TSTP Solution File: GEO190+3 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO190+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n014.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 02:52:30 EDT 2022
% Result : Theorem 0.75s 1.15s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : GEO190+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.14 % Command : bliksem %s
% 0.15/0.36 % Computer : n014.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
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % DateTime : Fri Jun 17 20:47:19 EDT 2022
% 0.15/0.36 % 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 ),
% 0.75/1.15 apart_point_and_line( Y, T ) }.
% 0.75/1.15 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 0.75/1.15 apart_point_and_line( Z, Y ) }.
% 0.75/1.15 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 0.75/1.15 apart_point_and_line( X, Z ) }.
% 0.75/1.15 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 0.75/1.15 Z ) }.
% 0.75/1.15 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.75/1.15 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.75/1.15 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.75/1.15 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.75/1.15 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.75/1.15 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.75/1.15 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.75/1.15 , convergent_lines( Y, Z ) }.
% 0.75/1.15 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.75/1.15 , unorthogonal_lines( Y, Z ) }.
% 0.75/1.15 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.75/1.15 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.75/1.15 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.75/1.15 }.
% 0.75/1.15 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.75/1.15 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.75/1.15 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.75/1.15 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 0.75/1.15 unorthogonal_lines( Y, T ) }.
% 0.75/1.15 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.75/1.15 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.75/1.15 unorthogonal_lines( X, Y ) }.
% 0.75/1.15 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.75/1.15 unorthogonal_lines( X, Y ) }.
% 0.75/1.15 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.75/1.15 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.75/1.15 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.75/1.15 }.
% 0.75/1.15 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 0.75/1.15 convergent_lines( X, Y ) }.
% 0.75/1.15 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.75/1.15 line_connecting( X, Y ) ) }.
% 0.75/1.15 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 0.75/1.15 intersection_point( X, Y ) ) }.
% 0.75/1.15 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.75/1.15 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.75/1.15 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.75/1.15 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.75/1.15 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.75/1.15 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.75/1.15 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.75/1.15 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.75/1.15 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.75/1.15 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.75/1.15 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.75/1.15 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.75/1.15 { distinct_points( skol1, skol2 ) }.
% 0.75/1.15 { distinct_points( skol1, skol3 ) }.
% 0.75/1.15 { distinct_points( skol2, skol3 ) }.
% 0.75/1.15 { incident_point_and_line( skol3, line_connecting( skol1, skol2 ) ) }.
% 0.75/1.15 { ! incident_point_and_line( skol3, line_connecting( skol2, skol1 ) ) }.
% 0.75/1.15
% 0.75/1.15 percentage equality = 0.000000, percentage horn = 0.627451
% 0.75/1.15 This a non-horn, non-equality problem
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 Options Used:
% 0.75/1.15
% 0.75/1.15 useres = 1
% 0.75/1.15 useparamod = 0
% 0.75/1.15 useeqrefl = 0
% 0.75/1.15 useeqfact = 0
% 0.75/1.15 usefactor = 1
% 0.75/1.15 usesimpsplitting = 0
% 0.75/1.15 usesimpdemod = 0
% 0.75/1.15 usesimpres = 3
% 0.75/1.15
% 0.75/1.15 resimpinuse = 1000
% 0.75/1.15 resimpclauses = 20000
% 0.75/1.15 substype = standard
% 0.75/1.15 backwardsubs = 1
% 0.75/1.15 selectoldest = 5
% 0.75/1.15
% 0.75/1.15 litorderings [0] = split
% 0.75/1.15 litorderings [1] = liftord
% 0.75/1.15
% 0.75/1.15 termordering = none
% 0.75/1.15
% 0.75/1.15 litapriori = 1
% 0.75/1.15 termapriori = 0
% 0.75/1.15 litaposteriori = 0
% 0.75/1.15 termaposteriori = 0
% 0.75/1.15 demodaposteriori = 0
% 0.75/1.15 ordereqreflfact = 0
% 0.75/1.15
% 0.75/1.15 litselect = none
% 0.75/1.15
% 0.75/1.15 maxweight = 15
% 0.75/1.15 maxdepth = 30000
% 0.75/1.15 maxlength = 115
% 0.75/1.15 maxnrvars = 195
% 0.75/1.15 excuselevel = 1
% 0.75/1.15 increasemaxweight = 1
