%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO218+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n010.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 02:52:54 EDT 2022
% Result : Theorem 1.34s 1.71s
% Output : Refutation 1.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO218+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : bliksem %s
% 0.13/0.35 % Computer : n010.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 : Sat Jun 18 16:34:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.34/1.71 *** allocated 10000 integers for termspace/termends
% 1.34/1.71 *** allocated 10000 integers for clauses
% 1.34/1.71 *** allocated 10000 integers for justifications
% 1.34/1.71 Bliksem 1.12
% 1.34/1.71
% 1.34/1.71
% 1.34/1.71 Automatic Strategy Selection
% 1.34/1.71
% 1.34/1.71
% 1.34/1.71 Clauses:
% 1.34/1.71
% 1.34/1.71 { ! distinct_points( X, X ) }.
% 1.34/1.71 { ! distinct_lines( X, X ) }.
% 1.34/1.71 { ! convergent_lines( X, X ) }.
% 1.34/1.71 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 1.34/1.71 ) }.
% 1.34/1.71 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.34/1.71 }.
% 1.34/1.71 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 1.34/1.71 , Z ) }.
% 1.34/1.71 { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 1.34/1.71 , Y ) ), distinct_points( Z, X ) }.
% 1.34/1.71 { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 1.34/1.71 , Y ) ), distinct_points( Z, Y ) }.
% 1.34/1.71 { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, X ),
% 1.34/1.71 distinct_points( Z, intersection_point( X, Y ) ) }.
% 1.34/1.71 { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, Y ),
% 1.34/1.71 distinct_points( Z, intersection_point( X, Y ) ) }.
% 1.34/1.71 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 1.34/1.71 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 1.34/1.71 apart_point_and_line( Y, T ) }.
% 1.34/1.71 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 1.34/1.71 apart_point_and_line( Z, Y ) }.
% 1.34/1.71 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 1.34/1.71 apart_point_and_line( X, Z ) }.
% 1.34/1.71 { ! convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 1.34/1.71 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.34/1.71 { alpha1( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 1.34/1.71 unorthogonal_lines( X, Y ) }.
% 1.34/1.71 { alpha1( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 1.34/1.71 unorthogonal_lines( X, Y ) }.
% 1.34/1.71 { ! alpha1( X, Y ), convergent_lines( Y, X ) }.
% 1.34/1.71 { ! alpha1( X, Y ), unorthogonal_lines( Y, X ) }.
% 1.34/1.71 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha1( X, Y )
% 1.34/1.71 }.
% 1.34/1.71 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 1.34/1.71 convergent_lines( X, Y ) }.
% 1.34/1.71 { ! convergent_lines( skol3, skol1 ) }.
% 1.34/1.71 { ! unorthogonal_lines( skol3, skol2 ) }.
% 1.34/1.71 { unorthogonal_lines( skol1, skol2 ) }.
