71/25.12 parent1[1]: (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ),
% 24.71/25.12 distinct_lines( X, Y ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := Y
% 24.71/25.12 Y := X
% 24.71/25.12 end
% 24.71/25.12 substitution1:
% 24.71/25.12 X := X
% 24.71/25.12 Y := Y
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (29) {G2,W6,D2,L2,V2,M1} R(13,26) { ! convergent_lines( X, Y )
% 24.71/25.12 , distinct_lines( Y, X ) }.
% 24.71/25.12 parent0: (3123) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 24.71/25.12 convergent_lines( X, Y ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := X
% 24.71/25.12 Y := Y
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 1
% 24.71/25.12 1 ==> 0
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 resolution: (3124) {G1,W10,D3,L2,V1,M2} { ! convergent_lines( skol3, X ),
% 24.71/25.12 distinct_points( intersection_point( skol1, skol2 ), intersection_point(
% 24.71/25.12 skol3, X ) ) }.
% 24.71/25.12 parent0[2]: (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 24.71/25.12 distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 24.71/25.12 ( Z, X ) }.
% 24.71/25.12 parent1[0]: (17) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line(
% 24.71/25.12 intersection_point( skol1, skol2 ), skol3 ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := skol3
% 24.71/25.12 Y := X
% 24.71/25.12 Z := intersection_point( skol1, skol2 )
% 24.71/25.12 end
% 24.71/25.12 substitution1:
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (60) {G1,W10,D3,L2,V1,M1} R(8,17) { ! convergent_lines( skol3
% 24.71/25.12 , X ), distinct_points( intersection_point( skol1, skol2 ),
% 24.71/25.12 intersection_point( skol3, X ) ) }.
% 24.71/25.12 parent0: (3124) {G1,W10,D3,L2,V1,M2} { ! convergent_lines( skol3, X ),
% 24.71/25.12 distinct_points( intersection_point( skol1, skol2 ), intersection_point(
% 24.71/25.12 skol3, X ) ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := X
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 0
% 24.71/25.12 1 ==> 1
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 resolution: (3125) {G1,W19,D3,L5,V2,M5} { ! distinct_points(
% 24.71/25.12 intersection_point( skol1, skol3 ), X ), ! distinct_lines( Y, skol2 ),
% 24.71/25.12 apart_point_and_line( X, Y ), apart_point_and_line( X, skol2 ),
% 24.71/25.12 apart_point_and_line( intersection_point( skol1, skol3 ), Y ) }.
% 24.71/25.12 parent0[0]: (18) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line(
% 24.71/25.12 intersection_point( skol1, skol3 ), skol2 ) }.
% 24.71/25.12 parent1[2]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 24.71/25.12 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 24.71/25.12 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 24.71/25.12 apart_point_and_line( X, Z ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 end
% 24.71/25.12 substitution1:
% 24.71/25.12 X := intersection_point( skol1, skol3 )
% 24.71/25.12 Y := X
% 24.71/25.12 Z := Y
% 24.71/25.12 T := skol2
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 subsumption: (106) {G1,W19,D3,L5,V2,M3} R(10,18) { ! distinct_points(
% 24.71/25.12 intersection_point( skol1, skol3 ), X ), ! distinct_lines( Y, skol2 ),
% 24.71/25.12 apart_point_and_line( X, skol2 ), apart_point_and_line(
% 24.71/25.12 intersection_point( skol1, skol3 ), Y ), apart_point_and_line( X, Y ) }.
% 24.71/25.12 parent0: (3125) {G1,W19,D3,L5,V2,M5} { ! distinct_points(
% 24.71/25.12 intersection_point( skol1, skol3 ), X ), ! distinct_lines( Y, skol2 ),
% 24.71/25.12 apart_point_and_line( X, Y ), apart_point_and_line( X, skol2 ),
% 24.71/25.12 apart_point_and_line( intersection_point( skol1, skol3 ), Y ) }.
% 24.71/25.12 substitution0:
% 24.71/25.12 X := X
% 24.71/25.12 Y := Y
% 24.71/25.12 end
% 24.71/25.12 permutation0:
% 24.71/25.12 0 ==> 0
% 24.71/25.12 1 ==> 1
% 24.71/25.12 2 ==> 4
% 24.71/25.12 3 ==> 2
% 24.71/25.12 4 ==> 3
% 24.71/25.12 end
% 24.71/25.12
% 24.71/25.12 resolution: (3137) {G1,W19,D3,L5,V2,M5} { ! distinct_points(
% 24.71/25.12 intersection_point( skol1, skol3 ), X ), ! distinct_lines( skol2, Y ),
% 24.71/25.12 apart_point_and_line( intersection_point( skol1, skol3 ), Y ),
% 24.71/25.12 apart_point_and_line( X, skol2 ), apart_point_and_line( X, Y ) }.
% 24.71/25.13 parent0[0]: (18) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line(
% 24.71/25.13 intersection_point( skol1, skol3 ), skol2 ) }.
