TSTP Solution File: LCL096-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL096-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 07:50:16 EDT 2022
% Result : Unsatisfiable 1.48s 1.85s
% Output : Refutation 1.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : LCL096-1 : TPTP v8.1.0. Released v1.0.0.
% 0.09/0.12 % Command : bliksem %s
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Sun Jul 3 04:19:03 EDT 2022
% 0.12/0.32 % CPUTime :
% 1.48/1.85 *** allocated 10000 integers for termspace/termends
% 1.48/1.85 *** allocated 10000 integers for clauses
% 1.48/1.85 *** allocated 10000 integers for justifications
% 1.48/1.85 Bliksem 1.12
% 1.48/1.85
% 1.48/1.85
% 1.48/1.85 Automatic Strategy Selection
% 1.48/1.85
% 1.48/1.85 Clauses:
% 1.48/1.85 [
% 1.48/1.85 [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~( 'is_a_theorem'( X ) ),
% 1.48/1.85 'is_a_theorem'( Y ) ],
% 1.48/1.85 [ 'is_a_theorem'( equivalent( equivalent( equivalent( equivalent(
% 1.48/1.85 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ), T ), T )
% 1.48/1.85 ) ],
% 1.48/1.85 [ 'is_a_theorem'( equivalent( equivalent( equivalent( equivalent(
% 1.48/1.85 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent(
% 1.48/1.85 equivalent( Y, Z ), T ) ), U ), U ) ) ],
% 1.48/1.85 [ 'is_a_theorem'( equivalent( equivalent( equivalent( equivalent( X, Y )
% 1.48/1.85 , Z ), T ), equivalent( equivalent( equivalent( X, U ), Z ), equivalent(
% 1.48/1.85 equivalent( Y, U ), T ) ) ) ) ],
% 1.48/1.85 [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a, equivalent(
% 1.48/1.85 equivalent( b, b ), a ) ), c ), c ) ) ) ]
% 1.48/1.85 ] .
% 1.48/1.85
% 1.48/1.85
% 1.48/1.85 percentage equality = 0.000000, percentage horn = 1.000000
% 1.48/1.85 This is a near-Horn, non-equality problem
% 1.48/1.85
% 1.48/1.85
% 1.48/1.85 Options Used:
% 1.48/1.85
% 1.48/1.85 useres = 1
% 1.48/1.85 useparamod = 0
% 1.48/1.85 useeqrefl = 0
% 1.48/1.85 useeqfact = 0
% 1.48/1.85 usefactor = 1
% 1.48/1.85 usesimpsplitting = 0
% 1.48/1.85 usesimpdemod = 0
% 1.48/1.85 usesimpres = 4
% 1.48/1.85
% 1.48/1.85 resimpinuse = 1000
% 1.48/1.85 resimpclauses = 20000
% 1.48/1.85 substype = standard
% 1.48/1.85 backwardsubs = 1
% 1.48/1.85 selectoldest = 5
% 1.48/1.85
% 1.48/1.85 litorderings [0] = split
% 1.48/1.85 litorderings [1] = liftord
% 1.48/1.85
% 1.48/1.85 termordering = none
% 1.48/1.85
% 1.48/1.85 litapriori = 1
% 1.48/1.85 termapriori = 0
% 1.48/1.85 litaposteriori = 0
% 1.48/1.85 termaposteriori = 0
% 1.48/1.85 demodaposteriori = 0
% 1.48/1.85 ordereqreflfact = 0
% 1.48/1.85
% 1.48/1.85 litselect = negative
% 1.48/1.85
% 1.48/1.85 maxweight = 30000
% 1.48/1.85 maxdepth = 30000
% 1.48/1.85 maxlength = 115
% 1.48/1.85 maxnrvars = 195
% 1.48/1.85 excuselevel = 0
% 1.48/1.85 increasemaxweight = 0
% 1.48/1.85
% 1.48/1.85 maxselected = 10000000
% 1.48/1.85 maxnrclauses = 10000000
% 1.48/1.85
% 1.48/1.85 showgenerated = 0
% 1.48/1.85 showkept = 0
% 1.48/1.85 showselected = 0
% 1.48/1.85 showdeleted = 0
% 1.48/1.85 showresimp = 1
% 1.48/1.85 showstatus = 2000
% 1.48/1.85
% 1.48/1.85 prologoutput = 1
% 1.48/1.85 nrgoals = 5000000
% 1.48/1.85 totalproof = 1
% 1.48/1.85
% 1.48/1.85 Symbols occurring in the translation:
% 1.48/1.85
% 1.48/1.85 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.48/1.85 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 1.48/1.85 ! [4, 1] (w:1, o:17, a:1, s:1, b:0),
% 1.48/1.85 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.48/1.85 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.48/1.85 equivalent [41, 2] (w:1, o:48, a:1, s:1, b:0),
% 1.48/1.85 'is_a_theorem' [42, 1] (w:1, o:22, a:1, s:1, b:0),
% 1.48/1.85 a [46, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.48/1.85 b [47, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.48/1.85 c [48, 0] (w:1, o:16, a:1, s:1, b:0).
