TSTP Solution File: LCL096-10 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL096-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 07:50:16 EDT 2022
% Result : Unsatisfiable 2.10s 2.49s
% Output : Refutation 2.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL096-10 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Mon Jul 4 05:14:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.10/2.49 *** allocated 10000 integers for termspace/termends
% 2.10/2.49 *** allocated 10000 integers for clauses
% 2.10/2.49 *** allocated 10000 integers for justifications
% 2.10/2.49 Bliksem 1.12
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 Automatic Strategy Selection
% 2.10/2.49
% 2.10/2.49 Clauses:
% 2.10/2.49 [
% 2.10/2.49 [ =( ifeq( X, X, Y, Z ), Y ) ],
% 2.10/2.49 [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.49 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.49 ,
% 2.10/2.49 [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ), T ), T )
% 2.10/2.49 ), true ) ],
% 2.10/2.49 [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent(
% 2.10/2.49 equivalent( Y, Z ), T ) ), U ), U ) ), true ) ],
% 2.10/2.49 [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( equivalent( X,
% 2.10/2.49 Y ), Z ), T ), equivalent( equivalent( equivalent( X, U ), Z ),
% 2.10/2.49 equivalent( equivalent( Y, U ), T ) ) ) ), true ) ],
% 2.10/2.49 [ ~( =( 'is_a_theorem'( equivalent( equivalent( equivalent( a,
% 2.10/2.49 equivalent( equivalent( b, b ), a ) ), c ), c ) ), true ) ) ]
% 2.10/2.49 ] .
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 percentage equality = 1.000000, percentage horn = 1.000000
% 2.10/2.49 This is a pure equality problem
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 Options Used:
% 2.10/2.49
% 2.10/2.49 useres = 1
% 2.10/2.49 useparamod = 1
% 2.10/2.49 useeqrefl = 1
% 2.10/2.49 useeqfact = 1
% 2.10/2.49 usefactor = 1
% 2.10/2.49 usesimpsplitting = 0
% 2.10/2.49 usesimpdemod = 5
% 2.10/2.49 usesimpres = 3
% 2.10/2.49
% 2.10/2.49 resimpinuse = 1000
% 2.10/2.49 resimpclauses = 20000
% 2.10/2.49 substype = eqrewr
% 2.10/2.49 backwardsubs = 1
% 2.10/2.49 selectoldest = 5
% 2.10/2.49
% 2.10/2.49 litorderings [0] = split
% 2.10/2.49 litorderings [1] = extend the termordering, first sorting on arguments
% 2.10/2.49
% 2.10/2.49 termordering = kbo
% 2.10/2.49
% 2.10/2.49 litapriori = 0
% 2.10/2.49 termapriori = 1
% 2.10/2.49 litaposteriori = 0
% 2.10/2.49 termaposteriori = 0
% 2.10/2.49 demodaposteriori = 0
% 2.10/2.49 ordereqreflfact = 0
% 2.10/2.49
% 2.10/2.49 litselect = negord
% 2.10/2.49
% 2.10/2.49 maxweight = 15
% 2.10/2.49 maxdepth = 30000
% 2.10/2.49 maxlength = 115
% 2.10/2.49 maxnrvars = 195
% 2.10/2.49 excuselevel = 1
% 2.10/2.49 increasemaxweight = 1
% 2.10/2.49
% 2.10/2.49 maxselected = 10000000
% 2.10/2.49 maxnrclauses = 10000000
% 2.10/2.49
% 2.10/2.49 showgenerated = 0
% 2.10/2.49 showkept = 0
% 2.10/2.49 showselected = 0
% 2.10/2.49 showdeleted = 0
% 2.10/2.49 showresimp = 1
% 2.10/2.49 showstatus = 2000
% 2.10/2.49
% 2.10/2.49 prologoutput = 1
% 2.10/2.49 nrgoals = 5000000
% 2.10/2.49 totalproof = 1
% 2.10/2.49
% 2.10/2.49 Symbols occurring in the translation:
% 2.10/2.49
% 2.10/2.49 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.10/2.49 . [1, 2] (w:1, o:27, a:1, s:1, b:0),
% 2.10/2.49 ! [4, 1] (w:0, o:21, a:1, s:1, b:0),
% 2.10/2.49 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.10/2.49 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.10/2.49 ifeq [42, 4] (w:1, o:53, a:1, s:1, b:0),
% 2.10/2.49 equivalent [45, 2] (w:1, o:52, a:1, s:1, b:0),
% 2.10/2.49 'is_a_theorem' [46, 1] (w:1, o:26, a:1, s:1, b:0),
% 2.10/2.49 true [47, 0] (w:1, o:14, a:1, s:1, b:0),
% 2.10/2.49 a [51, 0] (w:1, o:18, a:1, s:1, b:0),
% 2.10/2.49 b [52, 0] (w:1, o:19, a:1, s:1, b:0),
% 2.10/2.49 c [53, 0] (w:1, o:20, a:1, s:1, b:0).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 Starting Search:
% 2.10/2.49
% 2.10/2.49 Resimplifying inuse:
% 2.10/2.49 Done
% 2.10/2.49
% 2.10/2.49 Failed to find proof!
% 2.10/2.49 maxweight = 15
% 2.10/2.49 maxnrclauses = 10000000
% 2.10/2.49 Generated: 270
% 2.10/2.49 Kept: 25
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 The strategy used was not complete!
% 2.10/2.49
% 2.10/2.49 Increased maxweight to 16
% 2.10/2.49
% 2.10/2.49 Starting Search:
% 2.10/2.49
% 2.10/2.49 Resimplifying inuse:
% 2.10/2.49 Done
% 2.10/2.49
% 2.10/2.49 Failed to find proof!
% 2.10/2.49 maxweight = 16
% 2.10/2.49 maxnrclauses = 10000000
% 2.10/2.49 Generated: 270
% 2.10/2.49 Kept: 25
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 The strategy used was not complete!
% 2.10/2.49
% 2.10/2.49 Increased maxweight to 17
% 2.10/2.49
% 2.10/2.49 Starting Search:
% 2.10/2.49
% 2.10/2.49 Resimplifying inuse:
% 2.10/2.49 Done
% 2.10/2.49
% 2.10/2.49 Failed to find proof!
% 2.10/2.49 maxweight = 17
% 2.10/2.49 maxnrclauses = 10000000
% 2.10/2.49 Generated: 459
% 2.10/2.49 Kept: 33
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 The strategy used was not complete!
% 2.10/2.49
% 2.10/2.49 Increased maxweight to 18
% 2.10/2.49
% 2.10/2.49 Starting Search:
% 2.10/2.49
% 2.10/2.49 Resimplifying inuse:
% 2.10/2.49 Done
% 2.10/2.49
% 2.10/2.49 Failed to find proof!
% 2.10/2.49 maxweight = 18
% 2.10/2.49 maxnrclauses = 10000000
% 2.10/2.49 Generated: 13111
% 2.10/2.49 Kept: 187
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 The strategy used was not complete!
% 2.10/2.49
% 2.10/2.49 Increased maxweight to 19
% 2.10/2.49
% 2.10/2.49 Starting Search:
% 2.10/2.49
% 2.10/2.49 Resimplifying inuse:
% 2.10/2.49 Done
% 2.10/2.49
% 2.10/2.49 Failed to find proof!
% 2.10/2.49 maxweight = 19
% 2.10/2.49 maxnrclauses = 10000000
% 2.10/2.49 Generated: 13111
% 2.10/2.49 Kept: 187
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 The strategy used was not complete!
% 2.10/2.49
% 2.10/2.49 Increased maxweight to 20
% 2.10/2.49
% 2.10/2.49 Starting Search:
% 2.10/2.49
% 2.10/2.49 Resimplifying inuse:
% 2.10/2.49 Done
% 2.10/2.49
% 2.10/2.49 Failed to find proof!
% 2.10/2.49 maxweight = 20
% 2.10/2.49 maxnrclauses = 10000000
% 2.10/2.49 Generated: 13111
% 2.10/2.49 Kept: 187
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 The strategy used was not complete!
% 2.10/2.49
% 2.10/2.49 Increased maxweight to 21
% 2.10/2.49
% 2.10/2.49 Starting Search:
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 Bliksems!, er is een bewijs:
% 2.10/2.49 % SZS status Unsatisfiable
% 2.10/2.49 % SZS output start Refutation
% 2.10/2.49
% 2.10/2.49 clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.49 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.49 )
% 2.10/2.49 .
% 2.10/2.49 clause( 2, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ), T ), T ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 3, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.49 equivalent( equivalent( Y, Z ), T ) ), U ), U ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 4, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 2.10/2.49 , Z ), equivalent( equivalent( Y, U ), T ) ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 5, [ ~( =( 'is_a_theorem'( equivalent( equivalent( equivalent( a,
% 2.10/2.49 equivalent( equivalent( b, b ), a ) ), c ), c ) ), true ) ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 6, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ), T ) ),
% 2.10/2.49 true, 'is_a_theorem'( T ), true ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 7, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 2.10/2.49 equivalent( Y, Z ) ), T ), T ), U ) ), true, 'is_a_theorem'( U ), true )
% 2.10/2.49 , true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 9, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent(
% 2.10/2.49 equivalent( Y, Z ), T ) ), U ) ), true, 'is_a_theorem'( U ), true ), true
% 2.10/2.49 ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 12, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, T )
% 2.10/2.49 , equivalent( X, Z ) ), equivalent( equivalent( Y, T ), equivalent( Y, Z
% 2.10/2.49 ) ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 16, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent( T,
% 2.10/2.49 Y ), equivalent( T, Z ) ) ), true ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 17, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( X,
% 2.10/2.49 Z ) ), equivalent( T, equivalent( X, Z ) ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 18, [ =( 'is_a_theorem'( equivalent( equivalent( U, T ), equivalent(
% 2.10/2.49 U, equivalent( equivalent( Y, Y ), T ) ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 19, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 2.10/2.49 , equivalent( X, Z ) ), equivalent( Y, Z ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 22, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Z ), equivalent(
% 2.10/2.49 Y, Z ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 26, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ), true
% 2.10/2.49 ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 28, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.49 'is_a_theorem'( equivalent( X, equivalent( equivalent( Z, Z ), Y ) ) ),
% 2.10/2.49 true ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 30, [ =( 'is_a_theorem'( equivalent( Y, equivalent( equivalent( Z,
% 2.10/2.49 Z ), Y ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 31, [ =( 'is_a_theorem'( equivalent( Y, Y ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 36, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 2.10/2.49 equivalent( equivalent( Y, Y ), X ) ), true ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 39, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( Y
% 2.10/2.49 , Z ), T ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 40, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Z )
% 2.10/2.49 , T ), equivalent( equivalent( Y, Z ), equivalent( equivalent( X, Y ), T
% 2.10/2.49 ) ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 43, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Y ), equivalent(
% 2.10/2.49 X, X ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 45, [ =( 'is_a_theorem'( equivalent( equivalent( Z, Z ), equivalent(
% 2.10/2.49 equivalent( X, X ), equivalent( Y, Y ) ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 51, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( X,
% 2.10/2.49 X ) ), equivalent( Z, equivalent( Y, Y ) ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 54, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ),
% 2.10/2.49 equivalent( T, T ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 101, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Z ),
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 104, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( equivalent( T, T ), equivalent( equivalent( Z, X ),
% 2.10/2.49 equivalent( Z, Y ) ) ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 106, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, Z ) ) ), equivalent( T, equivalent( Y
% 2.10/2.49 , Z ) ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 107, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.49 'is_a_theorem'( equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ),
% 2.10/2.49 true ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 112, [ =( 'is_a_theorem'( equivalent( Y, equivalent( equivalent( Z
% 2.10/2.49 , equivalent( X, X ) ), equivalent( Z, Y ) ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 118, [ =( 'is_a_theorem'( equivalent( Z, equivalent( X, equivalent(
% 2.10/2.49 equivalent( X, equivalent( Y, Y ) ), Z ) ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 129, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.49 equivalent( Y, equivalent( equivalent( Y, equivalent( Z, Z ) ), X ) ) ),
% 2.10/2.49 T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 138, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y, Z
% 2.10/2.49 ), T ), equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) )
% 2.10/2.49 , T ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 152, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( X
% 2.10/2.49 , Z ) ), equivalent( equivalent( equivalent( X, Y ), T ), equivalent( Y,
% 2.10/2.49 Z ) ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 230, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.49 equivalent( Y, Z ), equivalent( Y, T ) ) ) ), true, 'is_a_theorem'(
% 2.10/2.49 equivalent( X, equivalent( Z, T ) ) ), true ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 345, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y, T
% 2.10/2.49 ), X ), equivalent( T, equivalent( equivalent( Y, equivalent( Z, Z ) ),
% 2.10/2.49 X ) ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 367, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 2.10/2.49 ), equivalent( equivalent( Z, X ), T ) ), equivalent( equivalent( Z, Y )
% 2.10/2.49 , T ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 376, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 2.10/2.49 equivalent( X, X ), Z ) ), equivalent( T, Z ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 454, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.49 equivalent( Y, Y ), Z ) ) ), true, 'is_a_theorem'( equivalent( X, Z ) ),
% 2.10/2.49 true ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 489, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 2.10/2.49 ), equivalent( equivalent( Y, X ), Z ) ), Z ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 522, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ) ), equivalent(
% 2.10/2.49 T, Z ) ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 641, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.49 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ) ), true,
% 2.10/2.49 'is_a_theorem'( equivalent( X, T ) ), true ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 818, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 2.10/2.49 equivalent( equivalent( Y, Y ), X ) ), Z ), Z ) ), true ) ] )
% 2.10/2.49 .