% 24.71/25.13 parent1[5]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 24.71/25.13 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 24.71/25.13 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 24.71/25.13 apart_point_and_line( X, Z ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 X := intersection_point( skol1, skol3 )
% 24.71/25.13 Y := X
% 24.71/25.13 Z := skol2
% 24.71/25.13 T := Y
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (109) {G1,W19,D3,L5,V2,M3} R(10,18) { ! distinct_points(
% 24.71/25.13 intersection_point( skol1, skol3 ), X ), ! distinct_lines( skol2, Y ),
% 24.71/25.13 apart_point_and_line( X, skol2 ), apart_point_and_line( X, Y ),
% 24.71/25.13 apart_point_and_line( intersection_point( skol1, skol3 ), Y ) }.
% 24.71/25.13 parent0: (3137) {G1,W19,D3,L5,V2,M5} { ! distinct_points(
% 24.71/25.13 intersection_point( skol1, skol3 ), X ), ! distinct_lines( skol2, Y ),
% 24.71/25.13 apart_point_and_line( intersection_point( skol1, skol3 ), Y ),
% 24.71/25.13 apart_point_and_line( X, skol2 ), apart_point_and_line( X, Y ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := X
% 24.71/25.13 Y := Y
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 0
% 24.71/25.13 1 ==> 1
% 24.71/25.13 2 ==> 4
% 24.71/25.13 3 ==> 2
% 24.71/25.13 4 ==> 3
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3143) {G1,W14,D3,L4,V4,M4} { ! convergent_lines( X, Y ),
% 24.71/25.13 distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 24.71/25.13 , ! apart_point_and_line( T, Y ) }.
% 24.71/25.13 parent0[2]: (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 24.71/25.13 distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 24.71/25.13 ( Z, Y ) }.
% 24.71/25.13 parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 24.71/25.13 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := X
% 24.71/25.13 Y := Y
% 24.71/25.13 Z := Z
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 X := T
% 24.71/25.13 Y := Y
% 24.71/25.13 Z := Z
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (127) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y ),
% 24.71/25.13 ! convergent_lines( T, Z ), distinct_points( Y, intersection_point( T, Z
% 24.71/25.13 ) ), ! apart_point_and_line( X, Z ) }.
% 24.71/25.13 parent0: (3143) {G1,W14,D3,L4,V4,M4} { ! convergent_lines( X, Y ),
% 24.71/25.13 distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 24.71/25.13 , ! apart_point_and_line( T, Y ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := T
% 24.71/25.13 Y := Z
% 24.71/25.13 Z := Y
% 24.71/25.13 T := X
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 1
% 24.71/25.13 1 ==> 2
% 24.71/25.13 2 ==> 0
% 24.71/25.13 3 ==> 3
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3145) {G1,W14,D3,L4,V4,M4} { ! convergent_lines( X, Y ),
% 24.71/25.13 distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 24.71/25.13 , ! apart_point_and_line( T, X ) }.
% 24.71/25.13 parent0[2]: (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 24.71/25.13 distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 24.71/25.13 ( Z, X ) }.
% 24.71/25.13 parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 24.71/25.13 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := X
% 24.71/25.13 Y := Y
% 24.71/25.13 Z := Z
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 X := T
% 24.71/25.13 Y := X
% 24.71/25.13 Z := Z
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (128) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y ),
% 24.71/25.13 ! convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z, T
% 24.71/25.13 ) ), ! apart_point_and_line( X, Z ) }.
% 24.71/25.13 parent0: (3145) {G1,W14,D3,L4,V4,M4} { ! convergent_lines( X, Y ),
% 24.71/25.13 distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 24.71/25.13 , ! apart_point_and_line( T, X ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := Z
% 24.71/25.13 Y := T
% 24.71/25.13 Z := Y
% 24.71/25.13 T := X
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 1
% 24.71/25.13 1 ==> 2
% 24.71/25.13 2 ==> 0
% 24.71/25.13 3 ==> 3
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 factor: (3147) {G1,W15,D3,L3,V2,M3} { distinct_points( intersection_point
% 24.71/25.13 ( X, Y ), intersection_point( X, Y ) ), ! convergent_lines( X, Y ), !
% 24.71/25.13 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.71/25.13 parent0[0, 2]: (128) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y )
% 24.71/25.13 , ! convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z,
% 24.71/25.13 T ) ), ! apart_point_and_line( X, Z ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := intersection_point( X, Y )
% 24.71/25.13 Y := intersection_point( X, Y )
% 24.71/25.13 Z := X
% 24.71/25.13 T := Y
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3148) {G1,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 24.71/25.13 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.71/25.13 parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 24.71/25.13 parent1[0]: (3147) {G1,W15,D3,L3,V2,M3} { distinct_points(
% 24.71/25.13 intersection_point( X, Y ), intersection_point( X, Y ) ), !
