TSTP Solution File: LCL128-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL128-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 07:50:44 EDT 2022
% Result : Unsatisfiable 0.86s 1.23s
% Output : Refutation 0.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LCL128-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n017.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 : Mon Jul 4 05:31:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.86/1.23 *** allocated 10000 integers for termspace/termends
% 0.86/1.23 *** allocated 10000 integers for clauses
% 0.86/1.23 *** allocated 10000 integers for justifications
% 0.86/1.23 Bliksem 1.12
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 Automatic Strategy Selection
% 0.86/1.23
% 0.86/1.23 Clauses:
% 0.86/1.23 [
% 0.86/1.23 [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~( 'is_a_theorem'( X ) ),
% 0.86/1.23 'is_a_theorem'( Y ) ],
% 0.86/1.23 [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent( equivalent(
% 0.86/1.23 equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T ) ) ) ) ) ]
% 0.86/1.23 ,
% 0.86/1.23 [ ~( 'is_a_theorem'( equivalent( a, equivalent( a, equivalent(
% 0.86/1.23 equivalent( b, c ), equivalent( equivalent( b, e ), equivalent( c, e ) )
% 0.86/1.23 ) ) ) ) ) ]
% 0.86/1.23 ] .
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 percentage equality = 0.000000, percentage horn = 1.000000
% 0.86/1.23 This is a near-Horn, non-equality problem
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 Options Used:
% 0.86/1.23
% 0.86/1.23 useres = 1
% 0.86/1.23 useparamod = 0
% 0.86/1.23 useeqrefl = 0
% 0.86/1.23 useeqfact = 0
% 0.86/1.23 usefactor = 1
% 0.86/1.23 usesimpsplitting = 0
% 0.86/1.23 usesimpdemod = 0
% 0.86/1.23 usesimpres = 4
% 0.86/1.23
% 0.86/1.23 resimpinuse = 1000
% 0.86/1.23 resimpclauses = 20000
% 0.86/1.23 substype = standard
% 0.86/1.23 backwardsubs = 1
% 0.86/1.23 selectoldest = 5
% 0.86/1.23
% 0.86/1.23 litorderings [0] = split
% 0.86/1.23 litorderings [1] = liftord
% 0.86/1.23
% 0.86/1.23 termordering = none
% 0.86/1.23
% 0.86/1.23 litapriori = 1
% 0.86/1.23 termapriori = 0
% 0.86/1.23 litaposteriori = 0
% 0.86/1.23 termaposteriori = 0
% 0.86/1.23 demodaposteriori = 0
% 0.86/1.23 ordereqreflfact = 0
% 0.86/1.23
% 0.86/1.23 litselect = negative
% 0.86/1.23
% 0.86/1.23 maxweight = 30000
% 0.86/1.23 maxdepth = 30000
% 0.86/1.23 maxlength = 115
% 0.86/1.23 maxnrvars = 195
% 0.86/1.23 excuselevel = 0
% 0.86/1.23 increasemaxweight = 0
% 0.86/1.23
% 0.86/1.23 maxselected = 10000000
% 0.86/1.23 maxnrclauses = 10000000
% 0.86/1.23
% 0.86/1.23 showgenerated = 0
% 0.86/1.23 showkept = 0
% 0.86/1.23 showselected = 0
% 0.86/1.23 showdeleted = 0
% 0.86/1.23 showresimp = 1
% 0.86/1.23 showstatus = 2000
% 0.86/1.23
% 0.86/1.23 prologoutput = 1
% 0.86/1.23 nrgoals = 5000000
% 0.86/1.23 totalproof = 1
% 0.86/1.23
% 0.86/1.23 Symbols occurring in the translation:
% 0.86/1.23
% 0.86/1.23 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.86/1.23 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.86/1.23 ! [4, 1] (w:1, o:17, a:1, s:1, b:0),
% 0.86/1.23 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.86/1.23 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.86/1.23 equivalent [41, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.86/1.23 'is_a_theorem' [42, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.86/1.23 a [45, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.86/1.23 b [46, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.86/1.23 c [47, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.86/1.23 e [48, 0] (w:1, o:16, a:1, s:1, b:0).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 Starting Search:
% 0.86/1.23
% 0.86/1.23 Resimplifying inuse:
% 0.86/1.23 Done
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 Intermediate Status:
% 0.86/1.23 Generated: 6133
% 0.86/1.23 Kept: 2005
% 0.86/1.23 Inuse: 288
% 0.86/1.23 Deleted: 15
% 0.86/1.23 Deletedinuse: 4
% 0.86/1.23
% 0.86/1.23 Resimplifying inuse:
% 0.86/1.23 Done
% 0.86/1.23
% 0.86/1.23 Resimplifying inuse:
% 0.86/1.23 Done
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 Intermediate Status:
% 0.86/1.23 Generated: 10900
% 0.86/1.23 Kept: 4028
% 0.86/1.23 Inuse: 398
% 0.86/1.23 Deleted: 15
% 0.86/1.23 Deletedinuse: 4
% 0.86/1.23
% 0.86/1.23 Resimplifying inuse:
% 0.86/1.23 Done
% 0.86/1.23
% 0.86/1.23 Resimplifying inuse:
% 0.86/1.23 Done
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 Intermediate Status:
% 0.86/1.23 Generated: 15920
% 0.86/1.23 Kept: 6049
% 0.86/1.23 Inuse: 473
% 0.86/1.23 Deleted: 15
% 0.86/1.23 Deletedinuse: 4
% 0.86/1.23
% 0.86/1.23 Resimplifying inuse:
% 0.86/1.23 Done
% 0.86/1.23
% 0.86/1.23 Resimplifying inuse:
% 0.86/1.23 Done
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 Intermediate Status:
% 0.86/1.23 Generated: 21213
% 0.86/1.23 Kept: 8156
% 0.86/1.23 Inuse: 540
% 0.86/1.23 Deleted: 15
% 0.86/1.23 Deletedinuse: 4
% 0.86/1.23
% 0.86/1.23 Resimplifying inuse:
% 0.86/1.23
% 0.86/1.23 Bliksems!, er is een bewijs:
% 0.86/1.23 % SZS status Unsatisfiable
% 0.86/1.23 % SZS output start Refutation
% 0.86/1.23
% 0.86/1.23 clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.86/1.23 , ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 1, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.86/1.23 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.23 ) ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 2, [ ~( 'is_a_theorem'( equivalent( a, equivalent( a, equivalent(
% 0.86/1.23 equivalent( b, c ), equivalent( equivalent( b, e ), equivalent( c, e ) )
% 0.86/1.23 ) ) ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 3, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.86/1.23 X, equivalent( X, equivalent( equivalent( equivalent( Y, Z ), equivalent(
% 0.86/1.23 T, Z ) ), equivalent( Y, T ) ) ) ), U ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( X,
% 0.86/1.23 equivalent( equivalent( equivalent( Y, Z ), equivalent( T, Z ) ),
% 0.86/1.23 equivalent( Y, T ) ) ) ), equivalent( equivalent( equivalent( U, W ),
% 0.86/1.23 equivalent( V0, W ) ), equivalent( U, V0 ) ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 5, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.23 equivalent( Z, Y ) ), equivalent( X, Z ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 6, [ 'is_a_theorem'( V1 ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( X, equivalent( X, equivalent( equivalent(
% 0.86/1.23 equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T ) ) ) ),
% 0.86/1.23 equivalent( equivalent( equivalent( U, W ), equivalent( V0, W ) ),
% 0.86/1.23 equivalent( U, V0 ) ) ), V1 ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 7, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.86/1.23 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z )
% 0.86/1.23 ), T ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 8, [ 'is_a_theorem'( equivalent( equivalent( equivalent( equivalent(
% 0.86/1.23 X, Y ), equivalent( Z, Y ) ), equivalent( X, Z ) ), equivalent(
% 0.86/1.23 equivalent( equivalent( T, U ), equivalent( W, U ) ), equivalent( T, W )
% 0.86/1.23 ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 9, [ 'is_a_theorem'( V0 ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y
% 0.86/1.23 ) ), equivalent( X, Z ) ), equivalent( equivalent( equivalent( T, U ),
% 0.86/1.23 equivalent( W, U ) ), equivalent( T, W ) ) ), V0 ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 10, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.23 equivalent( Z, Y ) ), equivalent( equivalent( X, T ), equivalent( Z, T )
% 0.86/1.23 ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 12, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent(
% 0.86/1.23 equivalent( X, U ), equivalent( Z, U ) ), T ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 13, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.86/1.23 equivalent( X, equivalent( equivalent( equivalent( Z, T ), equivalent( U
% 0.86/1.23 , T ) ), equivalent( Z, U ) ) ), Y ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 14, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.86/1.23 equivalent( equivalent( X, T ), equivalent( Z, T ) ) ), U ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 16, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( X, Y )
% 0.86/1.23 , equivalent( equivalent( equivalent( equivalent( Z, T ), equivalent( U,
% 0.86/1.23 T ) ), equivalent( Z, U ) ), Y ) ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 20, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y
% 0.86/1.23 ) ), T ), equivalent( equivalent( equivalent( X, U ), equivalent( Z, U )
% 0.86/1.23 ), T ) ), W ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 32, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( X
% 0.86/1.23 , Y ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 35, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 38, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 40, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( X, X ), Y ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 49, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.23 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.23 ) ), X ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 50, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, X ), Y
% 0.86/1.23 ), equivalent( equivalent( equivalent( equivalent( Z, T ), equivalent( U
% 0.86/1.23 , T ) ), equivalent( Z, U ) ), Y ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 53, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent( X
% 0.86/1.23 , Z ), T ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 54, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( X, equivalent( equivalent( equivalent( Y, Z ),
% 0.86/1.23 equivalent( T, Z ) ), equivalent( Y, T ) ) ), X ), U ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 55, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.86/1.23 equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 59, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.86/1.23 equivalent( Y, Z ) ) ), T ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 60, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), Z
% 0.86/1.23 ), equivalent( equivalent( equivalent( X, T ), equivalent( Y, T ) ), Z )
% 0.86/1.23 ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 61, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.86/1.23 equivalent( equivalent( X, Z ), T ), equivalent( equivalent( Y, Z ), T )
