TSTP Solution File: ALG211+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.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 : Thu Jul 14 12:09:57 EDT 2022
% Result : Theorem 0.42s 1.06s
% Output : Refutation 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Wed Jun 8 06:39:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/1.06 *** allocated 10000 integers for termspace/termends
% 0.42/1.06 *** allocated 10000 integers for clauses
% 0.42/1.06 *** allocated 10000 integers for justifications
% 0.42/1.06 Bliksem 1.12
% 0.42/1.06
% 0.42/1.06
% 0.42/1.06 Automatic Strategy Selection
% 0.42/1.06
% 0.42/1.06
% 0.42/1.06 Clauses:
% 0.42/1.06
% 0.42/1.06 { ! basis_of( X, Y ), lin_ind_subset( X, Y ) }.
% 0.42/1.06 { ! basis_of( X, Y ), a_subset_of( X, vec_to_class( Y ) ) }.
% 0.42/1.06 { ! lin_ind_subset( X, Z ), ! basis_of( Y, Z ), a_subset_of( skol1( T, Y, U
% 0.42/1.06 ), Y ) }.
% 0.42/1.06 { ! lin_ind_subset( X, Z ), ! basis_of( Y, Z ), basis_of( union( X, skol1(
% 0.42/1.06 X, Y, Z ) ), Z ) }.
% 0.42/1.06 { ! a_vector_space( X ), basis_of( skol2( X ), X ) }.
% 0.42/1.06 { ! a_vector_subspace_of( X, Y ), a_vector_space( X ) }.
% 0.42/1.06 { ! a_vector_subspace_of( X, Y ), ! a_subset_of( Z, vec_to_class( X ) ), !
% 0.42/1.06 lin_ind_subset( Z, X ), lin_ind_subset( Z, Y ) }.
% 0.42/1.06 { ! a_vector_subspace_of( X, Y ), ! a_subset_of( Z, vec_to_class( X ) ), !
% 0.42/1.06 lin_ind_subset( Z, Y ), lin_ind_subset( Z, X ) }.
% 0.42/1.06 { a_vector_subspace_of( skol3, skol4 ) }.
% 0.42/1.06 { a_vector_space( skol4 ) }.
% 0.42/1.06 { ! basis_of( union( X, Y ), skol4 ), ! basis_of( X, skol3 ) }.
% 0.42/1.06
% 0.42/1.06 percentage equality = 0.000000, percentage horn = 1.000000
% 0.42/1.06 This is a near-Horn, non-equality problem
% 0.42/1.06
% 0.42/1.06
% 0.42/1.06 Options Used:
% 0.42/1.06
% 0.42/1.06 useres = 1
% 0.42/1.06 useparamod = 0
% 0.42/1.06 useeqrefl = 0
% 0.42/1.06 useeqfact = 0
% 0.42/1.06 usefactor = 1
% 0.42/1.06 usesimpsplitting = 0
% 0.42/1.06 usesimpdemod = 0
% 0.42/1.06 usesimpres = 4
% 0.42/1.06
% 0.42/1.06 resimpinuse = 1000
% 0.42/1.06 resimpclauses = 20000
% 0.42/1.06 substype = standard
% 0.42/1.06 backwardsubs = 1
% 0.42/1.06 selectoldest = 5
% 0.42/1.06
% 0.42/1.06 litorderings [0] = split
% 0.42/1.06 litorderings [1] = liftord
% 0.42/1.06
% 0.42/1.06 termordering = none
% 0.42/1.06
% 0.42/1.06 litapriori = 1
% 0.42/1.06 termapriori = 0
% 0.42/1.06 litaposteriori = 0
% 0.42/1.06 termaposteriori = 0
% 0.42/1.06 demodaposteriori = 0
% 0.42/1.06 ordereqreflfact = 0
% 0.42/1.06
% 0.42/1.06 litselect = negative
% 0.42/1.06
% 0.42/1.06 maxweight = 30000
% 0.42/1.06 maxdepth = 30000
% 0.42/1.06 maxlength = 115
% 0.42/1.06 maxnrvars = 195
% 0.42/1.06 excuselevel = 0
% 0.42/1.06 increasemaxweight = 0