% 24.71/25.13 convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X,
% 24.71/25.13 Y ), X ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := intersection_point( X, Y )
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 X := X
% 24.71/25.13 Y := Y
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X
% 24.71/25.13 , Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.71/25.13 parent0: (3148) {G1,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 24.71/25.13 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := X
% 24.71/25.13 Y := Y
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 0
% 24.71/25.13 1 ==> 1
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 factor: (3149) {G1,W15,D3,L3,V2,M3} { distinct_points( intersection_point
% 24.71/25.13 ( X, Y ), intersection_point( X, Y ) ), ! convergent_lines( X, Y ), !
% 24.71/25.13 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.71/25.13 parent0[0, 2]: (127) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y )
% 24.71/25.13 , ! convergent_lines( T, Z ), distinct_points( Y, intersection_point( T,
% 24.71/25.13 Z ) ), ! apart_point_and_line( X, Z ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := intersection_point( X, Y )
% 24.71/25.13 Y := intersection_point( X, Y )
% 24.71/25.13 Z := Y
% 24.71/25.13 T := X
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3150) {G1,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 24.71/25.13 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.71/25.13 parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 24.71/25.13 parent1[0]: (3149) {G1,W15,D3,L3,V2,M3} { distinct_points(
% 24.71/25.13 intersection_point( X, Y ), intersection_point( X, Y ) ), !
% 24.71/25.13 convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X,
% 24.71/25.13 Y ), Y ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := intersection_point( X, Y )
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 X := X
% 24.71/25.13 Y := Y
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (136) {G2,W8,D3,L2,V2,M1} F(127);r(0) { ! convergent_lines( X
% 24.71/25.13 , Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.71/25.13 parent0: (3150) {G1,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 24.71/25.13 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := X
% 24.71/25.13 Y := Y
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 0
% 24.71/25.13 1 ==> 1
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3151) {G1,W8,D3,L2,V1,M2} { distinct_lines( skol3, X ),
% 24.71/25.13 apart_point_and_line( intersection_point( skol1, skol2 ), X ) }.
% 24.71/25.13 parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 24.71/25.13 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 24.71/25.13 parent1[0]: (17) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line(
% 24.71/25.13 intersection_point( skol1, skol2 ), skol3 ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := intersection_point( skol1, skol2 )
% 24.71/25.13 Y := skol3
% 24.71/25.13 Z := X
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (151) {G1,W8,D3,L2,V1,M1} R(12,17) { distinct_lines( skol3, X
% 24.71/25.13 ), apart_point_and_line( intersection_point( skol1, skol2 ), X ) }.
% 24.71/25.13 parent0: (3151) {G1,W8,D3,L2,V1,M2} { distinct_lines( skol3, X ),
% 24.71/25.13 apart_point_and_line( intersection_point( skol1, skol2 ), X ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := X
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 0
% 24.71/25.13 1 ==> 1
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3152) {G2,W6,D2,L2,V0,M2} { ! convergent_lines( skol1, skol2
% 24.71/25.13 ), distinct_lines( skol3, skol2 ) }.
% 24.71/25.13 parent0[1]: (136) {G2,W8,D3,L2,V2,M1} F(127);r(0) { ! convergent_lines( X,
% 24.71/25.13 Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.71/25.13 parent1[1]: (151) {G1,W8,D3,L2,V1,M1} R(12,17) { distinct_lines( skol3, X )
% 24.71/25.13 , apart_point_and_line( intersection_point( skol1, skol2 ), X ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := skol1
% 24.71/25.13 Y := skol2
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 X := skol2
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3153) {G1,W3,D2,L1,V0,M1} { distinct_lines( skol3, skol2 )
% 24.71/25.13 }.
% 24.71/25.13 parent0[0]: (3152) {G2,W6,D2,L2,V0,M2} { ! convergent_lines( skol1, skol2
% 24.71/25.13 ), distinct_lines( skol3, skol2 ) }.
% 24.71/25.13 parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 24.71/25.13 }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (157) {G3,W3,D2,L1,V0,M1} R(151,136);r(14) { distinct_lines(
% 24.71/25.13 skol3, skol2 ) }.
% 24.71/25.13 parent0: (3153) {G1,W3,D2,L1,V0,M1} { distinct_lines( skol3, skol2 ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 0
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3156) {G2,W9,D2,L3,V3,M3} { distinct_points( Y, X ), !
% 24.71/25.13 distinct_points( Z, X ), distinct_points( Y, Z ) }.
% 24.71/25.13 parent0[0]: (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 24.71/25.13 distinct_points( X, Y ) }.
% 24.71/25.13 parent1[0]: (22) {G2,W9,D2,L3,V3,M3} R(21,3) { distinct_points( Z, X ), !