% 1.48/1.85
% 1.48/1.85
% 1.48/1.85 Starting Search:
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85
% 1.48/1.85 Intermediate Status:
% 1.48/1.85 Generated: 4097
% 1.48/1.85 Kept: 2003
% 1.48/1.85 Inuse: 215
% 1.48/1.85 Deleted: 3
% 1.48/1.85 Deletedinuse: 2
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85
% 1.48/1.85 Intermediate Status:
% 1.48/1.85 Generated: 9718
% 1.48/1.85 Kept: 4033
% 1.48/1.85 Inuse: 371
% 1.48/1.85 Deleted: 13
% 1.48/1.85 Deletedinuse: 4
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85
% 1.48/1.85 Intermediate Status:
% 1.48/1.85 Generated: 14766
% 1.48/1.85 Kept: 6111
% 1.48/1.85 Inuse: 447
% 1.48/1.85 Deleted: 13
% 1.48/1.85 Deletedinuse: 4
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85
% 1.48/1.85 Intermediate Status:
% 1.48/1.85 Generated: 20635
% 1.48/1.85 Kept: 8206
% 1.48/1.85 Inuse: 517
% 1.48/1.85 Deleted: 13
% 1.48/1.85 Deletedinuse: 4
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85
% 1.48/1.85 Intermediate Status:
% 1.48/1.85 Generated: 29038
% 1.48/1.85 Kept: 10209
% 1.48/1.85 Inuse: 642
% 1.48/1.85 Deleted: 13
% 1.48/1.85 Deletedinuse: 4
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85
% 1.48/1.85 Intermediate Status:
% 1.48/1.85 Generated: 38887
% 1.48/1.85 Kept: 12326
% 1.48/1.85 Inuse: 747
% 1.48/1.85 Deleted: 13
% 1.48/1.85 Deletedinuse: 4
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85
% 1.48/1.85 Intermediate Status:
% 1.48/1.85 Generated: 48351
% 1.48/1.85 Kept: 14349
% 1.48/1.85 Inuse: 872
% 1.48/1.85 Deleted: 23
% 1.48/1.85 Deletedinuse: 4
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85
% 1.48/1.85 Intermediate Status:
% 1.48/1.85 Generated: 57276
% 1.48/1.85 Kept: 16350
% 1.48/1.85 Inuse: 976
% 1.48/1.85 Deleted: 24
% 1.48/1.85 Deletedinuse: 4
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85
% 1.48/1.85 Intermediate Status:
% 1.48/1.85 Generated: 61664
% 1.48/1.85 Kept: 18354
% 1.48/1.85 Inuse: 1049
% 1.48/1.85 Deleted: 24
% 1.48/1.85 Deletedinuse: 4
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85 Resimplifying clauses:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85
% 1.48/1.85 Intermediate Status:
% 1.48/1.85 Generated: 69166
% 1.48/1.85 Kept: 20502
% 1.48/1.85 Inuse: 1131
% 1.48/1.85 Deleted: 83
% 1.48/1.85 Deletedinuse: 4
% 1.48/1.85
% 1.48/1.85 Resimplifying inuse:
% 1.48/1.85 Done
% 1.48/1.85
% 1.48/1.85
% 1.48/1.85 Bliksems!, er is een bewijs:
% 1.48/1.85 % SZS status Unsatisfiable
% 1.48/1.85 % SZS output start Refutation
% 1.48/1.85
% 1.48/1.85 clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y )
% 1.48/1.85 , ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 1, [ 'is_a_theorem'( equivalent( equivalent( equivalent( equivalent(
% 1.48/1.85 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ), T ), T )
% 1.48/1.85 ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 2, [ 'is_a_theorem'( equivalent( equivalent( equivalent( equivalent(
% 1.48/1.85 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent(
% 1.48/1.85 equivalent( Y, Z ), T ) ), U ), U ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 3, [ 'is_a_theorem'( equivalent( equivalent( equivalent( equivalent(
% 1.48/1.85 X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U ), Z ),
% 1.48/1.85 equivalent( equivalent( Y, U ), T ) ) ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 4, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a,
% 1.48/1.85 equivalent( equivalent( b, b ), a ) ), c ), c ) ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 5, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent( equivalent(
% 1.48/1.85 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 1.48/1.85 ) ), equivalent( Y, Z ) ), T ), T ), U ) ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 6, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( equivalent( equivalent(
% 1.48/1.85 equivalent( equivalent( equivalent( X, Y ), Z ), T ), equivalent(
% 1.48/1.85 equivalent( equivalent( X, U ), Z ), equivalent( equivalent( Y, U ), T )
% 1.48/1.85 ) ), W ) ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 7, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( equivalent( equivalent(
% 1.48/1.85 equivalent( equivalent( equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.85 equivalent( X, Z ) ), T ), equivalent( equivalent( Y, Z ), T ) ), U ), U
% 1.48/1.85 ), W ) ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( X
% 1.48/1.85 , Y ) ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent( equivalent(
% 1.48/1.85 equivalent( X, Y ), equivalent( X, Z ) ), T ), U ), equivalent(
% 1.48/1.85 equivalent( equivalent( Y, Z ), T ), U ) ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 10, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.85 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 11, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.85 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( Y
% 1.48/1.85 , Z ), T ) ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 12, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), Z
% 1.48/1.85 ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T ), Z ) )
% 1.48/1.85 ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 13, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.85 equivalent( X, Z ) ), equivalent( Y, Z ) ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 14, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 15, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.85 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 1.48/1.85 equivalent( Y, Z ) ), T ) ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 16, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.85 equivalent( X, X ), Y ) ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 17, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( Y, Y )
% 1.48/1.85 , X ) ) ) ] )
% 1.48/1.85 .
% 1.48/1.85 clause( 23, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( X, equivalent( equivalent( Y, Y ), X ) ), Z ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 27, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), U
% 1.48/1.86 ), W ), equivalent( equivalent( equivalent( equivalent( Y, Z ), T ), U )
% 1.48/1.86 , W ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 38, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), Z
% 1.48/1.86 ), equivalent( equivalent( equivalent( T, X ), equivalent( T, Y ) ), Z )
% 1.48/1.86 ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 57, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 1.48/1.86 equivalent( Z, X ), equivalent( Z, Y ) ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 62, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 1.48/1.86 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 78, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), Z ), equivalent( equivalent(
% 1.48/1.86 T, Y ), equivalent( equivalent( X, T ), Z ) ) ), U ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 94, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 1.48/1.86 ), equivalent( equivalent( equivalent( Y, T ), X ), equivalent( T, Z ) )
% 1.48/1.86 ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 98, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( equivalent( Z, X ), T ) ), equivalent( equivalent( Z, Y ), T
% 1.48/1.86 ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 101, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, X ), Y ), Z ), equivalent( Y, Z ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 109, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( X, X ), Y ), Z ),
% 1.48/1.86 equivalent( Y, Z ) ), T ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 135, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X
% 1.48/1.86 ), T ) ), equivalent( equivalent( Z, Y ), T ) ), U ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 182, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( X, Y ) ), Z ), Z ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 184, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Y
% 1.48/1.86 ) ), Z ), Z ), T ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 683, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 1.48/1.86 equivalent( Z, X ), equivalent( equivalent( T, Z ), equivalent( T, Y ) )
% 1.48/1.86 ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 716, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( Y, Z ), equivalent( Y, T ) ) ), equivalent( equivalent( U, X
% 1.48/1.86 ), equivalent( U, equivalent( Z, T ) ) ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 1847, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, X )
% 1.48/1.86 , Y ), Y ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 1848, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, X ), Y ), Y ), Z ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 1948, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 1.48/1.86 equivalent( Y, Y ) ), equivalent( X, Z ) ), Z ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 1962, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, equivalent( Y, Y ) ), equivalent(
% 1.48/1.86 X, Z ) ), Z ), T ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 5780, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 1.48/1.86 , equivalent( equivalent( Y, X ), Z ) ), Z ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 5915, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( equivalent( Y, X
% 1.48/1.86 ), Z ) ), Z ), T ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 6533, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( Y, Z ), T ) ), equivalent( equivalent( equivalent( Z, Y ), X
% 1.48/1.86 ), T ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 14502, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( equivalent( Y, Y ), equivalent( Z, T ) ), equivalent( Z, U )
% 1.48/1.86 ) ), equivalent( X, equivalent( T, U ) ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 20981, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 1.48/1.86 equivalent( equivalent( X, equivalent( Y, Y ) ), Z ) ), T ), equivalent(
% 1.48/1.86 Z, T ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 21106, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( Y, Y ), Z ), Z ), X ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 21182, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( X, equivalent( equivalent( equivalent( equivalent( Y, Y ), Z
% 1.48/1.86 ), Z ), X ) ), T ) ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 21461, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 1.48/1.86 equivalent( equivalent( Y, Y ), X ) ), Z ), Z ) ) ] )
% 1.48/1.86 .
% 1.48/1.86 clause( 21567, [] )
% 1.48/1.86 .
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 % SZS output end Refutation
% 1.48/1.86 found a proof!
