TSTP Solution File: GEO226+3 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO226+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n005.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 02:53:02 EDT 2022
% Result : Theorem 0.43s 1.12s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO226+3 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sat Jun 18 02:40:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.12 *** allocated 10000 integers for termspace/termends
% 0.43/1.12 *** allocated 10000 integers for clauses
% 0.43/1.12 *** allocated 10000 integers for justifications
% 0.43/1.12 Bliksem 1.12
% 0.43/1.12
% 0.43/1.12
% 0.43/1.12 Automatic Strategy Selection
% 0.43/1.12
% 0.43/1.12
% 0.43/1.12 Clauses:
% 0.43/1.12
% 0.43/1.12 { ! distinct_points( X, X ) }.
% 0.43/1.12 { ! distinct_lines( X, X ) }.
% 0.43/1.12 { ! convergent_lines( X, X ) }.
% 0.43/1.12 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.43/1.12 ) }.
% 0.43/1.12 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.43/1.12 }.
% 0.43/1.12 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.43/1.12 , Z ) }.
% 0.43/1.12 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.43/1.12 , Y ) ) }.
% 0.43/1.12 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.43/1.12 , Y ) ) }.
% 0.43/1.12 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.43/1.12 , Y ), X ) }.
% 0.43/1.12 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.43/1.12 , Y ), Y ) }.
% 0.43/1.12 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.43/1.12 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 0.43/1.12 apart_point_and_line( Y, T ) }.
% 0.43/1.12 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 0.43/1.12 apart_point_and_line( Z, Y ) }.
% 0.43/1.12 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 0.43/1.12 apart_point_and_line( X, Z ) }.
% 0.43/1.12 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 0.43/1.12 Z ) }.
% 0.43/1.12 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.43/1.12 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.43/1.12 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.43/1.12 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.43/1.12 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.43/1.12 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.43/1.12 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.43/1.12 , convergent_lines( Y, Z ) }.
% 0.43/1.12 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.43/1.12 , unorthogonal_lines( Y, Z ) }.
% 0.43/1.12 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.43/1.12 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.43/1.12 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.43/1.12 }.
% 0.43/1.12 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.43/1.12 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.43/1.12 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.43/1.12 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 0.43/1.12 unorthogonal_lines( Y, T ) }.
% 0.43/1.12 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.43/1.12 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.43/1.12 unorthogonal_lines( X, Y ) }.
% 0.43/1.12 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.43/1.12 unorthogonal_lines( X, Y ) }.
% 0.43/1.12 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.43/1.12 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.43/1.12 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.43/1.12 }.
% 0.43/1.12 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 0.43/1.12 convergent_lines( X, Y ) }.
% 0.43/1.12 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.43/1.12 line_connecting( X, Y ) ) }.
% 0.43/1.12 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 0.43/1.12 intersection_point( X, Y ) ) }.
% 0.43/1.12 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.43/1.12 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.43/1.12 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.43/1.12 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.43/1.12 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.43/1.12 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.43/1.12 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.43/1.12 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.43/1.12 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.43/1.12 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.43/1.12 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.43/1.12 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.43/1.12 { line( skol1 ) }.
% 0.43/1.12 { line( skol2 ) }.
% 0.43/1.12 { convergent_lines( skol1, skol2 ) }.
% 0.43/1.12 { point( X ) }.
% 0.43/1.12 { ! incident_point_and_line( X, skol1 ), ! incident_point_and_line( X,
% 0.43/1.12 skol2 ) }.
