TSTP Solution File: LCL121-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL121-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n008.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 07:50:39 EDT 2022
% Result : Unsatisfiable 0.89s 1.29s
% Output : Refutation 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL121-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Sat Jul 2 16:56:08 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.89/1.29 *** allocated 10000 integers for termspace/termends
% 0.89/1.29 *** allocated 10000 integers for clauses
% 0.89/1.29 *** allocated 10000 integers for justifications
% 0.89/1.29 Bliksem 1.12
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 Automatic Strategy Selection
% 0.89/1.29
% 0.89/1.29 Clauses:
% 0.89/1.29 [
% 0.89/1.29 [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~( 'is_a_theorem'( X ) ),
% 0.89/1.29 'is_a_theorem'( Y ) ],
% 0.89/1.29 [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent( equivalent(
% 0.89/1.29 Y, Z ), equivalent( equivalent( Y, T ), equivalent( Z, T ) ) ) ) ) ) ]
% 0.89/1.29 ,
% 0.89/1.29 [ ~( 'is_a_theorem'( equivalent( a, equivalent( a, equivalent(
% 0.89/1.29 equivalent( b, equivalent( c, c ) ), b ) ) ) ) ) ]
% 0.89/1.29 ] .
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 percentage equality = 0.000000, percentage horn = 1.000000
% 0.89/1.29 This is a near-Horn, non-equality problem
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 Options Used:
% 0.89/1.29
% 0.89/1.29 useres = 1
% 0.89/1.29 useparamod = 0
% 0.89/1.29 useeqrefl = 0
% 0.89/1.29 useeqfact = 0
% 0.89/1.29 usefactor = 1
% 0.89/1.29 usesimpsplitting = 0
% 0.89/1.29 usesimpdemod = 0
% 0.89/1.29 usesimpres = 4
% 0.89/1.29
% 0.89/1.29 resimpinuse = 1000
% 0.89/1.29 resimpclauses = 20000
% 0.89/1.29 substype = standard
% 0.89/1.29 backwardsubs = 1
% 0.89/1.29 selectoldest = 5
% 0.89/1.29
% 0.89/1.29 litorderings [0] = split
% 0.89/1.29 litorderings [1] = liftord
% 0.89/1.29
% 0.89/1.29 termordering = none
% 0.89/1.29
% 0.89/1.29 litapriori = 1
% 0.89/1.29 termapriori = 0
% 0.89/1.29 litaposteriori = 0
% 0.89/1.29 termaposteriori = 0
% 0.89/1.29 demodaposteriori = 0
% 0.89/1.29 ordereqreflfact = 0
% 0.89/1.29
% 0.89/1.29 litselect = negative
% 0.89/1.29
% 0.89/1.29 maxweight = 30000
% 0.89/1.29 maxdepth = 30000
% 0.89/1.29 maxlength = 115
% 0.89/1.29 maxnrvars = 195
% 0.89/1.29 excuselevel = 0
% 0.89/1.29 increasemaxweight = 0
% 0.89/1.29
% 0.89/1.29 maxselected = 10000000
% 0.89/1.29 maxnrclauses = 10000000
% 0.89/1.29
% 0.89/1.29 showgenerated = 0
% 0.89/1.29 showkept = 0
% 0.89/1.29 showselected = 0
% 0.89/1.29 showdeleted = 0
% 0.89/1.29 showresimp = 1
% 0.89/1.29 showstatus = 2000
% 0.89/1.29
% 0.89/1.29 prologoutput = 1
% 0.89/1.29 nrgoals = 5000000
% 0.89/1.29 totalproof = 1
% 0.89/1.29
% 0.89/1.29 Symbols occurring in the translation:
% 0.89/1.29
% 0.89/1.29 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.89/1.29 . [1, 2] (w:1, o:22, a:1, s:1, b:0),
% 0.89/1.29 ! [4, 1] (w:1, o:16, a:1, s:1, b:0),
% 0.89/1.29 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.89/1.29 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.89/1.29 equivalent [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.89/1.29 'is_a_theorem' [42, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.89/1.29 a [45, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.89/1.29 b [46, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.89/1.29 c [47, 0] (w:1, o:15, a:1, s:1, b:0).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 Starting Search:
% 0.89/1.29
% 0.89/1.29 Resimplifying inuse:
% 0.89/1.29 Done
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 Intermediate Status:
% 0.89/1.29 Generated: 4666
% 0.89/1.29 Kept: 2004
% 0.89/1.29 Inuse: 275
% 0.89/1.29 Deleted: 5
% 0.89/1.29 Deletedinuse: 2
% 0.89/1.29
% 0.89/1.29 Resimplifying inuse:
% 0.89/1.29 Done
% 0.89/1.29
% 0.89/1.29 Resimplifying inuse:
% 0.89/1.29 Done
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 Intermediate Status:
% 0.89/1.29 Generated: 9448
% 0.89/1.29 Kept: 4044
% 0.89/1.29 Inuse: 367
% 0.89/1.29 Deleted: 5
% 0.89/1.29 Deletedinuse: 2
% 0.89/1.29
% 0.89/1.29 Resimplifying inuse:
% 0.89/1.29 Done
% 0.89/1.29
% 0.89/1.29 Resimplifying inuse:
% 0.89/1.29 Done
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 Intermediate Status:
% 0.89/1.29 Generated: 14049
% 0.89/1.29 Kept: 6086
% 0.89/1.29 Inuse: 443
% 0.89/1.29 Deleted: 5
% 0.89/1.29 Deletedinuse: 2
% 0.89/1.29
% 0.89/1.29 Resimplifying inuse:
% 0.89/1.29 Done
% 0.89/1.29
% 0.89/1.29 Resimplifying inuse:
% 0.89/1.29 Done
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 Intermediate Status:
% 0.89/1.29 Generated: 18340
% 0.89/1.29 Kept: 8132
% 0.89/1.29 Inuse: 487
% 0.89/1.29 Deleted: 5
% 0.89/1.29 Deletedinuse: 2
% 0.89/1.29
% 0.89/1.29 Resimplifying inuse:
% 0.89/1.29 Done
% 0.89/1.29
% 0.89/1.29 Resimplifying inuse:
% 0.89/1.29 Done
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 Intermediate Status:
% 0.89/1.29 Generated: 22948
% 0.89/1.29 Kept: 10157
% 0.89/1.29 Inuse: 530
% 0.89/1.29 Deleted: 5
% 0.89/1.29 Deletedinuse: 2
% 0.89/1.29
% 0.89/1.29 Resimplifying inuse:
% 0.89/1.29 Done
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 Bliksems!, er is een bewijs:
% 0.89/1.29 % SZS status Unsatisfiable
% 0.89/1.29 % SZS output start Refutation
% 0.89/1.29
% 0.89/1.29 clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.89/1.29 , ~( 'is_a_theorem'( X ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 1, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.89/1.29 equivalent( Y, Z ), equivalent( equivalent( Y, T ), equivalent( Z, T ) )
% 0.89/1.29 ) ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 2, [ ~( 'is_a_theorem'( equivalent( a, equivalent( a, equivalent(
% 0.89/1.29 equivalent( b, equivalent( c, c ) ), b ) ) ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 3, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.89/1.29 X, equivalent( X, equivalent( equivalent( Y, Z ), equivalent( equivalent(
% 0.89/1.29 Y, T ), equivalent( Z, T ) ) ) ) ), U ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( X,
% 0.89/1.29 equivalent( equivalent( Y, Z ), equivalent( equivalent( Y, T ),
% 0.89/1.29 equivalent( Z, T ) ) ) ) ), equivalent( equivalent( U, W ), equivalent(
% 0.89/1.29 equivalent( U, V0 ), equivalent( W, V0 ) ) ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 5, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.89/1.29 equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 6, [ 'is_a_theorem'( V1 ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( X, equivalent( X, equivalent( equivalent( Y, Z )
% 0.89/1.29 , equivalent( equivalent( Y, T ), equivalent( Z, T ) ) ) ) ), equivalent(
% 0.89/1.29 equivalent( U, W ), equivalent( equivalent( U, V0 ), equivalent( W, V0 )
% 0.89/1.29 ) ) ), V1 ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 8, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.89/1.29 equivalent( X, Y ), equivalent( equivalent( X, Z ), equivalent( Y, Z ) )
% 0.89/1.29 ), T ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), Z
% 0.89/1.29 ), equivalent( equivalent( equivalent( X, T ), equivalent( Y, T ) ), Z )
% 0.89/1.29 ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 11, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.89/1.29 equivalent( Z, Y ) ), equivalent( equivalent( X, T ), equivalent( Z, T )
% 0.89/1.29 ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 13, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( equivalent( X, Y ), Z ), equivalent( equivalent(
% 0.89/1.29 equivalent( X, T ), equivalent( Y, T ) ), Z ) ), U ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 14, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.89/1.29 equivalent( equivalent( X, T ), equivalent( Z, T ) ) ), U ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 19, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.29 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), U ), equivalent(
% 0.89/1.29 equivalent( X, equivalent( Y, T ) ), U ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 23, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 0.89/1.29 ), equivalent( equivalent( X, T ), equivalent( equivalent( equivalent( Y
% 0.89/1.29 , U ), equivalent( Z, U ) ), T ) ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 25, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( equivalent( X, equivalent( equivalent( Y, Z ),
% 0.89/1.29 equivalent( T, Z ) ) ), U ), equivalent( equivalent( X, equivalent( Y, T
% 0.89/1.29 ) ), U ) ), W ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 27, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), Z
% 0.89/1.29 ), equivalent( equivalent( equivalent( equivalent( X, T ), U ),
% 0.89/1.29 equivalent( equivalent( Y, T ), U ) ), Z ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 31, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.29 equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z ) ),
% 0.89/1.29 equivalent( equivalent( X, U ), equivalent( T, U ) ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 36, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( X
% 0.89/1.29 , Y ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 43, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 47, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.89/1.29 equivalent( Z, Y ) ), equivalent( X, Z ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 50, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.29 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( X, equivalent( Y
% 0.89/1.29 , T ) ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 51, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.89/1.29 equivalent( X, Z ) ), T ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 57, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), equivalent( T
% 0.89/1.29 , Z ) ) ), equivalent( X, equivalent( Y, T ) ) ), U ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 84, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.29 equivalent( Y, Z ) ), equivalent( T, Y ) ), equivalent( X, equivalent( T