% 1.48/1.86
% 1.48/1.86 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.48/1.86
% 1.48/1.86 initialclauses(
% 1.48/1.86 [ clause( 21569, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~(
% 1.48/1.86 'is_a_theorem'( X ) ), 'is_a_theorem'( Y ) ] )
% 1.48/1.86 , clause( 21570, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 1.48/1.86 ), T ), T ) ) ] )
% 1.48/1.86 , clause( 21571, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 1.48/1.86 equivalent( equivalent( Y, Z ), T ) ), U ), U ) ) ] )
% 1.48/1.86 , clause( 21572, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 1.48/1.86 , Z ), equivalent( equivalent( Y, U ), T ) ) ) ) ] )
% 1.48/1.86 , clause( 21573, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a
% 1.48/1.86 , equivalent( equivalent( b, b ), a ) ), c ), c ) ) ) ] )
% 1.48/1.86 ] ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y )
% 1.48/1.86 , ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , clause( 21569, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~(
% 1.48/1.86 'is_a_theorem'( X ) ), 'is_a_theorem'( Y ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.48/1.86 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 1, [ 'is_a_theorem'( equivalent( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ), T ), T )
% 1.48/1.86 ) ] )
% 1.48/1.86 , clause( 21570, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 1.48/1.86 ), T ), T ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 2, [ 'is_a_theorem'( equivalent( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent(
% 1.48/1.86 equivalent( Y, Z ), T ) ), U ), U ) ) ] )
% 1.48/1.86 , clause( 21571, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 1.48/1.86 equivalent( equivalent( Y, Z ), T ) ), U ), U ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.48/1.86 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 3, [ 'is_a_theorem'( equivalent( equivalent( equivalent( equivalent(
% 1.48/1.86 X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U ), Z ),
% 1.48/1.86 equivalent( equivalent( Y, U ), T ) ) ) ) ] )
% 1.48/1.86 , clause( 21572, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 1.48/1.86 , Z ), equivalent( equivalent( Y, U ), T ) ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.48/1.86 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 4, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a,
% 1.48/1.86 equivalent( equivalent( b, b ), a ) ), c ), c ) ) ) ] )
% 1.48/1.86 , clause( 21573, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a
% 1.48/1.86 , equivalent( equivalent( b, b ), a ) ), c ), c ) ) ) ] )
% 1.48/1.86 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21575, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 1.48/1.86 equivalent( Y, Z ) ), T ), T ), U ) ) ), 'is_a_theorem'( U ) ] )
% 1.48/1.86 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 1.48/1.86 ), ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , 2, clause( 1, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 1.48/1.86 ), T ), T ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 1.48/1.86 ), T ), T ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )
% 1.48/1.86 , :=( Z, Z ), :=( T, T )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 5, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 1.48/1.86 ) ), equivalent( Y, Z ) ), T ), T ), U ) ) ) ] )
% 1.48/1.86 , clause( 21575, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 1.48/1.86 equivalent( Y, Z ) ), T ), T ), U ) ) ), 'is_a_theorem'( U ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.48/1.86 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21577, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), Z ), T ), equivalent( equivalent(
% 1.48/1.86 equivalent( X, U ), Z ), equivalent( equivalent( Y, U ), T ) ) ), W ) ) )
% 1.48/1.86 , 'is_a_theorem'( W ) ] )
% 1.48/1.86 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 1.48/1.86 ), ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , 2, clause( 3, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 1.48/1.86 , Z ), equivalent( equivalent( Y, U ), T ) ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 1.48/1.86 , Z ), equivalent( equivalent( Y, U ), T ) ) ) ), :=( Y, W )] ),
% 1.48/1.86 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.48/1.86 , U )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 6, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), Z ), T ), equivalent(
% 1.48/1.86 equivalent( equivalent( X, U ), Z ), equivalent( equivalent( Y, U ), T )
% 1.48/1.86 ) ), W ) ) ) ] )
% 1.48/1.86 , clause( 21577, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), Z ), T ), equivalent( equivalent(
% 1.48/1.86 equivalent( X, U ), Z ), equivalent( equivalent( Y, U ), T ) ) ), W ) ) )
% 1.48/1.86 , 'is_a_theorem'( W ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.48/1.86 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21579, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 1.48/1.86 ) ), T ), equivalent( equivalent( Y, Z ), T ) ), U ), U ), W ) ) ),
% 1.48/1.86 'is_a_theorem'( W ) ] )
% 1.48/1.86 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 1.48/1.86 ), ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , 2, clause( 2, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 1.48/1.86 equivalent( equivalent( Y, Z ), T ) ), U ), U ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 1.48/1.86 equivalent( equivalent( Y, Z ), T ) ), U ), U ) ), :=( Y, W )] ),
% 1.48/1.86 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.48/1.86 , U )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 7, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( X, Z ) ), T ), equivalent( equivalent( Y, Z ), T ) ), U ), U
% 1.48/1.86 ), W ) ) ) ] )
% 1.48/1.86 , clause( 21579, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 1.48/1.86 ) ), T ), equivalent( equivalent( Y, Z ), T ) ), U ), U ), W ) ) ),
% 1.48/1.86 'is_a_theorem'( W ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.48/1.86 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21580, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 1.48/1.86 X, Y ) ) ) ] )
% 1.48/1.86 , clause( 5, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( X, Z ) ), equivalent( Y, Z ) ), T ), T ), U ) ) ) ] )
% 1.48/1.86 , 1, clause( 2, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 1.48/1.86 equivalent( equivalent( Y, Z ), T ) ), U ), U ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T,
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Y ) ) ), :=( U, equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( X, Y ) ) )] ), substitution( 1, [ :=( X,
% 1.48/1.86 Z ), :=( Y, X ), :=( Z, Y ), :=( T, equivalent( X, Y ) ), :=( U,
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Y ) ) )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( X
% 1.48/1.86 , Y ) ) ) ] )
% 1.48/1.86 , clause( 21580, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( X, Y ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.48/1.86 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21581, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), U ),
% 1.48/1.86 equivalent( equivalent( equivalent( Y, Z ), T ), U ) ) ) ] )
% 1.48/1.86 , clause( 5, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( X, Z ) ), equivalent( Y, Z ) ), T ), T ), U ) ) ) ] )
% 1.48/1.86 , 1, clause( 3, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 1.48/1.86 , Z ), equivalent( equivalent( Y, U ), T ) ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, U ),
% 1.48/1.86 :=( U, equivalent( equivalent( equivalent( equivalent( equivalent( X, Y )
% 1.48/1.86 , equivalent( X, Z ) ), T ), U ), equivalent( equivalent( equivalent( Y,
% 1.48/1.86 Z ), T ), U ) ) )] ), substitution( 1, [ :=( X, equivalent( equivalent( X
% 1.48/1.86 , Y ), equivalent( X, Z ) ) ), :=( Y, equivalent( Y, Z ) ), :=( Z, U ),