% 0.86/1.23 ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 69, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z ) ),
% 0.86/1.23 equivalent( X, T ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 73, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( equivalent( equivalent( X, Y ), Z ), equivalent(
% 0.86/1.23 equivalent( T, Y ), Z ) ), equivalent( X, T ) ), U ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 79, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), T ), U ),
% 0.86/1.23 equivalent( equivalent( equivalent( X, Z ), T ), U ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 105, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.23 Z ), equivalent( equivalent( equivalent( X, T ), equivalent( U, T ) ),
% 0.86/1.23 equivalent( Z, equivalent( U, Y ) ) ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 114, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( X, Y ), Z ), equivalent( T, Z ) ), equivalent( equivalent( X
% 0.86/1.23 , U ), equivalent( T, equivalent( U, Y ) ) ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 139, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.23 equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent( equivalent(
% 0.86/1.23 X, T ), U ), equivalent( Z, U ) ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 141, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.23 equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent( X, T ), Z
% 0.86/1.23 ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 145, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.86/1.23 ) ), equivalent( X, equivalent( equivalent( Y, T ), equivalent( Z, T ) )
% 0.86/1.23 ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 150, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( X,
% 0.86/1.23 equivalent( equivalent( Y, T ), equivalent( Z, T ) ) ) ), U ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 159, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.23 equivalent( Y, Z ) ), T ), equivalent( equivalent( X, equivalent(
% 0.86/1.23 equivalent( Y, U ), equivalent( Z, U ) ) ), T ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 162, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.23 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( equivalent( X, U
% 0.86/1.23 ), equivalent( equivalent( Y, T ), U ) ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 176, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z )
% 0.86/1.23 ), U ), equivalent( equivalent( X, T ), U ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 239, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z ) ),
% 0.86/1.23 equivalent( T, T ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 242, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y
% 0.86/1.23 ) ), equivalent( X, Z ) ), equivalent( T, T ) ), U ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 265, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.23 Z ), equivalent( equivalent( X, T ), equivalent( Z, equivalent( T, Y ) )
% 0.86/1.23 ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 707, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.86/1.23 ) ), equivalent( equivalent( X, equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.23 ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 972, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z )
% 0.86/1.23 ), equivalent( U, T ) ), equivalent( X, U ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 996, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent( Y
% 0.86/1.23 , Y ) ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 1012, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( X, equivalent( X, equivalent( Y, Y ) ) ), Z ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 1031, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.86/1.23 equivalent( Z, Z ) ) ), equivalent( X, Y ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 1139, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 0.86/1.23 equivalent( X, Y ) ), T ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 6542, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.23 equivalent( Y, Z ), equivalent( equivalent( T, T ), Z ) ) ), equivalent(
% 0.86/1.23 X, Y ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 7227, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.23 equivalent( Y, Z ) ), equivalent( Z, Y ) ), X ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 7354, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent(
% 0.86/1.23 Z, Y ) ), X ), T ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 7847, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.23 equivalent( Y, Z ) ), T ), equivalent( X, equivalent( T, equivalent( Z, Y
% 0.86/1.23 ) ) ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 7907, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.86/1.23 equivalent( Y, Z ), equivalent( equivalent( Y, T ), equivalent( Z, T ) )
% 0.86/1.23 ) ) ) ) ] )
% 0.86/1.23 .
% 0.86/1.23 clause( 8156, [] )
% 0.86/1.23 .
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 % SZS output end Refutation
% 0.86/1.23 found a proof!
% 0.86/1.23
% 0.86/1.23 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.86/1.23
% 0.86/1.23 initialclauses(
% 0.86/1.23 [ clause( 8158, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~(
% 0.86/1.23 'is_a_theorem'( X ) ), 'is_a_theorem'( Y ) ] )
% 0.86/1.23 , clause( 8159, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.86/1.23 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.23 ) ) ) ) ] )
% 0.86/1.23 , clause( 8160, [ ~( 'is_a_theorem'( equivalent( a, equivalent( a,
% 0.86/1.23 equivalent( equivalent( b, c ), equivalent( equivalent( b, e ),
% 0.86/1.23 equivalent( c, e ) ) ) ) ) ) ) ] )
% 0.86/1.23 ] ).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 subsumption(
% 0.86/1.23 clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.86/1.23 , ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.23 , clause( 8158, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~(
% 0.86/1.23 'is_a_theorem'( X ) ), 'is_a_theorem'( Y ) ] )
% 0.86/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.86/1.23 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 subsumption(
% 0.86/1.23 clause( 1, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.86/1.23 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.23 ) ) ) ) ] )
% 0.86/1.23 , clause( 8159, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.86/1.23 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.23 ) ) ) ) ] )
% 0.86/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.23 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 subsumption(
% 0.86/1.23 clause( 2, [ ~( 'is_a_theorem'( equivalent( a, equivalent( a, equivalent(
% 0.86/1.23 equivalent( b, c ), equivalent( equivalent( b, e ), equivalent( c, e ) )
% 0.86/1.23 ) ) ) ) ) ] )
% 0.86/1.23 , clause( 8160, [ ~( 'is_a_theorem'( equivalent( a, equivalent( a,
% 0.86/1.23 equivalent( equivalent( b, c ), equivalent( equivalent( b, e ),
% 0.86/1.23 equivalent( c, e ) ) ) ) ) ) ) ] )
% 0.86/1.23 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 resolution(
% 0.86/1.23 clause( 8162, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent( X
% 0.86/1.23 , equivalent( equivalent( equivalent( Y, Z ), equivalent( T, Z ) ),
% 0.86/1.23 equivalent( Y, T ) ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.86/1.23 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.86/1.23 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.23 , 2, clause( 1, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.86/1.23 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.23 ) ) ) ) ] )
% 0.86/1.23 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( X, equivalent(
% 0.86/1.23 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.23 ) ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z
% 0.86/1.23 , Z ), :=( T, T )] )).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 subsumption(
% 0.86/1.23 clause( 3, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.86/1.23 X, equivalent( X, equivalent( equivalent( equivalent( Y, Z ), equivalent(
% 0.86/1.23 T, Z ) ), equivalent( Y, T ) ) ) ), U ) ) ) ] )
% 0.86/1.23 , clause( 8162, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.23 X, equivalent( equivalent( equivalent( Y, Z ), equivalent( T, Z ) ),
% 0.86/1.23 equivalent( Y, T ) ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.86/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.23 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 resolution(
% 0.86/1.23 clause( 8163, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( X,
% 0.86/1.23 equivalent( equivalent( equivalent( Y, Z ), equivalent( T, Z ) ),
% 0.86/1.23 equivalent( Y, T ) ) ) ), equivalent( equivalent( equivalent( U, W ),
% 0.86/1.23 equivalent( V0, W ) ), equivalent( U, V0 ) ) ) ) ] )
% 0.86/1.23 , clause( 3, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( X, equivalent( X, equivalent( equivalent( equivalent( Y, Z )
% 0.86/1.23 , equivalent( T, Z ) ), equivalent( Y, T ) ) ) ), U ) ) ) ] )
% 0.86/1.23 , 1, clause( 1, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.86/1.23 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.23 ) ) ) ) ] )
% 0.86/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 0.86/1.23 :=( U, equivalent( equivalent( X, equivalent( X, equivalent( equivalent(
% 0.86/1.23 equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T ) ) ) ),
% 0.86/1.23 equivalent( equivalent( equivalent( U, W ), equivalent( V0, W ) ),
% 0.86/1.23 equivalent( U, V0 ) ) ) )] ), substitution( 1, [ :=( X, equivalent( X,
% 0.86/1.23 equivalent( X, equivalent( equivalent( equivalent( Y, Z ), equivalent( T
% 0.86/1.23 , Z ) ), equivalent( Y, T ) ) ) ) ), :=( Y, U ), :=( Z, W ), :=( T, V0 )] )
% 0.86/1.23 ).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 subsumption(
% 0.86/1.23 clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( X,
% 0.86/1.23 equivalent( equivalent( equivalent( Y, Z ), equivalent( T, Z ) ),
% 0.86/1.23 equivalent( Y, T ) ) ) ), equivalent( equivalent( equivalent( U, W ),
% 0.86/1.23 equivalent( V0, W ) ), equivalent( U, V0 ) ) ) ) ] )
% 0.86/1.23 , clause( 8163, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( X
% 0.86/1.23 , equivalent( equivalent( equivalent( Y, Z ), equivalent( T, Z ) ),
% 0.86/1.23 equivalent( Y, T ) ) ) ), equivalent( equivalent( equivalent( U, W ),
% 0.86/1.23 equivalent( V0, W ) ), equivalent( U, V0 ) ) ) ) ] )