% 2.10/2.49 clause( 820, [] )
% 2.10/2.49 .
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 % SZS output end Refutation
% 2.10/2.49 found a proof!
% 2.10/2.49
% 2.10/2.49 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.10/2.49
% 2.10/2.49 initialclauses(
% 2.10/2.49 [ clause( 822, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.49 , clause( 823, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.49 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.49 )
% 2.10/2.49 , clause( 824, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ), T ), T ) ), true ) ] )
% 2.10/2.49 , clause( 825, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.49 equivalent( equivalent( Y, Z ), T ) ), U ), U ) ), true ) ] )
% 2.10/2.49 , clause( 826, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 2.10/2.49 , Z ), equivalent( equivalent( Y, U ), T ) ) ) ), true ) ] )
% 2.10/2.49 , clause( 827, [ ~( =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 a, equivalent( equivalent( b, b ), a ) ), c ), c ) ), true ) ) ] )
% 2.10/2.49 ] ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.49 , clause( 822, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.49 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.10/2.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.49 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.49 )
% 2.10/2.49 , clause( 823, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.49 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.49 )
% 2.10/2.49 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.10/2.49 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 2, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ), T ), T ) ), true ) ] )
% 2.10/2.49 , clause( 824, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ), T ), T ) ), true ) ] )
% 2.10/2.49 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 2.10/2.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 3, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.49 equivalent( equivalent( Y, Z ), T ) ), U ), U ) ), true ) ] )
% 2.10/2.49 , clause( 825, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.49 equivalent( equivalent( Y, Z ), T ) ), U ), U ) ), true ) ] )
% 2.10/2.49 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 2.10/2.49 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 4, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 2.10/2.49 , Z ), equivalent( equivalent( Y, U ), T ) ) ) ), true ) ] )
% 2.10/2.49 , clause( 826, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 2.10/2.49 , Z ), equivalent( equivalent( Y, U ), T ) ) ) ), true ) ] )
% 2.10/2.49 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 2.10/2.49 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 5, [ ~( =( 'is_a_theorem'( equivalent( equivalent( equivalent( a,
% 2.10/2.49 equivalent( equivalent( b, b ), a ) ), c ), c ) ), true ) ) ] )
% 2.10/2.49 , clause( 827, [ ~( =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 a, equivalent( equivalent( b, b ), a ) ), c ), c ) ), true ) ) ] )
% 2.10/2.49 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 850, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.49 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 2.10/2.49 )
% 2.10/2.49 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.49 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.49 )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 852, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 2.10/2.49 equivalent( Y, Z ) ), T ) ), true, 'is_a_theorem'( T ), true ), true ) )
% 2.10/2.49 ] )
% 2.10/2.49 , clause( 2, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ), T ), T ) ), true ) ] )
% 2.10/2.49 , 0, clause( 850, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 2.10/2.49 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 2.10/2.49 ) ) ] )
% 2.10/2.49 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.49 , substitution( 1, [ :=( X, equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ), T ) ),
% 2.10/2.49 :=( Y, T )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 857, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 2.10/2.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.49 , 0, clause( 852, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 2.10/2.49 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 2.10/2.49 ) ), equivalent( Y, Z ) ), T ) ), true, 'is_a_theorem'( T ), true ),
% 2.10/2.49 true ) ) ] )
% 2.10/2.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 2.10/2.49 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 2.10/2.49 ) ), equivalent( Y, Z ) ), T ) ), true, 'is_a_theorem'( T ), true ) ),
% 2.10/2.49 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 2.10/2.49 :=( T, T )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 858, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ), T ) ),
% 2.10/2.49 true, 'is_a_theorem'( T ), true ), true ) ] )
% 2.10/2.49 , clause( 857, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.49 ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 6, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ), T ) ),
% 2.10/2.49 true, 'is_a_theorem'( T ), true ), true ) ] )
% 2.10/2.49 , clause( 858, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ), T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 2.10/2.49 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 2.10/2.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 860, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.49 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 2.10/2.49 )
% 2.10/2.49 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.49 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.49 )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 863, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 2.10/2.49 ) ), equivalent( Y, Z ) ), T ), T ), U ) ), true, ifeq( true, true,
% 2.10/2.49 'is_a_theorem'( U ), true ), true ) ) ] )
% 2.10/2.49 , clause( 2, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ), T ), T ) ), true ) ] )
% 2.10/2.49 , 0, clause( 860, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 2.10/2.49 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 2.10/2.49 ) ) ] )
% 2.10/2.49 , 0, 23, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.49 , substitution( 1, [ :=( X, equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ), T ), T ) ), :=( Y, U )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 865, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 2.10/2.49 ) ), equivalent( Y, Z ) ), T ), T ), U ) ), true, 'is_a_theorem'( U ),
% 2.10/2.49 true ) ) ] )
% 2.10/2.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.49 , 0, clause( 863, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 2.10/2.49 ) ), equivalent( Y, Z ) ), T ), T ), U ) ), true, ifeq( true, true,
% 2.10/2.49 'is_a_theorem'( U ), true ), true ) ) ] )
% 2.10/2.49 , 0, 22, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( U ) ),
% 2.10/2.49 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 2.10/2.49 :=( T, T ), :=( U, U )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 866, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 2.10/2.49 equivalent( Y, Z ) ), T ), T ), U ) ), true, 'is_a_theorem'( U ), true )
% 2.10/2.49 , true ) ] )
% 2.10/2.49 , clause( 865, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 2.10/2.49 ) ), equivalent( Y, Z ) ), T ), T ), U ) ), true, 'is_a_theorem'( U ),
% 2.10/2.49 true ) ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 2.10/2.49 :=( U, U )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 7, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 2.10/2.49 equivalent( Y, Z ) ), T ), T ), U ) ), true, 'is_a_theorem'( U ), true )
% 2.10/2.49 , true ) ] )
% 2.10/2.49 , clause( 866, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 2.10/2.49 ) ), equivalent( Y, Z ) ), T ), T ), U ) ), true, 'is_a_theorem'( U ),
% 2.10/2.49 true ), true ) ] )
% 2.10/2.49 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 2.10/2.49 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 868, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.49 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 2.10/2.49 )
% 2.10/2.49 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.49 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.49 )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 870, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 2.10/2.49 ) ), T ), equivalent( equivalent( Y, Z ), T ) ), U ) ), true,
% 2.10/2.49 'is_a_theorem'( U ), true ), true ) ) ] )
% 2.10/2.49 , clause( 3, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.49 equivalent( equivalent( Y, Z ), T ) ), U ), U ) ), true ) ] )
% 2.10/2.49 , 0, clause( 868, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 2.10/2.49 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 2.10/2.49 ) ) ] )
% 2.10/2.49 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 2.10/2.49 :=( U, U )] ), substitution( 1, [ :=( X, equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.49 equivalent( equivalent( Y, Z ), T ) ), U ) ), :=( Y, U )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 875, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.49 equivalent( equivalent( Y, Z ), T ) ), U ) ), true, 'is_a_theorem'( U ),
% 2.10/2.49 true ) ) ] )
% 2.10/2.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.49 , 0, clause( 870, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 2.10/2.49 equivalent( equivalent( equivalent( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Z ) ), T ), equivalent( equivalent( Y, Z ), T ) ), U ) ),
% 2.10/2.49 true, 'is_a_theorem'( U ), true ), true ) ) ] )
% 2.10/2.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 2.10/2.49 equivalent( equivalent( equivalent( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Z ) ), T ), equivalent( equivalent( Y, Z ), T ) ), U ) ),
% 2.10/2.49 true, 'is_a_theorem'( U ), true ) ), :=( Z, true )] ), substitution( 1, [
% 2.10/2.49 :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U, U )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 876, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent(
% 2.10/2.49 equivalent( Y, Z ), T ) ), U ) ), true, 'is_a_theorem'( U ), true ), true
% 2.10/2.49 ) ] )
% 2.10/2.49 , clause( 875, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.49 equivalent( equivalent( Y, Z ), T ) ), U ) ), true, 'is_a_theorem'( U ),
% 2.10/2.49 true ) ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 2.10/2.49 :=( U, U )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 9, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent(
% 2.10/2.49 equivalent( Y, Z ), T ) ), U ) ), true, 'is_a_theorem'( U ), true ), true
% 2.10/2.49 ) ] )
% 2.10/2.49 , clause( 876, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.49 equivalent( equivalent( Y, Z ), T ) ), U ) ), true, 'is_a_theorem'( U ),
% 2.10/2.49 true ), true ) ] )
% 2.10/2.49 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 2.10/2.49 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 878, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 2.10/2.49 , clause( 6, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ), T ) ),
% 2.10/2.49 true, 'is_a_theorem'( T ), true ), true ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.49 ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 880, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( equivalent( X, T ), equivalent( X, Z ) ), equivalent(
% 2.10/2.49 equivalent( Y, T ), equivalent( Y, Z ) ) ) ), true ) ) ] )
% 2.10/2.49 , clause( 4, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 2.10/2.49 , Z ), equivalent( equivalent( Y, U ), T ) ) ) ), true ) ] )
% 2.10/2.49 , 0, clause( 878, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 2.10/2.49 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, equivalent( X, Z
% 2.10/2.49 ) ), :=( T, equivalent( Y, Z ) ), :=( U, T )] ), substitution( 1, [ :=(
% 2.10/2.49 X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, equivalent( equivalent( equivalent(
% 2.10/2.49 X, T ), equivalent( X, Z ) ), equivalent( equivalent( Y, T ), equivalent(
% 2.10/2.49 Y, Z ) ) ) )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 882, [ =( true, 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 X, Y ), equivalent( X, Z ) ), equivalent( equivalent( T, Y ), equivalent(
% 2.10/2.49 T, Z ) ) ) ) ) ] )
% 2.10/2.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.49 , 0, clause( 880, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( equivalent( X, T ), equivalent( X, Z ) ), equivalent(
% 2.10/2.49 equivalent( Y, T ), equivalent( Y, Z ) ) ) ), true ) ) ] )
% 2.10/2.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent(
% 2.10/2.49 equivalent( T, Y ), equivalent( T, Z ) ) ) ) ), :=( Z, true )] ),
% 2.10/2.49 substitution( 1, [ :=( X, X ), :=( Y, T ), :=( Z, Z ), :=( T, Y )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 883, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 2.10/2.49 ), equivalent( X, Z ) ), equivalent( equivalent( T, Y ), equivalent( T,
% 2.10/2.49 Z ) ) ) ), true ) ] )
% 2.10/2.49 , clause( 882, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( equivalent( T, Y )
% 2.10/2.49 , equivalent( T, Z ) ) ) ) ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.49 ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 12, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, T )
% 2.10/2.49 , equivalent( X, Z ) ), equivalent( equivalent( Y, T ), equivalent( Y, Z
% 2.10/2.49 ) ) ) ), true ) ] )
% 2.10/2.49 , clause( 883, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 2.10/2.49 Y ), equivalent( X, Z ) ), equivalent( equivalent( T, Y ), equivalent( T
% 2.10/2.49 , Z ) ) ) ), true ) ] )
% 2.10/2.49 , substitution( 0, [ :=( X, X ), :=( Y, T ), :=( Z, Z ), :=( T, Y )] ),
% 2.10/2.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 885, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.49 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 2.10/2.49 )
% 2.10/2.49 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.49 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.49 )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 887, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, Z ) ) ), true, 'is_a_theorem'(
