%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO220+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n016.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 02:52:56 EDT 2022
% Result : Theorem 0.77s 1.20s
% Output : Refutation 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO220+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.14 % Command : bliksem %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Fri Jun 17 20:18:06 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.77/1.20 *** allocated 10000 integers for termspace/termends
% 0.77/1.20 *** allocated 10000 integers for clauses
% 0.77/1.20 *** allocated 10000 integers for justifications
% 0.77/1.20 Bliksem 1.12
% 0.77/1.20
% 0.77/1.20
% 0.77/1.20 Automatic Strategy Selection
% 0.77/1.20
% 0.77/1.20
% 0.77/1.20 Clauses:
% 0.77/1.20
% 0.77/1.20 { ! distinct_points( X, X ) }.
% 0.77/1.20 { ! distinct_lines( X, X ) }.
% 0.77/1.20 { ! convergent_lines( X, X ) }.
% 0.77/1.20 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.77/1.20 ) }.
% 0.77/1.20 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.77/1.20 }.
% 0.77/1.20 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.77/1.20 , Z ) }.
% 0.77/1.20 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.77/1.20 , Y ) ) }.
% 0.77/1.20 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.77/1.20 , Y ) ) }.
% 0.77/1.20 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.77/1.20 , Y ), X ) }.
% 0.77/1.20 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.77/1.20 , Y ), Y ) }.
% 0.77/1.20 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.77/1.20 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 0.77/1.20 apart_point_and_line( Y, T ) }.
% 0.77/1.20 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 0.77/1.20 apart_point_and_line( Z, Y ) }.
% 0.77/1.20 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 0.77/1.20 apart_point_and_line( X, Z ) }.
% 0.77/1.20 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 0.77/1.20 Z ) }.
% 0.77/1.20 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.77/1.20 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.77/1.20 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.77/1.20 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.77/1.20 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.77/1.20 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.77/1.20 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.77/1.20 , convergent_lines( Y, Z ) }.
% 0.77/1.20 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.77/1.20 , unorthogonal_lines( Y, Z ) }.
% 0.77/1.20 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.77/1.20 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.77/1.20 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.77/1.20 }.
% 0.77/1.20 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.77/1.20 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.77/1.20 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.77/1.20 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 0.77/1.20 unorthogonal_lines( Y, T ) }.
% 0.77/1.20 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.77/1.20 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.77/1.20 unorthogonal_lines( X, Y ) }.
% 0.77/1.20 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.77/1.20 unorthogonal_lines( X, Y ) }.
% 0.77/1.20 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.77/1.20 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.77/1.20 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.77/1.20 }.
% 0.77/1.20 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 0.77/1.20 convergent_lines( X, Y ) }.
% 0.77/1.20 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.77/1.20 line_connecting( X, Y ) ) }.
% 0.77/1.20 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 0.77/1.20 intersection_point( X, Y ) ) }.
% 0.77/1.20 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.77/1.20 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.77/1.20 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.77/1.20 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.77/1.20 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.77/1.20 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.77/1.20 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.77/1.20 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.77/1.20 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.77/1.20 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.77/1.20 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.77/1.20 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.77/1.20 { orthogonal_lines( skol3, skol1 ) }.
% 0.77/1.20 { orthogonal_lines( skol3, skol2 ) }.
% 0.77/1.20 { ! parallel_lines( skol1, skol2 ) }.