% 1.48/1.86 :=( T, U ), :=( U, T )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( X, Z ) ), T ), U ), equivalent(
% 1.48/1.86 equivalent( equivalent( Y, Z ), T ), U ) ) ) ] )
% 1.48/1.86 , clause( 21581, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), U ),
% 1.48/1.86 equivalent( equivalent( equivalent( Y, Z ), T ), U ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.48/1.86 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21583, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 1.48/1.86 Y ), equivalent( X, Y ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 1.48/1.86 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 1.48/1.86 ), ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , 2, clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( X, Y ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 1.48/1.86 X, Y ) ) ), :=( Y, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 1.48/1.86 ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 10, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 1.48/1.86 , clause( 21583, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 1.48/1.86 , Y ), equivalent( X, Y ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21584, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( Y
% 1.48/1.86 , Z ), T ) ) ) ] )
% 1.48/1.86 , clause( 10, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 1.48/1.86 , 1, clause( 2, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 1.48/1.86 equivalent( equivalent( Y, Z ), T ) ), U ), U ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( X, Z ) ), T ) ), :=( Y, equivalent( equivalent( Y, Z ), T ) )
% 1.48/1.86 , :=( Z, equivalent( equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( X, Z ) ), T ), equivalent( equivalent( Y, Z ), T ) ) )] ),
% 1.48/1.86 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.48/1.86 , equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X,
% 1.48/1.86 Z ) ), T ), equivalent( equivalent( Y, Z ), T ) ) )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 11, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( Y
% 1.48/1.86 , Z ), T ) ) ) ] )
% 1.48/1.86 , clause( 21584, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( Y
% 1.48/1.86 , Z ), T ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21585, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 1.48/1.86 , Z ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T ), Z
% 1.48/1.86 ) ) ) ) ] )
% 1.48/1.86 , clause( 10, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 1.48/1.86 , 1, clause( 3, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 1.48/1.86 , Z ), equivalent( equivalent( Y, U ), T ) ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( X, T ) ), :=( Y, Z ), :=( Z,
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), Z ), equivalent( equivalent(
% 1.48/1.86 T, Y ), equivalent( equivalent( X, T ), Z ) ) ) )] ), substitution( 1, [
% 1.48/1.86 :=( X, X ), :=( Y, T ), :=( Z, Z ), :=( T, equivalent( equivalent( X, T )
% 1.48/1.86 , Z ) ), :=( U, Y )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 12, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), Z
% 1.48/1.86 ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T ), Z ) )
% 1.48/1.86 ) ) ] )
% 1.48/1.86 , clause( 21585, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 1.48/1.86 ), Z ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T ),
% 1.48/1.86 Z ) ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21586, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 1.48/1.86 , equivalent( X, Z ) ), equivalent( Y, Z ) ) ) ] )
% 1.48/1.86 , clause( 10, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 1.48/1.86 , 1, clause( 1, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 1.48/1.86 ), T ), T ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 1.48/1.86 X, Z ) ) ), :=( Y, equivalent( Y, Z ) ), :=( Z, equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ) )] ),
% 1.48/1.86 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 1.48/1.86 ) )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 13, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( X, Z ) ), equivalent( Y, Z ) ) ) ] )
% 1.48/1.86 , clause( 21586, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 1.48/1.86 ), equivalent( X, Z ) ), equivalent( Y, Z ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21587, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 1.48/1.86 , clause( 10, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 1.48/1.86 , 1, clause( 13, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 1.48/1.86 ), equivalent( X, Z ) ), equivalent( Y, Z ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, equivalent( X, X ) )] )
% 1.48/1.86 , substitution( 1, [ :=( X, Y ), :=( Y, X ), :=( Z, X )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 14, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 1.48/1.86 , clause( 21587, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21589, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ), T ) ) ),
% 1.48/1.86 'is_a_theorem'( T ) ] )
% 1.48/1.86 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 1.48/1.86 ), ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , 2, clause( 13, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 1.48/1.86 ), equivalent( X, Z ) ), equivalent( Y, Z ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( X, Z ) ), equivalent( Y, Z ) ) ), :=( Y, T )] ),
% 1.48/1.86 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 15, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 1.48/1.86 equivalent( Y, Z ) ), T ) ) ) ] )
% 1.48/1.86 , clause( 21589, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ), T ) ) ),
% 1.48/1.86 'is_a_theorem'( T ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21591, [ ~( 'is_a_theorem'( equivalent( equivalent( X, X ), Y ) ) )
% 1.48/1.86 , 'is_a_theorem'( Y ) ] )
% 1.48/1.86 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 1.48/1.86 ), ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , 2, clause( 14, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( X, X ) ), :=( Y, Y )] ),
% 1.48/1.86 substitution( 1, [ :=( X, X )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 16, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( X, X ), Y ) ) ) ] )
% 1.48/1.86 , clause( 21591, [ ~( 'is_a_theorem'( equivalent( equivalent( X, X ), Y ) )
% 1.48/1.86 ), 'is_a_theorem'( Y ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 1.48/1.86 ), ==>( 1, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21592, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( Y,
% 1.48/1.86 Y ), X ) ) ) ] )
% 1.48/1.86 , clause( 6, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( X, Y ), Z ), T ),
% 1.48/1.86 equivalent( equivalent( equivalent( X, U ), Z ), equivalent( equivalent(
% 1.48/1.86 Y, U ), T ) ) ), W ) ) ) ] )
% 1.48/1.86 , 1, clause( 13, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 1.48/1.86 ), equivalent( X, Z ) ), equivalent( Y, Z ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, T ), :=( T, X ),
% 1.48/1.86 :=( U, Y ), :=( W, equivalent( X, equivalent( equivalent( Y, Y ), X ) ) )] )
% 1.48/1.86 , substitution( 1, [ :=( X, equivalent( equivalent( Z, Y ), T ) ), :=( Y
% 1.48/1.86 , X ), :=( Z, equivalent( equivalent( Y, Y ), X ) )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 17, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( Y, Y )
% 1.48/1.86 , X ) ) ) ] )
% 1.48/1.86 , clause( 21592, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( Y
% 1.48/1.86 , Y ), X ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.48/1.86 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21594, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( Y, Y ), X ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 1.48/1.86 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 1.48/1.86 ), ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , 2, clause( 17, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( Y