% 0.86/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.23 , U ), :=( W, W ), :=( V0, V0 )] ), permutation( 0, [ ==>( 0, 0 )] )
% 0.86/1.23 ).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 resolution(
% 0.86/1.23 clause( 8164, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.86/1.23 , equivalent( Z, Y ) ), equivalent( X, Z ) ) ) ] )
% 0.86/1.23 , clause( 3, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( X, equivalent( X, equivalent( equivalent( equivalent( Y, Z )
% 0.86/1.23 , equivalent( T, Z ) ), equivalent( Y, T ) ) ) ), U ) ) ) ] )
% 0.86/1.23 , 1, clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( X
% 0.86/1.23 , equivalent( equivalent( equivalent( Y, Z ), equivalent( T, Z ) ),
% 0.86/1.23 equivalent( Y, T ) ) ) ), equivalent( equivalent( equivalent( U, W ),
% 0.86/1.23 equivalent( V0, W ) ), equivalent( U, V0 ) ) ) ) ] )
% 0.86/1.23 , 0, substitution( 0, [ :=( X, T ), :=( Y, U ), :=( Z, W ), :=( T, V0 ),
% 0.86/1.23 :=( U, equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.86/1.23 equivalent( X, Z ) ) )] ), substitution( 1, [ :=( X, T ), :=( Y, U ),
% 0.86/1.23 :=( Z, W ), :=( T, V0 ), :=( U, X ), :=( W, Y ), :=( V0, Z )] )).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 subsumption(
% 0.86/1.23 clause( 5, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.23 equivalent( Z, Y ) ), equivalent( X, Z ) ) ) ] )
% 0.86/1.23 , clause( 8164, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.23 ), equivalent( Z, Y ) ), equivalent( X, Z ) ) ) ] )
% 0.86/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.86/1.23 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 resolution(
% 0.86/1.23 clause( 8166, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.23 equivalent( X, equivalent( equivalent( equivalent( Y, Z ), equivalent( T
% 0.86/1.23 , Z ) ), equivalent( Y, T ) ) ) ), equivalent( equivalent( equivalent( U
% 0.86/1.23 , W ), equivalent( V0, W ) ), equivalent( U, V0 ) ) ), V1 ) ) ),
% 0.86/1.23 'is_a_theorem'( V1 ) ] )
% 0.86/1.23 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.86/1.23 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.23 , 2, clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( X
% 0.86/1.23 , equivalent( equivalent( equivalent( Y, Z ), equivalent( T, Z ) ),
% 0.86/1.23 equivalent( Y, T ) ) ) ), equivalent( equivalent( equivalent( U, W ),
% 0.86/1.23 equivalent( V0, W ) ), equivalent( U, V0 ) ) ) ) ] )
% 0.86/1.23 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, equivalent( X,
% 0.86/1.23 equivalent( equivalent( equivalent( Y, Z ), equivalent( T, Z ) ),
% 0.86/1.23 equivalent( Y, T ) ) ) ), equivalent( equivalent( equivalent( U, W ),
% 0.86/1.23 equivalent( V0, W ) ), equivalent( U, V0 ) ) ) ), :=( Y, V1 )] ),
% 0.86/1.23 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.23 , U ), :=( W, W ), :=( V0, V0 )] )).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 subsumption(
% 0.86/1.23 clause( 6, [ 'is_a_theorem'( V1 ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( X, equivalent( X, equivalent( equivalent(
% 0.86/1.23 equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T ) ) ) ),
% 0.86/1.23 equivalent( equivalent( equivalent( U, W ), equivalent( V0, W ) ),
% 0.86/1.23 equivalent( U, V0 ) ) ), V1 ) ) ) ] )
% 0.86/1.23 , clause( 8166, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.86/1.23 , equivalent( X, equivalent( equivalent( equivalent( Y, Z ), equivalent(
% 0.86/1.23 T, Z ) ), equivalent( Y, T ) ) ) ), equivalent( equivalent( equivalent( U
% 0.86/1.23 , W ), equivalent( V0, W ) ), equivalent( U, V0 ) ) ), V1 ) ) ),
% 0.86/1.23 'is_a_theorem'( V1 ) ] )
% 0.86/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.23 , U ), :=( W, W ), :=( V0, V0 ), :=( V1, V1 )] ), permutation( 0, [ ==>(
% 0.86/1.23 0, 1 ), ==>( 1, 0 )] ) ).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 resolution(
% 0.86/1.23 clause( 8168, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z ) ), T ) ) ),
% 0.86/1.23 'is_a_theorem'( T ) ] )
% 0.86/1.23 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.86/1.23 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.23 , 2, clause( 5, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.23 ), equivalent( Z, Y ) ), equivalent( X, Z ) ) ) ] )
% 0.86/1.23 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.23 equivalent( Z, Y ) ), equivalent( X, Z ) ) ), :=( Y, T )] ),
% 0.86/1.23 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 subsumption(
% 0.86/1.23 clause( 7, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.86/1.23 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z )
% 0.86/1.23 ), T ) ) ) ] )
% 0.86/1.23 , clause( 8168, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z ) ), T ) ) ),
% 0.86/1.23 'is_a_theorem'( T ) ] )
% 0.86/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.23 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 resolution(
% 0.86/1.23 clause( 8169, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z ) ),
% 0.86/1.23 equivalent( equivalent( equivalent( T, U ), equivalent( W, U ) ),
% 0.86/1.23 equivalent( T, W ) ) ) ) ] )
% 0.86/1.23 , clause( 7, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.86/1.23 equivalent( X, Z ) ), T ) ) ) ] )
% 0.86/1.23 , 1, clause( 1, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.86/1.23 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.23 ) ) ) ) ] )
% 0.86/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 0.86/1.23 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y
% 0.86/1.23 ) ), equivalent( X, Z ) ), equivalent( equivalent( equivalent( T, U ),
% 0.86/1.23 equivalent( W, U ) ), equivalent( T, W ) ) ) )] ), substitution( 1, [
% 0.86/1.23 :=( X, equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.86/1.23 equivalent( X, Z ) ) ), :=( Y, T ), :=( Z, U ), :=( T, W )] )).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 subsumption(
% 0.86/1.23 clause( 8, [ 'is_a_theorem'( equivalent( equivalent( equivalent( equivalent(
% 0.86/1.23 X, Y ), equivalent( Z, Y ) ), equivalent( X, Z ) ), equivalent(
% 0.86/1.23 equivalent( equivalent( T, U ), equivalent( W, U ) ), equivalent( T, W )
% 0.86/1.23 ) ) ) ] )
% 0.86/1.23 , clause( 8169, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z ) ),
% 0.86/1.23 equivalent( equivalent( equivalent( T, U ), equivalent( W, U ) ),
% 0.86/1.23 equivalent( T, W ) ) ) ) ] )
% 0.86/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.23 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 resolution(
% 0.86/1.23 clause( 8171, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z )
% 0.86/1.23 ), equivalent( equivalent( equivalent( T, U ), equivalent( W, U ) ),
% 0.86/1.23 equivalent( T, W ) ) ), V0 ) ) ), 'is_a_theorem'( V0 ) ] )
% 0.86/1.23 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.86/1.23 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.23 , 2, clause( 8, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z ) ),
% 0.86/1.23 equivalent( equivalent( equivalent( T, U ), equivalent( W, U ) ),
% 0.86/1.23 equivalent( T, W ) ) ) ) ] )
% 0.86/1.23 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z ) ),
% 0.86/1.23 equivalent( equivalent( equivalent( T, U ), equivalent( W, U ) ),
% 0.86/1.23 equivalent( T, W ) ) ) ), :=( Y, V0 )] ), substitution( 1, [ :=( X, X ),
% 0.86/1.23 :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U, U ), :=( W, W )] )).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 subsumption(
% 0.86/1.23 clause( 9, [ 'is_a_theorem'( V0 ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y
% 0.86/1.23 ) ), equivalent( X, Z ) ), equivalent( equivalent( equivalent( T, U ),
% 0.86/1.23 equivalent( W, U ) ), equivalent( T, W ) ) ), V0 ) ) ) ] )
% 0.86/1.23 , clause( 8171, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z )
% 0.86/1.23 ), equivalent( equivalent( equivalent( T, U ), equivalent( W, U ) ),
% 0.86/1.23 equivalent( T, W ) ) ), V0 ) ) ), 'is_a_theorem'( V0 ) ] )
% 0.86/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.23 , U ), :=( W, W ), :=( V0, V0 )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1
% 0.86/1.23 , 0 )] ) ).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 resolution(
% 0.86/1.23 clause( 8172, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.86/1.23 , equivalent( Z, Y ) ), equivalent( equivalent( X, T ), equivalent( Z, T
% 0.86/1.23 ) ) ) ) ] )
% 0.86/1.23 , clause( 9, [ 'is_a_theorem'( V0 ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y
% 0.86/1.23 ) ), equivalent( X, Z ) ), equivalent( equivalent( equivalent( T, U ),
% 0.86/1.23 equivalent( W, U ) ), equivalent( T, W ) ) ), V0 ) ) ) ] )
% 0.86/1.23 , 1, clause( 5, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.23 ), equivalent( Z, Y ) ), equivalent( X, Z ) ) ) ] )
% 0.86/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, X ),
% 0.86/1.23 :=( U, T ), :=( W, Z ), :=( V0, equivalent( equivalent( equivalent( X, Y
% 0.86/1.23 ), equivalent( Z, Y ) ), equivalent( equivalent( X, T ), equivalent( Z,
% 0.86/1.23 T ) ) ) )] ), substitution( 1, [ :=( X, equivalent( equivalent( X, Y ),
% 0.86/1.23 equivalent( Z, Y ) ) ), :=( Y, equivalent( X, Z ) ), :=( Z, equivalent(
% 0.86/1.23 equivalent( X, T ), equivalent( Z, T ) ) )] )).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 subsumption(
% 0.86/1.23 clause( 10, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.23 equivalent( Z, Y ) ), equivalent( equivalent( X, T ), equivalent( Z, T )
% 0.86/1.23 ) ) ) ] )
% 0.86/1.23 , clause( 8172, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.23 ), equivalent( Z, Y ) ), equivalent( equivalent( X, T ), equivalent( Z,
% 0.86/1.23 T ) ) ) ) ] )
% 0.86/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.23 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 resolution(
% 0.86/1.23 clause( 8173, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent(
% 0.86/1.23 equivalent( X, U ), equivalent( Z, U ) ), T ) ) ) ] )
% 0.86/1.23 , clause( 9, [ 'is_a_theorem'( V0 ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.23 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y
% 0.86/1.23 ) ), equivalent( X, Z ) ), equivalent( equivalent( equivalent( T, U ),
% 0.86/1.23 equivalent( W, U ) ), equivalent( T, W ) ) ), V0 ) ) ) ] )
% 0.86/1.23 , 1, clause( 10, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.23 ), equivalent( Z, Y ) ), equivalent( equivalent( X, T ), equivalent( Z,
% 0.86/1.23 T ) ) ) ) ] )
% 0.86/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, X ),
% 0.86/1.23 :=( U, U ), :=( W, Z ), :=( V0, equivalent( equivalent( equivalent(
