TSTP Solution File: LCL023-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL023-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.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 07:49:17 EDT 2022
% Result : Unsatisfiable 0.83s 1.32s
% Output : Refutation 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL023-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : bliksem %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Jul 2 18:59:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.83/1.32 *** allocated 10000 integers for termspace/termends
% 0.83/1.32 *** allocated 10000 integers for clauses
% 0.83/1.32 *** allocated 10000 integers for justifications
% 0.83/1.32 Bliksem 1.12
% 0.83/1.32
% 0.83/1.32
% 0.83/1.32 Automatic Strategy Selection
% 0.83/1.32
% 0.83/1.32 Clauses:
% 0.83/1.32 [
% 0.83/1.32 [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~( 'is_a_theorem'( X ) ),
% 0.83/1.32 'is_a_theorem'( Y ) ],
% 0.83/1.32 [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( equivalent(
% 0.83/1.32 Z, Y ), equivalent( X, Z ) ) ) ) ],
% 0.83/1.32 [ ~( 'is_a_theorem'( equivalent( equivalent( a, equivalent( b, c ) ),
% 0.83/1.32 equivalent( equivalent( a, b ), c ) ) ) ) ]
% 0.83/1.32 ] .
% 0.83/1.32
% 0.83/1.32
% 0.83/1.32 percentage equality = 0.000000, percentage horn = 1.000000
% 0.83/1.32 This is a near-Horn, non-equality problem
% 0.83/1.32
% 0.83/1.32
% 0.83/1.32 Options Used:
% 0.83/1.32
% 0.83/1.32 useres = 1
% 0.83/1.32 useparamod = 0
% 0.83/1.32 useeqrefl = 0
% 0.83/1.32 useeqfact = 0
% 0.83/1.32 usefactor = 1
% 0.83/1.32 usesimpsplitting = 0
% 0.83/1.32 usesimpdemod = 0
% 0.83/1.32 usesimpres = 4
% 0.83/1.32
% 0.83/1.32 resimpinuse = 1000
% 0.83/1.32 resimpclauses = 20000
% 0.83/1.32 substype = standard
% 0.83/1.32 backwardsubs = 1
% 0.83/1.32 selectoldest = 5
% 0.83/1.32
% 0.83/1.32 litorderings [0] = split
% 0.83/1.32 litorderings [1] = liftord
% 0.83/1.32
% 0.83/1.32 termordering = none
% 0.83/1.32
% 0.83/1.32 litapriori = 1
% 0.83/1.32 termapriori = 0
% 0.83/1.32 litaposteriori = 0
% 0.83/1.32 termaposteriori = 0
% 0.83/1.32 demodaposteriori = 0
% 0.83/1.32 ordereqreflfact = 0
% 0.83/1.32
% 0.83/1.32 litselect = negative
% 0.83/1.32
% 0.83/1.32 maxweight = 30000
% 0.83/1.32 maxdepth = 30000
% 0.83/1.32 maxlength = 115
% 0.83/1.32 maxnrvars = 195
% 0.83/1.32 excuselevel = 0
% 0.83/1.32 increasemaxweight = 0
% 0.83/1.32
% 0.83/1.32 maxselected = 10000000
% 0.83/1.32 maxnrclauses = 10000000
% 0.83/1.32
% 0.83/1.32 showgenerated = 0
% 0.83/1.32 showkept = 0
% 0.83/1.32 showselected = 0
% 0.83/1.32 showdeleted = 0
% 0.83/1.32 showresimp = 1
% 0.83/1.32 showstatus = 2000
% 0.83/1.32
% 0.83/1.32 prologoutput = 1
% 0.83/1.32 nrgoals = 5000000
% 0.83/1.32 totalproof = 1
% 0.83/1.32
% 0.83/1.32 Symbols occurring in the translation:
% 0.83/1.32
% 0.83/1.32 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.83/1.32 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.83/1.32 ! [4, 1] (w:1, o:15, a:1, s:1, b:0),
% 0.83/1.32 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.83/1.32 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.83/1.32 equivalent [41, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.83/1.32 'is_a_theorem' [42, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.83/1.32 a [44, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.83/1.32 b [45, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.83/1.32 c [46, 0] (w:1, o:14, a:1, s:1, b:0).
