TSTP Solution File: SEU324+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU324+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n026.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 : Tue Jul 19 07:12:28 EDT 2022
% Result : Theorem 0.72s 1.29s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU324+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n026.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 : Sun Jun 19 06:40:10 EDT 2022
% 0.18/0.33 % CPUTime :
% 0.72/1.29 *** allocated 10000 integers for termspace/termends
% 0.72/1.29 *** allocated 10000 integers for clauses
% 0.72/1.29 *** allocated 10000 integers for justifications
% 0.72/1.29 Bliksem 1.12
% 0.72/1.29
% 0.72/1.29
% 0.72/1.29 Automatic Strategy Selection
% 0.72/1.29
% 0.72/1.29
% 0.72/1.29 Clauses:
% 0.72/1.29
% 0.72/1.29 { ! top_str( X ), ! element( Y, powerset( the_carrier( X ) ) ), interior( X
% 0.72/1.29 , Y ) = subset_complement( the_carrier( X ), topstr_closure( X,
% 0.72/1.29 subset_complement( the_carrier( X ), Y ) ) ) }.
% 0.72/1.29 { ! top_str( X ), ! element( Y, powerset( the_carrier( X ) ) ), element(
% 0.72/1.29 interior( X, Y ), powerset( the_carrier( X ) ) ) }.
% 0.72/1.29 { && }.
% 0.72/1.29 { ! element( Y, powerset( X ) ), element( subset_complement( X, Y ),
% 0.72/1.29 powerset( X ) ) }.
% 0.72/1.29 { ! top_str( X ), ! element( Y, powerset( the_carrier( X ) ) ), element(
% 0.72/1.29 topstr_closure( X, Y ), powerset( the_carrier( X ) ) ) }.
% 0.72/1.29 { ! top_str( X ), one_sorted_str( X ) }.
% 0.72/1.29 { && }.
% 0.72/1.29 { && }.
% 0.72/1.29 { && }.
% 0.72/1.29 { top_str( skol1 ) }.
% 0.72/1.29 { one_sorted_str( skol2 ) }.
% 0.72/1.29 { element( skol3( X ), X ) }.
% 0.72/1.29 { ! topological_space( X ), ! top_str( X ), ! element( Y, powerset(
% 0.72/1.29 the_carrier( X ) ) ), closed_subset( topstr_closure( X, Y ), X ) }.
% 0.72/1.29 { ! topological_space( X ), ! top_str( X ), ! closed_subset( Y, X ), !
% 0.72/1.29 element( Y, powerset( the_carrier( X ) ) ), open_subset(
% 0.72/1.29 subset_complement( the_carrier( X ), Y ), X ) }.
% 0.72/1.29 { ! topological_space( X ), ! top_str( X ), ! open_subset( Y, X ), !
% 0.72/1.29 element( Y, powerset( the_carrier( X ) ) ), closed_subset(
% 0.72/1.29 subset_complement( the_carrier( X ), Y ), X ) }.
% 0.72/1.29 { ! topological_space( X ), ! top_str( X ), ! element( Y, powerset(
% 0.72/1.29 the_carrier( X ) ) ), open_subset( interior( X, Y ), X ) }.
% 0.72/1.29 { ! element( Y, powerset( X ) ), subset_complement( X, subset_complement( X
% 0.72/1.29 , Y ) ) = Y }.
% 0.72/1.29 { ! topological_space( X ), ! top_str( X ), element( skol4( X ), powerset(
% 0.72/1.29 the_carrier( X ) ) ) }.
% 0.72/1.29 { ! topological_space( X ), ! top_str( X ), open_subset( skol4( X ), X ) }
% 0.72/1.29 .
% 0.72/1.29 { ! topological_space( X ), ! top_str( X ), element( skol5( X ), powerset(
% 0.72/1.29 the_carrier( X ) ) ) }.
% 0.72/1.29 { ! topological_space( X ), ! top_str( X ), open_subset( skol5( X ), X ) }
% 0.72/1.29 .
% 0.72/1.29 { ! topological_space( X ), ! top_str( X ), closed_subset( skol5( X ), X )
% 0.72/1.29 }.
% 0.72/1.29 { ! topological_space( X ), ! top_str( X ), element( skol6( X ), powerset(
% 0.72/1.29 the_carrier( X ) ) ) }.
% 0.72/1.29 { ! topological_space( X ), ! top_str( X ), closed_subset( skol6( X ), X )
% 0.72/1.29 }.
% 0.72/1.29 { subset( X, X ) }.
% 0.72/1.29 { ! top_str( X ), ! element( Y, powerset( the_carrier( X ) ) ), !
% 0.72/1.29 open_subset( Y, X ), closed_subset( subset_complement( the_carrier( X ),
% 0.72/1.29 Y ), X ) }.
% 0.72/1.29 { ! top_str( X ), ! element( Y, powerset( the_carrier( X ) ) ), !
% 0.72/1.29 closed_subset( subset_complement( the_carrier( X ), Y ), X ), open_subset
% 0.72/1.29 ( Y, X ) }.
% 0.72/1.29 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.72/1.29 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.72/1.29 { ! top_str( X ), ! element( Y, powerset( the_carrier( X ) ) ), !
% 0.72/1.29 closed_subset( Y, X ), topstr_closure( X, Y ) = Y }.
% 0.72/1.29 { ! top_str( X ), ! element( Y, powerset( the_carrier( X ) ) ), !
% 0.72/1.29 topological_space( X ), ! topstr_closure( X, Y ) = Y, closed_subset( Y, X
% 0.72/1.29 ) }.
% 0.72/1.29 { topological_space( skol7 ) }.
% 0.72/1.29 { top_str( skol7 ) }.
% 0.72/1.29 { top_str( skol8 ) }.
% 0.72/1.29 { element( skol9, powerset( the_carrier( skol7 ) ) ) }.
% 0.72/1.29 { element( skol10, powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 { alpha1( skol8, skol10 ), interior( skol7, skol9 ) = skol9 }.
% 0.72/1.29 { alpha1( skol8, skol10 ), ! open_subset( skol9, skol7 ) }.
% 0.72/1.29 { ! alpha1( X, Y ), open_subset( Y, X ) }.
% 0.72/1.29 { ! alpha1( X, Y ), ! interior( X, Y ) = Y }.
% 0.72/1.29 { ! open_subset( Y, X ), interior( X, Y ) = Y, alpha1( X, Y ) }.
% 0.72/1.29
% 0.72/1.29 percentage equality = 0.072917, percentage horn = 0.947368
% 0.72/1.29 This is a problem with some equality
% 0.72/1.29
% 0.72/1.29
% 0.72/1.29
% 0.72/1.29 Options Used:
% 0.72/1.29
% 0.72/1.29 useres = 1
% 0.72/1.29 useparamod = 1
% 0.72/1.29 useeqrefl = 1
% 0.72/1.29 useeqfact = 1
% 0.72/1.29 usefactor = 1
% 0.72/1.29 usesimpsplitting = 0
% 0.72/1.29 usesimpdemod = 5
% 0.72/1.29 usesimpres = 3
% 0.72/1.29
% 0.72/1.29 resimpinuse = 1000
% 0.72/1.29 resimpclauses = 20000
% 0.72/1.29 substype = eqrewr
% 0.72/1.29 backwardsubs = 1
% 0.72/1.29 selectoldest = 5
% 0.72/1.29
% 0.72/1.29 litorderings [0] = split
% 0.72/1.29 litorderings [1] = extend the termordering, first sorting on arguments
% 0.72/1.29
% 0.72/1.29 termordering = kbo
% 0.72/1.29
% 0.72/1.29 litapriori = 0
% 0.72/1.29 termapriori = 1
% 0.72/1.29 litaposteriori = 0
% 0.72/1.29 termaposteriori = 0
% 0.72/1.29 demodaposteriori = 0
% 0.72/1.29 ordereqreflfact = 0
% 0.72/1.29
% 0.72/1.29 litselect = negord
% 0.72/1.29
% 0.72/1.29 maxweight = 15
% 0.72/1.29 maxdepth = 30000
% 0.72/1.29 maxlength = 115
% 0.72/1.29 maxnrvars = 195
% 0.72/1.29 excuselevel = 1
% 0.72/1.29 increasemaxweight = 1
% 0.72/1.29
% 0.72/1.29 maxselected = 10000000
% 0.72/1.29 maxnrclauses = 10000000
% 0.72/1.29
% 0.72/1.29 showgenerated = 0
% 0.72/1.29 showkept = 0
% 0.72/1.29 showselected = 0
% 0.72/1.29 showdeleted = 0
% 0.72/1.29 showresimp = 1
% 0.72/1.29 showstatus = 2000
% 0.72/1.29
% 0.72/1.29 prologoutput = 0
% 0.72/1.29 nrgoals = 5000000
% 0.72/1.29 totalproof = 1
% 0.72/1.29
% 0.72/1.29 Symbols occurring in the translation:
% 0.72/1.29
% 0.72/1.29 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.72/1.29 . [1, 2] (w:1, o:30, a:1, s:1, b:0),
% 0.72/1.29 && [3, 0] (w:1, o:4, a:1, s:1, b:0),
% 0.72/1.29 ! [4, 1] (w:0, o:16, a:1, s:1, b:0),
% 0.72/1.29 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.29 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.29 top_str [36, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.72/1.29 the_carrier [38, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.72/1.29 powerset [39, 1] (w:1, o:28, a:1, s:1, b:0),
% 0.72/1.29 element [40, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.72/1.29 interior [41, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.72/1.29 subset_complement [42, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.72/1.29 topstr_closure [43, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.72/1.29 one_sorted_str [44, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.72/1.29 topological_space [45, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.72/1.29 closed_subset [46, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.72/1.29 open_subset [47, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.72/1.29 subset [48, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.72/1.29 alpha1 [51, 2] (w:1, o:61, a:1, s:1, b:1),
% 0.72/1.29 skol1 [52, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.72/1.29 skol2 [53, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.72/1.29 skol3 [54, 1] (w:1, o:21, a:1, s:1, b:1),
% 0.72/1.29 skol4 [55, 1] (w:1, o:22, a:1, s:1, b:1),
% 0.72/1.29 skol5 [56, 1] (w:1, o:23, a:1, s:1, b:1),
% 0.72/1.29 skol6 [57, 1] (w:1, o:24, a:1, s:1, b:1),
% 0.72/1.29 skol7 [58, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.72/1.29 skol8 [59, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.72/1.29 skol9 [60, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.72/1.29 skol10 [61, 0] (w:1, o:11, a:1, s:1, b:1).