% 0.42/1.06
% 0.42/1.06 maxselected = 10000000
% 0.42/1.06 maxnrclauses = 10000000
% 0.42/1.06
% 0.42/1.06 showgenerated = 0
% 0.42/1.06 showkept = 0
% 0.42/1.06 showselected = 0
% 0.42/1.06 showdeleted = 0
% 0.42/1.06 showresimp = 1
% 0.42/1.06 showstatus = 2000
% 0.42/1.06
% 0.42/1.06 prologoutput = 0
% 0.42/1.06 nrgoals = 5000000
% 0.42/1.06 totalproof = 1
% 0.42/1.06
% 0.42/1.06 Symbols occurring in the translation:
% 0.42/1.06
% 0.42/1.06 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.42/1.06 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 0.42/1.06 ! [4, 1] (w:1, o:17, a:1, s:1, b:0),
% 0.42/1.06 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.42/1.06 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.42/1.06 basis_of [37, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.42/1.06 lin_ind_subset [38, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.42/1.06 vec_to_class [39, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.42/1.06 a_subset_of [40, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.42/1.06 union [44, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.42/1.06 a_vector_space [46, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.42/1.06 a_vector_subspace_of [47, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.42/1.06 skol1 [51, 3] (w:1, o:54, a:1, s:1, b:0),
% 0.42/1.06 skol2 [52, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.42/1.06 skol3 [53, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.42/1.06 skol4 [54, 0] (w:1, o:16, a:1, s:1, b:0).
% 0.42/1.06
% 0.42/1.06
% 0.42/1.06 Starting Search:
% 0.42/1.06
% 0.42/1.06
% 0.42/1.06 Bliksems!, er is een bewijs:
% 0.42/1.06 % SZS status Theorem
% 0.42/1.06 % SZS output start Refutation
% 0.42/1.06
% 0.42/1.06 (0) {G0,W7,D2,L2,V2,M1} I { lin_ind_subset( X, Y ), ! basis_of( X, Y ) }.
% 0.42/1.06 (1) {G0,W8,D3,L2,V2,M1} I { a_subset_of( X, vec_to_class( Y ) ), ! basis_of
% 0.42/1.06 ( X, Y ) }.
% 0.42/1.06 (3) {G0,W16,D4,L3,V3,M1} I { ! lin_ind_subset( X, Z ), basis_of( union( X,
% 0.42/1.06 skol1( X, Y, Z ) ), Z ), ! basis_of( Y, Z ) }.
% 0.42/1.06 (4) {G0,W7,D3,L2,V1,M1} I { basis_of( skol2( X ), X ), ! a_vector_space( X
% 0.42/1.06 ) }.
% 0.42/1.06 (5) {G0,W6,D2,L2,V2,M1} I { a_vector_space( X ), ! a_vector_subspace_of( X
% 0.42/1.06 , Y ) }.
% 0.42/1.06 (6) {G0,W16,D3,L4,V3,M1} I { ! a_subset_of( Z, vec_to_class( X ) ), !
% 0.42/1.06 a_vector_subspace_of( X, Y ), lin_ind_subset( Z, Y ), ! lin_ind_subset( Z
% 0.42/1.06 , X ) }.
% 0.42/1.06 (8) {G0,W3,D2,L1,V0,M1} I { a_vector_subspace_of( skol3, skol4 ) }.
% 0.42/1.06 (9) {G0,W2,D2,L1,V0,M1} I { a_vector_space( skol4 ) }.
% 0.42/1.06 (10) {G0,W10,D3,L2,V2,M1} I { ! basis_of( union( X, Y ), skol4 ), !
% 0.42/1.06 basis_of( X, skol3 ) }.
