TSTP Solution File: GEO189+3 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO189+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n004.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 02:52:29 EDT 2022
% Result : Theorem 0.75s 1.16s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : GEO189+3 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.15 % Command : bliksem %s
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % DateTime : Sat Jun 18 03:42:23 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.75/1.15 *** allocated 10000 integers for termspace/termends
% 0.75/1.15 *** allocated 10000 integers for clauses
% 0.75/1.15 *** allocated 10000 integers for justifications
% 0.75/1.15 Bliksem 1.12
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 Automatic Strategy Selection
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 Clauses:
% 0.75/1.15
% 0.75/1.15 { ! distinct_points( X, X ) }.
% 0.75/1.15 { ! distinct_lines( X, X ) }.
% 0.75/1.15 { ! convergent_lines( X, X ) }.
% 0.75/1.15 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.75/1.15 ) }.
% 0.75/1.15 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.75/1.15 }.
% 0.75/1.15 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.75/1.15 , Z ) }.
% 0.75/1.15 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.75/1.15 , Y ) ) }.
% 0.75/1.15 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.75/1.15 , Y ) ) }.
% 0.75/1.15 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.75/1.15 , Y ), X ) }.
% 0.75/1.15 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.75/1.15 , Y ), Y ) }.
% 0.75/1.15 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.75/1.15 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 0.75/1.16 apart_point_and_line( Y, T ) }.
% 0.75/1.16 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 0.75/1.16 apart_point_and_line( Z, Y ) }.
% 0.75/1.16 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 0.75/1.16 apart_point_and_line( X, Z ) }.
% 0.75/1.16 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 0.75/1.16 Z ) }.
% 0.75/1.16 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.75/1.16 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.75/1.16 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.75/1.16 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.75/1.16 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.75/1.16 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.75/1.16 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.75/1.16 , convergent_lines( Y, Z ) }.
% 0.75/1.16 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.75/1.16 , unorthogonal_lines( Y, Z ) }.
% 0.75/1.16 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.75/1.16 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.75/1.16 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.75/1.16 }.
% 0.75/1.16 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.75/1.16 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.75/1.16 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.75/1.16 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 0.75/1.16 unorthogonal_lines( Y, T ) }.
% 0.75/1.16 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.75/1.16 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.75/1.16 unorthogonal_lines( X, Y ) }.
% 0.75/1.16 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.75/1.16 unorthogonal_lines( X, Y ) }.
% 0.75/1.16 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.75/1.16 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.75/1.16 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.75/1.16 }.
% 0.75/1.16 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 0.75/1.16 convergent_lines( X, Y ) }.
% 0.75/1.16 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.75/1.16 line_connecting( X, Y ) ) }.
% 0.75/1.16 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 0.75/1.16 intersection_point( X, Y ) ) }.
% 0.75/1.16 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.75/1.16 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.75/1.16 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.75/1.16 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.75/1.16 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.75/1.16 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.75/1.16 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.75/1.16 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.75/1.16 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.75/1.16 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.75/1.16 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.75/1.16 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.75/1.16 { distinct_points( skol1, skol2 ) }.
% 0.75/1.16 { distinct_points( skol1, skol3 ) }.
% 0.75/1.16 { distinct_points( skol2, skol3 ) }.
% 0.75/1.16 { incident_point_and_line( skol3, line_connecting( skol1, skol2 ) ) }.
% 0.75/1.16 { ! incident_point_and_line( skol2, line_connecting( skol1, skol3 ) ) }.