% 1.34/1.71
% 1.34/1.71 percentage equality = 0.000000, percentage horn = 0.583333
% 1.34/1.71 This a non-horn, non-equality problem
% 1.34/1.71
% 1.34/1.71
% 1.34/1.71 Options Used:
% 1.34/1.71
% 1.34/1.71 useres = 1
% 1.34/1.71 useparamod = 0
% 1.34/1.71 useeqrefl = 0
% 1.34/1.71 useeqfact = 0
% 1.34/1.71 usefactor = 1
% 1.34/1.71 usesimpsplitting = 0
% 1.34/1.71 usesimpdemod = 0
% 1.34/1.71 usesimpres = 3
% 1.34/1.71
% 1.34/1.71 resimpinuse = 1000
% 1.34/1.71 resimpclauses = 20000
% 1.34/1.71 substype = standard
% 1.34/1.71 backwardsubs = 1
% 1.34/1.71 selectoldest = 5
% 1.34/1.71
% 1.34/1.71 litorderings [0] = split
% 1.34/1.71 litorderings [1] = liftord
% 1.34/1.71
% 1.34/1.71 termordering = none
% 1.34/1.71
% 1.34/1.71 litapriori = 1
% 1.34/1.71 termapriori = 0
% 1.34/1.71 litaposteriori = 0
% 1.34/1.71 termaposteriori = 0
% 1.34/1.71 demodaposteriori = 0
% 1.34/1.71 ordereqreflfact = 0
% 1.34/1.71
% 1.34/1.71 litselect = none
% 1.34/1.71
% 1.34/1.71 maxweight = 15
% 1.34/1.71 maxdepth = 30000
% 1.34/1.71 maxlength = 115
% 1.34/1.71 maxnrvars = 195
% 1.34/1.71 excuselevel = 1
% 1.34/1.71 increasemaxweight = 1
% 1.34/1.71
% 1.34/1.71 maxselected = 10000000
% 1.34/1.71 maxnrclauses = 10000000
% 1.34/1.71
% 1.34/1.71 showgenerated = 0
% 1.34/1.71 showkept = 0
% 1.34/1.71 showselected = 0
% 1.34/1.71 showdeleted = 0
% 1.34/1.71 showresimp = 1
% 1.34/1.71 showstatus = 2000
% 1.34/1.71
% 1.34/1.71 prologoutput = 0
% 1.34/1.71 nrgoals = 5000000
% 1.34/1.71 totalproof = 1
% 1.34/1.71
% 1.34/1.71 Symbols occurring in the translation:
% 1.34/1.71
% 1.34/1.71 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.34/1.71 . [1, 2] (w:1, o:22, a:1, s:1, b:0),
% 1.34/1.71 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 1.34/1.71 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.34/1.71 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.34/1.71 distinct_points [36, 2] (w:1, o:47, a:1, s:1, b:0),
% 1.34/1.71 distinct_lines [37, 2] (w:1, o:48, a:1, s:1, b:0),
% 1.34/1.71 convergent_lines [38, 2] (w:1, o:46, a:1, s:1, b:0),
% 1.34/1.71 line_connecting [41, 2] (w:1, o:49, a:1, s:1, b:0),
% 1.34/1.71 apart_point_and_line [42, 2] (w:1, o:50, a:1, s:1, b:0),
% 1.34/1.71 intersection_point [43, 2] (w:1, o:51, a:1, s:1, b:0),
% 1.34/1.71 unorthogonal_lines [48, 2] (w:1, o:52, a:1, s:1, b:0),
% 1.34/1.71 alpha1 [50, 2] (w:1, o:53, a:1, s:1, b:0),
% 1.34/1.71 skol1 [51, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.34/1.71 skol2 [52, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.34/1.71 skol3 [53, 0] (w:1, o:16, a:1, s:1, b:0).
% 1.34/1.71
% 1.34/1.71
% 1.34/1.71 Starting Search:
% 1.34/1.71
% 1.34/1.71 *** allocated 15000 integers for clauses
% 1.34/1.71 *** allocated 22500 integers for clauses
% 1.34/1.71 *** allocated 33750 integers for clauses
% 1.34/1.71 *** allocated 15000 integers for termspace/termends
% 1.34/1.71
% 1.34/1.71 Bliksems!, er is een bewijs:
% 1.34/1.71 % SZS status Theorem
% 1.34/1.71 % SZS output start Refutation
% 1.34/1.71
% 1.34/1.71 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.34/1.71 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 1.34/1.71 Z ), ! convergent_lines( X, Y ) }.
% 1.34/1.71 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines(
% 1.34/1.71 X, Y ) }.
% 1.34/1.71 (15) {G0,W12,D2,L4,V3,M1} I { convergent_lines( Z, Y ), ! convergent_lines
% 1.34/1.71 ( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z ) }.
% 1.34/1.71 (18) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( Y, X ), ! alpha1( X, Y )
% 1.34/1.71 }.