% 0.83/1.32
% 0.83/1.32
% 0.83/1.32 Starting Search:
% 0.83/1.32
% 0.83/1.32 Resimplifying inuse:
% 0.83/1.32 Done
% 0.83/1.32
% 0.83/1.32
% 0.83/1.32 Intermediate Status:
% 0.83/1.32 Generated: 3865
% 0.83/1.32 Kept: 2012
% 0.83/1.32 Inuse: 221
% 0.83/1.32 Deleted: 4
% 0.83/1.32 Deletedinuse: 3
% 0.83/1.32
% 0.83/1.32 Resimplifying inuse:
% 0.83/1.32 Done
% 0.83/1.32
% 0.83/1.32 Resimplifying inuse:
% 0.83/1.32 Done
% 0.83/1.32
% 0.83/1.32
% 0.83/1.32 Intermediate Status:
% 0.83/1.32 Generated: 8259
% 0.83/1.32 Kept: 4018
% 0.83/1.32 Inuse: 387
% 0.83/1.32 Deleted: 4
% 0.83/1.32 Deletedinuse: 3
% 0.83/1.32
% 0.83/1.32 Resimplifying inuse:
% 0.83/1.32 Done
% 0.83/1.32
% 0.83/1.32 Resimplifying inuse:
% 0.83/1.32 Done
% 0.83/1.32
% 0.83/1.32
% 0.83/1.32 Intermediate Status:
% 0.83/1.32 Generated: 12910
% 0.83/1.32 Kept: 6027
% 0.83/1.32 Inuse: 486
% 0.83/1.32 Deleted: 4
% 0.83/1.32 Deletedinuse: 3
% 0.83/1.32
% 0.83/1.32 Resimplifying inuse:
% 0.83/1.32 Done
% 0.83/1.32
% 0.83/1.32 Resimplifying inuse:
% 0.83/1.32 Done
% 0.83/1.32
% 0.83/1.32
% 0.83/1.32 Bliksems!, er is een bewijs:
% 0.83/1.32 % SZS status Unsatisfiable
% 0.83/1.32 % SZS output start Refutation
% 0.83/1.32
% 0.83/1.32 clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.83/1.32 , ~( 'is_a_theorem'( X ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.32 equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 2, [ ~( 'is_a_theorem'( equivalent( equivalent( a, equivalent( b, c
% 0.83/1.32 ) ), equivalent( equivalent( a, b ), c ) ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 3, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.83/1.32 equivalent( X, Y ), equivalent( equivalent( Z, Y ), equivalent( X, Z ) )
% 0.83/1.32 ), T ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.32 equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent( equivalent( T, Z
% 0.83/1.32 ), X ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 5, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( X
% 0.83/1.32 , Y ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 6, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.83/1.32 equivalent( X, equivalent( equivalent( Y, Z ), equivalent( T, Y ) ) ),
% 0.83/1.32 equivalent( equivalent( T, Z ), X ) ), U ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 7, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.83/1.32 equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 0.83/1.32 ), equivalent( equivalent( Y, Z ), X ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.83/1.32 equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 11, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 12, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.32 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, X ) ),
% 0.83/1.32 equivalent( Z, Y ) ), T ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 13, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.32 equivalent( X, X ), Y ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 15, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.32 equivalent( X, Z ), equivalent( equivalent( T, Y ), equivalent( Z, T ) )
% 0.83/1.32 ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 17, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( Y
% 0.83/1.32 , X ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 18, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.32 equivalent( equivalent( X, Y ), equivalent( Y, X ) ), Z ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 19, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.32 equivalent( X, Z ), equivalent( Z, Y ) ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 20, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 0.83/1.32 ), equivalent( equivalent( Z, Y ), X ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 22, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.83/1.32 equivalent( equivalent( Y, Z ), equivalent( T, Y ) ) ), U ), equivalent(
% 0.83/1.32 U, equivalent( equivalent( T, Z ), X ) ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 23, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.32 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.83/1.32 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 29, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.83/1.32 equivalent( Y, Z ) ), equivalent( X, Z ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 30, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.32 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( equivalent(
% 0.83/1.32 Z, Y ), X ) ), T ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 31, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.32 equivalent( equivalent( equivalent( X, Y ), equivalent( Y, Z ) ),
% 0.83/1.32 equivalent( X, Z ) ), T ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 33, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.83/1.32 equivalent( X, Y ), equivalent( Z, X ) ), T ), equivalent( T, equivalent(
% 0.83/1.32 Z, Y ) ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 38, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.83/1.32 equivalent( equivalent( X, Z ), T ) ), equivalent( equivalent( Z, Y ), T
% 0.83/1.32 ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 42, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, X )
% 0.83/1.32 ), Y ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 45, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.32 equivalent( equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z
% 0.83/1.32 ), T ) ), equivalent( equivalent( Z, Y ), T ) ), U ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 50, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.32 equivalent( equivalent( X, equivalent( Y, X ) ), Y ), Z ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 60, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.32 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.83/1.32 equivalent( equivalent( T, Y ), equivalent( Z, T ) ) ) ), U ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 96, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.32 equivalent( Z, Y ), equivalent( Z, X ) ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 120, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.32 equivalent( Y, Z ), equivalent( Z, T ) ) ), equivalent( X, equivalent( Y
% 0.83/1.32 , T ) ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 235, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.32 equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 241, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.83/1.32 equivalent( Y, X ) ), Z ), equivalent( Y, Z ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 258, [ 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Y
% 0.83/1.32 , X ) ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 274, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.32 equivalent( X, equivalent( Y, equivalent( Y, X ) ) ), Z ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 3604, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.32 X, equivalent( equivalent( Z, Y ), Z ) ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 3635, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.32 equivalent( Z, equivalent( Y, X ) ), Z ) ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 6141, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.32 equivalent( Y, equivalent( Y, Z ) ), Z ) ), X ) ) ] )
% 0.83/1.32 .
% 0.83/1.32 clause( 7059, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.83/1.33 ) ), equivalent( equivalent( X, Y ), Z ) ) ) ] )
% 0.83/1.33 .
% 0.83/1.33 clause( 7064, [] )
% 0.83/1.33 .
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 % SZS output end Refutation
% 0.83/1.33 found a proof!