% 0.75/1.15
% 0.75/1.15 maxselected = 10000000
% 0.75/1.15 maxnrclauses = 10000000
% 0.75/1.15
% 0.75/1.15 showgenerated = 0
% 0.75/1.15 showkept = 0
% 0.75/1.15 showselected = 0
% 0.75/1.15 showdeleted = 0
% 0.75/1.15 showresimp = 1
% 0.75/1.15 showstatus = 2000
% 0.75/1.15
% 0.75/1.15 prologoutput = 0
% 0.75/1.15 nrgoals = 5000000
% 0.75/1.15 totalproof = 1
% 0.75/1.15
% 0.75/1.15 Symbols occurring in the translation:
% 0.75/1.15
% 0.75/1.15 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.75/1.15 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 0.75/1.15 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 0.75/1.15 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.15 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.15 distinct_points [36, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.75/1.15 distinct_lines [37, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.75/1.15 convergent_lines [38, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.75/1.15 line_connecting [41, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.75/1.15 apart_point_and_line [42, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.75/1.15 intersection_point [43, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.75/1.15 parallel_through_point [46, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.75/1.15 unorthogonal_lines [49, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.75/1.15 orthogonal_through_point [52, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.75/1.15 point [54, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.75/1.15 line [55, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.75/1.15 equal_points [56, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.75/1.15 equal_lines [57, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.75/1.15 parallel_lines [58, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.75/1.15 incident_point_and_line [59, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.75/1.15 orthogonal_lines [60, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.75/1.15 alpha1 [61, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.75/1.15 alpha2 [62, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.75/1.15 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.75/1.15 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.75/1.15 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0).
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 Starting Search:
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 Bliksems!, er is een bewijs:
% 0.75/1.15 % SZS status Theorem
% 0.75/1.15 % SZS output start Refutation
% 0.75/1.15
% 0.75/1.15 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.75/1.15 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.75/1.15 , ! distinct_lines( X, Y ) }.
% 0.75/1.15 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 0.75/1.15 X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.75/1.15 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 0.75/1.15 , Y ) }.
% 0.75/1.15 (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 0.75/1.15 , X ), Y ) }.
% 0.75/1.15 (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.75/1.15 parallel_through_point( Y, X ) ) }.
% 0.75/1.15 (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.75/1.15 incident_point_and_line( X, Y ) }.
% 0.75/1.15 (50) {G0,W5,D3,L1,V0,M1} I { ! incident_point_and_line( skol3,
% 0.75/1.15 line_connecting( skol2, skol1 ) ) }.
% 0.75/1.15 (59) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 0.75/1.15 ( X, Y ) }.
% 0.75/1.15 (78) {G1,W5,D3,L1,V0,M1} R(43,50) { apart_point_and_line( skol3,
% 0.75/1.15 line_connecting( skol2, skol1 ) ) }.
% 0.75/1.15 (123) {G2,W6,D2,L2,V2,M1} R(14,59) { convergent_lines( X, Y ), !
% 0.75/1.15 distinct_lines( Y, X ) }.
% 0.75/1.15 (138) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.75/1.15 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.75/1.15 (170) {G2,W7,D3,L1,V1,M1} R(138,78) { distinct_lines( line_connecting(
% 0.75/1.15 skol2, skol1 ), parallel_through_point( X, skol3 ) ) }.
% 0.75/1.15 (171) {G3,W7,D3,L1,V1,M1} R(170,123) { convergent_lines(
% 0.75/1.15 parallel_through_point( X, skol3 ), line_connecting( skol2, skol1 ) ) }.
% 0.75/1.15 (176) {G4,W0,D0,L0,V0,M0} R(171,15) { }.
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 % SZS output end Refutation
% 0.75/1.15 found a proof!
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 Unprocessed initial clauses:
% 0.75/1.15
% 0.75/1.15 (178) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.75/1.15 (179) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.75/1.15 (180) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.75/1.15 (181) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.75/1.15 , Z ), distinct_points( Y, Z ) }.
% 0.75/1.15 (182) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.75/1.15 ), distinct_lines( Y, Z ) }.
% 0.75/1.15 (183) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines(
% 0.75/1.15 X, Z ), convergent_lines( Y, Z ) }.