% 1.34/1.71 (21) {G0,W3,D2,L1,V0,M1} I { ! convergent_lines( skol3, skol1 ) }.
% 1.34/1.71 (22) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol3, skol2 ) }.
% 1.34/1.71 (23) {G0,W3,D2,L1,V0,M1} I { unorthogonal_lines( skol1, skol2 ) }.
% 1.34/1.71 (34) {G1,W3,D2,L1,V0,M1} R(14,22) { convergent_lines( skol3, skol2 ) }.
% 1.34/1.71 (39) {G2,W6,D2,L2,V1,M1} R(5,34) { convergent_lines( skol2, X ),
% 1.34/1.71 convergent_lines( skol3, X ) }.
% 1.34/1.71 (42) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.34/1.71 convergent_lines( X, Y ) }.
% 1.34/1.71 (46) {G2,W3,D2,L1,V0,M1} R(42,21) { ! convergent_lines( skol1, skol3 ) }.
% 1.34/1.71 (48) {G3,W6,D2,L2,V1,M1} R(46,5) { ! convergent_lines( X, skol1 ),
% 1.34/1.71 convergent_lines( X, skol3 ) }.
% 1.34/1.71 (53) {G4,W6,D2,L2,V1,M2} R(48,42) { convergent_lines( skol3, X ), !
% 1.34/1.71 convergent_lines( X, skol1 ) }.
% 1.34/1.71 (57) {G5,W3,D2,L1,V0,M1} R(39,53);r(2) { convergent_lines( skol2, skol1 )
% 1.34/1.71 }.
% 1.34/1.71 (60) {G6,W3,D2,L1,V0,M1} R(57,42) { convergent_lines( skol1, skol2 ) }.
% 1.34/1.71 (159) {G1,W12,D2,L4,V3,M2} R(15,18) { convergent_lines( X, Y ), !
% 1.34/1.71 convergent_lines( Z, Y ), unorthogonal_lines( X, Z ), !
% 1.34/1.71 unorthogonal_lines( Z, Y ) }.
% 1.34/1.71 (660) {G3,W6,D2,L2,V1,M1} R(159,22);r(39) { convergent_lines( skol3, X ), !
% 1.34/1.71 unorthogonal_lines( skol2, X ) }.
% 1.34/1.71 (661) {G7,W6,D2,L2,V1,M1} R(159,23);r(60) { convergent_lines( X, skol2 ),
% 1.34/1.71 unorthogonal_lines( X, skol1 ) }.
% 1.34/1.71 (666) {G8,W3,D2,L1,V0,M1} R(661,660);r(2) { convergent_lines( skol3, skol1
% 1.34/1.71 ) }.
% 1.34/1.71 (668) {G9,W0,D0,L0,V0,M0} S(666);r(21) { }.
% 1.34/1.71
% 1.34/1.71
% 1.34/1.71 % SZS output end Refutation
% 1.34/1.71 found a proof!
% 1.34/1.71
% 1.34/1.71
% 1.34/1.71 Unprocessed initial clauses:
% 1.34/1.71
% 1.34/1.71 (670) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 1.34/1.71 (671) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 1.34/1.71 (672) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 1.34/1.71 (673) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 1.34/1.71 , Z ), distinct_points( Y, Z ) }.
% 1.34/1.71 (674) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 1.34/1.71 ), distinct_lines( Y, Z ) }.
% 1.34/1.71 (675) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines(
% 1.34/1.71 X, Z ), convergent_lines( Y, Z ) }.
% 1.34/1.71 (676) {G0,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ), !
% 1.34/1.71 apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, X
% 1.34/1.71 ) }.
% 1.34/1.71 (677) {G0,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ), !
% 1.34/1.71 apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, Y
% 1.34/1.71 ) }.
% 1.34/1.71 (678) {G0,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ), !
% 1.34/1.71 apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X,
% 1.34/1.71 Y ) ) }.