% 0.43/1.12
% 0.43/1.12 percentage equality = 0.000000, percentage horn = 0.627451
% 0.43/1.12 This a non-horn, non-equality problem
% 0.43/1.12
% 0.43/1.12
% 0.43/1.12 Options Used:
% 0.43/1.12
% 0.43/1.12 useres = 1
% 0.43/1.12 useparamod = 0
% 0.43/1.12 useeqrefl = 0
% 0.43/1.12 useeqfact = 0
% 0.43/1.12 usefactor = 1
% 0.43/1.12 usesimpsplitting = 0
% 0.43/1.12 usesimpdemod = 0
% 0.43/1.12 usesimpres = 3
% 0.43/1.12
% 0.43/1.12 resimpinuse = 1000
% 0.43/1.12 resimpclauses = 20000
% 0.43/1.12 substype = standard
% 0.43/1.12 backwardsubs = 1
% 0.43/1.12 selectoldest = 5
% 0.43/1.12
% 0.43/1.12 litorderings [0] = split
% 0.43/1.12 litorderings [1] = liftord
% 0.43/1.12
% 0.43/1.12 termordering = none
% 0.43/1.12
% 0.43/1.12 litapriori = 1
% 0.43/1.12 termapriori = 0
% 0.43/1.12 litaposteriori = 0
% 0.43/1.12 termaposteriori = 0
% 0.43/1.12 demodaposteriori = 0
% 0.43/1.12 ordereqreflfact = 0
% 0.43/1.12
% 0.43/1.12 litselect = none
% 0.43/1.12
% 0.43/1.12 maxweight = 15
% 0.43/1.12 maxdepth = 30000
% 0.43/1.12 maxlength = 115
% 0.43/1.12 maxnrvars = 195
% 0.43/1.12 excuselevel = 1
% 0.43/1.12 increasemaxweight = 1
% 0.43/1.12
% 0.43/1.12 maxselected = 10000000
% 0.43/1.12 maxnrclauses = 10000000
% 0.43/1.12
% 0.43/1.12 showgenerated = 0
% 0.43/1.12 showkept = 0
% 0.43/1.12 showselected = 0
% 0.43/1.12 showdeleted = 0
% 0.43/1.12 showresimp = 1
% 0.43/1.12 showstatus = 2000
% 0.43/1.12
% 0.43/1.12 prologoutput = 0
% 0.43/1.12 nrgoals = 5000000
% 0.43/1.12 totalproof = 1
% 0.43/1.12
% 0.43/1.12 Symbols occurring in the translation:
% 0.43/1.12
% 0.43/1.12 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.43/1.12 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 0.43/1.12 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 0.43/1.12 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.43/1.12 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.43/1.12 distinct_points [36, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.43/1.12 distinct_lines [37, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.43/1.12 convergent_lines [38, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.43/1.12 line_connecting [41, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.43/1.12 apart_point_and_line [42, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.43/1.12 intersection_point [43, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.43/1.12 parallel_through_point [46, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.43/1.12 unorthogonal_lines [49, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.43/1.12 orthogonal_through_point [52, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.43/1.12 point [54, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.43/1.12 line [55, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.43/1.12 equal_points [56, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.43/1.12 equal_lines [57, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.43/1.12 parallel_lines [58, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.43/1.12 incident_point_and_line [59, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.43/1.12 orthogonal_lines [60, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.43/1.12 alpha1 [61, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.43/1.12 alpha2 [62, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.43/1.12 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.43/1.12 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0).
% 0.43/1.12
% 0.43/1.12
% 0.43/1.12 Starting Search:
% 0.43/1.12
% 0.43/1.12 *** allocated 15000 integers for clauses
% 0.43/1.12 *** allocated 22500 integers for clauses
% 0.43/1.12 *** allocated 33750 integers for clauses
% 0.43/1.12
% 0.43/1.12 Bliksems!, er is een bewijs:
% 0.43/1.12 % SZS status Theorem
% 0.43/1.12 % SZS output start Refutation
% 0.43/1.12
% 0.43/1.12 (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 0.43/1.12 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.43/1.12 (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 0.43/1.12 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.43/1.12 (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.43/1.12 incident_point_and_line( X, Y ) }.
% 0.43/1.12 (48) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 ) }.
% 0.43/1.12 (50) {G0,W6,D2,L2,V1,M1} I { ! incident_point_and_line( X, skol1 ), !
% 0.43/1.12 incident_point_and_line( X, skol2 ) }.