% 24.71/25.13 distinct_points( Y, Z ), distinct_points( X, Y ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := Y
% 24.71/25.13 Y := X
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 X := Y
% 24.71/25.13 Y := Z
% 24.71/25.13 Z := X
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (211) {G3,W9,D2,L3,V3,M3} R(22,21) { distinct_points( Z, X ),
% 24.71/25.13 distinct_points( Z, Y ), ! distinct_points( X, Y ) }.
% 24.71/25.13 parent0: (3156) {G2,W9,D2,L3,V3,M3} { distinct_points( Y, X ), !
% 24.71/25.13 distinct_points( Z, X ), distinct_points( Y, Z ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := Y
% 24.71/25.13 Y := Z
% 24.71/25.13 Z := X
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 1
% 24.71/25.13 1 ==> 2
% 24.71/25.13 2 ==> 0
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3160) {G2,W13,D3,L3,V2,M3} { distinct_points( X,
% 24.71/25.13 intersection_point( skol1, skol2 ) ), distinct_points( X,
% 24.71/25.13 intersection_point( skol3, Y ) ), ! convergent_lines( skol3, Y ) }.
% 24.71/25.13 parent0[2]: (211) {G3,W9,D2,L3,V3,M3} R(22,21) { distinct_points( Z, X ),
% 24.71/25.13 distinct_points( Z, Y ), ! distinct_points( X, Y ) }.
% 24.71/25.13 parent1[1]: (60) {G1,W10,D3,L2,V1,M1} R(8,17) { ! convergent_lines( skol3,
% 24.71/25.13 X ), distinct_points( intersection_point( skol1, skol2 ),
% 24.71/25.13 intersection_point( skol3, X ) ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := intersection_point( skol1, skol2 )
% 24.71/25.13 Y := intersection_point( skol3, Y )
% 24.71/25.13 Z := X
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 X := Y
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (468) {G4,W13,D3,L3,V2,M2} R(60,211) { ! convergent_lines(
% 24.71/25.13 skol3, X ), distinct_points( Y, intersection_point( skol3, X ) ),
% 24.71/25.13 distinct_points( Y, intersection_point( skol1, skol2 ) ) }.
% 24.71/25.13 parent0: (3160) {G2,W13,D3,L3,V2,M3} { distinct_points( X,
% 24.71/25.13 intersection_point( skol1, skol2 ) ), distinct_points( X,
% 24.71/25.13 intersection_point( skol3, Y ) ), ! convergent_lines( skol3, Y ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := Y
% 24.71/25.13 Y := X
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 2
% 24.71/25.13 1 ==> 1
% 24.71/25.13 2 ==> 0
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3162) {G2,W17,D3,L5,V1,M5} { ! convergent_lines( skol1, skol3
% 24.71/25.13 ), ! distinct_points( intersection_point( skol1, skol3 ), X ), !
% 24.71/25.13 distinct_lines( skol3, skol2 ), apart_point_and_line( X, skol2 ),
% 24.71/25.13 apart_point_and_line( X, skol3 ) }.
% 24.71/25.13 parent0[1]: (136) {G2,W8,D3,L2,V2,M1} F(127);r(0) { ! convergent_lines( X,
% 24.71/25.13 Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.71/25.13 parent1[3]: (106) {G1,W19,D3,L5,V2,M3} R(10,18) { ! distinct_points(
% 24.71/25.13 intersection_point( skol1, skol3 ), X ), ! distinct_lines( Y, skol2 ),
% 24.71/25.13 apart_point_and_line( X, skol2 ), apart_point_and_line(
% 24.71/25.13 intersection_point( skol1, skol3 ), Y ), apart_point_and_line( X, Y ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := skol1
% 24.71/25.13 Y := skol3
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 X := X
% 24.71/25.13 Y := skol3
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3164) {G3,W14,D3,L4,V1,M4} { ! convergent_lines( skol1, skol3
% 24.71/25.13 ), ! distinct_points( intersection_point( skol1, skol3 ), X ),
% 24.71/25.13 apart_point_and_line( X, skol2 ), apart_point_and_line( X, skol3 ) }.
% 24.71/25.13 parent0[2]: (3162) {G2,W17,D3,L5,V1,M5} { ! convergent_lines( skol1, skol3
% 24.71/25.13 ), ! distinct_points( intersection_point( skol1, skol3 ), X ), !
% 24.71/25.13 distinct_lines( skol3, skol2 ), apart_point_and_line( X, skol2 ),
% 24.71/25.13 apart_point_and_line( X, skol3 ) }.
% 24.71/25.13 parent1[0]: (157) {G3,W3,D2,L1,V0,M1} R(151,136);r(14) { distinct_lines(
% 24.71/25.13 skol3, skol2 ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := X
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (1458) {G4,W14,D3,L4,V1,M1} R(106,136);r(157) { !
% 24.71/25.13 distinct_points( intersection_point( skol1, skol3 ), X ),
% 24.71/25.13 apart_point_and_line( X, skol2 ), ! convergent_lines( skol1, skol3 ),
% 24.71/25.13 apart_point_and_line( X, skol3 ) }.