% 2.10/2.49 equivalent( equivalent( T, Y ), equivalent( T, Z ) ) ), true ), true ) )
% 2.10/2.49 ] )
% 2.10/2.49 , clause( 12, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, T
% 2.10/2.49 ), equivalent( X, Z ) ), equivalent( equivalent( Y, T ), equivalent( Y,
% 2.10/2.49 Z ) ) ) ), true ) ] )
% 2.10/2.49 , 0, clause( 885, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 2.10/2.49 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 2.10/2.49 ) ) ] )
% 2.10/2.49 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, T ), :=( Z, Z ), :=( T, Y )] )
% 2.10/2.49 , substitution( 1, [ :=( X, equivalent( equivalent( X, Y ), equivalent( X
% 2.10/2.49 , Z ) ) ), :=( Y, equivalent( equivalent( T, Y ), equivalent( T, Z ) ) )] )
% 2.10/2.49 ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 892, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y
% 2.10/2.49 ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 T, Y ), equivalent( T, Z ) ) ), true ) ) ] )
% 2.10/2.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.49 , 0, clause( 887, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ) ), true,
% 2.10/2.49 'is_a_theorem'( equivalent( equivalent( T, Y ), equivalent( T, Z ) ) ),
% 2.10/2.49 true ), true ) ) ] )
% 2.10/2.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ) ), true,
% 2.10/2.49 'is_a_theorem'( equivalent( equivalent( T, Y ), equivalent( T, Z ) ) ),
% 2.10/2.49 true ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 2.10/2.49 :=( Z, Z ), :=( T, T )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 893, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent( T,
% 2.10/2.49 Y ), equivalent( T, Z ) ) ), true ), true ) ] )
% 2.10/2.49 , clause( 892, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.49 Y ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 T, Y ), equivalent( T, Z ) ) ), true ) ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.49 ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 16, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent( T,
% 2.10/2.49 Y ), equivalent( T, Z ) ) ), true ), true ) ] )
% 2.10/2.49 , clause( 893, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent( T,
% 2.10/2.49 Y ), equivalent( T, Z ) ) ), true ), true ) ] )
% 2.10/2.49 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 2.10/2.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 895, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y
% 2.10/2.49 ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 T, Y ), equivalent( T, Z ) ) ), true ) ) ] )
% 2.10/2.49 , clause( 16, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent( T,
% 2.10/2.49 Y ), equivalent( T, Z ) ) ), true ), true ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.49 ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 897, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( T, equivalent( X, Z ) ), equivalent( T, equivalent( X, Z ) )
% 2.10/2.49 ) ), true ) ) ] )
% 2.10/2.49 , clause( 12, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, T
% 2.10/2.49 ), equivalent( X, Z ) ), equivalent( equivalent( Y, T ), equivalent( Y,
% 2.10/2.49 Z ) ) ) ), true ) ] )
% 2.10/2.49 , 0, clause( 895, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 X, Y ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( T, Y ), equivalent( T, Z ) ) ), true ) ) ] )
% 2.10/2.49 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, Z ), :=( T, Y )] )
% 2.10/2.49 , substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, equivalent( X, Z
% 2.10/2.49 ) ), :=( Z, equivalent( X, Z ) ), :=( T, T )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 899, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.49 equivalent( Y, Z ) ), equivalent( X, equivalent( Y, Z ) ) ) ) ) ] )
% 2.10/2.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.49 , 0, clause( 897, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( T, equivalent( X, Z ) ), equivalent( T, equivalent( X, Z ) )
% 2.10/2.49 ) ), true ) ) ] )
% 2.10/2.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( X, equivalent( Y, Z ) ), equivalent( X, equivalent( Y, Z ) )
% 2.10/2.49 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, T ), :=(
% 2.10/2.49 Z, Z ), :=( T, X )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 900, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 2.10/2.49 , Z ) ), equivalent( X, equivalent( Y, Z ) ) ) ), true ) ] )
% 2.10/2.49 , clause( 899, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.49 equivalent( Y, Z ) ), equivalent( X, equivalent( Y, Z ) ) ) ) ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 17, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( X,
% 2.10/2.49 Z ) ), equivalent( T, equivalent( X, Z ) ) ) ), true ) ] )
% 2.10/2.49 , clause( 900, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 2.10/2.49 Y, Z ) ), equivalent( X, equivalent( Y, Z ) ) ) ), true ) ] )
% 2.10/2.49 , substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Z )] ),
% 2.10/2.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 902, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y
% 2.10/2.49 ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 T, Y ), equivalent( T, Z ) ) ), true ) ) ] )
% 2.10/2.49 , clause( 16, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent( T,
% 2.10/2.49 Y ), equivalent( T, Z ) ) ), true ), true ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.49 ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 904, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( U, T ), equivalent( U, equivalent( equivalent( Y, Y ), T ) )
% 2.10/2.49 ) ), true ) ) ] )
% 2.10/2.49 , clause( 4, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), Z ), T ), equivalent( equivalent( equivalent( X, U )
% 2.10/2.49 , Z ), equivalent( equivalent( Y, U ), T ) ) ) ), true ) ] )
% 2.10/2.49 , 0, clause( 902, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 X, Y ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( T, Y ), equivalent( T, Z ) ) ), true ) ) ] )
% 2.10/2.49 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 2.10/2.49 :=( U, Y )] ), substitution( 1, [ :=( X, equivalent( equivalent( X, Y ),
% 2.10/2.49 Z ) ), :=( Y, T ), :=( Z, equivalent( equivalent( Y, Y ), T ) ), :=( T, U
% 2.10/2.49 )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 906, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, equivalent( equivalent( Z, Z ), Y ) ) ) ) ) ] )
% 2.10/2.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.49 , 0, clause( 904, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( U, T ), equivalent( U, equivalent( equivalent( Y, Y ), T ) )
% 2.10/2.49 ) ), true ) ) ] )
% 2.10/2.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, equivalent( equivalent( Z, Z ), Y ) )
% 2.10/2.49 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, T ), :=( Y, Z ), :=(
% 2.10/2.49 Z, U ), :=( T, Y ), :=( U, X )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 907, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, equivalent( equivalent( Z, Z ), Y ) ) ) ), true ) ] )
% 2.10/2.49 , clause( 906, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, equivalent( equivalent( Z, Z ), Y ) ) ) ) ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 18, [ =( 'is_a_theorem'( equivalent( equivalent( U, T ), equivalent(
% 2.10/2.49 U, equivalent( equivalent( Y, Y ), T ) ) ) ), true ) ] )
% 2.10/2.49 , clause( 907, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, equivalent( equivalent( Z, Z ), Y ) ) ) ), true ) ] )
% 2.10/2.49 , substitution( 0, [ :=( X, U ), :=( Y, T ), :=( Z, Y )] ),
% 2.10/2.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 909, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 2.10/2.49 , clause( 6, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ), T ) ),
% 2.10/2.49 true, 'is_a_theorem'( T ), true ), true ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.49 ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 911, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ) ), true ) ) ] )
% 2.10/2.49 , clause( 17, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( X
% 2.10/2.49 , Z ) ), equivalent( T, equivalent( X, Z ) ) ) ), true ) ] )
% 2.10/2.49 , 0, clause( 909, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 2.10/2.49 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, T ), :=( Z, Z ), :=( T,
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ) )] ), substitution(
% 2.10/2.49 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ) )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 913, [ =( true, 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ) ) ) ] )
% 2.10/2.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.49 , 0, clause( 911, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ) ), true ) ) ] )
% 2.10/2.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.49 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=(
% 2.10/2.49 Z, Z )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 914, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 2.10/2.49 ), equivalent( X, Z ) ), equivalent( Y, Z ) ) ), true ) ] )
% 2.10/2.49 , clause( 913, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ) ) ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 19, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 2.10/2.49 , equivalent( X, Z ) ), equivalent( Y, Z ) ) ), true ) ] )
% 2.10/2.49 , clause( 914, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 2.10/2.49 Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ) ), true ) ] )
% 2.10/2.49 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.10/2.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 916, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 2.10/2.49 ) ), equivalent( Y, Z ) ), T ), T ), U ) ), true, 'is_a_theorem'( U ),
% 2.10/2.49 true ) ) ] )
% 2.10/2.49 , clause( 7, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 2.10/2.49 equivalent( Y, Z ) ), T ), T ), U ) ), true, 'is_a_theorem'( U ), true )
% 2.10/2.49 , true ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 2.10/2.49 :=( U, U )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 918, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( Y, Z ), equivalent( Y, Z ) ) ), true ) ) ] )
% 2.10/2.49 , clause( 3, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.49 equivalent( equivalent( Y, Z ), T ) ), U ), U ) ), true ) ] )
% 2.10/2.49 , 0, clause( 916, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 2.10/2.49 ) ), equivalent( Y, Z ) ), T ), T ), U ) ), true, 'is_a_theorem'( U ),
% 2.10/2.49 true ) ) ] )
% 2.10/2.49 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 2.10/2.49 equivalent( Y, Z ) ), :=( U, equivalent( equivalent( Y, Z ), equivalent(
% 2.10/2.49 Y, Z ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 2.10/2.49 :=( T, equivalent( equivalent( Y, Z ), equivalent( Y, Z ) ) ), :=( U,
% 2.10/2.49 equivalent( equivalent( Y, Z ), equivalent( Y, Z ) ) )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 920, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Y ) ) ) ) ] )
% 2.10/2.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.49 , 0, clause( 918, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( Y, Z ), equivalent( Y, Z ) ) ), true ) ) ] )
% 2.10/2.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, Y ) ) ) ), :=( Z, true )] ),
% 2.10/2.49 substitution( 1, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 921, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Y ) ) ), true ) ] )
% 2.10/2.49 , clause( 920, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Y ) ) ) ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 22, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Z ), equivalent(
% 2.10/2.49 Y, Z ) ) ), true ) ] )
% 2.10/2.49 , clause( 921, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Y ) ) ), true ) ] )
% 2.10/2.49 , substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), permutation( 0, [ ==>( 0, 0
% 2.10/2.49 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 923, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.49 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 2.10/2.49 )
% 2.10/2.49 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.49 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.49 )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 925, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( equivalent(
% 2.10/2.49 equivalent( X, Y ), equivalent( X, Z ) ) ), true, 'is_a_theorem'(
% 2.10/2.49 equivalent( Y, Z ) ), true ), true ) ) ] )
% 2.10/2.49 , clause( 19, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 2.10/2.49 ), equivalent( X, Z ) ), equivalent( Y, Z ) ) ), true ) ] )
% 2.10/2.49 , 0, clause( 923, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 2.10/2.49 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 2.10/2.49 ) ) ] )
% 2.10/2.49 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.10/2.49 substitution( 1, [ :=( X, equivalent( equivalent( X, Y ), equivalent( X,
% 2.10/2.49 Z ) ) ), :=( Y, equivalent( Y, Z ) )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 930, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y
% 2.10/2.49 ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ),
% 2.10/2.49 true ) ) ] )
% 2.10/2.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.49 , 0, clause( 925, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ) ), true,
% 2.10/2.49 'is_a_theorem'( equivalent( Y, Z ) ), true ), true ) ) ] )
% 2.10/2.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 2.10/2.49 equivalent( equivalent( X, Y ), equivalent( X, Z ) ) ), true,
% 2.10/2.49 'is_a_theorem'( equivalent( Y, Z ) ), true ) ), :=( Z, true )] ),
% 2.10/2.49 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 931, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ), true
% 2.10/2.49 ), true ) ] )
% 2.10/2.49 , clause( 930, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.49 Y ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ),
% 2.10/2.49 true ) ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 26, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ), true