% 0.77/1.20
% 0.77/1.20 percentage equality = 0.000000, percentage horn = 0.612245
% 0.77/1.20 This a non-horn, non-equality problem
% 0.77/1.20
% 0.77/1.20
% 0.77/1.20 Options Used:
% 0.77/1.20
% 0.77/1.20 useres = 1
% 0.77/1.20 useparamod = 0
% 0.77/1.20 useeqrefl = 0
% 0.77/1.20 useeqfact = 0
% 0.77/1.20 usefactor = 1
% 0.77/1.20 usesimpsplitting = 0
% 0.77/1.20 usesimpdemod = 0
% 0.77/1.20 usesimpres = 3
% 0.77/1.20
% 0.77/1.20 resimpinuse = 1000
% 0.77/1.20 resimpclauses = 20000
% 0.77/1.20 substype = standard
% 0.77/1.20 backwardsubs = 1
% 0.77/1.20 selectoldest = 5
% 0.77/1.20
% 0.77/1.20 litorderings [0] = split
% 0.77/1.20 litorderings [1] = liftord
% 0.77/1.20
% 0.77/1.20 termordering = none
% 0.77/1.20
% 0.77/1.20 litapriori = 1
% 0.77/1.20 termapriori = 0
% 0.77/1.20 litaposteriori = 0
% 0.77/1.20 termaposteriori = 0
% 0.77/1.20 demodaposteriori = 0
% 0.77/1.20 ordereqreflfact = 0
% 0.77/1.20
% 0.77/1.20 litselect = none
% 0.77/1.20
% 0.77/1.20 maxweight = 15
% 0.77/1.20 maxdepth = 30000
% 0.77/1.20 maxlength = 115
% 0.77/1.20 maxnrvars = 195
% 0.77/1.20 excuselevel = 1
% 0.77/1.20 increasemaxweight = 1
% 0.77/1.20
% 0.77/1.20 maxselected = 10000000
% 0.77/1.20 maxnrclauses = 10000000
% 0.77/1.20
% 0.77/1.20 showgenerated = 0
% 0.77/1.20 showkept = 0
% 0.77/1.20 showselected = 0
% 0.77/1.20 showdeleted = 0
% 0.77/1.20 showresimp = 1
% 0.77/1.20 showstatus = 2000
% 0.77/1.20
% 0.77/1.20 prologoutput = 0
% 0.77/1.20 nrgoals = 5000000
% 0.77/1.20 totalproof = 1
% 0.77/1.20
% 0.77/1.20 Symbols occurring in the translation:
% 0.77/1.20
% 0.77/1.20 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.77/1.20 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 0.77/1.20 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 0.77/1.20 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.77/1.20 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.77/1.20 distinct_points [36, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.77/1.20 distinct_lines [37, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.77/1.20 convergent_lines [38, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.77/1.20 line_connecting [41, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.77/1.20 apart_point_and_line [42, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.77/1.20 intersection_point [43, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.77/1.20 parallel_through_point [46, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.77/1.20 unorthogonal_lines [49, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.77/1.20 orthogonal_through_point [52, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.77/1.20 point [54, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.77/1.20 line [55, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.77/1.20 equal_points [56, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.77/1.20 equal_lines [57, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.77/1.20 parallel_lines [58, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.77/1.20 incident_point_and_line [59, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.77/1.20 orthogonal_lines [60, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.77/1.20 alpha1 [61, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.77/1.20 alpha2 [62, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.77/1.20 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.77/1.20 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.77/1.20 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0).
% 0.77/1.20
% 0.77/1.20
% 0.77/1.20 Starting Search:
% 0.77/1.20
% 0.77/1.20 *** allocated 15000 integers for clauses
% 0.77/1.20 *** allocated 22500 integers for clauses
% 0.77/1.20 *** allocated 33750 integers for clauses
% 0.77/1.20 *** allocated 15000 integers for termspace/termends
% 0.77/1.20 *** allocated 50625 integers for clauses
% 0.77/1.20 Resimplifying inuse:
% 0.77/1.20 Done
% 0.77/1.20
% 0.77/1.20 *** allocated 22500 integers for termspace/termends
% 0.77/1.20
% 0.77/1.20 Bliksems!, er is een bewijs:
% 0.77/1.20 % SZS status Theorem
% 0.77/1.20 % SZS output start Refutation
% 0.77/1.20
% 0.77/1.20 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.77/1.20 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 0.77/1.20 Z ), ! convergent_lines( X, Y ) }.
% 0.77/1.20 (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ), unorthogonal_lines
% 0.77/1.20 ( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.77/1.20 (41) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), parallel_lines( X, Y
% 0.77/1.20 ) }.
% 0.77/1.20 (44) {G0,W6,D2,L2,V2,M1} I { ! orthogonal_lines( X, Y ), !
% 0.77/1.20 unorthogonal_lines( X, Y ) }.
% 0.77/1.20 (46) {G0,W3,D2,L1,V0,M1} I { orthogonal_lines( skol3, skol1 ) }.
% 0.77/1.20 (47) {G0,W3,D2,L1,V0,M1} I { orthogonal_lines( skol3, skol2 ) }.