% 0.72/1.29
% 0.72/1.29
% 0.72/1.29 Starting Search:
% 0.72/1.29
% 0.72/1.29 *** allocated 15000 integers for clauses
% 0.72/1.29 *** allocated 22500 integers for clauses
% 0.72/1.29 *** allocated 33750 integers for clauses
% 0.72/1.29 *** allocated 50625 integers for clauses
% 0.72/1.29 *** allocated 75937 integers for clauses
% 0.72/1.29 *** allocated 15000 integers for termspace/termends
% 0.72/1.29 *** allocated 113905 integers for clauses
% 0.72/1.29 Resimplifying inuse:
% 0.72/1.29 Done
% 0.72/1.29
% 0.72/1.29 *** allocated 22500 integers for termspace/termends
% 0.72/1.29 *** allocated 170857 integers for clauses
% 0.72/1.29 *** allocated 33750 integers for termspace/termends
% 0.72/1.29
% 0.72/1.29 Intermediate Status:
% 0.72/1.29 Generated: 7229
% 0.72/1.29 Kept: 2006
% 0.72/1.29 Inuse: 424
% 0.72/1.29 Deleted: 51
% 0.72/1.29 Deletedinuse: 10
% 0.72/1.29
% 0.72/1.29 Resimplifying inuse:
% 0.72/1.29 Done
% 0.72/1.29
% 0.72/1.29 *** allocated 256285 integers for clauses
% 0.72/1.29 *** allocated 50625 integers for termspace/termends
% 0.72/1.29 Resimplifying inuse:
% 0.72/1.29 Done
% 0.72/1.29
% 0.72/1.29 *** allocated 384427 integers for clauses
% 0.72/1.29
% 0.72/1.29 Bliksems!, er is een bewijs:
% 0.72/1.29 % SZS status Theorem
% 0.72/1.29 % SZS output start Refutation
% 0.72/1.29
% 0.72/1.29 (0) {G0,W20,D6,L3,V2,M3} I { ! top_str( X ), ! element( Y, powerset(
% 0.72/1.29 the_carrier( X ) ) ), subset_complement( the_carrier( X ), topstr_closure
% 0.72/1.29 ( X, subset_complement( the_carrier( X ), Y ) ) ) ==> interior( X, Y )
% 0.72/1.29 }.
% 0.72/1.29 (1) {G0,W14,D4,L3,V2,M3} I { ! top_str( X ), ! element( Y, powerset(
% 0.72/1.29 the_carrier( X ) ) ), element( interior( X, Y ), powerset( the_carrier( X
% 0.72/1.29 ) ) ) }.
% 0.72/1.29 (3) {G0,W10,D3,L2,V2,M2} I { ! element( Y, powerset( X ) ), element(
% 0.72/1.29 subset_complement( X, Y ), powerset( X ) ) }.
% 0.72/1.29 (4) {G0,W14,D4,L3,V2,M3} I { ! top_str( X ), ! element( Y, powerset(
% 0.72/1.29 the_carrier( X ) ) ), element( topstr_closure( X, Y ), powerset(
% 0.72/1.29 the_carrier( X ) ) ) }.
% 0.72/1.29 (12) {G0,W14,D4,L4,V2,M4} I { ! topological_space( X ), ! top_str( X ), !
% 0.72/1.29 element( Y, powerset( the_carrier( X ) ) ), open_subset( interior( X, Y )
% 0.72/1.29 , X ) }.
% 0.72/1.29 (13) {G0,W11,D4,L2,V2,M2} I { ! element( Y, powerset( X ) ),
% 0.72/1.29 subset_complement( X, subset_complement( X, Y ) ) ==> Y }.
% 0.72/1.29 (22) {G0,W16,D4,L4,V2,M4} I { ! top_str( X ), ! element( Y, powerset(
% 0.72/1.29 the_carrier( X ) ) ), ! open_subset( Y, X ), closed_subset(
% 0.72/1.29 subset_complement( the_carrier( X ), Y ), X ) }.
% 0.72/1.29 (26) {G0,W15,D4,L4,V2,M4} I { ! top_str( X ), ! element( Y, powerset(
% 0.72/1.29 the_carrier( X ) ) ), ! closed_subset( Y, X ), topstr_closure( X, Y ) ==>
% 0.72/1.29 Y }.
% 0.72/1.29 (28) {G0,W2,D2,L1,V0,M1} I { topological_space( skol7 ) }.
% 0.72/1.29 (29) {G0,W2,D2,L1,V0,M1} I { top_str( skol7 ) }.
% 0.72/1.29 (30) {G0,W2,D2,L1,V0,M1} I { top_str( skol8 ) }.
% 0.72/1.29 (31) {G0,W5,D4,L1,V0,M1} I { element( skol9, powerset( the_carrier( skol7 )
% 0.72/1.29 ) ) }.
% 0.72/1.29 (32) {G0,W5,D4,L1,V0,M1} I { element( skol10, powerset( the_carrier( skol8
% 0.72/1.29 ) ) ) }.
% 0.72/1.29 (33) {G0,W8,D3,L2,V0,M2} I { alpha1( skol8, skol10 ), interior( skol7,
% 0.72/1.29 skol9 ) ==> skol9 }.
% 0.72/1.29 (34) {G0,W6,D2,L2,V0,M2} I { alpha1( skol8, skol10 ), ! open_subset( skol9
% 0.72/1.29 , skol7 ) }.
% 0.72/1.29 (35) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), open_subset( Y, X ) }.
% 0.72/1.29 (36) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), ! interior( X, Y ) ==> Y }.
% 0.72/1.29 (52) {G1,W7,D4,L1,V0,M1} R(32,1);r(30) { element( interior( skol8, skol10 )
% 0.72/1.29 , powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 (53) {G1,W13,D6,L1,V0,M1} R(32,0);r(30) { subset_complement( the_carrier(
% 0.72/1.29 skol8 ), topstr_closure( skol8, subset_complement( the_carrier( skol8 ),
% 0.72/1.29 skol10 ) ) ) ==> interior( skol8, skol10 ) }.
% 0.72/1.29 (54) {G1,W8,D4,L1,V0,M1} R(3,32) { element( subset_complement( the_carrier
% 0.72/1.29 ( skol8 ), skol10 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 (133) {G1,W7,D3,L2,V0,M2} R(12,31);r(28) { ! top_str( skol7 ), open_subset
% 0.72/1.29 ( interior( skol7, skol9 ), skol7 ) }.
% 0.72/1.29 (141) {G2,W5,D3,L1,V0,M1} S(133);r(29) { open_subset( interior( skol7,
% 0.72/1.29 skol9 ), skol7 ) }.
% 0.72/1.29 (148) {G1,W9,D5,L1,V0,M1} R(13,32) { subset_complement( the_carrier( skol8
% 0.72/1.29 ), subset_complement( the_carrier( skol8 ), skol10 ) ) ==> skol10 }.
% 0.72/1.29 (160) {G2,W13,D5,L1,V0,M1} R(52,13) { subset_complement( the_carrier( skol8
% 0.72/1.29 ), subset_complement( the_carrier( skol8 ), interior( skol8, skol10 ) )
% 0.72/1.29 ) ==> interior( skol8, skol10 ) }.
% 0.72/1.29 (217) {G3,W3,D2,L1,V0,M1} P(33,141);r(34) { alpha1( skol8, skol10 ) }.
% 0.72/1.29 (221) {G4,W5,D3,L1,V0,M1} R(217,36) { ! interior( skol8, skol10 ) ==>
% 0.72/1.29 skol10 }.
% 0.72/1.29 (222) {G4,W3,D2,L1,V0,M1} R(217,35) { open_subset( skol10, skol8 ) }.
% 0.72/1.29 (281) {G1,W9,D4,L2,V0,M2} R(22,32);r(30) { ! open_subset( skol10, skol8 ),
% 0.72/1.29 closed_subset( subset_complement( the_carrier( skol8 ), skol10 ), skol8 )
% 0.72/1.29 }.