% 0.42/1.06 (11) {G1,W2,D2,L1,V0,M1} R(5,8) { a_vector_space( skol3 ) }.
% 0.42/1.06 (12) {G2,W4,D3,L1,V0,M1} R(4,11) { basis_of( skol2( skol3 ), skol3 ) }.
% 0.42/1.06 (13) {G1,W4,D3,L1,V0,M1} R(4,9) { basis_of( skol2( skol4 ), skol4 ) }.
% 0.42/1.06 (14) {G3,W5,D3,L1,V0,M1} R(12,1) { a_subset_of( skol2( skol3 ),
% 0.42/1.06 vec_to_class( skol3 ) ) }.
% 0.42/1.06 (15) {G3,W4,D3,L1,V0,M1} R(12,0) { lin_ind_subset( skol2( skol3 ), skol3 )
% 0.42/1.06 }.
% 0.42/1.06 (20) {G3,W7,D4,L1,V1,M1} R(10,12) { ! basis_of( union( skol2( skol3 ), X )
% 0.42/1.06 , skol4 ) }.
% 0.42/1.06 (21) {G2,W13,D5,L2,V1,M1} R(3,13) { basis_of( union( X, skol1( X, skol2(
% 0.42/1.06 skol4 ), skol4 ) ), skol4 ), ! lin_ind_subset( X, skol4 ) }.
% 0.42/1.06 (26) {G4,W8,D3,L2,V1,M1} R(6,15);r(14) { lin_ind_subset( skol2( skol3 ), X
% 0.42/1.06 ), ! a_vector_subspace_of( skol3, X ) }.
% 0.42/1.06 (27) {G5,W4,D3,L1,V0,M1} R(26,8) { lin_ind_subset( skol2( skol3 ), skol4 )
% 0.42/1.06 }.
% 0.42/1.06 (32) {G6,W0,D0,L0,V0,M0} R(21,27);r(20) { }.
% 0.42/1.06
% 0.42/1.06
% 0.42/1.06 % SZS output end Refutation
% 0.42/1.06 found a proof!
% 0.42/1.06
% 0.42/1.06
% 0.42/1.06 Unprocessed initial clauses:
% 0.42/1.06
% 0.42/1.06 (34) {G0,W7,D2,L2,V2,M2} { ! basis_of( X, Y ), lin_ind_subset( X, Y ) }.
% 0.42/1.06 (35) {G0,W8,D3,L2,V2,M2} { ! basis_of( X, Y ), a_subset_of( X,
% 0.42/1.06 vec_to_class( Y ) ) }.
% 0.42/1.06 (36) {G0,W14,D3,L3,V5,M3} { ! lin_ind_subset( X, Z ), ! basis_of( Y, Z ),
% 0.42/1.06 a_subset_of( skol1( T, Y, U ), Y ) }.
% 0.42/1.06 (37) {G0,W16,D4,L3,V3,M3} { ! lin_ind_subset( X, Z ), ! basis_of( Y, Z ),
% 0.42/1.06 basis_of( union( X, skol1( X, Y, Z ) ), Z ) }.
% 0.42/1.06 (38) {G0,W7,D3,L2,V1,M2} { ! a_vector_space( X ), basis_of( skol2( X ), X
% 0.42/1.06 ) }.
% 0.42/1.06 (39) {G0,W6,D2,L2,V2,M2} { ! a_vector_subspace_of( X, Y ), a_vector_space
% 0.42/1.06 ( X ) }.
% 0.42/1.06 (40) {G0,W16,D3,L4,V3,M4} { ! a_vector_subspace_of( X, Y ), ! a_subset_of
% 0.42/1.06 ( Z, vec_to_class( X ) ), ! lin_ind_subset( Z, X ), lin_ind_subset( Z, Y
% 0.42/1.06 ) }.