% 0.83/1.33
% 0.83/1.33 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.83/1.33
% 0.83/1.33 initialclauses(
% 0.83/1.33 [ clause( 7066, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~(
% 0.83/1.33 'is_a_theorem'( X ) ), 'is_a_theorem'( Y ) ] )
% 0.83/1.33 , clause( 7067, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.83/1.33 , clause( 7068, [ ~( 'is_a_theorem'( equivalent( equivalent( a, equivalent(
% 0.83/1.33 b, c ) ), equivalent( equivalent( a, b ), c ) ) ) ) ] )
% 0.83/1.33 ] ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.83/1.33 , ~( 'is_a_theorem'( X ) ) ] )
% 0.83/1.33 , clause( 7066, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~(
% 0.83/1.33 'is_a_theorem'( X ) ), 'is_a_theorem'( Y ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.83/1.33 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.83/1.33 , clause( 7067, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 2, [ ~( 'is_a_theorem'( equivalent( equivalent( a, equivalent( b, c
% 0.83/1.33 ) ), equivalent( equivalent( a, b ), c ) ) ) ) ] )
% 0.83/1.33 , clause( 7068, [ ~( 'is_a_theorem'( equivalent( equivalent( a, equivalent(
% 0.83/1.33 b, c ) ), equivalent( equivalent( a, b ), c ) ) ) ) ] )
% 0.83/1.33 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7070, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.83/1.33 ), equivalent( equivalent( Z, Y ), equivalent( X, Z ) ) ), T ) ) ),
% 0.83/1.33 'is_a_theorem'( T ) ] )
% 0.83/1.33 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.83/1.33 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.83/1.33 , 2, clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 equivalent( Z, Y ), equivalent( X, Z ) ) ) ), :=( Y, T )] ),
% 0.83/1.33 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 3, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.83/1.33 equivalent( X, Y ), equivalent( equivalent( Z, Y ), equivalent( X, Z ) )
% 0.83/1.33 ), T ) ) ) ] )
% 0.83/1.33 , clause( 7070, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.83/1.33 , Y ), equivalent( equivalent( Z, Y ), equivalent( X, Z ) ) ), T ) ) ),
% 0.83/1.33 'is_a_theorem'( T ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7071, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent( equivalent( T, Z
% 0.83/1.33 ), X ) ) ) ] )
% 0.83/1.33 , clause( 3, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, Y ),
% 0.83/1.33 equivalent( X, Z ) ) ), T ) ) ) ] )
% 0.83/1.33 , 1, clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, T ), :=( Y, Z ), :=( Z, Y ), :=( T,
% 0.83/1.33 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), equivalent( T
% 0.83/1.33 , Y ) ) ), equivalent( equivalent( T, Z ), X ) ) )] ), substitution( 1, [
% 0.83/1.33 :=( X, equivalent( T, Z ) ), :=( Y, equivalent( equivalent( Y, Z ),
% 0.83/1.33 equivalent( T, Y ) ) ), :=( Z, X )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent( equivalent( T, Z
% 0.83/1.33 ), X ) ) ) ] )
% 0.83/1.33 , clause( 7071, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent( equivalent( T, Z
% 0.83/1.33 ), X ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7072, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 X, Y ) ) ) ] )
% 0.83/1.33 , clause( 3, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, Y ),
% 0.83/1.33 equivalent( X, Z ) ) ), T ) ) ) ] )
% 0.83/1.33 , 1, clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent( equivalent( T, Z
% 0.83/1.33 ), X ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 0.83/1.33 equivalent( equivalent( X, Y ), equivalent( X, Y ) ) )] ), substitution(
% 0.83/1.33 1, [ :=( X, equivalent( X, Y ) ), :=( Y, Z ), :=( Z, Y ), :=( T, X )] )
% 0.83/1.33 ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 5, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( X
% 0.83/1.33 , Y ) ) ) ] )
% 0.83/1.33 , clause( 7072, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( X, Y ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.83/1.33 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7074, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.83/1.33 equivalent( equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent(
% 0.83/1.33 equivalent( T, Z ), X ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.83/1.33 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.83/1.33 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.83/1.33 , 2, clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent( equivalent( T, Z
% 0.83/1.33 ), X ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent( equivalent( T, Z
% 0.83/1.33 ), X ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 0.83/1.33 :=( Z, Z ), :=( T, T )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 6, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.83/1.33 equivalent( X, equivalent( equivalent( Y, Z ), equivalent( T, Y ) ) ),
% 0.83/1.33 equivalent( equivalent( T, Z ), X ) ), U ) ) ) ] )
% 0.83/1.33 , clause( 7074, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.83/1.33 , equivalent( equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent(
% 0.83/1.33 equivalent( T, Z ), X ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.83/1.33 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7076, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.83/1.33 ), equivalent( X, Y ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.83/1.33 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.83/1.33 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.83/1.33 , 2, clause( 5, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( X, Y ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 X, Y ) ) ), :=( Y, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 0.83/1.33 ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 7, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.83/1.33 equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 0.83/1.33 , clause( 7076, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.83/1.33 , Y ), equivalent( X, Y ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7077, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.83/1.33 ) ), equivalent( equivalent( Y, Z ), X ) ) ) ] )
% 0.83/1.33 , clause( 7, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 0.83/1.33 , 1, clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, equivalent(
% 0.83/1.33 equivalent( X, equivalent( Y, Z ) ), equivalent( equivalent( Y, Z ), X )
% 0.83/1.33 ) )] ), substitution( 1, [ :=( X, equivalent( Y, Z ) ), :=( Y,
