TSTP Solution File: LCL084-10 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL084-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 07:50:03 EDT 2022
% Result : Unsatisfiable 44.17s 44.57s
% Output : Refutation 44.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL084-10 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.13 % Command : bliksem %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Mon Jul 4 16:56:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 44.17/44.57 *** allocated 10000 integers for termspace/termends
% 44.17/44.57 *** allocated 10000 integers for clauses
% 44.17/44.57 *** allocated 10000 integers for justifications
% 44.17/44.57 Bliksem 1.12
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 Automatic Strategy Selection
% 44.17/44.57
% 44.17/44.57 Clauses:
% 44.17/44.57 [
% 44.17/44.57 [ =( ifeq( X, X, Y, Z ), Y ) ],
% 44.17/44.57 [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq( 'is_a_theorem'(
% 44.17/44.57 X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ],
% 44.17/44.57 [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z ), implies(
% 44.17/44.57 implies( Z, X ), implies( T, X ) ) ) ), true ) ],
% 44.17/44.57 [ =( 'is_a_theorem'( implies( X, X ) ), true ) ],
% 44.17/44.57 [ ~( =( 'is_a_theorem'( implies( implies( a, b ), implies( implies( b, c
% 44.17/44.57 ), implies( a, c ) ) ) ), true ) ) ]
% 44.17/44.57 ] .
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 percentage equality = 1.000000, percentage horn = 1.000000
% 44.17/44.57 This is a pure equality problem
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 Options Used:
% 44.17/44.57
% 44.17/44.57 useres = 1
% 44.17/44.57 useparamod = 1
% 44.17/44.57 useeqrefl = 1
% 44.17/44.57 useeqfact = 1
% 44.17/44.57 usefactor = 1
% 44.17/44.57 usesimpsplitting = 0
% 44.17/44.57 usesimpdemod = 5
% 44.17/44.57 usesimpres = 3
% 44.17/44.57
% 44.17/44.57 resimpinuse = 1000
% 44.17/44.57 resimpclauses = 20000
% 44.17/44.57 substype = eqrewr
% 44.17/44.57 backwardsubs = 1
% 44.17/44.57 selectoldest = 5
% 44.17/44.57
% 44.17/44.57 litorderings [0] = split
% 44.17/44.57 litorderings [1] = extend the termordering, first sorting on arguments
% 44.17/44.57
% 44.17/44.57 termordering = kbo
% 44.17/44.57
% 44.17/44.57 litapriori = 0
% 44.17/44.57 termapriori = 1
% 44.17/44.57 litaposteriori = 0
% 44.17/44.57 termaposteriori = 0
% 44.17/44.57 demodaposteriori = 0
% 44.17/44.57 ordereqreflfact = 0
% 44.17/44.57
% 44.17/44.57 litselect = negord
% 44.17/44.57
% 44.17/44.57 maxweight = 15
% 44.17/44.57 maxdepth = 30000
% 44.17/44.57 maxlength = 115
% 44.17/44.57 maxnrvars = 195
% 44.17/44.57 excuselevel = 1
% 44.17/44.57 increasemaxweight = 1
% 44.17/44.57
% 44.17/44.57 maxselected = 10000000
% 44.17/44.57 maxnrclauses = 10000000
% 44.17/44.57
% 44.17/44.57 showgenerated = 0
% 44.17/44.57 showkept = 0
% 44.17/44.57 showselected = 0
% 44.17/44.57 showdeleted = 0
% 44.17/44.57 showresimp = 1
% 44.17/44.57 showstatus = 2000
% 44.17/44.57
% 44.17/44.57 prologoutput = 1
% 44.17/44.57 nrgoals = 5000000
% 44.17/44.57 totalproof = 1
% 44.17/44.57
% 44.17/44.57 Symbols occurring in the translation:
% 44.17/44.57
% 44.17/44.57 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 44.17/44.57 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 44.17/44.57 ! [4, 1] (w:0, o:20, a:1, s:1, b:0),
% 44.17/44.57 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 44.17/44.57 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 44.17/44.57 ifeq [42, 4] (w:1, o:52, a:1, s:1, b:0),
% 44.17/44.57 implies [45, 2] (w:1, o:51, a:1, s:1, b:0),
% 44.17/44.57 'is_a_theorem' [46, 1] (w:1, o:25, a:1, s:1, b:0),
% 44.17/44.57 true [47, 0] (w:1, o:14, a:1, s:1, b:0),
% 44.17/44.57 a [50, 0] (w:1, o:17, a:1, s:1, b:0),
% 44.17/44.57 b [51, 0] (w:1, o:18, a:1, s:1, b:0),
% 44.17/44.57 c [52, 0] (w:1, o:19, a:1, s:1, b:0).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 Starting Search:
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57 Failed to find proof!
% 44.17/44.57 maxweight = 15
% 44.17/44.57 maxnrclauses = 10000000
% 44.17/44.57 Generated: 395
% 44.17/44.57 Kept: 27
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 The strategy used was not complete!
% 44.17/44.57
% 44.17/44.57 Increased maxweight to 16
% 44.17/44.57
% 44.17/44.57 Starting Search:
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57 Failed to find proof!
% 44.17/44.57 maxweight = 16
% 44.17/44.57 maxnrclauses = 10000000
% 44.17/44.57 Generated: 583
% 44.17/44.57 Kept: 32
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 The strategy used was not complete!
% 44.17/44.57
% 44.17/44.57 Increased maxweight to 17
% 44.17/44.57
% 44.17/44.57 Starting Search:
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57 Failed to find proof!
% 44.17/44.57 maxweight = 17
% 44.17/44.57 maxnrclauses = 10000000
% 44.17/44.57 Generated: 659
% 44.17/44.57 Kept: 34
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 The strategy used was not complete!
% 44.17/44.57
% 44.17/44.57 Increased maxweight to 18
% 44.17/44.57
% 44.17/44.57 Starting Search:
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57 Failed to find proof!
% 44.17/44.57 maxweight = 18
% 44.17/44.57 maxnrclauses = 10000000
% 44.17/44.57 Generated: 4574
% 44.17/44.57 Kept: 81
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 The strategy used was not complete!
% 44.17/44.57
% 44.17/44.57 Increased maxweight to 19
% 44.17/44.57
% 44.17/44.57 Starting Search:
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57 Failed to find proof!
% 44.17/44.57 maxweight = 19
% 44.17/44.57 maxnrclauses = 10000000
% 44.17/44.57 Generated: 5509
% 44.17/44.57 Kept: 88
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 The strategy used was not complete!
% 44.17/44.57
% 44.17/44.57 Increased maxweight to 20
% 44.17/44.57
% 44.17/44.57 Starting Search:
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57 Failed to find proof!
% 44.17/44.57 maxweight = 20
% 44.17/44.57 maxnrclauses = 10000000
% 44.17/44.57 Generated: 200782
% 44.17/44.57 Kept: 529
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 The strategy used was not complete!
% 44.17/44.57
% 44.17/44.57 Increased maxweight to 21
% 44.17/44.57
% 44.17/44.57 Starting Search:
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57 Failed to find proof!
% 44.17/44.57 maxweight = 21
% 44.17/44.57 maxnrclauses = 10000000
% 44.17/44.57 Generated: 256546
% 44.17/44.57 Kept: 595
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 The strategy used was not complete!
% 44.17/44.57
% 44.17/44.57 Increased maxweight to 22
% 44.17/44.57
% 44.17/44.57 Starting Search:
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57 Failed to find proof!
% 44.17/44.57 maxweight = 22
% 44.17/44.57 maxnrclauses = 10000000
% 44.17/44.57 Generated: 1852749
% 44.17/44.57 Kept: 1572
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 The strategy used was not complete!
% 44.17/44.57
% 44.17/44.57 Increased maxweight to 23
% 44.17/44.57
% 44.17/44.57 Starting Search:
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 Intermediate Status:
% 44.17/44.57 Generated: 2674252
% 44.17/44.57 Kept: 2035
% 44.17/44.57 Inuse: 1867
% 44.17/44.57 Deleted: 40
% 44.17/44.57 Deletedinuse: 13
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 Intermediate Status:
% 44.17/44.57 Generated: 4049887
% 44.17/44.57 Kept: 4038
% 44.17/44.57 Inuse: 2347
% 44.17/44.57 Deleted: 40
% 44.17/44.57 Deletedinuse: 13
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 Intermediate Status:
% 44.17/44.57 Generated: 7430575
% 44.17/44.57 Kept: 6040
% 44.17/44.57 Inuse: 3248
% 44.17/44.57 Deleted: 46
% 44.17/44.57 Deletedinuse: 15
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 Intermediate Status:
% 44.17/44.57 Generated: 12072535
% 44.17/44.57 Kept: 8045
% 44.17/44.57 Inuse: 4223
% 44.17/44.57 Deleted: 46
% 44.17/44.57 Deletedinuse: 15
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57 Resimplifying inuse:
% 44.17/44.57 Done
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 Bliksems!, er is een bewijs:
% 44.17/44.57 % SZS status Unsatisfiable
% 44.17/44.57 % SZS output start Refutation
% 44.17/44.57
% 44.17/44.57 clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.57 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 2, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 44.17/44.57 implies( implies( Z, X ), implies( T, X ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 3, [ =( 'is_a_theorem'( implies( X, X ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 4, [ ~( =( 'is_a_theorem'( implies( implies( a, b ), implies(
% 44.17/44.57 implies( b, c ), implies( a, c ) ) ) ), true ) ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 6, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ), Y ) ), true
% 44.17/44.57 , 'is_a_theorem'( Y ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ), true
% 44.17/44.57 , 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true ),
% 44.17/44.57 true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 9, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.57 , Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U ) ), true,
% 44.17/44.57 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 11, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X ),
% 44.17/44.57 implies( Z, X ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 15, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), X ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( Z, X ) ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 16, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, Y ), X ), implies( Z, X ) ), T ) ), true, 'is_a_theorem'( T ), true )
% 44.17/44.57 , true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 23, [ =( 'is_a_theorem'( implies( Y, implies( X, X ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 26, [ =( 'is_a_theorem'( implies( implies( implies( Z, Z ), X ),
% 44.17/44.57 implies( T, X ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 27, [ =( 'is_a_theorem'( implies( implies( implies( Z, X ), implies(
% 44.17/44.57 X, Y ) ), implies( T, implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 30, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ), Y ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( Z, Y ) ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 31, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, X ), Y ), implies( Z, Y ) ), T ) ), true, 'is_a_theorem'( T ), true )
% 44.17/44.57 , true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 32, [ =( 'is_a_theorem'( implies( Z, implies( Y, implies( X, X ) )
% 44.17/44.57 ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 34, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies( T,
% 44.17/44.57 T ) ), X ), implies( U, X ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 37, [ =( 'is_a_theorem'( implies( T, implies( Z, implies( X,
% 44.17/44.57 implies( Y, Y ) ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 40, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies( T,
% 44.17/44.57 implies( U, U ) ) ), X ), implies( W, X ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 46, [ =( 'is_a_theorem'( implies( implies( implies( T, implies( Y,
% 44.17/44.57 Z ) ), implies( X, Y ) ), implies( U, implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 48, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, Y ), implies( Y, Z ) ), implies( T, implies( Y, Z ) ) ), U ) ), true,
% 44.17/44.57 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 49, [ =( 'is_a_theorem'( implies( W, implies( implies( implies( Z,
% 44.17/44.57 implies( T, T ) ), X ), implies( U, X ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 50, [ =( 'is_a_theorem'( implies( U, implies( T, implies( X,
% 44.17/44.57 implies( Y, implies( Z, Z ) ) ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 52, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, implies( Y, implies( Z, Z ) ) ), T ), implies( U, T ) ), W ) ), true,
% 44.17/44.57 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 54, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.57 implies( Z, implies( T, implies( U, U ) ) ) ) ), W ) ), true,
% 44.17/44.57 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 56, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.57 implies( implies( Y, implies( Z, Z ) ), T ), implies( U, T ) ) ), W ) ),
% 44.17/44.57 true, 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 57, [ =( 'is_a_theorem'( implies( U, implies( implies( implies(
% 44.17/44.57 implies( Z, X ), T ), X ), implies( Z, X ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 58, [ =( 'is_a_theorem'( implies( implies( implies( U, implies( T,
% 44.17/44.57 Y ) ), implies( X, implies( Y, Z ) ) ), implies( W, implies( X, implies(
% 44.17/44.57 Y, Z ) ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 60, [ =( 'is_a_theorem'( implies( implies( implies( implies( T, U )
% 44.17/44.57 , W ), U ), implies( T, U ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 63, [ =( 'is_a_theorem'( implies( X, implies( Y, X ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 65, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), implies(
% 44.17/44.57 implies( X, Y ), Z ) ), implies( T, implies( implies( X, Y ), Z ) ) ) ),
% 44.17/44.57 true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 66, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y ), Z
% 44.17/44.57 ), Y ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 69, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies( X,
% 44.17/44.57 Y ) ), X ), implies( T, X ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 70, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( implies(
% 44.17/44.57 Y, X ) ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 72, [ =( 'is_a_theorem'( implies( Z, implies( X, implies( Y, X ) )
% 44.17/44.57 ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 82, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies( T,
% 44.17/44.57 Z ) ), X ), implies( U, X ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 97, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, implies( Y, X ) ), Z ), implies( T, Z ) ), U ) ), true, 'is_a_theorem'(
% 44.17/44.57 U ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 170, [ =( 'is_a_theorem'( implies( T, implies( implies( implies( X
% 44.17/44.57 , Y ), implies( Y, Z ) ), implies( Y, Z ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 174, [ =( 'is_a_theorem'( implies( Z, implies( implies( implies( X
% 44.17/44.57 , Y ), X ), X ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 182, [ =( 'is_a_theorem'( implies( implies( implies( W, V0 ), W ),
% 44.17/44.57 W ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 186, [ =( 'is_a_theorem'( implies( implies( X, implies( X, Y ) ),
% 44.17/44.57 implies( Z, implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 190, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( Z, implies( X, Y ) ) ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 191, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.57 implies( X, Y ) ), implies( Z, implies( X, Y ) ) ), T ) ), true,
% 44.17/44.57 'is_a_theorem'( T ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 208, [ =( 'is_a_theorem'( implies( implies( implies( W, V0 ),
% 44.17/44.57 implies( V0, V1 ) ), implies( V0, V1 ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 212, [ =( 'is_a_theorem'( implies( implies( implies( Y, Z ),
% 44.17/44.57 implies( X, Y ) ), implies( T, implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 213, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.57 Y, Z ) ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 215, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z, X ) )
% 44.17/44.57 ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 222, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies( T
% 44.17/44.57 , implies( X, Y ) ) ), X ), implies( U, X ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 224, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.57 implies( Z, X ) ) ), T ) ), true, 'is_a_theorem'( T ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 257, [ =( 'is_a_theorem'( implies( U, implies( implies( implies( Z
% 44.17/44.57 , T ), X ), implies( T, X ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 259, [ =( 'is_a_theorem'( implies( implies( implies( W, V0 ), V1 )
% 44.17/44.57 , implies( V0, V1 ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 264, [ =( 'is_a_theorem'( implies( Z, implies( implies( Z, X ),
% 44.17/44.57 implies( T, X ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 265, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( Y, Z ) ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 266, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, Y ), Z ), implies( Y, Z ) ), T ) ), true, 'is_a_theorem'( T ), true )
% 44.17/44.57 , true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 269, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), Z ), implies( T, Z ) ), X ), implies( U, X ) ) ), true )
% 44.17/44.57 ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 270, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( implies(
% 44.17/44.57 implies( X, Y ), implies( Z, Y ) ) ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 271, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.57 implies( X, Y ), implies( Z, Y ) ) ), T ) ), true, 'is_a_theorem'( T ),
% 44.17/44.57 true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 412, [ =( 'is_a_theorem'( implies( Z, implies( implies( X, implies(
% 44.17/44.57 X, Y ) ), implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 420, [ =( 'is_a_theorem'( implies( T, implies( implies( implies( X
% 44.17/44.57 , implies( Y, Z ) ), Y ), Y ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 423, [ =( 'is_a_theorem'( implies( implies( Y, implies( Y, Z ) ),
% 44.17/44.57 implies( Y, Z ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 431, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 437, [ =( 'is_a_theorem'( implies( implies( implies( U, implies( W
% 44.17/44.57 , V0 ) ), W ), W ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 444, [ =( 'is_a_theorem'( implies( implies( Y, implies( X, implies(
% 44.17/44.57 Y, Z ) ) ), implies( T, implies( X, implies( Y, Z ) ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 452, [ =( 'is_a_theorem'( implies( implies( implies( X, implies( Y
% 44.17/44.57 , implies( Z, T ) ) ), Z ), Z ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 474, [ =( 'is_a_theorem'( implies( implies( Z, implies( X, implies(
% 44.17/44.57 Y, implies( Z, T ) ) ) ), implies( U, implies( X, implies( Y, implies( Z
% 44.17/44.57 , T ) ) ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 574, [ =( 'is_a_theorem'( implies( implies( X, implies( Y, implies(
% 44.17/44.57 X, Z ) ) ), implies( Y, implies( X, Z ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 583, [ =( 'is_a_theorem'( implies( implies( Z, X ), implies(
% 44.17/44.57 implies( implies( X, Y ), Z ), X ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 584, [ =( ifeq( 'is_a_theorem'( implies( X, implies( Y, implies( X
% 44.17/44.57 , Z ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( X, Z ) ) ), true
% 44.17/44.57 ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 589, [ =( 'is_a_theorem'( implies( implies( implies( implies( Y,
% 44.17/44.57 implies( Z, X ) ), T ), X ), implies( Y, implies( Z, X ) ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 600, [ =( 'is_a_theorem'( implies( implies( implies( implies( Z, Y
% 44.17/44.57 ), T ), implies( implies( X, X ), Y ) ), implies( Z, Y ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 601, [ =( 'is_a_theorem'( implies( implies( implies( implies( Z, X
% 44.17/44.57 ), T ), implies( implies( X, Y ), X ) ), implies( Z, X ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 602, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 implies( Y, Z ), X ), Y ), X ), implies( T, X ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 603, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.57 'is_a_theorem'( implies( implies( implies( Y, Z ), X ), Y ) ), true ),
% 44.17/44.57 true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 623, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), Z ), X ), Z ), Z ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 640, [ =( 'is_a_theorem'( implies( implies( Z, implies( implies(
% 44.17/44.57 implies( X, Y ), Z ), X ) ), implies( T, implies( implies( implies( X, Y
% 44.17/44.57 ), Z ), X ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 671, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), implies( Z, Y ) ), T ), X ), implies( implies( X, Y ),
% 44.17/44.57 implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 702, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.57 Z ), implies( implies( T, T ), Y ) ) ), true, 'is_a_theorem'( implies( X
% 44.17/44.57 , Y ) ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 705, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.57 Z ), implies( implies( Y, T ), Y ) ) ), true, 'is_a_theorem'( implies( X
% 44.17/44.57 , Y ) ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 723, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), Z ), implies( T, Z ) ), X ), X ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 756, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.57 implies( Y, Z ) ), T ), Z ) ), true, 'is_a_theorem'( implies( X, implies(