% 0.89/1.29 , Z ) ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 86, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.29 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent( X
% 0.89/1.29 , Z ), T ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 89, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent(
% 0.89/1.29 T, Y ) ), equivalent( X, equivalent( T, Z ) ) ), U ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 90, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.89/1.29 equivalent( equivalent( X, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.89/1.29 ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 95, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.29 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( U
% 0.89/1.29 , T ) ), equivalent( equivalent( X, Z ), U ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 127, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.89/1.29 ) ), equivalent( equivalent( X, equivalent( T, Z ) ), equivalent( Y, T )
% 0.89/1.29 ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 130, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.29 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( T, equivalent( Z, U
% 0.89/1.29 ) ) ), equivalent( equivalent( X, U ), T ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 135, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.29 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( equivalent( X, U
% 0.89/1.29 ), equivalent( equivalent( Y, T ), U ) ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 139, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.29 equivalent( X, Y ), equivalent( Z, equivalent( Y, T ) ) ), U ),
% 0.89/1.29 equivalent( equivalent( equivalent( X, T ), Z ), U ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 167, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.89/1.29 Z ), equivalent( equivalent( equivalent( X, T ), U ), equivalent(
% 0.89/1.29 equivalent( Z, equivalent( T, Y ) ), U ) ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 187, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.29 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 0.89/1.29 , equivalent( Z, equivalent( U, Y ) ) ), T ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 195, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.89/1.29 equivalent( equivalent( Z, T ), equivalent( Y, T ) ) ), equivalent(
% 0.89/1.29 equivalent( X, U ), equivalent( Z, U ) ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 197, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.89/1.29 equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent( equivalent(
% 0.89/1.29 X, T ), U ), equivalent( Z, U ) ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 235, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.29 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( U,
% 0.89/1.29 equivalent( Y, T ) ) ), equivalent( X, U ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 241, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Y
% 0.89/1.29 ) ), X ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 244, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( X, equivalent( Y, Y ) ), X ), Z ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 247, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.29 equivalent( X, equivalent( equivalent( Y, Y ), Z ) ), Z ), T ),
% 0.89/1.29 equivalent( X, T ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 248, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.29 equivalent( X, Y ), equivalent( equivalent( Z, Z ), Y ) ), T ),
% 0.89/1.29 equivalent( X, T ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 892, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( X,
% 0.89/1.29 equivalent( Y, Z ) ), equivalent( Z, Y ) ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 919, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( X, equivalent( equivalent( X, equivalent( Y, Z ) ),
% 0.89/1.29 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 2020, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent( Y
% 0.89/1.29 , equivalent( Y, equivalent( Z, Z ) ) ) ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 2106, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( X, equivalent( X, equivalent( Y, equivalent( Y, equivalent( Z
% 0.89/1.29 , Z ) ) ) ) ), T ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 9704, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.89/1.29 equivalent( Z, equivalent( Z, equivalent( T, T ) ) ) ) ), equivalent( X,
% 0.89/1.29 Y ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 10309, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.89/1.29 equivalent( Y, equivalent( Z, Z ) ), Y ) ) ) ) ] )
% 0.89/1.29 .
% 0.89/1.29 clause( 10376, [] )
% 0.89/1.29 .
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 % SZS output end Refutation
% 0.89/1.29 found a proof!
% 0.89/1.29
% 0.89/1.29 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.89/1.29
% 0.89/1.29 initialclauses(
% 0.89/1.29 [ clause( 10378, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~(
% 0.89/1.29 'is_a_theorem'( X ) ), 'is_a_theorem'( Y ) ] )
% 0.89/1.29 , clause( 10379, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.89/1.29 equivalent( Y, Z ), equivalent( equivalent( Y, T ), equivalent( Z, T ) )
% 0.89/1.29 ) ) ) ) ] )
% 0.89/1.29 , clause( 10380, [ ~( 'is_a_theorem'( equivalent( a, equivalent( a,
% 0.89/1.29 equivalent( equivalent( b, equivalent( c, c ) ), b ) ) ) ) ) ] )
% 0.89/1.29 ] ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 subsumption(
% 0.89/1.29 clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.89/1.29 , ~( 'is_a_theorem'( X ) ) ] )
% 0.89/1.29 , clause( 10378, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~(
% 0.89/1.29 'is_a_theorem'( X ) ), 'is_a_theorem'( Y ) ] )
% 0.89/1.29 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.89/1.29 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 subsumption(
% 0.89/1.29 clause( 1, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.89/1.29 equivalent( Y, Z ), equivalent( equivalent( Y, T ), equivalent( Z, T ) )
% 0.89/1.29 ) ) ) ) ] )
% 0.89/1.29 , clause( 10379, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.89/1.29 equivalent( Y, Z ), equivalent( equivalent( Y, T ), equivalent( Z, T ) )
% 0.89/1.29 ) ) ) ) ] )
% 0.89/1.29 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.89/1.29 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 subsumption(
% 0.89/1.29 clause( 2, [ ~( 'is_a_theorem'( equivalent( a, equivalent( a, equivalent(
% 0.89/1.29 equivalent( b, equivalent( c, c ) ), b ) ) ) ) ) ] )
% 0.89/1.29 , clause( 10380, [ ~( 'is_a_theorem'( equivalent( a, equivalent( a,
% 0.89/1.29 equivalent( equivalent( b, equivalent( c, c ) ), b ) ) ) ) ) ] )
% 0.89/1.29 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 resolution(
% 0.89/1.29 clause( 10382, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.29 X, equivalent( equivalent( Y, Z ), equivalent( equivalent( Y, T ),
% 0.89/1.29 equivalent( Z, T ) ) ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.89/1.29 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.89/1.29 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.89/1.29 , 2, clause( 1, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.89/1.29 equivalent( Y, Z ), equivalent( equivalent( Y, T ), equivalent( Z, T ) )
% 0.89/1.29 ) ) ) ) ] )
% 0.89/1.29 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( X, equivalent(
% 0.89/1.29 equivalent( Y, Z ), equivalent( equivalent( Y, T ), equivalent( Z, T ) )
% 0.89/1.29 ) ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z
% 0.89/1.29 , Z ), :=( T, T )] )).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 subsumption(
% 0.89/1.29 clause( 3, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.89/1.29 X, equivalent( X, equivalent( equivalent( Y, Z ), equivalent( equivalent(
% 0.89/1.29 Y, T ), equivalent( Z, T ) ) ) ) ), U ) ) ) ] )
% 0.89/1.29 , clause( 10382, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.29 X, equivalent( equivalent( Y, Z ), equivalent( equivalent( Y, T ),
% 0.89/1.29 equivalent( Z, T ) ) ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.89/1.29 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.29 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 resolution(
% 0.89/1.29 clause( 10383, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( X,
% 0.89/1.29 equivalent( equivalent( Y, Z ), equivalent( equivalent( Y, T ),
% 0.89/1.29 equivalent( Z, T ) ) ) ) ), equivalent( equivalent( U, W ), equivalent(
% 0.89/1.29 equivalent( U, V0 ), equivalent( W, V0 ) ) ) ) ) ] )
% 0.89/1.29 , clause( 3, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( X, equivalent( X, equivalent( equivalent( Y, Z ), equivalent(
% 0.89/1.29 equivalent( Y, T ), equivalent( Z, T ) ) ) ) ), U ) ) ) ] )
% 0.89/1.29 , 1, clause( 1, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.89/1.29 equivalent( Y, Z ), equivalent( equivalent( Y, T ), equivalent( Z, T ) )
% 0.89/1.29 ) ) ) ) ] )
% 0.89/1.29 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 0.89/1.29 :=( U, equivalent( equivalent( X, equivalent( X, equivalent( equivalent(
% 0.89/1.29 Y, Z ), equivalent( equivalent( Y, T ), equivalent( Z, T ) ) ) ) ),
% 0.89/1.29 equivalent( equivalent( U, W ), equivalent( equivalent( U, V0 ),
% 0.89/1.29 equivalent( W, V0 ) ) ) ) )] ), substitution( 1, [ :=( X, equivalent( X,
% 0.89/1.29 equivalent( X, equivalent( equivalent( Y, Z ), equivalent( equivalent( Y
% 0.89/1.29 , T ), equivalent( Z, T ) ) ) ) ) ), :=( Y, U ), :=( Z, W ), :=( T, V0 )] )
% 0.89/1.29 ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 subsumption(
% 0.89/1.29 clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( X,
% 0.89/1.29 equivalent( equivalent( Y, Z ), equivalent( equivalent( Y, T ),
% 0.89/1.29 equivalent( Z, T ) ) ) ) ), equivalent( equivalent( U, W ), equivalent(
