TSTP Solution File: REL031+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : REL031+1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Mon Jul 18 19:00:51 EDT 2022
% Result : Theorem 1.31s 1.69s
% Output : Refutation 1.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : REL031+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % 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 : Fri Jul 8 11:44:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.31/1.69 *** allocated 10000 integers for termspace/termends
% 1.31/1.69 *** allocated 10000 integers for clauses
% 1.31/1.69 *** allocated 10000 integers for justifications
% 1.31/1.69 Bliksem 1.12
% 1.31/1.69
% 1.31/1.69
% 1.31/1.69 Automatic Strategy Selection
% 1.31/1.69
% 1.31/1.69
% 1.31/1.69 Clauses:
% 1.31/1.69
% 1.31/1.69 { join( X, Y ) = join( Y, X ) }.
% 1.31/1.69 { join( X, join( Y, Z ) ) = join( join( X, Y ), Z ) }.
% 1.31/1.69 { X = join( complement( join( complement( X ), complement( Y ) ) ),
% 1.31/1.69 complement( join( complement( X ), Y ) ) ) }.
% 1.31/1.69 { meet( X, Y ) = complement( join( complement( X ), complement( Y ) ) ) }.
% 1.31/1.69 { composition( X, composition( Y, Z ) ) = composition( composition( X, Y )
% 1.31/1.69 , Z ) }.
% 1.31/1.69 { composition( X, one ) = X }.
% 1.31/1.69 { composition( join( X, Y ), Z ) = join( composition( X, Z ), composition(
% 1.31/1.69 Y, Z ) ) }.
% 1.31/1.69 { converse( converse( X ) ) = X }.
% 1.31/1.69 { converse( join( X, Y ) ) = join( converse( X ), converse( Y ) ) }.
% 1.31/1.69 { converse( composition( X, Y ) ) = composition( converse( Y ), converse( X
% 1.31/1.69 ) ) }.
% 1.31/1.69 { join( composition( converse( X ), complement( composition( X, Y ) ) ),
% 1.31/1.69 complement( Y ) ) = complement( Y ) }.
% 1.31/1.69 { top = join( X, complement( X ) ) }.
% 1.31/1.69 { zero = meet( X, complement( X ) ) }.
% 1.31/1.69 { join( composition( converse( skol1 ), skol1 ), one ) = one }.
% 1.31/1.69 { join( composition( converse( skol2 ), skol2 ), one ) = one }.
% 1.31/1.69 { ! join( composition( converse( composition( skol1, skol2 ) ), composition
% 1.31/1.69 ( skol1, skol2 ) ), one ) = one }.
% 1.31/1.69
% 1.31/1.69 percentage equality = 1.000000, percentage horn = 1.000000
% 1.31/1.69 This is a pure equality problem
% 1.31/1.69
% 1.31/1.69
% 1.31/1.69
% 1.31/1.69 Options Used:
% 1.31/1.69
% 1.31/1.69 useres = 1
% 1.31/1.69 useparamod = 1
% 1.31/1.69 useeqrefl = 1
% 1.31/1.69 useeqfact = 1
% 1.31/1.69 usefactor = 1
% 1.31/1.69 usesimpsplitting = 0
% 1.31/1.69 usesimpdemod = 5
% 1.31/1.69 usesimpres = 3
% 1.31/1.69
% 1.31/1.69 resimpinuse = 1000
% 1.31/1.69 resimpclauses = 20000
% 1.31/1.69 substype = eqrewr
% 1.31/1.69 backwardsubs = 1
% 1.31/1.69 selectoldest = 5
% 1.31/1.69
% 1.31/1.69 litorderings [0] = split
% 1.31/1.69 litorderings [1] = extend the termordering, first sorting on arguments
% 1.31/1.69
% 1.31/1.69 termordering = kbo
% 1.31/1.69
% 1.31/1.69 litapriori = 0
% 1.31/1.69 termapriori = 1
% 1.31/1.69 litaposteriori = 0
% 1.31/1.69 termaposteriori = 0
% 1.31/1.69 demodaposteriori = 0
% 1.31/1.69 ordereqreflfact = 0
% 1.31/1.69
% 1.31/1.69 litselect = negord
% 1.31/1.69
% 1.31/1.69 maxweight = 15
% 1.31/1.69 maxdepth = 30000
% 1.31/1.69 maxlength = 115
% 1.31/1.69 maxnrvars = 195
% 1.31/1.69 excuselevel = 1
% 1.31/1.69 increasemaxweight = 1
% 1.31/1.69
% 1.31/1.69 maxselected = 10000000
% 1.31/1.69 maxnrclauses = 10000000
% 1.31/1.69
% 1.31/1.69 showgenerated = 0
% 1.31/1.69 showkept = 0
% 1.31/1.69 showselected = 0
% 1.31/1.69 showdeleted = 0
% 1.31/1.69 showresimp = 1
% 1.31/1.69 showstatus = 2000
% 1.31/1.69
% 1.31/1.69 prologoutput = 0
% 1.31/1.69 nrgoals = 5000000
% 1.31/1.69 totalproof = 1
% 1.31/1.69
% 1.31/1.69 Symbols occurring in the translation:
% 1.31/1.69
% 1.31/1.69 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.31/1.69 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 1.31/1.69 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 1.31/1.69 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.31/1.69 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.31/1.69 join [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 1.31/1.69 complement [39, 1] (w:1, o:19, a:1, s:1, b:0),
% 1.31/1.69 meet [40, 2] (w:1, o:46, a:1, s:1, b:0),
% 1.31/1.69 composition [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 1.31/1.69 one [42, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.31/1.69 converse [43, 1] (w:1, o:20, a:1, s:1, b:0),
% 1.31/1.69 top [44, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.31/1.69 zero [45, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.31/1.69 skol1 [46, 0] (w:1, o:10, a:1, s:1, b:1),
% 1.31/1.69 skol2 [47, 0] (w:1, o:11, a:1, s:1, b:1).