% 0.75/1.16
% 0.75/1.16 percentage equality = 0.000000, percentage horn = 0.627451
% 0.75/1.16 This a non-horn, non-equality problem
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 Options Used:
% 0.75/1.16
% 0.75/1.16 useres = 1
% 0.75/1.16 useparamod = 0
% 0.75/1.16 useeqrefl = 0
% 0.75/1.16 useeqfact = 0
% 0.75/1.16 usefactor = 1
% 0.75/1.16 usesimpsplitting = 0
% 0.75/1.16 usesimpdemod = 0
% 0.75/1.16 usesimpres = 3
% 0.75/1.16
% 0.75/1.16 resimpinuse = 1000
% 0.75/1.16 resimpclauses = 20000
% 0.75/1.16 substype = standard
% 0.75/1.16 backwardsubs = 1
% 0.75/1.16 selectoldest = 5
% 0.75/1.16
% 0.75/1.16 litorderings [0] = split
% 0.75/1.16 litorderings [1] = liftord
% 0.75/1.16
% 0.75/1.16 termordering = none
% 0.75/1.16
% 0.75/1.16 litapriori = 1
% 0.75/1.16 termapriori = 0
% 0.75/1.16 litaposteriori = 0
% 0.75/1.16 termaposteriori = 0
% 0.75/1.16 demodaposteriori = 0
% 0.75/1.16 ordereqreflfact = 0
% 0.75/1.16
% 0.75/1.16 litselect = none
% 0.75/1.16
% 0.75/1.16 maxweight = 15
% 0.75/1.16 maxdepth = 30000
% 0.75/1.16 maxlength = 115
% 0.75/1.16 maxnrvars = 195
% 0.75/1.16 excuselevel = 1
% 0.75/1.16 increasemaxweight = 1
% 0.75/1.16
% 0.75/1.16 maxselected = 10000000
% 0.75/1.16 maxnrclauses = 10000000
% 0.75/1.16
% 0.75/1.16 showgenerated = 0
% 0.75/1.16 showkept = 0
% 0.75/1.16 showselected = 0
% 0.75/1.16 showdeleted = 0
% 0.75/1.16 showresimp = 1
% 0.75/1.16 showstatus = 2000
% 0.75/1.16
% 0.75/1.16 prologoutput = 0
% 0.75/1.16 nrgoals = 5000000
% 0.75/1.16 totalproof = 1
% 0.75/1.16
% 0.75/1.16 Symbols occurring in the translation:
% 0.75/1.16
% 0.75/1.16 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.75/1.16 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 0.75/1.16 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 0.75/1.16 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.16 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.16 distinct_points [36, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.75/1.16 distinct_lines [37, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.75/1.16 convergent_lines [38, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.75/1.16 line_connecting [41, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.75/1.16 apart_point_and_line [42, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.75/1.16 intersection_point [43, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.75/1.16 parallel_through_point [46, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.75/1.16 unorthogonal_lines [49, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.75/1.16 orthogonal_through_point [52, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.75/1.16 point [54, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.75/1.16 line [55, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.75/1.16 equal_points [56, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.75/1.16 equal_lines [57, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.75/1.16 parallel_lines [58, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.75/1.16 incident_point_and_line [59, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.75/1.16 orthogonal_lines [60, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.75/1.16 alpha1 [61, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.75/1.16 alpha2 [62, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.75/1.16 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.75/1.16 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.75/1.16 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 Starting Search:
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 Bliksems!, er is een bewijs:
% 0.75/1.16 % SZS status Theorem
% 0.75/1.16 % SZS output start Refutation
% 0.75/1.16
% 0.75/1.16 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.75/1.16 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.75/1.16 , ! distinct_lines( X, Y ) }.
% 0.75/1.16 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 0.75/1.16 X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.75/1.16 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 0.75/1.16 , Y ) }.
% 0.75/1.16 (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 0.75/1.16 , X ), Y ) }.
% 0.75/1.16 (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.75/1.16 parallel_through_point( Y, X ) ) }.
% 0.75/1.16 (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.75/1.16 incident_point_and_line( X, Y ) }.
% 0.75/1.16 (50) {G0,W5,D3,L1,V0,M1} I { ! incident_point_and_line( skol2,
% 0.75/1.16 line_connecting( skol1, skol3 ) ) }.
% 0.75/1.16 (59) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 0.75/1.16 ( X, Y ) }.
% 0.75/1.16 (78) {G1,W5,D3,L1,V0,M1} R(43,50) { apart_point_and_line( skol2,
% 0.75/1.16 line_connecting( skol1, skol3 ) ) }.