% 44.17/44.57 Y, Z ) ) ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 1210, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 implies( implies( X, Y ), Z ), implies( X, Y ) ), T ), Y ), implies( X, Y
% 44.17/44.57 ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 1211, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), X ), Z ), implies( implies( X, Y ), X ) ), X ) ), true )
% 44.17/44.57 ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 1219, [ =( 'is_a_theorem'( implies( implies( X, implies( implies(
% 44.17/44.57 implies( X, Y ), X ), Z ) ), implies( T, implies( implies( implies( X, Y
% 44.17/44.57 ), X ), Z ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 1223, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 implies( X, X ), Y ), Z ), implies( implies( X, X ), Y ) ), Y ) ), true )
% 44.17/44.57 ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 1264, [ =( 'is_a_theorem'( implies( implies( Y, implies( implies(
% 44.17/44.57 implies( X, X ), Y ), Z ) ), implies( T, implies( implies( implies( X, X
% 44.17/44.57 ), Y ), Z ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 1302, [ =( 'is_a_theorem'( implies( implies( X, implies( Y, implies(
% 44.17/44.57 Z, implies( X, T ) ) ) ), implies( Y, implies( Z, implies( X, T ) ) ) ) )
% 44.17/44.57 , true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 1304, [ =( ifeq( 'is_a_theorem'( implies( X, implies( Y, implies( Z
% 44.17/44.57 , implies( X, T ) ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( Z,
% 44.17/44.57 implies( X, T ) ) ) ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 1324, [ =( 'is_a_theorem'( implies( implies( implies( T, implies(
% 44.17/44.57 implies( implies( Y, Y ), X ), Z ) ), X ), implies( U, X ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 1369, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.57 implies( implies( Y, Y ), Z ), T ) ), Z ), Z ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 1379, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, implies( implies( implies( Y, Y ), Z ), T ) ), Z ), Z ), U ) ), true,
% 44.17/44.57 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 1492, [ =( 'is_a_theorem'( implies( implies( implies( T, implies(
% 44.17/44.57 implies( implies( X, Y ), X ), Z ) ), X ), implies( U, X ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 1510, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.57 implies( implies( Y, Z ), Y ), T ) ), Y ), Y ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 1520, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, implies( implies( implies( Y, Z ), Y ), T ) ), Y ), Y ), U ) ), true,
% 44.17/44.57 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 1596, [ =( 'is_a_theorem'( implies( implies( implies( T, implies(
% 44.17/44.57 implies( implies( Y, Z ), X ), Y ) ), X ), implies( U, X ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 1597, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.57 implies( implies( Y, Z ), T ), Y ) ), T ), T ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 1607, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, implies( implies( implies( Y, Z ), T ), Y ) ), T ), T ), U ) ), true,
% 44.17/44.57 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2102, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.57 implies( implies( Z, Z ), X ), Y ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2134, [ =( 'is_a_theorem'( implies( implies( implies( T, T ),
% 44.17/44.57 implies( implies( X, Y ), Z ) ), implies( Y, Z ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2161, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ), implies(
% 44.17/44.57 implies( Y, Z ), T ) ) ), true, 'is_a_theorem'( implies( Z, T ) ), true )
% 44.17/44.57 , true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2341, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.57 implies( implies( X, Z ), X ), Y ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2352, [ =( 'is_a_theorem'( implies( implies( implies( X, T ), X ),
% 44.17/44.57 implies( implies( X, Y ), implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2359, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.57 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true ),
% 44.17/44.57 true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2362, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( implies(
% 44.17/44.57 X, Z ), implies( T, Z ) ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2366, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Z
% 44.17/44.57 ), implies( T, Z ) ), implies( X, Y ) ), implies( U, implies( X, Y ) ) )
% 44.17/44.57 ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2398, [ =( 'is_a_theorem'( implies( implies( implies( X, U ), X ),
% 44.17/44.57 implies( Y, implies( implies( X, Z ), implies( T, Z ) ) ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 2403, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z,
% 44.17/44.57 implies( implies( X, T ), implies( U, T ) ) ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2422, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.57 implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) ), W ) ),
% 44.17/44.57 true, 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2467, [ =( 'is_a_theorem'( implies( Z, implies( X, implies( implies(
% 44.17/44.57 X, Y ), Y ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2468, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.57 ), implies( Z, Y ) ), implies( X, T ) ), implies( X, T ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 2474, [ =( 'is_a_theorem'( implies( U, implies( implies( U, W ), W
% 44.17/44.57 ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2477, [ =( 'is_a_theorem'( implies( Z, implies( implies( implies( Y
% 44.17/44.57 , Z ), T ), T ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2489, [ =( 'is_a_theorem'( implies( implies( implies( X, Z ), X ),
% 44.17/44.57 implies( implies( X, Y ), Y ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2496, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), Y ), Z ), X ), implies( implies( X, Y ), Y ) ) ), true )
% 44.17/44.57 ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2606, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.57 implies( implies( Y, X ), Z ), Z ) ), T ) ), true, 'is_a_theorem'( T ),
% 44.17/44.57 true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2791, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( implies(
% 44.17/44.57 X, Z ), Z ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2799, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Z
% 44.17/44.57 ), Z ), implies( X, Y ) ), implies( T, implies( X, Y ) ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 2822, [ =( 'is_a_theorem'( implies( Y, implies( Z, implies( implies(
% 44.17/44.57 implies( X, Y ), T ), T ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 2855, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.57 implies( implies( implies( Z, X ), T ), T ) ) ), U ) ), true,
% 44.17/44.57 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 3239, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.57 ), Y ), implies( X, Z ) ), implies( X, Z ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 3253, [ =( 'is_a_theorem'( implies( implies( implies( X, Z ),
% 44.17/44.57 implies( implies( X, Y ), Y ) ), implies( T, implies( implies( X, Y ), Y
% 44.17/44.57 ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 3254, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.57 , Y ), implies( X, Z ) ) ), true, 'is_a_theorem'( implies( X, Z ) ), true
% 44.17/44.57 ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 3277, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.57 , implies( Z, Y ) ), implies( X, T ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.57 X, T ) ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 3323, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, Y ), Y ), Z ), X ) ), true, 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.57 Y ) ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 3494, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.57 implies( X, Y ), Y ), Z ), implies( T, Z ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 3544, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.57 ), Y ), Z ), implies( X, Z ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 3572, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 implies( implies( X, Y ), Y ), Z ), implies( X, Z ) ), T ), implies( U, T
% 44.17/44.57 ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 3574, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.57 , Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 4554, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.57 implies( implies( X, Z ), Z ) ), implies( implies( X, Z ), Z ) ) ), true
% 44.17/44.57 ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 4560, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.57 implies( X, Z ), Z ) ) ), true, 'is_a_theorem'( implies( implies( X, Z )
% 44.17/44.57 , Z ) ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 4878, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.57 ), Y ), Z ), implies( T, implies( X, Z ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 5198, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( X,
% 44.17/44.57 implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 5272, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.57 'is_a_theorem'( implies( X, implies( Z, Y ) ) ), true ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 5275, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( T,
% 44.17/44.57 implies( X, implies( Z, Y ) ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 5654, [ =( 'is_a_theorem'( implies( X, implies( implies( X, Y ),
% 44.17/44.57 implies( T, implies( Z, Y ) ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 5667, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.57 ), U ), implies( X, Y ) ), implies( Z, implies( X, implies( T, Y ) ) ) )
% 44.17/44.57 ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 5697, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.57 implies( X, Y ), Y ), Z ), implies( T, implies( U, Z ) ) ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 6223, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.57 ), Y ), Z ), implies( X, implies( T, Z ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 6228, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.57 ), Y ), Z ), implies( U, implies( X, implies( T, Z ) ) ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 6241, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( X,
% 44.17/44.57 implies( T, implies( Z, Y ) ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 6270, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.57 'is_a_theorem'( implies( X, implies( Z, implies( T, Y ) ) ) ), true ),
% 44.17/44.57 true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 7778, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.57 ), Z ), implies( X, implies( T, Y ) ) ), implies( X, implies( T, Y ) ) )
% 44.17/44.57 ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 8141, [ =( 'is_a_theorem'( implies( X, implies( implies( implies( T
% 44.17/44.57 , implies( implies( X, Y ), Z ) ), Y ), Y ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 8180, [ =( 'is_a_theorem'( implies( implies( implies( X, U ), X ),
% 44.17/44.57 implies( implies( implies( Y, implies( implies( X, Z ), T ) ), Z ), Z ) )
% 44.17/44.57 ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 8230, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.57 implies( X, Y ), Z ) ), Y ), Y ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 8244, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.57 implies( X, Y ), Z ) ), Y ), implies( T, implies( U, Y ) ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 8282, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.57 implies( X, Y ), Z ) ), implies( T, Y ) ), implies( T, Y ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 .
% 44.17/44.57 clause( 8291, [ =( 'is_a_theorem'( implies( implies( implies( T, implies( X
% 44.17/44.57 , implies( implies( X, Y ), Z ) ) ), Y ), Y ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 8302, [ =( 'is_a_theorem'( implies( implies( X, implies( Y, implies(
% 44.17/44.57 implies( Y, X ), Z ) ) ), implies( Y, implies( implies( Y, X ), Z ) ) ) )
% 44.17/44.57 , true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 8358, [ =( 'is_a_theorem'( implies( Y, implies( implies( Y, X ),
% 44.17/44.57 implies( implies( X, Z ), implies( T, Z ) ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 9344, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.57 implies( Y, Z ), implies( X, Z ) ) ) ), true ) ] )
% 44.17/44.57 .
% 44.17/44.57 clause( 9389, [] )
% 44.17/44.57 .
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 % SZS output end Refutation
% 44.17/44.57 found a proof!
% 44.17/44.57
% 44.17/44.57 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 44.17/44.57
% 44.17/44.57 initialclauses(
% 44.17/44.57 [ clause( 9391, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , clause( 9392, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.57 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , clause( 9393, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z )
% 44.17/44.57 , implies( implies( Z, X ), implies( T, X ) ) ) ), true ) ] )
% 44.17/44.57 , clause( 9394, [ =( 'is_a_theorem'( implies( X, X ) ), true ) ] )
% 44.17/44.57 , clause( 9395, [ ~( =( 'is_a_theorem'( implies( implies( a, b ), implies(
% 44.17/44.57 implies( b, c ), implies( a, c ) ) ) ), true ) ) ] )
% 44.17/44.57 ] ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , clause( 9391, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.57 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , clause( 9392, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.57 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 44.17/44.57 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 2, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 44.17/44.57 implies( implies( Z, X ), implies( T, X ) ) ) ), true ) ] )
% 44.17/44.57 , clause( 9393, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z )
% 44.17/44.57 , implies( implies( Z, X ), implies( T, X ) ) ) ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 3, [ =( 'is_a_theorem'( implies( X, X ) ), true ) ] )
% 44.17/44.57 , clause( 9394, [ =( 'is_a_theorem'( implies( X, X ) ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 4, [ ~( =( 'is_a_theorem'( implies( implies( a, b ), implies(
% 44.17/44.57 implies( b, c ), implies( a, c ) ) ) ), true ) ) ] )
% 44.17/44.57 , clause( 9395, [ ~( =( 'is_a_theorem'( implies( implies( a, b ), implies(
% 44.17/44.57 implies( b, c ), implies( a, c ) ) ) ), true ) ) ] )
% 44.17/44.57 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9412, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.57 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.57 )
% 44.17/44.57 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.57 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9415, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X ), Y
% 44.17/44.57 ) ), true, ifeq( true, true, 'is_a_theorem'( Y ), true ), true ) ) ] )
% 44.17/44.57 , clause( 3, [ =( 'is_a_theorem'( implies( X, X ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9412, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.57 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.57 ] )
% 44.17/44.57 , 0, 11, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 44.17/44.57 implies( X, X ) ), :=( Y, Y )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9417, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X ), Y
% 44.17/44.57 ) ), true, 'is_a_theorem'( Y ), true ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9415, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X
% 44.17/44.57 ), Y ) ), true, ifeq( true, true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.57 ] )
% 44.17/44.57 , 0, 10, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( Y ) ),
% 44.17/44.57 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9418, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ), Y ) ),
% 44.17/44.57 true, 'is_a_theorem'( Y ), true ), true ) ] )
% 44.17/44.57 , clause( 9417, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X ),
% 44.17/44.57 Y ) ), true, 'is_a_theorem'( Y ), true ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 6, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ), Y ) ), true
% 44.17/44.57 , 'is_a_theorem'( Y ), true ), true ) ] )
% 44.17/44.57 , clause( 9418, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ), Y ) )
% 44.17/44.57 , true, 'is_a_theorem'( Y ), true ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 44.17/44.57 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9420, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.57 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.57 )
% 44.17/44.57 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.57 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9422, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.57 implies( X, Y ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ),
% 44.17/44.57 implies( T, X ) ) ), true ), true ) ) ] )
% 44.17/44.57 , clause( 2, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 44.17/44.57 implies( implies( Z, X ), implies( T, X ) ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9420, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.57 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.57 ] )
% 44.17/44.57 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.57 , substitution( 1, [ :=( X, implies( implies( X, Y ), Z ) ), :=( Y,
% 44.17/44.57 implies( implies( Z, X ), implies( T, X ) ) )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9427, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.57 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.57 , true ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9422, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.57 implies( implies( X, Y ), Z ) ), true, 'is_a_theorem'( implies( implies(
% 44.17/44.57 Z, X ), implies( T, X ) ) ), true ), true ) ) ] )
% 44.17/44.57 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.57 implies( implies( X, Y ), Z ) ), true, 'is_a_theorem'( implies( implies(
% 44.17/44.57 Z, X ), implies( T, X ) ) ), true ) ), :=( Z, true )] ), substitution( 1
% 44.17/44.57 , [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9428, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.57 ), true ) ] )
% 44.17/44.57 , clause( 9427, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.57 Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) )
% 44.17/44.57 ), true ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.57 ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ), true
% 44.17/44.57 , 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true ),
% 44.17/44.57 true ) ] )
% 44.17/44.57 , clause( 9428, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) )
% 44.17/44.57 , true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ),
% 44.17/44.57 true ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9430, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.57 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.57 )
% 44.17/44.57 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.57 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9433, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U )
% 44.17/44.57 ), true, ifeq( true, true, 'is_a_theorem'( U ), true ), true ) ) ] )
% 44.17/44.57 , clause( 2, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 44.17/44.57 implies( implies( Z, X ), implies( T, X ) ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9430, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.57 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.57 ] )
% 44.17/44.57 , 0, 21, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.57 , substitution( 1, [ :=( X, implies( implies( implies( X, Y ), Z ),
% 44.17/44.57 implies( implies( Z, X ), implies( T, X ) ) ) ), :=( Y, U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9435, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U )
% 44.17/44.57 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9433, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.57 implies( implies( X, Y ), Z ), implies( implies( Z, X ), implies( T, X )
% 44.17/44.57 ) ), U ) ), true, ifeq( true, true, 'is_a_theorem'( U ), true ), true )
% 44.17/44.57 ) ] )
% 44.17/44.57 , 0, 20, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( U ) ),
% 44.17/44.57 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.57 :=( T, T ), :=( U, U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9436, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U ) ), true,
% 44.17/44.57 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.57 , clause( 9435, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U )
% 44.17/44.57 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.57 :=( U, U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 9, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.57 , Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U ) ), true,
% 44.17/44.57 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.57 , clause( 9436, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U )
% 44.17/44.57 ), true, 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 44.17/44.57 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9438, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X ), Y