% 1.31/1.69
% 1.31/1.69
% 1.31/1.69 Starting Search:
% 1.31/1.69
% 1.31/1.69 *** allocated 15000 integers for clauses
% 1.31/1.69 *** allocated 22500 integers for clauses
% 1.31/1.69 *** allocated 33750 integers for clauses
% 1.31/1.69 *** allocated 50625 integers for clauses
% 1.31/1.69 *** allocated 75937 integers for clauses
% 1.31/1.69 *** allocated 113905 integers for clauses
% 1.31/1.69 *** allocated 15000 integers for termspace/termends
% 1.31/1.69 Resimplifying inuse:
% 1.31/1.69 Done
% 1.31/1.69
% 1.31/1.69 *** allocated 170857 integers for clauses
% 1.31/1.69 *** allocated 22500 integers for termspace/termends
% 1.31/1.69 *** allocated 256285 integers for clauses
% 1.31/1.69 *** allocated 33750 integers for termspace/termends
% 1.31/1.69
% 1.31/1.69 Intermediate Status:
% 1.31/1.69 Generated: 32814
% 1.31/1.69 Kept: 2026
% 1.31/1.69 Inuse: 315
% 1.31/1.69 Deleted: 199
% 1.31/1.69 Deletedinuse: 69
% 1.31/1.69
% 1.31/1.69 Resimplifying inuse:
% 1.31/1.69 Done
% 1.31/1.69
% 1.31/1.69 *** allocated 384427 integers for clauses
% 1.31/1.69 *** allocated 50625 integers for termspace/termends
% 1.31/1.69 Resimplifying inuse:
% 1.31/1.69 Done
% 1.31/1.69
% 1.31/1.69 *** allocated 576640 integers for clauses
% 1.31/1.69 *** allocated 75937 integers for termspace/termends
% 1.31/1.69
% 1.31/1.69 Intermediate Status:
% 1.31/1.69 Generated: 78490
% 1.31/1.69 Kept: 4127
% 1.31/1.69 Inuse: 451
% 1.31/1.69 Deleted: 317
% 1.31/1.69 Deletedinuse: 88
% 1.31/1.69
% 1.31/1.69 Resimplifying inuse:
% 1.31/1.69 Done
% 1.31/1.69
% 1.31/1.69 Resimplifying inuse:
% 1.31/1.69 Done
% 1.31/1.69
% 1.31/1.69 *** allocated 864960 integers for clauses
% 1.31/1.69 *** allocated 113905 integers for termspace/termends
% 1.31/1.69
% 1.31/1.69 Intermediate Status:
% 1.31/1.69 Generated: 121373
% 1.31/1.69 Kept: 6138
% 1.31/1.69 Inuse: 590
% 1.31/1.69 Deleted: 351
% 1.31/1.69 Deletedinuse: 89
% 1.31/1.69
% 1.31/1.69 Resimplifying inuse:
% 1.31/1.69 Done
% 1.31/1.69
% 1.31/1.69 Resimplifying inuse:
% 1.31/1.69 Done
% 1.31/1.69
% 1.31/1.69 *** allocated 1297440 integers for clauses
% 1.31/1.69
% 1.31/1.69 Intermediate Status:
% 1.31/1.69 Generated: 170732
% 1.31/1.69 Kept: 8162
% 1.31/1.69 Inuse: 732
% 1.31/1.69 Deleted: 387
% 1.31/1.69 Deletedinuse: 89
% 1.31/1.69
% 1.31/1.69 Resimplifying inuse:
% 1.31/1.69
% 1.31/1.69 Bliksems!, er is een bewijs:
% 1.31/1.69 % SZS status Theorem
% 1.31/1.69 % SZS output start Refutation
% 1.31/1.69
% 1.31/1.69 (1) {G0,W11,D4,L1,V3,M1} I { join( X, join( Y, Z ) ) ==> join( join( X, Y )
% 1.31/1.69 , Z ) }.
% 1.31/1.69 (4) {G0,W11,D4,L1,V3,M1} I { composition( X, composition( Y, Z ) ) ==>
% 1.31/1.69 composition( composition( X, Y ), Z ) }.
% 1.31/1.69 (5) {G0,W5,D3,L1,V1,M1} I { composition( X, one ) ==> X }.
% 1.31/1.69 (6) {G0,W13,D4,L1,V3,M1} I { join( composition( X, Z ), composition( Y, Z )
% 1.31/1.69 ) ==> composition( join( X, Y ), Z ) }.
% 1.31/1.69 (7) {G0,W5,D4,L1,V1,M1} I { converse( converse( X ) ) ==> X }.
% 1.31/1.69 (8) {G0,W10,D4,L1,V2,M1} I { join( converse( X ), converse( Y ) ) ==>
% 1.31/1.69 converse( join( X, Y ) ) }.
% 1.31/1.69 (9) {G0,W10,D4,L1,V2,M1} I { composition( converse( Y ), converse( X ) )
% 1.31/1.69 ==> converse( composition( X, Y ) ) }.
% 1.31/1.69 (13) {G0,W8,D5,L1,V0,M1} I { join( composition( converse( skol1 ), skol1 )
% 1.31/1.69 , one ) ==> one }.
% 1.31/1.69 (14) {G0,W8,D5,L1,V0,M1} I { join( composition( converse( skol2 ), skol2 )
% 1.31/1.69 , one ) ==> one }.
% 1.31/1.69 (15) {G1,W12,D7,L1,V0,M1} I;d(4) { ! join( composition( composition(
% 1.31/1.69 converse( composition( skol1, skol2 ) ), skol1 ), skol2 ), one ) ==> one
% 1.31/1.69 }.
% 1.31/1.69 (22) {G1,W12,D6,L1,V1,M1} P(14,1) { join( join( X, composition( converse(
% 1.31/1.69 skol2 ), skol2 ) ), one ) ==> join( X, one ) }.
% 1.31/1.69 (73) {G1,W10,D5,L1,V2,M1} P(7,8) { converse( join( Y, converse( X ) ) ) ==>
% 1.31/1.69 join( converse( Y ), X ) }.
% 1.31/1.69 (89) {G1,W10,D5,L1,V2,M1} P(7,9) { converse( composition( Y, converse( X )
% 1.31/1.69 ) ) ==> composition( X, converse( Y ) ) }.
% 1.31/1.69 (90) {G1,W10,D5,L1,V2,M1} P(7,9) { converse( composition( converse( X ), Y
% 1.31/1.69 ) ) ==> composition( converse( Y ), X ) }.
% 1.31/1.69 (227) {G2,W6,D4,L1,V1,M1} P(5,90);d(7) { composition( converse( one ), X )
% 1.31/1.69 ==> X }.
% 1.31/1.69 (233) {G3,W4,D3,L1,V0,M1} P(227,5) { converse( one ) ==> one }.
% 1.31/1.69 (234) {G4,W5,D3,L1,V1,M1} P(233,227) { composition( one, X ) ==> X }.
% 1.31/1.69 (243) {G5,W11,D4,L1,V2,M1} P(234,6) { join( composition( Y, X ), X ) =
% 1.31/1.69 composition( join( Y, one ), X ) }.
% 1.31/1.69 (262) {G2,W14,D6,L1,V1,M1} P(6,22) { join( composition( join( X, converse(
% 1.31/1.69 skol2 ) ), skol2 ), one ) ==> join( composition( X, skol2 ), one ) }.
% 1.31/1.69 (6601) {G6,W10,D6,L1,V1,M1} P(13,243);d(234) { join( composition(
% 1.31/1.69 composition( converse( skol1 ), skol1 ), X ), X ) ==> X }.
% 1.31/1.69 (7863) {G7,W10,D6,L1,V1,M1} P(6601,73);d(7);d(89);d(90);d(4) { join(
% 1.31/1.69 composition( composition( X, converse( skol1 ) ), skol1 ), X ) ==> X }.