% 1.48/1.86 , Y ), X ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( equivalent( Y, Y
% 1.48/1.86 ), X ) ) ), :=( Y, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 1.48/1.86 ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 23, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( X, equivalent( equivalent( Y, Y ), X ) ), Z ) ) ) ] )
% 1.48/1.86 , clause( 21594, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( Y, Y ), X ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21595, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), U
% 1.48/1.86 ), W ), equivalent( equivalent( equivalent( equivalent( Y, Z ), T ), U )
% 1.48/1.86 , W ) ) ) ] )
% 1.48/1.86 , clause( 7, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( equivalent( equivalent( X
% 1.48/1.86 , Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( Y, Z ), T ) ),
% 1.48/1.86 U ), U ), W ) ) ) ] )
% 1.48/1.86 , 1, clause( 3, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 1.48/1.86 , Z ), equivalent( equivalent( Y, U ), T ) ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 1.48/1.86 :=( U, W ), :=( W, equivalent( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), U ), W ),
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( Y, Z ), T ), U ), W ) ) )] )
% 1.48/1.86 , substitution( 1, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( X, Z ) ), T ) ), :=( Y, equivalent( equivalent( Y, Z ), T ) )
% 1.48/1.86 , :=( Z, W ), :=( T, W ), :=( U, U )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 27, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), U
% 1.48/1.86 ), W ), equivalent( equivalent( equivalent( equivalent( Y, Z ), T ), U )
% 1.48/1.86 , W ) ) ) ] )
% 1.48/1.86 , clause( 21595, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), U
% 1.48/1.86 ), W ), equivalent( equivalent( equivalent( equivalent( Y, Z ), T ), U )
% 1.48/1.86 , W ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.48/1.86 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21596, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 1.48/1.86 , Z ), equivalent( equivalent( equivalent( T, X ), equivalent( T, Y ) ),
% 1.48/1.86 Z ) ) ) ] )
% 1.48/1.86 , clause( 16, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( X, X ), Y ) ) ) ] )
% 1.48/1.86 , 1, clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), U ),
% 1.48/1.86 equivalent( equivalent( equivalent( Y, Z ), T ), U ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( T, X ),
% 1.48/1.86 equivalent( T, Y ) ), Z ) ), :=( Y, equivalent( equivalent( equivalent( X
% 1.48/1.86 , Y ), Z ), equivalent( equivalent( equivalent( T, X ), equivalent( T, Y
% 1.48/1.86 ) ), Z ) ) )] ), substitution( 1, [ :=( X, T ), :=( Y, X ), :=( Z, Y ),
% 1.48/1.86 :=( T, Z ), :=( U, equivalent( equivalent( equivalent( T, X ), equivalent(
% 1.48/1.86 T, Y ) ), Z ) )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 38, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), Z
% 1.48/1.86 ), equivalent( equivalent( equivalent( T, X ), equivalent( T, Y ) ), Z )
% 1.48/1.86 ) ) ] )
% 1.48/1.86 , clause( 21596, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 1.48/1.86 ), Z ), equivalent( equivalent( equivalent( T, X ), equivalent( T, Y ) )
% 1.48/1.86 , Z ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21597, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 1.48/1.86 equivalent( Z, X ), equivalent( Z, Y ) ) ) ) ] )
% 1.48/1.86 , clause( 16, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( X, X ), Y ) ) ) ] )
% 1.48/1.86 , 1, clause( 11, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( Y
% 1.48/1.86 , Z ), T ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( Z, X ), equivalent(
% 1.48/1.86 Z, Y ) ) ), :=( Y, equivalent( equivalent( X, Y ), equivalent( equivalent(
% 1.48/1.86 Z, X ), equivalent( Z, Y ) ) ) )] ), substitution( 1, [ :=( X, Z ), :=( Y
% 1.48/1.86 , X ), :=( Z, Y ), :=( T, equivalent( equivalent( Z, X ), equivalent( Z,
% 1.48/1.86 Y ) ) )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 57, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 1.48/1.86 equivalent( Z, X ), equivalent( Z, Y ) ) ) ) ] )
% 1.48/1.86 , clause( 21597, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21599, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 1.48/1.86 Y ), equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ), T ) ) ),
% 1.48/1.86 'is_a_theorem'( T ) ] )
% 1.48/1.86 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 1.48/1.86 ), ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , 2, clause( 57, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 1.48/1.86 equivalent( Z, X ), equivalent( Z, Y ) ) ) ), :=( Y, T )] ),
% 1.48/1.86 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 62, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 1.48/1.86 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 1.48/1.86 , clause( 21599, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 1.48/1.86 , Y ), equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ), T ) ) ),
% 1.48/1.86 'is_a_theorem'( T ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21601, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), equivalent(
% 1.48/1.86 equivalent( X, T ), Z ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 1.48/1.86 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 1.48/1.86 ), ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , 2, clause( 12, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 1.48/1.86 ), Z ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T ),
% 1.48/1.86 Z ) ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.86 Z ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T ), Z )
% 1.48/1.86 ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z,
% 1.48/1.86 Z ), :=( T, T )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 78, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), Z ), equivalent( equivalent(
% 1.48/1.86 T, Y ), equivalent( equivalent( X, T ), Z ) ) ), U ) ) ) ] )
% 1.48/1.86 , clause( 21601, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), equivalent(
% 1.48/1.86 equivalent( X, T ), Z ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.48/1.86 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21602, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 1.48/1.86 Z ) ), equivalent( equivalent( equivalent( Y, T ), X ), equivalent( T, Z
% 1.48/1.86 ) ) ) ) ] )
% 1.48/1.86 , clause( 15, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 1.48/1.86 equivalent( Y, Z ) ), T ) ) ) ] )
% 1.48/1.86 , 1, clause( 12, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 1.48/1.86 ), Z ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T ),
% 1.48/1.86 Z ) ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, Y ), :=( Y, T ), :=( Z, Z ), :=( T,
% 1.48/1.86 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( equivalent(
% 1.48/1.86 equivalent( Y, T ), X ), equivalent( T, Z ) ) ) )] ), substitution( 1, [
% 1.48/1.86 :=( X, equivalent( Y, T ) ), :=( Y, equivalent( Y, Z ) ), :=( Z,
% 1.48/1.86 equivalent( T, Z ) ), :=( T, X )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 94, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 1.48/1.86 ), equivalent( equivalent( equivalent( Y, T ), X ), equivalent( T, Z ) )
% 1.48/1.86 ) ) ] )
% 1.48/1.86 , clause( 21602, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 1.48/1.86 , Z ) ), equivalent( equivalent( equivalent( Y, T ), X ), equivalent( T,
% 1.48/1.86 Z ) ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21603, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 1.48/1.86 , equivalent( equivalent( Z, X ), T ) ), equivalent( equivalent( Z, Y ),
% 1.48/1.86 T ) ) ) ] )