% 0.75/1.15 (184) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.75/1.15 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.75/1.15 (185) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.75/1.15 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.75/1.15 (186) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.75/1.15 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.75/1.15 (187) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.75/1.15 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.75/1.15 (188) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines(
% 0.75/1.15 Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 0.75/1.15 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.75/1.15 (189) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.75/1.15 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.75/1.15 (190) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ), distinct_lines
% 0.75/1.15 ( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.75/1.15 (191) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.75/1.15 , Z ), convergent_lines( X, Z ) }.
% 0.75/1.15 (192) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 0.75/1.15 , Y ) }.
% 0.75/1.15 (193) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 0.75/1.15 , X ), Y ) }.
% 0.75/1.15 (194) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.75/1.15 parallel_through_point( Y, X ) ) }.
% 0.75/1.15 (195) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 0.75/1.15 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.75/1.15 convergent_lines( X, Y ) }.
% 0.75/1.15 (196) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.75/1.15 X, Y ) }.
% 0.75/1.15 (197) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.75/1.15 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.75/1.15 (198) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.75/1.15 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.75/1.15 }.
% 0.75/1.15 (199) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.75/1.15 (200) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.75/1.15 }.
% 0.75/1.15 (201) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 0.75/1.15 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.75/1.15 (202) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines( orthogonal_through_point
% 0.75/1.15 ( Y, X ), Y ) }.
% 0.75/1.15 (203) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.75/1.15 orthogonal_through_point( Y, X ) ) }.
% 0.75/1.15 (204) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 0.75/1.15 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.75/1.15 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.75/1.15 (205) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.75/1.15 X, Y ) }.
% 0.75/1.15 (206) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 0.75/1.15 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.75/1.15 (207) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ), !
% 0.75/1.15 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.75/1.15 (208) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.75/1.15 (209) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.75/1.15 }.
% 0.75/1.15 (210) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 0.75/1.15 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.75/1.15 (211) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ), unorthogonal_lines
% 0.75/1.15 ( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.75/1.15 (212) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.75/1.15 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.75/1.15 (213) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 0.75/1.15 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.75/1.15 (214) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.75/1.15 parallel_through_point( X, Y ) ) }.
% 0.75/1.15 (215) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.75/1.15 orthogonal_through_point( X, Y ) ) }.
% 0.75/1.15 (216) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X,
% 0.75/1.15 Y ) }.
% 0.75/1.15 (217) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 0.75/1.15 }.
% 0.75/1.15 (218) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.75/1.15 ) }.
% 0.75/1.15 (219) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.75/1.15 }.
% 0.75/1.15 (220) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines(
% 0.75/1.15 X, Y ) }.
% 0.75/1.15 (221) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X, Y
% 0.75/1.15 ) }.
% 0.75/1.15 (222) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 0.75/1.15 apart_point_and_line( X, Y ) }.
% 0.75/1.15 (223) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.75/1.15 incident_point_and_line( X, Y ) }.
% 0.75/1.15 (224) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.75/1.15 unorthogonal_lines( X, Y ) }.
% 0.75/1.15 (225) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines(
% 0.75/1.15 X, Y ) }.
% 0.75/1.15 (226) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 0.75/1.15 (227) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol3 ) }.
% 0.75/1.15 (228) {G0,W3,D2,L1,V0,M1} { distinct_points( skol2, skol3 ) }.
% 0.75/1.15 (229) {G0,W5,D3,L1,V0,M1} { incident_point_and_line( skol3,
% 0.75/1.15 line_connecting( skol1, skol2 ) ) }.
% 0.75/1.15 (230) {G0,W5,D3,L1,V0,M1} { ! incident_point_and_line( skol3,
% 0.75/1.15 line_connecting( skol2, skol1 ) ) }.
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 Total Proof:
% 0.75/1.15
% 0.75/1.15 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.75/1.15 parent0: (179) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 0
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.75/1.15 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.75/1.15 parent0: (182) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 0.75/1.15 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 Y := Y
% 0.75/1.15 Z := Z
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 2
% 0.75/1.15 1 ==> 0
% 0.75/1.15 2 ==> 1
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.75/1.15 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.75/1.15 parent0: (190) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.75/1.15 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 Y := Y
% 0.75/1.15 Z := Z
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 2
% 0.75/1.15 1 ==> 0
% 0.75/1.15 2 ==> 1
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.75/1.15 distinct_lines( X, Y ) }.