% 0.42/1.06 (41) {G0,W16,D3,L4,V3,M4} { ! a_vector_subspace_of( X, Y ), ! a_subset_of
% 0.42/1.06 ( Z, vec_to_class( X ) ), ! lin_ind_subset( Z, Y ), lin_ind_subset( Z, X
% 0.42/1.06 ) }.
% 0.42/1.06 (42) {G0,W3,D2,L1,V0,M1} { a_vector_subspace_of( skol3, skol4 ) }.
% 0.42/1.06 (43) {G0,W2,D2,L1,V0,M1} { a_vector_space( skol4 ) }.
% 0.42/1.06 (44) {G0,W10,D3,L2,V2,M2} { ! basis_of( union( X, Y ), skol4 ), ! basis_of
% 0.42/1.06 ( X, skol3 ) }.
% 0.42/1.06
% 0.42/1.06
% 0.42/1.06 Total Proof:
% 0.42/1.06
% 0.42/1.06 subsumption: (0) {G0,W7,D2,L2,V2,M1} I { lin_ind_subset( X, Y ), ! basis_of
% 0.42/1.06 ( X, Y ) }.
% 0.42/1.06 parent0: (34) {G0,W7,D2,L2,V2,M2} { ! basis_of( X, Y ), lin_ind_subset( X
% 0.42/1.06 , Y ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := X
% 0.42/1.06 Y := Y
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 1
% 0.42/1.06 1 ==> 0
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (1) {G0,W8,D3,L2,V2,M1} I { a_subset_of( X, vec_to_class( Y )
% 0.42/1.06 ), ! basis_of( X, Y ) }.
% 0.42/1.06 parent0: (35) {G0,W8,D3,L2,V2,M2} { ! basis_of( X, Y ), a_subset_of( X,
% 0.42/1.06 vec_to_class( Y ) ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := X
% 0.42/1.06 Y := Y
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 1
% 0.42/1.06 1 ==> 0
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (3) {G0,W16,D4,L3,V3,M1} I { ! lin_ind_subset( X, Z ),
% 0.42/1.06 basis_of( union( X, skol1( X, Y, Z ) ), Z ), ! basis_of( Y, Z ) }.
% 0.42/1.06 parent0: (37) {G0,W16,D4,L3,V3,M3} { ! lin_ind_subset( X, Z ), ! basis_of
% 0.42/1.06 ( Y, Z ), basis_of( union( X, skol1( X, Y, Z ) ), Z ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := X
% 0.42/1.06 Y := Y
% 0.42/1.06 Z := Z
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 0
% 0.42/1.06 1 ==> 2
% 0.42/1.06 2 ==> 1
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (4) {G0,W7,D3,L2,V1,M1} I { basis_of( skol2( X ), X ), !
% 0.42/1.06 a_vector_space( X ) }.
% 0.42/1.06 parent0: (38) {G0,W7,D3,L2,V1,M2} { ! a_vector_space( X ), basis_of( skol2
% 0.42/1.06 ( X ), X ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := X
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 1
% 0.42/1.06 1 ==> 0
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (5) {G0,W6,D2,L2,V2,M1} I { a_vector_space( X ), !
% 0.42/1.06 a_vector_subspace_of( X, Y ) }.
% 0.42/1.06 parent0: (39) {G0,W6,D2,L2,V2,M2} { ! a_vector_subspace_of( X, Y ),
% 0.42/1.06 a_vector_space( X ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := X
% 0.42/1.06 Y := Y
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 1
% 0.42/1.06 1 ==> 0
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (6) {G0,W16,D3,L4,V3,M1} I { ! a_subset_of( Z, vec_to_class( X
% 0.42/1.06 ) ), ! a_vector_subspace_of( X, Y ), lin_ind_subset( Z, Y ), !
% 0.42/1.06 lin_ind_subset( Z, X ) }.
% 0.42/1.06 parent0: (40) {G0,W16,D3,L4,V3,M4} { ! a_vector_subspace_of( X, Y ), !