% 0.43/1.12 (133) {G1,W6,D2,L2,V1,M1} R(50,43) { apart_point_and_line( X, skol2 ), !
% 0.43/1.12 incident_point_and_line( X, skol1 ) }.
% 0.43/1.12 (146) {G2,W6,D2,L2,V1,M1} R(133,43) { apart_point_and_line( X, skol1 ),
% 0.43/1.12 apart_point_and_line( X, skol2 ) }.
% 0.43/1.12 (149) {G3,W8,D3,L2,V1,M1} R(146,9) { ! convergent_lines( X, skol2 ),
% 0.43/1.12 apart_point_and_line( intersection_point( X, skol2 ), skol1 ) }.
% 0.43/1.12 (652) {G4,W0,D0,L0,V0,M0} R(149,8);f;r(48) { }.
% 0.43/1.12
% 0.43/1.12
% 0.43/1.12 % SZS output end Refutation
% 0.43/1.12 found a proof!
% 0.43/1.12
% 0.43/1.12
% 0.43/1.12 Unprocessed initial clauses:
% 0.43/1.12
% 0.43/1.12 (654) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.43/1.12 (655) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.43/1.12 (656) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.43/1.12 (657) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.43/1.12 , Z ), distinct_points( Y, Z ) }.
% 0.43/1.12 (658) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.43/1.12 ), distinct_lines( Y, Z ) }.
% 0.43/1.12 (659) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines(
% 0.43/1.12 X, Z ), convergent_lines( Y, Z ) }.
% 0.43/1.12 (660) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.43/1.12 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.43/1.12 (661) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.43/1.12 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.43/1.12 (662) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.43/1.12 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.43/1.12 (663) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.43/1.12 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.43/1.12 (664) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines(
% 0.43/1.12 Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 0.43/1.12 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.43/1.12 (665) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.43/1.12 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.43/1.12 (666) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ), distinct_lines
% 0.43/1.12 ( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.43/1.12 (667) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.43/1.12 , Z ), convergent_lines( X, Z ) }.
% 0.43/1.12 (668) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 0.43/1.12 , Y ) }.
% 0.43/1.12 (669) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 0.43/1.12 , X ), Y ) }.
% 0.43/1.12 (670) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.43/1.12 parallel_through_point( Y, X ) ) }.
% 0.43/1.12 (671) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 0.43/1.12 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.43/1.12 convergent_lines( X, Y ) }.
% 0.43/1.12 (672) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.43/1.12 X, Y ) }.
% 0.43/1.12 (673) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.43/1.12 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.43/1.12 (674) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.43/1.12 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.43/1.12 }.
% 0.43/1.12 (675) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.43/1.12 (676) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.43/1.12 }.
% 0.43/1.12 (677) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 0.43/1.12 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.43/1.12 (678) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines( orthogonal_through_point
% 0.43/1.12 ( Y, X ), Y ) }.
% 0.43/1.12 (679) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.43/1.12 orthogonal_through_point( Y, X ) ) }.
% 0.43/1.12 (680) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 0.43/1.12 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.43/1.12 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.43/1.12 (681) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.43/1.12 X, Y ) }.
% 0.43/1.12 (682) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 0.43/1.12 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.43/1.12 (683) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ), !
% 0.43/1.12 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.43/1.12 (684) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.43/1.12 (685) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.43/1.12 }.
% 0.43/1.12 (686) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 0.43/1.12 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.43/1.12 (687) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ), unorthogonal_lines
% 0.43/1.12 ( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.43/1.12 (688) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.43/1.12 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.43/1.12 (689) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 0.43/1.12 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.43/1.12 (690) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.43/1.12 parallel_through_point( X, Y ) ) }.
% 0.43/1.12 (691) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.43/1.12 orthogonal_through_point( X, Y ) ) }.
% 0.43/1.12 (692) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X,
% 0.43/1.12 Y ) }.
% 0.43/1.12 (693) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 0.43/1.12 }.