% 2.10/2.49 ), true ) ] )
% 2.10/2.49 , clause( 931, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ), true
% 2.10/2.49 ), true ) ] )
% 2.10/2.49 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.10/2.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 933, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.49 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 2.10/2.49 )
% 2.10/2.49 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.49 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.49 )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 935, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( equivalent(
% 2.10/2.49 X, Y ) ), true, 'is_a_theorem'( equivalent( X, equivalent( equivalent( Z
% 2.10/2.49 , Z ), Y ) ) ), true ), true ) ) ] )
% 2.10/2.49 , clause( 18, [ =( 'is_a_theorem'( equivalent( equivalent( U, T ),
% 2.10/2.49 equivalent( U, equivalent( equivalent( Y, Y ), T ) ) ) ), true ) ] )
% 2.10/2.49 , 0, clause( 933, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 2.10/2.49 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 2.10/2.49 ) ) ] )
% 2.10/2.49 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, Z ), :=( Z, U ), :=( T, Y ),
% 2.10/2.49 :=( U, X )] ), substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y,
% 2.10/2.49 equivalent( X, equivalent( equivalent( Z, Z ), Y ) ) )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 940, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.49 'is_a_theorem'( equivalent( X, equivalent( equivalent( Z, Z ), Y ) ) ),
% 2.10/2.49 true ) ) ] )
% 2.10/2.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.49 , 0, clause( 935, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 2.10/2.49 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.49 equivalent( Z, Z ), Y ) ) ), true ), true ) ) ] )
% 2.10/2.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 2.10/2.49 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.49 equivalent( Z, Z ), Y ) ) ), true ) ), :=( Z, true )] ), substitution( 1
% 2.10/2.49 , [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 941, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.49 'is_a_theorem'( equivalent( X, equivalent( equivalent( Z, Z ), Y ) ) ),
% 2.10/2.49 true ), true ) ] )
% 2.10/2.49 , clause( 940, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 2.10/2.49 , 'is_a_theorem'( equivalent( X, equivalent( equivalent( Z, Z ), Y ) ) )
% 2.10/2.49 , true ) ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 28, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.49 'is_a_theorem'( equivalent( X, equivalent( equivalent( Z, Z ), Y ) ) ),
% 2.10/2.49 true ), true ) ] )
% 2.10/2.49 , clause( 941, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.49 'is_a_theorem'( equivalent( X, equivalent( equivalent( Z, Z ), Y ) ) ),
% 2.10/2.49 true ), true ) ] )
% 2.10/2.49 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.10/2.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 943, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y
% 2.10/2.49 ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ),
% 2.10/2.49 true ) ) ] )
% 2.10/2.49 , clause( 26, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ), true
% 2.10/2.49 ), true ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 945, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( Y,
% 2.10/2.49 equivalent( equivalent( Z, Z ), Y ) ) ), true ) ) ] )
% 2.10/2.49 , clause( 18, [ =( 'is_a_theorem'( equivalent( equivalent( U, T ),
% 2.10/2.49 equivalent( U, equivalent( equivalent( Y, Y ), T ) ) ) ), true ) ] )
% 2.10/2.49 , 0, clause( 943, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 X, Y ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z )
% 2.10/2.49 ), true ) ) ] )
% 2.10/2.49 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, Z ), :=( Z, U ), :=( T, Y ),
% 2.10/2.49 :=( U, X )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z,
% 2.10/2.49 equivalent( equivalent( Z, Z ), Y ) )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 947, [ =( true, 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.49 equivalent( Y, Y ), X ) ) ) ) ] )
% 2.10/2.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.49 , 0, clause( 945, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.49 Y, equivalent( equivalent( Z, Z ), Y ) ) ), true ) ) ] )
% 2.10/2.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.49 X, equivalent( equivalent( Y, Y ), X ) ) ) ), :=( Z, true )] ),
% 2.10/2.49 substitution( 1, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 948, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent( Y
% 2.10/2.49 , Y ), X ) ) ), true ) ] )
% 2.10/2.49 , clause( 947, [ =( true, 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.49 equivalent( Y, Y ), X ) ) ) ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 subsumption(
% 2.10/2.49 clause( 30, [ =( 'is_a_theorem'( equivalent( Y, equivalent( equivalent( Z,
% 2.10/2.49 Z ), Y ) ) ), true ) ] )
% 2.10/2.49 , clause( 948, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 2.10/2.49 Y, Y ), X ) ) ), true ) ] )
% 2.10/2.49 , substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), permutation( 0, [ ==>( 0, 0
% 2.10/2.49 )] ) ).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 eqswap(
% 2.10/2.49 clause( 950, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y
% 2.10/2.49 ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ),
% 2.10/2.49 true ) ) ] )
% 2.10/2.49 , clause( 26, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.49 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ), true
% 2.10/2.49 ), true ) ] )
% 2.10/2.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.49
% 2.10/2.49
% 2.10/2.49 paramod(
% 2.10/2.49 clause( 952, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( Y, Y
% 2.10/2.49 ) ), true ) ) ] )
% 2.10/2.49 , clause( 22, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Z ),
% 2.10/2.49 equivalent( Y, Z ) ) ), true ) ] )
% 2.10/2.49 , 0, clause( 950, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.49 X, Y ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z )
% 2.10/2.49 ), true ) ) ] )
% 2.10/2.49 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 2.10/2.50 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Y )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 956, [ =( true, 'is_a_theorem'( equivalent( X, X ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 952, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 Y, Y ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 X, X ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, X )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 957, [ =( 'is_a_theorem'( equivalent( X, X ) ), true ) ] )
% 2.10/2.50 , clause( 956, [ =( true, 'is_a_theorem'( equivalent( X, X ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 31, [ =( 'is_a_theorem'( equivalent( Y, Y ) ), true ) ] )
% 2.10/2.50 , clause( 957, [ =( 'is_a_theorem'( equivalent( X, X ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, Y )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 959, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.50 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 2.10/2.50 )
% 2.10/2.50 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.50 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.50 )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 961, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( X ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( equivalent( Y, Y ), X ) ), true ), true ) ) ]
% 2.10/2.50 )
% 2.10/2.50 , clause( 30, [ =( 'is_a_theorem'( equivalent( Y, equivalent( equivalent( Z
% 2.10/2.50 , Z ), Y ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 959, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 2.10/2.50 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 2.10/2.50 ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 2.10/2.50 substitution( 1, [ :=( X, X ), :=( Y, equivalent( equivalent( Y, Y ), X )
% 2.10/2.50 )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 966, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( equivalent( Y, Y ), X ) ), true ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 961, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( X ),
% 2.10/2.50 true, 'is_a_theorem'( equivalent( equivalent( Y, Y ), X ) ), true ), true
% 2.10/2.50 ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'( X )
% 2.10/2.50 , true, 'is_a_theorem'( equivalent( equivalent( Y, Y ), X ) ), true ) ),
% 2.10/2.50 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 967, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( equivalent( Y, Y ), X ) ), true ), true ) ] )
% 2.10/2.50 , clause( 966, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( equivalent( Y, Y ), X ) ), true ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 36, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( equivalent( Y, Y ), X ) ), true ), true ) ] )
% 2.10/2.50 , clause( 967, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( equivalent( Y, Y ), X ) ), true ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.10/2.50 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 969, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.50 equivalent( equivalent( Y, Z ), T ) ), U ) ), true, 'is_a_theorem'( U ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , clause( 9, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent(
% 2.10/2.50 equivalent( Y, Z ), T ) ), U ) ), true, 'is_a_theorem'( U ), true ), true
% 2.10/2.50 ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 2.10/2.50 :=( U, U )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 971, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.50 equivalent( equivalent( Y, Z ), T ) ) ), true ) ) ] )
% 2.10/2.50 , clause( 31, [ =( 'is_a_theorem'( equivalent( Y, Y ) ), true ) ] )
% 2.10/2.50 , 0, clause( 969, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.50 equivalent( equivalent( Y, Z ), T ) ), U ) ), true, 'is_a_theorem'( U ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, U ), :=( Y, equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent(
% 2.10/2.50 equivalent( Y, Z ), T ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )
% 2.10/2.50 , :=( Z, Z ), :=( T, T ), :=( U, equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( Y
% 2.10/2.50 , Z ), T ) ) )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 973, [ =( true, 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( Y
% 2.10/2.50 , Z ), T ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 971, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.50 equivalent( equivalent( Y, Z ), T ) ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.50 equivalent( equivalent( Y, Z ), T ) ) ) ), :=( Z, true )] ),
% 2.10/2.50 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 974, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( Y
% 2.10/2.50 , Z ), T ) ) ), true ) ] )
% 2.10/2.50 , clause( 973, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent(
% 2.10/2.50 equivalent( Y, Z ), T ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 39, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( Y
% 2.10/2.50 , Z ), T ) ) ), true ) ] )
% 2.10/2.50 , clause( 974, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( Y
% 2.10/2.50 , Z ), T ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 976, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.50 equivalent( equivalent( Y, Z ), T ) ), U ) ), true, 'is_a_theorem'( U ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , clause( 9, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent(
% 2.10/2.50 equivalent( Y, Z ), T ) ), U ) ), true, 'is_a_theorem'( U ), true ), true
% 2.10/2.50 ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 2.10/2.50 :=( U, U )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 978, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Z ), T ), equivalent( equivalent( Y, Z ),
% 2.10/2.50 equivalent( equivalent( X, Y ), T ) ) ) ), true ) ) ] )
% 2.10/2.50 , clause( 3, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.50 equivalent( equivalent( Y, Z ), T ) ), U ), U ) ), true ) ] )
% 2.10/2.50 , 0, clause( 976, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.50 equivalent( equivalent( Y, Z ), T ) ), U ) ), true, 'is_a_theorem'( U ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 2.10/2.50 equivalent( equivalent( X, Y ), T ) ), :=( U, equivalent( equivalent(
% 2.10/2.50 equivalent( X, Z ), T ), equivalent( equivalent( Y, Z ), equivalent(
% 2.10/2.50 equivalent( X, Y ), T ) ) ) )] ), substitution( 1, [ :=( X, equivalent( X
% 2.10/2.50 , Y ) ), :=( Y, equivalent( X, Z ) ), :=( Z, T ), :=( T, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( equivalent( X, Y ), T ) ) ), :=( U,
% 2.10/2.50 equivalent( equivalent( equivalent( X, Z ), T ), equivalent( equivalent(
% 2.10/2.50 Y, Z ), equivalent( equivalent( X, Y ), T ) ) ) )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 980, [ =( true, 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 X, Y ), Z ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T
% 2.10/2.50 ), Z ) ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 978, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Z ), T ), equivalent( equivalent( Y, Z ),
% 2.10/2.50 equivalent( equivalent( X, Y ), T ) ) ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ),
% 2.10/2.50 equivalent( equivalent( X, T ), Z ) ) ) ) ), :=( Z, true )] ),
% 2.10/2.50 substitution( 1, [ :=( X, X ), :=( Y, T ), :=( Z, Y ), :=( T, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 981, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 2.10/2.50 ), Z ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T ),
% 2.10/2.50 Z ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 980, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), Z ), equivalent( equivalent( T, Y ), equivalent(
% 2.10/2.50 equivalent( X, T ), Z ) ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 40, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Z )
% 2.10/2.50 , T ), equivalent( equivalent( Y, Z ), equivalent( equivalent( X, Y ), T