% 0.72/1.29 (366) {G1,W13,D4,L3,V1,M3} R(26,30) { ! element( X, powerset( the_carrier(
% 0.72/1.29 skol8 ) ) ), ! closed_subset( X, skol8 ), topstr_closure( skol8, X ) ==>
% 0.72/1.29 X }.
% 0.72/1.29 (424) {G2,W10,D5,L1,V0,M1} R(54,4);r(30) { element( topstr_closure( skol8,
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ) ), powerset(
% 0.72/1.29 the_carrier( skol8 ) ) ) }.
% 0.72/1.29 (632) {G3,W13,D5,L1,V0,M1} P(53,13);r(424) { topstr_closure( skol8,
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ) ) ==> subset_complement
% 0.72/1.29 ( the_carrier( skol8 ), interior( skol8, skol10 ) ) }.
% 0.72/1.29 (892) {G5,W6,D4,L1,V0,M1} S(281);r(222) { closed_subset( subset_complement
% 0.72/1.29 ( the_carrier( skol8 ), skol10 ), skol8 ) }.
% 0.72/1.29 (3611) {G6,W11,D4,L1,V0,M1} R(366,892);d(632);r(54) { subset_complement(
% 0.72/1.29 the_carrier( skol8 ), interior( skol8, skol10 ) ) ==> subset_complement(
% 0.72/1.29 the_carrier( skol8 ), skol10 ) }.
% 0.72/1.29 (3614) {G7,W5,D3,L1,V0,M1} P(3611,160);d(148) { interior( skol8, skol10 )
% 0.72/1.29 ==> skol10 }.
% 0.72/1.29 (3615) {G8,W0,D0,L0,V0,M0} S(3614);r(221) { }.
% 0.72/1.29
% 0.72/1.29
% 0.72/1.29 % SZS output end Refutation
% 0.72/1.29 found a proof!
% 0.72/1.29
% 0.72/1.29
% 0.72/1.29 Unprocessed initial clauses:
% 0.72/1.29
% 0.72/1.29 (3617) {G0,W20,D6,L3,V2,M3} { ! top_str( X ), ! element( Y, powerset(
% 0.72/1.29 the_carrier( X ) ) ), interior( X, Y ) = subset_complement( the_carrier(
% 0.72/1.29 X ), topstr_closure( X, subset_complement( the_carrier( X ), Y ) ) ) }.
% 0.72/1.29 (3618) {G0,W14,D4,L3,V2,M3} { ! top_str( X ), ! element( Y, powerset(
% 0.72/1.29 the_carrier( X ) ) ), element( interior( X, Y ), powerset( the_carrier( X
% 0.72/1.29 ) ) ) }.
% 0.72/1.29 (3619) {G0,W1,D1,L1,V0,M1} { && }.
% 0.72/1.29 (3620) {G0,W10,D3,L2,V2,M2} { ! element( Y, powerset( X ) ), element(
% 0.72/1.29 subset_complement( X, Y ), powerset( X ) ) }.
% 0.72/1.29 (3621) {G0,W14,D4,L3,V2,M3} { ! top_str( X ), ! element( Y, powerset(
% 0.72/1.29 the_carrier( X ) ) ), element( topstr_closure( X, Y ), powerset(
% 0.72/1.29 the_carrier( X ) ) ) }.
% 0.72/1.29 (3622) {G0,W4,D2,L2,V1,M2} { ! top_str( X ), one_sorted_str( X ) }.
% 0.72/1.29 (3623) {G0,W1,D1,L1,V0,M1} { && }.
% 0.72/1.29 (3624) {G0,W1,D1,L1,V0,M1} { && }.
% 0.72/1.29 (3625) {G0,W1,D1,L1,V0,M1} { && }.
% 0.72/1.29 (3626) {G0,W2,D2,L1,V0,M1} { top_str( skol1 ) }.
% 0.72/1.29 (3627) {G0,W2,D2,L1,V0,M1} { one_sorted_str( skol2 ) }.
% 0.72/1.29 (3628) {G0,W4,D3,L1,V1,M1} { element( skol3( X ), X ) }.
% 0.72/1.29 (3629) {G0,W14,D4,L4,V2,M4} { ! topological_space( X ), ! top_str( X ), !
% 0.72/1.29 element( Y, powerset( the_carrier( X ) ) ), closed_subset( topstr_closure
% 0.72/1.29 ( X, Y ), X ) }.
% 0.72/1.29 (3630) {G0,W18,D4,L5,V2,M5} { ! topological_space( X ), ! top_str( X ), !
% 0.72/1.29 closed_subset( Y, X ), ! element( Y, powerset( the_carrier( X ) ) ),
% 0.72/1.29 open_subset( subset_complement( the_carrier( X ), Y ), X ) }.
% 0.72/1.29 (3631) {G0,W18,D4,L5,V2,M5} { ! topological_space( X ), ! top_str( X ), !
% 0.72/1.29 open_subset( Y, X ), ! element( Y, powerset( the_carrier( X ) ) ),
% 0.72/1.29 closed_subset( subset_complement( the_carrier( X ), Y ), X ) }.
% 0.72/1.29 (3632) {G0,W14,D4,L4,V2,M4} { ! topological_space( X ), ! top_str( X ), !
% 0.72/1.29 element( Y, powerset( the_carrier( X ) ) ), open_subset( interior( X, Y )
% 0.72/1.29 , X ) }.
% 0.72/1.29 (3633) {G0,W11,D4,L2,V2,M2} { ! element( Y, powerset( X ) ),
% 0.72/1.29 subset_complement( X, subset_complement( X, Y ) ) = Y }.
% 0.72/1.29 (3634) {G0,W10,D4,L3,V1,M3} { ! topological_space( X ), ! top_str( X ),
% 0.72/1.29 element( skol4( X ), powerset( the_carrier( X ) ) ) }.
% 0.72/1.29 (3635) {G0,W8,D3,L3,V1,M3} { ! topological_space( X ), ! top_str( X ),
% 0.72/1.29 open_subset( skol4( X ), X ) }.
% 0.72/1.29 (3636) {G0,W10,D4,L3,V1,M3} { ! topological_space( X ), ! top_str( X ),
% 0.72/1.29 element( skol5( X ), powerset( the_carrier( X ) ) ) }.
% 0.72/1.29 (3637) {G0,W8,D3,L3,V1,M3} { ! topological_space( X ), ! top_str( X ),
% 0.72/1.29 open_subset( skol5( X ), X ) }.
% 0.72/1.29 (3638) {G0,W8,D3,L3,V1,M3} { ! topological_space( X ), ! top_str( X ),
% 0.72/1.29 closed_subset( skol5( X ), X ) }.
% 0.72/1.29 (3639) {G0,W10,D4,L3,V1,M3} { ! topological_space( X ), ! top_str( X ),
% 0.72/1.29 element( skol6( X ), powerset( the_carrier( X ) ) ) }.
% 0.72/1.29 (3640) {G0,W8,D3,L3,V1,M3} { ! topological_space( X ), ! top_str( X ),
% 0.72/1.29 closed_subset( skol6( X ), X ) }.
% 0.72/1.29 (3641) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.72/1.29 (3642) {G0,W16,D4,L4,V2,M4} { ! top_str( X ), ! element( Y, powerset(
% 0.72/1.29 the_carrier( X ) ) ), ! open_subset( Y, X ), closed_subset(
% 0.72/1.29 subset_complement( the_carrier( X ), Y ), X ) }.
% 0.72/1.29 (3643) {G0,W16,D4,L4,V2,M4} { ! top_str( X ), ! element( Y, powerset(
% 0.72/1.29 the_carrier( X ) ) ), ! closed_subset( subset_complement( the_carrier( X
% 0.72/1.29 ), Y ), X ), open_subset( Y, X ) }.
% 0.72/1.29 (3644) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y )
% 0.72/1.29 }.
% 0.72/1.29 (3645) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.72/1.29 }.
% 0.72/1.29 (3646) {G0,W15,D4,L4,V2,M4} { ! top_str( X ), ! element( Y, powerset(
% 0.72/1.29 the_carrier( X ) ) ), ! closed_subset( Y, X ), topstr_closure( X, Y ) = Y
% 0.72/1.29 }.
% 0.72/1.29 (3647) {G0,W17,D4,L5,V2,M5} { ! top_str( X ), ! element( Y, powerset(
% 0.72/1.29 the_carrier( X ) ) ), ! topological_space( X ), ! topstr_closure( X, Y )
% 0.72/1.29 = Y, closed_subset( Y, X ) }.
% 0.72/1.29 (3648) {G0,W2,D2,L1,V0,M1} { topological_space( skol7 ) }.
% 0.72/1.29 (3649) {G0,W2,D2,L1,V0,M1} { top_str( skol7 ) }.
% 0.72/1.29 (3650) {G0,W2,D2,L1,V0,M1} { top_str( skol8 ) }.
% 0.72/1.29 (3651) {G0,W5,D4,L1,V0,M1} { element( skol9, powerset( the_carrier( skol7
% 0.72/1.29 ) ) ) }.
% 0.72/1.29 (3652) {G0,W5,D4,L1,V0,M1} { element( skol10, powerset( the_carrier( skol8
% 0.72/1.29 ) ) ) }.
% 0.72/1.29 (3653) {G0,W8,D3,L2,V0,M2} { alpha1( skol8, skol10 ), interior( skol7,
% 0.72/1.29 skol9 ) = skol9 }.