% 44.17/44.57 ) ), true, 'is_a_theorem'( Y ), true ) ) ] )
% 44.17/44.57 , clause( 6, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ), Y ) ),
% 44.17/44.57 true, 'is_a_theorem'( Y ), true ), true ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9440, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.57 implies( X, Y ), X ), implies( Z, X ) ) ), true ) ) ] )
% 44.17/44.57 , clause( 2, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 44.17/44.57 implies( implies( Z, X ), implies( T, X ) ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9438, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X
% 44.17/44.57 ), Y ) ), true, 'is_a_theorem'( Y ), true ) ) ] )
% 44.17/44.57 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( X, Y ) )
% 44.17/44.57 , :=( T, Z )] ), substitution( 1, [ :=( X, implies( X, Y ) ), :=( Y,
% 44.17/44.57 implies( implies( implies( X, Y ), X ), implies( Z, X ) ) )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9442, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.57 , X ), implies( Z, X ) ) ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9440, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.57 implies( implies( X, Y ), X ), implies( Z, X ) ) ), true ) ) ] )
% 44.17/44.57 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.57 implies( implies( X, Y ), X ), implies( Z, X ) ) ) ), :=( Z, true )] ),
% 44.17/44.57 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9443, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X ),
% 44.17/44.57 implies( Z, X ) ) ), true ) ] )
% 44.17/44.57 , clause( 9442, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.57 ), X ), implies( Z, X ) ) ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 11, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X ),
% 44.17/44.57 implies( Z, X ) ) ), true ) ] )
% 44.17/44.57 , clause( 9443, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X )
% 44.17/44.57 , implies( Z, X ) ) ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9445, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.57 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.57 )
% 44.17/44.57 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.57 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9447, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.57 implies( X, Y ), X ) ), true, 'is_a_theorem'( implies( Z, X ) ), true ),
% 44.17/44.57 true ) ) ] )
% 44.17/44.57 , clause( 11, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X ),
% 44.17/44.57 implies( Z, X ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9445, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.57 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.57 ] )
% 44.17/44.57 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.57 substitution( 1, [ :=( X, implies( implies( X, Y ), X ) ), :=( Y, implies(
% 44.17/44.57 Z, X ) )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9452, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), X
% 44.17/44.57 ) ), true, 'is_a_theorem'( implies( Z, X ) ), true ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9447, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.57 implies( implies( X, Y ), X ) ), true, 'is_a_theorem'( implies( Z, X ) )
% 44.17/44.57 , true ), true ) ) ] )
% 44.17/44.57 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.57 implies( implies( X, Y ), X ) ), true, 'is_a_theorem'( implies( Z, X ) )
% 44.17/44.57 , true ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 44.17/44.57 :=( Z, Z )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9453, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), X ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( Z, X ) ), true ), true ) ] )
% 44.17/44.57 , clause( 9452, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.57 X ) ), true, 'is_a_theorem'( implies( Z, X ) ), true ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 15, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), X ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( Z, X ) ), true ), true ) ] )
% 44.17/44.57 , clause( 9453, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), X ) )
% 44.17/44.57 , true, 'is_a_theorem'( implies( Z, X ) ), true ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9455, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.57 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.57 )
% 44.17/44.57 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.57 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9458, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), X ), implies( Z, X ) ), T ) ), true, ifeq( true, true,
% 44.17/44.57 'is_a_theorem'( T ), true ), true ) ) ] )
% 44.17/44.57 , clause( 11, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X ),
% 44.17/44.57 implies( Z, X ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9455, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.57 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.57 ] )
% 44.17/44.57 , 0, 17, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.57 substitution( 1, [ :=( X, implies( implies( implies( X, Y ), X ), implies(
% 44.17/44.57 Z, X ) ) ), :=( Y, T )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9460, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), X ), implies( Z, X ) ), T ) ), true, 'is_a_theorem'( T )
% 44.17/44.57 , true ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9458, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.57 implies( implies( X, Y ), X ), implies( Z, X ) ), T ) ), true, ifeq( true
% 44.17/44.57 , true, 'is_a_theorem'( T ), true ), true ) ) ] )
% 44.17/44.57 , 0, 16, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( T ) ),
% 44.17/44.57 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.57 :=( T, T )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9461, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, Y ), X ), implies( Z, X ) ), T ) ), true, 'is_a_theorem'( T ), true )
% 44.17/44.57 , true ) ] )
% 44.17/44.57 , clause( 9460, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), X ), implies( Z, X ) ), T ) ), true, 'is_a_theorem'( T )
% 44.17/44.57 , true ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.57 ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 16, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, Y ), X ), implies( Z, X ) ), T ) ), true, 'is_a_theorem'( T ), true )
% 44.17/44.57 , true ) ] )
% 44.17/44.57 , clause( 9461, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), X ), implies( Z, X ) ), T ) ), true, 'is_a_theorem'( T )
% 44.17/44.57 , true ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9463, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), X
% 44.17/44.57 ) ), true, 'is_a_theorem'( implies( Z, X ) ), true ) ) ] )
% 44.17/44.57 , clause( 15, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), X ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( Z, X ) ), true ), true ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9465, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Y,
% 44.17/44.57 implies( X, X ) ) ), true ) ) ] )
% 44.17/44.57 , clause( 11, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X ),
% 44.17/44.57 implies( Z, X ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9463, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.57 ), X ) ), true, 'is_a_theorem'( implies( Z, X ) ), true ) ) ] )
% 44.17/44.57 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, X )] ),
% 44.17/44.57 substitution( 1, [ :=( X, implies( X, X ) ), :=( Y, X ), :=( Z, Y )] )
% 44.17/44.57 ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9467, [ =( true, 'is_a_theorem'( implies( X, implies( Y, Y ) ) ) )
% 44.17/44.57 ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9465, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Y
% 44.17/44.57 , implies( X, X ) ) ), true ) ) ] )
% 44.17/44.57 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.57 , implies( Y, Y ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y )
% 44.17/44.57 , :=( Y, X )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9468, [ =( 'is_a_theorem'( implies( X, implies( Y, Y ) ) ), true )
% 44.17/44.57 ] )
% 44.17/44.57 , clause( 9467, [ =( true, 'is_a_theorem'( implies( X, implies( Y, Y ) ) )
% 44.17/44.57 ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 23, [ =( 'is_a_theorem'( implies( Y, implies( X, X ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , clause( 9468, [ =( 'is_a_theorem'( implies( X, implies( Y, Y ) ) ), true
% 44.17/44.57 ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 44.17/44.57 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9470, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.57 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.57 , true ) ) ] )
% 44.17/44.57 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.57 ), true ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.57 ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9472, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.57 implies( Z, Z ), X ), implies( T, X ) ) ), true ) ) ] )
% 44.17/44.57 , clause( 23, [ =( 'is_a_theorem'( implies( Y, implies( X, X ) ) ), true )
% 44.17/44.57 ] )
% 44.17/44.57 , 0, clause( 9470, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.57 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.57 ) ) ), true ) ) ] )
% 44.17/44.57 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, implies( X, Y ) )] ),
% 44.17/44.57 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( Z, Z ) ), :=(
% 44.17/44.57 T, T )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9474, [ =( true, 'is_a_theorem'( implies( implies( implies( X, X )
% 44.17/44.57 , Y ), implies( Z, Y ) ) ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9472, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.57 implies( implies( Z, Z ), X ), implies( T, X ) ) ), true ) ) ] )
% 44.17/44.57 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.57 implies( implies( X, X ), Y ), implies( Z, Y ) ) ) ), :=( Z, true )] ),
% 44.17/44.57 substitution( 1, [ :=( X, Y ), :=( Y, T ), :=( Z, X ), :=( T, Z )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9475, [ =( 'is_a_theorem'( implies( implies( implies( X, X ), Y ),
% 44.17/44.57 implies( Z, Y ) ) ), true ) ] )
% 44.17/44.57 , clause( 9474, [ =( true, 'is_a_theorem'( implies( implies( implies( X, X
% 44.17/44.57 ), Y ), implies( Z, Y ) ) ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 26, [ =( 'is_a_theorem'( implies( implies( implies( Z, Z ), X ),
% 44.17/44.57 implies( T, X ) ) ), true ) ] )
% 44.17/44.57 , clause( 9475, [ =( 'is_a_theorem'( implies( implies( implies( X, X ), Y )
% 44.17/44.57 , implies( Z, Y ) ) ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, T )] ),
% 44.17/44.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9477, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.57 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.57 , true ) ) ] )
% 44.17/44.57 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.57 ), true ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.57 ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9479, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.57 implies( Z, X ), implies( X, Y ) ), implies( T, implies( X, Y ) ) ) ),
% 44.17/44.57 true ) ) ] )
% 44.17/44.57 , clause( 11, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X ),
% 44.17/44.57 implies( Z, X ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9477, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.57 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.57 ) ) ), true ) ) ] )
% 44.17/44.57 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.57 substitution( 1, [ :=( X, implies( X, Y ) ), :=( Y, X ), :=( Z, implies(
% 44.17/44.57 Z, X ) ), :=( T, T )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9481, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.57 , implies( Y, Z ) ), implies( T, implies( Y, Z ) ) ) ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9479, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.57 implies( implies( Z, X ), implies( X, Y ) ), implies( T, implies( X, Y )
% 44.17/44.57 ) ) ), true ) ) ] )
% 44.17/44.57 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.57 implies( implies( X, Y ), implies( Y, Z ) ), implies( T, implies( Y, Z )
% 44.17/44.57 ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ),
% 44.17/44.57 :=( Z, X ), :=( T, T )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9482, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.57 implies( Y, Z ) ), implies( T, implies( Y, Z ) ) ) ), true ) ] )
% 44.17/44.57 , clause( 9481, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.57 ), implies( Y, Z ) ), implies( T, implies( Y, Z ) ) ) ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.57 ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 27, [ =( 'is_a_theorem'( implies( implies( implies( Z, X ), implies(
% 44.17/44.57 X, Y ) ), implies( T, implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.57 , clause( 9482, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.57 implies( Y, Z ) ), implies( T, implies( Y, Z ) ) ) ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T )] ),
% 44.17/44.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9484, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.57 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.57 )
% 44.17/44.57 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.57 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9486, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.57 implies( X, X ), Y ) ), true, 'is_a_theorem'( implies( Z, Y ) ), true ),
% 44.17/44.57 true ) ) ] )
% 44.17/44.57 , clause( 26, [ =( 'is_a_theorem'( implies( implies( implies( Z, Z ), X ),
% 44.17/44.57 implies( T, X ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9484, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.57 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.57 ] )
% 44.17/44.57 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, T ), :=( Z, X ), :=( T, Z )] )
% 44.17/44.57 , substitution( 1, [ :=( X, implies( implies( X, X ), Y ) ), :=( Y,
% 44.17/44.57 implies( Z, Y ) )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9491, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X ), Y
% 44.17/44.57 ) ), true, 'is_a_theorem'( implies( Z, Y ) ), true ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9486, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.57 implies( implies( X, X ), Y ) ), true, 'is_a_theorem'( implies( Z, Y ) )
% 44.17/44.57 , true ), true ) ) ] )
% 44.17/44.57 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.57 implies( implies( X, X ), Y ) ), true, 'is_a_theorem'( implies( Z, Y ) )
% 44.17/44.57 , true ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 44.17/44.57 :=( Z, Z )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9492, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ), Y ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( Z, Y ) ), true ), true ) ] )
% 44.17/44.57 , clause( 9491, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X ),
% 44.17/44.57 Y ) ), true, 'is_a_theorem'( implies( Z, Y ) ), true ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 30, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ), Y ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( Z, Y ) ), true ), true ) ] )
% 44.17/44.57 , clause( 9492, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ), Y ) )
% 44.17/44.57 , true, 'is_a_theorem'( implies( Z, Y ) ), true ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9494, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.57 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.57 )
% 44.17/44.57 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.57 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9497, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, X ), Y ), implies( Z, Y ) ), T ) ), true, ifeq( true, true,
% 44.17/44.57 'is_a_theorem'( T ), true ), true ) ) ] )
% 44.17/44.57 , clause( 26, [ =( 'is_a_theorem'( implies( implies( implies( Z, Z ), X ),
% 44.17/44.57 implies( T, X ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9494, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.57 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.57 ] )
% 44.17/44.57 , 0, 17, substitution( 0, [ :=( X, Y ), :=( Y, U ), :=( Z, X ), :=( T, Z )] )
% 44.17/44.57 , substitution( 1, [ :=( X, implies( implies( implies( X, X ), Y ),
% 44.17/44.57 implies( Z, Y ) ) ), :=( Y, T )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9499, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, X ), Y ), implies( Z, Y ) ), T ) ), true, 'is_a_theorem'( T )
% 44.17/44.57 , true ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9497, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.57 implies( implies( X, X ), Y ), implies( Z, Y ) ), T ) ), true, ifeq( true
% 44.17/44.57 , true, 'is_a_theorem'( T ), true ), true ) ) ] )
% 44.17/44.57 , 0, 16, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( T ) ),
% 44.17/44.57 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.57 :=( T, T )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9500, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, X ), Y ), implies( Z, Y ) ), T ) ), true, 'is_a_theorem'( T ), true )
% 44.17/44.57 , true ) ] )
% 44.17/44.57 , clause( 9499, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, X ), Y ), implies( Z, Y ) ), T ) ), true, 'is_a_theorem'( T )
% 44.17/44.57 , true ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.57 ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 31, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, X ), Y ), implies( Z, Y ) ), T ) ), true, 'is_a_theorem'( T ), true )
% 44.17/44.57 , true ) ] )
% 44.17/44.57 , clause( 9500, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, X ), Y ), implies( Z, Y ) ), T ) ), true, 'is_a_theorem'( T )
% 44.17/44.57 , true ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9502, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X ), Y
% 44.17/44.57 ) ), true, 'is_a_theorem'( implies( Z, Y ) ), true ) ) ] )
% 44.17/44.57 , clause( 30, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ), Y ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( Z, Y ) ), true ), true ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9504, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Z,
% 44.17/44.57 implies( Y, implies( X, X ) ) ) ), true ) ) ] )
% 44.17/44.57 , clause( 26, [ =( 'is_a_theorem'( implies( implies( implies( Z, Z ), X ),
% 44.17/44.57 implies( T, X ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9502, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X
% 44.17/44.57 ), Y ) ), true, 'is_a_theorem'( implies( Z, Y ) ), true ) ) ] )
% 44.17/44.57 , 0, 3, substitution( 0, [ :=( X, implies( X, X ) ), :=( Y, T ), :=( Z, X )
% 44.17/44.57 , :=( T, Y )] ), substitution( 1, [ :=( X, implies( X, X ) ), :=( Y,
% 44.17/44.57 implies( Y, implies( X, X ) ) ), :=( Z, Z )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9506, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies( Z
% 44.17/44.57 , Z ) ) ) ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9504, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Z
% 44.17/44.57 , implies( Y, implies( X, X ) ) ) ), true ) ) ] )
% 44.17/44.57 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.57 , implies( Y, implies( Z, Z ) ) ) ) ), :=( Z, true )] ), substitution( 1
% 44.17/44.57 , [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9507, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z, Z )
% 44.17/44.57 ) ) ), true ) ] )
% 44.17/44.57 , clause( 9506, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.57 Z, Z ) ) ) ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 32, [ =( 'is_a_theorem'( implies( Z, implies( Y, implies( X, X ) )
% 44.17/44.57 ) ), true ) ] )
% 44.17/44.57 , clause( 9507, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z, Z
% 44.17/44.57 ) ) ) ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 44.17/44.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9509, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.57 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.57 , true ) ) ] )
% 44.17/44.57 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.57 ), true ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.57 ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9511, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.57 implies( Z, implies( T, T ) ), X ), implies( U, X ) ) ), true ) ) ] )
% 44.17/44.57 , clause( 32, [ =( 'is_a_theorem'( implies( Z, implies( Y, implies( X, X )
% 44.17/44.57 ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9509, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.57 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.57 ) ) ), true ) ) ] )
% 44.17/44.57 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, Z ), :=( Z, implies( X, Y ) )] )
% 44.17/44.57 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( Z, implies(
% 44.17/44.57 T, T ) ) ), :=( T, U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9513, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.57 implies( Y, Y ) ), Z ), implies( T, Z ) ) ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9511, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.57 implies( implies( Z, implies( T, T ) ), X ), implies( U, X ) ) ), true )
% 44.17/44.57 ) ] )