% 0.43/1.12 (694) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.43/1.12 ) }.
% 0.43/1.12 (695) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.43/1.12 }.
% 0.43/1.12 (696) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines(
% 0.43/1.12 X, Y ) }.
% 0.43/1.12 (697) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X, Y
% 0.43/1.12 ) }.
% 0.43/1.12 (698) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 0.43/1.12 apart_point_and_line( X, Y ) }.
% 0.43/1.12 (699) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.43/1.12 incident_point_and_line( X, Y ) }.
% 0.43/1.12 (700) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.43/1.12 unorthogonal_lines( X, Y ) }.
% 0.43/1.12 (701) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines(
% 0.43/1.12 X, Y ) }.
% 0.43/1.12 (702) {G0,W2,D2,L1,V0,M1} { line( skol1 ) }.
% 0.43/1.12 (703) {G0,W2,D2,L1,V0,M1} { line( skol2 ) }.
% 0.43/1.12 (704) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 0.43/1.12 (705) {G0,W2,D2,L1,V1,M1} { point( X ) }.
% 0.43/1.12 (706) {G0,W6,D2,L2,V1,M2} { ! incident_point_and_line( X, skol1 ), !
% 0.43/1.12 incident_point_and_line( X, skol2 ) }.
% 0.43/1.12
% 0.43/1.12
% 0.43/1.12 Total Proof:
% 0.43/1.12
% 0.43/1.12 subsumption: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 0.43/1.12 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.43/1.12 parent0: (662) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.43/1.12 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.43/1.12 substitution0:
% 0.43/1.12 X := X
% 0.43/1.12 Y := Y
% 0.43/1.12 end
% 0.43/1.12 permutation0:
% 0.43/1.12 0 ==> 0
% 0.43/1.12 1 ==> 1
% 0.43/1.12 end
% 0.43/1.12
% 0.43/1.12 subsumption: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 0.43/1.12 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.43/1.12 parent0: (663) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.43/1.12 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.43/1.12 substitution0:
% 0.43/1.12 X := X
% 0.43/1.12 Y := Y
% 0.43/1.12 end
% 0.43/1.12 permutation0:
% 0.43/1.12 0 ==> 0
% 0.43/1.12 1 ==> 1
% 0.43/1.12 end
% 0.43/1.12
% 0.43/1.12 subsumption: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.43/1.12 incident_point_and_line( X, Y ) }.
% 0.43/1.12 parent0: (699) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.43/1.12 incident_point_and_line( X, Y ) }.
% 0.43/1.12 substitution0:
% 0.43/1.12 X := X
% 0.43/1.12 Y := Y
% 0.43/1.12 end
% 0.43/1.12 permutation0:
% 0.43/1.12 0 ==> 0
% 0.43/1.12 1 ==> 1
% 0.43/1.12 end
% 0.43/1.12
% 0.43/1.12 subsumption: (48) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 0.43/1.12 }.
% 0.43/1.12 parent0: (704) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 0.43/1.12 substitution0:
% 0.43/1.12 end
% 0.43/1.12 permutation0:
% 0.43/1.12 0 ==> 0
% 0.43/1.12 end
% 0.43/1.12
% 0.43/1.12 subsumption: (50) {G0,W6,D2,L2,V1,M1} I { ! incident_point_and_line( X,
% 0.43/1.12 skol1 ), ! incident_point_and_line( X, skol2 ) }.
% 0.43/1.12 parent0: (706) {G0,W6,D2,L2,V1,M2} { ! incident_point_and_line( X, skol1 )
% 0.43/1.12 , ! incident_point_and_line( X, skol2 ) }.
% 0.43/1.12 substitution0:
% 0.43/1.12 X := X
% 0.43/1.12 end
% 0.43/1.12 permutation0:
% 0.43/1.12 0 ==> 0
% 0.43/1.12 1 ==> 1
% 0.43/1.12 end
% 0.43/1.12
% 0.43/1.12 resolution: (759) {G1,W6,D2,L2,V1,M2} { ! incident_point_and_line( X,
% 0.43/1.12 skol1 ), apart_point_and_line( X, skol2 ) }.