% 24.71/25.13 parent0: (3164) {G3,W14,D3,L4,V1,M4} { ! convergent_lines( skol1, skol3 )
% 24.71/25.13 , ! distinct_points( intersection_point( skol1, skol3 ), X ),
% 24.71/25.13 apart_point_and_line( X, skol2 ), apart_point_and_line( X, skol3 ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := X
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 2
% 24.71/25.13 1 ==> 0
% 24.71/25.13 2 ==> 1
% 24.71/25.13 3 ==> 3
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3167) {G2,W17,D3,L5,V1,M5} { ! convergent_lines( skol1, skol3
% 24.71/25.13 ), ! distinct_points( intersection_point( skol1, skol3 ), X ), !
% 24.71/25.13 distinct_lines( skol2, skol1 ), apart_point_and_line( X, skol2 ),
% 24.71/25.13 apart_point_and_line( X, skol1 ) }.
% 24.71/25.13 parent0[1]: (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X,
% 24.71/25.13 Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.71/25.13 parent1[4]: (109) {G1,W19,D3,L5,V2,M3} R(10,18) { ! distinct_points(
% 24.71/25.13 intersection_point( skol1, skol3 ), X ), ! distinct_lines( skol2, Y ),
% 24.71/25.13 apart_point_and_line( X, skol2 ), apart_point_and_line( X, Y ),
% 24.71/25.13 apart_point_and_line( intersection_point( skol1, skol3 ), Y ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := skol1
% 24.71/25.13 Y := skol3
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 X := X
% 24.71/25.13 Y := skol1
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3168) {G1,W14,D3,L4,V1,M4} { ! distinct_points(
% 24.71/25.13 intersection_point( skol1, skol3 ), X ), ! distinct_lines( skol2, skol1 )
% 24.71/25.13 , apart_point_and_line( X, skol2 ), apart_point_and_line( X, skol1 ) }.
% 24.71/25.13 parent0[0]: (3167) {G2,W17,D3,L5,V1,M5} { ! convergent_lines( skol1, skol3
% 24.71/25.13 ), ! distinct_points( intersection_point( skol1, skol3 ), X ), !
% 24.71/25.13 distinct_lines( skol2, skol1 ), apart_point_and_line( X, skol2 ),
% 24.71/25.13 apart_point_and_line( X, skol1 ) }.
% 24.71/25.13 parent1[0]: (16) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol3 )
% 24.71/25.13 }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := X
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (1506) {G3,W14,D3,L4,V1,M1} R(109,135);r(16) { !
% 24.71/25.13 distinct_points( intersection_point( skol1, skol3 ), X ), !
% 24.71/25.13 distinct_lines( skol2, skol1 ), apart_point_and_line( X, skol1 ),
% 24.71/25.13 apart_point_and_line( X, skol2 ) }.
% 24.71/25.13 parent0: (3168) {G1,W14,D3,L4,V1,M4} { ! distinct_points(
% 24.71/25.13 intersection_point( skol1, skol3 ), X ), ! distinct_lines( skol2, skol1 )
% 24.71/25.13 , apart_point_and_line( X, skol2 ), apart_point_and_line( X, skol1 ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := X
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 0
% 24.71/25.13 1 ==> 1
% 24.71/25.13 2 ==> 3
% 24.71/25.13 3 ==> 2
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3170) {G3,W18,D3,L4,V1,M4} { ! convergent_lines( X, skol2 ),
% 24.71/25.13 ! distinct_points( intersection_point( skol1, skol3 ), intersection_point
% 24.71/25.13 ( X, skol2 ) ), ! distinct_lines( skol2, skol1 ), apart_point_and_line(
% 24.71/25.13 intersection_point( X, skol2 ), skol1 ) }.
% 24.71/25.13 parent0[1]: (136) {G2,W8,D3,L2,V2,M1} F(127);r(0) { ! convergent_lines( X,
% 24.71/25.13 Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.71/25.13 parent1[3]: (1506) {G3,W14,D3,L4,V1,M1} R(109,135);r(16) { !
% 24.71/25.13 distinct_points( intersection_point( skol1, skol3 ), X ), !
% 24.71/25.13 distinct_lines( skol2, skol1 ), apart_point_and_line( X, skol1 ),
% 24.71/25.13 apart_point_and_line( X, skol2 ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := X
% 24.71/25.13 Y := skol2
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 X := intersection_point( X, skol2 )
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (1647) {G4,W18,D3,L4,V1,M1} R(1506,136) { ! distinct_points(
% 24.71/25.13 intersection_point( skol1, skol3 ), intersection_point( X, skol2 ) ), !
% 24.71/25.13 distinct_lines( skol2, skol1 ), ! convergent_lines( X, skol2 ),
% 24.71/25.13 apart_point_and_line( intersection_point( X, skol2 ), skol1 ) }.
% 24.71/25.13 parent0: (3170) {G3,W18,D3,L4,V1,M4} { ! convergent_lines( X, skol2 ), !