% 0.75/1.16 (123) {G2,W6,D2,L2,V2,M1} R(14,59) { convergent_lines( X, Y ), !
% 0.75/1.16 distinct_lines( Y, X ) }.
% 0.75/1.16 (138) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.75/1.16 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.75/1.16 (170) {G2,W7,D3,L1,V1,M1} R(138,78) { distinct_lines( line_connecting(
% 0.75/1.16 skol1, skol3 ), parallel_through_point( X, skol2 ) ) }.
% 0.75/1.16 (171) {G3,W7,D3,L1,V1,M1} R(170,123) { convergent_lines(
% 0.75/1.16 parallel_through_point( X, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 0.75/1.16 (176) {G4,W0,D0,L0,V0,M0} R(171,15) { }.
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 % SZS output end Refutation
% 0.75/1.16 found a proof!
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 Unprocessed initial clauses:
% 0.75/1.16
% 0.75/1.16 (178) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.75/1.16 (179) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.75/1.16 (180) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.75/1.16 (181) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.75/1.16 , Z ), distinct_points( Y, Z ) }.
% 0.75/1.16 (182) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.75/1.16 ), distinct_lines( Y, Z ) }.
% 0.75/1.16 (183) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines(
% 0.75/1.16 X, Z ), convergent_lines( Y, Z ) }.
% 0.75/1.16 (184) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.75/1.16 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.75/1.16 (185) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.75/1.16 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.75/1.16 (186) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.75/1.16 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.75/1.16 (187) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.75/1.16 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.75/1.16 (188) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines(
% 0.75/1.16 Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 0.75/1.16 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.75/1.16 (189) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.75/1.16 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.75/1.16 (190) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ), distinct_lines
% 0.75/1.16 ( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.75/1.16 (191) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.75/1.16 , Z ), convergent_lines( X, Z ) }.
% 0.75/1.16 (192) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 0.75/1.16 , Y ) }.
% 0.75/1.16 (193) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 0.75/1.16 , X ), Y ) }.
% 0.75/1.16 (194) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.75/1.16 parallel_through_point( Y, X ) ) }.
% 0.75/1.16 (195) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 0.75/1.16 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.75/1.16 convergent_lines( X, Y ) }.
% 0.75/1.16 (196) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.75/1.16 X, Y ) }.
% 0.75/1.16 (197) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.75/1.16 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.75/1.16 (198) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.75/1.16 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.75/1.16 }.
% 0.75/1.16 (199) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.75/1.16 (200) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.75/1.16 }.
% 0.75/1.16 (201) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 0.75/1.16 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.75/1.16 (202) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines( orthogonal_through_point
% 0.75/1.16 ( Y, X ), Y ) }.
% 0.75/1.16 (203) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.75/1.16 orthogonal_through_point( Y, X ) ) }.
% 0.75/1.16 (204) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 0.75/1.16 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.75/1.16 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.75/1.16 (205) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.75/1.16 X, Y ) }.
% 0.75/1.16 (206) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 0.75/1.16 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.75/1.16 (207) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ), !
% 0.75/1.16 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.75/1.16 (208) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.75/1.16 (209) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.75/1.16 }.
% 0.75/1.16 (210) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 0.75/1.16 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.75/1.16 (211) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ), unorthogonal_lines
% 0.75/1.16 ( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.75/1.16 (212) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.75/1.16 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.75/1.16 (213) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 0.75/1.16 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.75/1.16 (214) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.75/1.16 parallel_through_point( X, Y ) ) }.
% 0.75/1.16 (215) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.75/1.16 orthogonal_through_point( X, Y ) ) }.
% 0.75/1.16 (216) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X,
% 0.75/1.16 Y ) }.
% 0.75/1.16 (217) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 0.75/1.16 }.
% 0.75/1.16 (218) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.75/1.16 ) }.
% 0.75/1.16 (219) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.75/1.16 }.
% 0.75/1.16 (220) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines(
% 0.75/1.16 X, Y ) }.
% 0.75/1.16 (221) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X, Y
% 0.75/1.16 ) }.
% 0.75/1.16 (222) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 0.75/1.16 apart_point_and_line( X, Y ) }.