% 44.17/44.57 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.57 implies( implies( X, implies( Y, Y ) ), Z ), implies( T, Z ) ) ) ), :=( Z
% 44.17/44.57 , true )] ), substitution( 1, [ :=( X, Z ), :=( Y, U ), :=( Z, X ), :=( T
% 44.17/44.57 , Y ), :=( U, T )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9514, [ =( 'is_a_theorem'( implies( implies( implies( X, implies( Y
% 44.17/44.57 , Y ) ), Z ), implies( T, Z ) ) ), true ) ] )
% 44.17/44.57 , clause( 9513, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.57 implies( Y, Y ) ), Z ), implies( T, Z ) ) ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.57 ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 34, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies( T,
% 44.17/44.57 T ) ), X ), implies( U, X ) ) ), true ) ] )
% 44.17/44.57 , clause( 9514, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.57 Y, Y ) ), Z ), implies( T, Z ) ) ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, U )] ),
% 44.17/44.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9516, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X ), Y
% 44.17/44.57 ) ), true, 'is_a_theorem'( implies( Z, Y ) ), true ) ) ] )
% 44.17/44.57 , clause( 30, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ), Y ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( Z, Y ) ), true ), true ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9518, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( T,
% 44.17/44.57 implies( Z, implies( X, implies( Y, Y ) ) ) ) ), true ) ) ] )
% 44.17/44.57 , clause( 34, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies( T
% 44.17/44.57 , T ) ), X ), implies( U, X ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9516, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X
% 44.17/44.57 ), Y ) ), true, 'is_a_theorem'( implies( Z, Y ) ), true ) ) ] )
% 44.17/44.57 , 0, 3, substitution( 0, [ :=( X, implies( X, implies( Y, Y ) ) ), :=( Y, U
% 44.17/44.57 ), :=( Z, X ), :=( T, Y ), :=( U, Z )] ), substitution( 1, [ :=( X,
% 44.17/44.57 implies( X, implies( Y, Y ) ) ), :=( Y, implies( Z, implies( X, implies(
% 44.17/44.57 Y, Y ) ) ) ), :=( Z, T )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9520, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies( Z
% 44.17/44.57 , implies( T, T ) ) ) ) ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9518, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( T
% 44.17/44.57 , implies( Z, implies( X, implies( Y, Y ) ) ) ) ), true ) ) ] )
% 44.17/44.57 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.57 , implies( Y, implies( Z, implies( T, T ) ) ) ) ) ), :=( Z, true )] ),
% 44.17/44.57 substitution( 1, [ :=( X, Z ), :=( Y, T ), :=( Z, Y ), :=( T, X )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9521, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z,
% 44.17/44.57 implies( T, T ) ) ) ) ), true ) ] )
% 44.17/44.57 , clause( 9520, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.57 Z, implies( T, T ) ) ) ) ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.57 ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 37, [ =( 'is_a_theorem'( implies( T, implies( Z, implies( X,
% 44.17/44.57 implies( Y, Y ) ) ) ) ), true ) ] )
% 44.17/44.57 , clause( 9521, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z,
% 44.17/44.57 implies( T, T ) ) ) ) ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, T ), :=( Y, Z ), :=( Z, X ), :=( T, Y )] ),
% 44.17/44.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9523, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.57 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.57 , true ) ) ] )
% 44.17/44.57 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.57 ), true ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.57 ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9525, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.57 implies( Z, implies( T, implies( U, U ) ) ), X ), implies( W, X ) ) ),
% 44.17/44.57 true ) ) ] )
% 44.17/44.57 , clause( 37, [ =( 'is_a_theorem'( implies( T, implies( Z, implies( X,
% 44.17/44.57 implies( Y, Y ) ) ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9523, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.57 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.57 ) ) ), true ) ) ] )
% 44.17/44.57 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, U ), :=( Z, Z ), :=( T,
% 44.17/44.57 implies( X, Y ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z,
% 44.17/44.57 implies( Z, implies( T, implies( U, U ) ) ) ), :=( T, W )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9527, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.57 implies( Y, implies( Z, Z ) ) ), T ), implies( U, T ) ) ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9525, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.57 implies( implies( Z, implies( T, implies( U, U ) ) ), X ), implies( W, X
% 44.17/44.57 ) ) ), true ) ) ] )
% 44.17/44.57 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.57 implies( implies( X, implies( Y, implies( Z, Z ) ) ), T ), implies( U, T
% 44.17/44.57 ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, T ), :=( Y, W ),
% 44.17/44.57 :=( Z, X ), :=( T, Y ), :=( U, Z ), :=( W, U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9528, [ =( 'is_a_theorem'( implies( implies( implies( X, implies( Y
% 44.17/44.57 , implies( Z, Z ) ) ), T ), implies( U, T ) ) ), true ) ] )
% 44.17/44.57 , clause( 9527, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.57 implies( Y, implies( Z, Z ) ) ), T ), implies( U, T ) ) ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.57 :=( U, U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 40, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies( T,
% 44.17/44.57 implies( U, U ) ) ), X ), implies( W, X ) ) ), true ) ] )
% 44.17/44.57 , clause( 9528, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.57 Y, implies( Z, Z ) ) ), T ), implies( U, T ) ) ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, U ), :=( T, X ), :=( U
% 44.17/44.57 , W )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9530, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.57 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.57 , true ) ) ] )
% 44.17/44.57 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.57 ), true ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.57 ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9532, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.57 implies( T, implies( Y, Z ) ), implies( X, Y ) ), implies( U, implies( X
% 44.17/44.57 , Y ) ) ) ), true ) ) ] )
% 44.17/44.57 , clause( 27, [ =( 'is_a_theorem'( implies( implies( implies( Z, X ),
% 44.17/44.57 implies( X, Y ) ), implies( T, implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9530, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.57 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.57 ) ) ), true ) ) ] )
% 44.17/44.57 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T )] )
% 44.17/44.57 , substitution( 1, [ :=( X, implies( X, Y ) ), :=( Y, implies( Y, Z ) ),
% 44.17/44.57 :=( Z, implies( T, implies( Y, Z ) ) ), :=( T, U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9534, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.57 implies( Y, Z ) ), implies( T, Y ) ), implies( U, implies( T, Y ) ) ) ) )
% 44.17/44.57 ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9532, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.57 implies( implies( T, implies( Y, Z ) ), implies( X, Y ) ), implies( U,
% 44.17/44.57 implies( X, Y ) ) ) ), true ) ) ] )
% 44.17/44.57 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.57 implies( implies( X, implies( Y, Z ) ), implies( T, Y ) ), implies( U,
% 44.17/44.57 implies( T, Y ) ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, T )
% 44.17/44.57 , :=( Y, Y ), :=( Z, Z ), :=( T, X ), :=( U, U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9535, [ =( 'is_a_theorem'( implies( implies( implies( X, implies( Y
% 44.17/44.57 , Z ) ), implies( T, Y ) ), implies( U, implies( T, Y ) ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , clause( 9534, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.57 implies( Y, Z ) ), implies( T, Y ) ), implies( U, implies( T, Y ) ) ) ) )
% 44.17/44.57 ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.57 :=( U, U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 46, [ =( 'is_a_theorem'( implies( implies( implies( T, implies( Y,
% 44.17/44.57 Z ) ), implies( X, Y ) ), implies( U, implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.57 , clause( 9535, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.57 Y, Z ) ), implies( T, Y ) ), implies( U, implies( T, Y ) ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , substitution( 0, [ :=( X, T ), :=( Y, Y ), :=( Z, Z ), :=( T, X ), :=( U
% 44.17/44.57 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9537, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.57 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.57 )
% 44.17/44.57 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.57 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9540, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), implies( Y, Z ) ), implies( T, implies( Y, Z ) ) ), U )
% 44.17/44.57 ), true, ifeq( true, true, 'is_a_theorem'( U ), true ), true ) ) ] )
% 44.17/44.57 , clause( 27, [ =( 'is_a_theorem'( implies( implies( implies( Z, X ),
% 44.17/44.57 implies( X, Y ) ), implies( T, implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9537, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.57 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.57 ] )
% 44.17/44.57 , 0, 21, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T )] )
% 44.17/44.57 , substitution( 1, [ :=( X, implies( implies( implies( X, Y ), implies( Y
% 44.17/44.57 , Z ) ), implies( T, implies( Y, Z ) ) ) ), :=( Y, U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9542, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), implies( Y, Z ) ), implies( T, implies( Y, Z ) ) ), U )
% 44.17/44.57 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9540, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.57 implies( implies( X, Y ), implies( Y, Z ) ), implies( T, implies( Y, Z )
% 44.17/44.57 ) ), U ) ), true, ifeq( true, true, 'is_a_theorem'( U ), true ), true )
% 44.17/44.57 ) ] )
% 44.17/44.57 , 0, 20, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( U ) ),
% 44.17/44.57 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.57 :=( T, T ), :=( U, U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9543, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, Y ), implies( Y, Z ) ), implies( T, implies( Y, Z ) ) ), U ) ), true,
% 44.17/44.57 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.57 , clause( 9542, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), implies( Y, Z ) ), implies( T, implies( Y, Z ) ) ), U )
% 44.17/44.57 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.57 :=( U, U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 48, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, Y ), implies( Y, Z ) ), implies( T, implies( Y, Z ) ) ), U ) ), true,
% 44.17/44.57 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.57 , clause( 9543, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), implies( Y, Z ) ), implies( T, implies( Y, Z ) ) ), U )
% 44.17/44.57 ), true, 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 44.17/44.57 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9545, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U )
% 44.17/44.57 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.57 , clause( 9, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U ) ), true,
% 44.17/44.57 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.57 :=( U, U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9547, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( W,
% 44.17/44.57 implies( implies( implies( Z, implies( T, T ) ), X ), implies( U, X ) ) )
% 44.17/44.57 ), true ) ) ] )
% 44.17/44.57 , clause( 40, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies( T
% 44.17/44.57 , implies( U, U ) ) ), X ), implies( W, X ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9545, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.57 implies( implies( X, Y ), Z ), implies( implies( Z, X ), implies( T, X )
% 44.17/44.57 ) ), U ) ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.57 , 0, 3, substitution( 0, [ :=( X, implies( implies( implies( Z, implies( T
% 44.17/44.57 , T ) ), X ), implies( U, X ) ) ), :=( Y, V0 ), :=( Z, implies( X, Y ) )
% 44.17/44.57 , :=( T, Z ), :=( U, T ), :=( W, W )] ), substitution( 1, [ :=( X, X ),
% 44.17/44.57 :=( Y, Y ), :=( Z, implies( Z, implies( T, T ) ) ), :=( T, U ), :=( U,
% 44.17/44.57 implies( W, implies( implies( implies( Z, implies( T, T ) ), X ), implies(
% 44.17/44.57 U, X ) ) ) )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9549, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.57 implies( Y, implies( Z, Z ) ), T ), implies( U, T ) ) ) ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9547, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( W
% 44.17/44.57 , implies( implies( implies( Z, implies( T, T ) ), X ), implies( U, X ) )
% 44.17/44.57 ) ), true ) ) ] )
% 44.17/44.57 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.57 , implies( implies( implies( Y, implies( Z, Z ) ), T ), implies( U, T ) )
% 44.17/44.57 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, T ), :=( Y, W ), :=(
% 44.17/44.57 Z, Y ), :=( T, Z ), :=( U, U ), :=( W, X )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9550, [ =( 'is_a_theorem'( implies( X, implies( implies( implies( Y
% 44.17/44.57 , implies( Z, Z ) ), T ), implies( U, T ) ) ) ), true ) ] )
% 44.17/44.57 , clause( 9549, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.57 implies( Y, implies( Z, Z ) ), T ), implies( U, T ) ) ) ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.57 :=( U, U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 49, [ =( 'is_a_theorem'( implies( W, implies( implies( implies( Z,
% 44.17/44.57 implies( T, T ) ), X ), implies( U, X ) ) ) ), true ) ] )
% 44.17/44.57 , clause( 9550, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.57 Y, implies( Z, Z ) ), T ), implies( U, T ) ) ) ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, W ), :=( Y, Z ), :=( Z, T ), :=( T, X ), :=( U
% 44.17/44.57 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9552, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X ), Y
% 44.17/44.57 ) ), true, 'is_a_theorem'( implies( Z, Y ) ), true ) ) ] )
% 44.17/44.57 , clause( 30, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ), Y ) ),
% 44.17/44.57 true, 'is_a_theorem'( implies( Z, Y ) ), true ), true ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9554, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( U,
% 44.17/44.57 implies( T, implies( X, implies( Y, implies( Z, Z ) ) ) ) ) ), true ) ) ]
% 44.17/44.57 )
% 44.17/44.57 , clause( 40, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies( T
% 44.17/44.57 , implies( U, U ) ) ), X ), implies( W, X ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9552, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X
% 44.17/44.57 ), Y ) ), true, 'is_a_theorem'( implies( Z, Y ) ), true ) ) ] )
% 44.17/44.57 , 0, 3, substitution( 0, [ :=( X, implies( X, implies( Y, implies( Z, Z ) )
% 44.17/44.57 ) ), :=( Y, W ), :=( Z, X ), :=( T, Y ), :=( U, Z ), :=( W, T )] ),
% 44.17/44.57 substitution( 1, [ :=( X, implies( X, implies( Y, implies( Z, Z ) ) ) ),
% 44.17/44.57 :=( Y, implies( T, implies( X, implies( Y, implies( Z, Z ) ) ) ) ), :=( Z
% 44.17/44.57 , U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9556, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies( Z
% 44.17/44.57 , implies( T, implies( U, U ) ) ) ) ) ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9554, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( U
% 44.17/44.57 , implies( T, implies( X, implies( Y, implies( Z, Z ) ) ) ) ) ), true ) )
% 44.17/44.57 ] )
% 44.17/44.57 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.57 , implies( Y, implies( Z, implies( T, implies( U, U ) ) ) ) ) ) ), :=( Z
% 44.17/44.57 , true )] ), substitution( 1, [ :=( X, Z ), :=( Y, T ), :=( Z, U ), :=( T
% 44.17/44.57 , Y ), :=( U, X )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9557, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z,
% 44.17/44.57 implies( T, implies( U, U ) ) ) ) ) ), true ) ] )
% 44.17/44.57 , clause( 9556, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.57 Z, implies( T, implies( U, U ) ) ) ) ) ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.57 :=( U, U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 50, [ =( 'is_a_theorem'( implies( U, implies( T, implies( X,
% 44.17/44.57 implies( Y, implies( Z, Z ) ) ) ) ) ), true ) ] )
% 44.17/44.57 , clause( 9557, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z,
% 44.17/44.57 implies( T, implies( U, U ) ) ) ) ) ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, U ), :=( Y, T ), :=( Z, X ), :=( T, Y ), :=( U
% 44.17/44.57 , Z )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9559, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.57 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.57 )
% 44.17/44.57 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.57 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9562, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, implies( Y, implies( Z, Z ) ) ), T ), implies( U, T ) ), W )
% 44.17/44.57 ), true, ifeq( true, true, 'is_a_theorem'( W ), true ), true ) ) ] )
% 44.17/44.57 , clause( 40, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies( T
% 44.17/44.57 , implies( U, U ) ) ), X ), implies( W, X ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9559, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.57 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.57 ] )
% 44.17/44.57 , 0, 21, substitution( 0, [ :=( X, T ), :=( Y, V0 ), :=( Z, X ), :=( T, Y )
% 44.17/44.57 , :=( U, Z ), :=( W, U )] ), substitution( 1, [ :=( X, implies( implies(
% 44.17/44.57 implies( X, implies( Y, implies( Z, Z ) ) ), T ), implies( U, T ) ) ),
% 44.17/44.57 :=( Y, W )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9564, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, implies( Y, implies( Z, Z ) ) ), T ), implies( U, T ) ), W )
% 44.17/44.57 ), true, 'is_a_theorem'( W ), true ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9562, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.57 implies( implies( X, implies( Y, implies( Z, Z ) ) ), T ), implies( U, T
% 44.17/44.57 ) ), W ) ), true, ifeq( true, true, 'is_a_theorem'( W ), true ), true )
% 44.17/44.57 ) ] )
% 44.17/44.57 , 0, 20, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( W ) ),
% 44.17/44.57 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.57 :=( T, T ), :=( U, U ), :=( W, W )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9565, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, implies( Y, implies( Z, Z ) ) ), T ), implies( U, T ) ), W ) ), true,
% 44.17/44.57 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.57 , clause( 9564, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, implies( Y, implies( Z, Z ) ) ), T ), implies( U, T ) ), W )
% 44.17/44.57 ), true, 'is_a_theorem'( W ), true ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.57 :=( U, U ), :=( W, W )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 52, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, implies( Y, implies( Z, Z ) ) ), T ), implies( U, T ) ), W ) ), true,
% 44.17/44.57 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.57 , clause( 9565, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, implies( Y, implies( Z, Z ) ) ), T ), implies( U, T ) ), W )
% 44.17/44.57 ), true, 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 44.17/44.57 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9567, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.57 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.57 )
% 44.17/44.57 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.57 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9570, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.57 Y, implies( Z, implies( T, implies( U, U ) ) ) ) ), W ) ), true, ifeq(
% 44.17/44.57 true, true, 'is_a_theorem'( W ), true ), true ) ) ] )
% 44.17/44.57 , clause( 50, [ =( 'is_a_theorem'( implies( U, implies( T, implies( X,
% 44.17/44.57 implies( Y, implies( Z, Z ) ) ) ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9567, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.57 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.57 ] )
% 44.17/44.57 , 0, 19, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, U ), :=( T, Y )
% 44.17/44.57 , :=( U, X )] ), substitution( 1, [ :=( X, implies( X, implies( Y,
% 44.17/44.57 implies( Z, implies( T, implies( U, U ) ) ) ) ) ), :=( Y, W )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9572, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.57 Y, implies( Z, implies( T, implies( U, U ) ) ) ) ), W ) ), true,
% 44.17/44.57 'is_a_theorem'( W ), true ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9570, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.57 implies( Y, implies( Z, implies( T, implies( U, U ) ) ) ) ), W ) ), true
% 44.17/44.57 , ifeq( true, true, 'is_a_theorem'( W ), true ), true ) ) ] )
% 44.17/44.57 , 0, 18, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( W ) ),