% 0.89/1.29 equivalent( U, V0 ), equivalent( W, V0 ) ) ) ) ) ] )
% 0.89/1.29 , clause( 10383, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( X
% 0.89/1.29 , equivalent( equivalent( Y, Z ), equivalent( equivalent( Y, T ),
% 0.89/1.29 equivalent( Z, T ) ) ) ) ), equivalent( equivalent( U, W ), equivalent(
% 0.89/1.29 equivalent( U, V0 ), equivalent( W, V0 ) ) ) ) ) ] )
% 0.89/1.29 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.29 , U ), :=( W, W ), :=( V0, V0 )] ), permutation( 0, [ ==>( 0, 0 )] )
% 0.89/1.29 ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 resolution(
% 0.89/1.29 clause( 10384, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.89/1.29 equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.89/1.29 , clause( 3, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( X, equivalent( X, equivalent( equivalent( Y, Z ), equivalent(
% 0.89/1.29 equivalent( Y, T ), equivalent( Z, T ) ) ) ) ), U ) ) ) ] )
% 0.89/1.29 , 1, clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( X
% 0.89/1.29 , equivalent( equivalent( Y, Z ), equivalent( equivalent( Y, T ),
% 0.89/1.29 equivalent( Z, T ) ) ) ) ), equivalent( equivalent( U, W ), equivalent(
% 0.89/1.29 equivalent( U, V0 ), equivalent( W, V0 ) ) ) ) ) ] )
% 0.89/1.29 , 0, substitution( 0, [ :=( X, T ), :=( Y, U ), :=( Z, W ), :=( T, V0 ),
% 0.89/1.29 :=( U, equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.89/1.29 equivalent( Y, Z ) ) ) )] ), substitution( 1, [ :=( X, T ), :=( Y, U ),
% 0.89/1.29 :=( Z, W ), :=( T, V0 ), :=( U, X ), :=( W, Y ), :=( V0, Z )] )).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 subsumption(
% 0.89/1.29 clause( 5, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.89/1.29 equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.89/1.29 , clause( 10384, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.89/1.29 equivalent( equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.89/1.29 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.89/1.29 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 resolution(
% 0.89/1.29 clause( 10386, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.29 equivalent( X, equivalent( equivalent( Y, Z ), equivalent( equivalent( Y
% 0.89/1.29 , T ), equivalent( Z, T ) ) ) ) ), equivalent( equivalent( U, W ),
% 0.89/1.29 equivalent( equivalent( U, V0 ), equivalent( W, V0 ) ) ) ), V1 ) ) ),
% 0.89/1.29 'is_a_theorem'( V1 ) ] )
% 0.89/1.29 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.89/1.29 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.89/1.29 , 2, clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( X
% 0.89/1.29 , equivalent( equivalent( Y, Z ), equivalent( equivalent( Y, T ),
% 0.89/1.29 equivalent( Z, T ) ) ) ) ), equivalent( equivalent( U, W ), equivalent(
% 0.89/1.29 equivalent( U, V0 ), equivalent( W, V0 ) ) ) ) ) ] )
% 0.89/1.29 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, equivalent( X,
% 0.89/1.29 equivalent( equivalent( Y, Z ), equivalent( equivalent( Y, T ),
% 0.89/1.29 equivalent( Z, T ) ) ) ) ), equivalent( equivalent( U, W ), equivalent(
% 0.89/1.29 equivalent( U, V0 ), equivalent( W, V0 ) ) ) ) ), :=( Y, V1 )] ),
% 0.89/1.29 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.29 , U ), :=( W, W ), :=( V0, V0 )] )).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 subsumption(
% 0.89/1.29 clause( 6, [ 'is_a_theorem'( V1 ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( X, equivalent( X, equivalent( equivalent( Y, Z )
% 0.89/1.29 , equivalent( equivalent( Y, T ), equivalent( Z, T ) ) ) ) ), equivalent(
% 0.89/1.29 equivalent( U, W ), equivalent( equivalent( U, V0 ), equivalent( W, V0 )
% 0.89/1.29 ) ) ), V1 ) ) ) ] )
% 0.89/1.29 , clause( 10386, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.89/1.29 , equivalent( X, equivalent( equivalent( Y, Z ), equivalent( equivalent(
% 0.89/1.29 Y, T ), equivalent( Z, T ) ) ) ) ), equivalent( equivalent( U, W ),
% 0.89/1.29 equivalent( equivalent( U, V0 ), equivalent( W, V0 ) ) ) ), V1 ) ) ),
% 0.89/1.29 'is_a_theorem'( V1 ) ] )
% 0.89/1.29 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.29 , U ), :=( W, W ), :=( V0, V0 ), :=( V1, V1 )] ), permutation( 0, [ ==>(
% 0.89/1.29 0, 1 ), ==>( 1, 0 )] ) ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 resolution(
% 0.89/1.29 clause( 10388, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.29 Y ), equivalent( equivalent( X, Z ), equivalent( Y, Z ) ) ), T ) ) ),
% 0.89/1.29 'is_a_theorem'( T ) ] )
% 0.89/1.29 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.89/1.29 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.89/1.29 , 2, clause( 5, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.89/1.29 equivalent( equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.89/1.29 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 0.89/1.29 equivalent( X, Z ), equivalent( Y, Z ) ) ) ), :=( Y, T )] ),
% 0.89/1.29 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 subsumption(
% 0.89/1.29 clause( 8, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.89/1.29 equivalent( X, Y ), equivalent( equivalent( X, Z ), equivalent( Y, Z ) )
% 0.89/1.29 ), T ) ) ) ] )
% 0.89/1.29 , clause( 10388, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.89/1.29 , Y ), equivalent( equivalent( X, Z ), equivalent( Y, Z ) ) ), T ) ) ),
% 0.89/1.29 'is_a_theorem'( T ) ] )
% 0.89/1.29 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.89/1.29 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 resolution(
% 0.89/1.29 clause( 10389, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.89/1.29 , Z ), equivalent( equivalent( equivalent( X, T ), equivalent( Y, T ) ),
% 0.89/1.29 Z ) ) ) ] )
% 0.89/1.29 , clause( 8, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.89/1.29 equivalent( Y, Z ) ) ), T ) ) ) ] )
% 0.89/1.29 , 1, clause( 5, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.89/1.29 equivalent( equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.89/1.29 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T,
% 0.89/1.29 equivalent( equivalent( equivalent( X, Y ), Z ), equivalent( equivalent(
% 0.89/1.29 equivalent( X, T ), equivalent( Y, T ) ), Z ) ) )] ), substitution( 1, [
% 0.89/1.29 :=( X, equivalent( X, Y ) ), :=( Y, equivalent( equivalent( X, T ),
% 0.89/1.29 equivalent( Y, T ) ) ), :=( Z, Z )] )).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 subsumption(
% 0.89/1.29 clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), Z
% 0.89/1.29 ), equivalent( equivalent( equivalent( X, T ), equivalent( Y, T ) ), Z )
% 0.89/1.29 ) ) ] )
% 0.89/1.29 , clause( 10389, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.89/1.29 ), Z ), equivalent( equivalent( equivalent( X, T ), equivalent( Y, T ) )
% 0.89/1.29 , Z ) ) ) ] )
% 0.89/1.29 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.89/1.29 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 resolution(
% 0.89/1.29 clause( 10390, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.89/1.29 , equivalent( Z, Y ) ), equivalent( equivalent( X, T ), equivalent( Z, T
% 0.89/1.29 ) ) ) ) ] )
% 0.89/1.29 , clause( 8, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.89/1.29 equivalent( Y, Z ) ) ), T ) ) ) ] )
% 0.89/1.29 , 1, clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.89/1.29 ), Z ), equivalent( equivalent( equivalent( X, T ), equivalent( Y, T ) )
% 0.89/1.29 , Z ) ) ) ] )
% 0.89/1.29 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, T ), :=( T,
% 0.89/1.29 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.89/1.29 equivalent( equivalent( X, T ), equivalent( Z, T ) ) ) )] ),
% 0.89/1.29 substitution( 1, [ :=( X, X ), :=( Y, Z ), :=( Z, equivalent( equivalent(
% 0.89/1.29 X, T ), equivalent( Z, T ) ) ), :=( T, Y )] )).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 subsumption(
% 0.89/1.29 clause( 11, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.89/1.29 equivalent( Z, Y ) ), equivalent( equivalent( X, T ), equivalent( Z, T )
% 0.89/1.29 ) ) ) ] )
% 0.89/1.29 , clause( 10390, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.89/1.29 ), equivalent( Z, Y ) ), equivalent( equivalent( X, T ), equivalent( Z,
% 0.89/1.29 T ) ) ) ) ] )
% 0.89/1.29 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.89/1.29 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 resolution(
% 0.89/1.29 clause( 10392, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.29 equivalent( X, Y ), Z ), equivalent( equivalent( equivalent( X, T ),
% 0.89/1.29 equivalent( Y, T ) ), Z ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.89/1.29 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.89/1.29 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.89/1.29 , 2, clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.89/1.29 ), Z ), equivalent( equivalent( equivalent( X, T ), equivalent( Y, T ) )
% 0.89/1.29 , Z ) ) ) ] )
% 0.89/1.29 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 0.89/1.29 Z ), equivalent( equivalent( equivalent( X, T ), equivalent( Y, T ) ), Z
% 0.89/1.29 ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z,
% 0.89/1.29 Z ), :=( T, T )] )).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 subsumption(
% 0.89/1.29 clause( 13, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( equivalent( X, Y ), Z ), equivalent( equivalent(
% 0.89/1.29 equivalent( X, T ), equivalent( Y, T ) ), Z ) ), U ) ) ) ] )
% 0.89/1.29 , clause( 10392, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.29 equivalent( X, Y ), Z ), equivalent( equivalent( equivalent( X, T ),
% 0.89/1.29 equivalent( Y, T ) ), Z ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.89/1.29 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.29 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 resolution(
% 0.89/1.29 clause( 10394, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.29 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( equivalent( X, T )