% 0.42/1.06 a_subset_of( Z, vec_to_class( X ) ), ! lin_ind_subset( Z, X ),
% 0.42/1.06 lin_ind_subset( Z, Y ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := X
% 0.42/1.06 Y := Y
% 0.42/1.06 Z := Z
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 1
% 0.42/1.06 1 ==> 0
% 0.42/1.06 2 ==> 3
% 0.42/1.06 3 ==> 2
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (8) {G0,W3,D2,L1,V0,M1} I { a_vector_subspace_of( skol3, skol4
% 0.42/1.06 ) }.
% 0.42/1.06 parent0: (42) {G0,W3,D2,L1,V0,M1} { a_vector_subspace_of( skol3, skol4 )
% 0.42/1.06 }.
% 0.42/1.06 substitution0:
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 0
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (9) {G0,W2,D2,L1,V0,M1} I { a_vector_space( skol4 ) }.
% 0.42/1.06 parent0: (43) {G0,W2,D2,L1,V0,M1} { a_vector_space( skol4 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 0
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (10) {G0,W10,D3,L2,V2,M1} I { ! basis_of( union( X, Y ), skol4
% 0.42/1.06 ), ! basis_of( X, skol3 ) }.
% 0.42/1.06 parent0: (44) {G0,W10,D3,L2,V2,M2} { ! basis_of( union( X, Y ), skol4 ), !
% 0.42/1.06 basis_of( X, skol3 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := X
% 0.42/1.06 Y := Y
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 0
% 0.42/1.06 1 ==> 1
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 resolution: (45) {G1,W2,D2,L1,V0,M1} { a_vector_space( skol3 ) }.
% 0.42/1.06 parent0[1]: (5) {G0,W6,D2,L2,V2,M1} I { a_vector_space( X ), !
% 0.42/1.06 a_vector_subspace_of( X, Y ) }.
% 0.42/1.06 parent1[0]: (8) {G0,W3,D2,L1,V0,M1} I { a_vector_subspace_of( skol3, skol4
% 0.42/1.06 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := skol3
% 0.42/1.06 Y := skol4
% 0.42/1.06 end
% 0.42/1.06 substitution1:
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (11) {G1,W2,D2,L1,V0,M1} R(5,8) { a_vector_space( skol3 ) }.
% 0.42/1.06 parent0: (45) {G1,W2,D2,L1,V0,M1} { a_vector_space( skol3 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 0
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 resolution: (46) {G1,W4,D3,L1,V0,M1} { basis_of( skol2( skol3 ), skol3 )
% 0.42/1.06 }.
% 0.42/1.06 parent0[1]: (4) {G0,W7,D3,L2,V1,M1} I { basis_of( skol2( X ), X ), !
% 0.42/1.06 a_vector_space( X ) }.
% 0.42/1.06 parent1[0]: (11) {G1,W2,D2,L1,V0,M1} R(5,8) { a_vector_space( skol3 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := skol3
% 0.42/1.06 end
% 0.42/1.06 substitution1:
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (12) {G2,W4,D3,L1,V0,M1} R(4,11) { basis_of( skol2( skol3 ),
% 0.42/1.06 skol3 ) }.
% 0.42/1.06 parent0: (46) {G1,W4,D3,L1,V0,M1} { basis_of( skol2( skol3 ), skol3 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 0
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 resolution: (47) {G1,W4,D3,L1,V0,M1} { basis_of( skol2( skol4 ), skol4 )
% 0.42/1.06 }.
% 0.42/1.06 parent0[1]: (4) {G0,W7,D3,L2,V1,M1} I { basis_of( skol2( X ), X ), !
% 0.42/1.06 a_vector_space( X ) }.
% 0.42/1.06 parent1[0]: (9) {G0,W2,D2,L1,V0,M1} I { a_vector_space( skol4 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := skol4
% 0.42/1.06 end
% 0.42/1.06 substitution1:
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (13) {G1,W4,D3,L1,V0,M1} R(4,9) { basis_of( skol2( skol4 ),
% 0.42/1.06 skol4 ) }.