% 2.10/2.50 ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 981, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 2.10/2.50 Y ), Z ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T )
% 2.10/2.50 , Z ) ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, T ), :=( T, Y )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 983, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( equivalent( Y, Y ), X ) ), true ) ) ] )
% 2.10/2.50 , clause( 36, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( equivalent( Y, Y ), X ) ), true ), true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 985, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( Y, Y ), equivalent( X, X ) ) ), true ) ) ] )
% 2.10/2.50 , clause( 31, [ =( 'is_a_theorem'( equivalent( Y, Y ) ), true ) ] )
% 2.10/2.50 , 0, clause( 983, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( equivalent( Y, Y ), X ) ), true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X )] ), substitution( 1, [
% 2.10/2.50 :=( X, equivalent( X, X ) ), :=( Y, Y )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 989, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, X ),
% 2.10/2.50 equivalent( Y, Y ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 985, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( Y, Y ), equivalent( X, X ) ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( X, X ), equivalent( Y, Y ) ) ) ), :=( Z, true )] ),
% 2.10/2.50 substitution( 1, [ :=( X, Y ), :=( Y, X )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 990, [ =( 'is_a_theorem'( equivalent( equivalent( X, X ),
% 2.10/2.50 equivalent( Y, Y ) ) ), true ) ] )
% 2.10/2.50 , clause( 989, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, X ),
% 2.10/2.50 equivalent( Y, Y ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 43, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Y ), equivalent(
% 2.10/2.50 X, X ) ) ), true ) ] )
% 2.10/2.50 , clause( 990, [ =( 'is_a_theorem'( equivalent( equivalent( X, X ),
% 2.10/2.50 equivalent( Y, Y ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 2.10/2.50 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 992, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( equivalent( Y, Y ), X ) ), true ) ) ] )
% 2.10/2.50 , clause( 36, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( equivalent( Y, Y ), X ) ), true ), true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 994, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( Z, Z ), equivalent( equivalent( X, X ), equivalent( Y, Y ) )
% 2.10/2.50 ) ), true ) ) ] )
% 2.10/2.50 , clause( 43, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Y ),
% 2.10/2.50 equivalent( X, X ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 992, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( equivalent( Y, Y ), X ) ), true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 2.10/2.50 :=( X, equivalent( equivalent( X, X ), equivalent( Y, Y ) ) ), :=( Y, Z )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 996, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, X ),
% 2.10/2.50 equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 994, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( Z, Z ), equivalent( equivalent( X, X ), equivalent( Y, Y ) )
% 2.10/2.50 ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( X, X ), equivalent( equivalent( Y, Y ), equivalent( Z, Z ) )
% 2.10/2.50 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=(
% 2.10/2.50 Z, X )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 997, [ =( 'is_a_theorem'( equivalent( equivalent( X, X ),
% 2.10/2.50 equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 996, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, X ),
% 2.10/2.50 equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 45, [ =( 'is_a_theorem'( equivalent( equivalent( Z, Z ), equivalent(
% 2.10/2.50 equivalent( X, X ), equivalent( Y, Y ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 997, [ =( 'is_a_theorem'( equivalent( equivalent( X, X ),
% 2.10/2.50 equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 999, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y
% 2.10/2.50 ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 T, Y ), equivalent( T, Z ) ) ), true ) ) ] )
% 2.10/2.50 , clause( 16, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.50 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent( T,
% 2.10/2.50 Y ), equivalent( T, Z ) ) ), true ), true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1001, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( Z, equivalent( X, X ) ), equivalent( Z, equivalent( Y, Y ) )
% 2.10/2.50 ) ), true ) ) ] )
% 2.10/2.50 , clause( 45, [ =( 'is_a_theorem'( equivalent( equivalent( Z, Z ),
% 2.10/2.50 equivalent( equivalent( X, X ), equivalent( Y, Y ) ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 999, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 X, Y ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( T, Y ), equivalent( T, Z ) ) ), true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, equivalent( X, X
% 2.10/2.50 ) )] ), substitution( 1, [ :=( X, equivalent( X, X ) ), :=( Y,
% 2.10/2.50 equivalent( X, X ) ), :=( Z, equivalent( Y, Y ) ), :=( T, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1003, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( Y, Y ) ), equivalent( X, equivalent( Z, Z ) ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1001, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( Z, equivalent( X, X ) ), equivalent( Z, equivalent( Y, Y ) )
% 2.10/2.50 ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( X, equivalent( Y, Y ) ), equivalent( X, equivalent( Z, Z ) )
% 2.10/2.50 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=(
% 2.10/2.50 Z, X )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1004, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 2.10/2.50 , Y ) ), equivalent( X, equivalent( Z, Z ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 1003, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( Y, Y ) ), equivalent( X, equivalent( Z, Z ) ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 51, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( X,
% 2.10/2.50 X ) ), equivalent( Z, equivalent( Y, Y ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 1004, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 2.10/2.50 Y, Y ) ), equivalent( X, equivalent( Z, Z ) ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1006, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.50 equivalent( equivalent( Y, Z ), T ) ), U ) ), true, 'is_a_theorem'( U ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , clause( 9, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent(
% 2.10/2.50 equivalent( Y, Z ), T ) ), U ) ), true, 'is_a_theorem'( U ), true ), true
% 2.10/2.50 ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 2.10/2.50 :=( U, U )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1008, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 2.10/2.50 equivalent( Y, Z ) ), equivalent( T, T ) ) ), true ) ) ] )
% 2.10/2.50 , clause( 51, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( X
% 2.10/2.50 , X ) ), equivalent( Z, equivalent( Y, Y ) ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1006, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ),
% 2.10/2.50 equivalent( equivalent( Y, Z ), T ) ), U ) ), true, 'is_a_theorem'( U ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, equivalent( Y, Z ) ), :=( Y, T ), :=( Z,
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 2.10/2.50 equivalent( Y, Z ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 2.10/2.50 :=( Z, Z ), :=( T, equivalent( Y, Z ) ), :=( U, equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.50 ), equivalent( T, T ) ) )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1010, [ =( true, 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ),
% 2.10/2.50 equivalent( T, T ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1008, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 2.10/2.50 equivalent( Y, Z ) ), equivalent( T, T ) ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 2.10/2.50 equivalent( Y, Z ) ), equivalent( T, T ) ) ) ), :=( Z, true )] ),
% 2.10/2.50 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1011, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ),
% 2.10/2.50 equivalent( T, T ) ) ), true ) ] )
% 2.10/2.50 , clause( 1010, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.50 ), equivalent( T, T ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 54, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ),
% 2.10/2.50 equivalent( T, T ) ) ), true ) ] )
% 2.10/2.50 , clause( 1011, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ),
% 2.10/2.50 equivalent( T, T ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1013, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y
% 2.10/2.50 ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , clause( 26, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.50 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ), true
% 2.10/2.50 ), true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1015, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( equivalent( X, Y ), equivalent( X, Z ) )
% 2.10/2.50 ) ), true ) ) ] )
% 2.10/2.50 , clause( 54, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ),
% 2.10/2.50 equivalent( T, T ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1013, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 X, Y ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z )
% 2.10/2.50 ), true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ) )] ), substitution(
% 2.10/2.50 1, [ :=( X, equivalent( equivalent( X, Y ), equivalent( X, Z ) ) ), :=( Y
% 2.10/2.50 , equivalent( Y, Z ) ), :=( Z, equivalent( equivalent( X, Y ), equivalent(
% 2.10/2.50 X, Z ) ) )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1017, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.50 equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1015, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( equivalent( X, Y ), equivalent( X, Z ) )
% 2.10/2.50 ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( equivalent( Z, X ), equivalent( Z, Y ) )
% 2.10/2.50 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, X ), :=(
% 2.10/2.50 Z, Y )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1018, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.50 equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 1017, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.50 equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 101, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Z ),
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 1018, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.50 equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1020, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( X, equivalent( equivalent( Z, Z ), Y ) ) ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , clause( 28, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( X, equivalent( equivalent( Z, Z ), Y ) ) ),
% 2.10/2.50 true ), true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1022, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( equivalent( T, T ), equivalent(
% 2.10/2.50 equivalent( Z, X ), equivalent( Z, Y ) ) ) ) ), true ) ) ] )
% 2.10/2.50 , clause( 101, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Z ),
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1020, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 2.10/2.50 true, 'is_a_theorem'( equivalent( X, equivalent( equivalent( Z, Z ), Y )
% 2.10/2.50 ) ), true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 2.10/2.50 substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, equivalent(
% 2.10/2.50 equivalent( Z, X ), equivalent( Z, Y ) ) ), :=( Z, T )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1024, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.50 equivalent( equivalent( Z, Z ), equivalent( equivalent( T, X ),
% 2.10/2.50 equivalent( T, Y ) ) ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1022, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( equivalent( T, T ), equivalent(
% 2.10/2.50 equivalent( Z, X ), equivalent( Z, Y ) ) ) ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( equivalent( Z, Z ), equivalent(
% 2.10/2.50 equivalent( T, X ), equivalent( T, Y ) ) ) ) ) ), :=( Z, true )] ),
% 2.10/2.50 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1025, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.50 equivalent( equivalent( Z, Z ), equivalent( equivalent( T, X ),
% 2.10/2.50 equivalent( T, Y ) ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 1024, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.50 equivalent( equivalent( Z, Z ), equivalent( equivalent( T, X ),
% 2.10/2.50 equivalent( T, Y ) ) ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 104, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.50 equivalent( equivalent( T, T ), equivalent( equivalent( Z, X ),
% 2.10/2.50 equivalent( Z, Y ) ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 1025, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.50 equivalent( equivalent( Z, Z ), equivalent( equivalent( T, X ),
% 2.10/2.50 equivalent( T, Y ) ) ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T, Z )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1027, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.50 ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 2.10/2.50 , clause( 6, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ), T ) ),
% 2.10/2.50 true, 'is_a_theorem'( T ), true ), true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1029, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( T, equivalent( equivalent( X, Y ), equivalent( X, Z ) ) ),
% 2.10/2.50 equivalent( T, equivalent( Y, Z ) ) ) ), true ) ) ] )
% 2.10/2.50 , clause( 101, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Z ),