% 0.72/1.29 (3654) {G0,W6,D2,L2,V0,M2} { alpha1( skol8, skol10 ), ! open_subset( skol9
% 0.72/1.29 , skol7 ) }.
% 0.72/1.29 (3655) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), open_subset( Y, X ) }.
% 0.72/1.29 (3656) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), ! interior( X, Y ) = Y }.
% 0.72/1.29 (3657) {G0,W11,D3,L3,V2,M3} { ! open_subset( Y, X ), interior( X, Y ) = Y
% 0.72/1.29 , alpha1( X, Y ) }.
% 0.72/1.29
% 0.72/1.29
% 0.72/1.29 Total Proof:
% 0.72/1.29
% 0.72/1.29 eqswap: (3658) {G0,W20,D6,L3,V2,M3} { subset_complement( the_carrier( X )
% 0.72/1.29 , topstr_closure( X, subset_complement( the_carrier( X ), Y ) ) ) =
% 0.72/1.29 interior( X, Y ), ! top_str( X ), ! element( Y, powerset( the_carrier( X
% 0.72/1.29 ) ) ) }.
% 0.72/1.29 parent0[2]: (3617) {G0,W20,D6,L3,V2,M3} { ! top_str( X ), ! element( Y,
% 0.72/1.29 powerset( the_carrier( X ) ) ), interior( X, Y ) = subset_complement(
% 0.72/1.29 the_carrier( X ), topstr_closure( X, subset_complement( the_carrier( X )
% 0.72/1.29 , Y ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (0) {G0,W20,D6,L3,V2,M3} I { ! top_str( X ), ! element( Y,
% 0.72/1.29 powerset( the_carrier( X ) ) ), subset_complement( the_carrier( X ),
% 0.72/1.29 topstr_closure( X, subset_complement( the_carrier( X ), Y ) ) ) ==>
% 0.72/1.29 interior( X, Y ) }.
% 0.72/1.29 parent0: (3658) {G0,W20,D6,L3,V2,M3} { subset_complement( the_carrier( X )
% 0.72/1.29 , topstr_closure( X, subset_complement( the_carrier( X ), Y ) ) ) =
% 0.72/1.29 interior( X, Y ), ! top_str( X ), ! element( Y, powerset( the_carrier( X
% 0.72/1.29 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 2
% 0.72/1.29 1 ==> 0
% 0.72/1.29 2 ==> 1
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (1) {G0,W14,D4,L3,V2,M3} I { ! top_str( X ), ! element( Y,
% 0.72/1.29 powerset( the_carrier( X ) ) ), element( interior( X, Y ), powerset(
% 0.72/1.29 the_carrier( X ) ) ) }.
% 0.72/1.29 parent0: (3618) {G0,W14,D4,L3,V2,M3} { ! top_str( X ), ! element( Y,
% 0.72/1.29 powerset( the_carrier( X ) ) ), element( interior( X, Y ), powerset(
% 0.72/1.29 the_carrier( X ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 1 ==> 1
% 0.72/1.29 2 ==> 2
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (3) {G0,W10,D3,L2,V2,M2} I { ! element( Y, powerset( X ) ),
% 0.72/1.29 element( subset_complement( X, Y ), powerset( X ) ) }.
% 0.72/1.29 parent0: (3620) {G0,W10,D3,L2,V2,M2} { ! element( Y, powerset( X ) ),
% 0.72/1.29 element( subset_complement( X, Y ), powerset( X ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 1 ==> 1
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (4) {G0,W14,D4,L3,V2,M3} I { ! top_str( X ), ! element( Y,
% 0.72/1.29 powerset( the_carrier( X ) ) ), element( topstr_closure( X, Y ), powerset
% 0.72/1.29 ( the_carrier( X ) ) ) }.
% 0.72/1.29 parent0: (3621) {G0,W14,D4,L3,V2,M3} { ! top_str( X ), ! element( Y,
% 0.72/1.29 powerset( the_carrier( X ) ) ), element( topstr_closure( X, Y ), powerset
% 0.72/1.29 ( the_carrier( X ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 1 ==> 1
% 0.72/1.29 2 ==> 2
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (12) {G0,W14,D4,L4,V2,M4} I { ! topological_space( X ), !
% 0.72/1.29 top_str( X ), ! element( Y, powerset( the_carrier( X ) ) ), open_subset(
% 0.72/1.29 interior( X, Y ), X ) }.
% 0.72/1.29 parent0: (3632) {G0,W14,D4,L4,V2,M4} { ! topological_space( X ), ! top_str
% 0.72/1.29 ( X ), ! element( Y, powerset( the_carrier( X ) ) ), open_subset(
% 0.72/1.29 interior( X, Y ), X ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 1 ==> 1
% 0.72/1.29 2 ==> 2
% 0.72/1.29 3 ==> 3
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (13) {G0,W11,D4,L2,V2,M2} I { ! element( Y, powerset( X ) ),
% 0.72/1.29 subset_complement( X, subset_complement( X, Y ) ) ==> Y }.
% 0.72/1.29 parent0: (3633) {G0,W11,D4,L2,V2,M2} { ! element( Y, powerset( X ) ),
% 0.72/1.29 subset_complement( X, subset_complement( X, Y ) ) = Y }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 1 ==> 1
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (22) {G0,W16,D4,L4,V2,M4} I { ! top_str( X ), ! element( Y,
% 0.72/1.29 powerset( the_carrier( X ) ) ), ! open_subset( Y, X ), closed_subset(
% 0.72/1.29 subset_complement( the_carrier( X ), Y ), X ) }.
% 0.72/1.29 parent0: (3642) {G0,W16,D4,L4,V2,M4} { ! top_str( X ), ! element( Y,
% 0.72/1.29 powerset( the_carrier( X ) ) ), ! open_subset( Y, X ), closed_subset(
% 0.72/1.29 subset_complement( the_carrier( X ), Y ), X ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 1 ==> 1
% 0.72/1.29 2 ==> 2
% 0.72/1.29 3 ==> 3
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (26) {G0,W15,D4,L4,V2,M4} I { ! top_str( X ), ! element( Y,
% 0.72/1.29 powerset( the_carrier( X ) ) ), ! closed_subset( Y, X ), topstr_closure(
% 0.72/1.29 X, Y ) ==> Y }.
% 0.72/1.29 parent0: (3646) {G0,W15,D4,L4,V2,M4} { ! top_str( X ), ! element( Y,
% 0.72/1.29 powerset( the_carrier( X ) ) ), ! closed_subset( Y, X ), topstr_closure(
% 0.72/1.29 X, Y ) = Y }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 1 ==> 1
% 0.72/1.29 2 ==> 2
% 0.72/1.29 3 ==> 3
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (28) {G0,W2,D2,L1,V0,M1} I { topological_space( skol7 ) }.
% 0.72/1.29 parent0: (3648) {G0,W2,D2,L1,V0,M1} { topological_space( skol7 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (29) {G0,W2,D2,L1,V0,M1} I { top_str( skol7 ) }.
% 0.72/1.29 parent0: (3649) {G0,W2,D2,L1,V0,M1} { top_str( skol7 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (30) {G0,W2,D2,L1,V0,M1} I { top_str( skol8 ) }.
% 0.72/1.29 parent0: (3650) {G0,W2,D2,L1,V0,M1} { top_str( skol8 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (31) {G0,W5,D4,L1,V0,M1} I { element( skol9, powerset(
% 0.72/1.29 the_carrier( skol7 ) ) ) }.
% 0.72/1.29 parent0: (3651) {G0,W5,D4,L1,V0,M1} { element( skol9, powerset(
% 0.72/1.29 the_carrier( skol7 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (32) {G0,W5,D4,L1,V0,M1} I { element( skol10, powerset(
% 0.72/1.29 the_carrier( skol8 ) ) ) }.
% 0.72/1.29 parent0: (3652) {G0,W5,D4,L1,V0,M1} { element( skol10, powerset(
% 0.72/1.29 the_carrier( skol8 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (33) {G0,W8,D3,L2,V0,M2} I { alpha1( skol8, skol10 ), interior
% 0.72/1.29 ( skol7, skol9 ) ==> skol9 }.
% 0.72/1.29 parent0: (3653) {G0,W8,D3,L2,V0,M2} { alpha1( skol8, skol10 ), interior(
% 0.72/1.29 skol7, skol9 ) = skol9 }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 1 ==> 1
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (34) {G0,W6,D2,L2,V0,M2} I { alpha1( skol8, skol10 ), !
% 0.72/1.29 open_subset( skol9, skol7 ) }.
% 0.72/1.29 parent0: (3654) {G0,W6,D2,L2,V0,M2} { alpha1( skol8, skol10 ), !
% 0.72/1.29 open_subset( skol9, skol7 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 1 ==> 1
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (35) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), open_subset( Y
% 0.72/1.29 , X ) }.
% 0.72/1.29 parent0: (3655) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), open_subset( Y, X
% 0.72/1.29 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 1 ==> 1
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 *** allocated 75937 integers for termspace/termends
% 0.72/1.29 subsumption: (36) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), ! interior( X,
% 0.72/1.29 Y ) ==> Y }.