% 24.71/25.13 distinct_points( intersection_point( skol1, skol3 ), intersection_point(
% 24.71/25.13 X, skol2 ) ), ! distinct_lines( skol2, skol1 ), apart_point_and_line(
% 24.71/25.13 intersection_point( X, skol2 ), skol1 ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := X
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 2
% 24.71/25.13 1 ==> 0
% 24.71/25.13 2 ==> 1
% 24.71/25.13 3 ==> 3
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3171) {G1,W11,D3,L3,V1,M3} { ! distinct_points(
% 24.71/25.13 intersection_point( skol1, skol3 ), X ), apart_point_and_line( X, skol2 )
% 24.71/25.13 , apart_point_and_line( X, skol3 ) }.
% 24.71/25.13 parent0[2]: (1458) {G4,W14,D3,L4,V1,M1} R(106,136);r(157) { !
% 24.71/25.13 distinct_points( intersection_point( skol1, skol3 ), X ),
% 24.71/25.13 apart_point_and_line( X, skol2 ), ! convergent_lines( skol1, skol3 ),
% 24.71/25.13 apart_point_and_line( X, skol3 ) }.
% 24.71/25.13 parent1[0]: (16) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol3 )
% 24.71/25.13 }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := X
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (1712) {G5,W11,D3,L3,V1,M1} S(1458);r(16) { ! distinct_points
% 24.71/25.13 ( intersection_point( skol1, skol3 ), X ), apart_point_and_line( X, skol2
% 24.71/25.13 ), apart_point_and_line( X, skol3 ) }.
% 24.71/25.13 parent0: (3171) {G1,W11,D3,L3,V1,M3} { ! distinct_points(
% 24.71/25.13 intersection_point( skol1, skol3 ), X ), apart_point_and_line( X, skol2 )
% 24.71/25.13 , apart_point_and_line( X, skol3 ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := X
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 0
% 24.71/25.13 1 ==> 1
% 24.71/25.13 2 ==> 2
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3173) {G3,W15,D3,L3,V1,M3} { ! convergent_lines( skol3, X ),
% 24.71/25.13 ! distinct_points( intersection_point( skol1, skol3 ), intersection_point
% 24.71/25.13 ( skol3, X ) ), apart_point_and_line( intersection_point( skol3, X ),
% 24.71/25.13 skol2 ) }.
% 24.71/25.13 parent0[1]: (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X,
% 24.71/25.13 Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.71/25.13 parent1[2]: (1712) {G5,W11,D3,L3,V1,M1} S(1458);r(16) { ! distinct_points(
% 24.71/25.13 intersection_point( skol1, skol3 ), X ), apart_point_and_line( X, skol2 )
% 24.71/25.13 , apart_point_and_line( X, skol3 ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := skol3
% 24.71/25.13 Y := X
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 X := intersection_point( skol3, X )
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (1738) {G6,W15,D3,L3,V1,M1} R(1712,135) { ! distinct_points(
% 24.71/25.13 intersection_point( skol1, skol3 ), intersection_point( skol3, X ) ), !
% 24.71/25.13 convergent_lines( skol3, X ), apart_point_and_line( intersection_point(
% 24.71/25.13 skol3, X ), skol2 ) }.
% 24.71/25.13 parent0: (3173) {G3,W15,D3,L3,V1,M3} { ! convergent_lines( skol3, X ), !
% 24.71/25.13 distinct_points( intersection_point( skol1, skol3 ), intersection_point(
% 24.71/25.13 skol3, X ) ), apart_point_and_line( intersection_point( skol3, X ), skol2
% 24.71/25.13 ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := X
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 1
% 24.71/25.13 1 ==> 0
% 24.71/25.13 2 ==> 2
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3174) {G3,W13,D3,L3,V0,M3} { ! convergent_lines( skol3, skol2
% 24.71/25.13 ), ! distinct_points( intersection_point( skol1, skol3 ),
% 24.71/25.13 intersection_point( skol3, skol2 ) ), ! convergent_lines( skol3, skol2 )
% 24.71/25.13 }.
% 24.71/25.13 parent0[1]: (136) {G2,W8,D3,L2,V2,M1} F(127);r(0) { ! convergent_lines( X,
% 24.71/25.13 Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.71/25.13 parent1[2]: (1738) {G6,W15,D3,L3,V1,M1} R(1712,135) { ! distinct_points(
% 24.71/25.13 intersection_point( skol1, skol3 ), intersection_point( skol3, X ) ), !
% 24.71/25.13 convergent_lines( skol3, X ), apart_point_and_line( intersection_point(
% 24.71/25.13 skol3, X ), skol2 ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := skol3
% 24.71/25.13 Y := skol2
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 X := skol2
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 factor: (3175) {G3,W10,D3,L2,V0,M2} { ! convergent_lines( skol3, skol2 ),
% 24.71/25.13 ! distinct_points( intersection_point( skol1, skol3 ), intersection_point
% 24.71/25.13 ( skol3, skol2 ) ) }.