% 0.86/1.23 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent(
% 0.86/1.24 equivalent( X, U ), equivalent( Z, U ) ), T ) ) )] ), substitution( 1, [
% 0.86/1.24 :=( X, equivalent( equivalent( X, Y ), equivalent( Z, Y ) ) ), :=( Y,
% 0.86/1.24 equivalent( X, Z ) ), :=( Z, equivalent( equivalent( X, U ), equivalent(
% 0.86/1.24 Z, U ) ) ), :=( T, T )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 12, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent(
% 0.86/1.24 equivalent( X, U ), equivalent( Z, U ) ), T ) ) ) ] )
% 0.86/1.24 , clause( 8173, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent(
% 0.86/1.24 equivalent( X, U ), equivalent( Z, U ) ), T ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8174, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.86/1.24 equivalent( X, equivalent( equivalent( equivalent( Z, T ), equivalent( U
% 0.86/1.24 , T ) ), equivalent( Z, U ) ) ), Y ) ) ) ] )
% 0.86/1.24 , clause( 3, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( X, equivalent( X, equivalent( equivalent( equivalent( Y, Z )
% 0.86/1.24 , equivalent( T, Z ) ), equivalent( Y, T ) ) ) ), U ) ) ) ] )
% 0.86/1.24 , 1, clause( 10, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.24 ), equivalent( Z, Y ) ), equivalent( equivalent( X, T ), equivalent( Z,
% 0.86/1.24 T ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( equivalent(
% 0.86/1.24 equivalent( Z, T ), equivalent( U, T ) ), equivalent( Z, U ) ) ) ), :=( Y
% 0.86/1.24 , Z ), :=( Z, T ), :=( T, U ), :=( U, equivalent( equivalent( X, Y ),
% 0.86/1.24 equivalent( equivalent( X, equivalent( equivalent( equivalent( Z, T ),
% 0.86/1.24 equivalent( U, T ) ), equivalent( Z, U ) ) ), Y ) ) )] ), substitution( 1
% 0.86/1.24 , [ :=( X, X ), :=( Y, equivalent( equivalent( equivalent( Z, T ),
% 0.86/1.24 equivalent( U, T ) ), equivalent( Z, U ) ) ), :=( Z, equivalent( X,
% 0.86/1.24 equivalent( equivalent( equivalent( Z, T ), equivalent( U, T ) ),
% 0.86/1.24 equivalent( Z, U ) ) ) ), :=( T, Y )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 13, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.86/1.24 equivalent( X, equivalent( equivalent( equivalent( Z, T ), equivalent( U
% 0.86/1.24 , T ) ), equivalent( Z, U ) ) ), Y ) ) ) ] )
% 0.86/1.24 , clause( 8174, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.86/1.24 equivalent( equivalent( X, equivalent( equivalent( equivalent( Z, T ),
% 0.86/1.24 equivalent( U, T ) ), equivalent( Z, U ) ) ), Y ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8176, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( equivalent( X, T )
% 0.86/1.24 , equivalent( Z, T ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.86/1.24 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.86/1.24 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.24 , 2, clause( 10, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.24 ), equivalent( Z, Y ) ), equivalent( equivalent( X, T ), equivalent( Z,
% 0.86/1.24 T ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.24 equivalent( Z, Y ) ), equivalent( equivalent( X, T ), equivalent( Z, T )
% 0.86/1.24 ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z,
% 0.86/1.24 Z ), :=( T, T )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 14, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.86/1.24 equivalent( equivalent( X, T ), equivalent( Z, T ) ) ), U ) ) ) ] )
% 0.86/1.24 , clause( 8176, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( equivalent( X, T )
% 0.86/1.24 , equivalent( Z, T ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8177, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( X, Y
% 0.86/1.24 ), equivalent( equivalent( equivalent( equivalent( Z, T ), equivalent( U
% 0.86/1.24 , T ) ), equivalent( Z, U ) ), Y ) ) ) ) ] )
% 0.86/1.24 , clause( 6, [ 'is_a_theorem'( V1 ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( X, equivalent( X, equivalent( equivalent(
% 0.86/1.24 equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T ) ) ) ),
% 0.86/1.24 equivalent( equivalent( equivalent( U, W ), equivalent( V0, W ) ),
% 0.86/1.24 equivalent( U, V0 ) ) ), V1 ) ) ) ] )
% 0.86/1.24 , 1, clause( 5, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.24 ), equivalent( Z, Y ) ), equivalent( X, Z ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, T ), :=( T, U ),
% 0.86/1.24 :=( U, X ), :=( W, Y ), :=( V0, equivalent( equivalent( equivalent( Z, T
% 0.86/1.24 ), equivalent( U, T ) ), equivalent( Z, U ) ) ), :=( V1, equivalent( X,
% 0.86/1.24 equivalent( equivalent( X, Y ), equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( Z, T ), equivalent( U, T ) ), equivalent( Z, U ) ), Y ) ) ) )] )
% 0.86/1.24 , substitution( 1, [ :=( X, X ), :=( Y, equivalent( X, equivalent(
% 0.86/1.24 equivalent( equivalent( Z, T ), equivalent( U, T ) ), equivalent( Z, U )
% 0.86/1.24 ) ) ), :=( Z, equivalent( equivalent( X, Y ), equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( Z, T ), equivalent( U, T ) ), equivalent( Z, U )
% 0.86/1.24 ), Y ) ) )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 16, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( X, Y )
% 0.86/1.24 , equivalent( equivalent( equivalent( equivalent( Z, T ), equivalent( U,
% 0.86/1.24 T ) ), equivalent( Z, U ) ), Y ) ) ) ) ] )
% 0.86/1.24 , clause( 8177, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( X
% 0.86/1.24 , Y ), equivalent( equivalent( equivalent( equivalent( Z, T ), equivalent(
% 0.86/1.24 U, T ) ), equivalent( Z, U ) ), Y ) ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8179, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent(
% 0.86/1.24 equivalent( equivalent( X, U ), equivalent( Z, U ) ), T ) ), W ) ) ),
% 0.86/1.24 'is_a_theorem'( W ) ] )
% 0.86/1.24 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.86/1.24 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.24 , 2, clause( 12, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent(
% 0.86/1.24 equivalent( X, U ), equivalent( Z, U ) ), T ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent(
% 0.86/1.24 equivalent( X, U ), equivalent( Z, U ) ), T ) ) ), :=( Y, W )] ),
% 0.86/1.24 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 20, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y
% 0.86/1.24 ) ), T ), equivalent( equivalent( equivalent( X, U ), equivalent( Z, U )
% 0.86/1.24 ), T ) ), W ) ) ) ] )
% 0.86/1.24 , clause( 8179, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent(
% 0.86/1.24 equivalent( equivalent( X, U ), equivalent( Z, U ) ), T ) ), W ) ) ),
% 0.86/1.24 'is_a_theorem'( W ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8180, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.86/1.24 X, Y ) ) ) ] )
% 0.86/1.24 , clause( 14, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.86/1.24 equivalent( equivalent( X, T ), equivalent( Z, T ) ) ), U ) ) ) ] )
% 0.86/1.24 , 1, clause( 5, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.24 ), equivalent( Z, Y ) ), equivalent( X, Z ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, Y ),
% 0.86/1.24 :=( U, equivalent( equivalent( X, Y ), equivalent( X, Y ) ) )] ),
% 0.86/1.24 substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, equivalent( Z, Y )
% 0.86/1.24 ), :=( Z, equivalent( X, Y ) )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 32, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( X
% 0.86/1.24 , Y ) ) ) ] )
% 0.86/1.24 , clause( 8180, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.86/1.24 equivalent( X, Y ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.86/1.24 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8182, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.24 ), equivalent( X, Y ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.86/1.24 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.86/1.24 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.24 , 2, clause( 32, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.86/1.24 equivalent( X, Y ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 0.86/1.24 X, Y ) ) ), :=( Y, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 0.86/1.24 ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 35, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 0.86/1.24 , clause( 8182, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.86/1.24 , Y ), equivalent( X, Y ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8183, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 0.86/1.24 , clause( 35, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 0.86/1.24 , 1, clause( 5, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.24 ), equivalent( Z, Y ) ), equivalent( X, Z ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, equivalent( X, X ) )] )
% 0.86/1.24 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, X )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 38, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 0.86/1.24 , clause( 8183, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8185, [ ~( 'is_a_theorem'( equivalent( equivalent( X, X ), Y ) ) )
% 0.86/1.24 , 'is_a_theorem'( Y ) ] )
% 0.86/1.24 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.86/1.24 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.24 , 2, clause( 38, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( X, X ) ), :=( Y, Y )] ),
% 0.86/1.24 substitution( 1, [ :=( X, X )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 40, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( X, X ), Y ) ) ) ] )
% 0.86/1.24 , clause( 8185, [ ~( 'is_a_theorem'( equivalent( equivalent( X, X ), Y ) )
% 0.86/1.24 ), 'is_a_theorem'( Y ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 0.86/1.24 ), ==>( 1, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8186, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.24 ) ), X ) ) ] )
% 0.86/1.24 , clause( 40, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( X, X ), Y ) ) ) ] )
% 0.86/1.24 , 1, clause( 13, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.86/1.24 equivalent( equivalent( X, equivalent( equivalent( equivalent( Z, T ),
% 0.86/1.24 equivalent( U, T ) ), equivalent( Z, U ) ) ), Y ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, equivalent( equivalent( X,
% 0.86/1.24 equivalent( equivalent( equivalent( Y, Z ), equivalent( T, Z ) ),
% 0.86/1.24 equivalent( Y, T ) ) ), X ) )] ), substitution( 1, [ :=( X, X ), :=( Y, X
% 0.86/1.24 ), :=( Z, Y ), :=( T, Z ), :=( U, T )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 49, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.24 ) ), X ) ) ] )