% 0.72/1.29 parent0: (3656) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), ! interior( X, Y )
% 0.72/1.29 = Y }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 1 ==> 1
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3711) {G1,W9,D4,L2,V0,M2} { ! top_str( skol8 ), element(
% 0.72/1.29 interior( skol8, skol10 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 parent0[1]: (1) {G0,W14,D4,L3,V2,M3} I { ! top_str( X ), ! element( Y,
% 0.72/1.29 powerset( the_carrier( X ) ) ), element( interior( X, Y ), powerset(
% 0.72/1.29 the_carrier( X ) ) ) }.
% 0.72/1.29 parent1[0]: (32) {G0,W5,D4,L1,V0,M1} I { element( skol10, powerset(
% 0.72/1.29 the_carrier( skol8 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := skol8
% 0.72/1.29 Y := skol10
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3712) {G1,W7,D4,L1,V0,M1} { element( interior( skol8, skol10
% 0.72/1.29 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 parent0[0]: (3711) {G1,W9,D4,L2,V0,M2} { ! top_str( skol8 ), element(
% 0.72/1.29 interior( skol8, skol10 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 parent1[0]: (30) {G0,W2,D2,L1,V0,M1} I { top_str( skol8 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (52) {G1,W7,D4,L1,V0,M1} R(32,1);r(30) { element( interior(
% 0.72/1.29 skol8, skol10 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 parent0: (3712) {G1,W7,D4,L1,V0,M1} { element( interior( skol8, skol10 ),
% 0.72/1.29 powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 eqswap: (3713) {G0,W20,D6,L3,V2,M3} { interior( X, Y ) ==>
% 0.72/1.29 subset_complement( the_carrier( X ), topstr_closure( X, subset_complement
% 0.72/1.29 ( the_carrier( X ), Y ) ) ), ! top_str( X ), ! element( Y, powerset(
% 0.72/1.29 the_carrier( X ) ) ) }.
% 0.72/1.29 parent0[2]: (0) {G0,W20,D6,L3,V2,M3} I { ! top_str( X ), ! element( Y,
% 0.72/1.29 powerset( the_carrier( X ) ) ), subset_complement( the_carrier( X ),
% 0.72/1.29 topstr_closure( X, subset_complement( the_carrier( X ), Y ) ) ) ==>
% 0.72/1.29 interior( X, Y ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3714) {G1,W15,D6,L2,V0,M2} { interior( skol8, skol10 ) ==>
% 0.72/1.29 subset_complement( the_carrier( skol8 ), topstr_closure( skol8,
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ) ) ), ! top_str( skol8 )
% 0.72/1.29 }.
% 0.72/1.29 parent0[2]: (3713) {G0,W20,D6,L3,V2,M3} { interior( X, Y ) ==>
% 0.72/1.29 subset_complement( the_carrier( X ), topstr_closure( X, subset_complement
% 0.72/1.29 ( the_carrier( X ), Y ) ) ), ! top_str( X ), ! element( Y, powerset(
% 0.72/1.29 the_carrier( X ) ) ) }.
% 0.72/1.29 parent1[0]: (32) {G0,W5,D4,L1,V0,M1} I { element( skol10, powerset(
% 0.72/1.29 the_carrier( skol8 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := skol8
% 0.72/1.29 Y := skol10
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3715) {G1,W13,D6,L1,V0,M1} { interior( skol8, skol10 ) ==>
% 0.72/1.29 subset_complement( the_carrier( skol8 ), topstr_closure( skol8,
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ) ) ) }.
% 0.72/1.29 parent0[1]: (3714) {G1,W15,D6,L2,V0,M2} { interior( skol8, skol10 ) ==>
% 0.72/1.29 subset_complement( the_carrier( skol8 ), topstr_closure( skol8,
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ) ) ), ! top_str( skol8 )
% 0.72/1.29 }.
% 0.72/1.29 parent1[0]: (30) {G0,W2,D2,L1,V0,M1} I { top_str( skol8 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 eqswap: (3716) {G1,W13,D6,L1,V0,M1} { subset_complement( the_carrier(
% 0.72/1.29 skol8 ), topstr_closure( skol8, subset_complement( the_carrier( skol8 ),
% 0.72/1.29 skol10 ) ) ) ==> interior( skol8, skol10 ) }.
% 0.72/1.29 parent0[0]: (3715) {G1,W13,D6,L1,V0,M1} { interior( skol8, skol10 ) ==>
% 0.72/1.29 subset_complement( the_carrier( skol8 ), topstr_closure( skol8,
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (53) {G1,W13,D6,L1,V0,M1} R(32,0);r(30) { subset_complement(
% 0.72/1.29 the_carrier( skol8 ), topstr_closure( skol8, subset_complement(
% 0.72/1.29 the_carrier( skol8 ), skol10 ) ) ) ==> interior( skol8, skol10 ) }.
% 0.72/1.29 parent0: (3716) {G1,W13,D6,L1,V0,M1} { subset_complement( the_carrier(
% 0.72/1.29 skol8 ), topstr_closure( skol8, subset_complement( the_carrier( skol8 ),
% 0.72/1.29 skol10 ) ) ) ==> interior( skol8, skol10 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3717) {G1,W8,D4,L1,V0,M1} { element( subset_complement(
% 0.72/1.29 the_carrier( skol8 ), skol10 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 parent0[0]: (3) {G0,W10,D3,L2,V2,M2} I { ! element( Y, powerset( X ) ),
% 0.72/1.29 element( subset_complement( X, Y ), powerset( X ) ) }.
% 0.72/1.29 parent1[0]: (32) {G0,W5,D4,L1,V0,M1} I { element( skol10, powerset(
% 0.72/1.29 the_carrier( skol8 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := the_carrier( skol8 )
% 0.72/1.29 Y := skol10
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (54) {G1,W8,D4,L1,V0,M1} R(3,32) { element( subset_complement
% 0.72/1.29 ( the_carrier( skol8 ), skol10 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 parent0: (3717) {G1,W8,D4,L1,V0,M1} { element( subset_complement(
% 0.72/1.29 the_carrier( skol8 ), skol10 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3718) {G1,W9,D3,L3,V0,M3} { ! topological_space( skol7 ), !
% 0.72/1.29 top_str( skol7 ), open_subset( interior( skol7, skol9 ), skol7 ) }.
% 0.72/1.29 parent0[2]: (12) {G0,W14,D4,L4,V2,M4} I { ! topological_space( X ), !
% 0.72/1.29 top_str( X ), ! element( Y, powerset( the_carrier( X ) ) ), open_subset(
% 0.72/1.29 interior( X, Y ), X ) }.
% 0.72/1.29 parent1[0]: (31) {G0,W5,D4,L1,V0,M1} I { element( skol9, powerset(
% 0.72/1.29 the_carrier( skol7 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := skol7
% 0.72/1.29 Y := skol9
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3719) {G1,W7,D3,L2,V0,M2} { ! top_str( skol7 ), open_subset(
% 0.72/1.29 interior( skol7, skol9 ), skol7 ) }.
% 0.72/1.29 parent0[0]: (3718) {G1,W9,D3,L3,V0,M3} { ! topological_space( skol7 ), !
% 0.72/1.29 top_str( skol7 ), open_subset( interior( skol7, skol9 ), skol7 ) }.
% 0.72/1.29 parent1[0]: (28) {G0,W2,D2,L1,V0,M1} I { topological_space( skol7 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (133) {G1,W7,D3,L2,V0,M2} R(12,31);r(28) { ! top_str( skol7 )
% 0.72/1.29 , open_subset( interior( skol7, skol9 ), skol7 ) }.
% 0.72/1.29 parent0: (3719) {G1,W7,D3,L2,V0,M2} { ! top_str( skol7 ), open_subset(
% 0.72/1.29 interior( skol7, skol9 ), skol7 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 1 ==> 1
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3720) {G1,W5,D3,L1,V0,M1} { open_subset( interior( skol7,
% 0.72/1.29 skol9 ), skol7 ) }.
% 0.72/1.29 parent0[0]: (133) {G1,W7,D3,L2,V0,M2} R(12,31);r(28) { ! top_str( skol7 ),
% 0.72/1.29 open_subset( interior( skol7, skol9 ), skol7 ) }.
% 0.72/1.29 parent1[0]: (29) {G0,W2,D2,L1,V0,M1} I { top_str( skol7 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (141) {G2,W5,D3,L1,V0,M1} S(133);r(29) { open_subset( interior
% 0.72/1.29 ( skol7, skol9 ), skol7 ) }.
% 0.72/1.29 parent0: (3720) {G1,W5,D3,L1,V0,M1} { open_subset( interior( skol7, skol9
% 0.72/1.29 ), skol7 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 eqswap: (3721) {G0,W11,D4,L2,V2,M2} { Y ==> subset_complement( X,
% 0.72/1.29 subset_complement( X, Y ) ), ! element( Y, powerset( X ) ) }.
% 0.72/1.29 parent0[1]: (13) {G0,W11,D4,L2,V2,M2} I { ! element( Y, powerset( X ) ),
% 0.72/1.29 subset_complement( X, subset_complement( X, Y ) ) ==> Y }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3722) {G1,W9,D5,L1,V0,M1} { skol10 ==> subset_complement(
% 0.72/1.29 the_carrier( skol8 ), subset_complement( the_carrier( skol8 ), skol10 ) )
% 0.72/1.29 }.