% 0.77/1.20 (48) {G0,W3,D2,L1,V0,M1} I { ! parallel_lines( skol1, skol2 ) }.
% 0.77/1.20 (64) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.77/1.20 convergent_lines( X, Y ) }.
% 0.77/1.20 (70) {G1,W3,D2,L1,V0,M1} R(41,48) { convergent_lines( skol1, skol2 ) }.
% 0.77/1.20 (71) {G2,W3,D2,L1,V0,M1} R(70,64) { convergent_lines( skol2, skol1 ) }.
% 0.77/1.20 (209) {G1,W9,D2,L3,V3,M1} R(31,44) { ! convergent_lines( X, Y ), !
% 0.77/1.20 orthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.77/1.20 (1259) {G2,W9,D2,L3,V3,M2} R(209,44) { ! convergent_lines( X, Y ), !
% 0.77/1.20 orthogonal_lines( Z, Y ), ! orthogonal_lines( Z, X ) }.
% 0.77/1.20 (1260) {G3,W6,D2,L2,V1,M1} R(1259,46) { ! convergent_lines( X, skol1 ), !
% 0.77/1.20 orthogonal_lines( skol3, X ) }.
% 0.77/1.20 (1264) {G4,W0,D0,L0,V0,M0} R(1260,47);r(71) { }.
% 0.77/1.20
% 0.77/1.20
% 0.77/1.20 % SZS output end Refutation
% 0.77/1.20 found a proof!
% 0.77/1.20
% 0.77/1.20 *** allocated 75937 integers for clauses
% 0.77/1.20
% 0.77/1.20 Unprocessed initial clauses:
% 0.77/1.20
% 0.77/1.20 (1266) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.77/1.20 (1267) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.77/1.20 (1268) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.77/1.20 (1269) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.77/1.20 , Z ), distinct_points( Y, Z ) }.
% 0.77/1.20 (1270) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 0.77/1.20 Z ), distinct_lines( Y, Z ) }.
% 0.77/1.20 (1271) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 0.77/1.20 ( X, Z ), convergent_lines( Y, Z ) }.
% 0.77/1.20 (1272) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.77/1.20 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.77/1.20 (1273) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.77/1.20 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.77/1.20 (1274) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.77/1.20 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.77/1.20 (1275) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.77/1.20 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.77/1.20 (1276) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 0.77/1.20 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 0.77/1.20 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.77/1.20 (1277) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.77/1.20 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.77/1.20 (1278) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.77/1.20 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.77/1.20 (1279) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.77/1.20 , Z ), convergent_lines( X, Z ) }.
% 0.77/1.20 (1280) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 0.77/1.20 , Y ) }.
% 0.77/1.20 (1281) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 0.77/1.20 , X ), Y ) }.
% 0.77/1.20 (1282) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.77/1.20 parallel_through_point( Y, X ) ) }.
% 0.77/1.20 (1283) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 0.77/1.20 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.77/1.20 convergent_lines( X, Y ) }.
% 0.77/1.20 (1284) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 0.77/1.20 ( X, Y ) }.
% 0.77/1.20 (1285) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.77/1.20 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.77/1.20 (1286) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.77/1.20 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.77/1.20 }.
% 0.77/1.20 (1287) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 0.77/1.20 }.
% 0.77/1.20 (1288) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.77/1.20 }.
% 0.77/1.20 (1289) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 0.77/1.20 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.77/1.20 (1290) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 0.77/1.20 orthogonal_through_point( Y, X ), Y ) }.
% 0.77/1.20 (1291) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.77/1.20 orthogonal_through_point( Y, X ) ) }.
% 0.77/1.20 (1292) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 0.77/1.20 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.77/1.20 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.77/1.20 (1293) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 0.77/1.20 ( X, Y ) }.
% 0.77/1.20 (1294) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 0.77/1.20 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.77/1.20 (1295) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ),
% 0.77/1.20 ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.77/1.20 (1296) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X )
% 0.77/1.20 }.
% 0.77/1.20 (1297) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.77/1.20 }.
% 0.77/1.20 (1298) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 0.77/1.20 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.77/1.20 (1299) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 0.77/1.20 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.77/1.20 (1300) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), !
% 0.77/1.20 distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.77/1.20 (1301) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 0.77/1.20 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.77/1.20 (1302) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.77/1.20 parallel_through_point( X, Y ) ) }.