% 44.17/44.57 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.57 :=( T, T ), :=( U, U ), :=( W, W )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9573, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.57 implies( Z, implies( T, implies( U, U ) ) ) ) ), W ) ), true,
% 44.17/44.57 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.57 , clause( 9572, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.57 implies( Y, implies( Z, implies( T, implies( U, U ) ) ) ) ), W ) ), true
% 44.17/44.57 , 'is_a_theorem'( W ), true ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.57 :=( U, U ), :=( W, W )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 54, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.57 implies( Z, implies( T, implies( U, U ) ) ) ) ), W ) ), true,
% 44.17/44.57 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.57 , clause( 9573, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y
% 44.17/44.57 , implies( Z, implies( T, implies( U, U ) ) ) ) ), W ) ), true,
% 44.17/44.57 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 44.17/44.57 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9575, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.57 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.57 )
% 44.17/44.57 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.57 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9578, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.57 implies( implies( Y, implies( Z, Z ) ), T ), implies( U, T ) ) ), W ) ),
% 44.17/44.57 true, ifeq( true, true, 'is_a_theorem'( W ), true ), true ) ) ] )
% 44.17/44.57 , clause( 49, [ =( 'is_a_theorem'( implies( W, implies( implies( implies( Z
% 44.17/44.57 , implies( T, T ) ), X ), implies( U, X ) ) ) ), true ) ] )
% 44.17/44.57 , 0, clause( 9575, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.57 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.57 ] )
% 44.17/44.57 , 0, 21, substitution( 0, [ :=( X, T ), :=( Y, V0 ), :=( Z, Y ), :=( T, Z )
% 44.17/44.57 , :=( U, U ), :=( W, X )] ), substitution( 1, [ :=( X, implies( X,
% 44.17/44.57 implies( implies( implies( Y, implies( Z, Z ) ), T ), implies( U, T ) ) )
% 44.17/44.57 ), :=( Y, W )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9580, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.57 implies( implies( Y, implies( Z, Z ) ), T ), implies( U, T ) ) ), W ) ),
% 44.17/44.57 true, 'is_a_theorem'( W ), true ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9578, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.57 implies( implies( implies( Y, implies( Z, Z ) ), T ), implies( U, T ) ) )
% 44.17/44.57 , W ) ), true, ifeq( true, true, 'is_a_theorem'( W ), true ), true ) ) ]
% 44.17/44.57 )
% 44.17/44.57 , 0, 20, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( W ) ),
% 44.17/44.57 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.57 :=( T, T ), :=( U, U ), :=( W, W )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9581, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.57 implies( implies( Y, implies( Z, Z ) ), T ), implies( U, T ) ) ), W ) ),
% 44.17/44.57 true, 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.57 , clause( 9580, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.57 implies( implies( implies( Y, implies( Z, Z ) ), T ), implies( U, T ) ) )
% 44.17/44.57 , W ) ), true, 'is_a_theorem'( W ), true ) ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.57 :=( U, U ), :=( W, W )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 subsumption(
% 44.17/44.57 clause( 56, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.57 implies( implies( Y, implies( Z, Z ) ), T ), implies( U, T ) ) ), W ) ),
% 44.17/44.57 true, 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.57 , clause( 9581, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.57 implies( implies( Y, implies( Z, Z ) ), T ), implies( U, T ) ) ), W ) ),
% 44.17/44.57 true, 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 44.17/44.57 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9583, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.57 implies( X, Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U )
% 44.17/44.57 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.57 , clause( 9, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.57 X, Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U ) ), true,
% 44.17/44.57 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.57 :=( U, U )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9585, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( U,
% 44.17/44.57 implies( implies( implies( implies( Z, X ), T ), X ), implies( Z, X ) ) )
% 44.17/44.57 ), true ) ) ] )
% 44.17/44.57 , clause( 46, [ =( 'is_a_theorem'( implies( implies( implies( T, implies( Y
% 44.17/44.57 , Z ) ), implies( X, Y ) ), implies( U, implies( X, Y ) ) ) ), true ) ]
% 44.17/44.57 )
% 44.17/44.57 , 0, clause( 9583, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.57 implies( implies( X, Y ), Z ), implies( implies( Z, X ), implies( T, X )
% 44.17/44.57 ) ), U ) ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.57 , 0, 3, substitution( 0, [ :=( X, implies( implies( implies( Z, X ), T ), X
% 44.17/44.57 ) ), :=( Y, implies( Z, X ) ), :=( Z, T ), :=( T, implies( X, Y ) ),
% 44.17/44.57 :=( U, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, implies(
% 44.17/44.57 implies( Z, X ), T ) ), :=( T, Z ), :=( U, implies( U, implies( implies(
% 44.17/44.57 implies( implies( Z, X ), T ), X ), implies( Z, X ) ) ) )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 paramod(
% 44.17/44.57 clause( 9587, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.57 implies( implies( Y, Z ), T ), Z ), implies( Y, Z ) ) ) ) ) ] )
% 44.17/44.57 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.57 , 0, clause( 9585, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( U
% 44.17/44.57 , implies( implies( implies( implies( Z, X ), T ), X ), implies( Z, X ) )
% 44.17/44.57 ) ), true ) ) ] )
% 44.17/44.57 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.57 , implies( implies( implies( implies( Y, Z ), T ), Z ), implies( Y, Z ) )
% 44.17/44.57 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, U ), :=(
% 44.17/44.57 Z, Y ), :=( T, T ), :=( U, X )] )).
% 44.17/44.57
% 44.17/44.57
% 44.17/44.57 eqswap(
% 44.17/44.57 clause( 9588, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.58 implies( Y, Z ), T ), Z ), implies( Y, Z ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9587, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.58 implies( implies( Y, Z ), T ), Z ), implies( Y, Z ) ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 57, [ =( 'is_a_theorem'( implies( U, implies( implies( implies(
% 44.17/44.58 implies( Z, X ), T ), X ), implies( Z, X ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9588, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.58 implies( Y, Z ), T ), Z ), implies( Y, Z ) ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, U ), :=( Y, Z ), :=( Z, X ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9590, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.58 ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9592, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( U, implies( T, Y ) ), implies( X, implies( Y, Z ) ) ), implies(
% 44.17/44.58 W, implies( X, implies( Y, Z ) ) ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 46, [ =( 'is_a_theorem'( implies( implies( implies( T, implies( Y
% 44.17/44.58 , Z ) ), implies( X, Y ) ), implies( U, implies( X, Y ) ) ) ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, clause( 9590, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.58 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.58 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, Y ), :=( Z, Z ), :=( T, X ),
% 44.17/44.58 :=( U, U )] ), substitution( 1, [ :=( X, implies( X, implies( Y, Z ) ) )
% 44.17/44.58 , :=( Y, implies( T, Y ) ), :=( Z, implies( U, implies( T, Y ) ) ), :=( T
% 44.17/44.58 , W )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9594, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( Y, Z ) ), implies( T, implies( Z, U ) ) ), implies( W, implies(
% 44.17/44.58 T, implies( Z, U ) ) ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9592, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( U, implies( T, Y ) ), implies( X, implies( Y, Z ) ) ),
% 44.17/44.58 implies( W, implies( X, implies( Y, Z ) ) ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, implies( Y, Z ) ), implies( T, implies( Z, U ) ) ),
% 44.17/44.58 implies( W, implies( T, implies( Z, U ) ) ) ) ) ), :=( Z, true )] ),
% 44.17/44.58 substitution( 1, [ :=( X, T ), :=( Y, Z ), :=( Z, U ), :=( T, Y ), :=( U
% 44.17/44.58 , X ), :=( W, W )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9595, [ =( 'is_a_theorem'( implies( implies( implies( X, implies( Y
% 44.17/44.58 , Z ) ), implies( T, implies( Z, U ) ) ), implies( W, implies( T, implies(
% 44.17/44.58 Z, U ) ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9594, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( Y, Z ) ), implies( T, implies( Z, U ) ) ), implies( W, implies(
% 44.17/44.58 T, implies( Z, U ) ) ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.58 :=( U, U ), :=( W, W )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 58, [ =( 'is_a_theorem'( implies( implies( implies( U, implies( T,
% 44.17/44.58 Y ) ), implies( X, implies( Y, Z ) ) ), implies( W, implies( X, implies(
% 44.17/44.58 Y, Z ) ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9595, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.58 Y, Z ) ), implies( T, implies( Z, U ) ) ), implies( W, implies( T,
% 44.17/44.58 implies( Z, U ) ) ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, U ), :=( Y, T ), :=( Z, Y ), :=( T, X ), :=( U
% 44.17/44.58 , Z ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9597, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), X ), implies( Z, X ) ), T ) ), true, 'is_a_theorem'( T )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 16, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, Y ), X ), implies( Z, X ) ), T ) ), true, 'is_a_theorem'( T ), true )
% 44.17/44.58 , true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9599, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( T, U ), W ), U ), implies( T, U ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 57, [ =( 'is_a_theorem'( implies( U, implies( implies( implies(
% 44.17/44.58 implies( Z, X ), T ), X ), implies( Z, X ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9597, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), X ), implies( Z, X ) ), T ) ), true,
% 44.17/44.58 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, U ), :=( Y, V0 ), :=( Z, T ), :=( T, W )
% 44.17/44.58 , :=( U, implies( implies( implies( X, Y ), X ), implies( Z, X ) ) )] ),
% 44.17/44.58 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, implies(
% 44.17/44.58 implies( implies( implies( T, U ), W ), U ), implies( T, U ) ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9601, [ =( true, 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, Y ), Z ), Y ), implies( X, Y ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9599, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( T, U ), W ), U ), implies( T, U ) ) ), true )
% 44.17/44.58 ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( X, Y ), Z ), Y ), implies( X, Y ) ) ) ), :=( Z
% 44.17/44.58 , true )] ), substitution( 1, [ :=( X, T ), :=( Y, U ), :=( Z, W ), :=( T
% 44.17/44.58 , X ), :=( U, Y ), :=( W, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9602, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.58 ), Z ), Y ), implies( X, Y ) ) ), true ) ] )
% 44.17/44.58 , clause( 9601, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), Y ), implies( X, Y ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 60, [ =( 'is_a_theorem'( implies( implies( implies( implies( T, U )
% 44.17/44.58 , W ), U ), implies( T, U ) ) ), true ) ] )
% 44.17/44.58 , clause( 9602, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.58 , Y ), Z ), Y ), implies( X, Y ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, T ), :=( Y, U ), :=( Z, W )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9604, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), X ), implies( Z, X ) ), T ) ), true, 'is_a_theorem'( T )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 16, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, Y ), X ), implies( Z, X ) ), T ) ), true, 'is_a_theorem'( T ), true )
% 44.17/44.58 , true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9606, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X,
% 44.17/44.58 implies( Y, X ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 60, [ =( 'is_a_theorem'( implies( implies( implies( implies( T, U
% 44.17/44.58 ), W ), U ), implies( T, U ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9604, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), X ), implies( Z, X ) ), T ) ), true,
% 44.17/44.58 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, U ), :=( T, X ),
% 44.17/44.58 :=( U, implies( Y, X ) ), :=( W, X )] ), substitution( 1, [ :=( X, X ),
% 44.17/44.58 :=( Y, implies( Y, X ) ), :=( Z, Y ), :=( T, implies( X, implies( Y, X )
% 44.17/44.58 ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9608, [ =( true, 'is_a_theorem'( implies( X, implies( Y, X ) ) ) )
% 44.17/44.58 ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9606, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X
% 44.17/44.58 , implies( Y, X ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.58 , implies( Y, X ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X )
% 44.17/44.58 , :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9609, [ =( 'is_a_theorem'( implies( X, implies( Y, X ) ) ), true )
% 44.17/44.58 ] )
% 44.17/44.58 , clause( 9608, [ =( true, 'is_a_theorem'( implies( X, implies( Y, X ) ) )
% 44.17/44.58 ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 63, [ =( 'is_a_theorem'( implies( X, implies( Y, X ) ) ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 9609, [ =( 'is_a_theorem'( implies( X, implies( Y, X ) ) ), true
% 44.17/44.58 ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 44.17/44.58 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9611, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.58 ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9613, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( X, Y ), implies( implies( X, Y ), Z ) ), implies( T, implies(
% 44.17/44.58 implies( X, Y ), Z ) ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 60, [ =( 'is_a_theorem'( implies( implies( implies( implies( T, U
% 44.17/44.58 ), W ), U ), implies( T, U ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9611, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.58 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.58 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, U ), :=( Y, W ), :=( Z, V0 ), :=( T, X )
% 44.17/44.58 , :=( U, Y ), :=( W, Z )] ), substitution( 1, [ :=( X, implies( implies(
% 44.17/44.58 X, Y ), Z ) ), :=( Y, Y ), :=( Z, implies( X, Y ) ), :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9615, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.58 , implies( implies( X, Y ), Z ) ), implies( T, implies( implies( X, Y ),
% 44.17/44.58 Z ) ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9613, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, Y ), implies( implies( X, Y ), Z ) ), implies( T,
% 44.17/44.58 implies( implies( X, Y ), Z ) ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, Y ), implies( implies( X, Y ), Z ) ), implies( T,
% 44.17/44.58 implies( implies( X, Y ), Z ) ) ) ) ), :=( Z, true )] ), substitution( 1
% 44.17/44.58 , [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9616, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.58 implies( implies( X, Y ), Z ) ), implies( T, implies( implies( X, Y ), Z
% 44.17/44.58 ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9615, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.58 ), implies( implies( X, Y ), Z ) ), implies( T, implies( implies( X, Y )
% 44.17/44.58 , Z ) ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 65, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), implies(
% 44.17/44.58 implies( X, Y ), Z ) ), implies( T, implies( implies( X, Y ), Z ) ) ) ),
% 44.17/44.58 true ) ] )
% 44.17/44.58 , clause( 9616, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.58 implies( implies( X, Y ), Z ) ), implies( T, implies( implies( X, Y ), Z
% 44.17/44.58 ) ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9618, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9620, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), Y ) ), true, 'is_a_theorem'( implies( X, Y
% 44.17/44.58 ) ), true ), true ) ) ] )
% 44.17/44.58 , clause( 60, [ =( 'is_a_theorem'( implies( implies( implies( implies( T, U
% 44.17/44.58 ), W ), U ), implies( T, U ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9618, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, U ), :=( Z, W ), :=( T, X ),
% 44.17/44.58 :=( U, Y ), :=( W, Z )] ), substitution( 1, [ :=( X, implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), Y ) ), :=( Y, implies( X, Y ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9625, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies( X
% 44.17/44.58 , Y ), Z ), Y ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9620, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( implies( implies( X, Y ), Z ), Y ) ), true, 'is_a_theorem'(
% 44.17/44.58 implies( X, Y ) ), true ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( implies( implies( X, Y ), Z ), Y ) ), true, 'is_a_theorem'(
% 44.17/44.58 implies( X, Y ) ), true ) ), :=( Z, true )] ), substitution( 1, [ :=( X,
% 44.17/44.58 X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9626, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.58 , Z ), Y ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 9625, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 X, Y ), Z ), Y ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 66, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y ), Z
% 44.17/44.58 ), Y ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9626, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.58 ), Z ), Y ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9628, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.58 ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9630, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( Z, implies( X, Y ) ), X ), implies( T, X ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 63, [ =( 'is_a_theorem'( implies( X, implies( Y, X ) ) ), true )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, clause( 9628, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.58 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.58 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, implies( X, Y ) ), :=( Y, Z )] ),
% 44.17/44.58 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( Z, implies( X
% 44.17/44.58 , Y ) ) ), :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9631, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( Y, Z ) ), Y ), implies( T, Y ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9630, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( Z, implies( X, Y ) ), X ), implies( T, X ) ) ), true )
% 44.17/44.58 ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, implies( Y, Z ) ), Y ), implies( T, Y ) ) ) ), :=( Z
% 44.17/44.58 , true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T
% 44.17/44.58 , T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9632, [ =( 'is_a_theorem'( implies( implies( implies( X, implies( Y
% 44.17/44.58 , Z ) ), Y ), implies( T, Y ) ) ), true ) ] )
% 44.17/44.58 , clause( 9631, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( Y, Z ) ), Y ), implies( T, Y ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 69, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies( X,
% 44.17/44.58 Y ) ), X ), implies( T, X ) ) ), true ) ] )
% 44.17/44.58 , clause( 9632, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.58 Y, Z ) ), Y ), implies( T, Y ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9634, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9636, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( X ), true
% 44.17/44.58 , 'is_a_theorem'( implies( Y, X ) ), true ), true ) ) ] )
% 44.17/44.58 , clause( 63, [ =( 'is_a_theorem'( implies( X, implies( Y, X ) ) ), true )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, clause( 9634, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 44.17/44.58 :=( X, X ), :=( Y, implies( Y, X ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9641, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 44.17/44.58 implies( Y, X ) ), true ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9636, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( X ),
% 44.17/44.58 true, 'is_a_theorem'( implies( Y, X ) ), true ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'( X )
% 44.17/44.58 , true, 'is_a_theorem'( implies( Y, X ) ), true ) ), :=( Z, true )] ),
% 44.17/44.58 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9642, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( implies(