% 0.75/1.15 parent0: (192) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 0.75/1.15 convergent_lines( X, Y ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 Y := Y
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 1
% 0.75/1.15 1 ==> 0
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 *** allocated 15000 integers for clauses
% 0.75/1.15 subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.75/1.15 parallel_through_point( Y, X ), Y ) }.
% 0.75/1.15 parent0: (193) {G0,W5,D3,L1,V2,M1} { ! convergent_lines(
% 0.75/1.15 parallel_through_point( Y, X ), Y ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 Y := Y
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 0
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.75/1.15 parallel_through_point( Y, X ) ) }.
% 0.75/1.15 parent0: (194) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.75/1.15 parallel_through_point( Y, X ) ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 Y := Y
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 0
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.75/1.15 incident_point_and_line( X, Y ) }.
% 0.75/1.15 parent0: (223) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.75/1.15 incident_point_and_line( X, Y ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 Y := Y
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 0
% 0.75/1.15 1 ==> 1
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (50) {G0,W5,D3,L1,V0,M1} I { ! incident_point_and_line( skol3
% 0.75/1.15 , line_connecting( skol2, skol1 ) ) }.
% 0.75/1.15 parent0: (230) {G0,W5,D3,L1,V0,M1} { ! incident_point_and_line( skol3,
% 0.75/1.15 line_connecting( skol2, skol1 ) ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 0
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 resolution: (299) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.75/1.15 distinct_lines( X, Y ) }.
% 0.75/1.15 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.75/1.15 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.75/1.15 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 end
% 0.75/1.15 substitution1:
% 0.75/1.15 X := X
% 0.75/1.15 Y := Y
% 0.75/1.15 Z := X
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (59) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.75/1.15 distinct_lines( X, Y ) }.
% 0.75/1.15 parent0: (299) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.75/1.15 distinct_lines( X, Y ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := Y
% 0.75/1.15 Y := X
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 1
% 0.75/1.15 1 ==> 0
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 resolution: (301) {G1,W5,D3,L1,V0,M1} { apart_point_and_line( skol3,
% 0.75/1.15 line_connecting( skol2, skol1 ) ) }.
% 0.75/1.15 parent0[0]: (50) {G0,W5,D3,L1,V0,M1} I { ! incident_point_and_line( skol3,
% 0.75/1.15 line_connecting( skol2, skol1 ) ) }.
% 0.75/1.15 parent1[1]: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.75/1.15 incident_point_and_line( X, Y ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 end
% 0.75/1.15 substitution1:
% 0.75/1.15 X := skol3
% 0.75/1.15 Y := line_connecting( skol2, skol1 )
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (78) {G1,W5,D3,L1,V0,M1} R(43,50) { apart_point_and_line(
% 0.75/1.15 skol3, line_connecting( skol2, skol1 ) ) }.
% 0.75/1.15 parent0: (301) {G1,W5,D3,L1,V0,M1} { apart_point_and_line( skol3,
% 0.75/1.15 line_connecting( skol2, skol1 ) ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 0
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 resolution: (302) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.75/1.15 distinct_lines( Y, X ) }.
% 0.75/1.15 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.75/1.15 distinct_lines( X, Y ) }.
% 0.75/1.15 parent1[1]: (59) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.75/1.15 distinct_lines( X, Y ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 Y := Y
% 0.75/1.15 end
% 0.75/1.15 substitution1:
% 0.75/1.15 X := X
% 0.75/1.15 Y := Y
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (123) {G2,W6,D2,L2,V2,M1} R(14,59) { convergent_lines( X, Y )
% 0.75/1.15 , ! distinct_lines( Y, X ) }.
% 0.75/1.15 parent0: (302) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.75/1.15 distinct_lines( Y, X ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 Y := Y
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 0
% 0.75/1.15 1 ==> 1
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 resolution: (303) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.75/1.15 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.75/1.15 parent0[0]: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.75/1.15 parallel_through_point( Y, X ) ) }.
% 0.75/1.15 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.75/1.15 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 Y := Y
% 0.75/1.15 end
% 0.75/1.15 substitution1:
% 0.75/1.15 X := X
% 0.75/1.15 Y := Z
% 0.75/1.15 Z := parallel_through_point( Y, X )
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (138) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.75/1.15 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.75/1.15 parent0: (303) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.75/1.15 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := Z
% 0.75/1.15 Y := Y
% 0.75/1.15 Z := X
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 0
% 0.75/1.15 1 ==> 1
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 resolution: (304) {G2,W7,D3,L1,V1,M1} { distinct_lines( line_connecting(
% 0.75/1.15 skol2, skol1 ), parallel_through_point( X, skol3 ) ) }.