% 1.31/1.69 (7872) {G8,W12,D7,L1,V0,M1} P(7863,262);d(14);d(9) { join( composition(
% 1.31/1.69 composition( converse( composition( skol1, skol2 ) ), skol1 ), skol2 ),
% 1.31/1.69 one ) ==> one }.
% 1.31/1.69 (8195) {G9,W0,D0,L0,V0,M0} S(15);d(7872);q { }.
% 1.31/1.69
% 1.31/1.69
% 1.31/1.69 % SZS output end Refutation
% 1.31/1.69 found a proof!
% 1.31/1.69
% 1.31/1.69
% 1.31/1.69 Unprocessed initial clauses:
% 1.31/1.69
% 1.31/1.69 (8197) {G0,W7,D3,L1,V2,M1} { join( X, Y ) = join( Y, X ) }.
% 1.31/1.69 (8198) {G0,W11,D4,L1,V3,M1} { join( X, join( Y, Z ) ) = join( join( X, Y )
% 1.31/1.69 , Z ) }.
% 1.31/1.69 (8199) {G0,W14,D6,L1,V2,M1} { X = join( complement( join( complement( X )
% 1.31/1.69 , complement( Y ) ) ), complement( join( complement( X ), Y ) ) ) }.
% 1.31/1.69 (8200) {G0,W10,D5,L1,V2,M1} { meet( X, Y ) = complement( join( complement
% 1.31/1.69 ( X ), complement( Y ) ) ) }.
% 1.31/1.69 (8201) {G0,W11,D4,L1,V3,M1} { composition( X, composition( Y, Z ) ) =
% 1.31/1.69 composition( composition( X, Y ), Z ) }.
% 1.31/1.69 (8202) {G0,W5,D3,L1,V1,M1} { composition( X, one ) = X }.
% 1.31/1.69 (8203) {G0,W13,D4,L1,V3,M1} { composition( join( X, Y ), Z ) = join(
% 1.31/1.69 composition( X, Z ), composition( Y, Z ) ) }.
% 1.31/1.69 (8204) {G0,W5,D4,L1,V1,M1} { converse( converse( X ) ) = X }.
% 1.31/1.69 (8205) {G0,W10,D4,L1,V2,M1} { converse( join( X, Y ) ) = join( converse( X
% 1.31/1.69 ), converse( Y ) ) }.
% 1.31/1.69 (8206) {G0,W10,D4,L1,V2,M1} { converse( composition( X, Y ) ) =
% 1.31/1.69 composition( converse( Y ), converse( X ) ) }.
% 1.31/1.69 (8207) {G0,W13,D6,L1,V2,M1} { join( composition( converse( X ), complement
% 1.31/1.69 ( composition( X, Y ) ) ), complement( Y ) ) = complement( Y ) }.
% 1.31/1.69 (8208) {G0,W6,D4,L1,V1,M1} { top = join( X, complement( X ) ) }.
% 1.31/1.69 (8209) {G0,W6,D4,L1,V1,M1} { zero = meet( X, complement( X ) ) }.
% 1.31/1.69 (8210) {G0,W8,D5,L1,V0,M1} { join( composition( converse( skol1 ), skol1 )
% 1.31/1.69 , one ) = one }.
% 1.31/1.69 (8211) {G0,W8,D5,L1,V0,M1} { join( composition( converse( skol2 ), skol2 )
% 1.31/1.69 , one ) = one }.
% 1.31/1.69 (8212) {G0,W12,D6,L1,V0,M1} { ! join( composition( converse( composition(
% 1.31/1.69 skol1, skol2 ) ), composition( skol1, skol2 ) ), one ) = one }.
% 1.31/1.69
% 1.31/1.69
% 1.31/1.69 Total Proof:
% 1.31/1.69
% 1.31/1.69 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { join( X, join( Y, Z ) ) ==> join
% 1.31/1.69 ( join( X, Y ), Z ) }.
% 1.31/1.69 parent0: (8198) {G0,W11,D4,L1,V3,M1} { join( X, join( Y, Z ) ) = join(
% 1.31/1.69 join( X, Y ), Z ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 Y := Y
% 1.31/1.69 Z := Z
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (4) {G0,W11,D4,L1,V3,M1} I { composition( X, composition( Y, Z
% 1.31/1.69 ) ) ==> composition( composition( X, Y ), Z ) }.
% 1.31/1.69 parent0: (8201) {G0,W11,D4,L1,V3,M1} { composition( X, composition( Y, Z )
% 1.31/1.69 ) = composition( composition( X, Y ), Z ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 Y := Y
% 1.31/1.69 Z := Z
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { composition( X, one ) ==> X }.
% 1.31/1.69 parent0: (8202) {G0,W5,D3,L1,V1,M1} { composition( X, one ) = X }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8228) {G0,W13,D4,L1,V3,M1} { join( composition( X, Z ),
% 1.31/1.69 composition( Y, Z ) ) = composition( join( X, Y ), Z ) }.
% 1.31/1.69 parent0[0]: (8203) {G0,W13,D4,L1,V3,M1} { composition( join( X, Y ), Z ) =
% 1.31/1.69 join( composition( X, Z ), composition( Y, Z ) ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 Y := Y
% 1.31/1.69 Z := Z
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (6) {G0,W13,D4,L1,V3,M1} I { join( composition( X, Z ),
% 1.31/1.69 composition( Y, Z ) ) ==> composition( join( X, Y ), Z ) }.
% 1.31/1.69 parent0: (8228) {G0,W13,D4,L1,V3,M1} { join( composition( X, Z ),
% 1.31/1.69 composition( Y, Z ) ) = composition( join( X, Y ), Z ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 Y := Y
% 1.31/1.69 Z := Z
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (7) {G0,W5,D4,L1,V1,M1} I { converse( converse( X ) ) ==> X
% 1.31/1.69 }.
% 1.31/1.69 parent0: (8204) {G0,W5,D4,L1,V1,M1} { converse( converse( X ) ) = X }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8243) {G0,W10,D4,L1,V2,M1} { join( converse( X ), converse( Y ) )
% 1.31/1.69 = converse( join( X, Y ) ) }.
% 1.31/1.69 parent0[0]: (8205) {G0,W10,D4,L1,V2,M1} { converse( join( X, Y ) ) = join
% 1.31/1.69 ( converse( X ), converse( Y ) ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 Y := Y
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (8) {G0,W10,D4,L1,V2,M1} I { join( converse( X ), converse( Y
% 1.31/1.69 ) ) ==> converse( join( X, Y ) ) }.
% 1.31/1.69 parent0: (8243) {G0,W10,D4,L1,V2,M1} { join( converse( X ), converse( Y )
% 1.31/1.69 ) = converse( join( X, Y ) ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 Y := Y
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8252) {G0,W10,D4,L1,V2,M1} { composition( converse( Y ), converse
% 1.31/1.69 ( X ) ) = converse( composition( X, Y ) ) }.