% 0.89/1.29 , equivalent( Z, T ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.89/1.29 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.89/1.29 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.89/1.29 , 2, clause( 11, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.89/1.29 ), equivalent( Z, Y ) ), equivalent( equivalent( X, T ), equivalent( Z,
% 0.89/1.29 T ) ) ) ) ] )
% 0.89/1.29 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 0.89/1.29 equivalent( Z, Y ) ), equivalent( equivalent( X, T ), equivalent( Z, T )
% 0.89/1.29 ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z,
% 0.89/1.29 Z ), :=( T, T )] )).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 subsumption(
% 0.89/1.29 clause( 14, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.89/1.29 equivalent( equivalent( X, T ), equivalent( Z, T ) ) ), U ) ) ) ] )
% 0.89/1.29 , clause( 10394, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.29 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( equivalent( X, T )
% 0.89/1.29 , equivalent( Z, T ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.89/1.29 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.29 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 resolution(
% 0.89/1.29 clause( 10395, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.29 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), U ), equivalent(
% 0.89/1.29 equivalent( X, equivalent( Y, T ) ), U ) ) ) ] )
% 0.89/1.29 , clause( 6, [ 'is_a_theorem'( V1 ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( X, equivalent( X, equivalent( equivalent( Y, Z )
% 0.89/1.29 , equivalent( equivalent( Y, T ), equivalent( Z, T ) ) ) ) ), equivalent(
% 0.89/1.29 equivalent( U, W ), equivalent( equivalent( U, V0 ), equivalent( W, V0 )
% 0.89/1.29 ) ) ), V1 ) ) ) ] )
% 0.89/1.29 , 1, clause( 11, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.89/1.29 ), equivalent( Z, Y ) ), equivalent( equivalent( X, T ), equivalent( Z,
% 0.89/1.29 T ) ) ) ) ] )
% 0.89/1.29 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( equivalent( Y, Z
% 0.89/1.29 ), equivalent( T, Z ) ) ) ), :=( Y, Y ), :=( Z, T ), :=( T, Z ), :=( U,
% 0.89/1.29 X ), :=( W, equivalent( Y, T ) ), :=( V0, equivalent( equivalent( Y, Z )
% 0.89/1.29 , equivalent( T, Z ) ) ), :=( V1, equivalent( equivalent( equivalent( X,
% 0.89/1.29 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), U ), equivalent(
% 0.89/1.29 equivalent( X, equivalent( Y, T ) ), U ) ) )] ), substitution( 1, [ :=( X
% 0.89/1.29 , equivalent( X, equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ) )
% 0.89/1.29 , :=( Y, equivalent( equivalent( X, equivalent( equivalent( Y, Z ),
% 0.89/1.29 equivalent( T, Z ) ) ), equivalent( equivalent( Y, T ), equivalent(
% 0.89/1.29 equivalent( Y, Z ), equivalent( T, Z ) ) ) ) ), :=( Z, equivalent( X,
% 0.89/1.29 equivalent( Y, T ) ) ), :=( T, U )] )).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 subsumption(
% 0.89/1.29 clause( 19, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.29 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), U ), equivalent(
% 0.89/1.29 equivalent( X, equivalent( Y, T ) ), U ) ) ) ] )
% 0.89/1.29 , clause( 10395, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.29 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), U ), equivalent(
% 0.89/1.29 equivalent( X, equivalent( Y, T ) ), U ) ) ) ] )
% 0.89/1.29 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.29 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 resolution(
% 0.89/1.29 clause( 10396, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.89/1.29 Z ) ), equivalent( equivalent( X, T ), equivalent( equivalent( equivalent(
% 0.89/1.29 Y, U ), equivalent( Z, U ) ), T ) ) ) ) ] )
% 0.89/1.29 , clause( 8, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.89/1.29 equivalent( Y, Z ) ) ), T ) ) ) ] )
% 0.89/1.29 , 1, clause( 19, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.29 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), U ), equivalent(
% 0.89/1.29 equivalent( X, equivalent( Y, T ) ), U ) ) ) ] )
% 0.89/1.29 , 0, substitution( 0, [ :=( X, X ), :=( Y, equivalent( equivalent( Y, U ),
% 0.89/1.29 equivalent( Z, U ) ) ), :=( Z, T ), :=( T, equivalent( equivalent( X,
% 0.89/1.29 equivalent( Y, Z ) ), equivalent( equivalent( X, T ), equivalent(
% 0.89/1.29 equivalent( equivalent( Y, U ), equivalent( Z, U ) ), T ) ) ) )] ),
% 0.89/1.29 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, U ), :=( T, Z ), :=( U
% 0.89/1.29 , equivalent( equivalent( X, T ), equivalent( equivalent( equivalent( Y,
% 0.89/1.29 U ), equivalent( Z, U ) ), T ) ) )] )).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 subsumption(
% 0.89/1.29 clause( 23, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 0.89/1.29 ), equivalent( equivalent( X, T ), equivalent( equivalent( equivalent( Y
% 0.89/1.29 , U ), equivalent( Z, U ) ), T ) ) ) ) ] )
% 0.89/1.29 , clause( 10396, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.89/1.29 , Z ) ), equivalent( equivalent( X, T ), equivalent( equivalent(
% 0.89/1.29 equivalent( Y, U ), equivalent( Z, U ) ), T ) ) ) ) ] )
% 0.89/1.29 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.29 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 resolution(
% 0.89/1.29 clause( 10398, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.29 equivalent( X, equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), U
% 0.89/1.29 ), equivalent( equivalent( X, equivalent( Y, T ) ), U ) ), W ) ) ),
% 0.89/1.29 'is_a_theorem'( W ) ] )
% 0.89/1.29 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.89/1.29 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.89/1.29 , 2, clause( 19, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.29 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), U ), equivalent(
% 0.89/1.29 equivalent( X, equivalent( Y, T ) ), U ) ) ) ] )
% 0.89/1.29 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X,
% 0.89/1.29 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), U ), equivalent(
% 0.89/1.29 equivalent( X, equivalent( Y, T ) ), U ) ) ), :=( Y, W )] ),
% 0.89/1.29 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.29 , U )] )).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 subsumption(
% 0.89/1.29 clause( 25, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( equivalent( X, equivalent( equivalent( Y, Z ),
% 0.89/1.29 equivalent( T, Z ) ) ), U ), equivalent( equivalent( X, equivalent( Y, T
% 0.89/1.29 ) ), U ) ), W ) ) ) ] )
% 0.89/1.29 , clause( 10398, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.29 equivalent( X, equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), U
% 0.89/1.29 ), equivalent( equivalent( X, equivalent( Y, T ) ), U ) ), W ) ) ),
% 0.89/1.29 'is_a_theorem'( W ) ] )
% 0.89/1.29 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.29 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 resolution(
% 0.89/1.29 clause( 10399, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.89/1.29 , Z ), equivalent( equivalent( equivalent( equivalent( X, T ), U ),
% 0.89/1.29 equivalent( equivalent( Y, T ), U ) ), Z ) ) ) ] )
% 0.89/1.29 , clause( 8, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.29 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.89/1.29 equivalent( Y, Z ) ) ), T ) ) ) ] )
% 0.89/1.29 , 1, clause( 23, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.89/1.29 , Z ) ), equivalent( equivalent( X, T ), equivalent( equivalent(
% 0.89/1.29 equivalent( Y, U ), equivalent( Z, U ) ), T ) ) ) ) ] )
% 0.89/1.29 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T,
% 0.89/1.29 equivalent( equivalent( equivalent( X, Y ), Z ), equivalent( equivalent(
% 0.89/1.30 equivalent( equivalent( X, T ), U ), equivalent( equivalent( Y, T ), U )
% 0.89/1.30 ), Z ) ) )] ), substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y,
% 0.89/1.30 equivalent( X, T ) ), :=( Z, equivalent( Y, T ) ), :=( T, Z ), :=( U, U )] )
% 0.89/1.30 ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 27, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), Z
% 0.89/1.30 ), equivalent( equivalent( equivalent( equivalent( X, T ), U ),
% 0.89/1.30 equivalent( equivalent( Y, T ), U ) ), Z ) ) ) ] )
% 0.89/1.30 , clause( 10399, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.89/1.30 ), Z ), equivalent( equivalent( equivalent( equivalent( X, T ), U ),
% 0.89/1.30 equivalent( equivalent( Y, T ), U ) ), Z ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.30 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10400, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z ) ),
% 0.89/1.30 equivalent( equivalent( X, U ), equivalent( T, U ) ) ) ) ] )
% 0.89/1.30 , clause( 8, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.89/1.30 equivalent( Y, Z ) ) ), T ) ) ) ] )
% 0.89/1.30 , 1, clause( 27, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.89/1.30 ), Z ), equivalent( equivalent( equivalent( equivalent( X, T ), U ),
% 0.89/1.30 equivalent( equivalent( Y, T ), U ) ), Z ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, X ), :=( Y, T ), :=( Z, U ), :=( T,
% 0.89/1.30 equivalent( equivalent( equivalent( equivalent( X, Y ), Z ), equivalent(
% 0.89/1.30 equivalent( T, Y ), Z ) ), equivalent( equivalent( X, U ), equivalent( T
% 0.89/1.30 , U ) ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, T ), :=( Z,
% 0.89/1.30 equivalent( equivalent( X, U ), equivalent( T, U ) ) ), :=( T, Y ), :=( U
% 0.89/1.30 , Z )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 31, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z ) ),
% 0.89/1.30 equivalent( equivalent( X, U ), equivalent( T, U ) ) ) ) ] )
% 0.89/1.30 , clause( 10400, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z ) ),
% 0.89/1.30 equivalent( equivalent( X, U ), equivalent( T, U ) ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.30 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10401, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.89/1.30 X, Y ) ) ) ] )
% 0.89/1.30 , clause( 14, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.89/1.30 equivalent( equivalent( X, T ), equivalent( Z, T ) ) ), U ) ) ) ] )