% 0.75/1.16 (223) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.75/1.16 incident_point_and_line( X, Y ) }.
% 0.75/1.16 (224) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.75/1.16 unorthogonal_lines( X, Y ) }.
% 0.75/1.16 (225) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines(
% 0.75/1.16 X, Y ) }.
% 0.75/1.16 (226) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 0.75/1.16 (227) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol3 ) }.
% 0.75/1.16 (228) {G0,W3,D2,L1,V0,M1} { distinct_points( skol2, skol3 ) }.
% 0.75/1.16 (229) {G0,W5,D3,L1,V0,M1} { incident_point_and_line( skol3,
% 0.75/1.16 line_connecting( skol1, skol2 ) ) }.
% 0.75/1.16 (230) {G0,W5,D3,L1,V0,M1} { ! incident_point_and_line( skol2,
% 0.75/1.16 line_connecting( skol1, skol3 ) ) }.
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 Total Proof:
% 0.75/1.16
% 0.75/1.16 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.75/1.16 parent0: (179) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := X
% 0.75/1.16 end
% 0.75/1.16 permutation0:
% 0.75/1.16 0 ==> 0
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.75/1.16 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.75/1.16 parent0: (182) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 0.75/1.16 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := X
% 0.75/1.16 Y := Y
% 0.75/1.16 Z := Z
% 0.75/1.16 end
% 0.75/1.16 permutation0:
% 0.75/1.16 0 ==> 2
% 0.75/1.16 1 ==> 0
% 0.75/1.16 2 ==> 1
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.75/1.16 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.75/1.16 parent0: (190) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.75/1.16 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := X
% 0.75/1.16 Y := Y
% 0.75/1.16 Z := Z
% 0.75/1.16 end
% 0.75/1.16 permutation0:
% 0.75/1.16 0 ==> 2
% 0.75/1.16 1 ==> 0
% 0.75/1.16 2 ==> 1
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.75/1.16 distinct_lines( X, Y ) }.
% 0.75/1.16 parent0: (192) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 0.75/1.16 convergent_lines( X, Y ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := X
% 0.75/1.16 Y := Y
% 0.75/1.16 end
% 0.75/1.16 permutation0:
% 0.75/1.16 0 ==> 1
% 0.75/1.16 1 ==> 0
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 *** allocated 15000 integers for clauses
% 0.75/1.16 subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.75/1.16 parallel_through_point( Y, X ), Y ) }.
% 0.75/1.16 parent0: (193) {G0,W5,D3,L1,V2,M1} { ! convergent_lines(
% 0.75/1.16 parallel_through_point( Y, X ), Y ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := X
% 0.75/1.16 Y := Y
% 0.75/1.16 end
% 0.75/1.16 permutation0:
% 0.75/1.16 0 ==> 0
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 subsumption: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.75/1.16 parallel_through_point( Y, X ) ) }.
% 0.75/1.16 parent0: (194) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.75/1.16 parallel_through_point( Y, X ) ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := X
% 0.75/1.16 Y := Y
% 0.75/1.16 end
% 0.75/1.16 permutation0:
% 0.75/1.16 0 ==> 0
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 subsumption: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.75/1.16 incident_point_and_line( X, Y ) }.
% 0.75/1.16 parent0: (223) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.75/1.16 incident_point_and_line( X, Y ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := X
% 0.75/1.16 Y := Y
% 0.75/1.16 end
% 0.75/1.16 permutation0:
% 0.75/1.16 0 ==> 0
% 0.75/1.16 1 ==> 1
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 subsumption: (50) {G0,W5,D3,L1,V0,M1} I { ! incident_point_and_line( skol2
% 0.75/1.16 , line_connecting( skol1, skol3 ) ) }.
% 0.75/1.16 parent0: (230) {G0,W5,D3,L1,V0,M1} { ! incident_point_and_line( skol2,
% 0.75/1.16 line_connecting( skol1, skol3 ) ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 end
% 0.75/1.16 permutation0:
% 0.75/1.16 0 ==> 0
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 resolution: (299) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.75/1.16 distinct_lines( X, Y ) }.