% 24.71/25.13 parent0[0, 2]: (3174) {G3,W13,D3,L3,V0,M3} { ! convergent_lines( skol3,
% 24.71/25.13 skol2 ), ! distinct_points( intersection_point( skol1, skol3 ),
% 24.71/25.13 intersection_point( skol3, skol2 ) ), ! convergent_lines( skol3, skol2 )
% 24.71/25.13 }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3177) {G1,W7,D3,L1,V0,M1} { ! distinct_points(
% 24.71/25.13 intersection_point( skol1, skol3 ), intersection_point( skol3, skol2 ) )
% 24.71/25.13 }.
% 24.71/25.13 parent0[0]: (3175) {G3,W10,D3,L2,V0,M2} { ! convergent_lines( skol3, skol2
% 24.71/25.13 ), ! distinct_points( intersection_point( skol1, skol3 ),
% 24.71/25.13 intersection_point( skol3, skol2 ) ) }.
% 24.71/25.13 parent1[0]: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol2 )
% 24.71/25.13 }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (1766) {G7,W7,D3,L1,V0,M1} R(1738,136);f;r(15) { !
% 24.71/25.13 distinct_points( intersection_point( skol1, skol3 ), intersection_point(
% 24.71/25.13 skol3, skol2 ) ) }.
% 24.71/25.13 parent0: (3177) {G1,W7,D3,L1,V0,M1} { ! distinct_points(
% 24.71/25.13 intersection_point( skol1, skol3 ), intersection_point( skol3, skol2 ) )
% 24.71/25.13 }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 0
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3178) {G5,W10,D3,L2,V0,M2} { ! convergent_lines( skol3, skol2
% 24.71/25.13 ), distinct_points( intersection_point( skol1, skol3 ),
% 24.71/25.13 intersection_point( skol1, skol2 ) ) }.
% 24.71/25.13 parent0[0]: (1766) {G7,W7,D3,L1,V0,M1} R(1738,136);f;r(15) { !
% 24.71/25.13 distinct_points( intersection_point( skol1, skol3 ), intersection_point(
% 24.71/25.13 skol3, skol2 ) ) }.
% 24.71/25.13 parent1[1]: (468) {G4,W13,D3,L3,V2,M2} R(60,211) { ! convergent_lines(
% 24.71/25.13 skol3, X ), distinct_points( Y, intersection_point( skol3, X ) ),
% 24.71/25.13 distinct_points( Y, intersection_point( skol1, skol2 ) ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 X := skol2
% 24.71/25.13 Y := intersection_point( skol1, skol3 )
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3179) {G1,W7,D3,L1,V0,M1} { distinct_points(
% 24.71/25.13 intersection_point( skol1, skol3 ), intersection_point( skol1, skol2 ) )
% 24.71/25.13 }.
% 24.71/25.13 parent0[0]: (3178) {G5,W10,D3,L2,V0,M2} { ! convergent_lines( skol3, skol2
% 24.71/25.13 ), distinct_points( intersection_point( skol1, skol3 ),
% 24.71/25.13 intersection_point( skol1, skol2 ) ) }.
% 24.71/25.13 parent1[0]: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol2 )
% 24.71/25.13 }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (1835) {G8,W7,D3,L1,V0,M1} R(1766,468);r(15) { distinct_points
% 24.71/25.13 ( intersection_point( skol1, skol3 ), intersection_point( skol1, skol2 )
% 24.71/25.13 ) }.
% 24.71/25.13 parent0: (3179) {G1,W7,D3,L1,V0,M1} { distinct_points( intersection_point
% 24.71/25.13 ( skol1, skol3 ), intersection_point( skol1, skol2 ) ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 0
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3180) {G3,W16,D3,L4,V0,M4} { ! convergent_lines( skol1, skol2
% 24.71/25.13 ), ! distinct_points( intersection_point( skol1, skol3 ),
% 24.71/25.13 intersection_point( skol1, skol2 ) ), ! distinct_lines( skol2, skol1 ), !
% 24.71/25.13 convergent_lines( skol1, skol2 ) }.
% 24.71/25.13 parent0[1]: (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X,
% 24.71/25.13 Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.71/25.13 parent1[3]: (1647) {G4,W18,D3,L4,V1,M1} R(1506,136) { ! distinct_points(
% 24.71/25.13 intersection_point( skol1, skol3 ), intersection_point( X, skol2 ) ), !
% 24.71/25.13 distinct_lines( skol2, skol1 ), ! convergent_lines( X, skol2 ),
% 24.71/25.13 apart_point_and_line( intersection_point( X, skol2 ), skol1 ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 X := skol1
% 24.71/25.13 Y := skol2
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 X := skol1
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3182) {G4,W9,D2,L3,V0,M3} { ! convergent_lines( skol1, skol2
% 24.71/25.13 ), ! distinct_lines( skol2, skol1 ), ! convergent_lines( skol1, skol2 )
% 24.71/25.13 }.