% 0.89/1.30 , 1, clause( 31, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), Z ) ),
% 0.89/1.30 equivalent( equivalent( X, U ), equivalent( T, U ) ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, T ), :=( T, Z ),
% 0.89/1.30 :=( U, equivalent( equivalent( X, Y ), equivalent( X, Y ) ) )] ),
% 0.89/1.30 substitution( 1, [ :=( X, X ), :=( Y, Z ), :=( Z, equivalent( T, Z ) ),
% 0.89/1.30 :=( T, X ), :=( U, Y )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 36, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( X
% 0.89/1.30 , Y ) ) ) ] )
% 0.89/1.30 , clause( 10401, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.89/1.30 equivalent( X, Y ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.89/1.30 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10403, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.30 Y ), equivalent( X, Y ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.89/1.30 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.89/1.30 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.89/1.30 , 2, clause( 36, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.89/1.30 equivalent( X, Y ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 0.89/1.30 X, Y ) ) ), :=( Y, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 0.89/1.30 ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 43, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 0.89/1.30 , clause( 10403, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.89/1.30 , Y ), equivalent( X, Y ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10404, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.89/1.30 , equivalent( Z, Y ) ), equivalent( X, Z ) ) ) ] )
% 0.89/1.30 , clause( 43, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 0.89/1.30 , 1, clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.89/1.30 ), Z ), equivalent( equivalent( equivalent( X, T ), equivalent( Y, T ) )
% 0.89/1.30 , Z ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, equivalent(
% 0.89/1.30 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z )
% 0.89/1.30 ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Z ), :=( Z, equivalent( X
% 0.89/1.30 , Z ) ), :=( T, Y )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 47, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.89/1.30 equivalent( Z, Y ) ), equivalent( X, Z ) ) ) ] )
% 0.89/1.30 , clause( 10404, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.89/1.30 ), equivalent( Z, Y ) ), equivalent( X, Z ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10405, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( X, equivalent( Y
% 0.89/1.30 , T ) ) ) ) ] )
% 0.89/1.30 , clause( 6, [ 'is_a_theorem'( V1 ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( X, equivalent( X, equivalent( equivalent( Y, Z )
% 0.89/1.30 , equivalent( equivalent( Y, T ), equivalent( Z, T ) ) ) ) ), equivalent(
% 0.89/1.30 equivalent( U, W ), equivalent( equivalent( U, V0 ), equivalent( W, V0 )
% 0.89/1.30 ) ) ), V1 ) ) ) ] )
% 0.89/1.30 , 1, clause( 47, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.89/1.30 ), equivalent( Z, Y ) ), equivalent( X, Z ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( equivalent( Y, Z
% 0.89/1.30 ), equivalent( T, Z ) ) ) ), :=( Y, Y ), :=( Z, T ), :=( T, Z ), :=( U,
% 0.89/1.30 X ), :=( W, equivalent( Y, T ) ), :=( V0, equivalent( equivalent( Y, Z )
% 0.89/1.30 , equivalent( T, Z ) ) ), :=( V1, equivalent( equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( X, equivalent( Y
% 0.89/1.30 , T ) ) ) )] ), substitution( 1, [ :=( X, equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, Z ), equivalent( T, Z ) ) ) ), :=( Y, equivalent(
% 0.89/1.30 equivalent( X, equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ),
% 0.89/1.30 equivalent( equivalent( Y, T ), equivalent( equivalent( Y, Z ),
% 0.89/1.30 equivalent( T, Z ) ) ) ) ), :=( Z, equivalent( X, equivalent( Y, T ) ) )] )
% 0.89/1.30 ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 50, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( X, equivalent( Y
% 0.89/1.30 , T ) ) ) ) ] )
% 0.89/1.30 , clause( 10405, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( X, equivalent( Y
% 0.89/1.30 , T ) ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10407, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z ) ), T ) ) ),
% 0.89/1.30 'is_a_theorem'( T ) ] )
% 0.89/1.30 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.89/1.30 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.89/1.30 , 2, clause( 47, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.89/1.30 ), equivalent( Z, Y ) ), equivalent( X, Z ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 0.89/1.30 equivalent( Z, Y ) ), equivalent( X, Z ) ) ), :=( Y, T )] ),
% 0.89/1.30 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 51, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.89/1.30 equivalent( X, Z ) ), T ) ) ) ] )
% 0.89/1.30 , clause( 10407, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( X, Z ) ), T ) ) ),
% 0.89/1.30 'is_a_theorem'( T ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10409, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.30 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( X,
% 0.89/1.30 equivalent( Y, T ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.89/1.30 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.89/1.30 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.89/1.30 , 2, clause( 50, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( X, equivalent( Y
% 0.89/1.30 , T ) ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( X, equivalent( Y
% 0.89/1.30 , T ) ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 0.89/1.30 :=( Z, Z ), :=( T, T )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 57, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), equivalent( T
% 0.89/1.30 , Z ) ) ), equivalent( X, equivalent( Y, T ) ) ), U ) ) ) ] )
% 0.89/1.30 , clause( 10409, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.89/1.30 , equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( X,
% 0.89/1.30 equivalent( Y, T ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.30 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10410, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.30 equivalent( Y, Z ) ), equivalent( T, Y ) ), equivalent( X, equivalent( T
% 0.89/1.30 , Z ) ) ) ) ] )
% 0.89/1.30 , clause( 51, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.89/1.30 equivalent( X, Z ) ), T ) ) ) ] )
% 0.89/1.30 , 1, clause( 19, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.30 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), U ), equivalent(
% 0.89/1.30 equivalent( X, equivalent( Y, T ) ), U ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, X ), :=( Y, equivalent( Y, Z ) ), :=( Z,
% 0.89/1.30 equivalent( T, Z ) ), :=( T, equivalent( equivalent( equivalent( X,
% 0.89/1.30 equivalent( Y, Z ) ), equivalent( T, Y ) ), equivalent( X, equivalent( T
% 0.89/1.30 , Z ) ) ) )] ), substitution( 1, [ :=( X, equivalent( X, equivalent( Y, Z
% 0.89/1.30 ) ) ), :=( Y, T ), :=( Z, Z ), :=( T, Y ), :=( U, equivalent( X,
% 0.89/1.30 equivalent( T, Z ) ) )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 84, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.30 equivalent( Y, Z ) ), equivalent( T, Y ) ), equivalent( X, equivalent( T
% 0.89/1.30 , Z ) ) ) ) ] )
% 0.89/1.30 , clause( 10410, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.30 equivalent( Y, Z ) ), equivalent( T, Y ) ), equivalent( X, equivalent( T
% 0.89/1.30 , Z ) ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10411, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent( X
% 0.89/1.30 , Z ), T ) ) ) ] )
% 0.89/1.30 , clause( 51, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.89/1.30 equivalent( X, Z ) ), T ) ) ) ] )
% 0.89/1.30 , 1, clause( 5, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.89/1.30 equivalent( equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 0.89/1.30 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y
% 0.89/1.30 ) ), T ), equivalent( equivalent( X, Z ), T ) ) )] ), substitution( 1, [
% 0.89/1.30 :=( X, equivalent( equivalent( X, Y ), equivalent( Z, Y ) ) ), :=( Y,
% 0.89/1.30 equivalent( X, Z ) ), :=( Z, T )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 86, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent( X
% 0.89/1.30 , Z ), T ) ) ) ] )
% 0.89/1.30 , clause( 10411, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent( X
% 0.89/1.30 , Z ), T ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10413, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, equivalent( Y, Z ) ), equivalent( T, Y ) ), equivalent( X
% 0.89/1.30 , equivalent( T, Z ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.89/1.30 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.89/1.30 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.89/1.30 , 2, clause( 84, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.30 equivalent( Y, Z ) ), equivalent( T, Y ) ), equivalent( X, equivalent( T
% 0.89/1.30 , Z ) ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X,
% 0.89/1.30 equivalent( Y, Z ) ), equivalent( T, Y ) ), equivalent( X, equivalent( T
% 0.89/1.30 , Z ) ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 0.89/1.30 :=( Z, Z ), :=( T, T )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 89, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent(
% 0.89/1.30 T, Y ) ), equivalent( X, equivalent( T, Z ) ) ), U ) ) ) ] )
% 0.89/1.30 , clause( 10413, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, equivalent( Y, Z ) ), equivalent( T, Y ) ), equivalent( X
% 0.89/1.30 , equivalent( T, Z ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.30 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10414, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.89/1.30 equivalent( equivalent( X, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.89/1.30 ) ) ) ] )