% 0.43/1.12 parent0[1]: (50) {G0,W6,D2,L2,V1,M1} I { ! incident_point_and_line( X,
% 0.43/1.12 skol1 ), ! incident_point_and_line( X, skol2 ) }.
% 0.43/1.12 parent1[1]: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.43/1.12 incident_point_and_line( X, Y ) }.
% 0.43/1.12 substitution0:
% 0.43/1.12 X := X
% 0.43/1.12 end
% 0.43/1.12 substitution1:
% 0.43/1.12 X := X
% 0.43/1.12 Y := skol2
% 0.43/1.12 end
% 0.43/1.12
% 0.43/1.12 subsumption: (133) {G1,W6,D2,L2,V1,M1} R(50,43) { apart_point_and_line( X,
% 0.43/1.12 skol2 ), ! incident_point_and_line( X, skol1 ) }.
% 0.43/1.12 parent0: (759) {G1,W6,D2,L2,V1,M2} { ! incident_point_and_line( X, skol1 )
% 0.43/1.12 , apart_point_and_line( X, skol2 ) }.
% 0.43/1.12 substitution0:
% 0.43/1.12 X := X
% 0.43/1.12 end
% 0.43/1.12 permutation0:
% 0.43/1.12 0 ==> 1
% 0.43/1.12 1 ==> 0
% 0.43/1.12 end
% 0.43/1.12
% 0.43/1.12 resolution: (760) {G1,W6,D2,L2,V1,M2} { apart_point_and_line( X, skol2 ),
% 0.43/1.12 apart_point_and_line( X, skol1 ) }.
% 0.43/1.12 parent0[1]: (133) {G1,W6,D2,L2,V1,M1} R(50,43) { apart_point_and_line( X,
% 0.43/1.12 skol2 ), ! incident_point_and_line( X, skol1 ) }.
% 0.43/1.12 parent1[1]: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.43/1.12 incident_point_and_line( X, Y ) }.
% 0.43/1.12 substitution0:
% 0.43/1.12 X := X
% 0.43/1.12 end
% 0.43/1.12 substitution1:
% 0.43/1.12 X := X
% 0.43/1.12 Y := skol1
% 0.43/1.12 end
% 0.43/1.12
% 0.43/1.12 subsumption: (146) {G2,W6,D2,L2,V1,M1} R(133,43) { apart_point_and_line( X
% 0.43/1.12 , skol1 ), apart_point_and_line( X, skol2 ) }.
% 0.43/1.12 parent0: (760) {G1,W6,D2,L2,V1,M2} { apart_point_and_line( X, skol2 ),
% 0.43/1.12 apart_point_and_line( X, skol1 ) }.
% 0.43/1.12 substitution0:
% 0.43/1.12 X := X
% 0.43/1.12 end
% 0.43/1.12 permutation0:
% 0.43/1.12 0 ==> 1
% 0.43/1.12 1 ==> 0
% 0.43/1.12 end
% 0.43/1.12
% 0.43/1.12 resolution: (762) {G1,W8,D3,L2,V1,M2} { ! convergent_lines( X, skol2 ),
% 0.43/1.12 apart_point_and_line( intersection_point( X, skol2 ), skol1 ) }.
% 0.43/1.12 parent0[1]: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 0.43/1.12 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.43/1.12 parent1[1]: (146) {G2,W6,D2,L2,V1,M1} R(133,43) { apart_point_and_line( X,
% 0.43/1.12 skol1 ), apart_point_and_line( X, skol2 ) }.