% 0.75/1.16 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.75/1.16 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.75/1.16 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := X
% 0.75/1.16 end
% 0.75/1.16 substitution1:
% 0.75/1.16 X := X
% 0.75/1.16 Y := Y
% 0.75/1.16 Z := X
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 subsumption: (59) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.75/1.16 distinct_lines( X, Y ) }.
% 0.75/1.16 parent0: (299) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.75/1.16 distinct_lines( X, Y ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := Y
% 0.75/1.16 Y := X
% 0.75/1.16 end
% 0.75/1.16 permutation0:
% 0.75/1.16 0 ==> 1
% 0.75/1.16 1 ==> 0
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 resolution: (301) {G1,W5,D3,L1,V0,M1} { apart_point_and_line( skol2,
% 0.75/1.16 line_connecting( skol1, skol3 ) ) }.
% 0.75/1.16 parent0[0]: (50) {G0,W5,D3,L1,V0,M1} I { ! incident_point_and_line( skol2,
% 0.75/1.16 line_connecting( skol1, skol3 ) ) }.
% 0.75/1.16 parent1[1]: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.75/1.16 incident_point_and_line( X, Y ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 end
% 0.75/1.16 substitution1:
% 0.75/1.16 X := skol2
% 0.75/1.16 Y := line_connecting( skol1, skol3 )
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 subsumption: (78) {G1,W5,D3,L1,V0,M1} R(43,50) { apart_point_and_line(
% 0.75/1.16 skol2, line_connecting( skol1, skol3 ) ) }.
% 0.75/1.16 parent0: (301) {G1,W5,D3,L1,V0,M1} { apart_point_and_line( skol2,
% 0.75/1.16 line_connecting( skol1, skol3 ) ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 end
% 0.75/1.16 permutation0:
% 0.75/1.16 0 ==> 0
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 resolution: (302) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.75/1.16 distinct_lines( Y, X ) }.
% 0.75/1.16 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.75/1.16 distinct_lines( X, Y ) }.
% 0.75/1.16 parent1[1]: (59) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.75/1.16 distinct_lines( X, Y ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := X
% 0.75/1.16 Y := Y
% 0.75/1.16 end
% 0.75/1.16 substitution1:
% 0.75/1.16 X := X
% 0.75/1.16 Y := Y
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 subsumption: (123) {G2,W6,D2,L2,V2,M1} R(14,59) { convergent_lines( X, Y )
% 0.75/1.16 , ! distinct_lines( Y, X ) }.
% 0.75/1.16 parent0: (302) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.75/1.16 distinct_lines( Y, X ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := X
% 0.75/1.16 Y := Y
% 0.75/1.16 end
% 0.75/1.16 permutation0:
% 0.75/1.16 0 ==> 0
% 0.75/1.16 1 ==> 1
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 resolution: (303) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.75/1.16 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.75/1.16 parent0[0]: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.75/1.16 parallel_through_point( Y, X ) ) }.
% 0.75/1.16 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.75/1.16 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := X
% 0.75/1.16 Y := Y
% 0.75/1.16 end
% 0.75/1.16 substitution1:
% 0.75/1.16 X := X
% 0.75/1.16 Y := Z
% 0.75/1.16 Z := parallel_through_point( Y, X )
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 subsumption: (138) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.75/1.16 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.75/1.16 parent0: (303) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.75/1.16 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := Z
% 0.75/1.16 Y := Y
% 0.75/1.16 Z := X
% 0.75/1.16 end
% 0.75/1.16 permutation0:
% 0.75/1.16 0 ==> 0
% 0.75/1.16 1 ==> 1
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 resolution: (304) {G2,W7,D3,L1,V1,M1} { distinct_lines( line_connecting(
% 0.75/1.16 skol1, skol3 ), parallel_through_point( X, skol2 ) ) }.