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1027, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.50 ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, equivalent( equivalent( X, Y
% 2.10/2.50 ), equivalent( X, Z ) ) ), :=( Z, equivalent( Y, Z ) )] ),
% 2.10/2.50 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, equivalent(
% 2.10/2.50 equivalent( T, equivalent( equivalent( X, Y ), equivalent( X, Z ) ) ),
% 2.10/2.50 equivalent( T, equivalent( Y, Z ) ) ) )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1031, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( equivalent( Y, Z ), equivalent( Y, T ) ) ), equivalent( X,
% 2.10/2.50 equivalent( Z, T ) ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1029, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( T, equivalent( equivalent( X, Y ), equivalent( X, Z ) ) ),
% 2.10/2.50 equivalent( T, equivalent( Y, Z ) ) ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( X, equivalent( equivalent( Y, Z ), equivalent( Y, T ) ) ),
% 2.10/2.50 equivalent( X, equivalent( Z, T ) ) ) ) ), :=( Z, true )] ),
% 2.10/2.50 substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, X )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1032, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( Y, T ) ) ), equivalent( X, equivalent( Z
% 2.10/2.50 , T ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 1031, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( equivalent( Y, Z ), equivalent( Y, T ) ) ), equivalent( X,
% 2.10/2.50 equivalent( Z, T ) ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 106, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( X, Z ) ) ), equivalent( T, equivalent( Y
% 2.10/2.50 , Z ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 1032, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( Y, T ) ) ), equivalent( X, equivalent( Z
% 2.10/2.50 , T ) ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1034, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.50 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 2.10/2.50 )
% 2.10/2.50 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.50 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.50 )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1036, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( equivalent(
% 2.10/2.50 X, Y ) ), true, 'is_a_theorem'( equivalent( equivalent( Z, X ),
% 2.10/2.50 equivalent( Z, Y ) ) ), true ), true ) ) ] )
% 2.10/2.50 , clause( 101, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Z ),
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1034, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 2.10/2.50 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 2.10/2.50 ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 2.10/2.50 substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, equivalent(
% 2.10/2.50 equivalent( Z, X ), equivalent( Z, Y ) ) )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1041, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1036, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 2.10/2.50 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( equivalent( Z, X
% 2.10/2.50 ), equivalent( Z, Y ) ) ), true ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 2.10/2.50 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( equivalent( Z, X
% 2.10/2.50 ), equivalent( Z, Y ) ) ), true ) ), :=( Z, true )] ), substitution( 1
% 2.10/2.50 , [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1042, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ),
% 2.10/2.50 true ), true ) ] )
% 2.10/2.50 , clause( 1041, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 2.10/2.50 , 'is_a_theorem'( equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) )
% 2.10/2.50 , true ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 107, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ),
% 2.10/2.50 true ), true ) ] )
% 2.10/2.50 , clause( 1042, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ),
% 2.10/2.50 true ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1044, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y
% 2.10/2.50 ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , clause( 26, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.50 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ), true
% 2.10/2.50 ), true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1046, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( Y,
% 2.10/2.50 equivalent( equivalent( Z, equivalent( X, X ) ), equivalent( Z, Y ) ) ) )
% 2.10/2.50 , true ) ) ] )
% 2.10/2.50 , clause( 104, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.50 equivalent( equivalent( T, T ), equivalent( equivalent( Z, X ),
% 2.10/2.50 equivalent( Z, Y ) ) ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1044, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 X, Y ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z )
% 2.10/2.50 ), true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, equivalent( X, X ) ), :=( Y, Y ), :=( Z,
% 2.10/2.50 Z ), :=( T, X )] ), substitution( 1, [ :=( X, equivalent( X, X ) ), :=( Y
% 2.10/2.50 , Y ), :=( Z, equivalent( equivalent( Z, equivalent( X, X ) ), equivalent(
% 2.10/2.50 Z, Y ) ) )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1048, [ =( true, 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, equivalent( Z, Z ) ), equivalent( Y, X ) ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1046, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 Y, equivalent( equivalent( Z, equivalent( X, X ) ), equivalent( Z, Y ) )
% 2.10/2.50 ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 X, equivalent( equivalent( Y, equivalent( Z, Z ) ), equivalent( Y, X ) )
% 2.10/2.50 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, X ), :=(
% 2.10/2.50 Z, Y )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1049, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent( Y
% 2.10/2.50 , equivalent( Z, Z ) ), equivalent( Y, X ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 1048, [ =( true, 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, equivalent( Z, Z ) ), equivalent( Y, X ) ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 112, [ =( 'is_a_theorem'( equivalent( Y, equivalent( equivalent( Z
% 2.10/2.50 , equivalent( X, X ) ), equivalent( Z, Y ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 1049, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 2.10/2.50 Y, equivalent( Z, Z ) ), equivalent( Y, X ) ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1051, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y
% 2.10/2.50 ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , clause( 26, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.50 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ), true
% 2.10/2.50 ), true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1053, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( Z,
% 2.10/2.50 equivalent( X, equivalent( equivalent( X, equivalent( Y, Y ) ), Z ) ) ) )
% 2.10/2.50 , true ) ) ] )
% 2.10/2.50 , clause( 112, [ =( 'is_a_theorem'( equivalent( Y, equivalent( equivalent(
% 2.10/2.50 Z, equivalent( X, X ) ), equivalent( Z, Y ) ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1051, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 X, Y ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( Y, Z )
% 2.10/2.50 ), true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, equivalent( equivalent( X,
% 2.10/2.50 equivalent( Y, Y ) ), Z ) ), :=( Z, X )] ), substitution( 1, [ :=( X,
% 2.10/2.50 equivalent( X, equivalent( Y, Y ) ) ), :=( Y, Z ), :=( Z, equivalent( X,
% 2.10/2.50 equivalent( equivalent( X, equivalent( Y, Y ) ), Z ) ) )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1055, [ =( true, 'is_a_theorem'( equivalent( X, equivalent( Y,
% 2.10/2.50 equivalent( equivalent( Y, equivalent( Z, Z ) ), X ) ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1053, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 Z, equivalent( X, equivalent( equivalent( X, equivalent( Y, Y ) ), Z ) )
% 2.10/2.50 ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 X, equivalent( Y, equivalent( equivalent( Y, equivalent( Z, Z ) ), X ) )
% 2.10/2.50 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=(
% 2.10/2.50 Z, X )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1056, [ =( 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent(
% 2.10/2.50 equivalent( Y, equivalent( Z, Z ) ), X ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 1055, [ =( true, 'is_a_theorem'( equivalent( X, equivalent( Y,
% 2.10/2.50 equivalent( equivalent( Y, equivalent( Z, Z ) ), X ) ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 118, [ =( 'is_a_theorem'( equivalent( Z, equivalent( X, equivalent(
% 2.10/2.50 equivalent( X, equivalent( Y, Y ) ), Z ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 1056, [ =( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 2.10/2.50 equivalent( equivalent( Y, equivalent( Z, Z ) ), X ) ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1058, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.50 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 2.10/2.50 )
% 2.10/2.50 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.50 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.50 )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1061, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( Y, equivalent( equivalent( Y, equivalent( Z, Z ) ), X ) ) ),
% 2.10/2.50 T ) ), true, ifeq( true, true, 'is_a_theorem'( T ), true ), true ) ) ] )
% 2.10/2.50 , clause( 118, [ =( 'is_a_theorem'( equivalent( Z, equivalent( X,
% 2.10/2.50 equivalent( equivalent( X, equivalent( Y, Y ) ), Z ) ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1058, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 2.10/2.50 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 2.10/2.50 ) ) ] )
% 2.10/2.50 , 0, 19, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 2.10/2.50 substitution( 1, [ :=( X, equivalent( X, equivalent( Y, equivalent(
% 2.10/2.50 equivalent( Y, equivalent( Z, Z ) ), X ) ) ) ), :=( Y, T )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1063, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( Y, equivalent( equivalent( Y, equivalent( Z, Z ) ), X ) ) ),
% 2.10/2.50 T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1061, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 X, equivalent( Y, equivalent( equivalent( Y, equivalent( Z, Z ) ), X ) )
% 2.10/2.50 ), T ) ), true, ifeq( true, true, 'is_a_theorem'( T ), true ), true ) )
% 2.10/2.50 ] )
% 2.10/2.50 , 0, 18, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( T ) ),
% 2.10/2.50 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 2.10/2.50 :=( T, T )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1064, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( Y, equivalent( equivalent( Y, equivalent( Z, Z ) ), X ) ) ),
% 2.10/2.50 T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 2.10/2.50 , clause( 1063, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 2.10/2.50 , equivalent( Y, equivalent( equivalent( Y, equivalent( Z, Z ) ), X ) ) )
% 2.10/2.50 , T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 129, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( Y, equivalent( equivalent( Y, equivalent( Z, Z ) ), X ) ) ),
% 2.10/2.50 T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 2.10/2.50 , clause( 1064, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( Y, equivalent( equivalent( Y, equivalent( Z, Z ) ), X ) ) ),
% 2.10/2.50 T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1066, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 2.10/2.50 ) ), equivalent( Y, Z ) ), T ), T ), U ) ), true, 'is_a_theorem'( U ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , clause( 7, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 2.10/2.50 equivalent( Y, Z ) ), T ), T ), U ) ), true, 'is_a_theorem'( U ), true )
% 2.10/2.50 , true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 2.10/2.50 :=( U, U )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1068, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( Y, Z ), T ), equivalent( equivalent( equivalent(
% 2.10/2.50 X, Y ), equivalent( X, Z ) ), T ) ) ), true ) ) ] )
% 2.10/2.50 , clause( 39, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( Y
% 2.10/2.50 , Z ), T ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1066, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 2.10/2.50 ) ), equivalent( Y, Z ) ), T ), T ), U ) ), true, 'is_a_theorem'( U ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ),
% 2.10/2.50 equivalent( X, Z ) ) ), :=( Y, equivalent( Y, Z ) ), :=( Z, T ), :=( T,
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ) )] )
% 2.10/2.50 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 2.10/2.50 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ) ),
% 2.10/2.50 :=( U, equivalent( equivalent( equivalent( Y, Z ), T ), equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), T ) ) )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1070, [ =( true, 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 X, Y ), Z ), equivalent( equivalent( equivalent( T, X ), equivalent( T, Y
% 2.10/2.50 ) ), Z ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1068, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( Y, Z ), T ), equivalent( equivalent( equivalent(
% 2.10/2.50 X, Y ), equivalent( X, Z ) ), T ) ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), Z ), equivalent( equivalent( equivalent(
% 2.10/2.50 T, X ), equivalent( T, Y ) ), Z ) ) ) ), :=( Z, true )] ), substitution(
% 2.10/2.50 1, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1071, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 2.10/2.50 ), Z ), equivalent( equivalent( equivalent( T, X ), equivalent( T, Y ) )
% 2.10/2.50 , Z ) ) ), true ) ] )
% 2.10/2.50 , clause( 1070, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), Z ), equivalent( equivalent( equivalent( T, X ),
% 2.10/2.50 equivalent( T, Y ) ), Z ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 138, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y, Z