% 0.42/1.06 parent0: (47) {G1,W4,D3,L1,V0,M1} { basis_of( skol2( skol4 ), skol4 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 0
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 resolution: (48) {G1,W5,D3,L1,V0,M1} { a_subset_of( skol2( skol3 ),
% 0.42/1.06 vec_to_class( skol3 ) ) }.
% 0.42/1.06 parent0[1]: (1) {G0,W8,D3,L2,V2,M1} I { a_subset_of( X, vec_to_class( Y ) )
% 0.42/1.06 , ! basis_of( X, Y ) }.
% 0.42/1.06 parent1[0]: (12) {G2,W4,D3,L1,V0,M1} R(4,11) { basis_of( skol2( skol3 ),
% 0.42/1.06 skol3 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := skol2( skol3 )
% 0.42/1.06 Y := skol3
% 0.42/1.06 end
% 0.42/1.06 substitution1:
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (14) {G3,W5,D3,L1,V0,M1} R(12,1) { a_subset_of( skol2( skol3 )
% 0.42/1.06 , vec_to_class( skol3 ) ) }.
% 0.42/1.06 parent0: (48) {G1,W5,D3,L1,V0,M1} { a_subset_of( skol2( skol3 ),
% 0.42/1.06 vec_to_class( skol3 ) ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 0
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 resolution: (49) {G1,W4,D3,L1,V0,M1} { lin_ind_subset( skol2( skol3 ),
% 0.42/1.06 skol3 ) }.
% 0.42/1.06 parent0[1]: (0) {G0,W7,D2,L2,V2,M1} I { lin_ind_subset( X, Y ), ! basis_of
% 0.42/1.06 ( X, Y ) }.
% 0.42/1.06 parent1[0]: (12) {G2,W4,D3,L1,V0,M1} R(4,11) { basis_of( skol2( skol3 ),
% 0.42/1.06 skol3 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := skol2( skol3 )
% 0.42/1.06 Y := skol3
% 0.42/1.06 end
% 0.42/1.06 substitution1:
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (15) {G3,W4,D3,L1,V0,M1} R(12,0) { lin_ind_subset( skol2(
% 0.42/1.06 skol3 ), skol3 ) }.
% 0.42/1.06 parent0: (49) {G1,W4,D3,L1,V0,M1} { lin_ind_subset( skol2( skol3 ), skol3
% 0.42/1.06 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 0
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 resolution: (50) {G1,W7,D4,L1,V1,M1} { ! basis_of( union( skol2( skol3 ),
% 0.42/1.06 X ), skol4 ) }.
% 0.42/1.06 parent0[1]: (10) {G0,W10,D3,L2,V2,M1} I { ! basis_of( union( X, Y ), skol4
% 0.42/1.06 ), ! basis_of( X, skol3 ) }.
% 0.42/1.06 parent1[0]: (12) {G2,W4,D3,L1,V0,M1} R(4,11) { basis_of( skol2( skol3 ),
% 0.42/1.06 skol3 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := skol2( skol3 )
% 0.42/1.06 Y := X
% 0.42/1.06 end
% 0.42/1.06 substitution1:
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (20) {G3,W7,D4,L1,V1,M1} R(10,12) { ! basis_of( union( skol2(
% 0.42/1.06 skol3 ), X ), skol4 ) }.
% 0.42/1.06 parent0: (50) {G1,W7,D4,L1,V1,M1} { ! basis_of( union( skol2( skol3 ), X )
% 0.42/1.06 , skol4 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := X
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 0
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 resolution: (51) {G1,W13,D5,L2,V1,M2} { ! lin_ind_subset( X, skol4 ),
% 0.42/1.06 basis_of( union( X, skol1( X, skol2( skol4 ), skol4 ) ), skol4 ) }.