% 0.89/1.30 , clause( 13, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( equivalent( X, Y ), Z ), equivalent( equivalent(
% 0.89/1.30 equivalent( X, T ), equivalent( Y, T ) ), Z ) ), U ) ) ) ] )
% 0.89/1.30 , 1, clause( 86, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( equivalent( X
% 0.89/1.30 , Z ), T ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, X ), :=( Y, T ), :=( Z, equivalent( Y, T ) )
% 0.89/1.30 , :=( T, Z ), :=( U, equivalent( equivalent( X, Y ), equivalent(
% 0.89/1.30 equivalent( equivalent( X, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.89/1.30 ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, T ), :=( Z, Y ), :=( T,
% 0.89/1.30 equivalent( equivalent( equivalent( X, Z ), equivalent( T, Z ) ),
% 0.89/1.30 equivalent( Y, T ) ) )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 90, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.89/1.30 equivalent( equivalent( X, Z ), equivalent( T, Z ) ), equivalent( Y, T )
% 0.89/1.30 ) ) ) ] )
% 0.89/1.30 , clause( 10414, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.89/1.30 equivalent( equivalent( equivalent( X, Z ), equivalent( T, Z ) ),
% 0.89/1.30 equivalent( Y, T ) ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10415, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( U
% 0.89/1.30 , T ) ), equivalent( equivalent( X, Z ), U ) ) ) ] )
% 0.89/1.30 , clause( 51, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.89/1.30 equivalent( X, Z ) ), T ) ) ) ] )
% 0.89/1.30 , 1, clause( 90, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.89/1.30 equivalent( equivalent( equivalent( X, Z ), equivalent( T, Z ) ),
% 0.89/1.30 equivalent( Y, T ) ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 0.89/1.30 equivalent( equivalent( equivalent( equivalent( equivalent( X, Y ),
% 0.89/1.30 equivalent( Z, Y ) ), T ), equivalent( U, T ) ), equivalent( equivalent(
% 0.89/1.30 X, Z ), U ) ) )] ), substitution( 1, [ :=( X, equivalent( equivalent( X,
% 0.89/1.30 Y ), equivalent( Z, Y ) ) ), :=( Y, equivalent( X, Z ) ), :=( Z, T ),
% 0.89/1.30 :=( T, U )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 95, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( U
% 0.89/1.30 , T ) ), equivalent( equivalent( X, Z ), U ) ) ) ] )
% 0.89/1.30 , clause( 10415, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( U
% 0.89/1.30 , T ) ), equivalent( equivalent( X, Z ), U ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.30 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10416, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.89/1.30 Z ) ), equivalent( equivalent( X, equivalent( T, Z ) ), equivalent( Y, T
% 0.89/1.30 ) ) ) ) ] )
% 0.89/1.30 , clause( 6, [ 'is_a_theorem'( V1 ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( X, equivalent( X, equivalent( equivalent( Y, Z )
% 0.89/1.30 , equivalent( equivalent( Y, T ), equivalent( Z, T ) ) ) ) ), equivalent(
% 0.89/1.30 equivalent( U, W ), equivalent( equivalent( U, V0 ), equivalent( W, V0 )
% 0.89/1.30 ) ) ), V1 ) ) ) ] )
% 0.89/1.30 , 1, clause( 95, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( equivalent( X, Y ), equivalent( Z, Y ) ), T ), equivalent( U
% 0.89/1.30 , T ) ), equivalent( equivalent( X, Z ), U ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, equivalent( T, Z
% 0.89/1.30 ) ), equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ) ), :=( Y, Y
% 0.89/1.30 ), :=( Z, T ), :=( T, Z ), :=( U, equivalent( X, equivalent( T, Z ) ) )
% 0.89/1.30 , :=( W, equivalent( Y, T ) ), :=( V0, equivalent( equivalent( Y, Z ),
% 0.89/1.30 equivalent( T, Z ) ) ), :=( V1, equivalent( equivalent( X, equivalent( Y
% 0.89/1.30 , Z ) ), equivalent( equivalent( X, equivalent( T, Z ) ), equivalent( Y,
% 0.89/1.30 T ) ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, equivalent( T, Z ) )
% 0.89/1.30 , :=( Z, equivalent( Y, Z ) ), :=( T, equivalent( equivalent( equivalent(
% 0.89/1.30 X, equivalent( T, Z ) ), equivalent( equivalent( Y, Z ), equivalent( T, Z
% 0.89/1.30 ) ) ), equivalent( equivalent( Y, T ), equivalent( equivalent( Y, Z ),
% 0.89/1.30 equivalent( T, Z ) ) ) ) ), :=( U, equivalent( equivalent( X, equivalent(
% 0.89/1.30 T, Z ) ), equivalent( Y, T ) ) )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 127, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.89/1.30 ) ), equivalent( equivalent( X, equivalent( T, Z ) ), equivalent( Y, T )
% 0.89/1.30 ) ) ) ] )
% 0.89/1.30 , clause( 10416, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.89/1.30 , Z ) ), equivalent( equivalent( X, equivalent( T, Z ) ), equivalent( Y,
% 0.89/1.30 T ) ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10417, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( T, equivalent( Z, U
% 0.89/1.30 ) ) ), equivalent( equivalent( X, U ), T ) ) ) ] )
% 0.89/1.30 , clause( 14, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.89/1.30 equivalent( equivalent( X, T ), equivalent( Z, T ) ) ), U ) ) ) ] )
% 0.89/1.30 , 1, clause( 127, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 Y, Z ) ), equivalent( equivalent( X, equivalent( T, Z ) ), equivalent( Y
% 0.89/1.30 , T ) ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, U ),
% 0.89/1.30 :=( U, equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent(
% 0.89/1.30 Z, Y ) ), equivalent( T, equivalent( Z, U ) ) ), equivalent( equivalent(
% 0.89/1.30 X, U ), T ) ) )] ), substitution( 1, [ :=( X, equivalent( equivalent( X,
% 0.89/1.30 Y ), equivalent( Z, Y ) ) ), :=( Y, equivalent( X, U ) ), :=( Z,
% 0.89/1.30 equivalent( Z, U ) ), :=( T, T )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 130, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( T, equivalent( Z, U
% 0.89/1.30 ) ) ), equivalent( equivalent( X, U ), T ) ) ) ] )
% 0.89/1.30 , clause( 10417, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( T, equivalent( Z, U
% 0.89/1.30 ) ) ), equivalent( equivalent( X, U ), T ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.30 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10418, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( equivalent( X, U
% 0.89/1.30 ), equivalent( equivalent( Y, T ), U ) ) ) ) ] )
% 0.89/1.30 , clause( 3, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( X, equivalent( X, equivalent( equivalent( Y, Z ), equivalent(
% 0.89/1.30 equivalent( Y, T ), equivalent( Z, T ) ) ) ) ), U ) ) ) ] )
% 0.89/1.30 , 1, clause( 130, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( Z, Y ) ), equivalent( T, equivalent( Z, U
% 0.89/1.30 ) ) ), equivalent( equivalent( X, U ), T ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, U ), equivalent(
% 0.89/1.30 equivalent( Y, T ), U ) ) ), :=( Y, Y ), :=( Z, T ), :=( T, Z ), :=( U,
% 0.89/1.30 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), equivalent( T
% 0.89/1.30 , Z ) ) ), equivalent( equivalent( X, U ), equivalent( equivalent( Y, T )
% 0.89/1.30 , U ) ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, U ), :=( Z,
% 0.89/1.30 equivalent( Y, T ) ), :=( T, equivalent( equivalent( X, U ), equivalent(
% 0.89/1.30 equivalent( Y, T ), U ) ) ), :=( U, equivalent( equivalent( Y, Z ),
% 0.89/1.30 equivalent( T, Z ) ) )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 135, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( equivalent( X, U
% 0.89/1.30 ), equivalent( equivalent( Y, T ), U ) ) ) ) ] )
% 0.89/1.30 , clause( 10418, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( equivalent( X, U
% 0.89/1.30 ), equivalent( equivalent( Y, T ), U ) ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.30 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10419, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( Z, equivalent( Y, T ) ) ), U ),
% 0.89/1.30 equivalent( equivalent( equivalent( X, T ), Z ), U ) ) ) ] )
% 0.89/1.30 , clause( 13, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( equivalent( X, Y ), Z ), equivalent( equivalent(
% 0.89/1.30 equivalent( X, T ), equivalent( Y, T ) ), Z ) ), U ) ) ) ] )
% 0.89/1.30 , 1, clause( 135, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( equivalent( X, U
% 0.89/1.30 ), equivalent( equivalent( Y, T ), U ) ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, equivalent( Z,
% 0.89/1.30 equivalent( Y, T ) ) ), :=( T, T ), :=( U, equivalent( equivalent(
% 0.89/1.30 equivalent( equivalent( X, Y ), equivalent( Z, equivalent( Y, T ) ) ), U
% 0.89/1.30 ), equivalent( equivalent( equivalent( X, T ), Z ), U ) ) )] ),
% 0.89/1.30 substitution( 1, [ :=( X, equivalent( equivalent( X, Y ), equivalent( Z,
% 0.89/1.30 equivalent( Y, T ) ) ) ), :=( Y, equivalent( X, T ) ), :=( Z, equivalent(
% 0.89/1.30 Y, T ) ), :=( T, Z ), :=( U, U )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 139, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( Z, equivalent( Y, T ) ) ), U ),
% 0.89/1.30 equivalent( equivalent( equivalent( X, T ), Z ), U ) ) ) ] )
% 0.89/1.30 , clause( 10419, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( Z, equivalent( Y, T ) ) ), U ),
% 0.89/1.30 equivalent( equivalent( equivalent( X, T ), Z ), U ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.30 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10420, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.89/1.30 , Z ), equivalent( equivalent( equivalent( X, T ), U ), equivalent(
% 0.89/1.30 equivalent( Z, equivalent( T, Y ) ), U ) ) ) ) ] )
% 0.89/1.30 , clause( 8, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.89/1.30 equivalent( Y, Z ) ) ), T ) ) ) ] )
% 0.89/1.30 , 1, clause( 139, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( Z, equivalent( Y, T ) ) ), U ),
% 0.89/1.30 equivalent( equivalent( equivalent( X, T ), Z ), U ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, equivalent( X, T ) ), :=( Y, equivalent( Z,
% 0.89/1.30 equivalent( T, Y ) ) ), :=( Z, U ), :=( T, equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), Z ), equivalent( equivalent( equivalent( X, T ), U )
% 0.89/1.30 , equivalent( equivalent( Z, equivalent( T, Y ) ), U ) ) ) )] ),