% 0.72/1.29 parent0[1]: (3721) {G0,W11,D4,L2,V2,M2} { Y ==> subset_complement( X,
% 0.72/1.29 subset_complement( X, Y ) ), ! element( Y, powerset( X ) ) }.
% 0.72/1.29 parent1[0]: (32) {G0,W5,D4,L1,V0,M1} I { element( skol10, powerset(
% 0.72/1.29 the_carrier( skol8 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := the_carrier( skol8 )
% 0.72/1.29 Y := skol10
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 eqswap: (3723) {G1,W9,D5,L1,V0,M1} { subset_complement( the_carrier( skol8
% 0.72/1.29 ), subset_complement( the_carrier( skol8 ), skol10 ) ) ==> skol10 }.
% 0.72/1.29 parent0[0]: (3722) {G1,W9,D5,L1,V0,M1} { skol10 ==> subset_complement(
% 0.72/1.29 the_carrier( skol8 ), subset_complement( the_carrier( skol8 ), skol10 ) )
% 0.72/1.29 }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (148) {G1,W9,D5,L1,V0,M1} R(13,32) { subset_complement(
% 0.72/1.29 the_carrier( skol8 ), subset_complement( the_carrier( skol8 ), skol10 ) )
% 0.72/1.29 ==> skol10 }.
% 0.72/1.29 parent0: (3723) {G1,W9,D5,L1,V0,M1} { subset_complement( the_carrier(
% 0.72/1.29 skol8 ), subset_complement( the_carrier( skol8 ), skol10 ) ) ==> skol10
% 0.72/1.29 }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 eqswap: (3724) {G0,W11,D4,L2,V2,M2} { Y ==> subset_complement( X,
% 0.72/1.29 subset_complement( X, Y ) ), ! element( Y, powerset( X ) ) }.
% 0.72/1.29 parent0[1]: (13) {G0,W11,D4,L2,V2,M2} I { ! element( Y, powerset( X ) ),
% 0.72/1.29 subset_complement( X, subset_complement( X, Y ) ) ==> Y }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3725) {G1,W13,D5,L1,V0,M1} { interior( skol8, skol10 ) ==>
% 0.72/1.29 subset_complement( the_carrier( skol8 ), subset_complement( the_carrier(
% 0.72/1.29 skol8 ), interior( skol8, skol10 ) ) ) }.
% 0.72/1.29 parent0[1]: (3724) {G0,W11,D4,L2,V2,M2} { Y ==> subset_complement( X,
% 0.72/1.29 subset_complement( X, Y ) ), ! element( Y, powerset( X ) ) }.
% 0.72/1.29 parent1[0]: (52) {G1,W7,D4,L1,V0,M1} R(32,1);r(30) { element( interior(
% 0.72/1.29 skol8, skol10 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := the_carrier( skol8 )
% 0.72/1.29 Y := interior( skol8, skol10 )
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 eqswap: (3726) {G1,W13,D5,L1,V0,M1} { subset_complement( the_carrier(
% 0.72/1.29 skol8 ), subset_complement( the_carrier( skol8 ), interior( skol8, skol10
% 0.72/1.29 ) ) ) ==> interior( skol8, skol10 ) }.
% 0.72/1.29 parent0[0]: (3725) {G1,W13,D5,L1,V0,M1} { interior( skol8, skol10 ) ==>
% 0.72/1.29 subset_complement( the_carrier( skol8 ), subset_complement( the_carrier(
% 0.72/1.29 skol8 ), interior( skol8, skol10 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (160) {G2,W13,D5,L1,V0,M1} R(52,13) { subset_complement(
% 0.72/1.29 the_carrier( skol8 ), subset_complement( the_carrier( skol8 ), interior(
% 0.72/1.29 skol8, skol10 ) ) ) ==> interior( skol8, skol10 ) }.
% 0.72/1.29 parent0: (3726) {G1,W13,D5,L1,V0,M1} { subset_complement( the_carrier(
% 0.72/1.29 skol8 ), subset_complement( the_carrier( skol8 ), interior( skol8, skol10
% 0.72/1.29 ) ) ) ==> interior( skol8, skol10 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 paramod: (3728) {G1,W6,D2,L2,V0,M2} { open_subset( skol9, skol7 ), alpha1
% 0.72/1.29 ( skol8, skol10 ) }.
% 0.72/1.29 parent0[1]: (33) {G0,W8,D3,L2,V0,M2} I { alpha1( skol8, skol10 ), interior
% 0.72/1.29 ( skol7, skol9 ) ==> skol9 }.
% 0.72/1.29 parent1[0; 1]: (141) {G2,W5,D3,L1,V0,M1} S(133);r(29) { open_subset(
% 0.72/1.29 interior( skol7, skol9 ), skol7 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3729) {G1,W6,D2,L2,V0,M2} { alpha1( skol8, skol10 ), alpha1(
% 0.72/1.29 skol8, skol10 ) }.
% 0.72/1.29 parent0[1]: (34) {G0,W6,D2,L2,V0,M2} I { alpha1( skol8, skol10 ), !
% 0.72/1.29 open_subset( skol9, skol7 ) }.
% 0.72/1.29 parent1[0]: (3728) {G1,W6,D2,L2,V0,M2} { open_subset( skol9, skol7 ),
% 0.72/1.29 alpha1( skol8, skol10 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 factor: (3730) {G1,W3,D2,L1,V0,M1} { alpha1( skol8, skol10 ) }.
% 0.72/1.29 parent0[0, 1]: (3729) {G1,W6,D2,L2,V0,M2} { alpha1( skol8, skol10 ),
% 0.72/1.29 alpha1( skol8, skol10 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (217) {G3,W3,D2,L1,V0,M1} P(33,141);r(34) { alpha1( skol8,
% 0.72/1.29 skol10 ) }.
% 0.72/1.29 parent0: (3730) {G1,W3,D2,L1,V0,M1} { alpha1( skol8, skol10 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 eqswap: (3731) {G0,W8,D3,L2,V2,M2} { ! Y ==> interior( X, Y ), ! alpha1( X
% 0.72/1.29 , Y ) }.
% 0.72/1.29 parent0[1]: (36) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), ! interior( X, Y
% 0.72/1.29 ) ==> Y }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3732) {G1,W5,D3,L1,V0,M1} { ! skol10 ==> interior( skol8,
% 0.72/1.29 skol10 ) }.
% 0.72/1.29 parent0[1]: (3731) {G0,W8,D3,L2,V2,M2} { ! Y ==> interior( X, Y ), !
% 0.72/1.29 alpha1( X, Y ) }.
% 0.72/1.29 parent1[0]: (217) {G3,W3,D2,L1,V0,M1} P(33,141);r(34) { alpha1( skol8,
% 0.72/1.29 skol10 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := skol8
% 0.72/1.29 Y := skol10
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 eqswap: (3733) {G1,W5,D3,L1,V0,M1} { ! interior( skol8, skol10 ) ==>
% 0.72/1.29 skol10 }.
% 0.72/1.29 parent0[0]: (3732) {G1,W5,D3,L1,V0,M1} { ! skol10 ==> interior( skol8,
% 0.72/1.29 skol10 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (221) {G4,W5,D3,L1,V0,M1} R(217,36) { ! interior( skol8,
% 0.72/1.29 skol10 ) ==> skol10 }.
% 0.72/1.29 parent0: (3733) {G1,W5,D3,L1,V0,M1} { ! interior( skol8, skol10 ) ==>
% 0.72/1.29 skol10 }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3734) {G1,W3,D2,L1,V0,M1} { open_subset( skol10, skol8 ) }.
% 0.72/1.29 parent0[0]: (35) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), open_subset( Y,
% 0.72/1.29 X ) }.
% 0.72/1.29 parent1[0]: (217) {G3,W3,D2,L1,V0,M1} P(33,141);r(34) { alpha1( skol8,
% 0.72/1.29 skol10 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := skol8
% 0.72/1.29 Y := skol10
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (222) {G4,W3,D2,L1,V0,M1} R(217,35) { open_subset( skol10,
% 0.72/1.29 skol8 ) }.
% 0.72/1.29 parent0: (3734) {G1,W3,D2,L1,V0,M1} { open_subset( skol10, skol8 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3735) {G1,W11,D4,L3,V0,M3} { ! top_str( skol8 ), !
% 0.72/1.29 open_subset( skol10, skol8 ), closed_subset( subset_complement(
% 0.72/1.29 the_carrier( skol8 ), skol10 ), skol8 ) }.
% 0.72/1.29 parent0[1]: (22) {G0,W16,D4,L4,V2,M4} I { ! top_str( X ), ! element( Y,
% 0.72/1.29 powerset( the_carrier( X ) ) ), ! open_subset( Y, X ), closed_subset(
% 0.72/1.29 subset_complement( the_carrier( X ), Y ), X ) }.
% 0.72/1.29 parent1[0]: (32) {G0,W5,D4,L1,V0,M1} I { element( skol10, powerset(
% 0.72/1.29 the_carrier( skol8 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := skol8
% 0.72/1.29 Y := skol10
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3736) {G1,W9,D4,L2,V0,M2} { ! open_subset( skol10, skol8 ),
% 0.72/1.29 closed_subset( subset_complement( the_carrier( skol8 ), skol10 ), skol8 )
% 0.72/1.29 }.