% 0.42/1.06 parent0[2]: (3) {G0,W16,D4,L3,V3,M1} I { ! lin_ind_subset( X, Z ), basis_of
% 0.42/1.06 ( union( X, skol1( X, Y, Z ) ), Z ), ! basis_of( Y, Z ) }.
% 0.42/1.06 parent1[0]: (13) {G1,W4,D3,L1,V0,M1} R(4,9) { basis_of( skol2( skol4 ),
% 0.42/1.06 skol4 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := X
% 0.42/1.06 Y := skol2( skol4 )
% 0.42/1.06 Z := skol4
% 0.42/1.06 end
% 0.42/1.06 substitution1:
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (21) {G2,W13,D5,L2,V1,M1} R(3,13) { basis_of( union( X, skol1
% 0.42/1.06 ( X, skol2( skol4 ), skol4 ) ), skol4 ), ! lin_ind_subset( X, skol4 ) }.
% 0.42/1.06 parent0: (51) {G1,W13,D5,L2,V1,M2} { ! lin_ind_subset( X, skol4 ),
% 0.42/1.06 basis_of( union( X, skol1( X, skol2( skol4 ), skol4 ) ), skol4 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := X
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 1
% 0.42/1.06 1 ==> 0
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 resolution: (52) {G1,W14,D3,L3,V1,M3} { ! a_subset_of( skol2( skol3 ),
% 0.42/1.06 vec_to_class( skol3 ) ), ! a_vector_subspace_of( skol3, X ),
% 0.42/1.06 lin_ind_subset( skol2( skol3 ), X ) }.
% 0.42/1.06 parent0[3]: (6) {G0,W16,D3,L4,V3,M1} I { ! a_subset_of( Z, vec_to_class( X
% 0.42/1.06 ) ), ! a_vector_subspace_of( X, Y ), lin_ind_subset( Z, Y ), !
% 0.42/1.06 lin_ind_subset( Z, X ) }.
% 0.42/1.06 parent1[0]: (15) {G3,W4,D3,L1,V0,M1} R(12,0) { lin_ind_subset( skol2( skol3
% 0.42/1.06 ), skol3 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := skol3
% 0.42/1.06 Y := X
% 0.42/1.06 Z := skol2( skol3 )
% 0.42/1.06 end
% 0.42/1.06 substitution1:
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 resolution: (53) {G2,W8,D3,L2,V1,M2} { ! a_vector_subspace_of( skol3, X )
% 0.42/1.06 , lin_ind_subset( skol2( skol3 ), X ) }.
% 0.42/1.06 parent0[0]: (52) {G1,W14,D3,L3,V1,M3} { ! a_subset_of( skol2( skol3 ),
% 0.42/1.06 vec_to_class( skol3 ) ), ! a_vector_subspace_of( skol3, X ),
% 0.42/1.06 lin_ind_subset( skol2( skol3 ), X ) }.
% 0.42/1.06 parent1[0]: (14) {G3,W5,D3,L1,V0,M1} R(12,1) { a_subset_of( skol2( skol3 )
% 0.42/1.06 , vec_to_class( skol3 ) ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := X
% 0.42/1.06 end
% 0.42/1.06 substitution1:
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (26) {G4,W8,D3,L2,V1,M1} R(6,15);r(14) { lin_ind_subset( skol2
% 0.42/1.06 ( skol3 ), X ), ! a_vector_subspace_of( skol3, X ) }.
% 0.42/1.06 parent0: (53) {G2,W8,D3,L2,V1,M2} { ! a_vector_subspace_of( skol3, X ),
% 0.42/1.06 lin_ind_subset( skol2( skol3 ), X ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := X
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 1
% 0.42/1.06 1 ==> 0
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 resolution: (54) {G1,W4,D3,L1,V0,M1} { lin_ind_subset( skol2( skol3 ),
% 0.42/1.06 skol4 ) }.