% 0.86/1.24 , clause( 8186, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.24 ) ), X ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8187, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, X )
% 0.86/1.24 , Y ), equivalent( equivalent( equivalent( equivalent( Z, T ), equivalent(
% 0.86/1.24 U, T ) ), equivalent( Z, U ) ), Y ) ) ) ] )
% 0.86/1.24 , clause( 40, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( X, X ), Y ) ) ) ] )
% 0.86/1.24 , 1, clause( 16, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( X
% 0.86/1.24 , Y ), equivalent( equivalent( equivalent( equivalent( Z, T ), equivalent(
% 0.86/1.24 U, T ) ), equivalent( Z, U ) ), Y ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, equivalent( equivalent(
% 0.86/1.24 equivalent( X, X ), Y ), equivalent( equivalent( equivalent( equivalent(
% 0.86/1.24 Z, T ), equivalent( U, T ) ), equivalent( Z, U ) ), Y ) ) )] ),
% 0.86/1.24 substitution( 1, [ :=( X, equivalent( X, X ) ), :=( Y, Y ), :=( Z, Z ),
% 0.86/1.24 :=( T, T ), :=( U, U )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 50, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, X ), Y
% 0.86/1.24 ), equivalent( equivalent( equivalent( equivalent( Z, T ), equivalent( U
% 0.86/1.24 , T ) ), equivalent( Z, U ) ), Y ) ) ) ] )
% 0.86/1.24 , clause( 8187, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, X
% 0.86/1.24 ), Y ), equivalent( equivalent( equivalent( equivalent( Z, T ),
% 0.86/1.24 equivalent( U, T ) ), equivalent( Z, U ) ), Y ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8188, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent( X
% 0.86/1.24 , Z ), T ) ) ) ] )
% 0.86/1.24 , clause( 7, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.86/1.24 equivalent( X, Z ) ), T ) ) ) ] )
% 0.86/1.24 , 1, clause( 49, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.24 ) ), X ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 0.86/1.24 Z, Y ) ) ), :=( Y, T ), :=( Z, equivalent( X, Z ) ), :=( T, equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), T ),
% 0.86/1.24 equivalent( equivalent( X, Z ), T ) ) )] ), substitution( 1, [ :=( X,
% 0.86/1.24 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y
% 0.86/1.24 ) ), T ), equivalent( equivalent( X, Z ), T ) ) ), :=( Y, X ), :=( Z, Y
% 0.86/1.24 ), :=( T, Z )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 53, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent( X
% 0.86/1.24 , Z ), T ) ) ) ] )
% 0.86/1.24 , clause( 8188, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent( X
% 0.86/1.24 , Z ), T ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8190, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 equivalent( equivalent( equivalent( Y, Z ), equivalent( T, Z ) ),
% 0.86/1.24 equivalent( Y, T ) ) ), X ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.86/1.24 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.86/1.24 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.24 , 2, clause( 49, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.24 ) ), X ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.24 ) ), X ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 0.86/1.24 :=( Z, Z ), :=( T, T )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 54, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( X, equivalent( equivalent( equivalent( Y, Z ),
% 0.86/1.24 equivalent( T, Z ) ), equivalent( Y, T ) ) ), X ), U ) ) ) ] )
% 0.86/1.24 , clause( 8190, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.86/1.24 , equivalent( equivalent( equivalent( Y, Z ), equivalent( T, Z ) ),
% 0.86/1.24 equivalent( Y, T ) ) ), X ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8191, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.86/1.24 equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.86/1.24 , clause( 40, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( X, X ), Y ) ) ) ] )
% 0.86/1.24 , 1, clause( 53, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent( X
% 0.86/1.24 , Z ), T ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Z ), equivalent(
% 0.86/1.24 Y, Z ) ) ), :=( Y, equivalent( equivalent( X, Y ), equivalent( equivalent(
% 0.86/1.24 X, Z ), equivalent( Y, Z ) ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y
% 0.86/1.24 , Z ), :=( Z, Y ), :=( T, equivalent( equivalent( X, Z ), equivalent( Y,
% 0.86/1.24 Z ) ) )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 55, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.86/1.24 equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.86/1.24 , clause( 8191, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.86/1.24 equivalent( equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8193, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.24 ), equivalent( equivalent( X, Z ), equivalent( Y, Z ) ) ), T ) ) ),
% 0.86/1.24 'is_a_theorem'( T ) ] )
% 0.86/1.24 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.86/1.24 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.24 , 2, clause( 55, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.86/1.24 equivalent( equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 0.86/1.24 equivalent( X, Z ), equivalent( Y, Z ) ) ) ), :=( Y, T )] ),
% 0.86/1.24 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 59, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.86/1.24 equivalent( Y, Z ) ) ), T ) ) ) ] )
% 0.86/1.24 , clause( 8193, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.86/1.24 , Y ), equivalent( equivalent( X, Z ), equivalent( Y, Z ) ) ), T ) ) ),
% 0.86/1.24 'is_a_theorem'( T ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8194, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.86/1.24 , Z ), equivalent( equivalent( equivalent( X, T ), equivalent( Y, T ) ),
% 0.86/1.24 Z ) ) ) ] )
% 0.86/1.24 , clause( 59, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.86/1.24 equivalent( Y, Z ) ) ), T ) ) ) ] )
% 0.86/1.24 , 1, clause( 55, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.86/1.24 equivalent( equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T,
% 0.86/1.24 equivalent( equivalent( equivalent( X, Y ), Z ), equivalent( equivalent(
% 0.86/1.24 equivalent( X, T ), equivalent( Y, T ) ), Z ) ) )] ), substitution( 1, [
% 0.86/1.24 :=( X, equivalent( X, Y ) ), :=( Y, equivalent( equivalent( X, T ),
% 0.86/1.24 equivalent( Y, T ) ) ), :=( Z, Z )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 60, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), Z
% 0.86/1.24 ), equivalent( equivalent( equivalent( X, T ), equivalent( Y, T ) ), Z )
% 0.86/1.24 ) ) ] )
% 0.86/1.24 , clause( 8194, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.24 ), Z ), equivalent( equivalent( equivalent( X, T ), equivalent( Y, T ) )
% 0.86/1.24 , Z ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8195, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.86/1.24 equivalent( equivalent( X, Z ), T ), equivalent( equivalent( Y, Z ), T )
% 0.86/1.24 ) ) ) ] )
% 0.86/1.24 , clause( 59, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.86/1.24 equivalent( Y, Z ) ) ), T ) ) ) ] )
% 0.86/1.24 , 1, clause( 53, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent( X
% 0.86/1.24 , Z ), T ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( X, Z ) ), :=( Y, equivalent( Y,
% 0.86/1.24 Z ) ), :=( Z, T ), :=( T, equivalent( equivalent( X, Y ), equivalent(
% 0.86/1.24 equivalent( equivalent( X, Z ), T ), equivalent( equivalent( Y, Z ), T )
% 0.86/1.24 ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T,
% 0.86/1.24 equivalent( equivalent( equivalent( X, Z ), T ), equivalent( equivalent(
% 0.86/1.24 Y, Z ), T ) ) )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 61, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.86/1.24 equivalent( equivalent( X, Z ), T ), equivalent( equivalent( Y, Z ), T )
% 0.86/1.24 ) ) ) ] )
% 0.86/1.24 , clause( 8195, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.86/1.24 equivalent( equivalent( equivalent( X, Z ), T ), equivalent( equivalent(
% 0.86/1.24 Y, Z ), T ) ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8196, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z ) ),
% 0.86/1.24 equivalent( X, T ) ) ) ] )
% 0.86/1.24 , clause( 7, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.86/1.24 equivalent( X, Z ) ), T ) ) ) ] )
% 0.86/1.24 , 1, clause( 60, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.24 ), Z ), equivalent( equivalent( equivalent( X, T ), equivalent( Y, T ) )
% 0.86/1.24 , Z ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T,
% 0.86/1.24 equivalent( equivalent( equivalent( equivalent( X, Y ), Z ), equivalent(
% 0.86/1.24 equivalent( T, Y ), Z ) ), equivalent( X, T ) ) )] ), substitution( 1, [
% 0.86/1.24 :=( X, equivalent( X, Y ) ), :=( Y, equivalent( T, Y ) ), :=( Z,
% 0.86/1.24 equivalent( X, T ) ), :=( T, Z )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 69, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z ) ),
% 0.86/1.24 equivalent( X, T ) ) ) ] )
% 0.86/1.24 , clause( 8196, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z ) ),
% 0.86/1.24 equivalent( X, T ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8198, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z )
% 0.86/1.24 ), equivalent( X, T ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.86/1.24 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.86/1.24 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.24 , 2, clause( 69, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z ) ),
% 0.86/1.24 equivalent( X, T ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z ) ),
% 0.86/1.24 equivalent( X, T ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ),
% 0.86/1.24 :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 73, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( equivalent( X, Y ), Z ), equivalent(
% 0.86/1.24 equivalent( T, Y ), Z ) ), equivalent( X, T ) ), U ) ) ) ] )
% 0.86/1.24 , clause( 8198, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z )
% 0.86/1.24 ), equivalent( X, T ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8199, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), T ), U ),
% 0.86/1.24 equivalent( equivalent( equivalent( X, Z ), T ), U ) ) ) ] )
% 0.86/1.24 , clause( 7, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.86/1.24 equivalent( X, Z ) ), T ) ) ) ] )
% 0.86/1.24 , 1, clause( 61, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.86/1.24 equivalent( equivalent( equivalent( X, Z ), T ), equivalent( equivalent(