% 0.83/1.33 equivalent( Y, Z ) ), :=( Z, X )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 0.83/1.33 ), equivalent( equivalent( Y, Z ), X ) ) ) ] )
% 0.83/1.33 , clause( 7077, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.83/1.33 , Z ) ), equivalent( equivalent( Y, Z ), X ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7078, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.83/1.33 , equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ] )
% 0.83/1.33 , clause( 3, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, Y ),
% 0.83/1.33 equivalent( X, Z ) ) ), T ) ) ) ] )
% 0.83/1.33 , 1, clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.83/1.33 , Z ) ), equivalent( equivalent( Y, Z ), X ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X ), :=( T,
% 0.83/1.33 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, X ) ),
% 0.83/1.33 equivalent( Z, Y ) ) )] ), substitution( 1, [ :=( X, equivalent( Z, Y ) )
% 0.83/1.33 , :=( Y, equivalent( X, Y ) ), :=( Z, equivalent( Z, X ) )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ] )
% 0.83/1.33 , clause( 7078, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.83/1.33 ), equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7079, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 0.83/1.33 , clause( 7, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 0.83/1.33 , 1, clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.83/1.33 ), equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, equivalent( X, X ) )] )
% 0.83/1.33 , substitution( 1, [ :=( X, X ), :=( Y, X ), :=( Z, X )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 11, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 0.83/1.33 , clause( 7079, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7081, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.83/1.33 equivalent( X, Y ), equivalent( Z, X ) ), equivalent( Z, Y ) ), T ) ) ),
% 0.83/1.33 'is_a_theorem'( T ) ] )
% 0.83/1.33 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.83/1.33 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.83/1.33 , 2, clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.83/1.33 ), equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( Z, X ) ), equivalent( Z, Y ) ) ), :=( Y, T )] ),
% 0.83/1.33 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 12, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, X ) ),
% 0.83/1.33 equivalent( Z, Y ) ), T ) ) ) ] )
% 0.83/1.33 , clause( 7081, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.83/1.33 equivalent( X, Y ), equivalent( Z, X ) ), equivalent( Z, Y ) ), T ) ) ),
% 0.83/1.33 'is_a_theorem'( T ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7083, [ ~( 'is_a_theorem'( equivalent( equivalent( X, X ), Y ) ) )
% 0.83/1.33 , 'is_a_theorem'( Y ) ] )
% 0.83/1.33 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.83/1.33 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.83/1.33 , 2, clause( 11, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( X, X ) ), :=( Y, Y )] ),
% 0.83/1.33 substitution( 1, [ :=( X, X )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 13, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( X, X ), Y ) ) ) ] )
% 0.83/1.33 , clause( 7083, [ ~( 'is_a_theorem'( equivalent( equivalent( X, X ), Y ) )
% 0.83/1.33 ), 'is_a_theorem'( Y ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 0.83/1.33 ), ==>( 1, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7084, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 equivalent( X, Z ), equivalent( equivalent( T, Y ), equivalent( Z, T ) )
% 0.83/1.33 ) ) ) ] )
% 0.83/1.33 , clause( 6, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), equivalent( T
% 0.83/1.33 , Y ) ) ), equivalent( equivalent( T, Z ), X ) ), U ) ) ) ] )
% 0.83/1.33 , 1, clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent( equivalent( T, Z
% 0.83/1.33 ), X ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( X, Z ) ), :=( Y, T ), :=( Z, Y )
% 0.83/1.33 , :=( T, Z ), :=( U, equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 equivalent( X, Z ), equivalent( equivalent( T, Y ), equivalent( Z, T ) )
% 0.83/1.33 ) ) )] ), substitution( 1, [ :=( X, equivalent( equivalent( X, Z ),
% 0.83/1.33 equivalent( equivalent( T, Y ), equivalent( Z, T ) ) ) ), :=( Y, Z ),
% 0.83/1.33 :=( Z, Y ), :=( T, X )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 15, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 equivalent( X, Z ), equivalent( equivalent( T, Y ), equivalent( Z, T ) )
% 0.83/1.33 ) ) ) ] )
% 0.83/1.33 , clause( 7084, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( X, Z ), equivalent( equivalent( T, Y ),
% 0.83/1.33 equivalent( Z, T ) ) ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7085, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 Y, X ) ) ) ] )
% 0.83/1.33 , clause( 13, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( X, X ), Y ) ) ) ] )
% 0.83/1.33 , 1, clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, Y ), :=( Y, equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( Y, X ) ) )] ), substitution( 1, [ :=( X, Y ), :=( Y, Y ),
% 0.83/1.33 :=( Z, X )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 17, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( Y
% 0.83/1.33 , X ) ) ) ] )
% 0.83/1.33 , clause( 7085, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( Y, X ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.83/1.33 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7087, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.83/1.33 ), equivalent( Y, X ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.83/1.33 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.83/1.33 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.83/1.33 , 2, clause( 17, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( Y, X ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 Y, X ) ) ), :=( Y, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 0.83/1.33 ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 18, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, Y ), equivalent( Y, X ) ), Z ) ) ) ] )
% 0.83/1.33 , clause( 7087, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.83/1.33 , Y ), equivalent( Y, X ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7088, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 equivalent( X, Z ), equivalent( Z, Y ) ) ) ) ] )
% 0.83/1.33 , clause( 18, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, Y ), equivalent( Y, X ) ), Z ) ) ) ] )