% 0.77/1.20 (1303) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.77/1.20 orthogonal_through_point( X, Y ) ) }.
% 0.77/1.20 (1304) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X
% 0.77/1.20 , Y ) }.
% 0.77/1.20 (1305) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 0.77/1.20 }.
% 0.77/1.20 (1306) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.77/1.20 ) }.
% 0.77/1.20 (1307) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.77/1.20 }.
% 0.77/1.20 (1308) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines
% 0.77/1.20 ( X, Y ) }.
% 0.77/1.20 (1309) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X,
% 0.77/1.20 Y ) }.
% 0.77/1.20 (1310) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 0.77/1.20 apart_point_and_line( X, Y ) }.
% 0.77/1.20 (1311) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.77/1.20 incident_point_and_line( X, Y ) }.
% 0.77/1.20 (1312) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.77/1.20 unorthogonal_lines( X, Y ) }.
% 0.77/1.20 (1313) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines
% 0.77/1.20 ( X, Y ) }.
% 0.77/1.20 (1314) {G0,W3,D2,L1,V0,M1} { orthogonal_lines( skol3, skol1 ) }.
% 0.77/1.20 (1315) {G0,W3,D2,L1,V0,M1} { orthogonal_lines( skol3, skol2 ) }.
% 0.77/1.20 (1316) {G0,W3,D2,L1,V0,M1} { ! parallel_lines( skol1, skol2 ) }.
% 0.77/1.20
% 0.77/1.20
% 0.77/1.20 Total Proof:
% 0.77/1.20
% 0.77/1.20 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.77/1.20 parent0: (1268) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.77/1.20 substitution0:
% 0.77/1.20 X := X
% 0.77/1.20 end
% 0.77/1.20 permutation0:
% 0.77/1.20 0 ==> 0
% 0.77/1.20 end
% 0.77/1.20
% 0.77/1.20 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.77/1.20 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.77/1.20 parent0: (1271) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 0.77/1.20 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 0.77/1.20 substitution0:
% 0.77/1.20 X := X
% 0.77/1.20 Y := Y
% 0.77/1.20 Z := Z
% 0.77/1.20 end
% 0.77/1.20 permutation0:
% 0.77/1.20 0 ==> 2
% 0.77/1.20 1 ==> 0
% 0.77/1.20 2 ==> 1
% 0.77/1.20 end
% 0.77/1.20
% 0.77/1.20 subsumption: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 0.77/1.20 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.77/1.20 parent0: (1299) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 0.77/1.20 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.77/1.20 substitution0:
% 0.77/1.20 X := X
% 0.77/1.20 Y := Y
% 0.77/1.20 Z := Z
% 0.77/1.20 end
% 0.77/1.20 permutation0:
% 0.77/1.20 0 ==> 1
% 0.77/1.20 1 ==> 2
% 0.77/1.20 2 ==> 0
% 0.77/1.20 end
% 0.77/1.20
% 0.77/1.20 subsumption: (41) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.77/1.20 parallel_lines( X, Y ) }.
% 0.77/1.20 parent0: (1309) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 0.77/1.20 parallel_lines( X, Y ) }.
% 0.77/1.20 substitution0:
% 0.77/1.20 X := X
% 0.77/1.20 Y := Y
% 0.77/1.20 end
% 0.77/1.20 permutation0:
% 0.77/1.20 0 ==> 0
% 0.77/1.20 1 ==> 1
% 0.77/1.20 end
% 0.77/1.20
% 0.77/1.20 subsumption: (44) {G0,W6,D2,L2,V2,M1} I { ! orthogonal_lines( X, Y ), !
% 0.77/1.20 unorthogonal_lines( X, Y ) }.
% 0.77/1.20 parent0: (1312) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.77/1.20 unorthogonal_lines( X, Y ) }.
% 0.77/1.20 substitution0:
% 0.77/1.20 X := X
% 0.77/1.20 Y := Y
% 0.77/1.20 end
% 0.77/1.20 permutation0:
% 0.77/1.20 0 ==> 0
% 0.77/1.20 1 ==> 1
% 0.77/1.20 end
% 0.77/1.20
% 0.77/1.20 subsumption: (46) {G0,W3,D2,L1,V0,M1} I { orthogonal_lines( skol3, skol1 )
% 0.77/1.20 }.