% 0.86/1.24 Y, Z ), T ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 0.86/1.24 equivalent( equivalent( equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.24 equivalent( Z, Y ) ), T ), U ), equivalent( equivalent( equivalent( X, Z
% 0.86/1.24 ), T ), U ) ) )] ), substitution( 1, [ :=( X, equivalent( equivalent( X
% 0.86/1.24 , Y ), equivalent( Z, Y ) ) ), :=( Y, equivalent( X, Z ) ), :=( Z, T ),
% 0.86/1.24 :=( T, U )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 79, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), T ), U ),
% 0.86/1.24 equivalent( equivalent( equivalent( X, Z ), T ), U ) ) ) ] )
% 0.86/1.24 , clause( 8199, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), T ), U ),
% 0.86/1.24 equivalent( equivalent( equivalent( X, Z ), T ), U ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8200, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.86/1.24 , Z ), equivalent( equivalent( equivalent( X, T ), equivalent( U, T ) ),
% 0.86/1.24 equivalent( Z, equivalent( U, Y ) ) ) ) ) ] )
% 0.86/1.24 , clause( 20, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y
% 0.86/1.24 ) ), T ), equivalent( equivalent( equivalent( X, U ), equivalent( Z, U )
% 0.86/1.24 ), T ) ), W ) ) ) ] )
% 0.86/1.24 , 1, clause( 53, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent( X
% 0.86/1.24 , Z ), T ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, U ), :=( T,
% 0.86/1.24 equivalent( Z, equivalent( U, Y ) ) ), :=( U, T ), :=( W, equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( equivalent(
% 0.86/1.24 X, T ), equivalent( U, T ) ), equivalent( Z, equivalent( U, Y ) ) ) ) )] )
% 0.86/1.24 , substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, equivalent( U, Y
% 0.86/1.24 ) ), :=( Z, Z ), :=( T, equivalent( equivalent( equivalent( X, T ),
% 0.86/1.24 equivalent( U, T ) ), equivalent( Z, equivalent( U, Y ) ) ) )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 105, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.24 Z ), equivalent( equivalent( equivalent( X, T ), equivalent( U, T ) ),
% 0.86/1.24 equivalent( Z, equivalent( U, Y ) ) ) ) ) ] )
% 0.86/1.24 , clause( 8200, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.24 ), Z ), equivalent( equivalent( equivalent( X, T ), equivalent( U, T ) )
% 0.86/1.24 , equivalent( Z, equivalent( U, Y ) ) ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8201, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), Z ), equivalent( T, Z ) ), equivalent( equivalent( X
% 0.86/1.24 , U ), equivalent( T, equivalent( U, Y ) ) ) ) ) ] )
% 0.86/1.24 , clause( 7, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.86/1.24 equivalent( X, Z ) ), T ) ) ) ] )
% 0.86/1.24 , 1, clause( 105, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 Y ), Z ), equivalent( equivalent( equivalent( X, T ), equivalent( U, T )
% 0.86/1.24 ), equivalent( Z, equivalent( U, Y ) ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, U ), :=( T,
% 0.86/1.24 equivalent( equivalent( equivalent( equivalent( X, Y ), Z ), equivalent(
% 0.86/1.24 T, Z ) ), equivalent( equivalent( X, U ), equivalent( T, equivalent( U, Y
% 0.86/1.24 ) ) ) ) )] ), substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y,
% 0.86/1.24 equivalent( U, Y ) ), :=( Z, equivalent( X, U ) ), :=( T, Z ), :=( U, T )] )
% 0.86/1.24 ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 114, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), Z ), equivalent( T, Z ) ), equivalent( equivalent( X
% 0.86/1.24 , U ), equivalent( T, equivalent( U, Y ) ) ) ) ) ] )
% 0.86/1.24 , clause( 8201, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), Z ), equivalent( T, Z ) ), equivalent( equivalent( X
% 0.86/1.24 , U ), equivalent( T, equivalent( U, Y ) ) ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8202, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.86/1.24 , equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent(
% 0.86/1.24 equivalent( X, T ), U ), equivalent( Z, U ) ) ) ) ] )
% 0.86/1.24 , clause( 14, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.86/1.24 equivalent( equivalent( X, T ), equivalent( Z, T ) ) ), U ) ) ) ] )
% 0.86/1.24 , 1, clause( 79, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), T ), U ),
% 0.86/1.24 equivalent( equivalent( equivalent( X, Z ), T ), U ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( X, T ) ), :=( Y, equivalent( Y,
% 0.86/1.24 T ) ), :=( Z, Z ), :=( T, U ), :=( U, equivalent( equivalent( equivalent(
% 0.86/1.24 X, Y ), equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent(
% 0.86/1.24 equivalent( X, T ), U ), equivalent( Z, U ) ) ) )] ), substitution( 1, [
% 0.86/1.24 :=( X, X ), :=( Y, T ), :=( Z, Y ), :=( T, equivalent( Z, equivalent( Y,
% 0.86/1.24 T ) ) ), :=( U, equivalent( equivalent( equivalent( X, T ), U ),
% 0.86/1.24 equivalent( Z, U ) ) )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 139, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.24 equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent( equivalent(
% 0.86/1.24 X, T ), U ), equivalent( Z, U ) ) ) ) ] )
% 0.86/1.24 , clause( 8202, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.24 ), equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent(
% 0.86/1.24 equivalent( X, T ), U ), equivalent( Z, U ) ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8203, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.86/1.24 , equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent( X, T ),
% 0.86/1.24 Z ) ) ) ] )
% 0.86/1.24 , clause( 7, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.86/1.24 equivalent( X, Z ) ), T ) ) ) ] )
% 0.86/1.24 , 1, clause( 79, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), T ), U ),
% 0.86/1.24 equivalent( equivalent( equivalent( X, Z ), T ), U ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( X, T ) ), :=( Y, equivalent( Y,
% 0.86/1.24 T ) ), :=( Z, Z ), :=( T, equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.24 equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent( X, T ), Z
% 0.86/1.24 ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, T ), :=( Z, Y ), :=( T,
% 0.86/1.24 equivalent( Z, equivalent( Y, T ) ) ), :=( U, equivalent( equivalent( X,
% 0.86/1.24 T ), Z ) )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 141, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.24 equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent( X, T ), Z
% 0.86/1.24 ) ) ) ] )
% 0.86/1.24 , clause( 8203, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.24 ), equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent( X, T )
% 0.86/1.24 , Z ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8204, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.86/1.24 ) ), equivalent( X, equivalent( equivalent( Y, T ), equivalent( Z, T ) )
% 0.86/1.24 ) ) ) ] )
% 0.86/1.24 , clause( 3, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( X, equivalent( X, equivalent( equivalent( equivalent( Y, Z )
% 0.86/1.24 , equivalent( T, Z ) ), equivalent( Y, T ) ) ) ), U ) ) ) ] )
% 0.86/1.24 , 1, clause( 141, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 Y ), equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent( X, T
% 0.86/1.24 ), Z ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( equivalent( Y, T
% 0.86/1.24 ), equivalent( Z, T ) ) ) ), :=( Y, Y ), :=( Z, T ), :=( T, Z ), :=( U,
% 0.86/1.24 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( X,
% 0.86/1.24 equivalent( equivalent( Y, T ), equivalent( Z, T ) ) ) ) )] ),
% 0.86/1.24 substitution( 1, [ :=( X, X ), :=( Y, equivalent( equivalent( Y, T ),
% 0.86/1.24 equivalent( Z, T ) ) ), :=( Z, equivalent( X, equivalent( equivalent( Y,
% 0.86/1.24 T ), equivalent( Z, T ) ) ) ), :=( T, equivalent( Y, Z ) )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 145, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.86/1.24 ) ), equivalent( X, equivalent( equivalent( Y, T ), equivalent( Z, T ) )
% 0.86/1.24 ) ) ) ] )
% 0.86/1.24 , clause( 8204, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.86/1.24 , Z ) ), equivalent( X, equivalent( equivalent( Y, T ), equivalent( Z, T
% 0.86/1.24 ) ) ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8206, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 equivalent( Y, Z ) ), equivalent( X, equivalent( equivalent( Y, T ),
% 0.86/1.24 equivalent( Z, T ) ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.86/1.24 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.86/1.24 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.24 , 2, clause( 145, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 Y, Z ) ), equivalent( X, equivalent( equivalent( Y, T ), equivalent( Z, T
% 0.86/1.24 ) ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, equivalent( Y, Z
% 0.86/1.24 ) ), equivalent( X, equivalent( equivalent( Y, T ), equivalent( Z, T ) )
% 0.86/1.24 ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z,
% 0.86/1.24 Z ), :=( T, T )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 150, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( X,
% 0.86/1.24 equivalent( equivalent( Y, T ), equivalent( Z, T ) ) ) ), U ) ) ) ] )
% 0.86/1.24 , clause( 8206, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.86/1.24 , equivalent( Y, Z ) ), equivalent( X, equivalent( equivalent( Y, T ),
% 0.86/1.24 equivalent( Z, T ) ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8207, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 equivalent( Y, Z ) ), T ), equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( Y, U ), equivalent( Z, U ) ) ), T ) ) ) ] )
% 0.86/1.24 , clause( 3, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( X, equivalent( X, equivalent( equivalent( equivalent( Y, Z )
% 0.86/1.24 , equivalent( T, Z ) ), equivalent( Y, T ) ) ) ), U ) ) ) ] )
% 0.86/1.24 , 1, clause( 139, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 Y ), equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent(
% 0.86/1.24 equivalent( X, T ), U ), equivalent( Z, U ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( equivalent( Y, U
% 0.86/1.24 ), equivalent( Z, U ) ) ) ), :=( Y, Y ), :=( Z, U ), :=( T, Z ), :=( U,
% 0.86/1.24 equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ), T ),
% 0.86/1.24 equivalent( equivalent( X, equivalent( equivalent( Y, U ), equivalent( Z
% 0.86/1.24 , U ) ) ), T ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, equivalent(