% 1.34/1.71 (679) {G0,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ), !
% 1.34/1.71 apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X,
% 1.34/1.71 Y ) ) }.
% 1.34/1.71 (680) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines(
% 1.34/1.71 Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 1.34/1.71 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 1.34/1.71 (681) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.34/1.71 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 1.34/1.71 (682) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ), distinct_lines
% 1.34/1.71 ( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.34/1.71 (683) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ), distinct_lines( X
% 1.34/1.71 , Y ) }.
% 1.34/1.71 (684) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 1.34/1.71 X, Y ) }.
% 1.34/1.71 (685) {G0,W12,D2,L4,V3,M4} { alpha1( X, Z ), convergent_lines( Z, Y ), !
% 1.34/1.71 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.34/1.71 (686) {G0,W12,D2,L4,V3,M4} { alpha1( X, Z ), unorthogonal_lines( Z, Y ), !
% 1.34/1.71 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.34/1.71 (687) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( Y, X ) }.
% 1.34/1.71 (688) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( Y, X )
% 1.34/1.71 }.
% 1.34/1.71 (689) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 1.34/1.71 unorthogonal_lines( Y, X ), alpha1( X, Y ) }.
% 1.34/1.71 (690) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ), unorthogonal_lines
% 1.34/1.71 ( Z, Y ), ! convergent_lines( X, Y ) }.
% 1.34/1.71 (691) {G0,W3,D2,L1,V0,M1} { ! convergent_lines( skol3, skol1 ) }.
% 1.34/1.71 (692) {G0,W3,D2,L1,V0,M1} { ! unorthogonal_lines( skol3, skol2 ) }.
% 1.34/1.71 (693) {G0,W3,D2,L1,V0,M1} { unorthogonal_lines( skol1, skol2 ) }.
% 1.34/1.71
% 1.34/1.71
% 1.34/1.71 Total Proof:
% 1.34/1.71
% 1.34/1.71 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.34/1.71 parent0: (672) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := X
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 0
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.34/1.71 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.34/1.71 parent0: (675) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 1.34/1.71 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := X
% 1.34/1.71 Y := Y
% 1.34/1.71 Z := Z
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 2
% 1.34/1.71 1 ==> 0
% 1.34/1.71 2 ==> 1
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 1.34/1.71 unorthogonal_lines( X, Y ) }.
% 1.34/1.71 parent0: (684) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 1.34/1.71 unorthogonal_lines( X, Y ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := X
% 1.34/1.71 Y := Y
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 0
% 1.34/1.71 1 ==> 1
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (15) {G0,W12,D2,L4,V3,M1} I { convergent_lines( Z, Y ), !
% 1.34/1.71 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.34/1.71 }.
% 1.34/1.71 parent0: (685) {G0,W12,D2,L4,V3,M4} { alpha1( X, Z ), convergent_lines( Z
% 1.34/1.71 , Y ), ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := X
% 1.34/1.71 Y := Y
% 1.34/1.71 Z := Z
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 3
% 1.34/1.71 1 ==> 0
% 1.34/1.71 2 ==> 1
% 1.34/1.71 3 ==> 2
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (18) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( Y, X ), !
% 1.34/1.71 alpha1( X, Y ) }.
% 1.34/1.71 parent0: (688) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines
% 1.34/1.71 ( Y, X ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := X
% 1.34/1.71 Y := Y
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 1
% 1.34/1.71 1 ==> 0
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (21) {G0,W3,D2,L1,V0,M1} I { ! convergent_lines( skol3, skol1
% 1.34/1.71 ) }.
% 1.34/1.71 parent0: (691) {G0,W3,D2,L1,V0,M1} { ! convergent_lines( skol3, skol1 )
% 1.34/1.71 }.
% 1.34/1.71 substitution0:
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 0
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (22) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol3,
% 1.34/1.71 skol2 ) }.