% 0.77/1.20 parent0: (1314) {G0,W3,D2,L1,V0,M1} { orthogonal_lines( skol3, skol1 ) }.
% 0.77/1.20 substitution0:
% 0.77/1.20 end
% 0.77/1.20 permutation0:
% 0.77/1.20 0 ==> 0
% 0.77/1.20 end
% 0.77/1.20
% 0.77/1.20 subsumption: (47) {G0,W3,D2,L1,V0,M1} I { orthogonal_lines( skol3, skol2 )
% 0.77/1.20 }.
% 0.77/1.20 parent0: (1315) {G0,W3,D2,L1,V0,M1} { orthogonal_lines( skol3, skol2 ) }.
% 0.77/1.20 substitution0:
% 0.77/1.20 end
% 0.77/1.20 permutation0:
% 0.77/1.20 0 ==> 0
% 0.77/1.20 end
% 0.77/1.20
% 0.77/1.20 subsumption: (48) {G0,W3,D2,L1,V0,M1} I { ! parallel_lines( skol1, skol2 )
% 0.77/1.20 }.
% 0.77/1.20 parent0: (1316) {G0,W3,D2,L1,V0,M1} { ! parallel_lines( skol1, skol2 ) }.
% 0.77/1.20 substitution0:
% 0.77/1.20 end
% 0.77/1.20 permutation0:
% 0.77/1.20 0 ==> 0
% 0.77/1.20 end
% 0.77/1.20
% 0.77/1.20 resolution: (1408) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.77/1.20 convergent_lines( X, Y ) }.
% 0.77/1.20 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.77/1.20 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.77/1.20 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.77/1.20 substitution0:
% 0.77/1.20 X := X
% 0.77/1.20 end
% 0.77/1.20 substitution1:
% 0.77/1.20 X := X
% 0.77/1.20 Y := Y
% 0.77/1.20 Z := X
% 0.77/1.20 end
% 0.77/1.20
% 0.77/1.20 subsumption: (64) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.77/1.20 convergent_lines( X, Y ) }.
% 0.77/1.20 parent0: (1408) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.77/1.20 convergent_lines( X, Y ) }.
% 0.77/1.20 substitution0:
% 0.77/1.20 X := Y
% 0.77/1.20 Y := X
% 0.77/1.20 end
% 0.77/1.20 permutation0:
% 0.77/1.20 0 ==> 1
% 0.77/1.20 1 ==> 0
% 0.77/1.20 end
% 0.77/1.20
% 0.77/1.20 resolution: (1410) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 )
% 0.77/1.20 }.
% 0.77/1.20 parent0[0]: (48) {G0,W3,D2,L1,V0,M1} I { ! parallel_lines( skol1, skol2 )
% 0.77/1.20 }.
% 0.77/1.20 parent1[1]: (41) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.77/1.20 parallel_lines( X, Y ) }.
% 0.77/1.20 substitution0:
% 0.77/1.20 end
% 0.77/1.20 substitution1:
% 0.77/1.20 X := skol1
% 0.77/1.20 Y := skol2
% 0.77/1.20 end
% 0.77/1.20
% 0.77/1.20 subsumption: (70) {G1,W3,D2,L1,V0,M1} R(41,48) { convergent_lines( skol1,
% 0.77/1.20 skol2 ) }.
% 0.77/1.20 parent0: (1410) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 0.77/1.20 substitution0:
% 0.77/1.20 end
% 0.77/1.20 permutation0:
% 0.77/1.20 0 ==> 0
% 0.77/1.20 end
% 0.77/1.20
% 0.77/1.20 resolution: (1411) {G2,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol1 )
% 0.77/1.20 }.
% 0.77/1.20 parent0[0]: (64) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.77/1.20 convergent_lines( X, Y ) }.
% 0.77/1.20 parent1[0]: (70) {G1,W3,D2,L1,V0,M1} R(41,48) { convergent_lines( skol1,
% 0.77/1.20 skol2 ) }.
% 0.77/1.20 substitution0:
% 0.77/1.20 X := skol2
% 0.77/1.20 Y := skol1
% 0.77/1.20 end
% 0.77/1.20 substitution1:
% 0.77/1.20 end
% 0.77/1.20
% 0.77/1.20 subsumption: (71) {G2,W3,D2,L1,V0,M1} R(70,64) { convergent_lines( skol2,
% 0.77/1.20 skol1 ) }.