% 2.10/2.50 ), T ), equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) )
% 2.10/2.50 , T ) ) ), true ) ] )
% 2.10/2.50 , clause( 1071, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 2.10/2.50 , Y ), Z ), equivalent( equivalent( equivalent( T, X ), equivalent( T, Y
% 2.10/2.50 ) ), Z ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, X )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1073, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.50 ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 2.10/2.50 , clause( 6, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ), T ) ),
% 2.10/2.50 true, 'is_a_theorem'( T ), true ), true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1075, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( T, equivalent( X, Z ) ), equivalent( equivalent( equivalent(
% 2.10/2.50 X, Y ), T ), equivalent( Y, Z ) ) ) ), true ) ) ] )
% 2.10/2.50 , clause( 40, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Z
% 2.10/2.50 ), T ), equivalent( equivalent( Y, Z ), equivalent( equivalent( X, Y ),
% 2.10/2.50 T ) ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1073, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z )
% 2.10/2.50 ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, equivalent( X, Y ) ), :=( Y, T ), :=( Z,
% 2.10/2.50 equivalent( X, Z ) ), :=( T, equivalent( Y, Z ) )] ), substitution( 1, [
% 2.10/2.50 :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, equivalent( equivalent( T,
% 2.10/2.50 equivalent( X, Z ) ), equivalent( equivalent( equivalent( X, Y ), T ),
% 2.10/2.50 equivalent( Y, Z ) ) ) )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1077, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( Y, Z ) ), equivalent( equivalent( equivalent( Y, T ), X ),
% 2.10/2.50 equivalent( T, Z ) ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1075, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( T, equivalent( X, Z ) ), equivalent( equivalent( equivalent(
% 2.10/2.50 X, Y ), T ), equivalent( Y, Z ) ) ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( X, equivalent( Y, Z ) ), equivalent( equivalent( equivalent(
% 2.10/2.50 Y, T ), X ), equivalent( T, Z ) ) ) ) ), :=( Z, true )] ), substitution(
% 2.10/2.50 1, [ :=( X, Y ), :=( Y, T ), :=( Z, Z ), :=( T, X )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1078, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 2.10/2.50 , Z ) ), equivalent( equivalent( equivalent( Y, T ), X ), equivalent( T,
% 2.10/2.50 Z ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 1077, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( Y, Z ) ), equivalent( equivalent( equivalent( Y, T ), X ),
% 2.10/2.50 equivalent( T, Z ) ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 152, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( X
% 2.10/2.50 , Z ) ), equivalent( equivalent( equivalent( X, Y ), T ), equivalent( Y,
% 2.10/2.50 Z ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 1078, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 2.10/2.50 Y, Z ) ), equivalent( equivalent( equivalent( Y, T ), X ), equivalent( T
% 2.10/2.50 , Z ) ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Z ), :=( T, Y )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1080, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.50 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 2.10/2.50 )
% 2.10/2.50 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.50 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.50 )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1082, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( equivalent(
% 2.10/2.50 X, equivalent( equivalent( Y, Z ), equivalent( Y, T ) ) ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( X, equivalent( Z, T ) ) ), true ), true ) ) ]
% 2.10/2.50 )
% 2.10/2.50 , clause( 106, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( X, Z ) ) ), equivalent( T, equivalent( Y
% 2.10/2.50 , Z ) ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1080, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 2.10/2.50 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 2.10/2.50 ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, X )] )
% 2.10/2.50 , substitution( 1, [ :=( X, equivalent( X, equivalent( equivalent( Y, Z )
% 2.10/2.50 , equivalent( Y, T ) ) ) ), :=( Y, equivalent( X, equivalent( Z, T ) ) )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1087, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( Y, T ) ) ) ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( X, equivalent( Z, T ) ) ), true ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1082, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 2.10/2.50 equivalent( X, equivalent( equivalent( Y, Z ), equivalent( Y, T ) ) ) ),
% 2.10/2.50 true, 'is_a_theorem'( equivalent( X, equivalent( Z, T ) ) ), true ), true
% 2.10/2.50 ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 2.10/2.50 equivalent( X, equivalent( equivalent( Y, Z ), equivalent( Y, T ) ) ) ),
% 2.10/2.50 true, 'is_a_theorem'( equivalent( X, equivalent( Z, T ) ) ), true ) ),
% 2.10/2.50 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 2.10/2.50 :=( T, T )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1088, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( Y, T ) ) ) ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( X, equivalent( Z, T ) ) ), true ), true ) ] )
% 2.10/2.50 , clause( 1087, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( Y, T ) ) ) ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( X, equivalent( Z, T ) ) ), true ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 230, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( Y, T ) ) ) ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( X, equivalent( Z, T ) ) ), true ), true ) ] )
% 2.10/2.50 , clause( 1088, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( Y, T ) ) ) ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( X, equivalent( Z, T ) ) ), true ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1090, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( Y, equivalent( equivalent( Y, equivalent( Z, Z ) ), X ) ) ),
% 2.10/2.50 T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 2.10/2.50 , clause( 129, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( Y, equivalent( equivalent( Y, equivalent( Z, Z ) ), X ) ) ),
% 2.10/2.50 T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1092, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( Y, T ), X ), equivalent( T, equivalent(
% 2.10/2.50 equivalent( Y, equivalent( Z, Z ) ), X ) ) ) ), true ) ) ] )
% 2.10/2.50 , clause( 152, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 2.10/2.50 X, Z ) ), equivalent( equivalent( equivalent( X, Y ), T ), equivalent( Y
% 2.10/2.50 , Z ) ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1090, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 X, equivalent( Y, equivalent( equivalent( Y, equivalent( Z, Z ) ), X ) )
% 2.10/2.50 ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, T ), :=( Z, equivalent(
% 2.10/2.50 equivalent( Y, equivalent( Z, Z ) ), X ) ), :=( T, X )] ), substitution(
% 2.10/2.50 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, equivalent( equivalent(
% 2.10/2.50 equivalent( Y, T ), X ), equivalent( T, equivalent( equivalent( Y,
% 2.10/2.50 equivalent( Z, Z ) ), X ) ) ) )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1094, [ =( true, 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 X, Y ), Z ), equivalent( Y, equivalent( equivalent( X, equivalent( T, T )
% 2.10/2.50 ), Z ) ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1092, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( Y, T ), X ), equivalent( T, equivalent(
% 2.10/2.50 equivalent( Y, equivalent( Z, Z ) ), X ) ) ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), Z ), equivalent( Y, equivalent(
% 2.10/2.50 equivalent( X, equivalent( T, T ) ), Z ) ) ) ) ), :=( Z, true )] ),
% 2.10/2.50 substitution( 1, [ :=( X, Z ), :=( Y, X ), :=( Z, T ), :=( T, Y )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1095, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 2.10/2.50 ), Z ), equivalent( Y, equivalent( equivalent( X, equivalent( T, T ) ),
% 2.10/2.50 Z ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 1094, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), Z ), equivalent( Y, equivalent( equivalent( X,
% 2.10/2.50 equivalent( T, T ) ), Z ) ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 345, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y, T
% 2.10/2.50 ), X ), equivalent( T, equivalent( equivalent( Y, equivalent( Z, Z ) ),
% 2.10/2.50 X ) ) ) ), true ) ] )
% 2.10/2.50 , clause( 1095, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 2.10/2.50 , Y ), Z ), equivalent( Y, equivalent( equivalent( X, equivalent( T, T )
% 2.10/2.50 ), Z ) ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, Y ), :=( Y, T ), :=( Z, X ), :=( T, Z )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1097, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( Y, T ) ) ) ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( X, equivalent( Z, T ) ) ), true ) ) ] )
% 2.10/2.50 , clause( 230, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( Y, T ) ) ) ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( X, equivalent( Z, T ) ) ), true ), true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1099, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ), T ) ),
% 2.10/2.50 equivalent( equivalent( Z, Y ), T ) ) ), true ) ) ] )
% 2.10/2.50 , clause( 138, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y,
% 2.10/2.50 Z ), T ), equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z )
% 2.10/2.50 ), T ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1097, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 2.10/2.50 equivalent( equivalent( Y, Z ), equivalent( Y, T ) ) ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( X, equivalent( Z, T ) ) ), true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T,
% 2.10/2.50 equivalent( equivalent( Z, X ), T ) )] ), substitution( 1, [ :=( X,
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ), T ) ) ),
% 2.10/2.50 :=( Y, equivalent( Z, X ) ), :=( Z, equivalent( Z, Y ) ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1101, [ =( true, 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 X, Y ), equivalent( equivalent( Z, X ), T ) ), equivalent( equivalent( Z
% 2.10/2.50 , Y ), T ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1099, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ), T ) ),
% 2.10/2.50 equivalent( equivalent( Z, Y ), T ) ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ), T ) ),
% 2.10/2.50 equivalent( equivalent( Z, Y ), T ) ) ) ), :=( Z, true )] ),
% 2.10/2.50 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1102, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 2.10/2.50 ), equivalent( equivalent( Z, X ), T ) ), equivalent( equivalent( Z, Y )
% 2.10/2.50 , T ) ) ), true ) ] )
% 2.10/2.50 , clause( 1101, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( equivalent( Z, X ), T ) ), equivalent(
% 2.10/2.50 equivalent( Z, Y ), T ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 367, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 2.10/2.50 ), equivalent( equivalent( Z, X ), T ) ), equivalent( equivalent( Z, Y )
% 2.10/2.50 , T ) ) ), true ) ] )
% 2.10/2.50 , clause( 1102, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 2.10/2.50 , Y ), equivalent( equivalent( Z, X ), T ) ), equivalent( equivalent( Z,
% 2.10/2.50 Y ), T ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1104, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y
% 2.10/2.50 ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 T, Y ), equivalent( T, Z ) ) ), true ) ) ] )
% 2.10/2.50 , clause( 16, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 2.10/2.50 equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent( T,
% 2.10/2.50 Y ), equivalent( T, Z ) ) ), true ), true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1106, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( T, equivalent( equivalent( X, X ), Z ) ), equivalent( T, Z )
% 2.10/2.50 ) ), true ) ) ] )
% 2.10/2.50 , clause( 367, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 2.10/2.50 Y ), equivalent( equivalent( Z, X ), T ) ), equivalent( equivalent( Z, Y
% 2.10/2.50 ), T ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1104, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 X, Y ), equivalent( X, Z ) ) ), true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( T, Y ), equivalent( T, Z ) ) ), true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, X ), :=( T, Z )] )
% 2.10/2.50 , substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, equivalent(
% 2.10/2.50 equivalent( X, X ), Z ) ), :=( Z, Z ), :=( T, T )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1108, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( equivalent( Y, Y ), Z ) ), equivalent( X, Z ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1106, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( T, equivalent( equivalent( X, X ), Z ) ), equivalent( T, Z )
% 2.10/2.50 ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( X, equivalent( equivalent( Y, Y ), Z ) ), equivalent( X, Z )
% 2.10/2.50 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, T ), :=(
% 2.10/2.50 Z, Z ), :=( T, X )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1109, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Y ), Z ) ), equivalent( X, Z ) ) ), true ) ] )
% 2.10/2.50 , clause( 1108, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( equivalent( Y, Y ), Z ) ), equivalent( X, Z ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 376, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 2.10/2.50 equivalent( X, X ), Z ) ), equivalent( T, Z ) ) ), true ) ] )
% 2.10/2.50 , clause( 1109, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Y ), Z ) ), equivalent( X, Z ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Z )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1111, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.50 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 2.10/2.50 )