% 1.48/1.86 , clause( 15, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 1.48/1.86 equivalent( Y, Z ) ), T ) ) ) ] )
% 1.48/1.86 , 1, clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), U ),
% 1.48/1.86 equivalent( equivalent( equivalent( Y, Z ), T ), U ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( Z, X ) ), :=( Y, equivalent( Z,
% 1.48/1.86 Y ) ), :=( Z, T ), :=( T, equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( equivalent( Z, X ), T ) ), equivalent( equivalent( Z, Y ), T
% 1.48/1.86 ) ) )] ), substitution( 1, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T,
% 1.48/1.86 equivalent( equivalent( Z, X ), T ) ), :=( U, equivalent( equivalent( Z,
% 1.48/1.86 Y ), T ) )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 98, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( equivalent( Z, X ), T ) ), equivalent( equivalent( Z, Y ), T
% 1.48/1.86 ) ) ) ] )
% 1.48/1.86 , clause( 21603, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 1.48/1.86 ), equivalent( equivalent( Z, X ), T ) ), equivalent( equivalent( Z, Y )
% 1.48/1.86 , T ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21604, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, X ), Y ), Z ), equivalent( Y, Z ) ) ) ] )
% 1.48/1.86 , clause( 23, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( X, equivalent( equivalent( Y, Y ), X ) ), Z ) ) ) ] )
% 1.48/1.86 , 1, clause( 94, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 1.48/1.86 , Z ) ), equivalent( equivalent( equivalent( Y, T ), X ), equivalent( T,
% 1.48/1.86 Z ) ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, X ), Y ), Z ), equivalent( Y, Z )
% 1.48/1.86 ) )] ), substitution( 1, [ :=( X, Z ), :=( Y, equivalent( X, X ) ), :=(
% 1.48/1.86 Z, Z ), :=( T, Y )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 101, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, X ), Y ), Z ), equivalent( Y, Z ) ) ) ] )
% 1.48/1.86 , clause( 21604, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, X ), Y ), Z ), equivalent( Y, Z ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21606, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, X ), Y ), Z ), equivalent( Y, Z ) ), T ) ) ),
% 1.48/1.86 'is_a_theorem'( T ) ] )
% 1.48/1.86 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 1.48/1.86 ), ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , 2, clause( 101, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, X ), Y ), Z ), equivalent( Y, Z ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, X ), Y ), Z ), equivalent( Y, Z ) ) ), :=( Y, T )] ),
% 1.48/1.86 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 109, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( X, X ), Y ), Z ),
% 1.48/1.86 equivalent( Y, Z ) ), T ) ) ) ] )
% 1.48/1.86 , clause( 21606, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, X ), Y ), Z ), equivalent( Y, Z ) ), T ) ) ),
% 1.48/1.86 'is_a_theorem'( T ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21608, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( equivalent( Z, X ), T ) ), equivalent(
% 1.48/1.86 equivalent( Z, Y ), T ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 1.48/1.86 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 1.48/1.86 ), ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , 2, clause( 98, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 1.48/1.86 ), equivalent( equivalent( Z, X ), T ) ), equivalent( equivalent( Z, Y )
% 1.48/1.86 , T ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( equivalent( Z, X ), T ) ), equivalent( equivalent( Z, Y ), T
% 1.48/1.86 ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z,
% 1.48/1.86 Z ), :=( T, T )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 135, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X
% 1.48/1.86 ), T ) ), equivalent( equivalent( Z, Y ), T ) ), U ) ) ) ] )
% 1.48/1.86 , clause( 21608, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( equivalent( Z, X ), T ) ), equivalent(
% 1.48/1.86 equivalent( Z, Y ), T ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.48/1.86 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21609, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( X, Y ) ), Z ), Z ) ) ] )
% 1.48/1.86 , clause( 5, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( X, Z ) ), equivalent( Y, Z ) ), T ), T ), U ) ) ) ] )
% 1.48/1.86 , 1, clause( 27, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), U
% 1.48/1.86 ), W ), equivalent( equivalent( equivalent( equivalent( Y, Z ), T ), U )
% 1.48/1.86 , W ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z ),
% 1.48/1.86 :=( U, equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent(
% 1.48/1.86 X, Y ) ), Z ), Z ) )] ), substitution( 1, [ :=( X, T ), :=( Y, X ), :=( Z
% 1.48/1.86 , Y ), :=( T, equivalent( X, Y ) ), :=( U, Z ), :=( W, Z )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 182, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( X, Y ) ), Z ), Z ) ) ] )
% 1.48/1.86 , clause( 21609, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( X, Y ) ), Z ), Z ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21611, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ), Z ), T ) ) ),
% 1.48/1.86 'is_a_theorem'( T ) ] )
% 1.48/1.86 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 1.48/1.86 ), ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , 2, clause( 182, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( X, Y ) ), Z ), Z ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( X, Y ) ), Z ), Z ) ), :=( Y, T )] ),
% 1.48/1.86 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 184, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Y
% 1.48/1.86 ) ), Z ), Z ), T ) ) ) ] )
% 1.48/1.86 , clause( 21611, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ), Z ), T ) ) ),
% 1.48/1.86 'is_a_theorem'( T ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21612, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 1.48/1.86 equivalent( Z, X ), equivalent( equivalent( T, Z ), equivalent( T, Y ) )
% 1.48/1.86 ) ) ) ] )
% 1.48/1.86 , clause( 62, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 1.48/1.86 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 1.48/1.86 , 1, clause( 12, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 1.48/1.86 ), Z ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T ),
% 1.48/1.86 Z ) ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, T ), :=( T,
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 1.48/1.86 equivalent( equivalent( T, Z ), equivalent( T, Y ) ) ) ) )] ),
% 1.48/1.86 substitution( 1, [ :=( X, Z ), :=( Y, Y ), :=( Z, equivalent( equivalent(
% 1.48/1.86 T, Z ), equivalent( T, Y ) ) ), :=( T, X )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 683, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 1.48/1.86 equivalent( Z, X ), equivalent( equivalent( T, Z ), equivalent( T, Y ) )
% 1.48/1.86 ) ) ) ] )
% 1.48/1.86 , clause( 21612, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( equivalent( Z, X ), equivalent( equivalent( T, Z ),
% 1.48/1.86 equivalent( T, Y ) ) ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21613, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( Y, Z ), equivalent( Y, T ) ) ), equivalent( equivalent( U, X
% 1.48/1.86 ), equivalent( U, equivalent( Z, T ) ) ) ) ) ] )
% 1.48/1.86 , clause( 15, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 1.48/1.86 equivalent( Y, Z ) ), T ) ) ) ] )
% 1.48/1.86 , 1, clause( 683, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( equivalent( Z, X ), equivalent( equivalent( T, Z ),
% 1.48/1.86 equivalent( T, Y ) ) ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T,
% 1.48/1.86 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), equivalent( Y
% 1.48/1.86 , T ) ) ), equivalent( equivalent( U, X ), equivalent( U, equivalent( Z,