% 0.89/1.30 substitution( 1, [ :=( X, X ), :=( Y, T ), :=( Z, Z ), :=( T, Y ), :=( U
% 0.89/1.30 , equivalent( equivalent( equivalent( X, T ), U ), equivalent( equivalent(
% 0.89/1.30 Z, equivalent( T, Y ) ), U ) ) )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 167, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.89/1.30 Z ), equivalent( equivalent( equivalent( X, T ), U ), equivalent(
% 0.89/1.30 equivalent( Z, equivalent( T, Y ) ), U ) ) ) ) ] )
% 0.89/1.30 , clause( 10420, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.89/1.30 ), Z ), equivalent( equivalent( equivalent( X, T ), U ), equivalent(
% 0.89/1.30 equivalent( Z, equivalent( T, Y ) ), U ) ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.30 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10421, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 0.89/1.30 , equivalent( Z, equivalent( U, Y ) ) ), T ) ) ) ] )
% 0.89/1.30 , clause( 51, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.89/1.30 equivalent( X, Z ) ), T ) ) ) ] )
% 0.89/1.30 , 1, clause( 167, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.30 Y ), Z ), equivalent( equivalent( equivalent( X, T ), U ), equivalent(
% 0.89/1.30 equivalent( Z, equivalent( T, Y ) ), U ) ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, U ), :=( T,
% 0.89/1.30 equivalent( equivalent( equivalent( equivalent( X, Y ), Z ), T ),
% 0.89/1.30 equivalent( equivalent( equivalent( X, U ), equivalent( Z, equivalent( U
% 0.89/1.30 , Y ) ) ), T ) ) )] ), substitution( 1, [ :=( X, equivalent( X, Y ) ),
% 0.89/1.30 :=( Y, equivalent( U, Y ) ), :=( Z, equivalent( X, U ) ), :=( T, Z ),
% 0.89/1.30 :=( U, T )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 187, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 0.89/1.30 , equivalent( Z, equivalent( U, Y ) ) ), T ) ) ) ] )
% 0.89/1.30 , clause( 10421, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 0.89/1.30 , equivalent( Z, equivalent( U, Y ) ) ), T ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.30 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10422, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.89/1.30 , equivalent( equivalent( Z, T ), equivalent( Y, T ) ) ), equivalent(
% 0.89/1.30 equivalent( X, U ), equivalent( Z, U ) ) ) ) ] )
% 0.89/1.30 , clause( 14, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.89/1.30 equivalent( equivalent( X, T ), equivalent( Z, T ) ) ), U ) ) ) ] )
% 0.89/1.30 , 1, clause( 187, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 0.89/1.30 , equivalent( Z, equivalent( U, Y ) ) ), T ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, X ), :=( Y, T ), :=( Z, Z ), :=( T, U ),
% 0.89/1.30 :=( U, equivalent( equivalent( equivalent( X, Y ), equivalent( equivalent(
% 0.89/1.30 Z, T ), equivalent( Y, T ) ) ), equivalent( equivalent( X, U ),
% 0.89/1.30 equivalent( Z, U ) ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, T ),
% 0.89/1.30 :=( Z, equivalent( Z, T ) ), :=( T, equivalent( equivalent( X, U ),
% 0.89/1.30 equivalent( Z, U ) ) ), :=( U, Y )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 195, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.89/1.30 equivalent( equivalent( Z, T ), equivalent( Y, T ) ) ), equivalent(
% 0.89/1.30 equivalent( X, U ), equivalent( Z, U ) ) ) ) ] )
% 0.89/1.30 , clause( 10422, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.89/1.30 ), equivalent( equivalent( Z, T ), equivalent( Y, T ) ) ), equivalent(
% 0.89/1.30 equivalent( X, U ), equivalent( Z, U ) ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.30 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10423, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.89/1.30 , equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent(
% 0.89/1.30 equivalent( X, T ), U ), equivalent( Z, U ) ) ) ) ] )
% 0.89/1.30 , clause( 8, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.89/1.30 equivalent( Y, Z ) ) ), T ) ) ) ] )
% 0.89/1.30 , 1, clause( 187, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 0.89/1.30 , equivalent( Z, equivalent( U, Y ) ) ), T ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, equivalent( X, T ) ), :=( Y, Z ), :=( Z, U )
% 0.89/1.30 , :=( T, equivalent( equivalent( equivalent( X, Y ), equivalent( Z,
% 0.89/1.30 equivalent( Y, T ) ) ), equivalent( equivalent( equivalent( X, T ), U ),
% 0.89/1.30 equivalent( Z, U ) ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, T ),
% 0.89/1.30 :=( Z, Z ), :=( T, equivalent( equivalent( equivalent( X, T ), U ),
% 0.89/1.30 equivalent( Z, U ) ) ), :=( U, Y )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 197, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.89/1.30 equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent( equivalent(
% 0.89/1.30 X, T ), U ), equivalent( Z, U ) ) ) ) ] )
% 0.89/1.30 , clause( 10423, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.89/1.30 ), equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent(
% 0.89/1.30 equivalent( X, T ), U ), equivalent( Z, U ) ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.30 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10424, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.30 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( U,
% 0.89/1.30 equivalent( Y, T ) ) ), equivalent( X, U ) ) ) ] )
% 0.89/1.30 , clause( 25, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( equivalent( X, equivalent( equivalent( Y, Z ),
% 0.89/1.30 equivalent( T, Z ) ) ), U ), equivalent( equivalent( X, equivalent( Y, T
% 0.89/1.30 ) ), U ) ), W ) ) ) ] )
% 0.89/1.30 , 1, clause( 50, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( X, equivalent( Y
% 0.89/1.30 , T ) ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 0.89/1.30 :=( U, equivalent( U, equivalent( Y, T ) ) ), :=( W, equivalent(
% 0.89/1.30 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), equivalent( T
% 0.89/1.30 , Z ) ) ), equivalent( U, equivalent( Y, T ) ) ), equivalent( X, U ) ) )] )
% 0.89/1.30 , substitution( 1, [ :=( X, equivalent( equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( U, equivalent( Y
% 0.89/1.30 , T ) ) ) ), :=( Y, X ), :=( Z, equivalent( Y, T ) ), :=( T, U )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 235, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.30 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( U,
% 0.89/1.30 equivalent( Y, T ) ) ), equivalent( X, U ) ) ) ] )
% 0.89/1.30 , clause( 10424, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.30 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( U,
% 0.89/1.30 equivalent( Y, T ) ) ), equivalent( X, U ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.89/1.30 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10425, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.89/1.30 Y ) ), X ) ) ] )
% 0.89/1.30 , clause( 51, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, Y ) ),
% 0.89/1.30 equivalent( X, Z ) ), T ) ) ) ] )
% 0.89/1.30 , 1, clause( 235, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.30 equivalent( equivalent( Y, Z ), equivalent( T, Z ) ) ), equivalent( U,
% 0.89/1.30 equivalent( Y, T ) ) ), equivalent( X, U ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, X ), :=( Y, equivalent( Y, Y ) ), :=( Z,
% 0.89/1.30 equivalent( Z, Y ) ), :=( T, equivalent( equivalent( X, equivalent( Y, Y
% 0.89/1.30 ) ), X ) )] ), substitution( 1, [ :=( X, equivalent( X, equivalent( Y, Y
% 0.89/1.30 ) ) ), :=( Y, Z ), :=( Z, Y ), :=( T, Y ), :=( U, X )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 241, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Y
% 0.89/1.30 ) ), X ) ) ] )
% 0.89/1.30 , clause( 10425, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.89/1.30 , Y ) ), X ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.89/1.30 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10427, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.30 equivalent( Y, Y ) ), X ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.89/1.30 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.89/1.30 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.89/1.30 , 2, clause( 241, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 Y, Y ) ), X ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, equivalent( Y, Y
% 0.89/1.30 ) ), X ) ), :=( Y, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 0.89/1.30 ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 244, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( X, equivalent( Y, Y ) ), X ), Z ) ) ) ] )
% 0.89/1.30 , clause( 10427, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.89/1.30 , equivalent( Y, Y ) ), X ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10428, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, equivalent( equivalent( Y, Y ), Z ) ), Z ), T ),
% 0.89/1.30 equivalent( X, T ) ) ) ] )
% 0.89/1.30 , clause( 244, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( X, equivalent( Y, Y ) ), X ), Z ) ) ) ] )
% 0.89/1.30 , 1, clause( 197, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.30 Y ), equivalent( Z, equivalent( Y, T ) ) ), equivalent( equivalent(
% 0.89/1.30 equivalent( X, T ), U ), equivalent( Z, U ) ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( equivalent( Y, Y
% 0.89/1.30 ), Z ) ) ), :=( Y, Y ), :=( Z, equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, equivalent( equivalent( Y, Y ), Z ) ), Z ), T ),
% 0.89/1.30 equivalent( X, T ) ) )] ), substitution( 1, [ :=( X, equivalent( X,
% 0.89/1.30 equivalent( equivalent( Y, Y ), Z ) ) ), :=( Y, equivalent( Y, Y ) ),
% 0.89/1.30 :=( Z, X ), :=( T, Z ), :=( U, T )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 247, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, equivalent( equivalent( Y, Y ), Z ) ), Z ), T ),
% 0.89/1.30 equivalent( X, T ) ) ) ] )
% 0.89/1.30 , clause( 10428, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, equivalent( equivalent( Y, Y ), Z ) ), Z ), T ),