% 0.75/1.16 parent0[1]: (138) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.75/1.16 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.75/1.16 parent1[0]: (78) {G1,W5,D3,L1,V0,M1} R(43,50) { apart_point_and_line( skol2
% 0.75/1.16 , line_connecting( skol1, skol3 ) ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := line_connecting( skol1, skol3 )
% 0.75/1.16 Y := X
% 0.75/1.16 Z := skol2
% 0.75/1.16 end
% 0.75/1.16 substitution1:
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 subsumption: (170) {G2,W7,D3,L1,V1,M1} R(138,78) { distinct_lines(
% 0.75/1.16 line_connecting( skol1, skol3 ), parallel_through_point( X, skol2 ) ) }.
% 0.75/1.16 parent0: (304) {G2,W7,D3,L1,V1,M1} { distinct_lines( line_connecting(
% 0.75/1.16 skol1, skol3 ), parallel_through_point( X, skol2 ) ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := X
% 0.75/1.16 end
% 0.75/1.16 permutation0:
% 0.75/1.16 0 ==> 0
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 resolution: (305) {G3,W7,D3,L1,V1,M1} { convergent_lines(
% 0.75/1.16 parallel_through_point( X, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 0.75/1.16 parent0[1]: (123) {G2,W6,D2,L2,V2,M1} R(14,59) { convergent_lines( X, Y ),
% 0.75/1.16 ! distinct_lines( Y, X ) }.
% 0.75/1.16 parent1[0]: (170) {G2,W7,D3,L1,V1,M1} R(138,78) { distinct_lines(
% 0.75/1.16 line_connecting( skol1, skol3 ), parallel_through_point( X, skol2 ) ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := parallel_through_point( X, skol2 )
% 0.75/1.16 Y := line_connecting( skol1, skol3 )
% 0.75/1.16 end
% 0.75/1.16 substitution1:
% 0.75/1.16 X := X
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 subsumption: (171) {G3,W7,D3,L1,V1,M1} R(170,123) { convergent_lines(
% 0.75/1.16 parallel_through_point( X, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 0.75/1.16 parent0: (305) {G3,W7,D3,L1,V1,M1} { convergent_lines(
% 0.75/1.16 parallel_through_point( X, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := X
% 0.75/1.16 end
% 0.75/1.16 permutation0:
% 0.75/1.16 0 ==> 0
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 resolution: (306) {G1,W0,D0,L0,V0,M0} { }.
% 0.75/1.16 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.75/1.16 parallel_through_point( Y, X ), Y ) }.
% 0.75/1.16 parent1[0]: (171) {G3,W7,D3,L1,V1,M1} R(170,123) { convergent_lines(
% 0.75/1.16 parallel_through_point( X, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 0.75/1.16 substitution0:
% 0.75/1.16 X := skol2
% 0.75/1.16 Y := line_connecting( skol1, skol3 )
% 0.75/1.16 end
% 0.75/1.16 substitution1:
% 0.75/1.16 X := line_connecting( skol1, skol3 )
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 subsumption: (176) {G4,W0,D0,L0,V0,M0} R(171,15) { }.
% 0.75/1.16 parent0: (306) {G1,W0,D0,L0,V0,M0} { }.
% 0.75/1.16 substitution0:
% 0.75/1.16 end
% 0.75/1.16 permutation0:
% 0.75/1.16 end
% 0.75/1.16
% 0.75/1.16 Proof check complete!
% 0.75/1.16
% 0.75/1.16 Memory use:
% 0.75/1.16
% 0.75/1.16 space for terms: 3258
% 0.75/1.16 space for clauses: 8222
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 clauses generated: 466
% 0.75/1.16 clauses kept: 177
% 0.75/1.16 clauses selected: 70
% 0.75/1.16 clauses deleted: 0
% 0.75/1.16 clauses inuse deleted: 0
% 0.75/1.16
% 0.75/1.16 subsentry: 772
% 0.75/1.16 literals s-matched: 607
% 0.75/1.16 literals matched: 577
% 0.75/1.16 full subsumption: 169
% 0.75/1.16
% 0.75/1.16 checksum: 1766367427
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 Bliksem ended
%------------------------------------------------------------------------------