% 0.83/1.33 , 1, clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent( equivalent( T, Z
% 0.83/1.33 ), X ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( X, Z ) ), :=( Y, equivalent( Z,
% 0.83/1.33 Y ) ), :=( Z, equivalent( equivalent( X, Y ), equivalent( equivalent( X,
% 0.83/1.33 Z ), equivalent( Z, Y ) ) ) )] ), substitution( 1, [ :=( X, equivalent(
% 0.83/1.33 equivalent( X, Z ), equivalent( Z, Y ) ) ), :=( Y, Z ), :=( Z, Y ), :=( T
% 0.83/1.33 , X )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 19, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 equivalent( X, Z ), equivalent( Z, Y ) ) ) ) ] )
% 0.83/1.33 , clause( 7088, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( X, Z ), equivalent( Z, Y ) ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7089, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.83/1.33 ) ), equivalent( equivalent( Z, Y ), X ) ) ) ] )
% 0.83/1.33 , clause( 18, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, Y ), equivalent( Y, X ) ), Z ) ) ) ] )
% 0.83/1.33 , 1, clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, equivalent(
% 0.83/1.33 equivalent( X, equivalent( Y, Z ) ), equivalent( equivalent( Z, Y ), X )
% 0.83/1.33 ) )] ), substitution( 1, [ :=( X, equivalent( Z, Y ) ), :=( Y,
% 0.83/1.33 equivalent( Y, Z ) ), :=( Z, X )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 20, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 0.83/1.33 ), equivalent( equivalent( Z, Y ), X ) ) ) ] )
% 0.83/1.33 , clause( 7089, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.83/1.33 , Z ) ), equivalent( equivalent( Z, Y ), X ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7090, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.83/1.33 equivalent( equivalent( Y, Z ), equivalent( T, Y ) ) ), U ), equivalent(
% 0.83/1.33 U, equivalent( equivalent( T, Z ), X ) ) ) ) ] )
% 0.83/1.33 , clause( 6, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), equivalent( T
% 0.83/1.33 , Y ) ) ), equivalent( equivalent( T, Z ), X ) ), U ) ) ) ] )
% 0.83/1.33 , 1, clause( 19, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( X, Z ), equivalent( Z, Y ) ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 0.83/1.33 :=( U, equivalent( equivalent( equivalent( X, equivalent( equivalent( Y,
% 0.83/1.33 Z ), equivalent( T, Y ) ) ), U ), equivalent( U, equivalent( equivalent(
% 0.83/1.33 T, Z ), X ) ) ) )] ), substitution( 1, [ :=( X, equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, Z ), equivalent( T, Y ) ) ) ), :=( Y, equivalent(
% 0.83/1.33 equivalent( T, Z ), X ) ), :=( Z, U )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 22, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.83/1.33 equivalent( equivalent( Y, Z ), equivalent( T, Y ) ) ), U ), equivalent(
% 0.83/1.33 U, equivalent( equivalent( T, Z ), X ) ) ) ) ] )
% 0.83/1.33 , clause( 7090, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.83/1.33 equivalent( equivalent( Y, Z ), equivalent( T, Y ) ) ), U ), equivalent(
% 0.83/1.33 U, equivalent( equivalent( T, Z ), X ) ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.83/1.33 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7092, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.83/1.33 ), equivalent( equivalent( X, Z ), equivalent( Z, Y ) ) ), T ) ) ),
% 0.83/1.33 'is_a_theorem'( T ) ] )
% 0.83/1.33 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.83/1.33 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.83/1.33 , 2, clause( 19, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( X, Z ), equivalent( Z, Y ) ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 equivalent( X, Z ), equivalent( Z, Y ) ) ) ), :=( Y, T )] ),
% 0.83/1.33 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 23, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.83/1.33 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 0.83/1.33 , clause( 7092, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.83/1.33 , Y ), equivalent( equivalent( X, Z ), equivalent( Z, Y ) ) ), T ) ) ),
% 0.83/1.33 'is_a_theorem'( T ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7093, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.83/1.33 , equivalent( Y, Z ) ), equivalent( X, Z ) ) ) ] )
% 0.83/1.33 , clause( 3, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, Y ),
% 0.83/1.33 equivalent( X, Z ) ) ), T ) ) ) ] )
% 0.83/1.33 , 1, clause( 20, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.83/1.33 , Z ) ), equivalent( equivalent( Z, Y ), X ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T,
% 0.83/1.33 equivalent( equivalent( equivalent( X, Y ), equivalent( Y, Z ) ),
% 0.83/1.33 equivalent( X, Z ) ) )] ), substitution( 1, [ :=( X, equivalent( X, Z ) )
% 0.83/1.33 , :=( Y, equivalent( Y, Z ) ), :=( Z, equivalent( X, Y ) )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 29, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( Y, Z ) ), equivalent( X, Z ) ) ) ] )
% 0.83/1.33 , clause( 7093, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.83/1.33 ), equivalent( Y, Z ) ), equivalent( X, Z ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7095, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.83/1.33 equivalent( Y, Z ) ), equivalent( equivalent( Z, Y ), X ) ), T ) ) ),
% 0.83/1.33 'is_a_theorem'( T ) ] )
% 0.83/1.33 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.83/1.33 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.83/1.33 , 2, clause( 20, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.83/1.33 , Z ) ), equivalent( equivalent( Z, Y ), X ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, equivalent( Y, Z
% 0.83/1.33 ) ), equivalent( equivalent( Z, Y ), X ) ) ), :=( Y, T )] ),
% 0.83/1.33 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 30, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( equivalent(
% 0.83/1.33 Z, Y ), X ) ), T ) ) ) ] )
% 0.83/1.33 , clause( 7095, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.83/1.33 , equivalent( Y, Z ) ), equivalent( equivalent( Z, Y ), X ) ), T ) ) ),
% 0.83/1.33 'is_a_theorem'( T ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7097, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.83/1.33 equivalent( X, Y ), equivalent( Y, Z ) ), equivalent( X, Z ) ), T ) ) ),
% 0.83/1.33 'is_a_theorem'( T ) ] )