% 1.31/1.69 parent0[0]: (8206) {G0,W10,D4,L1,V2,M1} { converse( composition( X, Y ) )
% 1.31/1.69 = composition( converse( Y ), converse( X ) ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 Y := Y
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (9) {G0,W10,D4,L1,V2,M1} I { composition( converse( Y ),
% 1.31/1.69 converse( X ) ) ==> converse( composition( X, Y ) ) }.
% 1.31/1.69 parent0: (8252) {G0,W10,D4,L1,V2,M1} { composition( converse( Y ),
% 1.31/1.69 converse( X ) ) = converse( composition( X, Y ) ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 Y := Y
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (13) {G0,W8,D5,L1,V0,M1} I { join( composition( converse(
% 1.31/1.69 skol1 ), skol1 ), one ) ==> one }.
% 1.31/1.69 parent0: (8210) {G0,W8,D5,L1,V0,M1} { join( composition( converse( skol1 )
% 1.31/1.69 , skol1 ), one ) = one }.
% 1.31/1.69 substitution0:
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (14) {G0,W8,D5,L1,V0,M1} I { join( composition( converse(
% 1.31/1.69 skol2 ), skol2 ), one ) ==> one }.
% 1.31/1.69 parent0: (8211) {G0,W8,D5,L1,V0,M1} { join( composition( converse( skol2 )
% 1.31/1.69 , skol2 ), one ) = one }.
% 1.31/1.69 substitution0:
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 paramod: (8313) {G1,W12,D7,L1,V0,M1} { ! join( composition( composition(
% 1.31/1.69 converse( composition( skol1, skol2 ) ), skol1 ), skol2 ), one ) = one
% 1.31/1.69 }.
% 1.31/1.69 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { composition( X, composition( Y, Z
% 1.31/1.69 ) ) ==> composition( composition( X, Y ), Z ) }.
% 1.31/1.69 parent1[0; 3]: (8212) {G0,W12,D6,L1,V0,M1} { ! join( composition( converse
% 1.31/1.69 ( composition( skol1, skol2 ) ), composition( skol1, skol2 ) ), one ) =
% 1.31/1.69 one }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := converse( composition( skol1, skol2 ) )
% 1.31/1.69 Y := skol1
% 1.31/1.69 Z := skol2
% 1.31/1.69 end
% 1.31/1.69 substitution1:
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (15) {G1,W12,D7,L1,V0,M1} I;d(4) { ! join( composition(
% 1.31/1.69 composition( converse( composition( skol1, skol2 ) ), skol1 ), skol2 ),
% 1.31/1.69 one ) ==> one }.
% 1.31/1.69 parent0: (8313) {G1,W12,D7,L1,V0,M1} { ! join( composition( composition(
% 1.31/1.69 converse( composition( skol1, skol2 ) ), skol1 ), skol2 ), one ) = one
% 1.31/1.69 }.
% 1.31/1.69 substitution0:
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8316) {G0,W11,D4,L1,V3,M1} { join( join( X, Y ), Z ) ==> join( X
% 1.31/1.69 , join( Y, Z ) ) }.
% 1.31/1.69 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { join( X, join( Y, Z ) ) ==> join(
% 1.31/1.69 join( X, Y ), Z ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 Y := Y
% 1.31/1.69 Z := Z
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 paramod: (8318) {G1,W12,D6,L1,V1,M1} { join( join( X, composition(
% 1.31/1.69 converse( skol2 ), skol2 ) ), one ) ==> join( X, one ) }.
% 1.31/1.69 parent0[0]: (14) {G0,W8,D5,L1,V0,M1} I { join( composition( converse( skol2
% 1.31/1.69 ), skol2 ), one ) ==> one }.
% 1.31/1.69 parent1[0; 11]: (8316) {G0,W11,D4,L1,V3,M1} { join( join( X, Y ), Z ) ==>
% 1.31/1.69 join( X, join( Y, Z ) ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 end
% 1.31/1.69 substitution1:
% 1.31/1.69 X := X
% 1.31/1.69 Y := composition( converse( skol2 ), skol2 )
% 1.31/1.69 Z := one
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (22) {G1,W12,D6,L1,V1,M1} P(14,1) { join( join( X, composition
% 1.31/1.69 ( converse( skol2 ), skol2 ) ), one ) ==> join( X, one ) }.
% 1.31/1.69 parent0: (8318) {G1,W12,D6,L1,V1,M1} { join( join( X, composition(
% 1.31/1.69 converse( skol2 ), skol2 ) ), one ) ==> join( X, one ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8322) {G0,W10,D4,L1,V2,M1} { converse( join( X, Y ) ) ==> join(
% 1.31/1.69 converse( X ), converse( Y ) ) }.
% 1.31/1.69 parent0[0]: (8) {G0,W10,D4,L1,V2,M1} I { join( converse( X ), converse( Y )
% 1.31/1.69 ) ==> converse( join( X, Y ) ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 Y := Y
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 paramod: (8324) {G1,W10,D5,L1,V2,M1} { converse( join( X, converse( Y ) )
% 1.31/1.69 ) ==> join( converse( X ), Y ) }.
% 1.31/1.69 parent0[0]: (7) {G0,W5,D4,L1,V1,M1} I { converse( converse( X ) ) ==> X }.
% 1.31/1.69 parent1[0; 9]: (8322) {G0,W10,D4,L1,V2,M1} { converse( join( X, Y ) ) ==>
% 1.31/1.69 join( converse( X ), converse( Y ) ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := Y
% 1.31/1.69 end
% 1.31/1.69 substitution1:
% 1.31/1.69 X := X
% 1.31/1.69 Y := converse( Y )
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (73) {G1,W10,D5,L1,V2,M1} P(7,8) { converse( join( Y, converse
% 1.31/1.69 ( X ) ) ) ==> join( converse( Y ), X ) }.
% 1.31/1.69 parent0: (8324) {G1,W10,D5,L1,V2,M1} { converse( join( X, converse( Y ) )
% 1.31/1.69 ) ==> join( converse( X ), Y ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := Y
% 1.31/1.69 Y := X
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8328) {G0,W10,D4,L1,V2,M1} { converse( composition( Y, X ) ) ==>
% 1.31/1.69 composition( converse( X ), converse( Y ) ) }.
% 1.31/1.69 parent0[0]: (9) {G0,W10,D4,L1,V2,M1} I { composition( converse( Y ),
% 1.31/1.69 converse( X ) ) ==> converse( composition( X, Y ) ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := Y
% 1.31/1.69 Y := X
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 paramod: (8329) {G1,W10,D5,L1,V2,M1} { converse( composition( X, converse
% 1.31/1.69 ( Y ) ) ) ==> composition( Y, converse( X ) ) }.
% 1.31/1.69 parent0[0]: (7) {G0,W5,D4,L1,V1,M1} I { converse( converse( X ) ) ==> X }.