% 1.48/1.86 T ) ) ) ) )] ), substitution( 1, [ :=( X, equivalent( equivalent( Y, Z )
% 1.48/1.86 , equivalent( Y, T ) ) ), :=( Y, equivalent( Z, T ) ), :=( Z, X ), :=( T
% 1.48/1.86 , U )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 716, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( Y, Z ), equivalent( Y, T ) ) ), equivalent( equivalent( U, X
% 1.48/1.86 ), equivalent( U, equivalent( Z, T ) ) ) ) ) ] )
% 1.48/1.86 , clause( 21613, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( Y, Z ), equivalent( Y, T ) ) ), equivalent( equivalent( U, X
% 1.48/1.86 ), equivalent( U, equivalent( Z, T ) ) ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.48/1.86 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21614, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, X )
% 1.48/1.86 , Y ), Y ) ) ] )
% 1.48/1.86 , clause( 184, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Y
% 1.48/1.86 ) ), Z ), Z ), T ) ) ) ] )
% 1.48/1.86 , 1, clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), U ),
% 1.48/1.86 equivalent( equivalent( equivalent( Y, Z ), T ), U ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T,
% 1.48/1.86 equivalent( equivalent( equivalent( X, X ), Y ), Y ) )] ), substitution(
% 1.48/1.86 1, [ :=( X, Z ), :=( Y, X ), :=( Z, X ), :=( T, Y ), :=( U, Y )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 1847, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, X )
% 1.48/1.86 , Y ), Y ) ) ] )
% 1.48/1.86 , clause( 21614, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, X
% 1.48/1.86 ), Y ), Y ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.48/1.86 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21616, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, X ), Y ), Y ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 1.48/1.86 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 1.48/1.86 ), ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , 2, clause( 1847, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 1.48/1.86 , X ), Y ), Y ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, X ),
% 1.48/1.86 Y ), Y ) ), :=( Y, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 1.48/1.86 ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 1848, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, X ), Y ), Y ), Z ) ) ) ] )
% 1.48/1.86 , clause( 21616, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, X ), Y ), Y ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21617, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 1.48/1.86 equivalent( Y, Y ) ), equivalent( X, Z ) ), Z ) ) ] )
% 1.48/1.86 , clause( 1848, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, X ), Y ), Y ), Z ) ) ) ] )
% 1.48/1.86 , 1, clause( 38, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 1.48/1.86 ), Z ), equivalent( equivalent( equivalent( T, X ), equivalent( T, Y ) )
% 1.48/1.86 , Z ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, equivalent(
% 1.48/1.86 equivalent( equivalent( X, equivalent( Y, Y ) ), equivalent( X, Z ) ), Z
% 1.48/1.86 ) )] ), substitution( 1, [ :=( X, equivalent( Y, Y ) ), :=( Y, Z ), :=(
% 1.48/1.86 Z, Z ), :=( T, X )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 1948, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 1.48/1.86 equivalent( Y, Y ) ), equivalent( X, Z ) ), Z ) ) ] )
% 1.48/1.86 , clause( 21617, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 1.48/1.86 equivalent( Y, Y ) ), equivalent( X, Z ) ), Z ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21619, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, equivalent( Y, Y ) ), equivalent( X, Z ) ), Z ), T ) ) ),
% 1.48/1.86 'is_a_theorem'( T ) ] )
% 1.48/1.86 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 1.48/1.86 ), ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , 2, clause( 1948, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 1.48/1.86 , equivalent( Y, Y ) ), equivalent( X, Z ) ), Z ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X,
% 1.48/1.86 equivalent( Y, Y ) ), equivalent( X, Z ) ), Z ) ), :=( Y, T )] ),
% 1.48/1.86 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 1962, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, equivalent( Y, Y ) ), equivalent(
% 1.48/1.86 X, Z ) ), Z ), T ) ) ) ] )
% 1.48/1.86 , clause( 21619, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, equivalent( Y, Y ) ), equivalent( X, Z ) ), Z ), T ) ) ),
% 1.48/1.86 'is_a_theorem'( T ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21620, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 1.48/1.86 , equivalent( equivalent( Y, X ), Z ) ), Z ) ) ] )
% 1.48/1.86 , clause( 1962, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, equivalent( Y, Y ) ), equivalent(
% 1.48/1.86 X, Z ) ), Z ), T ) ) ) ] )
% 1.48/1.86 , 1, clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), U ),
% 1.48/1.86 equivalent( equivalent( equivalent( Y, Z ), T ), U ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( Y, X ) ), :=( Y, Y ), :=( Z, Z )
% 1.48/1.86 , :=( T, equivalent( equivalent( equivalent( X, Y ), equivalent(
% 1.48/1.86 equivalent( Y, X ), Z ) ), Z ) )] ), substitution( 1, [ :=( X, Y ), :=( Y
% 1.48/1.86 , X ), :=( Z, Y ), :=( T, equivalent( equivalent( Y, X ), Z ) ), :=( U, Z
% 1.48/1.86 )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 5780, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 1.48/1.86 , equivalent( equivalent( Y, X ), Z ) ), Z ) ) ] )
% 1.48/1.86 , clause( 21620, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 1.48/1.86 ), equivalent( equivalent( Y, X ), Z ) ), Z ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21622, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ), Z ), T ) ) ),
% 1.48/1.86 'is_a_theorem'( T ) ] )
% 1.48/1.86 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 1.48/1.86 ), ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , 2, clause( 5780, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 1.48/1.86 , Y ), equivalent( equivalent( Y, X ), Z ) ), Z ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 1.48/1.86 equivalent( equivalent( Y, X ), Z ) ), Z ) ), :=( Y, T )] ),
% 1.48/1.86 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 5915, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( equivalent( Y, X
% 1.48/1.86 ), Z ) ), Z ), T ) ) ) ] )
% 1.48/1.86 , clause( 21622, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 1.48/1.86 equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ), Z ), T ) ) ),
% 1.48/1.86 'is_a_theorem'( T ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21623, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( Y, Z ), T ) ), equivalent( equivalent( equivalent( Z, Y ), X
% 1.48/1.86 ), T ) ) ) ] )
% 1.48/1.86 , clause( 5915, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( equivalent( Y, X
% 1.48/1.86 ), Z ) ), Z ), T ) ) ) ] )
% 1.48/1.86 , 1, clause( 12, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 1.48/1.86 ), Z ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T ),
% 1.48/1.86 Z ) ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, T ), :=( T,
% 1.48/1.86 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), T ) ),
% 1.48/1.86 equivalent( equivalent( equivalent( Z, Y ), X ), T ) ) )] ),
% 1.48/1.86 substitution( 1, [ :=( X, equivalent( Z, Y ) ), :=( Y, equivalent(
% 1.48/1.86 equivalent( Y, Z ), T ) ), :=( Z, T ), :=( T, X )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 6533, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( Y, Z ), T ) ), equivalent( equivalent( equivalent( Z, Y ), X
% 1.48/1.86 ), T ) ) ) ] )
% 1.48/1.86 , clause( 21623, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( Y, Z ), T ) ), equivalent( equivalent( equivalent( Z, Y ), X
% 1.48/1.86 ), T ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21624, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( equivalent( Y, Y ), equivalent( Z, T ) ), equivalent( Z, U )