% 0.83/1.33 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.83/1.33 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.83/1.33 , 2, clause( 29, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.83/1.33 ), equivalent( Y, Z ) ), equivalent( X, Z ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( Y, Z ) ), equivalent( X, Z ) ) ), :=( Y, T )] ),
% 0.83/1.33 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 31, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( equivalent( X, Y ), equivalent( Y, Z ) ),
% 0.83/1.33 equivalent( X, Z ) ), T ) ) ) ] )
% 0.83/1.33 , clause( 7097, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.83/1.33 equivalent( X, Y ), equivalent( Y, Z ) ), equivalent( X, Z ) ), T ) ) ),
% 0.83/1.33 'is_a_theorem'( T ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7098, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.83/1.33 equivalent( X, Y ), equivalent( Z, X ) ), T ), equivalent( T, equivalent(
% 0.83/1.33 Z, Y ) ) ) ) ] )
% 0.83/1.33 , clause( 12, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, X ) ),
% 0.83/1.33 equivalent( Z, Y ) ), T ) ) ) ] )
% 0.83/1.33 , 1, clause( 19, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( X, Z ), equivalent( Z, Y ) ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 0.83/1.33 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( Z, X
% 0.83/1.33 ) ), T ), equivalent( T, equivalent( Z, Y ) ) ) )] ), substitution( 1, [
% 0.83/1.33 :=( X, equivalent( equivalent( X, Y ), equivalent( Z, X ) ) ), :=( Y,
% 0.83/1.33 equivalent( Z, Y ) ), :=( Z, T )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 33, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.83/1.33 equivalent( X, Y ), equivalent( Z, X ) ), T ), equivalent( T, equivalent(
% 0.83/1.33 Z, Y ) ) ) ) ] )
% 0.83/1.33 , clause( 7098, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.83/1.33 equivalent( X, Y ), equivalent( Z, X ) ), T ), equivalent( T, equivalent(
% 0.83/1.33 Z, Y ) ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7099, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.83/1.33 , equivalent( equivalent( X, Z ), T ) ), equivalent( equivalent( Z, Y ),
% 0.83/1.33 T ) ) ) ] )
% 0.83/1.33 , clause( 6, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), equivalent( T
% 0.83/1.33 , Y ) ) ), equivalent( equivalent( T, Z ), X ) ), U ) ) ) ] )
% 0.83/1.33 , 1, clause( 33, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.83/1.33 equivalent( X, Y ), equivalent( Z, X ) ), T ), equivalent( T, equivalent(
% 0.83/1.33 Z, Y ) ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Z ), T ) ), :=( Y
% 0.83/1.33 , Z ), :=( Z, Y ), :=( T, X ), :=( U, equivalent( equivalent( equivalent(
% 0.83/1.33 X, Y ), equivalent( equivalent( X, Z ), T ) ), equivalent( equivalent( Z
% 0.83/1.33 , Y ), T ) ) )] ), substitution( 1, [ :=( X, equivalent( X, Z ) ), :=( Y
% 0.83/1.33 , T ), :=( Z, equivalent( Z, Y ) ), :=( T, equivalent( equivalent( X, Y )
% 0.83/1.33 , equivalent( equivalent( X, Z ), T ) ) )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 38, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( X, Z ), T ) ), equivalent( equivalent( Z, Y ), T
% 0.83/1.33 ) ) ) ] )
% 0.83/1.33 , clause( 7099, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.83/1.33 ), equivalent( equivalent( X, Z ), T ) ), equivalent( equivalent( Z, Y )
% 0.83/1.33 , T ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7100, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, X
% 0.83/1.33 ) ), Y ) ) ] )
% 0.83/1.33 , clause( 18, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, Y ), equivalent( Y, X ) ), Z ) ) ) ] )
% 0.83/1.33 , 1, clause( 38, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.83/1.33 ), equivalent( equivalent( X, Z ), T ) ), equivalent( equivalent( Z, Y )
% 0.83/1.33 , T ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, Y ), :=( Y, equivalent( Y, X ) ), :=( Z,
% 0.83/1.33 equivalent( equivalent( X, equivalent( Y, X ) ), Y ) )] ), substitution(
% 0.83/1.33 1, [ :=( X, Y ), :=( Y, equivalent( Y, X ) ), :=( Z, X ), :=( T, Y )] )
% 0.83/1.33 ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 42, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, X )
% 0.83/1.33 ), Y ) ) ] )
% 0.83/1.33 , clause( 7100, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.83/1.33 , X ) ), Y ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.83/1.33 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7102, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.83/1.33 equivalent( X, Y ), equivalent( equivalent( X, Z ), T ) ), equivalent(
% 0.83/1.33 equivalent( Z, Y ), T ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.83/1.33 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.83/1.33 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.83/1.33 , 2, clause( 38, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.83/1.33 ), equivalent( equivalent( X, Z ), T ) ), equivalent( equivalent( Z, Y )
% 0.83/1.33 , T ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( X, Z ), T ) ), equivalent( equivalent( Z, Y ), T
% 0.83/1.33 ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z,
% 0.83/1.33 Z ), :=( T, T )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 45, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z
% 0.83/1.33 ), T ) ), equivalent( equivalent( Z, Y ), T ) ), U ) ) ) ] )
% 0.83/1.33 , clause( 7102, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.83/1.33 equivalent( X, Y ), equivalent( equivalent( X, Z ), T ) ), equivalent(
% 0.83/1.33 equivalent( Z, Y ), T ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.83/1.33 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7104, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.83/1.33 equivalent( Y, X ) ), Y ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.83/1.33 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.83/1.33 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.83/1.33 , 2, clause( 42, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.83/1.33 , X ) ), Y ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, equivalent( Y, X
% 0.83/1.33 ) ), Y ) ), :=( Y, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 0.83/1.33 ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 50, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, equivalent( Y, X ) ), Y ), Z ) ) ) ] )
% 0.83/1.33 , clause( 7104, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.83/1.33 , equivalent( Y, X ) ), Y ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7106, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.83/1.33 ), equivalent( equivalent( X, Z ), equivalent( equivalent( T, Y ),