% 2.10/2.50 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.50 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.50 )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1113, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( equivalent(
% 2.10/2.50 X, equivalent( equivalent( Y, Y ), Z ) ) ), true, 'is_a_theorem'(
% 2.10/2.50 equivalent( X, Z ) ), true ), true ) ) ] )
% 2.10/2.50 , clause( 376, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 2.10/2.50 equivalent( X, X ), Z ) ), equivalent( T, Z ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1111, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 2.10/2.50 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 2.10/2.50 ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, T ), :=( Z, Z ), :=( T, X )] )
% 2.10/2.50 , substitution( 1, [ :=( X, equivalent( X, equivalent( equivalent( Y, Y )
% 2.10/2.50 , Z ) ) ), :=( Y, equivalent( X, Z ) )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1118, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Y ), Z ) ) ), true, 'is_a_theorem'( equivalent( X, Z ) ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1113, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 2.10/2.50 equivalent( X, equivalent( equivalent( Y, Y ), Z ) ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( X, Z ) ), true ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 2.10/2.50 equivalent( X, equivalent( equivalent( Y, Y ), Z ) ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( X, Z ) ), true ) ), :=( Z, true )] ),
% 2.10/2.50 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1119, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Y ), Z ) ) ), true, 'is_a_theorem'( equivalent( X, Z ) ),
% 2.10/2.50 true ), true ) ] )
% 2.10/2.50 , clause( 1118, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Y ), Z ) ) ), true, 'is_a_theorem'( equivalent( X, Z ) ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 454, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Y ), Z ) ) ), true, 'is_a_theorem'( equivalent( X, Z ) ),
% 2.10/2.50 true ), true ) ] )
% 2.10/2.50 , clause( 1119, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Y ), Z ) ) ), true, 'is_a_theorem'( equivalent( X, Z ) ),
% 2.10/2.50 true ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1121, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Y ), Z ) ) ), true, 'is_a_theorem'( equivalent( X, Z ) ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , clause( 454, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Y ), Z ) ) ), true, 'is_a_theorem'( equivalent( X, Z ) ),
% 2.10/2.50 true ), true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1123, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ), Z
% 2.10/2.50 ) ), true ) ) ] )
% 2.10/2.50 , clause( 367, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 2.10/2.50 Y ), equivalent( equivalent( Z, X ), T ) ), equivalent( equivalent( Z, Y
% 2.10/2.50 ), T ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1121, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 2.10/2.50 equivalent( equivalent( Y, Y ), Z ) ) ), true, 'is_a_theorem'( equivalent(
% 2.10/2.50 X, Z ) ), true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y ), :=( T, Z )] )
% 2.10/2.50 , substitution( 1, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 2.10/2.50 equivalent( Y, X ), Z ) ) ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1125, [ =( true, 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 X, Y ), equivalent( equivalent( Y, X ), Z ) ), Z ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1123, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ), Z
% 2.10/2.50 ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ), Z
% 2.10/2.50 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=(
% 2.10/2.50 Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1126, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 2.10/2.50 ), equivalent( equivalent( Y, X ), Z ) ), Z ) ), true ) ] )
% 2.10/2.50 , clause( 1125, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ), Z ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 489, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 2.10/2.50 ), equivalent( equivalent( Y, X ), Z ) ), Z ) ), true ) ] )
% 2.10/2.50 , clause( 1126, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 2.10/2.50 , Y ), equivalent( equivalent( Y, X ), Z ) ), Z ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1128, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , clause( 107, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ),
% 2.10/2.50 true ), true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1130, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( T, equivalent( equivalent( X, Y ), equivalent( equivalent( Y
% 2.10/2.50 , X ), Z ) ) ), equivalent( T, Z ) ) ), true ) ) ] )
% 2.10/2.50 , clause( 489, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 2.10/2.50 Y ), equivalent( equivalent( Y, X ), Z ) ), Z ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1128, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 2.10/2.50 true, 'is_a_theorem'( equivalent( equivalent( Z, X ), equivalent( Z, Y )
% 2.10/2.50 ) ), true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.10/2.50 substitution( 1, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 2.10/2.50 equivalent( Y, X ), Z ) ) ), :=( Y, Z ), :=( Z, T )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1134, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ),
% 2.10/2.50 equivalent( X, T ) ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1130, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( T, equivalent( equivalent( X, Y ), equivalent( equivalent( Y
% 2.10/2.50 , X ), Z ) ) ), equivalent( T, Z ) ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( X, equivalent( equivalent( Y, Z ), equivalent( equivalent( Z
% 2.10/2.50 , Y ), T ) ) ), equivalent( X, T ) ) ) ), :=( Z, true )] ),
% 2.10/2.50 substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, X )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1135, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ), equivalent(
% 2.10/2.50 X, T ) ) ), true ) ] )
% 2.10/2.50 , clause( 1134, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 2.10/2.50 equivalent( equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ),
% 2.10/2.50 equivalent( X, T ) ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 522, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ) ), equivalent(
% 2.10/2.50 T, Z ) ) ), true ) ] )
% 2.10/2.50 , clause( 1135, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ), equivalent(
% 2.10/2.50 X, T ) ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1137, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 2.10/2.50 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 2.10/2.50 )
% 2.10/2.50 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 2.10/2.50 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 2.10/2.50 )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1139, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( equivalent(
% 2.10/2.50 X, equivalent( equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) )
% 2.10/2.50 ) ), true, 'is_a_theorem'( equivalent( X, T ) ), true ), true ) ) ] )
% 2.10/2.50 , clause( 522, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 2.10/2.50 equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ) ), equivalent(
% 2.10/2.50 T, Z ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1137, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 2.10/2.50 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 2.10/2.50 ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, X )] )
% 2.10/2.50 , substitution( 1, [ :=( X, equivalent( X, equivalent( equivalent( Y, Z )
% 2.10/2.50 , equivalent( equivalent( Z, Y ), T ) ) ) ), :=( Y, equivalent( X, T ) )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1144, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( X, T ) ), true ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1139, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 2.10/2.50 equivalent( X, equivalent( equivalent( Y, Z ), equivalent( equivalent( Z
% 2.10/2.50 , Y ), T ) ) ) ), true, 'is_a_theorem'( equivalent( X, T ) ), true ),
% 2.10/2.50 true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 2.10/2.50 equivalent( X, equivalent( equivalent( Y, Z ), equivalent( equivalent( Z
% 2.10/2.50 , Y ), T ) ) ) ), true, 'is_a_theorem'( equivalent( X, T ) ), true ) ),
% 2.10/2.50 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 2.10/2.50 :=( T, T )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1145, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( X, T ) ), true ), true ) ] )
% 2.10/2.50 , clause( 1144, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( X, T ) ), true ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 641, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( X, T ) ), true ), true ) ] )
% 2.10/2.50 , clause( 1145, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( X, T ) ), true ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1147, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( X, T ) ), true ) ) ] )
% 2.10/2.50 , clause( 641, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 2.10/2.50 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ) ), true,
% 2.10/2.50 'is_a_theorem'( equivalent( X, T ) ), true ), true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 2.10/2.50 ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1149, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( X, equivalent( equivalent( Y, Y ), X ) ), Z ), Z
% 2.10/2.50 ) ), true ) ) ] )
% 2.10/2.50 , clause( 345, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y,
% 2.10/2.50 T ), X ), equivalent( T, equivalent( equivalent( Y, equivalent( Z, Z ) )
% 2.10/2.50 , X ) ) ) ), true ) ] )
% 2.10/2.50 , 0, clause( 1147, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 2.10/2.50 equivalent( equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ) )
% 2.10/2.50 , true, 'is_a_theorem'( equivalent( X, T ) ), true ) ) ] )
% 2.10/2.50 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T,
% 2.10/2.50 equivalent( equivalent( Y, Y ), X ) )] ), substitution( 1, [ :=( X,
% 2.10/2.50 equivalent( equivalent( X, equivalent( equivalent( Y, Y ), X ) ), Z ) ),
% 2.10/2.50 :=( Y, equivalent( Y, Y ) ), :=( Z, X ), :=( T, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 paramod(
% 2.10/2.50 clause( 1151, [ =( true, 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 X, equivalent( equivalent( Y, Y ), X ) ), Z ), Z ) ) ) ] )
% 2.10/2.50 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 2.10/2.50 , 0, clause( 1149, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( X, equivalent( equivalent( Y, Y ), X ) ), Z ), Z
% 2.10/2.50 ) ), true ) ) ] )
% 2.10/2.50 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 2.10/2.50 equivalent( equivalent( X, equivalent( equivalent( Y, Y ), X ) ), Z ), Z
% 2.10/2.50 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=(
% 2.10/2.50 Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1152, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 2.10/2.50 equivalent( equivalent( Y, Y ), X ) ), Z ), Z ) ), true ) ] )
% 2.10/2.50 , clause( 1151, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( X, equivalent( equivalent( Y, Y ), X ) ), Z ), Z ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 818, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 2.10/2.50 equivalent( equivalent( Y, Y ), X ) ), Z ), Z ) ), true ) ] )
% 2.10/2.50 , clause( 1152, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 2.10/2.50 , equivalent( equivalent( Y, Y ), X ) ), Z ), Z ) ), true ) ] )
% 2.10/2.50 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.10/2.50 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1153, [ =( true, 'is_a_theorem'( equivalent( equivalent( equivalent(
% 2.10/2.50 X, equivalent( equivalent( Y, Y ), X ) ), Z ), Z ) ) ) ] )
% 2.10/2.50 , clause( 818, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 2.10/2.50 equivalent( equivalent( Y, Y ), X ) ), Z ), Z ) ), true ) ] )
% 2.10/2.50 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 eqswap(
% 2.10/2.50 clause( 1154, [ ~( =( true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( a, equivalent( equivalent( b, b ), a ) ), c ), c ) ) ) ) ] )
% 2.10/2.50 , clause( 5, [ ~( =( 'is_a_theorem'( equivalent( equivalent( equivalent( a
% 2.10/2.50 , equivalent( equivalent( b, b ), a ) ), c ), c ) ), true ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 resolution(
% 2.10/2.50 clause( 1155, [] )
% 2.10/2.50 , clause( 1154, [ ~( =( true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( a, equivalent( equivalent( b, b ), a ) ), c ), c ) ) ) ) ] )
% 2.10/2.50 , 0, clause( 1153, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 2.10/2.50 equivalent( X, equivalent( equivalent( Y, Y ), X ) ), Z ), Z ) ) ) ] )
% 2.10/2.50 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, b ), :=(
% 2.10/2.50 Z, c )] )).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 subsumption(
% 2.10/2.50 clause( 820, [] )
% 2.10/2.50 , clause( 1155, [] )
% 2.10/2.50 , substitution( 0, [] ), permutation( 0, [] ) ).
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 end.
% 2.10/2.50
% 2.10/2.50 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.10/2.50
% 2.10/2.50 Memory use:
% 2.10/2.50
% 2.10/2.50 space for terms: 15830
% 2.10/2.50 space for clauses: 119154
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 clauses generated: 259784
% 2.10/2.50 clauses kept: 821
% 2.10/2.50 clauses selected: 737
% 2.10/2.50 clauses deleted: 11
% 2.10/2.50 clauses inuse deleted: 0
% 2.10/2.50
% 2.10/2.50 subsentry: 693
% 2.10/2.50 literals s-matched: 234
% 2.10/2.50 literals matched: 234
% 2.10/2.50 full subsumption: 0
% 2.10/2.50
% 2.10/2.50 checksum: 1305354707
% 2.10/2.50
% 2.10/2.50
% 2.10/2.50 Bliksem ended
%------------------------------------------------------------------------------