% 1.34/1.71 parent0: (692) {G0,W3,D2,L1,V0,M1} { ! unorthogonal_lines( skol3, skol2 )
% 1.34/1.71 }.
% 1.34/1.71 substitution0:
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 0
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (23) {G0,W3,D2,L1,V0,M1} I { unorthogonal_lines( skol1, skol2
% 1.34/1.71 ) }.
% 1.34/1.71 parent0: (693) {G0,W3,D2,L1,V0,M1} { unorthogonal_lines( skol1, skol2 )
% 1.34/1.71 }.
% 1.34/1.71 substitution0:
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 0
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (754) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol2 )
% 1.34/1.71 }.
% 1.34/1.71 parent0[0]: (22) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol3, skol2
% 1.34/1.71 ) }.
% 1.34/1.71 parent1[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 1.34/1.71 unorthogonal_lines( X, Y ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 X := skol3
% 1.34/1.71 Y := skol2
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (34) {G1,W3,D2,L1,V0,M1} R(14,22) { convergent_lines( skol3,
% 1.34/1.71 skol2 ) }.
% 1.34/1.71 parent0: (754) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol2 ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 0
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (755) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ),
% 1.34/1.71 convergent_lines( skol2, X ) }.
% 1.34/1.71 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.34/1.71 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.34/1.71 parent1[0]: (34) {G1,W3,D2,L1,V0,M1} R(14,22) { convergent_lines( skol3,
% 1.34/1.71 skol2 ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := skol3
% 1.34/1.71 Y := skol2
% 1.34/1.71 Z := X
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (39) {G2,W6,D2,L2,V1,M1} R(5,34) { convergent_lines( skol2, X
% 1.34/1.71 ), convergent_lines( skol3, X ) }.
% 1.34/1.71 parent0: (755) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ),
% 1.34/1.71 convergent_lines( skol2, X ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := X
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 1
% 1.34/1.71 1 ==> 0
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (756) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 1.34/1.71 convergent_lines( X, Y ) }.
% 1.34/1.71 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.34/1.71 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.34/1.71 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := X
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 X := X
% 1.34/1.71 Y := Y
% 1.34/1.71 Z := X
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (42) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.34/1.71 convergent_lines( X, Y ) }.
% 1.34/1.71 parent0: (756) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 1.34/1.71 convergent_lines( X, Y ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := Y
% 1.34/1.71 Y := X
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 1
% 1.34/1.71 1 ==> 0
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (758) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol1, skol3 )
% 1.34/1.71 }.
% 1.34/1.71 parent0[0]: (21) {G0,W3,D2,L1,V0,M1} I { ! convergent_lines( skol3, skol1 )
% 1.34/1.71 }.
% 1.34/1.71 parent1[1]: (42) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.34/1.71 convergent_lines( X, Y ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 X := skol3
% 1.34/1.71 Y := skol1
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (46) {G2,W3,D2,L1,V0,M1} R(42,21) { ! convergent_lines( skol1
% 1.34/1.71 , skol3 ) }.
% 1.34/1.71 parent0: (758) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol1, skol3 )
% 1.34/1.71 }.
% 1.34/1.71 substitution0:
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 0
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (760) {G1,W6,D2,L2,V1,M2} { convergent_lines( X, skol3 ), !
% 1.34/1.71 convergent_lines( X, skol1 ) }.
% 1.34/1.71 parent0[0]: (46) {G2,W3,D2,L1,V0,M1} R(42,21) { ! convergent_lines( skol1,
% 1.34/1.71 skol3 ) }.
% 1.34/1.71 parent1[1]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.34/1.71 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 X := X
% 1.34/1.71 Y := skol1
% 1.34/1.71 Z := skol3
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (48) {G3,W6,D2,L2,V1,M1} R(46,5) { ! convergent_lines( X,
% 1.34/1.71 skol1 ), convergent_lines( X, skol3 ) }.
% 1.34/1.71 parent0: (760) {G1,W6,D2,L2,V1,M2} { convergent_lines( X, skol3 ), !