% 0.86/1.24 equivalent( Y, U ), equivalent( Z, U ) ) ), :=( Z, equivalent( X,
% 0.86/1.24 equivalent( equivalent( Y, U ), equivalent( Z, U ) ) ) ), :=( T,
% 0.86/1.24 equivalent( Y, Z ) ), :=( U, T )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 159, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 equivalent( Y, Z ) ), T ), equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( Y, U ), equivalent( Z, U ) ) ), T ) ) ) ] )
% 0.86/1.24 , clause( 8207, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 equivalent( Y, Z ) ), T ), equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( Y, U ), equivalent( Z, U ) ) ), T ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8208, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( equivalent( X, U
% 0.86/1.24 ), equivalent( equivalent( Y, T ), U ) ) ) ) ] )
% 0.86/1.24 , clause( 59, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.86/1.24 equivalent( Y, Z ) ) ), T ) ) ) ] )
% 0.86/1.24 , 1, clause( 159, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 equivalent( Y, Z ) ), T ), equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( Y, U ), equivalent( Z, U ) ) ), T ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, equivalent( Y, T ) ), :=( Z, U )
% 0.86/1.24 , :=( T, equivalent( equivalent( X, equivalent( equivalent( Y, Z ),
% 0.86/1.24 equivalent( T, Z ) ) ), equivalent( equivalent( X, U ), equivalent(
% 0.86/1.24 equivalent( Y, T ), U ) ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y
% 0.86/1.24 ), :=( Z, T ), :=( T, equivalent( equivalent( X, U ), equivalent(
% 0.86/1.24 equivalent( Y, T ), U ) ) ), :=( U, Z )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 162, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( equivalent( X, U
% 0.86/1.24 ), equivalent( equivalent( Y, T ), U ) ) ) ) ] )
% 0.86/1.24 , clause( 8208, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( equivalent( X, U
% 0.86/1.24 ), equivalent( equivalent( Y, T ), U ) ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8209, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z )
% 0.86/1.24 ), U ), equivalent( equivalent( X, T ), U ) ) ) ] )
% 0.86/1.24 , clause( 7, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.86/1.24 equivalent( X, Z ) ), T ) ) ) ] )
% 0.86/1.24 , 1, clause( 162, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( equivalent( X, U
% 0.86/1.24 ), equivalent( equivalent( Y, T ), U ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( X, Y ) ), :=( Y, Z ), :=( Z,
% 0.86/1.24 equivalent( T, Y ) ), :=( T, equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z )
% 0.86/1.24 ), U ), equivalent( equivalent( X, T ), U ) ) )] ), substitution( 1, [
% 0.86/1.24 :=( X, equivalent( equivalent( equivalent( X, Y ), Z ), equivalent(
% 0.86/1.24 equivalent( T, Y ), Z ) ) ), :=( Y, X ), :=( Z, Y ), :=( T, T ), :=( U, U
% 0.86/1.24 )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 176, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z )
% 0.86/1.24 ), U ), equivalent( equivalent( X, T ), U ) ) ) ] )
% 0.86/1.24 , clause( 8209, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z )
% 0.86/1.24 ), U ), equivalent( equivalent( X, T ), U ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8210, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z ) ),
% 0.86/1.24 equivalent( T, T ) ) ) ] )
% 0.86/1.24 , clause( 40, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( X, X ), Y ) ) ) ] )
% 0.86/1.24 , 1, clause( 50, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, X
% 0.86/1.24 ), Y ), equivalent( equivalent( equivalent( equivalent( Z, T ),
% 0.86/1.24 equivalent( U, T ) ), equivalent( Z, U ) ), Y ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( T, T ) ), :=( Y, equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.86/1.24 equivalent( X, Z ) ), equivalent( T, T ) ) )] ), substitution( 1, [ :=( X
% 0.86/1.24 , T ), :=( Y, equivalent( T, T ) ), :=( Z, X ), :=( T, Y ), :=( U, Z )] )
% 0.86/1.24 ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 239, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z ) ),
% 0.86/1.24 equivalent( T, T ) ) ) ] )
% 0.86/1.24 , clause( 8210, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z ) ),
% 0.86/1.24 equivalent( T, T ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8212, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z )
% 0.86/1.24 ), equivalent( T, T ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.86/1.24 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.86/1.24 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.24 , 2, clause( 239, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z ) ),
% 0.86/1.24 equivalent( T, T ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z ) ),
% 0.86/1.24 equivalent( T, T ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ),
% 0.86/1.24 :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 242, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y
% 0.86/1.24 ) ), equivalent( X, Z ) ), equivalent( T, T ) ), U ) ) ) ] )
% 0.86/1.24 , clause( 8212, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z )
% 0.86/1.24 ), equivalent( T, T ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8213, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.86/1.24 , Z ), equivalent( equivalent( X, T ), equivalent( Z, equivalent( T, Y )
% 0.86/1.24 ) ) ) ) ] )
% 0.86/1.24 , clause( 242, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y
% 0.86/1.24 ) ), equivalent( X, Z ) ), equivalent( T, T ) ), U ) ) ) ] )
% 0.86/1.24 , 1, clause( 114, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, Y ), Z ), equivalent( T, Z ) ), equivalent( equivalent( X
% 0.86/1.24 , U ), equivalent( T, equivalent( U, Y ) ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T,
% 0.86/1.24 equivalent( X, T ) ), :=( U, equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.24 Z ), equivalent( equivalent( X, T ), equivalent( Z, equivalent( T, Y ) )
% 0.86/1.24 ) ) )] ), substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y,
% 0.86/1.24 equivalent( T, Y ) ), :=( Z, equivalent( X, T ) ), :=( T, equivalent( X,
% 0.86/1.24 T ) ), :=( U, Z )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 265, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.86/1.24 Z ), equivalent( equivalent( X, T ), equivalent( Z, equivalent( T, Y ) )
% 0.86/1.24 ) ) ) ] )
% 0.86/1.24 , clause( 8213, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.86/1.24 ), Z ), equivalent( equivalent( X, T ), equivalent( Z, equivalent( T, Y
% 0.86/1.24 ) ) ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8214, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.86/1.24 ) ), equivalent( equivalent( X, equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.24 ) ) ) ] )
% 0.86/1.24 , clause( 54, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( X, equivalent( equivalent( equivalent( Y, Z ),
% 0.86/1.24 equivalent( T, Z ) ), equivalent( Y, T ) ) ), X ), U ) ) ) ] )
% 0.86/1.24 , 1, clause( 176, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z )
% 0.86/1.24 ), U ), equivalent( equivalent( X, T ), U ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, equivalent( T, Z
% 0.86/1.24 ) ), equivalent( Y, T ) ) ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U,
% 0.86/1.24 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( equivalent(
% 0.86/1.24 X, equivalent( T, Z ) ), equivalent( Y, T ) ) ) )] ), substitution( 1, [
% 0.86/1.24 :=( X, X ), :=( Y, equivalent( T, Z ) ), :=( Z, equivalent( Y, T ) ),
% 0.86/1.24 :=( T, equivalent( Y, Z ) ), :=( U, equivalent( equivalent( X, equivalent(
% 0.86/1.24 T, Z ) ), equivalent( Y, T ) ) )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 707, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.86/1.24 ) ), equivalent( equivalent( X, equivalent( T, Z ) ), equivalent( Y, T )
% 0.86/1.24 ) ) ) ] )
% 0.86/1.24 , clause( 8214, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.86/1.24 , Z ) ), equivalent( equivalent( X, equivalent( T, Z ) ), equivalent( Y,
% 0.86/1.24 T ) ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8215, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z )
% 0.86/1.24 ), equivalent( U, T ) ), equivalent( X, U ) ) ) ] )
% 0.86/1.24 , clause( 73, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( equivalent( X, Y ), Z ), equivalent(
% 0.86/1.24 equivalent( T, Y ), Z ) ), equivalent( X, T ) ), U ) ) ) ] )
% 0.86/1.24 , 1, clause( 707, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 Y, Z ) ), equivalent( equivalent( X, equivalent( T, Z ) ), equivalent( Y
% 0.86/1.24 , T ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 0.86/1.24 :=( U, equivalent( equivalent( equivalent( equivalent( equivalent( X, Y )
% 0.86/1.24 , Z ), equivalent( equivalent( T, Y ), Z ) ), equivalent( U, T ) ),
% 0.86/1.24 equivalent( X, U ) ) )] ), substitution( 1, [ :=( X, equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z )
% 0.86/1.24 ) ), :=( Y, X ), :=( Z, T ), :=( T, U )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 972, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z )
% 0.86/1.24 ), equivalent( U, T ) ), equivalent( X, U ) ) ) ] )
% 0.86/1.24 , clause( 8215, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z )
% 0.86/1.24 ), equivalent( U, T ) ), equivalent( X, U ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.86/1.24 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8216, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent( Y
% 0.86/1.24 , Y ) ) ) ) ] )
% 0.86/1.24 , clause( 54, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( X, equivalent( equivalent( equivalent( Y, Z ),
% 0.86/1.24 equivalent( T, Z ) ), equivalent( Y, T ) ) ), X ), U ) ) ) ] )
% 0.86/1.24 , 1, clause( 972, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z )
% 0.86/1.24 ), equivalent( U, T ) ), equivalent( X, U ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, equivalent( Y, Y
% 0.86/1.24 ) ), equivalent( Z, Y ) ) ), :=( Y, Z ), :=( Z, Y ), :=( T, Y ), :=( U,
% 0.86/1.24 equivalent( X, equivalent( X, equivalent( Y, Y ) ) ) )] ), substitution(
% 0.86/1.24 1, [ :=( X, X ), :=( Y, equivalent( Y, Y ) ), :=( Z, equivalent( Z, Y ) )
% 0.86/1.24 , :=( T, equivalent( Z, Y ) ), :=( U, equivalent( X, equivalent( Y, Y ) )
% 0.86/1.24 )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 996, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent( Y
% 0.86/1.24 , Y ) ) ) ) ] )
% 0.86/1.24 , clause( 8216, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.86/1.24 Y, Y ) ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.86/1.24 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8218, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent( X