% 0.83/1.33 equivalent( Z, T ) ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.83/1.33 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.83/1.33 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.83/1.33 , 2, clause( 15, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( X, Z ), equivalent( equivalent( T, Y ),
% 0.83/1.33 equivalent( Z, T ) ) ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 equivalent( X, Z ), equivalent( equivalent( T, Y ), equivalent( Z, T ) )
% 0.83/1.33 ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z,
% 0.83/1.33 Z ), :=( T, T )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 60, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.83/1.33 equivalent( equivalent( T, Y ), equivalent( Z, T ) ) ) ), U ) ) ) ] )
% 0.83/1.33 , clause( 7106, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.83/1.33 , Y ), equivalent( equivalent( X, Z ), equivalent( equivalent( T, Y ),
% 0.83/1.33 equivalent( Z, T ) ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.83/1.33 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7107, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 equivalent( Z, Y ), equivalent( Z, X ) ) ) ) ] )
% 0.83/1.33 , clause( 50, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, equivalent( Y, X ) ), Y ), Z ) ) ) ] )
% 0.83/1.33 , 1, clause( 22, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.83/1.33 equivalent( equivalent( Y, Z ), equivalent( T, Y ) ) ), U ), equivalent(
% 0.83/1.33 U, equivalent( equivalent( T, Z ), X ) ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( Z, X ) ), :=( Y, equivalent( X,
% 0.83/1.33 Y ) ), :=( Z, equivalent( equivalent( X, Y ), equivalent( equivalent( Z,
% 0.83/1.33 Y ), equivalent( Z, X ) ) ) )] ), substitution( 1, [ :=( X, equivalent( Z
% 0.83/1.33 , X ) ), :=( Y, X ), :=( Z, Y ), :=( T, Z ), :=( U, equivalent( X, Y ) )] )
% 0.83/1.33 ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 96, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 equivalent( Z, Y ), equivalent( Z, X ) ) ) ) ] )
% 0.83/1.33 , clause( 7107, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( Z, Y ), equivalent( Z, X ) ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7108, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, Z ), equivalent( Z, T ) ) ), equivalent( X, equivalent( Y
% 0.83/1.33 , T ) ) ) ) ] )
% 0.83/1.33 , clause( 23, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.83/1.33 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 0.83/1.33 , 1, clause( 96, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( Z, Y ), equivalent( Z, X ) ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, Y ), :=( Y, T ), :=( Z, Z ), :=( T,
% 0.83/1.33 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), equivalent( Z
% 0.83/1.33 , T ) ) ), equivalent( X, equivalent( Y, T ) ) ) )] ), substitution( 1, [
% 0.83/1.33 :=( X, equivalent( Y, T ) ), :=( Y, equivalent( equivalent( Y, Z ),
% 0.83/1.33 equivalent( Z, T ) ) ), :=( Z, X )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 120, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, Z ), equivalent( Z, T ) ) ), equivalent( X, equivalent( Y
% 0.83/1.33 , T ) ) ) ) ] )
% 0.83/1.33 , clause( 7108, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, Z ), equivalent( Z, T ) ) ), equivalent( X, equivalent( Y
% 0.83/1.33 , T ) ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7109, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.83/1.33 , clause( 30, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( equivalent(
% 0.83/1.33 Z, Y ), X ) ), T ) ) ) ] )
% 0.83/1.33 , 1, clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent( equivalent( T, Z
% 0.83/1.33 ), X ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( X, Z ) ), :=( Y, Y ), :=( Z, Z )
% 0.83/1.33 , :=( T, equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.83/1.33 equivalent( Y, Z ) ) ) )] ), substitution( 1, [ :=( X, equivalent(
% 0.83/1.33 equivalent( X, Z ), equivalent( Y, Z ) ) ), :=( Y, Z ), :=( Z, Y ), :=( T
% 0.83/1.33 , X )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 235, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.83/1.33 , clause( 7109, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7110, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.83/1.33 equivalent( Y, X ) ), Z ), equivalent( Y, Z ) ) ) ] )
% 0.83/1.33 , clause( 50, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, equivalent( Y, X ) ), Y ), Z ) ) ) ] )
% 0.83/1.33 , 1, clause( 235, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( X, Z ), equivalent( Y, Z ) ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, equivalent(
% 0.83/1.33 equivalent( equivalent( X, equivalent( Y, X ) ), Z ), equivalent( Y, Z )
% 0.83/1.33 ) )] ), substitution( 1, [ :=( X, equivalent( X, equivalent( Y, X ) ) )
% 0.83/1.33 , :=( Y, Y ), :=( Z, Z )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 241, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.83/1.33 equivalent( Y, X ) ), Z ), equivalent( Y, Z ) ) ) ] )
% 0.83/1.33 , clause( 7110, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.83/1.33 equivalent( Y, X ) ), Z ), equivalent( Y, Z ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7111, [ 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Y
% 0.83/1.33 , X ) ) ) ) ] )
% 0.83/1.33 , clause( 31, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( equivalent( X, Y ), equivalent( Y, Z ) ),
% 0.83/1.33 equivalent( X, Z ) ), T ) ) ) ] )
% 0.83/1.33 , 1, clause( 241, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.83/1.33 equivalent( Y, X ) ), Z ), equivalent( Y, Z ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, equivalent( Y, X ) )
% 0.83/1.33 , :=( T, equivalent( X, equivalent( Y, equivalent( Y, X ) ) ) )] ),
% 0.83/1.33 substitution( 1, [ :=( X, equivalent( Y, X ) ), :=( Y, X ), :=( Z,
% 0.83/1.33 equivalent( Y, equivalent( Y, X ) ) )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 258, [ 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Y
% 0.83/1.33 , X ) ) ) ) ] )
% 0.83/1.33 , clause( 7111, [ 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent(
% 0.83/1.33 Y, X ) ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.83/1.33 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7113, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.83/1.33 , equivalent( Y, X ) ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.83/1.33 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.83/1.33 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.83/1.33 , 2, clause( 258, [ 'is_a_theorem'( equivalent( X, equivalent( Y,