% 1.34/1.71 convergent_lines( X, skol1 ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := X
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 1
% 1.34/1.71 1 ==> 0
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (762) {G2,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ), !
% 1.34/1.71 convergent_lines( X, skol1 ) }.
% 1.34/1.71 parent0[0]: (42) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.34/1.71 convergent_lines( X, Y ) }.
% 1.34/1.71 parent1[1]: (48) {G3,W6,D2,L2,V1,M1} R(46,5) { ! convergent_lines( X, skol1
% 1.34/1.71 ), convergent_lines( X, skol3 ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := skol3
% 1.34/1.71 Y := X
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 X := X
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (53) {G4,W6,D2,L2,V1,M2} R(48,42) { convergent_lines( skol3, X
% 1.34/1.71 ), ! convergent_lines( X, skol1 ) }.
% 1.34/1.71 parent0: (762) {G2,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ), !
% 1.34/1.71 convergent_lines( X, skol1 ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := X
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 0
% 1.34/1.71 1 ==> 1
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (764) {G3,W6,D2,L2,V0,M2} { convergent_lines( skol3, skol3 ),
% 1.34/1.71 convergent_lines( skol2, skol1 ) }.
% 1.34/1.71 parent0[1]: (53) {G4,W6,D2,L2,V1,M2} R(48,42) { convergent_lines( skol3, X
% 1.34/1.71 ), ! convergent_lines( X, skol1 ) }.
% 1.34/1.71 parent1[1]: (39) {G2,W6,D2,L2,V1,M1} R(5,34) { convergent_lines( skol2, X )
% 1.34/1.71 , convergent_lines( skol3, X ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := skol3
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 X := skol1
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (765) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol1 )
% 1.34/1.71 }.
% 1.34/1.71 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.34/1.71 parent1[0]: (764) {G3,W6,D2,L2,V0,M2} { convergent_lines( skol3, skol3 ),
% 1.34/1.71 convergent_lines( skol2, skol1 ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := skol3
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (57) {G5,W3,D2,L1,V0,M1} R(39,53);r(2) { convergent_lines(
% 1.34/1.71 skol2, skol1 ) }.
% 1.34/1.71 parent0: (765) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol1 ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 0
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (766) {G2,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 )
% 1.34/1.71 }.
% 1.34/1.71 parent0[0]: (42) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.34/1.71 convergent_lines( X, Y ) }.
% 1.34/1.71 parent1[0]: (57) {G5,W3,D2,L1,V0,M1} R(39,53);r(2) { convergent_lines(
% 1.34/1.71 skol2, skol1 ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := skol1
% 1.34/1.71 Y := skol2
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (60) {G6,W3,D2,L1,V0,M1} R(57,42) { convergent_lines( skol1,
% 1.34/1.71 skol2 ) }.
% 1.34/1.71 parent0: (766) {G2,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 0
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (768) {G1,W12,D2,L4,V3,M4} { unorthogonal_lines( X, Y ),
% 1.34/1.71 convergent_lines( X, Z ), ! convergent_lines( Y, Z ), !
% 1.34/1.71 unorthogonal_lines( Y, Z ) }.
% 1.34/1.71 parent0[1]: (18) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( Y, X ), !
% 1.34/1.71 alpha1( X, Y ) }.
% 1.34/1.71 parent1[3]: (15) {G0,W12,D2,L4,V3,M1} I { convergent_lines( Z, Y ), !
% 1.34/1.71 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.34/1.71 }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := Y
% 1.34/1.71 Y := X
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 X := Y
% 1.34/1.71 Y := Z
% 1.34/1.71 Z := X
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (159) {G1,W12,D2,L4,V3,M2} R(15,18) { convergent_lines( X, Y )
% 1.34/1.71 , ! convergent_lines( Z, Y ), unorthogonal_lines( X, Z ), !