% 44.17/44.58 Y, X ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9641, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 44.17/44.58 implies( Y, X ) ), true ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 70, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( implies(
% 44.17/44.58 Y, X ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9642, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 44.17/44.58 implies( Y, X ) ), true ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 44.17/44.58 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9644, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 44.17/44.58 implies( Y, X ) ), true ) ) ] )
% 44.17/44.58 , clause( 70, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( implies(
% 44.17/44.58 Y, X ) ), true ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9646, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Z,
% 44.17/44.58 implies( X, implies( Y, X ) ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 63, [ =( 'is_a_theorem'( implies( X, implies( Y, X ) ) ), true )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, clause( 9644, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 44.17/44.58 'is_a_theorem'( implies( Y, X ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 44.17/44.58 :=( X, implies( X, implies( Y, X ) ) ), :=( Y, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9648, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies( Z
% 44.17/44.58 , Y ) ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9646, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Z
% 44.17/44.58 , implies( X, implies( Y, X ) ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.58 , implies( Y, implies( Z, Y ) ) ) ) ), :=( Z, true )] ), substitution( 1
% 44.17/44.58 , [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9649, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z, Y )
% 44.17/44.58 ) ) ), true ) ] )
% 44.17/44.58 , clause( 9648, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.58 Z, Y ) ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 72, [ =( 'is_a_theorem'( implies( Z, implies( X, implies( Y, X ) )
% 44.17/44.58 ) ), true ) ] )
% 44.17/44.58 , clause( 9649, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z, Y
% 44.17/44.58 ) ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9651, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.58 ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9653, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( Z, implies( T, Z ) ), X ), implies( U, X ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 72, [ =( 'is_a_theorem'( implies( Z, implies( X, implies( Y, X )
% 44.17/44.58 ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9651, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.58 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.58 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, implies( X, Y ) )] )
% 44.17/44.58 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( Z, implies(
% 44.17/44.58 T, Z ) ) ), :=( T, U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9655, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( Y, X ) ), Z ), implies( T, Z ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9653, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( Z, implies( T, Z ) ), X ), implies( U, X ) ) ), true )
% 44.17/44.58 ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, implies( Y, X ) ), Z ), implies( T, Z ) ) ) ), :=( Z
% 44.17/44.58 , true )] ), substitution( 1, [ :=( X, Z ), :=( Y, U ), :=( Z, X ), :=( T
% 44.17/44.58 , Y ), :=( U, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9656, [ =( 'is_a_theorem'( implies( implies( implies( X, implies( Y
% 44.17/44.58 , X ) ), Z ), implies( T, Z ) ) ), true ) ] )
% 44.17/44.58 , clause( 9655, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( Y, X ) ), Z ), implies( T, Z ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 82, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies( T,
% 44.17/44.58 Z ) ), X ), implies( U, X ) ) ), true ) ] )
% 44.17/44.58 , clause( 9656, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.58 Y, X ) ), Z ), implies( T, Z ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, U )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9658, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9661, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, implies( Y, X ) ), Z ), implies( T, Z ) ), U ) ), true, ifeq(
% 44.17/44.58 true, true, 'is_a_theorem'( U ), true ), true ) ) ] )
% 44.17/44.58 , clause( 82, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies( T
% 44.17/44.58 , Z ) ), X ), implies( U, X ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9658, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 19, substitution( 0, [ :=( X, Z ), :=( Y, W ), :=( Z, X ), :=( T, Y )
% 44.17/44.58 , :=( U, T )] ), substitution( 1, [ :=( X, implies( implies( implies( X,
% 44.17/44.58 implies( Y, X ) ), Z ), implies( T, Z ) ) ), :=( Y, U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9663, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, implies( Y, X ) ), Z ), implies( T, Z ) ), U ) ), true,
% 44.17/44.58 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9661, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( X, implies( Y, X ) ), Z ), implies( T, Z ) ), U ) ),
% 44.17/44.58 true, ifeq( true, true, 'is_a_theorem'( U ), true ), true ) ) ] )
% 44.17/44.58 , 0, 18, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( U ) ),
% 44.17/44.58 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.58 :=( T, T ), :=( U, U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9664, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, implies( Y, X ) ), Z ), implies( T, Z ) ), U ) ), true, 'is_a_theorem'(
% 44.17/44.58 U ), true ), true ) ] )
% 44.17/44.58 , clause( 9663, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, implies( Y, X ) ), Z ), implies( T, Z ) ), U ) ), true,
% 44.17/44.58 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.58 :=( U, U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 97, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, implies( Y, X ) ), Z ), implies( T, Z ) ), U ) ), true, 'is_a_theorem'(
% 44.17/44.58 U ), true ), true ) ] )
% 44.17/44.58 , clause( 9664, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, implies( Y, X ) ), Z ), implies( T, Z ) ), U ) ), true,
% 44.17/44.58 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 44.17/44.58 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9666, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), implies( Y, Z ) ), implies( T, implies( Y, Z ) ) ), U )
% 44.17/44.58 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.58 , clause( 48, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, Y ), implies( Y, Z ) ), implies( T, implies( Y, Z ) ) ), U ) ), true,
% 44.17/44.58 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.58 :=( U, U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9668, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( T,
% 44.17/44.58 implies( implies( implies( X, Y ), implies( Y, Z ) ), implies( Y, Z ) ) )
% 44.17/44.58 ), true ) ) ] )
% 44.17/44.58 , clause( 65, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.58 implies( implies( X, Y ), Z ) ), implies( T, implies( implies( X, Y ), Z
% 44.17/44.58 ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9666, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), implies( Y, Z ) ), implies( T, implies( Y, Z )
% 44.17/44.58 ) ), U ) ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, implies( X, Y ) ), :=( Y, implies( Y, Z )
% 44.17/44.58 ), :=( Z, implies( Y, Z ) ), :=( T, T )] ), substitution( 1, [ :=( X, X
% 44.17/44.58 ), :=( Y, Y ), :=( Z, Z ), :=( T, implies( implies( X, Y ), implies( Y,
% 44.17/44.58 Z ) ) ), :=( U, implies( T, implies( implies( implies( X, Y ), implies( Y
% 44.17/44.58 , Z ) ), implies( Y, Z ) ) ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9670, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.58 implies( Y, Z ), implies( Z, T ) ), implies( Z, T ) ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9668, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( T
% 44.17/44.58 , implies( implies( implies( X, Y ), implies( Y, Z ) ), implies( Y, Z ) )
% 44.17/44.58 ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.58 , implies( implies( implies( Y, Z ), implies( Z, T ) ), implies( Z, T ) )
% 44.17/44.58 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=(
% 44.17/44.58 Z, T ), :=( T, X )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9671, [ =( 'is_a_theorem'( implies( X, implies( implies( implies( Y
% 44.17/44.58 , Z ), implies( Z, T ) ), implies( Z, T ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9670, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.58 implies( Y, Z ), implies( Z, T ) ), implies( Z, T ) ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 170, [ =( 'is_a_theorem'( implies( T, implies( implies( implies( X
% 44.17/44.58 , Y ), implies( Y, Z ) ), implies( Y, Z ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9671, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.58 Y, Z ), implies( Z, T ) ), implies( Z, T ) ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9673, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), X ), implies( Z, X ) ), T ) ), true, 'is_a_theorem'( T )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 16, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, Y ), X ), implies( Z, X ) ), T ) ), true, 'is_a_theorem'( T ), true )
% 44.17/44.58 , true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9675, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Z,
% 44.17/44.58 implies( implies( implies( X, Y ), X ), X ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 65, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.58 implies( implies( X, Y ), Z ) ), implies( T, implies( implies( X, Y ), Z
% 44.17/44.58 ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9673, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), X ), implies( Z, X ) ), T ) ), true,
% 44.17/44.58 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, implies( X, Y ) ), :=( Y, X ), :=( Z, X )
% 44.17/44.58 , :=( T, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z,
% 44.17/44.58 implies( implies( X, Y ), X ) ), :=( T, implies( Z, implies( implies(
% 44.17/44.58 implies( X, Y ), X ), X ) ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9677, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.58 implies( Y, Z ), Y ), Y ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9675, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Z
% 44.17/44.58 , implies( implies( implies( X, Y ), X ), X ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.58 , implies( implies( implies( Y, Z ), Y ), Y ) ) ) ), :=( Z, true )] ),
% 44.17/44.58 substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9678, [ =( 'is_a_theorem'( implies( X, implies( implies( implies( Y
% 44.17/44.58 , Z ), Y ), Y ) ) ), true ) ] )
% 44.17/44.58 , clause( 9677, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.58 implies( Y, Z ), Y ), Y ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 174, [ =( 'is_a_theorem'( implies( Z, implies( implies( implies( X
% 44.17/44.58 , Y ), X ), X ) ) ), true ) ] )
% 44.17/44.58 , clause( 9678, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.58 Y, Z ), Y ), Y ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9680, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, implies( Y, implies( Z, Z ) ) ), T ), implies( U, T ) ), W )
% 44.17/44.58 ), true, 'is_a_theorem'( W ), true ) ) ] )
% 44.17/44.58 , clause( 52, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, implies( Y, implies( Z, Z ) ) ), T ), implies( U, T ) ), W ) ), true,
% 44.17/44.58 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.58 :=( U, U ), :=( W, W )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9682, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( W, V0 ), W ), W ) ), true ) ) ] )
% 44.17/44.58 , clause( 174, [ =( 'is_a_theorem'( implies( Z, implies( implies( implies(
% 44.17/44.58 X, Y ), X ), X ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9680, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( X, implies( Y, implies( Z, Z ) ) ), T ), implies( U, T
% 44.17/44.58 ) ), W ) ), true, 'is_a_theorem'( W ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, W ), :=( Y, V0 ), :=( Z, implies( implies(
% 44.17/44.58 implies( X, implies( Y, implies( Z, Z ) ) ), T ), implies( U, T ) ) )] )
% 44.17/44.58 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=(
% 44.17/44.58 U, U ), :=( W, implies( implies( implies( W, V0 ), W ), W ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9684, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.58 , X ), X ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9682, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( W, V0 ), W ), W ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, Y ), X ), X ) ) ), :=( Z, true )] ), substitution( 1
% 44.17/44.58 , [ :=( X, Z ), :=( Y, T ), :=( Z, U ), :=( T, W ), :=( U, V0 ), :=( W, X
% 44.17/44.58 ), :=( V0, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9685, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X ),
% 44.17/44.58 X ) ), true ) ] )
% 44.17/44.58 , clause( 9684, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.58 ), X ), X ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 182, [ =( 'is_a_theorem'( implies( implies( implies( W, V0 ), W ),
% 44.17/44.58 W ) ), true ) ] )
% 44.17/44.58 , clause( 9685, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X )
% 44.17/44.58 , X ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, W ), :=( Y, V0 )] ), permutation( 0, [ ==>( 0,
% 44.17/44.58 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9687, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.58 ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9689, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 X, implies( X, Y ) ), implies( Z, implies( X, Y ) ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 182, [ =( 'is_a_theorem'( implies( implies( implies( W, V0 ), W )
% 44.17/44.58 , W ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9687, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.58 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.58 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, U ), :=( Z, W ), :=( T, V0 )
% 44.17/44.58 , :=( U, V1 ), :=( W, X ), :=( V0, Y )] ), substitution( 1, [ :=( X,
% 44.17/44.58 implies( X, Y ) ), :=( Y, X ), :=( Z, X ), :=( T, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9690, [ =( true, 'is_a_theorem'( implies( implies( X, implies( X, Y
% 44.17/44.58 ) ), implies( Z, implies( X, Y ) ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9689, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( X, implies( X, Y ) ), implies( Z, implies( X, Y ) ) ) ), true )
% 44.17/44.58 ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( X, implies( X, Y ) ), implies( Z, implies( X, Y ) ) ) ) ), :=( Z
% 44.17/44.58 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9691, [ =( 'is_a_theorem'( implies( implies( X, implies( X, Y ) ),
% 44.17/44.58 implies( Z, implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9690, [ =( true, 'is_a_theorem'( implies( implies( X, implies( X
% 44.17/44.58 , Y ) ), implies( Z, implies( X, Y ) ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 186, [ =( 'is_a_theorem'( implies( implies( X, implies( X, Y ) ),
% 44.17/44.58 implies( Z, implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9691, [ =( 'is_a_theorem'( implies( implies( X, implies( X, Y ) )
% 44.17/44.58 , implies( Z, implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9693, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9695, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies( X
% 44.17/44.58 , implies( X, Y ) ) ), true, 'is_a_theorem'( implies( Z, implies( X, Y )
% 44.17/44.58 ) ), true ), true ) ) ] )
% 44.17/44.58 , clause( 186, [ =( 'is_a_theorem'( implies( implies( X, implies( X, Y ) )
% 44.17/44.58 , implies( Z, implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9693, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.58 substitution( 1, [ :=( X, implies( X, implies( X, Y ) ) ), :=( Y, implies(
% 44.17/44.58 Z, implies( X, Y ) ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9700, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y )
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( Z, implies( X, Y ) ) ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9695, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( X, implies( X, Y ) ) ), true, 'is_a_theorem'( implies( Z,
% 44.17/44.58 implies( X, Y ) ) ), true ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( X, implies( X, Y ) ) ), true, 'is_a_theorem'( implies( Z,
% 44.17/44.58 implies( X, Y ) ) ), true ) ), :=( Z, true )] ), substitution( 1, [ :=( X
% 44.17/44.58 , X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9701, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( Z, implies( X, Y ) ) ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 9700, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y
% 44.17/44.58 ) ) ), true, 'is_a_theorem'( implies( Z, implies( X, Y ) ) ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 190, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( Z, implies( X, Y ) ) ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 9701, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) )
% 44.17/44.58 , true, 'is_a_theorem'( implies( Z, implies( X, Y ) ) ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9703, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9706, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies( X
% 44.17/44.58 , implies( X, Y ) ), implies( Z, implies( X, Y ) ) ), T ) ), true, ifeq(
% 44.17/44.58 true, true, 'is_a_theorem'( T ), true ), true ) ) ] )
% 44.17/44.58 , clause( 186, [ =( 'is_a_theorem'( implies( implies( X, implies( X, Y ) )
% 44.17/44.58 , implies( Z, implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9703, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 19, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.58 substitution( 1, [ :=( X, implies( implies( X, implies( X, Y ) ), implies(
% 44.17/44.58 Z, implies( X, Y ) ) ) ), :=( Y, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9708, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies( X
% 44.17/44.58 , implies( X, Y ) ), implies( Z, implies( X, Y ) ) ), T ) ), true,
% 44.17/44.58 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9706, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( X, implies( X, Y ) ), implies( Z, implies( X, Y ) ) ), T ) ),
% 44.17/44.58 true, ifeq( true, true, 'is_a_theorem'( T ), true ), true ) ) ] )
% 44.17/44.58 , 0, 18, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( T ) ),
% 44.17/44.58 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.58 :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9709, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( X, Y ) ), implies( Z, implies( X, Y ) ) ), T ) ), true,
% 44.17/44.58 'is_a_theorem'( T ), true ), true ) ] )
% 44.17/44.58 , clause( 9708, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 X, implies( X, Y ) ), implies( Z, implies( X, Y ) ) ), T ) ), true,
% 44.17/44.58 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 191, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( X, Y ) ), implies( Z, implies( X, Y ) ) ), T ) ), true,
% 44.17/44.58 'is_a_theorem'( T ), true ), true ) ] )
% 44.17/44.58 , clause( 9709, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( X, Y ) ), implies( Z, implies( X, Y ) ) ), T ) ), true,
% 44.17/44.58 'is_a_theorem'( T ), true ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9711, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.58 Y, implies( Z, implies( T, implies( U, U ) ) ) ) ), W ) ), true,
% 44.17/44.58 'is_a_theorem'( W ), true ) ) ] )
% 44.17/44.58 , clause( 54, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.58 implies( Z, implies( T, implies( U, U ) ) ) ) ), W ) ), true,
% 44.17/44.58 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.58 :=( U, U ), :=( W, W )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9713, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( W, V0 ), implies( V0, V1 ) ), implies( V0, V1 ) ) ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 170, [ =( 'is_a_theorem'( implies( T, implies( implies( implies(
% 44.17/44.58 X, Y ), implies( Y, Z ) ), implies( Y, Z ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9711, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.58 implies( Y, implies( Z, implies( T, implies( U, U ) ) ) ) ), W ) ), true
% 44.17/44.58 , 'is_a_theorem'( W ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, W ), :=( Y, V0 ), :=( Z, V1 ), :=( T,
% 44.17/44.58 implies( X, implies( Y, implies( Z, implies( T, implies( U, U ) ) ) ) ) )] )
% 44.17/44.58 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=(
% 44.17/44.58 U, U ), :=( W, implies( implies( implies( W, V0 ), implies( V0, V1 ) ),
% 44.17/44.58 implies( V0, V1 ) ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9715, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.58 , implies( Y, Z ) ), implies( Y, Z ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9713, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( W, V0 ), implies( V0, V1 ) ), implies( V0, V1 ) ) ),
% 44.17/44.58 true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, Y ), implies( Y, Z ) ), implies( Y, Z ) ) ) ), :=( Z