% 0.77/1.20 parent0: (1411) {G2,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol1 ) }.
% 0.77/1.20 substitution0:
% 0.77/1.20 end
% 0.77/1.21 permutation0:
% 0.77/1.21 0 ==> 0
% 0.77/1.21 end
% 0.77/1.21
% 0.77/1.21 resolution: (1412) {G1,W9,D2,L3,V3,M3} { ! orthogonal_lines( X, Y ), !
% 0.77/1.21 convergent_lines( Y, Z ), unorthogonal_lines( X, Z ) }.
% 0.77/1.21 parent0[1]: (44) {G0,W6,D2,L2,V2,M1} I { ! orthogonal_lines( X, Y ), !
% 0.77/1.21 unorthogonal_lines( X, Y ) }.
% 0.77/1.21 parent1[1]: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 0.77/1.21 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.77/1.21 substitution0:
% 0.77/1.21 X := X
% 0.77/1.21 Y := Y
% 0.77/1.21 end
% 0.77/1.21 substitution1:
% 0.77/1.21 X := Y
% 0.77/1.21 Y := Z
% 0.77/1.21 Z := X
% 0.77/1.21 end
% 0.77/1.21
% 0.77/1.21 subsumption: (209) {G1,W9,D2,L3,V3,M1} R(31,44) { ! convergent_lines( X, Y
% 0.77/1.21 ), ! orthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.77/1.21 parent0: (1412) {G1,W9,D2,L3,V3,M3} { ! orthogonal_lines( X, Y ), !
% 0.77/1.21 convergent_lines( Y, Z ), unorthogonal_lines( X, Z ) }.
% 0.77/1.21 substitution0:
% 0.77/1.21 X := Z
% 0.77/1.21 Y := X
% 0.77/1.21 Z := Y
% 0.77/1.21 end
% 0.77/1.21 permutation0:
% 0.77/1.21 0 ==> 1
% 0.77/1.21 1 ==> 0
% 0.77/1.21 2 ==> 2
% 0.77/1.21 end
% 0.77/1.21
% 0.77/1.21 resolution: (1414) {G1,W9,D2,L3,V3,M3} { ! orthogonal_lines( X, Y ), !
% 0.77/1.21 convergent_lines( Z, Y ), ! orthogonal_lines( X, Z ) }.
% 0.77/1.21 parent0[1]: (44) {G0,W6,D2,L2,V2,M1} I { ! orthogonal_lines( X, Y ), !
% 0.77/1.21 unorthogonal_lines( X, Y ) }.
% 0.77/1.21 parent1[2]: (209) {G1,W9,D2,L3,V3,M1} R(31,44) { ! convergent_lines( X, Y )
% 0.77/1.21 , ! orthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.77/1.21 substitution0:
% 0.77/1.21 X := X
% 0.77/1.21 Y := Y
% 0.77/1.21 end
% 0.77/1.21 substitution1:
% 0.77/1.21 X := Z
% 0.77/1.21 Y := Y
% 0.77/1.21 Z := X
% 0.77/1.21 end
% 0.77/1.21
% 0.77/1.21 subsumption: (1259) {G2,W9,D2,L3,V3,M2} R(209,44) { ! convergent_lines( X,
% 0.77/1.21 Y ), ! orthogonal_lines( Z, Y ), ! orthogonal_lines( Z, X ) }.
% 0.77/1.21 parent0: (1414) {G1,W9,D2,L3,V3,M3} { ! orthogonal_lines( X, Y ), !
% 0.77/1.21 convergent_lines( Z, Y ), ! orthogonal_lines( X, Z ) }.
% 0.77/1.21 substitution0:
% 0.77/1.21 X := Z
% 0.77/1.21 Y := Y
% 0.77/1.21 Z := X
% 0.77/1.21 end
% 0.77/1.21 permutation0:
% 0.77/1.21 0 ==> 1
% 0.77/1.21 1 ==> 0
% 0.77/1.21 2 ==> 2
% 0.77/1.21 end
% 0.77/1.21
% 0.77/1.21 resolution: (1416) {G1,W6,D2,L2,V1,M2} { ! convergent_lines( X, skol1 ), !