% 0.75/1.15 parent0[1]: (138) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.75/1.15 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.75/1.15 parent1[0]: (78) {G1,W5,D3,L1,V0,M1} R(43,50) { apart_point_and_line( skol3
% 0.75/1.15 , line_connecting( skol2, skol1 ) ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := line_connecting( skol2, skol1 )
% 0.75/1.15 Y := X
% 0.75/1.15 Z := skol3
% 0.75/1.15 end
% 0.75/1.15 substitution1:
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (170) {G2,W7,D3,L1,V1,M1} R(138,78) { distinct_lines(
% 0.75/1.15 line_connecting( skol2, skol1 ), parallel_through_point( X, skol3 ) ) }.
% 0.75/1.15 parent0: (304) {G2,W7,D3,L1,V1,M1} { distinct_lines( line_connecting(
% 0.75/1.15 skol2, skol1 ), parallel_through_point( X, skol3 ) ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 0
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 resolution: (305) {G3,W7,D3,L1,V1,M1} { convergent_lines(
% 0.75/1.15 parallel_through_point( X, skol3 ), line_connecting( skol2, skol1 ) ) }.
% 0.75/1.15 parent0[1]: (123) {G2,W6,D2,L2,V2,M1} R(14,59) { convergent_lines( X, Y ),
% 0.75/1.15 ! distinct_lines( Y, X ) }.
% 0.75/1.15 parent1[0]: (170) {G2,W7,D3,L1,V1,M1} R(138,78) { distinct_lines(
% 0.75/1.15 line_connecting( skol2, skol1 ), parallel_through_point( X, skol3 ) ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := parallel_through_point( X, skol3 )
% 0.75/1.15 Y := line_connecting( skol2, skol1 )
% 0.75/1.15 end
% 0.75/1.15 substitution1:
% 0.75/1.15 X := X
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (171) {G3,W7,D3,L1,V1,M1} R(170,123) { convergent_lines(
% 0.75/1.15 parallel_through_point( X, skol3 ), line_connecting( skol2, skol1 ) ) }.
% 0.75/1.15 parent0: (305) {G3,W7,D3,L1,V1,M1} { convergent_lines(
% 0.75/1.15 parallel_through_point( X, skol3 ), line_connecting( skol2, skol1 ) ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 0
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 resolution: (306) {G1,W0,D0,L0,V0,M0} { }.
% 0.75/1.15 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.75/1.15 parallel_through_point( Y, X ), Y ) }.
% 0.75/1.15 parent1[0]: (171) {G3,W7,D3,L1,V1,M1} R(170,123) { convergent_lines(
% 0.75/1.15 parallel_through_point( X, skol3 ), line_connecting( skol2, skol1 ) ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := skol3
% 0.75/1.15 Y := line_connecting( skol2, skol1 )
% 0.75/1.15 end
% 0.75/1.15 substitution1:
% 0.75/1.15 X := line_connecting( skol2, skol1 )
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (176) {G4,W0,D0,L0,V0,M0} R(171,15) { }.
% 0.75/1.15 parent0: (306) {G1,W0,D0,L0,V0,M0} { }.
% 0.75/1.15 substitution0:
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 Proof check complete!
% 0.75/1.15
% 0.75/1.15 Memory use:
% 0.75/1.15
% 0.75/1.15 space for terms: 3258
% 0.75/1.15 space for clauses: 8222
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 clauses generated: 466
% 0.75/1.15 clauses kept: 177
% 0.75/1.15 clauses selected: 70
% 0.75/1.15 clauses deleted: 0
% 0.75/1.15 clauses inuse deleted: 0
% 0.75/1.15
% 0.75/1.15 subsentry: 772
% 0.75/1.15 literals s-matched: 607
% 0.75/1.15 literals matched: 577
% 0.75/1.15 full subsumption: 169
% 0.75/1.15
% 0.75/1.15 checksum: 1998101875
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 Bliksem ended
%------------------------------------------------------------------------------