% 0.72/1.29 parent0[0]: (3735) {G1,W11,D4,L3,V0,M3} { ! top_str( skol8 ), !
% 0.72/1.29 open_subset( skol10, skol8 ), closed_subset( subset_complement(
% 0.72/1.29 the_carrier( skol8 ), skol10 ), skol8 ) }.
% 0.72/1.29 parent1[0]: (30) {G0,W2,D2,L1,V0,M1} I { top_str( skol8 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (281) {G1,W9,D4,L2,V0,M2} R(22,32);r(30) { ! open_subset(
% 0.72/1.29 skol10, skol8 ), closed_subset( subset_complement( the_carrier( skol8 ),
% 0.72/1.29 skol10 ), skol8 ) }.
% 0.72/1.29 parent0: (3736) {G1,W9,D4,L2,V0,M2} { ! open_subset( skol10, skol8 ),
% 0.72/1.29 closed_subset( subset_complement( the_carrier( skol8 ), skol10 ), skol8 )
% 0.72/1.29 }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 1 ==> 1
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 eqswap: (3737) {G0,W15,D4,L4,V2,M4} { Y ==> topstr_closure( X, Y ), !
% 0.72/1.29 top_str( X ), ! element( Y, powerset( the_carrier( X ) ) ), !
% 0.72/1.29 closed_subset( Y, X ) }.
% 0.72/1.29 parent0[3]: (26) {G0,W15,D4,L4,V2,M4} I { ! top_str( X ), ! element( Y,
% 0.72/1.29 powerset( the_carrier( X ) ) ), ! closed_subset( Y, X ), topstr_closure(
% 0.72/1.29 X, Y ) ==> Y }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3738) {G1,W13,D4,L3,V1,M3} { X ==> topstr_closure( skol8, X )
% 0.72/1.29 , ! element( X, powerset( the_carrier( skol8 ) ) ), ! closed_subset( X,
% 0.72/1.29 skol8 ) }.
% 0.72/1.29 parent0[1]: (3737) {G0,W15,D4,L4,V2,M4} { Y ==> topstr_closure( X, Y ), !
% 0.72/1.29 top_str( X ), ! element( Y, powerset( the_carrier( X ) ) ), !
% 0.72/1.29 closed_subset( Y, X ) }.
% 0.72/1.29 parent1[0]: (30) {G0,W2,D2,L1,V0,M1} I { top_str( skol8 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := skol8
% 0.72/1.29 Y := X
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 eqswap: (3739) {G1,W13,D4,L3,V1,M3} { topstr_closure( skol8, X ) ==> X, !
% 0.72/1.29 element( X, powerset( the_carrier( skol8 ) ) ), ! closed_subset( X, skol8
% 0.72/1.29 ) }.
% 0.72/1.29 parent0[0]: (3738) {G1,W13,D4,L3,V1,M3} { X ==> topstr_closure( skol8, X )
% 0.72/1.29 , ! element( X, powerset( the_carrier( skol8 ) ) ), ! closed_subset( X,
% 0.72/1.29 skol8 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (366) {G1,W13,D4,L3,V1,M3} R(26,30) { ! element( X, powerset(
% 0.72/1.29 the_carrier( skol8 ) ) ), ! closed_subset( X, skol8 ), topstr_closure(
% 0.72/1.29 skol8, X ) ==> X }.
% 0.72/1.29 parent0: (3739) {G1,W13,D4,L3,V1,M3} { topstr_closure( skol8, X ) ==> X, !
% 0.72/1.29 element( X, powerset( the_carrier( skol8 ) ) ), ! closed_subset( X,
% 0.72/1.29 skol8 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 2
% 0.72/1.29 1 ==> 0
% 0.72/1.29 2 ==> 1
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3740) {G1,W12,D5,L2,V0,M2} { ! top_str( skol8 ), element(
% 0.72/1.29 topstr_closure( skol8, subset_complement( the_carrier( skol8 ), skol10 )
% 0.72/1.29 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 parent0[1]: (4) {G0,W14,D4,L3,V2,M3} I { ! top_str( X ), ! element( Y,
% 0.72/1.29 powerset( the_carrier( X ) ) ), element( topstr_closure( X, Y ), powerset
% 0.72/1.29 ( the_carrier( X ) ) ) }.
% 0.72/1.29 parent1[0]: (54) {G1,W8,D4,L1,V0,M1} R(3,32) { element( subset_complement(
% 0.72/1.29 the_carrier( skol8 ), skol10 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := skol8
% 0.72/1.29 Y := subset_complement( the_carrier( skol8 ), skol10 )
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3741) {G1,W10,D5,L1,V0,M1} { element( topstr_closure( skol8,
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ) ), powerset(
% 0.72/1.29 the_carrier( skol8 ) ) ) }.
% 0.72/1.29 parent0[0]: (3740) {G1,W12,D5,L2,V0,M2} { ! top_str( skol8 ), element(
% 0.72/1.29 topstr_closure( skol8, subset_complement( the_carrier( skol8 ), skol10 )
% 0.72/1.29 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 parent1[0]: (30) {G0,W2,D2,L1,V0,M1} I { top_str( skol8 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (424) {G2,W10,D5,L1,V0,M1} R(54,4);r(30) { element(
% 0.72/1.29 topstr_closure( skol8, subset_complement( the_carrier( skol8 ), skol10 )
% 0.72/1.29 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 parent0: (3741) {G1,W10,D5,L1,V0,M1} { element( topstr_closure( skol8,
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ) ), powerset(
% 0.72/1.29 the_carrier( skol8 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 eqswap: (3743) {G0,W11,D4,L2,V2,M2} { Y ==> subset_complement( X,
% 0.72/1.29 subset_complement( X, Y ) ), ! element( Y, powerset( X ) ) }.
% 0.72/1.29 parent0[1]: (13) {G0,W11,D4,L2,V2,M2} I { ! element( Y, powerset( X ) ),
% 0.72/1.29 subset_complement( X, subset_complement( X, Y ) ) ==> Y }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 Y := Y
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 paramod: (3744) {G1,W23,D5,L2,V0,M2} { topstr_closure( skol8,
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ) ) ==> subset_complement
% 0.72/1.29 ( the_carrier( skol8 ), interior( skol8, skol10 ) ), ! element(
% 0.72/1.29 topstr_closure( skol8, subset_complement( the_carrier( skol8 ), skol10 )
% 0.72/1.29 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 parent0[0]: (53) {G1,W13,D6,L1,V0,M1} R(32,0);r(30) { subset_complement(
% 0.72/1.29 the_carrier( skol8 ), topstr_closure( skol8, subset_complement(
% 0.72/1.29 the_carrier( skol8 ), skol10 ) ) ) ==> interior( skol8, skol10 ) }.
% 0.72/1.29 parent1[0; 10]: (3743) {G0,W11,D4,L2,V2,M2} { Y ==> subset_complement( X,
% 0.72/1.29 subset_complement( X, Y ) ), ! element( Y, powerset( X ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 X := the_carrier( skol8 )
% 0.72/1.29 Y := topstr_closure( skol8, subset_complement( the_carrier( skol8 ),
% 0.72/1.29 skol10 ) )
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3745) {G2,W13,D5,L1,V0,M1} { topstr_closure( skol8,
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ) ) ==> subset_complement
% 0.72/1.29 ( the_carrier( skol8 ), interior( skol8, skol10 ) ) }.
% 0.72/1.29 parent0[1]: (3744) {G1,W23,D5,L2,V0,M2} { topstr_closure( skol8,
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ) ) ==> subset_complement
% 0.72/1.29 ( the_carrier( skol8 ), interior( skol8, skol10 ) ), ! element(
% 0.72/1.29 topstr_closure( skol8, subset_complement( the_carrier( skol8 ), skol10 )
% 0.72/1.29 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 parent1[0]: (424) {G2,W10,D5,L1,V0,M1} R(54,4);r(30) { element(
% 0.72/1.29 topstr_closure( skol8, subset_complement( the_carrier( skol8 ), skol10 )
% 0.72/1.29 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (632) {G3,W13,D5,L1,V0,M1} P(53,13);r(424) { topstr_closure(
% 0.72/1.29 skol8, subset_complement( the_carrier( skol8 ), skol10 ) ) ==>
% 0.72/1.29 subset_complement( the_carrier( skol8 ), interior( skol8, skol10 ) ) }.
% 0.72/1.29 parent0: (3745) {G2,W13,D5,L1,V0,M1} { topstr_closure( skol8,
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ) ) ==> subset_complement
% 0.72/1.29 ( the_carrier( skol8 ), interior( skol8, skol10 ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3747) {G2,W6,D4,L1,V0,M1} { closed_subset( subset_complement
% 0.72/1.29 ( the_carrier( skol8 ), skol10 ), skol8 ) }.
% 0.72/1.29 parent0[0]: (281) {G1,W9,D4,L2,V0,M2} R(22,32);r(30) { ! open_subset(
% 0.72/1.29 skol10, skol8 ), closed_subset( subset_complement( the_carrier( skol8 ),
% 0.72/1.29 skol10 ), skol8 ) }.
% 0.72/1.29 parent1[0]: (222) {G4,W3,D2,L1,V0,M1} R(217,35) { open_subset( skol10,
% 0.72/1.29 skol8 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (892) {G5,W6,D4,L1,V0,M1} S(281);r(222) { closed_subset(
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ), skol8 ) }.