% 1.34/1.71 unorthogonal_lines( Z, Y ) }.
% 1.34/1.71 parent0: (768) {G1,W12,D2,L4,V3,M4} { unorthogonal_lines( X, Y ),
% 1.34/1.71 convergent_lines( X, Z ), ! convergent_lines( Y, Z ), !
% 1.34/1.71 unorthogonal_lines( Y, Z ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := X
% 1.34/1.71 Y := Z
% 1.34/1.71 Z := Y
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 2
% 1.34/1.71 1 ==> 0
% 1.34/1.71 2 ==> 1
% 1.34/1.71 3 ==> 3
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (769) {G1,W9,D2,L3,V1,M3} { convergent_lines( skol3, X ), !
% 1.34/1.71 convergent_lines( skol2, X ), ! unorthogonal_lines( skol2, X ) }.
% 1.34/1.71 parent0[0]: (22) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol3, skol2
% 1.34/1.71 ) }.
% 1.34/1.71 parent1[2]: (159) {G1,W12,D2,L4,V3,M2} R(15,18) { convergent_lines( X, Y )
% 1.34/1.71 , ! convergent_lines( Z, Y ), unorthogonal_lines( X, Z ), !
% 1.34/1.71 unorthogonal_lines( Z, Y ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 X := skol3
% 1.34/1.71 Y := X
% 1.34/1.71 Z := skol2
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (770) {G2,W9,D2,L3,V1,M3} { convergent_lines( skol3, X ), !
% 1.34/1.71 unorthogonal_lines( skol2, X ), convergent_lines( skol3, X ) }.
% 1.34/1.71 parent0[1]: (769) {G1,W9,D2,L3,V1,M3} { convergent_lines( skol3, X ), !
% 1.34/1.71 convergent_lines( skol2, X ), ! unorthogonal_lines( skol2, X ) }.
% 1.34/1.71 parent1[0]: (39) {G2,W6,D2,L2,V1,M1} R(5,34) { convergent_lines( skol2, X )
% 1.34/1.71 , convergent_lines( skol3, X ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := X
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 X := X
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 factor: (771) {G2,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ), !
% 1.34/1.71 unorthogonal_lines( skol2, X ) }.
% 1.34/1.71 parent0[0, 2]: (770) {G2,W9,D2,L3,V1,M3} { convergent_lines( skol3, X ), !
% 1.34/1.71 unorthogonal_lines( skol2, X ), convergent_lines( skol3, X ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := X
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (660) {G3,W6,D2,L2,V1,M1} R(159,22);r(39) { convergent_lines(
% 1.34/1.71 skol3, X ), ! unorthogonal_lines( skol2, X ) }.
% 1.34/1.71 parent0: (771) {G2,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ), !
% 1.34/1.71 unorthogonal_lines( skol2, X ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := X
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 0
% 1.34/1.71 1 ==> 1
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (772) {G1,W9,D2,L3,V1,M3} { convergent_lines( X, skol2 ), !
% 1.34/1.71 convergent_lines( skol1, skol2 ), unorthogonal_lines( X, skol1 ) }.
% 1.34/1.71 parent0[3]: (159) {G1,W12,D2,L4,V3,M2} R(15,18) { convergent_lines( X, Y )
% 1.34/1.71 , ! convergent_lines( Z, Y ), unorthogonal_lines( X, Z ), !
% 1.34/1.71 unorthogonal_lines( Z, Y ) }.
% 1.34/1.71 parent1[0]: (23) {G0,W3,D2,L1,V0,M1} I { unorthogonal_lines( skol1, skol2 )
% 1.34/1.71 }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := X
% 1.34/1.71 Y := skol2
% 1.34/1.71 Z := skol1
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (773) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol2 ),
% 1.34/1.71 unorthogonal_lines( X, skol1 ) }.
% 1.34/1.71 parent0[1]: (772) {G1,W9,D2,L3,V1,M3} { convergent_lines( X, skol2 ), !