% 24.71/25.13 parent0[1]: (3180) {G3,W16,D3,L4,V0,M4} { ! convergent_lines( skol1, skol2
% 24.71/25.13 ), ! distinct_points( intersection_point( skol1, skol3 ),
% 24.71/25.13 intersection_point( skol1, skol2 ) ), ! distinct_lines( skol2, skol1 ), !
% 24.71/25.13 convergent_lines( skol1, skol2 ) }.
% 24.71/25.13 parent1[0]: (1835) {G8,W7,D3,L1,V0,M1} R(1766,468);r(15) { distinct_points
% 24.71/25.13 ( intersection_point( skol1, skol3 ), intersection_point( skol1, skol2 )
% 24.71/25.13 ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 factor: (3183) {G4,W6,D2,L2,V0,M2} { ! convergent_lines( skol1, skol2 ), !
% 24.71/25.13 distinct_lines( skol2, skol1 ) }.
% 24.71/25.13 parent0[0, 2]: (3182) {G4,W9,D2,L3,V0,M3} { ! convergent_lines( skol1,
% 24.71/25.13 skol2 ), ! distinct_lines( skol2, skol1 ), ! convergent_lines( skol1,
% 24.71/25.13 skol2 ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (2481) {G9,W6,D2,L2,V0,M1} R(1647,135);f;r(1835) { !
% 24.71/25.13 convergent_lines( skol1, skol2 ), ! distinct_lines( skol2, skol1 ) }.
% 24.71/25.13 parent0: (3183) {G4,W6,D2,L2,V0,M2} { ! convergent_lines( skol1, skol2 ),
% 24.71/25.13 ! distinct_lines( skol2, skol1 ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 0
% 24.71/25.13 1 ==> 1
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3184) {G1,W3,D2,L1,V0,M1} { ! distinct_lines( skol2, skol1 )
% 24.71/25.13 }.
% 24.71/25.13 parent0[0]: (2481) {G9,W6,D2,L2,V0,M1} R(1647,135);f;r(1835) { !
% 24.71/25.13 convergent_lines( skol1, skol2 ), ! distinct_lines( skol2, skol1 ) }.
% 24.71/25.13 parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 24.71/25.13 }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (2482) {G10,W3,D2,L1,V0,M1} S(2481);r(14) { ! distinct_lines(
% 24.71/25.13 skol2, skol1 ) }.
% 24.71/25.13 parent0: (3184) {G1,W3,D2,L1,V0,M1} { ! distinct_lines( skol2, skol1 ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 0 ==> 0
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3185) {G3,W3,D2,L1,V0,M1} { ! convergent_lines( skol1, skol2
% 24.71/25.13 ) }.
% 24.71/25.13 parent0[0]: (2482) {G10,W3,D2,L1,V0,M1} S(2481);r(14) { ! distinct_lines(
% 24.71/25.13 skol2, skol1 ) }.
% 24.71/25.13 parent1[1]: (29) {G2,W6,D2,L2,V2,M1} R(13,26) { ! convergent_lines( X, Y )
% 24.71/25.13 , distinct_lines( Y, X ) }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 X := skol1
% 24.71/25.13 Y := skol2
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 resolution: (3186) {G1,W0,D0,L0,V0,M0} { }.
% 24.71/25.13 parent0[0]: (3185) {G3,W3,D2,L1,V0,M1} { ! convergent_lines( skol1, skol2
% 24.71/25.13 ) }.
% 24.71/25.13 parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 24.71/25.13 }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13 substitution1:
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 subsumption: (3005) {G11,W0,D0,L0,V0,M0} R(2482,29);r(14) { }.
% 24.71/25.13 parent0: (3186) {G1,W0,D0,L0,V0,M0} { }.
% 24.71/25.13 substitution0:
% 24.71/25.13 end
% 24.71/25.13 permutation0:
% 24.71/25.13 end
% 24.71/25.13
% 24.71/25.13 Proof check complete!
% 24.71/25.13
% 24.71/25.13 Memory use:
% 24.71/25.13
% 24.71/25.13 space for terms: 47864
% 24.71/25.13 space for clauses: 105927
% 24.71/25.13
% 24.71/25.13
% 24.71/25.13 clauses generated: 884997
% 24.71/25.13 clauses kept: 3006
% 24.71/25.13 clauses selected: 2143
% 24.71/25.13 clauses deleted: 10
% 24.71/25.13 clauses inuse deleted: 0
% 24.71/25.13
% 24.71/25.13 subsentry: 4000564
% 24.71/25.13 literals s-matched: 1478680
% 24.71/25.13 literals matched: 1478635
% 24.71/25.13 full subsumption: 1319556
% 24.71/25.13
% 24.71/25.13 checksum: -1623283306
% 24.71/25.13
% 24.71/25.13
% 24.71/25.13 Bliksem ended
%------------------------------------------------------------------------------