% 1.31/1.69 parent1[0; 7]: (8328) {G0,W10,D4,L1,V2,M1} { converse( composition( Y, X )
% 1.31/1.69 ) ==> composition( converse( X ), converse( Y ) ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := Y
% 1.31/1.69 end
% 1.31/1.69 substitution1:
% 1.31/1.69 X := converse( Y )
% 1.31/1.69 Y := X
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (89) {G1,W10,D5,L1,V2,M1} P(7,9) { converse( composition( Y,
% 1.31/1.69 converse( X ) ) ) ==> composition( X, converse( Y ) ) }.
% 1.31/1.69 parent0: (8329) {G1,W10,D5,L1,V2,M1} { converse( composition( X, converse
% 1.31/1.69 ( Y ) ) ) ==> composition( Y, converse( X ) ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := Y
% 1.31/1.69 Y := X
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8334) {G0,W10,D4,L1,V2,M1} { converse( composition( Y, X ) ) ==>
% 1.31/1.69 composition( converse( X ), converse( Y ) ) }.
% 1.31/1.69 parent0[0]: (9) {G0,W10,D4,L1,V2,M1} I { composition( converse( Y ),
% 1.31/1.69 converse( X ) ) ==> converse( composition( X, Y ) ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := Y
% 1.31/1.69 Y := X
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 paramod: (8336) {G1,W10,D5,L1,V2,M1} { converse( composition( converse( X
% 1.31/1.69 ), Y ) ) ==> composition( converse( Y ), X ) }.
% 1.31/1.69 parent0[0]: (7) {G0,W5,D4,L1,V1,M1} I { converse( converse( X ) ) ==> X }.
% 1.31/1.69 parent1[0; 9]: (8334) {G0,W10,D4,L1,V2,M1} { converse( composition( Y, X )
% 1.31/1.69 ) ==> composition( converse( X ), converse( Y ) ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 end
% 1.31/1.69 substitution1:
% 1.31/1.69 X := Y
% 1.31/1.69 Y := converse( X )
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (90) {G1,W10,D5,L1,V2,M1} P(7,9) { converse( composition(
% 1.31/1.69 converse( X ), Y ) ) ==> composition( converse( Y ), X ) }.
% 1.31/1.69 parent0: (8336) {G1,W10,D5,L1,V2,M1} { converse( composition( converse( X
% 1.31/1.69 ), Y ) ) ==> composition( converse( Y ), X ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 Y := Y
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8340) {G1,W10,D5,L1,V2,M1} { composition( converse( Y ), X ) ==>
% 1.31/1.69 converse( composition( converse( X ), Y ) ) }.
% 1.31/1.69 parent0[0]: (90) {G1,W10,D5,L1,V2,M1} P(7,9) { converse( composition(
% 1.31/1.69 converse( X ), Y ) ) ==> composition( converse( Y ), X ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 Y := Y
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 paramod: (8343) {G1,W8,D4,L1,V1,M1} { composition( converse( one ), X )
% 1.31/1.69 ==> converse( converse( X ) ) }.
% 1.31/1.69 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { composition( X, one ) ==> X }.
% 1.31/1.69 parent1[0; 6]: (8340) {G1,W10,D5,L1,V2,M1} { composition( converse( Y ), X
% 1.31/1.69 ) ==> converse( composition( converse( X ), Y ) ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := converse( X )
% 1.31/1.69 end
% 1.31/1.69 substitution1:
% 1.31/1.69 X := X
% 1.31/1.69 Y := one
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 paramod: (8344) {G1,W6,D4,L1,V1,M1} { composition( converse( one ), X )
% 1.31/1.69 ==> X }.
% 1.31/1.69 parent0[0]: (7) {G0,W5,D4,L1,V1,M1} I { converse( converse( X ) ) ==> X }.
% 1.31/1.69 parent1[0; 5]: (8343) {G1,W8,D4,L1,V1,M1} { composition( converse( one ),
% 1.31/1.69 X ) ==> converse( converse( X ) ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 end
% 1.31/1.69 substitution1:
% 1.31/1.69 X := X
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (227) {G2,W6,D4,L1,V1,M1} P(5,90);d(7) { composition( converse
% 1.31/1.69 ( one ), X ) ==> X }.
% 1.31/1.69 parent0: (8344) {G1,W6,D4,L1,V1,M1} { composition( converse( one ), X )
% 1.31/1.69 ==> X }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8346) {G2,W6,D4,L1,V1,M1} { X ==> composition( converse( one ), X
% 1.31/1.69 ) }.
% 1.31/1.69 parent0[0]: (227) {G2,W6,D4,L1,V1,M1} P(5,90);d(7) { composition( converse
% 1.31/1.69 ( one ), X ) ==> X }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 paramod: (8348) {G1,W4,D3,L1,V0,M1} { one ==> converse( one ) }.
% 1.31/1.69 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { composition( X, one ) ==> X }.
% 1.31/1.69 parent1[0; 2]: (8346) {G2,W6,D4,L1,V1,M1} { X ==> composition( converse(
% 1.31/1.69 one ), X ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := converse( one )
% 1.31/1.69 end
% 1.31/1.69 substitution1:
% 1.31/1.69 X := one
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8349) {G1,W4,D3,L1,V0,M1} { converse( one ) ==> one }.
% 1.31/1.69 parent0[0]: (8348) {G1,W4,D3,L1,V0,M1} { one ==> converse( one ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (233) {G3,W4,D3,L1,V0,M1} P(227,5) { converse( one ) ==> one
% 1.31/1.69 }.
% 1.31/1.69 parent0: (8349) {G1,W4,D3,L1,V0,M1} { converse( one ) ==> one }.
% 1.31/1.69 substitution0:
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8351) {G2,W6,D4,L1,V1,M1} { X ==> composition( converse( one ), X
% 1.31/1.69 ) }.
% 1.31/1.69 parent0[0]: (227) {G2,W6,D4,L1,V1,M1} P(5,90);d(7) { composition( converse
% 1.31/1.69 ( one ), X ) ==> X }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 paramod: (8352) {G3,W5,D3,L1,V1,M1} { X ==> composition( one, X ) }.
% 1.31/1.69 parent0[0]: (233) {G3,W4,D3,L1,V0,M1} P(227,5) { converse( one ) ==> one
% 1.31/1.69 }.
% 1.31/1.69 parent1[0; 3]: (8351) {G2,W6,D4,L1,V1,M1} { X ==> composition( converse(
% 1.31/1.69 one ), X ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 end
% 1.31/1.69 substitution1:
% 1.31/1.69 X := X
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8353) {G3,W5,D3,L1,V1,M1} { composition( one, X ) ==> X }.
% 1.31/1.69 parent0[0]: (8352) {G3,W5,D3,L1,V1,M1} { X ==> composition( one, X ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (234) {G4,W5,D3,L1,V1,M1} P(233,227) { composition( one, X )
% 1.31/1.69 ==> X }.