% 0.86/1.24 , equivalent( Y, Y ) ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.86/1.24 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.86/1.24 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.24 , 2, clause( 996, [ 'is_a_theorem'( equivalent( X, equivalent( X,
% 0.86/1.24 equivalent( Y, Y ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( X, equivalent( Y
% 0.86/1.24 , Y ) ) ) ), :=( Y, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 0.86/1.24 ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 1012, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( X, equivalent( X, equivalent( Y, Y ) ) ), Z ) ) ) ] )
% 0.86/1.24 , clause( 8218, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 X, equivalent( Y, Y ) ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8219, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.86/1.24 equivalent( Z, Z ) ) ), equivalent( X, Y ) ) ) ] )
% 0.86/1.24 , clause( 1012, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( X, equivalent( X, equivalent( Y, Y ) ) ), Z ) ) ) ] )
% 0.86/1.24 , 1, clause( 707, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 Y, Z ) ), equivalent( equivalent( X, equivalent( T, Z ) ), equivalent( Y
% 0.86/1.24 , T ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, equivalent(
% 0.86/1.24 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ), equivalent( X, Y )
% 0.86/1.24 ) )] ), substitution( 1, [ :=( X, X ), :=( Y, X ), :=( Z, equivalent( Z
% 0.86/1.24 , Z ) ), :=( T, Y )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 1031, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.86/1.24 equivalent( Z, Z ) ) ), equivalent( X, Y ) ) ) ] )
% 0.86/1.24 , clause( 8219, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.86/1.24 , equivalent( Z, Z ) ) ), equivalent( X, Y ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8221, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( X, Y ) ), T ) ) ),
% 0.86/1.24 'is_a_theorem'( T ) ] )
% 0.86/1.24 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.86/1.24 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.24 , 2, clause( 1031, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 Y, equivalent( Z, Z ) ) ), equivalent( X, Y ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, equivalent( Y,
% 0.86/1.24 equivalent( Z, Z ) ) ), equivalent( X, Y ) ) ), :=( Y, T )] ),
% 0.86/1.24 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 1139, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 0.86/1.24 equivalent( X, Y ) ), T ) ) ) ] )
% 0.86/1.24 , clause( 8221, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.86/1.24 , equivalent( Y, equivalent( Z, Z ) ) ), equivalent( X, Y ) ), T ) ) ),
% 0.86/1.24 'is_a_theorem'( T ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8222, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( Y, Z ), equivalent( equivalent( T, T ), Z ) ) ), equivalent(
% 0.86/1.24 X, Y ) ) ) ] )
% 0.86/1.24 , clause( 1139, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 0.86/1.24 equivalent( X, Y ) ), T ) ) ) ] )
% 0.86/1.24 , 1, clause( 159, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 equivalent( Y, Z ) ), T ), equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( Y, U ), equivalent( Z, U ) ) ), T ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T,
% 0.86/1.24 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), equivalent(
% 0.86/1.24 equivalent( T, T ), Z ) ) ), equivalent( X, Y ) ) )] ), substitution( 1
% 0.86/1.24 , [ :=( X, X ), :=( Y, Y ), :=( Z, equivalent( T, T ) ), :=( T,
% 0.86/1.24 equivalent( X, Y ) ), :=( U, Z )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 6542, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( Y, Z ), equivalent( equivalent( T, T ), Z ) ) ), equivalent(
% 0.86/1.24 X, Y ) ) ) ] )
% 0.86/1.24 , clause( 8222, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( Y, Z ), equivalent( equivalent( T, T ), Z ) ) ), equivalent(
% 0.86/1.24 X, Y ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8223, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 equivalent( Y, Z ) ), equivalent( Z, Y ) ), X ) ) ] )
% 0.86/1.24 , clause( 150, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( X,
% 0.86/1.24 equivalent( equivalent( Y, T ), equivalent( Z, T ) ) ) ), U ) ) ) ] )
% 0.86/1.24 , 1, clause( 6542, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.86/1.24 equivalent( Y, Z ), equivalent( equivalent( T, T ), Z ) ) ), equivalent(
% 0.86/1.24 X, Y ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( Y, Z ) ) ), :=( Y
% 0.86/1.24 , Z ), :=( Z, Y ), :=( T, Z ), :=( U, equivalent( equivalent( equivalent(
% 0.86/1.24 X, equivalent( Y, Z ) ), equivalent( Z, Y ) ), X ) )] ), substitution( 1
% 0.86/1.24 , [ :=( X, equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( Z
% 0.86/1.24 , Y ) ) ), :=( Y, X ), :=( Z, equivalent( Y, Z ) ), :=( T, Z )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 7227, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 equivalent( Y, Z ) ), equivalent( Z, Y ) ), X ) ) ] )
% 0.86/1.24 , clause( 8223, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 equivalent( Y, Z ) ), equivalent( Z, Y ) ), X ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8225, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, equivalent( Y, Z ) ), equivalent( Z, Y ) ), X ), T ) ) ),
% 0.86/1.24 'is_a_theorem'( T ) ] )
% 0.86/1.24 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.86/1.24 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.86/1.24 , 2, clause( 7227, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.86/1.24 , equivalent( Y, Z ) ), equivalent( Z, Y ) ), X ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X,
% 0.86/1.24 equivalent( Y, Z ) ), equivalent( Z, Y ) ), X ) ), :=( Y, T )] ),
% 0.86/1.24 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 7354, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent(
% 0.86/1.24 Z, Y ) ), X ), T ) ) ) ] )
% 0.86/1.24 , clause( 8225, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.86/1.24 equivalent( X, equivalent( Y, Z ) ), equivalent( Z, Y ) ), X ), T ) ) ),
% 0.86/1.24 'is_a_theorem'( T ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8226, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 equivalent( Y, Z ) ), T ), equivalent( X, equivalent( T, equivalent( Z, Y
% 0.86/1.24 ) ) ) ) ) ] )
% 0.86/1.24 , clause( 7354, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent(
% 0.86/1.24 Z, Y ) ), X ), T ) ) ) ] )
% 0.86/1.24 , 1, clause( 265, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 Y ), Z ), equivalent( equivalent( X, T ), equivalent( Z, equivalent( T, Y
% 0.86/1.24 ) ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 0.86/1.24 equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ), T ),
% 0.86/1.24 equivalent( X, equivalent( T, equivalent( Z, Y ) ) ) ) )] ),
% 0.86/1.24 substitution( 1, [ :=( X, equivalent( X, equivalent( Y, Z ) ) ), :=( Y,
% 0.86/1.24 equivalent( Z, Y ) ), :=( Z, X ), :=( T, T )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 7847, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 equivalent( Y, Z ) ), T ), equivalent( X, equivalent( T, equivalent( Z, Y
% 0.86/1.24 ) ) ) ) ) ] )
% 0.86/1.24 , clause( 8226, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.86/1.24 equivalent( Y, Z ) ), T ), equivalent( X, equivalent( T, equivalent( Z, Y
% 0.86/1.24 ) ) ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8227, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.86/1.24 equivalent( Y, Z ), equivalent( equivalent( Y, T ), equivalent( Z, T ) )
% 0.86/1.24 ) ) ) ) ] )
% 0.86/1.24 , clause( 54, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.86/1.24 equivalent( equivalent( X, equivalent( equivalent( equivalent( Y, Z ),
% 0.86/1.24 equivalent( T, Z ) ), equivalent( Y, T ) ) ), X ), U ) ) ) ] )
% 0.86/1.24 , 1, clause( 7847, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.86/1.24 , equivalent( Y, Z ) ), T ), equivalent( X, equivalent( T, equivalent( Z
% 0.86/1.24 , Y ) ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T, Z ),
% 0.86/1.24 :=( U, equivalent( X, equivalent( X, equivalent( equivalent( Y, Z ),
% 0.86/1.24 equivalent( equivalent( Y, T ), equivalent( Z, T ) ) ) ) ) )] ),
% 0.86/1.24 substitution( 1, [ :=( X, X ), :=( Y, equivalent( equivalent( Y, T ),
% 0.86/1.24 equivalent( Z, T ) ) ), :=( Z, equivalent( Y, Z ) ), :=( T, X )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 7907, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.86/1.24 equivalent( Y, Z ), equivalent( equivalent( Y, T ), equivalent( Z, T ) )
% 0.86/1.24 ) ) ) ) ] )
% 0.86/1.24 , clause( 8227, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.86/1.24 equivalent( Y, Z ), equivalent( equivalent( Y, T ), equivalent( Z, T ) )
% 0.86/1.24 ) ) ) ) ] )
% 0.86/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.86/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 resolution(
% 0.86/1.24 clause( 8228, [] )
% 0.86/1.24 , clause( 2, [ ~( 'is_a_theorem'( equivalent( a, equivalent( a, equivalent(
% 0.86/1.24 equivalent( b, c ), equivalent( equivalent( b, e ), equivalent( c, e ) )
% 0.86/1.24 ) ) ) ) ) ] )
% 0.86/1.24 , 0, clause( 7907, [ 'is_a_theorem'( equivalent( X, equivalent( X,
% 0.86/1.24 equivalent( equivalent( Y, Z ), equivalent( equivalent( Y, T ),
% 0.86/1.24 equivalent( Z, T ) ) ) ) ) ) ] )
% 0.86/1.24 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, b ), :=(
% 0.86/1.24 Z, c ), :=( T, e )] )).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 subsumption(
% 0.86/1.24 clause( 8156, [] )
% 0.86/1.24 , clause( 8228, [] )
% 0.86/1.24 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 end.
% 0.86/1.24
% 0.86/1.24 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.86/1.24
% 0.86/1.24 Memory use:
% 0.86/1.24
% 0.86/1.24 space for terms: 225543
% 0.86/1.24 space for clauses: 945698
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 clauses generated: 21214
% 0.86/1.24 clauses kept: 8157
% 0.86/1.24 clauses selected: 540
% 0.86/1.24 clauses deleted: 16
% 0.86/1.24 clauses inuse deleted: 5
% 0.86/1.24
% 0.86/1.24 subsentry: 13997
% 0.86/1.24 literals s-matched: 13073
% 0.86/1.24 literals matched: 13073
% 0.86/1.24 full subsumption: 0
% 0.86/1.24
% 0.86/1.24 checksum: -1841918027
% 0.86/1.24
% 0.86/1.24
% 0.86/1.24 Bliksem ended
%------------------------------------------------------------------------------