% 0.72/1.29 parent0: (3747) {G2,W6,D4,L1,V0,M1} { closed_subset( subset_complement(
% 0.72/1.29 the_carrier( skol8 ), skol10 ), skol8 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 eqswap: (3748) {G1,W13,D4,L3,V1,M3} { X ==> topstr_closure( skol8, X ), !
% 0.72/1.29 element( X, powerset( the_carrier( skol8 ) ) ), ! closed_subset( X, skol8
% 0.72/1.29 ) }.
% 0.72/1.29 parent0[2]: (366) {G1,W13,D4,L3,V1,M3} R(26,30) { ! element( X, powerset(
% 0.72/1.29 the_carrier( skol8 ) ) ), ! closed_subset( X, skol8 ), topstr_closure(
% 0.72/1.29 skol8, X ) ==> X }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := X
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3750) {G2,W19,D5,L2,V0,M2} { subset_complement( the_carrier(
% 0.72/1.29 skol8 ), skol10 ) ==> topstr_closure( skol8, subset_complement(
% 0.72/1.29 the_carrier( skol8 ), skol10 ) ), ! element( subset_complement(
% 0.72/1.29 the_carrier( skol8 ), skol10 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 parent0[2]: (3748) {G1,W13,D4,L3,V1,M3} { X ==> topstr_closure( skol8, X )
% 0.72/1.29 , ! element( X, powerset( the_carrier( skol8 ) ) ), ! closed_subset( X,
% 0.72/1.29 skol8 ) }.
% 0.72/1.29 parent1[0]: (892) {G5,W6,D4,L1,V0,M1} S(281);r(222) { closed_subset(
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ), skol8 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 X := subset_complement( the_carrier( skol8 ), skol10 )
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 paramod: (3751) {G3,W19,D4,L2,V0,M2} { subset_complement( the_carrier(
% 0.72/1.29 skol8 ), skol10 ) ==> subset_complement( the_carrier( skol8 ), interior(
% 0.72/1.29 skol8, skol10 ) ), ! element( subset_complement( the_carrier( skol8 ),
% 0.72/1.29 skol10 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 parent0[0]: (632) {G3,W13,D5,L1,V0,M1} P(53,13);r(424) { topstr_closure(
% 0.72/1.29 skol8, subset_complement( the_carrier( skol8 ), skol10 ) ) ==>
% 0.72/1.29 subset_complement( the_carrier( skol8 ), interior( skol8, skol10 ) ) }.
% 0.72/1.29 parent1[0; 5]: (3750) {G2,W19,D5,L2,V0,M2} { subset_complement(
% 0.72/1.29 the_carrier( skol8 ), skol10 ) ==> topstr_closure( skol8,
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ) ), ! element(
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ), powerset( the_carrier
% 0.72/1.29 ( skol8 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3752) {G2,W11,D4,L1,V0,M1} { subset_complement( the_carrier(
% 0.72/1.29 skol8 ), skol10 ) ==> subset_complement( the_carrier( skol8 ), interior(
% 0.72/1.29 skol8, skol10 ) ) }.
% 0.72/1.29 parent0[1]: (3751) {G3,W19,D4,L2,V0,M2} { subset_complement( the_carrier(
% 0.72/1.29 skol8 ), skol10 ) ==> subset_complement( the_carrier( skol8 ), interior(
% 0.72/1.29 skol8, skol10 ) ), ! element( subset_complement( the_carrier( skol8 ),
% 0.72/1.29 skol10 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 parent1[0]: (54) {G1,W8,D4,L1,V0,M1} R(3,32) { element( subset_complement(
% 0.72/1.29 the_carrier( skol8 ), skol10 ), powerset( the_carrier( skol8 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 eqswap: (3753) {G2,W11,D4,L1,V0,M1} { subset_complement( the_carrier(
% 0.72/1.29 skol8 ), interior( skol8, skol10 ) ) ==> subset_complement( the_carrier(
% 0.72/1.29 skol8 ), skol10 ) }.
% 0.72/1.29 parent0[0]: (3752) {G2,W11,D4,L1,V0,M1} { subset_complement( the_carrier(
% 0.72/1.29 skol8 ), skol10 ) ==> subset_complement( the_carrier( skol8 ), interior(
% 0.72/1.29 skol8, skol10 ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (3611) {G6,W11,D4,L1,V0,M1} R(366,892);d(632);r(54) {
% 0.72/1.29 subset_complement( the_carrier( skol8 ), interior( skol8, skol10 ) ) ==>
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ) }.
% 0.72/1.29 parent0: (3753) {G2,W11,D4,L1,V0,M1} { subset_complement( the_carrier(
% 0.72/1.29 skol8 ), interior( skol8, skol10 ) ) ==> subset_complement( the_carrier(
% 0.72/1.29 skol8 ), skol10 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 eqswap: (3755) {G2,W13,D5,L1,V0,M1} { interior( skol8, skol10 ) ==>
% 0.72/1.29 subset_complement( the_carrier( skol8 ), subset_complement( the_carrier(
% 0.72/1.29 skol8 ), interior( skol8, skol10 ) ) ) }.
% 0.72/1.29 parent0[0]: (160) {G2,W13,D5,L1,V0,M1} R(52,13) { subset_complement(
% 0.72/1.29 the_carrier( skol8 ), subset_complement( the_carrier( skol8 ), interior(
% 0.72/1.29 skol8, skol10 ) ) ) ==> interior( skol8, skol10 ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 paramod: (3757) {G3,W11,D5,L1,V0,M1} { interior( skol8, skol10 ) ==>
% 0.72/1.29 subset_complement( the_carrier( skol8 ), subset_complement( the_carrier(
% 0.72/1.29 skol8 ), skol10 ) ) }.
% 0.72/1.29 parent0[0]: (3611) {G6,W11,D4,L1,V0,M1} R(366,892);d(632);r(54) {
% 0.72/1.29 subset_complement( the_carrier( skol8 ), interior( skol8, skol10 ) ) ==>
% 0.72/1.29 subset_complement( the_carrier( skol8 ), skol10 ) }.
% 0.72/1.29 parent1[0; 7]: (3755) {G2,W13,D5,L1,V0,M1} { interior( skol8, skol10 ) ==>
% 0.72/1.29 subset_complement( the_carrier( skol8 ), subset_complement( the_carrier
% 0.72/1.29 ( skol8 ), interior( skol8, skol10 ) ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 paramod: (3758) {G2,W5,D3,L1,V0,M1} { interior( skol8, skol10 ) ==> skol10
% 0.72/1.29 }.
% 0.72/1.29 parent0[0]: (148) {G1,W9,D5,L1,V0,M1} R(13,32) { subset_complement(
% 0.72/1.29 the_carrier( skol8 ), subset_complement( the_carrier( skol8 ), skol10 ) )
% 0.72/1.29 ==> skol10 }.
% 0.72/1.29 parent1[0; 4]: (3757) {G3,W11,D5,L1,V0,M1} { interior( skol8, skol10 ) ==>
% 0.72/1.29 subset_complement( the_carrier( skol8 ), subset_complement( the_carrier
% 0.72/1.29 ( skol8 ), skol10 ) ) }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (3614) {G7,W5,D3,L1,V0,M1} P(3611,160);d(148) { interior(
% 0.72/1.29 skol8, skol10 ) ==> skol10 }.
% 0.72/1.29 parent0: (3758) {G2,W5,D3,L1,V0,M1} { interior( skol8, skol10 ) ==> skol10
% 0.72/1.29 }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 0 ==> 0
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 resolution: (3762) {G5,W0,D0,L0,V0,M0} { }.
% 0.72/1.29 parent0[0]: (221) {G4,W5,D3,L1,V0,M1} R(217,36) { ! interior( skol8, skol10
% 0.72/1.29 ) ==> skol10 }.
% 0.72/1.29 parent1[0]: (3614) {G7,W5,D3,L1,V0,M1} P(3611,160);d(148) { interior( skol8
% 0.72/1.29 , skol10 ) ==> skol10 }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 substitution1:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 subsumption: (3615) {G8,W0,D0,L0,V0,M0} S(3614);r(221) { }.
% 0.72/1.29 parent0: (3762) {G5,W0,D0,L0,V0,M0} { }.
% 0.72/1.29 substitution0:
% 0.72/1.29 end
% 0.72/1.29 permutation0:
% 0.72/1.29 end
% 0.72/1.29
% 0.72/1.29 Proof check complete!
% 0.72/1.29
% 0.72/1.29 Memory use:
% 0.72/1.29
% 0.72/1.29 space for terms: 49354
% 0.72/1.29 space for clauses: 257523
% 0.72/1.29
% 0.72/1.29
% 0.72/1.29 clauses generated: 23272
% 0.72/1.29 clauses kept: 3616
% 0.72/1.29 clauses selected: 848
% 0.72/1.29 clauses deleted: 234
% 0.72/1.29 clauses inuse deleted: 68
% 0.72/1.29
% 0.72/1.29 subsentry: 10091
% 0.72/1.29 literals s-matched: 9739
% 0.72/1.29 literals matched: 9739
% 0.72/1.29 full subsumption: 1
% 0.72/1.29
% 0.72/1.29 checksum: -2144965910
% 0.72/1.29
% 0.72/1.29
% 0.72/1.29 Bliksem ended
%------------------------------------------------------------------------------