% 1.31/1.69 parent0: (8353) {G3,W5,D3,L1,V1,M1} { composition( one, X ) ==> X }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8355) {G0,W13,D4,L1,V3,M1} { composition( join( X, Z ), Y ) ==>
% 1.31/1.69 join( composition( X, Y ), composition( Z, Y ) ) }.
% 1.31/1.69 parent0[0]: (6) {G0,W13,D4,L1,V3,M1} I { join( composition( X, Z ),
% 1.31/1.69 composition( Y, Z ) ) ==> composition( join( X, Y ), Z ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 Y := Z
% 1.31/1.69 Z := Y
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 paramod: (8357) {G1,W11,D4,L1,V2,M1} { composition( join( X, one ), Y )
% 1.31/1.69 ==> join( composition( X, Y ), Y ) }.
% 1.31/1.69 parent0[0]: (234) {G4,W5,D3,L1,V1,M1} P(233,227) { composition( one, X )
% 1.31/1.69 ==> X }.
% 1.31/1.69 parent1[0; 10]: (8355) {G0,W13,D4,L1,V3,M1} { composition( join( X, Z ), Y
% 1.31/1.69 ) ==> join( composition( X, Y ), composition( Z, Y ) ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := Y
% 1.31/1.69 end
% 1.31/1.69 substitution1:
% 1.31/1.69 X := X
% 1.31/1.69 Y := Y
% 1.31/1.69 Z := one
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8359) {G1,W11,D4,L1,V2,M1} { join( composition( X, Y ), Y ) ==>
% 1.31/1.69 composition( join( X, one ), Y ) }.
% 1.31/1.69 parent0[0]: (8357) {G1,W11,D4,L1,V2,M1} { composition( join( X, one ), Y )
% 1.31/1.69 ==> join( composition( X, Y ), Y ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 Y := Y
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (243) {G5,W11,D4,L1,V2,M1} P(234,6) { join( composition( Y, X
% 1.31/1.69 ), X ) = composition( join( Y, one ), X ) }.
% 1.31/1.69 parent0: (8359) {G1,W11,D4,L1,V2,M1} { join( composition( X, Y ), Y ) ==>
% 1.31/1.69 composition( join( X, one ), Y ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := Y
% 1.31/1.69 Y := X
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8361) {G1,W12,D6,L1,V1,M1} { join( X, one ) ==> join( join( X,
% 1.31/1.69 composition( converse( skol2 ), skol2 ) ), one ) }.
% 1.31/1.69 parent0[0]: (22) {G1,W12,D6,L1,V1,M1} P(14,1) { join( join( X, composition
% 1.31/1.69 ( converse( skol2 ), skol2 ) ), one ) ==> join( X, one ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 paramod: (8364) {G1,W14,D6,L1,V1,M1} { join( composition( X, skol2 ), one
% 1.31/1.69 ) ==> join( composition( join( X, converse( skol2 ) ), skol2 ), one )
% 1.31/1.69 }.
% 1.31/1.69 parent0[0]: (6) {G0,W13,D4,L1,V3,M1} I { join( composition( X, Z ),
% 1.31/1.69 composition( Y, Z ) ) ==> composition( join( X, Y ), Z ) }.
% 1.31/1.69 parent1[0; 7]: (8361) {G1,W12,D6,L1,V1,M1} { join( X, one ) ==> join( join
% 1.31/1.69 ( X, composition( converse( skol2 ), skol2 ) ), one ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 Y := converse( skol2 )
% 1.31/1.69 Z := skol2
% 1.31/1.69 end
% 1.31/1.69 substitution1:
% 1.31/1.69 X := composition( X, skol2 )
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8365) {G1,W14,D6,L1,V1,M1} { join( composition( join( X, converse
% 1.31/1.69 ( skol2 ) ), skol2 ), one ) ==> join( composition( X, skol2 ), one ) }.
% 1.31/1.69 parent0[0]: (8364) {G1,W14,D6,L1,V1,M1} { join( composition( X, skol2 ),
% 1.31/1.69 one ) ==> join( composition( join( X, converse( skol2 ) ), skol2 ), one )
% 1.31/1.69 }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 subsumption: (262) {G2,W14,D6,L1,V1,M1} P(6,22) { join( composition( join(
% 1.31/1.69 X, converse( skol2 ) ), skol2 ), one ) ==> join( composition( X, skol2 )
% 1.31/1.69 , one ) }.
% 1.31/1.69 parent0: (8365) {G1,W14,D6,L1,V1,M1} { join( composition( join( X,
% 1.31/1.69 converse( skol2 ) ), skol2 ), one ) ==> join( composition( X, skol2 ),
% 1.31/1.69 one ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := X
% 1.31/1.69 end
% 1.31/1.69 permutation0:
% 1.31/1.69 0 ==> 0
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 eqswap: (8367) {G5,W11,D4,L1,V2,M1} { composition( join( X, one ), Y ) =
% 1.31/1.69 join( composition( X, Y ), Y ) }.
% 1.31/1.69 parent0[0]: (243) {G5,W11,D4,L1,V2,M1} P(234,6) { join( composition( Y, X )
% 1.31/1.69 , X ) = composition( join( Y, one ), X ) }.
% 1.31/1.69 substitution0:
% 1.31/1.69 X := Y
% 1.31/1.69 Y := X
% 1.31/1.69 end
% 1.31/1.69
% 1.31/1.69 paramod: (8369) {G1,W12,D6,L1,V1,M1} { composition( one, X ) = join(
% 1.31/1.69 composition( composition( converse( skol1 ), skol1 ), X ), X ) }.
% 1.31/1.69 parent0[0]: (13) {G0,W8,D5,L1,V0,M1} I { join( composition( converse( skol1
% 1.31/1.69 ), skol1 ), one ) ==> one }.
% 1.31/1.70 parent1[0; 2]: (8367) {G5,W11,D4,L1,V2,M1} { composition( join( X, one ),
% 1.31/1.70 Y ) = join( composition( X, Y ), Y ) }.
% 1.31/1.70 substitution0:
% 1.31/1.70 end
% 1.31/1.70 substitution1:
% 1.31/1.70 X := composition( converse( skol1 ), skol1 )
% 1.31/1.70 Y := X
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 paramod: (8370) {G2,W10,D6,L1,V1,M1} { X = join( composition( composition
% 1.31/1.70 ( converse( skol1 ), skol1 ), X ), X ) }.
% 1.31/1.70 parent0[0]: (234) {G4,W5,D3,L1,V1,M1} P(233,227) { composition( one, X )
% 1.31/1.70 ==> X }.
% 1.31/1.70 parent1[0; 1]: (8369) {G1,W12,D6,L1,V1,M1} { composition( one, X ) = join
% 1.31/1.70 ( composition( composition( converse( skol1 ), skol1 ), X ), X ) }.