% 44.17/44.58 , true )] ), substitution( 1, [ :=( X, T ), :=( Y, U ), :=( Z, W ), :=( T
% 44.17/44.58 , V0 ), :=( U, V1 ), :=( W, X ), :=( V0, Y ), :=( V1, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9716, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.58 implies( Y, Z ) ), implies( Y, Z ) ) ), true ) ] )
% 44.17/44.58 , clause( 9715, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.58 ), implies( Y, Z ) ), implies( Y, Z ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 208, [ =( 'is_a_theorem'( implies( implies( implies( W, V0 ),
% 44.17/44.58 implies( V0, V1 ) ), implies( V0, V1 ) ) ), true ) ] )
% 44.17/44.58 , clause( 9716, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.58 implies( Y, Z ) ), implies( Y, Z ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, W ), :=( Y, V0 ), :=( Z, V1 )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9718, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.58 ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9720, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( Y, Z ), implies( X, Y ) ), implies( T, implies( X, Y ) ) ) ),
% 44.17/44.58 true ) ) ] )
% 44.17/44.58 , clause( 208, [ =( 'is_a_theorem'( implies( implies( implies( W, V0 ),
% 44.17/44.58 implies( V0, V1 ) ), implies( V0, V1 ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9718, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.58 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.58 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, U ), :=( Y, W ), :=( Z, V0 ), :=( T, V1 )
% 44.17/44.58 , :=( U, V2 ), :=( W, X ), :=( V0, Y ), :=( V1, Z )] ), substitution( 1
% 44.17/44.58 , [ :=( X, implies( X, Y ) ), :=( Y, implies( Y, Z ) ), :=( Z, implies( Y
% 44.17/44.58 , Z ) ), :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9721, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.58 , implies( Z, X ) ), implies( T, implies( Z, X ) ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9720, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( Y, Z ), implies( X, Y ) ), implies( T, implies( X, Y )
% 44.17/44.58 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, Y ), implies( Z, X ) ), implies( T, implies( Z, X )
% 44.17/44.58 ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, X ),
% 44.17/44.58 :=( Z, Y ), :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9722, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.58 implies( Z, X ) ), implies( T, implies( Z, X ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9721, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.58 ), implies( Z, X ) ), implies( T, implies( Z, X ) ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 212, [ =( 'is_a_theorem'( implies( implies( implies( Y, Z ),
% 44.17/44.58 implies( X, Y ) ), implies( T, implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9722, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.58 implies( Z, X ) ), implies( T, implies( Z, X ) ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9724, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9726, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.58 implies( X, Y ), implies( Y, Z ) ) ), true, 'is_a_theorem'( implies( Y, Z
% 44.17/44.58 ) ), true ), true ) ) ] )
% 44.17/44.58 , clause( 208, [ =( 'is_a_theorem'( implies( implies( implies( W, V0 ),
% 44.17/44.58 implies( V0, V1 ) ), implies( V0, V1 ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9724, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, U ), :=( Z, W ), :=( T, V0 )
% 44.17/44.58 , :=( U, V1 ), :=( W, X ), :=( V0, Y ), :=( V1, Z )] ), substitution( 1
% 44.17/44.58 , [ :=( X, implies( implies( X, Y ), implies( Y, Z ) ) ), :=( Y, implies(
% 44.17/44.58 Y, Z ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9731, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.58 implies( Y, Z ) ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9726, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( implies( X, Y ), implies( Y, Z ) ) ), true, 'is_a_theorem'(
% 44.17/44.58 implies( Y, Z ) ), true ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( implies( X, Y ), implies( Y, Z ) ) ), true, 'is_a_theorem'(
% 44.17/44.58 implies( Y, Z ) ), true ) ), :=( Z, true )] ), substitution( 1, [ :=( X,
% 44.17/44.58 X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9732, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.58 Y, Z ) ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9731, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.58 implies( Y, Z ) ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 213, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.58 Y, Z ) ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9732, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.58 implies( Y, Z ) ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ),
% 44.17/44.58 true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9734, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies( X
% 44.17/44.58 , Y ), Z ), Y ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , clause( 66, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.58 , Z ), Y ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9736, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X,
% 44.17/44.58 implies( Y, implies( Z, X ) ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 212, [ =( 'is_a_theorem'( implies( implies( implies( Y, Z ),
% 44.17/44.58 implies( X, Y ) ), implies( T, implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9734, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), Y ) ), true, 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.58 true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, implies( Y,
% 44.17/44.58 implies( Z, X ) ) ), :=( T, Y )] ), substitution( 1, [ :=( X, X ), :=( Y
% 44.17/44.58 , implies( Y, implies( Z, X ) ) ), :=( Z, implies( Z, X ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9738, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies( Z
% 44.17/44.58 , X ) ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9736, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X
% 44.17/44.58 , implies( Y, implies( Z, X ) ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.58 , implies( Y, implies( Z, X ) ) ) ) ), :=( Z, true )] ), substitution( 1
% 44.17/44.58 , [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9739, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z, X )
% 44.17/44.58 ) ) ), true ) ] )
% 44.17/44.58 , clause( 9738, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.58 Z, X ) ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 215, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z, X ) )
% 44.17/44.58 ) ), true ) ] )
% 44.17/44.58 , clause( 9739, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z, X
% 44.17/44.58 ) ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9741, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.58 ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9743, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( Z, implies( T, implies( X, Y ) ) ), X ), implies( U, X ) ) ),
% 44.17/44.58 true ) ) ] )
% 44.17/44.58 , clause( 215, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z, X )
% 44.17/44.58 ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9741, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.58 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.58 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, implies( X, Y ) ), :=( Y, Z ), :=( Z, T )] )
% 44.17/44.58 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( Z, implies(
% 44.17/44.58 T, implies( X, Y ) ) ) ), :=( T, U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9744, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( Y, implies( Z, T ) ) ), Z ), implies( U, Z ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9743, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( Z, implies( T, implies( X, Y ) ) ), X ), implies( U, X
% 44.17/44.58 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, implies( Y, implies( Z, T ) ) ), Z ), implies( U, Z
% 44.17/44.58 ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, T ),
% 44.17/44.58 :=( Z, X ), :=( T, Y ), :=( U, U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9745, [ =( 'is_a_theorem'( implies( implies( implies( X, implies( Y
% 44.17/44.58 , implies( Z, T ) ) ), Z ), implies( U, Z ) ) ), true ) ] )
% 44.17/44.58 , clause( 9744, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( Y, implies( Z, T ) ) ), Z ), implies( U, Z ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.58 :=( U, U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 222, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies( T
% 44.17/44.58 , implies( X, Y ) ) ), X ), implies( U, X ) ) ), true ) ] )
% 44.17/44.58 , clause( 9745, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.58 Y, implies( Z, T ) ) ), Z ), implies( U, Z ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y ), :=( U
% 44.17/44.58 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9747, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9750, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.58 Y, implies( Z, X ) ) ), T ) ), true, ifeq( true, true, 'is_a_theorem'( T
% 44.17/44.58 ), true ), true ) ) ] )
% 44.17/44.58 , clause( 215, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z, X )
% 44.17/44.58 ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9747, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 15, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.58 substitution( 1, [ :=( X, implies( X, implies( Y, implies( Z, X ) ) ) ),
% 44.17/44.58 :=( Y, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9752, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.58 Y, implies( Z, X ) ) ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9750, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.58 implies( Y, implies( Z, X ) ) ), T ) ), true, ifeq( true, true,
% 44.17/44.58 'is_a_theorem'( T ), true ), true ) ) ] )
% 44.17/44.58 , 0, 14, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( T ) ),
% 44.17/44.58 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.58 :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9753, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.58 implies( Z, X ) ) ), T ) ), true, 'is_a_theorem'( T ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 9752, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.58 implies( Y, implies( Z, X ) ) ), T ) ), true, 'is_a_theorem'( T ), true )
% 44.17/44.58 ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 224, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.58 implies( Z, X ) ) ), T ) ), true, 'is_a_theorem'( T ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 9753, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y
% 44.17/44.58 , implies( Z, X ) ) ), T ) ), true, 'is_a_theorem'( T ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9755, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U )
% 44.17/44.58 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.58 , clause( 9, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U ) ), true,
% 44.17/44.58 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.58 :=( U, U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9757, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( U,
% 44.17/44.58 implies( implies( implies( Z, T ), X ), implies( T, X ) ) ) ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 58, [ =( 'is_a_theorem'( implies( implies( implies( U, implies( T
% 44.17/44.58 , Y ) ), implies( X, implies( Y, Z ) ) ), implies( W, implies( X, implies(
% 44.17/44.58 Y, Z ) ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9755, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), implies( implies( Z, X ), implies( T, X )
% 44.17/44.58 ) ), U ) ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, implies( implies( Z, T ), X ) ), :=( Y, T
% 44.17/44.58 ), :=( Z, X ), :=( T, Z ), :=( U, implies( X, Y ) ), :=( W, U )] ),
% 44.17/44.58 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( Z, T ) ), :=(
% 44.17/44.58 T, T ), :=( U, implies( U, implies( implies( implies( Z, T ), X ),
% 44.17/44.58 implies( T, X ) ) ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9759, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.58 implies( Y, Z ), T ), implies( Z, T ) ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9757, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( U
% 44.17/44.58 , implies( implies( implies( Z, T ), X ), implies( T, X ) ) ) ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.58 , implies( implies( implies( Y, Z ), T ), implies( Z, T ) ) ) ) ), :=( Z
% 44.17/44.58 , true )] ), substitution( 1, [ :=( X, T ), :=( Y, U ), :=( Z, Y ), :=( T
% 44.17/44.58 , Z ), :=( U, X )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9760, [ =( 'is_a_theorem'( implies( X, implies( implies( implies( Y
% 44.17/44.58 , Z ), T ), implies( Z, T ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9759, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.58 implies( Y, Z ), T ), implies( Z, T ) ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 257, [ =( 'is_a_theorem'( implies( U, implies( implies( implies( Z
% 44.17/44.58 , T ), X ), implies( T, X ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9760, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.58 Y, Z ), T ), implies( Z, T ) ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, U ), :=( Y, Z ), :=( Z, T ), :=( T, X )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9762, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.58 implies( implies( Y, implies( Z, Z ) ), T ), implies( U, T ) ) ), W ) ),
% 44.17/44.58 true, 'is_a_theorem'( W ), true ) ) ] )
% 44.17/44.58 , clause( 56, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.58 implies( implies( Y, implies( Z, Z ) ), T ), implies( U, T ) ) ), W ) ),
% 44.17/44.58 true, 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.58 :=( U, U ), :=( W, W )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9764, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( W, V0 ), V1 ), implies( V0, V1 ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 257, [ =( 'is_a_theorem'( implies( U, implies( implies( implies(
% 44.17/44.58 Z, T ), X ), implies( T, X ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9762, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.58 implies( implies( implies( Y, implies( Z, Z ) ), T ), implies( U, T ) ) )
% 44.17/44.58 , W ) ), true, 'is_a_theorem'( W ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, V1 ), :=( Y, V2 ), :=( Z, W ), :=( T, V0
% 44.17/44.58 ), :=( U, implies( X, implies( implies( implies( Y, implies( Z, Z ) ), T
% 44.17/44.58 ), implies( U, T ) ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 44.17/44.58 :=( Z, Z ), :=( T, T ), :=( U, U ), :=( W, implies( implies( implies( W,
% 44.17/44.58 V0 ), V1 ), implies( V0, V1 ) ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9766, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.58 , Z ), implies( Y, Z ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9764, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( W, V0 ), V1 ), implies( V0, V1 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), implies( Y, Z ) ) ) ), :=( Z, true )] ),
% 44.17/44.58 substitution( 1, [ :=( X, T ), :=( Y, U ), :=( Z, W ), :=( T, V0 ), :=( U
% 44.17/44.58 , V1 ), :=( W, X ), :=( V0, Y ), :=( V1, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9767, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 44.17/44.58 implies( Y, Z ) ) ), true ) ] )
% 44.17/44.58 , clause( 9766, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.58 ), Z ), implies( Y, Z ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 259, [ =( 'is_a_theorem'( implies( implies( implies( W, V0 ), V1 )
% 44.17/44.58 , implies( V0, V1 ) ) ), true ) ] )
% 44.17/44.58 , clause( 9767, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z )
% 44.17/44.58 , implies( Y, Z ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, W ), :=( Y, V0 ), :=( Z, V1 )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9769, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U )
% 44.17/44.58 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.58 , clause( 9, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U ) ), true,
% 44.17/44.58 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.58 :=( U, U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9771, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Z,
% 44.17/44.58 implies( implies( Z, X ), implies( T, X ) ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 259, [ =( 'is_a_theorem'( implies( implies( implies( W, V0 ), V1
% 44.17/44.58 ), implies( V0, V1 ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9769, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), implies( implies( Z, X ), implies( T, X )
% 44.17/44.58 ) ), U ) ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, U ), :=( Y, W ), :=( Z, V0 ), :=( T, V1 )
% 44.17/44.58 , :=( U, V2 ), :=( W, implies( X, Y ) ), :=( V0, Z ), :=( V1, implies(
% 44.17/44.58 implies( Z, X ), implies( T, X ) ) )] ), substitution( 1, [ :=( X, X ),
% 44.17/44.58 :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U, implies( Z, implies( implies(
% 44.17/44.58 Z, X ), implies( T, X ) ) ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9773, [ =( true, 'is_a_theorem'( implies( X, implies( implies( X, Y
% 44.17/44.58 ), implies( Z, Y ) ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9771, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Z
% 44.17/44.58 , implies( implies( Z, X ), implies( T, X ) ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.58 , implies( implies( X, Y ), implies( Z, Y ) ) ) ) ), :=( Z, true )] ),
% 44.17/44.58 substitution( 1, [ :=( X, Y ), :=( Y, T ), :=( Z, X ), :=( T, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9774, [ =( 'is_a_theorem'( implies( X, implies( implies( X, Y ),
% 44.17/44.58 implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9773, [ =( true, 'is_a_theorem'( implies( X, implies( implies( X
% 44.17/44.58 , Y ), implies( Z, Y ) ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 264, [ =( 'is_a_theorem'( implies( Z, implies( implies( Z, X ),
% 44.17/44.58 implies( T, X ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9774, [ =( 'is_a_theorem'( implies( X, implies( implies( X, Y ),
% 44.17/44.58 implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9776, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9778, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.58 implies( X, Y ), Z ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ),
% 44.17/44.58 true ) ) ] )
% 44.17/44.58 , clause( 259, [ =( 'is_a_theorem'( implies( implies( implies( W, V0 ), V1
% 44.17/44.58 ), implies( V0, V1 ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9776, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, U ), :=( Z, W ), :=( T, V0 )
% 44.17/44.58 , :=( U, V1 ), :=( W, X ), :=( V0, Y ), :=( V1, Z )] ), substitution( 1
% 44.17/44.58 , [ :=( X, implies( implies( X, Y ), Z ) ), :=( Y, implies( Y, Z ) )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9783, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9778, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( implies( X, Y ), Z ) ), true, 'is_a_theorem'( implies( Y, Z ) )
% 44.17/44.58 , true ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( implies( X, Y ), Z ) ), true, 'is_a_theorem'( implies( Y, Z ) )
% 44.17/44.58 , true ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 44.17/44.58 :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9784, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( Y, Z ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9783, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.58 Z ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 265, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( Y, Z ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9784, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) )
% 44.17/44.58 , true, 'is_a_theorem'( implies( Y, Z ) ), true ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9786, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9789, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( Y, Z ) ), T ) ), true, ifeq( true, true,
% 44.17/44.58 'is_a_theorem'( T ), true ), true ) ) ] )
% 44.17/44.58 , clause( 259, [ =( 'is_a_theorem'( implies( implies( implies( W, V0 ), V1
% 44.17/44.58 ), implies( V0, V1 ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9786, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 17, substitution( 0, [ :=( X, U ), :=( Y, W ), :=( Z, V0 ), :=( T, V1
% 44.17/44.58 ), :=( U, V2 ), :=( W, X ), :=( V0, Y ), :=( V1, Z )] ), substitution( 1
% 44.17/44.58 , [ :=( X, implies( implies( implies( X, Y ), Z ), implies( Y, Z ) ) ),
% 44.17/44.58 :=( Y, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9791, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( Y, Z ) ), T ) ), true, 'is_a_theorem'( T )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9789, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), implies( Y, Z ) ), T ) ), true, ifeq( true
% 44.17/44.58 , true, 'is_a_theorem'( T ), true ), true ) ) ] )
% 44.17/44.58 , 0, 16, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( T ) ),
% 44.17/44.58 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.58 :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9792, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, Y ), Z ), implies( Y, Z ) ), T ) ), true, 'is_a_theorem'( T ), true )