% 0.42/1.06 parent0[1]: (26) {G4,W8,D3,L2,V1,M1} R(6,15);r(14) { lin_ind_subset( skol2
% 0.42/1.06 ( skol3 ), X ), ! a_vector_subspace_of( skol3, X ) }.
% 0.42/1.06 parent1[0]: (8) {G0,W3,D2,L1,V0,M1} I { a_vector_subspace_of( skol3, skol4
% 0.42/1.06 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := skol4
% 0.42/1.06 end
% 0.42/1.06 substitution1:
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (27) {G5,W4,D3,L1,V0,M1} R(26,8) { lin_ind_subset( skol2(
% 0.42/1.06 skol3 ), skol4 ) }.
% 0.42/1.06 parent0: (54) {G1,W4,D3,L1,V0,M1} { lin_ind_subset( skol2( skol3 ), skol4
% 0.42/1.06 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 0 ==> 0
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 resolution: (55) {G3,W11,D5,L1,V0,M1} { basis_of( union( skol2( skol3 ),
% 0.42/1.06 skol1( skol2( skol3 ), skol2( skol4 ), skol4 ) ), skol4 ) }.
% 0.42/1.06 parent0[1]: (21) {G2,W13,D5,L2,V1,M1} R(3,13) { basis_of( union( X, skol1(
% 0.42/1.06 X, skol2( skol4 ), skol4 ) ), skol4 ), ! lin_ind_subset( X, skol4 ) }.
% 0.42/1.06 parent1[0]: (27) {G5,W4,D3,L1,V0,M1} R(26,8) { lin_ind_subset( skol2( skol3
% 0.42/1.06 ), skol4 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := skol2( skol3 )
% 0.42/1.06 end
% 0.42/1.06 substitution1:
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 resolution: (56) {G4,W0,D0,L0,V0,M0} { }.
% 0.42/1.06 parent0[0]: (20) {G3,W7,D4,L1,V1,M1} R(10,12) { ! basis_of( union( skol2(
% 0.42/1.06 skol3 ), X ), skol4 ) }.
% 0.42/1.06 parent1[0]: (55) {G3,W11,D5,L1,V0,M1} { basis_of( union( skol2( skol3 ),
% 0.42/1.06 skol1( skol2( skol3 ), skol2( skol4 ), skol4 ) ), skol4 ) }.
% 0.42/1.06 substitution0:
% 0.42/1.06 X := skol1( skol2( skol3 ), skol2( skol4 ), skol4 )
% 0.42/1.06 end
% 0.42/1.06 substitution1:
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 subsumption: (32) {G6,W0,D0,L0,V0,M0} R(21,27);r(20) { }.
% 0.42/1.06 parent0: (56) {G4,W0,D0,L0,V0,M0} { }.
% 0.42/1.06 substitution0:
% 0.42/1.06 end
% 0.42/1.06 permutation0:
% 0.42/1.06 end
% 0.42/1.06
% 0.42/1.06 Proof check complete!
% 0.42/1.06
% 0.42/1.06 Memory use:
% 0.42/1.06
% 0.42/1.06 space for terms: 533
% 0.42/1.06 space for clauses: 1948
% 0.42/1.06
% 0.42/1.06
% 0.42/1.06 clauses generated: 34
% 0.42/1.06 clauses kept: 33
% 0.42/1.06 clauses selected: 27
% 0.42/1.06 clauses deleted: 0
% 0.42/1.06 clauses inuse deleted: 0
% 0.42/1.06
% 0.42/1.06 subsentry: 7
% 0.42/1.06 literals s-matched: 4
% 0.42/1.06 literals matched: 4
% 0.42/1.06 full subsumption: 0
% 0.42/1.06
% 0.42/1.06 checksum: 883375465
% 0.42/1.06
% 0.42/1.06
% 0.42/1.06 Bliksem ended
%------------------------------------------------------------------------------