% 1.34/1.71 convergent_lines( skol1, skol2 ), unorthogonal_lines( X, skol1 ) }.
% 1.34/1.71 parent1[0]: (60) {G6,W3,D2,L1,V0,M1} R(57,42) { convergent_lines( skol1,
% 1.34/1.71 skol2 ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := X
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (661) {G7,W6,D2,L2,V1,M1} R(159,23);r(60) { convergent_lines(
% 1.34/1.71 X, skol2 ), unorthogonal_lines( X, skol1 ) }.
% 1.34/1.71 parent0: (773) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol2 ),
% 1.34/1.71 unorthogonal_lines( X, skol1 ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := X
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 0
% 1.34/1.71 1 ==> 1
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (774) {G4,W6,D2,L2,V0,M2} { convergent_lines( skol3, skol1 ),
% 1.34/1.71 convergent_lines( skol2, skol2 ) }.
% 1.34/1.71 parent0[1]: (660) {G3,W6,D2,L2,V1,M1} R(159,22);r(39) { convergent_lines(
% 1.34/1.71 skol3, X ), ! unorthogonal_lines( skol2, X ) }.
% 1.34/1.71 parent1[1]: (661) {G7,W6,D2,L2,V1,M1} R(159,23);r(60) { convergent_lines( X
% 1.34/1.71 , skol2 ), unorthogonal_lines( X, skol1 ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := skol1
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 X := skol2
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (775) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol1 )
% 1.34/1.71 }.
% 1.34/1.71 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.34/1.71 parent1[1]: (774) {G4,W6,D2,L2,V0,M2} { convergent_lines( skol3, skol1 ),
% 1.34/1.71 convergent_lines( skol2, skol2 ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 X := skol2
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (666) {G8,W3,D2,L1,V0,M1} R(661,660);r(2) { convergent_lines(
% 1.34/1.71 skol3, skol1 ) }.
% 1.34/1.71 parent0: (775) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol1 ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 0 ==> 0
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 resolution: (776) {G1,W0,D0,L0,V0,M0} { }.
% 1.34/1.71 parent0[0]: (21) {G0,W3,D2,L1,V0,M1} I { ! convergent_lines( skol3, skol1 )
% 1.34/1.71 }.
% 1.34/1.71 parent1[0]: (666) {G8,W3,D2,L1,V0,M1} R(661,660);r(2) { convergent_lines(
% 1.34/1.71 skol3, skol1 ) }.
% 1.34/1.71 substitution0:
% 1.34/1.71 end
% 1.34/1.71 substitution1:
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 subsumption: (668) {G9,W0,D0,L0,V0,M0} S(666);r(21) { }.
% 1.34/1.71 parent0: (776) {G1,W0,D0,L0,V0,M0} { }.
% 1.34/1.71 substitution0:
% 1.34/1.71 end
% 1.34/1.71 permutation0:
% 1.34/1.71 end
% 1.34/1.71
% 1.34/1.71 Proof check complete!
% 1.34/1.71
% 1.34/1.71 Memory use:
% 1.34/1.71
% 1.34/1.71 space for terms: 10087
% 1.34/1.71 space for clauses: 23746
% 1.34/1.71
% 1.34/1.71
% 1.34/1.71 clauses generated: 40317
% 1.34/1.71 clauses kept: 669
% 1.34/1.71 clauses selected: 278
% 1.34/1.71 clauses deleted: 1
% 1.34/1.71 clauses inuse deleted: 0
% 1.34/1.71
% 1.34/1.71 subsentry: 580459
% 1.34/1.71 literals s-matched: 376160
% 1.34/1.71 literals matched: 376130
% 1.34/1.71 full subsumption: 341834
% 1.34/1.71
% 1.34/1.71 checksum: 326352
% 1.34/1.71
% 1.34/1.71
% 1.34/1.71 Bliksem ended
%------------------------------------------------------------------------------