% 0.43/1.12 substitution0:
% 0.43/1.12 X := X
% 0.43/1.12 Y := skol2
% 0.43/1.12 end
% 0.43/1.12 substitution1:
% 0.43/1.12 X := intersection_point( X, skol2 )
% 0.43/1.12 end
% 0.43/1.12
% 0.43/1.12 subsumption: (149) {G3,W8,D3,L2,V1,M1} R(146,9) { ! convergent_lines( X,
% 0.43/1.12 skol2 ), apart_point_and_line( intersection_point( X, skol2 ), skol1 )
% 0.43/1.12 }.
% 0.43/1.12 parent0: (762) {G1,W8,D3,L2,V1,M2} { ! convergent_lines( X, skol2 ),
% 0.43/1.12 apart_point_and_line( intersection_point( X, skol2 ), skol1 ) }.
% 0.43/1.12 substitution0:
% 0.43/1.12 X := X
% 0.43/1.12 end
% 0.43/1.12 permutation0:
% 0.43/1.12 0 ==> 0
% 0.43/1.12 1 ==> 1
% 0.43/1.12 end
% 0.43/1.12
% 0.43/1.12 resolution: (763) {G1,W6,D2,L2,V0,M2} { ! convergent_lines( skol1, skol2 )
% 0.43/1.12 , ! convergent_lines( skol1, skol2 ) }.
% 0.43/1.12 parent0[1]: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 0.43/1.12 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.43/1.12 parent1[1]: (149) {G3,W8,D3,L2,V1,M1} R(146,9) { ! convergent_lines( X,
% 0.43/1.12 skol2 ), apart_point_and_line( intersection_point( X, skol2 ), skol1 )
% 0.43/1.12 }.
% 0.43/1.12 substitution0:
% 0.43/1.12 X := skol1
% 0.43/1.12 Y := skol2
% 0.43/1.12 end
% 0.43/1.12 substitution1:
% 0.43/1.12 X := skol1
% 0.43/1.12 end
% 0.43/1.12
% 0.43/1.12 factor: (764) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol1, skol2 ) }.
% 0.43/1.12 parent0[0, 1]: (763) {G1,W6,D2,L2,V0,M2} { ! convergent_lines( skol1,
% 0.43/1.12 skol2 ), ! convergent_lines( skol1, skol2 ) }.
% 0.43/1.12 substitution0:
% 0.43/1.12 end
% 0.43/1.12
% 0.43/1.12 resolution: (766) {G1,W0,D0,L0,V0,M0} { }.
% 0.43/1.12 parent0[0]: (764) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol1, skol2 )
% 0.43/1.12 }.
% 0.43/1.12 parent1[0]: (48) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 0.43/1.12 }.
% 0.43/1.12 substitution0:
% 0.43/1.12 end
% 0.43/1.12 substitution1:
% 0.43/1.12 end
% 0.43/1.12
% 0.43/1.12 subsumption: (652) {G4,W0,D0,L0,V0,M0} R(149,8);f;r(48) { }.
% 0.43/1.12 parent0: (766) {G1,W0,D0,L0,V0,M0} { }.
% 0.43/1.12 substitution0:
% 0.43/1.12 end
% 0.43/1.12 permutation0:
% 0.43/1.12 end
% 0.43/1.12
% 0.43/1.12 Proof check complete!
% 0.43/1.12
% 0.43/1.12 Memory use:
% 0.43/1.12
% 0.43/1.12 space for terms: 8664
% 0.43/1.12 space for clauses: 28270
% 0.43/1.12
% 0.43/1.12
% 0.43/1.12 clauses generated: 2686
% 0.43/1.12 clauses kept: 653
% 0.43/1.12 clauses selected: 167
% 0.43/1.12 clauses deleted: 5
% 0.43/1.12 clauses inuse deleted: 0
% 0.43/1.12
% 0.43/1.12 subsentry: 12481
% 0.43/1.12 literals s-matched: 7898
% 0.43/1.12 literals matched: 7883
% 0.43/1.12 full subsumption: 4717
% 0.43/1.12
% 0.43/1.12 checksum: 770282056
% 0.43/1.12
% 0.43/1.12
% 0.43/1.12 Bliksem ended
%------------------------------------------------------------------------------