% 1.48/1.86 ) ), equivalent( X, equivalent( T, U ) ) ) ) ] )
% 1.48/1.86 , clause( 109, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( X, X ), Y ), Z ),
% 1.48/1.86 equivalent( Y, Z ) ), T ) ) ) ] )
% 1.48/1.86 , 1, clause( 716, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( Y, Z ), equivalent( Y, T ) ) ), equivalent( equivalent( U, X
% 1.48/1.86 ), equivalent( U, equivalent( Z, T ) ) ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, Y ), :=( Y, equivalent( Z, T ) ), :=( Z,
% 1.48/1.86 equivalent( Z, U ) ), :=( T, equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( equivalent( Y, Y ), equivalent( Z, T ) ), equivalent( Z, U )
% 1.48/1.86 ) ), equivalent( X, equivalent( T, U ) ) ) )] ), substitution( 1, [ :=(
% 1.48/1.86 X, equivalent( equivalent( equivalent( Y, Y ), equivalent( Z, T ) ),
% 1.48/1.86 equivalent( Z, U ) ) ), :=( Y, Z ), :=( Z, T ), :=( T, U ), :=( U, X )] )
% 1.48/1.86 ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 14502, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( equivalent( Y, Y ), equivalent( Z, T ) ), equivalent( Z, U )
% 1.48/1.86 ) ), equivalent( X, equivalent( T, U ) ) ) ) ] )
% 1.48/1.86 , clause( 21624, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( equivalent( Y, Y ), equivalent( Z, T ) ), equivalent( Z, U )
% 1.48/1.86 ) ), equivalent( X, equivalent( T, U ) ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.48/1.86 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21625, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 1.48/1.86 equivalent( equivalent( X, equivalent( Y, Y ) ), Z ) ), T ), equivalent(
% 1.48/1.86 Z, T ) ) ) ] )
% 1.48/1.86 , clause( 78, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), Z ), equivalent( equivalent(
% 1.48/1.86 T, Y ), equivalent( equivalent( X, T ), Z ) ) ), U ) ) ) ] )
% 1.48/1.86 , 1, clause( 14502, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( equivalent( Y, Y ), equivalent( Z, T ) ), equivalent( Z, U )
% 1.48/1.86 ) ), equivalent( X, equivalent( T, U ) ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, X ), :=( Y, equivalent( equivalent( X,
% 1.48/1.86 equivalent( Y, Y ) ), Z ) ), :=( Z, T ), :=( T, equivalent( Y, Y ) ),
% 1.48/1.86 :=( U, equivalent( equivalent( equivalent( X, equivalent( equivalent( X,
% 1.48/1.86 equivalent( Y, Y ) ), Z ) ), T ), equivalent( Z, T ) ) )] ),
% 1.48/1.86 substitution( 1, [ :=( X, equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( X, equivalent( Y, Y ) ), Z ) ), T ) ), :=( Y, Y ), :=( Z,
% 1.48/1.86 equivalent( X, equivalent( Y, Y ) ) ), :=( T, Z ), :=( U, T )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 20981, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 1.48/1.86 equivalent( equivalent( X, equivalent( Y, Y ) ), Z ) ), T ), equivalent(
% 1.48/1.86 Z, T ) ) ) ] )
% 1.48/1.86 , clause( 21625, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 1.48/1.86 equivalent( equivalent( X, equivalent( Y, Y ) ), Z ) ), T ), equivalent(
% 1.48/1.86 Z, T ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21626, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( Y, Y ), Z ), Z ), X ) ) ) ] )
% 1.48/1.86 , clause( 135, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X
% 1.48/1.86 ), T ) ), equivalent( equivalent( Z, Y ), T ) ), U ) ) ) ] )
% 1.48/1.86 , 1, clause( 20981, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 1.48/1.86 , equivalent( equivalent( X, equivalent( Y, Y ) ), Z ) ), T ), equivalent(
% 1.48/1.86 Z, T ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( Y, Y ) ), :=( Y, Z ), :=( Z,
% 1.48/1.86 equivalent( equivalent( Y, Y ), Z ) ), :=( T, X ), :=( U, equivalent( X,
% 1.48/1.86 equivalent( equivalent( equivalent( equivalent( Y, Y ), Z ), Z ), X ) ) )] )
% 1.48/1.86 , substitution( 1, [ :=( X, equivalent( equivalent( Y, Y ), Z ) ), :=( Y
% 1.48/1.86 , Y ), :=( Z, X ), :=( T, equivalent( equivalent( equivalent( equivalent(
% 1.48/1.86 Y, Y ), Z ), Z ), X ) )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 21106, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( Y, Y ), Z ), Z ), X ) ) ) ] )
% 1.48/1.86 , clause( 21626, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( Y, Y ), Z ), Z ), X ) ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21628, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( Y, Y ), Z ), Z ), X ) ), T ) ) ),
% 1.48/1.86 'is_a_theorem'( T ) ] )
% 1.48/1.86 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 1.48/1.86 ), ~( 'is_a_theorem'( X ) ) ] )
% 1.48/1.86 , 2, clause( 21106, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( Y, Y ), Z ), Z ), X ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( equivalent(
% 1.48/1.86 equivalent( equivalent( Y, Y ), Z ), Z ), X ) ) ), :=( Y, T )] ),
% 1.48/1.86 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 21182, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( X, equivalent( equivalent( equivalent( equivalent( Y, Y ), Z
% 1.48/1.86 ), Z ), X ) ), T ) ) ) ] )
% 1.48/1.86 , clause( 21628, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( equivalent( equivalent( Y, Y ), Z ), Z ), X ) ), T ) ) ),
% 1.48/1.86 'is_a_theorem'( T ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21629, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 1.48/1.86 equivalent( equivalent( Y, Y ), X ) ), Z ), Z ) ) ] )
% 1.48/1.86 , clause( 21182, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 1.48/1.86 equivalent( X, equivalent( equivalent( equivalent( equivalent( Y, Y ), Z
% 1.48/1.86 ), Z ), X ) ), T ) ) ) ] )
% 1.48/1.86 , 1, clause( 6533, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 1.48/1.86 equivalent( Y, Z ), T ) ), equivalent( equivalent( equivalent( Z, Y ), X
% 1.48/1.86 ), T ) ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X ), :=( T,
% 1.48/1.86 equivalent( equivalent( equivalent( X, equivalent( equivalent( Y, Y ), X
% 1.48/1.86 ) ), Z ), Z ) )] ), substitution( 1, [ :=( X, Z ), :=( Y, equivalent(
% 1.48/1.86 equivalent( Y, Y ), X ) ), :=( Z, X ), :=( T, Z )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 21461, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 1.48/1.86 equivalent( equivalent( Y, Y ), X ) ), Z ), Z ) ) ] )
% 1.48/1.86 , clause( 21629, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 1.48/1.86 equivalent( equivalent( Y, Y ), X ) ), Z ), Z ) ) ] )
% 1.48/1.86 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.48/1.86 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 resolution(
% 1.48/1.86 clause( 21630, [] )
% 1.48/1.86 , clause( 4, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a,
% 1.48/1.86 equivalent( equivalent( b, b ), a ) ), c ), c ) ) ) ] )
% 1.48/1.86 , 0, clause( 21461, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 1.48/1.86 , equivalent( equivalent( Y, Y ), X ) ), Z ), Z ) ) ] )
% 1.48/1.86 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, b ), :=(
% 1.48/1.86 Z, c )] )).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 subsumption(
% 1.48/1.86 clause( 21567, [] )
% 1.48/1.86 , clause( 21630, [] )
% 1.48/1.86 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 end.
% 1.48/1.86
% 1.48/1.86 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.48/1.86
% 1.48/1.86 Memory use:
% 1.48/1.86
% 1.48/1.86 space for terms: 565164
% 1.48/1.86 space for clauses: 2349787
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 clauses generated: 73112
% 1.48/1.86 clauses kept: 21568
% 1.48/1.86 clauses selected: 1162
% 1.48/1.86 clauses deleted: 83
% 1.48/1.86 clauses inuse deleted: 4
% 1.48/1.86
% 1.48/1.86 subsentry: 55036
% 1.48/1.86 literals s-matched: 51629
% 1.48/1.86 literals matched: 51628
% 1.48/1.86 full subsumption: 0
% 1.48/1.86
% 1.48/1.86 checksum: 1578527923
% 1.48/1.86
% 1.48/1.86
% 1.48/1.86 Bliksem ended
%------------------------------------------------------------------------------