% 0.89/1.30 equivalent( X, T ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10429, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( equivalent( Z, Z ), Y ) ), T ),
% 0.89/1.30 equivalent( X, T ) ) ) ] )
% 0.89/1.30 , clause( 244, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( X, equivalent( Y, Y ) ), X ), Z ) ) ) ] )
% 0.89/1.30 , 1, clause( 195, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.89/1.30 Y ), equivalent( equivalent( Z, T ), equivalent( Y, T ) ) ), equivalent(
% 0.89/1.30 equivalent( X, U ), equivalent( Z, U ) ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 0.89/1.30 equivalent( Z, Z ), Y ) ) ), :=( Y, Z ), :=( Z, equivalent( equivalent(
% 0.89/1.30 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, Z ), Y ) ), T
% 0.89/1.30 ), equivalent( X, T ) ) )] ), substitution( 1, [ :=( X, equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( equivalent( Z, Z ), Y ) ) ), :=( Y,
% 0.89/1.30 equivalent( Z, Z ) ), :=( Z, X ), :=( T, Y ), :=( U, T )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 248, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( equivalent( Z, Z ), Y ) ), T ),
% 0.89/1.30 equivalent( X, T ) ) ) ] )
% 0.89/1.30 , clause( 10429, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( equivalent( Z, Z ), Y ) ), T ),
% 0.89/1.30 equivalent( X, T ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10430, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( X,
% 0.89/1.30 equivalent( Y, Z ) ), equivalent( Z, Y ) ) ) ) ] )
% 0.89/1.30 , clause( 57, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), equivalent( T
% 0.89/1.30 , Z ) ) ), equivalent( X, equivalent( Y, T ) ) ), U ) ) ) ] )
% 0.89/1.30 , 1, clause( 248, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, Y ), equivalent( equivalent( Z, Z ), Y ) ), T ),
% 0.89/1.30 equivalent( X, T ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( Y, Z ) ) ), :=( Y
% 0.89/1.30 , Z ), :=( Z, Z ), :=( T, Y ), :=( U, equivalent( X, equivalent(
% 0.89/1.30 equivalent( X, equivalent( Y, Z ) ), equivalent( Z, Y ) ) ) )] ),
% 0.89/1.30 substitution( 1, [ :=( X, X ), :=( Y, equivalent( Y, Z ) ), :=( Z, Z ),
% 0.89/1.30 :=( T, equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( Z, Y
% 0.89/1.30 ) ) )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 892, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( X,
% 0.89/1.30 equivalent( Y, Z ) ), equivalent( Z, Y ) ) ) ) ] )
% 0.89/1.30 , clause( 10430, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( X
% 0.89/1.30 , equivalent( Y, Z ) ), equivalent( Z, Y ) ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10432, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 equivalent( X, equivalent( Y, Z ) ), equivalent( Z, Y ) ) ), T ) ) ),
% 0.89/1.30 'is_a_theorem'( T ) ] )
% 0.89/1.30 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.89/1.30 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.89/1.30 , 2, clause( 892, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 0.89/1.30 X, equivalent( Y, Z ) ), equivalent( Z, Y ) ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( equivalent( X,
% 0.89/1.30 equivalent( Y, Z ) ), equivalent( Z, Y ) ) ) ), :=( Y, T )] ),
% 0.89/1.30 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 919, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( X, equivalent( equivalent( X, equivalent( Y, Z ) ),
% 0.89/1.30 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 0.89/1.30 , clause( 10432, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 equivalent( X, equivalent( Y, Z ) ), equivalent( Z, Y ) ) ), T ) ) ),
% 0.89/1.30 'is_a_theorem'( T ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10433, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.89/1.30 Y, equivalent( Y, equivalent( Z, Z ) ) ) ) ) ) ] )
% 0.89/1.30 , clause( 89, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent(
% 0.89/1.30 T, Y ) ), equivalent( X, equivalent( T, Z ) ) ), U ) ) ) ] )
% 0.89/1.30 , 1, clause( 247, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.89/1.30 equivalent( X, equivalent( equivalent( Y, Y ), Z ) ), Z ), T ),
% 0.89/1.30 equivalent( X, T ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, X ), :=( Y, equivalent( Z, Z ) ), :=( Z,
% 0.89/1.30 equivalent( Y, equivalent( Z, Z ) ) ), :=( T, Y ), :=( U, equivalent( X,
% 0.89/1.30 equivalent( X, equivalent( Y, equivalent( Y, equivalent( Z, Z ) ) ) ) ) )] )
% 0.89/1.30 , substitution( 1, [ :=( X, X ), :=( Y, Z ), :=( Z, equivalent( Y,
% 0.89/1.30 equivalent( Z, Z ) ) ), :=( T, equivalent( X, equivalent( Y, equivalent(
% 0.89/1.30 Y, equivalent( Z, Z ) ) ) ) )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 2020, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent( Y
% 0.89/1.30 , equivalent( Y, equivalent( Z, Z ) ) ) ) ) ) ] )
% 0.89/1.30 , clause( 10433, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.89/1.30 Y, equivalent( Y, equivalent( Z, Z ) ) ) ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10435, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 X, equivalent( Y, equivalent( Y, equivalent( Z, Z ) ) ) ) ), T ) ) ),
% 0.89/1.30 'is_a_theorem'( T ) ] )
% 0.89/1.30 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.89/1.30 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.89/1.30 , 2, clause( 2020, [ 'is_a_theorem'( equivalent( X, equivalent( X,
% 0.89/1.30 equivalent( Y, equivalent( Y, equivalent( Z, Z ) ) ) ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( X, equivalent( Y
% 0.89/1.30 , equivalent( Y, equivalent( Z, Z ) ) ) ) ) ), :=( Y, T )] ),
% 0.89/1.30 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 2106, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( X, equivalent( X, equivalent( Y, equivalent( Y, equivalent( Z
% 0.89/1.30 , Z ) ) ) ) ), T ) ) ) ] )
% 0.89/1.30 , clause( 10435, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 X, equivalent( Y, equivalent( Y, equivalent( Z, Z ) ) ) ) ), T ) ) ),
% 0.89/1.30 'is_a_theorem'( T ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10436, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.89/1.30 equivalent( Z, equivalent( Z, equivalent( T, T ) ) ) ) ), equivalent( X,
% 0.89/1.30 Y ) ) ) ] )
% 0.89/1.30 , clause( 2106, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( X, equivalent( X, equivalent( Y, equivalent( Y, equivalent( Z
% 0.89/1.30 , Z ) ) ) ) ), T ) ) ) ] )
% 0.89/1.30 , 1, clause( 127, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 Y, Z ) ), equivalent( equivalent( X, equivalent( T, Z ) ), equivalent( Y
% 0.89/1.30 , T ) ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, T ), :=( T,
% 0.89/1.30 equivalent( equivalent( X, equivalent( Y, equivalent( Z, equivalent( Z,
% 0.89/1.30 equivalent( T, T ) ) ) ) ), equivalent( X, Y ) ) )] ), substitution( 1, [
% 0.89/1.30 :=( X, X ), :=( Y, X ), :=( Z, equivalent( Z, equivalent( Z, equivalent(
% 0.89/1.30 T, T ) ) ) ), :=( T, Y )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 9704, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.89/1.30 equivalent( Z, equivalent( Z, equivalent( T, T ) ) ) ) ), equivalent( X,
% 0.89/1.30 Y ) ) ) ] )
% 0.89/1.30 , clause( 10436, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.89/1.30 , equivalent( Z, equivalent( Z, equivalent( T, T ) ) ) ) ), equivalent( X
% 0.89/1.30 , Y ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10437, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, equivalent( Z, Z ) ), Y ) ) ) ) ] )
% 0.89/1.30 , clause( 919, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.89/1.30 equivalent( X, equivalent( equivalent( X, equivalent( Y, Z ) ),
% 0.89/1.30 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 0.89/1.30 , 1, clause( 9704, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.89/1.30 Y, equivalent( Z, equivalent( Z, equivalent( T, T ) ) ) ) ), equivalent(
% 0.89/1.30 X, Y ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [ :=( X, X ), :=( Y, equivalent( Y, equivalent( Z, Z
% 0.89/1.30 ) ) ), :=( Z, Y ), :=( T, equivalent( X, equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, equivalent( Z, Z ) ), Y ) ) ) )] ), substitution( 1, [
% 0.89/1.30 :=( X, X ), :=( Y, equivalent( X, equivalent( equivalent( Y, equivalent(
% 0.89/1.30 Z, Z ) ), Y ) ) ), :=( Z, Y ), :=( T, Z )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 10309, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, equivalent( Z, Z ) ), Y ) ) ) ) ] )
% 0.89/1.30 , clause( 10437, [ 'is_a_theorem'( equivalent( X, equivalent( X, equivalent(
% 0.89/1.30 equivalent( Y, equivalent( Z, Z ) ), Y ) ) ) ) ] )
% 0.89/1.30 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.89/1.30 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 resolution(
% 0.89/1.30 clause( 10438, [] )
% 0.89/1.30 , clause( 2, [ ~( 'is_a_theorem'( equivalent( a, equivalent( a, equivalent(
% 0.89/1.30 equivalent( b, equivalent( c, c ) ), b ) ) ) ) ) ] )
% 0.89/1.30 , 0, clause( 10309, [ 'is_a_theorem'( equivalent( X, equivalent( X,
% 0.89/1.30 equivalent( equivalent( Y, equivalent( Z, Z ) ), Y ) ) ) ) ] )
% 0.89/1.30 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, b ), :=(
% 0.89/1.30 Z, c )] )).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 subsumption(
% 0.89/1.30 clause( 10376, [] )
% 0.89/1.30 , clause( 10438, [] )
% 0.89/1.30 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 end.
% 0.89/1.30
% 0.89/1.30 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.89/1.30
% 0.89/1.30 Memory use:
% 0.89/1.30
% 0.89/1.30 space for terms: 276655
% 0.89/1.30 space for clauses: 1143405
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 clauses generated: 23455
% 0.89/1.30 clauses kept: 10377
% 0.89/1.30 clauses selected: 541
% 0.89/1.30 clauses deleted: 5
% 0.89/1.30 clauses inuse deleted: 2
% 0.89/1.30
% 0.89/1.30 subsentry: 14109
% 0.89/1.30 literals s-matched: 13083
% 0.89/1.30 literals matched: 13083
% 0.89/1.30 full subsumption: 0
% 0.89/1.30
% 0.89/1.30 checksum: -879161401
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 Bliksem ended
%------------------------------------------------------------------------------