% 1.31/1.70 substitution0:
% 1.31/1.70 X := X
% 1.31/1.70 end
% 1.31/1.70 substitution1:
% 1.31/1.70 X := X
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 eqswap: (8371) {G2,W10,D6,L1,V1,M1} { join( composition( composition(
% 1.31/1.70 converse( skol1 ), skol1 ), X ), X ) = X }.
% 1.31/1.70 parent0[0]: (8370) {G2,W10,D6,L1,V1,M1} { X = join( composition(
% 1.31/1.70 composition( converse( skol1 ), skol1 ), X ), X ) }.
% 1.31/1.70 substitution0:
% 1.31/1.70 X := X
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 subsumption: (6601) {G6,W10,D6,L1,V1,M1} P(13,243);d(234) { join(
% 1.31/1.70 composition( composition( converse( skol1 ), skol1 ), X ), X ) ==> X }.
% 1.31/1.70 parent0: (8371) {G2,W10,D6,L1,V1,M1} { join( composition( composition(
% 1.31/1.70 converse( skol1 ), skol1 ), X ), X ) = X }.
% 1.31/1.70 substitution0:
% 1.31/1.70 X := X
% 1.31/1.70 end
% 1.31/1.70 permutation0:
% 1.31/1.70 0 ==> 0
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 eqswap: (8373) {G1,W10,D5,L1,V2,M1} { join( converse( X ), Y ) ==>
% 1.31/1.70 converse( join( X, converse( Y ) ) ) }.
% 1.31/1.70 parent0[0]: (73) {G1,W10,D5,L1,V2,M1} P(7,8) { converse( join( Y, converse
% 1.31/1.70 ( X ) ) ) ==> join( converse( Y ), X ) }.
% 1.31/1.70 substitution0:
% 1.31/1.70 X := Y
% 1.31/1.70 Y := X
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 paramod: (8378) {G2,W14,D7,L1,V1,M1} { join( converse( composition(
% 1.31/1.70 composition( converse( skol1 ), skol1 ), converse( X ) ) ), X ) ==>
% 1.31/1.70 converse( converse( X ) ) }.
% 1.31/1.70 parent0[0]: (6601) {G6,W10,D6,L1,V1,M1} P(13,243);d(234) { join(
% 1.31/1.70 composition( composition( converse( skol1 ), skol1 ), X ), X ) ==> X }.
% 1.31/1.70 parent1[0; 12]: (8373) {G1,W10,D5,L1,V2,M1} { join( converse( X ), Y ) ==>
% 1.31/1.70 converse( join( X, converse( Y ) ) ) }.
% 1.31/1.70 substitution0:
% 1.31/1.70 X := converse( X )
% 1.31/1.70 end
% 1.31/1.70 substitution1:
% 1.31/1.70 X := composition( composition( converse( skol1 ), skol1 ), converse( X )
% 1.31/1.70 )
% 1.31/1.70 Y := X
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 paramod: (8379) {G1,W12,D7,L1,V1,M1} { join( converse( composition(
% 1.31/1.70 composition( converse( skol1 ), skol1 ), converse( X ) ) ), X ) ==> X }.
% 1.31/1.70 parent0[0]: (7) {G0,W5,D4,L1,V1,M1} I { converse( converse( X ) ) ==> X }.
% 1.31/1.70 parent1[0; 11]: (8378) {G2,W14,D7,L1,V1,M1} { join( converse( composition
% 1.31/1.70 ( composition( converse( skol1 ), skol1 ), converse( X ) ) ), X ) ==>
% 1.31/1.70 converse( converse( X ) ) }.
% 1.31/1.70 substitution0:
% 1.31/1.70 X := X
% 1.31/1.70 end
% 1.31/1.70 substitution1:
% 1.31/1.70 X := X
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 paramod: (8380) {G2,W11,D7,L1,V1,M1} { join( composition( X, converse(
% 1.31/1.70 composition( converse( skol1 ), skol1 ) ) ), X ) ==> X }.
% 1.31/1.70 parent0[0]: (89) {G1,W10,D5,L1,V2,M1} P(7,9) { converse( composition( Y,
% 1.31/1.70 converse( X ) ) ) ==> composition( X, converse( Y ) ) }.
% 1.31/1.70 parent1[0; 2]: (8379) {G1,W12,D7,L1,V1,M1} { join( converse( composition(
% 1.31/1.70 composition( converse( skol1 ), skol1 ), converse( X ) ) ), X ) ==> X }.
% 1.31/1.70 substitution0:
% 1.31/1.70 X := X
% 1.31/1.70 Y := composition( converse( skol1 ), skol1 )
% 1.31/1.70 end
% 1.31/1.70 substitution1:
% 1.31/1.70 X := X
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 paramod: (8381) {G2,W10,D6,L1,V1,M1} { join( composition( X, composition(
% 1.31/1.70 converse( skol1 ), skol1 ) ), X ) ==> X }.
% 1.31/1.70 parent0[0]: (90) {G1,W10,D5,L1,V2,M1} P(7,9) { converse( composition(
% 1.31/1.70 converse( X ), Y ) ) ==> composition( converse( Y ), X ) }.
% 1.31/1.70 parent1[0; 4]: (8380) {G2,W11,D7,L1,V1,M1} { join( composition( X,
% 1.31/1.70 converse( composition( converse( skol1 ), skol1 ) ) ), X ) ==> X }.
% 1.31/1.70 substitution0:
% 1.31/1.70 X := skol1
% 1.31/1.70 Y := skol1
% 1.31/1.70 end
% 1.31/1.70 substitution1:
% 1.31/1.70 X := X
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 paramod: (8382) {G1,W10,D6,L1,V1,M1} { join( composition( composition( X,
% 1.31/1.70 converse( skol1 ) ), skol1 ), X ) ==> X }.
% 1.31/1.70 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { composition( X, composition( Y, Z
% 1.31/1.70 ) ) ==> composition( composition( X, Y ), Z ) }.
% 1.31/1.70 parent1[0; 2]: (8381) {G2,W10,D6,L1,V1,M1} { join( composition( X,
% 1.31/1.70 composition( converse( skol1 ), skol1 ) ), X ) ==> X }.
% 1.31/1.70 substitution0:
% 1.31/1.70 X := X
% 1.31/1.70 Y := converse( skol1 )
% 1.31/1.70 Z := skol1
% 1.31/1.70 end
% 1.31/1.70 substitution1:
% 1.31/1.70 X := X
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 subsumption: (7863) {G7,W10,D6,L1,V1,M1} P(6601,73);d(7);d(89);d(90);d(4)
% 1.31/1.70 { join( composition( composition( X, converse( skol1 ) ), skol1 ), X )
% 1.31/1.70 ==> X }.
% 1.31/1.70 parent0: (8382) {G1,W10,D6,L1,V1,M1} { join( composition( composition( X,
% 1.31/1.70 converse( skol1 ) ), skol1 ), X ) ==> X }.