% 0.83/1.33 equivalent( Y, X ) ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( Y, equivalent( Y
% 0.83/1.33 , X ) ) ) ), :=( Y, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 0.83/1.33 ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 274, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( X, equivalent( Y, equivalent( Y, X ) ) ), Z ) ) ) ] )
% 0.83/1.33 , clause( 7113, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 Y, equivalent( Y, X ) ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7114, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 X, equivalent( equivalent( Z, Y ), Z ) ) ) ) ] )
% 0.83/1.33 , clause( 60, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z ),
% 0.83/1.33 equivalent( equivalent( T, Y ), equivalent( Z, T ) ) ) ), U ) ) ) ] )
% 0.83/1.33 , 1, clause( 120, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, Z ), equivalent( Z, T ) ) ), equivalent( X, equivalent( Y
% 0.83/1.33 , T ) ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, equivalent( Z, Y ) )
% 0.83/1.33 , :=( T, Z ), :=( U, equivalent( equivalent( X, Y ), equivalent( X,
% 0.83/1.33 equivalent( equivalent( Z, Y ), Z ) ) ) )] ), substitution( 1, [ :=( X,
% 0.83/1.33 equivalent( X, Y ) ), :=( Y, X ), :=( Z, equivalent( Z, Y ) ), :=( T,
% 0.83/1.33 equivalent( equivalent( Z, Y ), Z ) )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 3604, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 X, equivalent( equivalent( Z, Y ), Z ) ) ) ) ] )
% 0.83/1.33 , clause( 7114, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( X, equivalent( equivalent( Z, Y ), Z ) ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7115, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 equivalent( Z, equivalent( Y, X ) ), Z ) ) ) ] )
% 0.83/1.33 , clause( 18, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( X, Y ), equivalent( Y, X ) ), Z ) ) ) ] )
% 0.83/1.33 , 1, clause( 3604, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( X, equivalent( equivalent( Z, Y ), Z ) ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, equivalent(
% 0.83/1.33 equivalent( X, Y ), equivalent( equivalent( Z, equivalent( Y, X ) ), Z )
% 0.83/1.33 ) )] ), substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y,
% 0.83/1.33 equivalent( Y, X ) ), :=( Z, Z )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 3635, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.83/1.33 equivalent( Z, equivalent( Y, X ) ), Z ) ) ) ] )
% 0.83/1.33 , clause( 7115, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( Z, equivalent( Y, X ) ), Z ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7116, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, equivalent( Y, Z ) ), Z ) ), X ) ) ] )
% 0.83/1.33 , clause( 274, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( X, equivalent( Y, equivalent( Y, X ) ) ), Z ) ) ) ] )
% 0.83/1.33 , 1, clause( 3635, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.83/1.33 equivalent( equivalent( Z, equivalent( Y, X ) ), Z ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, equivalent(
% 0.83/1.33 equivalent( X, equivalent( equivalent( Y, equivalent( Y, Z ) ), Z ) ), X
% 0.83/1.33 ) )] ), substitution( 1, [ :=( X, Z ), :=( Y, equivalent( Y, equivalent(
% 0.83/1.33 Y, Z ) ) ), :=( Z, X )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 6141, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, equivalent( Y, Z ) ), Z ) ), X ) ) ] )
% 0.83/1.33 , clause( 7116, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, equivalent( Y, Z ) ), Z ) ), X ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7117, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.83/1.33 ) ), equivalent( equivalent( X, Y ), Z ) ) ) ] )
% 0.83/1.33 , clause( 45, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.83/1.33 equivalent( equivalent( equivalent( X, Y ), equivalent( equivalent( X, Z
% 0.83/1.33 ), T ) ), equivalent( equivalent( Z, Y ), T ) ), U ) ) ) ] )
% 0.83/1.33 , 1, clause( 6141, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 equivalent( Y, equivalent( Y, Z ) ), Z ) ), X ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [ :=( X, X ), :=( Y, equivalent( Y, Z ) ), :=( Z, Y )
% 0.83/1.33 , :=( T, Z ), :=( U, equivalent( equivalent( X, equivalent( Y, Z ) ),
% 0.83/1.33 equivalent( equivalent( X, Y ), Z ) ) )] ), substitution( 1, [ :=( X,
% 0.83/1.33 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( equivalent(
% 0.83/1.33 X, Y ), Z ) ) ), :=( Y, Y ), :=( Z, Z )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 7059, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.83/1.33 ) ), equivalent( equivalent( X, Y ), Z ) ) ) ] )
% 0.83/1.33 , clause( 7117, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.83/1.33 , Z ) ), equivalent( equivalent( X, Y ), Z ) ) ) ] )
% 0.83/1.33 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.83/1.33 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 resolution(
% 0.83/1.33 clause( 7118, [] )
% 0.83/1.33 , clause( 2, [ ~( 'is_a_theorem'( equivalent( equivalent( a, equivalent( b
% 0.83/1.33 , c ) ), equivalent( equivalent( a, b ), c ) ) ) ) ] )
% 0.83/1.33 , 0, clause( 7059, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.83/1.33 Y, Z ) ), equivalent( equivalent( X, Y ), Z ) ) ) ] )
% 0.83/1.33 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, b ), :=(
% 0.83/1.33 Z, c )] )).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 subsumption(
% 0.83/1.33 clause( 7064, [] )
% 0.83/1.33 , clause( 7118, [] )
% 0.83/1.33 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 end.
% 0.83/1.33
% 0.83/1.33 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.83/1.33
% 0.83/1.33 Memory use:
% 0.83/1.33
% 0.83/1.33 space for terms: 133993
% 0.83/1.33 space for clauses: 607949
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 clauses generated: 15050
% 0.83/1.33 clauses kept: 7065
% 0.83/1.33 clauses selected: 544
% 0.83/1.33 clauses deleted: 4
% 0.83/1.33 clauses inuse deleted: 3
% 0.83/1.33
% 0.83/1.33 subsentry: 8769
% 0.83/1.33 literals s-matched: 7990
% 0.83/1.33 literals matched: 7990
% 0.83/1.33 full subsumption: 0
% 0.83/1.33
% 0.83/1.33 checksum: 928142542
% 0.83/1.33
% 0.83/1.33
% 0.83/1.33 Bliksem ended
%------------------------------------------------------------------------------