% 0.77/1.21 orthogonal_lines( skol3, X ) }.
% 0.77/1.21 parent0[1]: (1259) {G2,W9,D2,L3,V3,M2} R(209,44) { ! convergent_lines( X, Y
% 0.77/1.21 ), ! orthogonal_lines( Z, Y ), ! orthogonal_lines( Z, X ) }.
% 0.77/1.21 parent1[0]: (46) {G0,W3,D2,L1,V0,M1} I { orthogonal_lines( skol3, skol1 )
% 0.77/1.21 }.
% 0.77/1.21 substitution0:
% 0.77/1.21 X := X
% 0.77/1.21 Y := skol1
% 0.77/1.21 Z := skol3
% 0.77/1.21 end
% 0.77/1.21 substitution1:
% 0.77/1.21 end
% 0.77/1.21
% 0.77/1.21 subsumption: (1260) {G3,W6,D2,L2,V1,M1} R(1259,46) { ! convergent_lines( X
% 0.77/1.21 , skol1 ), ! orthogonal_lines( skol3, X ) }.
% 0.77/1.21 parent0: (1416) {G1,W6,D2,L2,V1,M2} { ! convergent_lines( X, skol1 ), !
% 0.77/1.21 orthogonal_lines( skol3, X ) }.
% 0.77/1.21 substitution0:
% 0.77/1.21 X := X
% 0.77/1.21 end
% 0.77/1.21 permutation0:
% 0.77/1.21 0 ==> 0
% 0.77/1.21 1 ==> 1
% 0.77/1.21 end
% 0.77/1.21
% 0.77/1.21 resolution: (1418) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol2, skol1
% 0.77/1.21 ) }.
% 0.77/1.21 parent0[1]: (1260) {G3,W6,D2,L2,V1,M1} R(1259,46) { ! convergent_lines( X,
% 0.77/1.21 skol1 ), ! orthogonal_lines( skol3, X ) }.
% 0.77/1.21 parent1[0]: (47) {G0,W3,D2,L1,V0,M1} I { orthogonal_lines( skol3, skol2 )
% 0.77/1.21 }.
% 0.77/1.21 substitution0:
% 0.77/1.21 X := skol2
% 0.77/1.21 end
% 0.77/1.21 substitution1:
% 0.77/1.21 end
% 0.77/1.21
% 0.77/1.21 resolution: (1419) {G2,W0,D0,L0,V0,M0} { }.
% 0.77/1.21 parent0[0]: (1418) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol2, skol1
% 0.77/1.21 ) }.
% 0.77/1.21 parent1[0]: (71) {G2,W3,D2,L1,V0,M1} R(70,64) { convergent_lines( skol2,
% 0.77/1.21 skol1 ) }.
% 0.77/1.21 substitution0:
% 0.77/1.21 end
% 0.77/1.21 substitution1:
% 0.77/1.21 end
% 0.77/1.21
% 0.77/1.21 subsumption: (1264) {G4,W0,D0,L0,V0,M0} R(1260,47);r(71) { }.
% 0.77/1.21 parent0: (1419) {G2,W0,D0,L0,V0,M0} { }.
% 0.77/1.21 substitution0:
% 0.77/1.21 end
% 0.77/1.21 permutation0:
% 0.77/1.21 end
% 0.77/1.21
% 0.77/1.21 Proof check complete!
% 0.77/1.21
% 0.77/1.21 Memory use:
% 0.77/1.21
% 0.77/1.21 space for terms: 16604
% 0.77/1.21 space for clauses: 49544
% 0.77/1.21
% 0.77/1.21
% 0.77/1.21 clauses generated: 6311
% 0.77/1.21 clauses kept: 1265
% 0.77/1.21 clauses selected: 241
% 0.77/1.21 clauses deleted: 1
% 0.77/1.21 clauses inuse deleted: 0
% 0.77/1.21
% 0.77/1.21 subsentry: 57266
% 0.77/1.21 literals s-matched: 36038
% 0.77/1.21 literals matched: 36008
% 0.77/1.21 full subsumption: 25209
% 0.77/1.21
% 0.77/1.21 checksum: -1202374916
% 0.77/1.21
% 0.77/1.21
% 0.77/1.21 Bliksem ended
%------------------------------------------------------------------------------