% 1.31/1.70 substitution0:
% 1.31/1.70 X := X
% 1.31/1.70 end
% 1.31/1.70 permutation0:
% 1.31/1.70 0 ==> 0
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 eqswap: (8385) {G2,W14,D6,L1,V1,M1} { join( composition( X, skol2 ), one )
% 1.31/1.70 ==> join( composition( join( X, converse( skol2 ) ), skol2 ), one ) }.
% 1.31/1.70 parent0[0]: (262) {G2,W14,D6,L1,V1,M1} P(6,22) { join( composition( join( X
% 1.31/1.70 , converse( skol2 ) ), skol2 ), one ) ==> join( composition( X, skol2 ),
% 1.31/1.70 one ) }.
% 1.31/1.70 substitution0:
% 1.31/1.70 X := X
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 paramod: (8388) {G3,W18,D7,L1,V0,M1} { join( composition( composition(
% 1.31/1.70 composition( converse( skol2 ), converse( skol1 ) ), skol1 ), skol2 ),
% 1.31/1.70 one ) ==> join( composition( converse( skol2 ), skol2 ), one ) }.
% 1.31/1.70 parent0[0]: (7863) {G7,W10,D6,L1,V1,M1} P(6601,73);d(7);d(89);d(90);d(4) {
% 1.31/1.70 join( composition( composition( X, converse( skol1 ) ), skol1 ), X ) ==>
% 1.31/1.70 X }.
% 1.31/1.70 parent1[0; 14]: (8385) {G2,W14,D6,L1,V1,M1} { join( composition( X, skol2
% 1.31/1.70 ), one ) ==> join( composition( join( X, converse( skol2 ) ), skol2 ),
% 1.31/1.70 one ) }.
% 1.31/1.70 substitution0:
% 1.31/1.70 X := converse( skol2 )
% 1.31/1.70 end
% 1.31/1.70 substitution1:
% 1.31/1.70 X := composition( composition( converse( skol2 ), converse( skol1 ) ),
% 1.31/1.70 skol1 )
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 paramod: (8389) {G1,W13,D7,L1,V0,M1} { join( composition( composition(
% 1.31/1.70 composition( converse( skol2 ), converse( skol1 ) ), skol1 ), skol2 ),
% 1.31/1.70 one ) ==> one }.
% 1.31/1.70 parent0[0]: (14) {G0,W8,D5,L1,V0,M1} I { join( composition( converse( skol2
% 1.31/1.70 ), skol2 ), one ) ==> one }.
% 1.31/1.70 parent1[0; 12]: (8388) {G3,W18,D7,L1,V0,M1} { join( composition(
% 1.31/1.70 composition( composition( converse( skol2 ), converse( skol1 ) ), skol1 )
% 1.31/1.70 , skol2 ), one ) ==> join( composition( converse( skol2 ), skol2 ), one )
% 1.31/1.70 }.
% 1.31/1.70 substitution0:
% 1.31/1.70 end
% 1.31/1.70 substitution1:
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 paramod: (8390) {G1,W12,D7,L1,V0,M1} { join( composition( composition(
% 1.31/1.70 converse( composition( skol1, skol2 ) ), skol1 ), skol2 ), one ) ==> one
% 1.31/1.70 }.
% 1.31/1.70 parent0[0]: (9) {G0,W10,D4,L1,V2,M1} I { composition( converse( Y ),
% 1.31/1.70 converse( X ) ) ==> converse( composition( X, Y ) ) }.
% 1.31/1.70 parent1[0; 4]: (8389) {G1,W13,D7,L1,V0,M1} { join( composition(
% 1.31/1.70 composition( composition( converse( skol2 ), converse( skol1 ) ), skol1 )
% 1.31/1.70 , skol2 ), one ) ==> one }.
% 1.31/1.70 substitution0:
% 1.31/1.70 X := skol1
% 1.31/1.70 Y := skol2
% 1.31/1.70 end
% 1.31/1.70 substitution1:
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 subsumption: (7872) {G8,W12,D7,L1,V0,M1} P(7863,262);d(14);d(9) { join(
% 1.31/1.70 composition( composition( converse( composition( skol1, skol2 ) ), skol1
% 1.31/1.70 ), skol2 ), one ) ==> one }.
% 1.31/1.70 parent0: (8390) {G1,W12,D7,L1,V0,M1} { join( composition( composition(
% 1.31/1.70 converse( composition( skol1, skol2 ) ), skol1 ), skol2 ), one ) ==> one
% 1.31/1.70 }.
% 1.31/1.70 substitution0:
% 1.31/1.70 end
% 1.31/1.70 permutation0:
% 1.31/1.70 0 ==> 0
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 paramod: (8394) {G2,W3,D2,L1,V0,M1} { ! one ==> one }.
% 1.31/1.70 parent0[0]: (7872) {G8,W12,D7,L1,V0,M1} P(7863,262);d(14);d(9) { join(
% 1.31/1.70 composition( composition( converse( composition( skol1, skol2 ) ), skol1
% 1.31/1.70 ), skol2 ), one ) ==> one }.
% 1.31/1.70 parent1[0; 2]: (15) {G1,W12,D7,L1,V0,M1} I;d(4) { ! join( composition(
% 1.31/1.70 composition( converse( composition( skol1, skol2 ) ), skol1 ), skol2 ),
% 1.31/1.70 one ) ==> one }.
% 1.31/1.70 substitution0:
% 1.31/1.70 end
% 1.31/1.70 substitution1:
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 eqrefl: (8395) {G0,W0,D0,L0,V0,M0} { }.
% 1.31/1.70 parent0[0]: (8394) {G2,W3,D2,L1,V0,M1} { ! one ==> one }.
% 1.31/1.70 substitution0:
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 subsumption: (8195) {G9,W0,D0,L0,V0,M0} S(15);d(7872);q { }.
% 1.31/1.70 parent0: (8395) {G0,W0,D0,L0,V0,M0} { }.
% 1.31/1.70 substitution0:
% 1.31/1.70 end
% 1.31/1.70 permutation0:
% 1.31/1.70 end
% 1.31/1.70
% 1.31/1.70 Proof check complete!
% 1.31/1.70
% 1.31/1.70 Memory use:
% 1.31/1.70
% 1.31/1.70 space for terms: 105601
% 1.31/1.70 space for clauses: 877441
% 1.31/1.70
% 1.31/1.70
% 1.31/1.70 clauses generated: 171714
% 1.31/1.70 clauses kept: 8196
% 1.31/1.70 clauses selected: 734
% 1.31/1.70 clauses deleted: 389
% 1.31/1.70 clauses inuse deleted: 90
% 1.31/1.70
% 1.31/1.70 subsentry: 7159
% 1.31/1.70 literals s-matched: 6764
% 1.31/1.70 literals matched: 6764
% 1.31/1.70 full subsumption: 0
% 1.31/1.70
% 1.31/1.70 checksum: -125193435
% 1.31/1.70
% 1.31/1.70
% 1.31/1.70 Bliksem ended
%------------------------------------------------------------------------------