% 44.17/44.58 , true ) ] )
% 44.17/44.58 , clause( 9791, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( Y, Z ) ), T ) ), true, 'is_a_theorem'( T )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 266, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, Y ), Z ), implies( Y, Z ) ), T ) ), true, 'is_a_theorem'( T ), true )
% 44.17/44.58 , true ) ] )
% 44.17/44.58 , clause( 9792, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( Y, Z ) ), T ) ), true, 'is_a_theorem'( T )
% 44.17/44.58 , true ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9794, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.58 ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9796, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( implies( X, Y ), Z ), implies( T, Z ) ), X ), implies(
% 44.17/44.58 U, X ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 264, [ =( 'is_a_theorem'( implies( Z, implies( implies( Z, X ),
% 44.17/44.58 implies( T, X ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9794, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.58 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.58 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, W ), :=( Z, implies( X, Y ) )
% 44.17/44.58 , :=( T, T )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z,
% 44.17/44.58 implies( implies( implies( X, Y ), Z ), implies( T, Z ) ) ), :=( T, U )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9798, [ =( true, 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( T, Z ) ), X ), implies( U, X ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9796, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( implies( X, Y ), Z ), implies( T, Z ) ), X ),
% 44.17/44.58 implies( U, X ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( implies( X, Y ), Z ), implies( T, Z ) ), X ),
% 44.17/44.58 implies( U, X ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ),
% 44.17/44.58 :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U, U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9799, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( T, Z ) ), X ), implies( U, X ) ) ), true )
% 44.17/44.58 ] )
% 44.17/44.58 , clause( 9798, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), implies( T, Z ) ), X ), implies( U, X ) )
% 44.17/44.58 ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.58 :=( U, U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 269, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( T, Z ) ), X ), implies( U, X ) ) ), true )
% 44.17/44.58 ] )
% 44.17/44.58 , clause( 9799, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( T, Z ) ), X ), implies( U, X ) ) ), true )
% 44.17/44.58 ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 44.17/44.58 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9801, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9803, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( X ), true
% 44.17/44.58 , 'is_a_theorem'( implies( implies( X, Y ), implies( Z, Y ) ) ), true ),
% 44.17/44.58 true ) ) ] )
% 44.17/44.58 , clause( 264, [ =( 'is_a_theorem'( implies( Z, implies( implies( Z, X ),
% 44.17/44.58 implies( T, X ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9801, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, T ), :=( Z, X ), :=( T, Z )] )
% 44.17/44.58 , substitution( 1, [ :=( X, X ), :=( Y, implies( implies( X, Y ), implies(
% 44.17/44.58 Z, Y ) ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9808, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 44.17/44.58 implies( implies( X, Y ), implies( Z, Y ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9803, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( X ),
% 44.17/44.58 true, 'is_a_theorem'( implies( implies( X, Y ), implies( Z, Y ) ) ), true
% 44.17/44.58 ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'( X )
% 44.17/44.58 , true, 'is_a_theorem'( implies( implies( X, Y ), implies( Z, Y ) ) ),
% 44.17/44.58 true ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 44.17/44.58 :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9809, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( X, Y ), implies( Z, Y ) ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9808, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 44.17/44.58 implies( implies( X, Y ), implies( Z, Y ) ) ), true ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 270, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( X, Y ), implies( Z, Y ) ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9809, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 44.17/44.58 implies( implies( X, Y ), implies( Z, Y ) ) ), true ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9811, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9814, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.58 implies( X, Y ), implies( Z, Y ) ) ), T ) ), true, ifeq( true, true,
% 44.17/44.58 'is_a_theorem'( T ), true ), true ) ) ] )
% 44.17/44.58 , clause( 264, [ =( 'is_a_theorem'( implies( Z, implies( implies( Z, X ),
% 44.17/44.58 implies( T, X ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9811, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 17, substitution( 0, [ :=( X, Y ), :=( Y, U ), :=( Z, X ), :=( T, Z )] )
% 44.17/44.58 , substitution( 1, [ :=( X, implies( X, implies( implies( X, Y ), implies(
% 44.17/44.58 Z, Y ) ) ) ), :=( Y, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9816, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.58 implies( X, Y ), implies( Z, Y ) ) ), T ) ), true, 'is_a_theorem'( T ),
% 44.17/44.58 true ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9814, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.58 implies( implies( X, Y ), implies( Z, Y ) ) ), T ) ), true, ifeq( true,
% 44.17/44.58 true, 'is_a_theorem'( T ), true ), true ) ) ] )
% 44.17/44.58 , 0, 16, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( T ) ),
% 44.17/44.58 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.58 :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9817, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.58 implies( X, Y ), implies( Z, Y ) ) ), T ) ), true, 'is_a_theorem'( T ),
% 44.17/44.58 true ), true ) ] )
% 44.17/44.58 , clause( 9816, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.58 implies( implies( X, Y ), implies( Z, Y ) ) ), T ) ), true,
% 44.17/44.58 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 271, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.58 implies( X, Y ), implies( Z, Y ) ) ), T ) ), true, 'is_a_theorem'( T ),
% 44.17/44.58 true ), true ) ] )
% 44.17/44.58 , clause( 9817, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.58 implies( X, Y ), implies( Z, Y ) ) ), T ) ), true, 'is_a_theorem'( T ),
% 44.17/44.58 true ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9819, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y )
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( Z, implies( X, Y ) ) ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 190, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( Z, implies( X, Y ) ) ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9821, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Z,
% 44.17/44.58 implies( implies( X, implies( X, Y ) ), implies( X, Y ) ) ) ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 186, [ =( 'is_a_theorem'( implies( implies( X, implies( X, Y ) )
% 44.17/44.58 , implies( Z, implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9819, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X
% 44.17/44.58 , Y ) ) ), true, 'is_a_theorem'( implies( Z, implies( X, Y ) ) ), true )
% 44.17/44.58 ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( X,
% 44.17/44.58 implies( X, Y ) ) )] ), substitution( 1, [ :=( X, implies( X, implies( X
% 44.17/44.58 , Y ) ) ), :=( Y, implies( X, Y ) ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9823, [ =( true, 'is_a_theorem'( implies( X, implies( implies( Y,
% 44.17/44.58 implies( Y, Z ) ), implies( Y, Z ) ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9821, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Z
% 44.17/44.58 , implies( implies( X, implies( X, Y ) ), implies( X, Y ) ) ) ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.58 , implies( implies( Y, implies( Y, Z ) ), implies( Y, Z ) ) ) ) ), :=( Z
% 44.17/44.58 , true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9824, [ =( 'is_a_theorem'( implies( X, implies( implies( Y, implies(
% 44.17/44.58 Y, Z ) ), implies( Y, Z ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9823, [ =( true, 'is_a_theorem'( implies( X, implies( implies( Y
% 44.17/44.58 , implies( Y, Z ) ), implies( Y, Z ) ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 412, [ =( 'is_a_theorem'( implies( Z, implies( implies( X, implies(
% 44.17/44.58 X, Y ) ), implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9824, [ =( 'is_a_theorem'( implies( X, implies( implies( Y,
% 44.17/44.58 implies( Y, Z ) ), implies( Y, Z ) ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9826, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y )
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( Z, implies( X, Y ) ) ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 190, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( Z, implies( X, Y ) ) ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9828, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( T,
% 44.17/44.58 implies( implies( implies( X, implies( Y, Z ) ), Y ), Y ) ) ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 69, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies( X
% 44.17/44.58 , Y ) ), X ), implies( T, X ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9826, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X
% 44.17/44.58 , Y ) ) ), true, 'is_a_theorem'( implies( Z, implies( X, Y ) ) ), true )
% 44.17/44.58 ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T,
% 44.17/44.58 implies( implies( X, implies( Y, Z ) ), Y ) )] ), substitution( 1, [ :=(
% 44.17/44.58 X, implies( implies( X, implies( Y, Z ) ), Y ) ), :=( Y, Y ), :=( Z, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9830, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.58 implies( Y, implies( Z, T ) ), Z ), Z ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9828, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( T
% 44.17/44.58 , implies( implies( implies( X, implies( Y, Z ) ), Y ), Y ) ) ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.58 , implies( implies( implies( Y, implies( Z, T ) ), Z ), Z ) ) ) ), :=( Z
% 44.17/44.58 , true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T
% 44.17/44.58 , X )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9831, [ =( 'is_a_theorem'( implies( X, implies( implies( implies( Y
% 44.17/44.58 , implies( Z, T ) ), Z ), Z ) ) ), true ) ] )
% 44.17/44.58 , clause( 9830, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.58 implies( Y, implies( Z, T ) ), Z ), Z ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 420, [ =( 'is_a_theorem'( implies( T, implies( implies( implies( X
% 44.17/44.58 , implies( Y, Z ) ), Y ), Y ) ) ), true ) ] )
% 44.17/44.58 , clause( 9831, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.58 Y, implies( Z, T ) ), Z ), Z ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9833, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.58 implies( Y, Z ) ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 213, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.58 Y, Z ) ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9835, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 Y, implies( Y, Z ) ), implies( Y, Z ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 412, [ =( 'is_a_theorem'( implies( Z, implies( implies( X,
% 44.17/44.58 implies( X, Y ) ), implies( X, Y ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9833, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.58 ), implies( Y, Z ) ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true )
% 44.17/44.58 ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, implies( X,
% 44.17/44.58 implies( Y, implies( Y, Z ) ) ) )] ), substitution( 1, [ :=( X, X ), :=(
% 44.17/44.58 Y, implies( Y, implies( Y, Z ) ) ), :=( Z, implies( Y, Z ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9837, [ =( true, 'is_a_theorem'( implies( implies( X, implies( X, Y
% 44.17/44.58 ) ), implies( X, Y ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9835, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( Y, implies( Y, Z ) ), implies( Y, Z ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( X, implies( X, Y ) ), implies( X, Y ) ) ) ), :=( Z, true )] ),
% 44.17/44.58 substitution( 1, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9838, [ =( 'is_a_theorem'( implies( implies( X, implies( X, Y ) ),
% 44.17/44.58 implies( X, Y ) ) ), true ) ] )
% 44.17/44.58 , clause( 9837, [ =( true, 'is_a_theorem'( implies( implies( X, implies( X
% 44.17/44.58 , Y ) ), implies( X, Y ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 423, [ =( 'is_a_theorem'( implies( implies( Y, implies( Y, Z ) ),
% 44.17/44.58 implies( Y, Z ) ) ), true ) ] )
% 44.17/44.58 , clause( 9838, [ =( 'is_a_theorem'( implies( implies( X, implies( X, Y ) )
% 44.17/44.58 , implies( X, Y ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), permutation( 0, [ ==>( 0, 0
% 44.17/44.58 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9840, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9842, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies( X
% 44.17/44.58 , implies( X, Y ) ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ),
% 44.17/44.58 true ) ) ] )
% 44.17/44.58 , clause( 423, [ =( 'is_a_theorem'( implies( implies( Y, implies( Y, Z ) )
% 44.17/44.58 , implies( Y, Z ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9840, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 44.17/44.58 substitution( 1, [ :=( X, implies( X, implies( X, Y ) ) ), :=( Y, implies(
% 44.17/44.58 X, Y ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9847, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y )
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9842, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( X, implies( X, Y ) ) ), true, 'is_a_theorem'( implies( X, Y ) )
% 44.17/44.58 , true ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( X, implies( X, Y ) ) ), true, 'is_a_theorem'( implies( X, Y ) )
% 44.17/44.58 , true ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9848, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9847, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y
% 44.17/44.58 ) ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 431, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9848, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) )
% 44.17/44.58 , true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 44.17/44.58 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9850, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, implies( Y, X ) ), Z ), implies( T, Z ) ), U ) ), true,
% 44.17/44.58 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.58 , clause( 97, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, implies( Y, X ) ), Z ), implies( T, Z ) ), U ) ), true, 'is_a_theorem'(
% 44.17/44.58 U ), true ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.58 :=( U, U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9852, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( U, implies( W, V0 ) ), W ), W ) ), true ) ) ] )
% 44.17/44.58 , clause( 420, [ =( 'is_a_theorem'( implies( T, implies( implies( implies(
% 44.17/44.58 X, implies( Y, Z ) ), Y ), Y ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9850, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( X, implies( Y, X ) ), Z ), implies( T, Z ) ), U ) ),
% 44.17/44.58 true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, U ), :=( Y, W ), :=( Z, V0 ), :=( T,
% 44.17/44.58 implies( implies( implies( X, implies( Y, X ) ), Z ), implies( T, Z ) ) )] )
% 44.17/44.58 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=(
% 44.17/44.58 U, implies( implies( implies( U, implies( W, V0 ) ), W ), W ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9854, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( Y, Z ) ), Y ), Y ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9852, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( U, implies( W, V0 ) ), W ), W ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, implies( Y, Z ) ), Y ), Y ) ) ), :=( Z, true )] ),
% 44.17/44.58 substitution( 1, [ :=( X, T ), :=( Y, U ), :=( Z, W ), :=( T, V0 ), :=( U
% 44.17/44.58 , X ), :=( W, Y ), :=( V0, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9855, [ =( 'is_a_theorem'( implies( implies( implies( X, implies( Y
% 44.17/44.58 , Z ) ), Y ), Y ) ), true ) ] )
% 44.17/44.58 , clause( 9854, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( Y, Z ) ), Y ), Y ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 437, [ =( 'is_a_theorem'( implies( implies( implies( U, implies( W
% 44.17/44.58 , V0 ) ), W ), W ) ), true ) ] )
% 44.17/44.58 , clause( 9855, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.58 Y, Z ) ), Y ), Y ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, U ), :=( Y, W ), :=( Z, V0 )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9857, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.58 ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9859, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 Y, implies( X, implies( Y, Z ) ) ), implies( T, implies( X, implies( Y, Z
% 44.17/44.58 ) ) ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 437, [ =( 'is_a_theorem'( implies( implies( implies( U, implies(
% 44.17/44.58 W, V0 ) ), W ), W ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9857, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.58 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.58 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, U ), :=( Y, W ), :=( Z, V0 ), :=( T, V1 )
% 44.17/44.58 , :=( U, X ), :=( W, Y ), :=( V0, Z )] ), substitution( 1, [ :=( X,
% 44.17/44.58 implies( X, implies( Y, Z ) ) ), :=( Y, Y ), :=( Z, Y ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9860, [ =( true, 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.58 implies( X, Z ) ) ), implies( T, implies( Y, implies( X, Z ) ) ) ) ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9859, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( Y, implies( X, implies( Y, Z ) ) ), implies( T, implies( X,
% 44.17/44.58 implies( Y, Z ) ) ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( X, implies( Y, implies( X, Z ) ) ), implies( T, implies( Y,
% 44.17/44.58 implies( X, Z ) ) ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y
% 44.17/44.58 ), :=( Y, X ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9861, [ =( 'is_a_theorem'( implies( implies( X, implies( Y, implies(
% 44.17/44.58 X, Z ) ) ), implies( T, implies( Y, implies( X, Z ) ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9860, [ =( true, 'is_a_theorem'( implies( implies( X, implies( Y
% 44.17/44.58 , implies( X, Z ) ) ), implies( T, implies( Y, implies( X, Z ) ) ) ) ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 444, [ =( 'is_a_theorem'( implies( implies( Y, implies( X, implies(
% 44.17/44.58 Y, Z ) ) ), implies( T, implies( X, implies( Y, Z ) ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9861, [ =( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.58 implies( X, Z ) ) ), implies( T, implies( Y, implies( X, Z ) ) ) ) ),
% 44.17/44.58 true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9863, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y )
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , clause( 431, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9865, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( X, implies( Y, implies( Z, T ) ) ), Z ), Z ) ), true ) ) ] )
% 44.17/44.58 , clause( 222, [ =( 'is_a_theorem'( implies( implies( implies( Z, implies(
% 44.17/44.58 T, implies( X, Y ) ) ), X ), implies( U, X ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9863, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X
% 44.17/44.58 , Y ) ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y ),
% 44.17/44.58 :=( U, implies( implies( X, implies( Y, implies( Z, T ) ) ), Z ) )] ),
% 44.17/44.58 substitution( 1, [ :=( X, implies( implies( X, implies( Y, implies( Z, T
% 44.17/44.58 ) ) ), Z ) ), :=( Y, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9867, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( Y, implies( Z, T ) ) ), Z ), Z ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9865, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, implies( Y, implies( Z, T ) ) ), Z ), Z ) ), true )
% 44.17/44.58 ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, implies( Y, implies( Z, T ) ) ), Z ), Z ) ) ), :=( Z
% 44.17/44.58 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T
% 44.17/44.58 , T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9868, [ =( 'is_a_theorem'( implies( implies( implies( X, implies( Y
% 44.17/44.58 , implies( Z, T ) ) ), Z ), Z ) ), true ) ] )
% 44.17/44.58 , clause( 9867, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( Y, implies( Z, T ) ) ), Z ), Z ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 452, [ =( 'is_a_theorem'( implies( implies( implies( X, implies( Y
% 44.17/44.58 , implies( Z, T ) ) ), Z ), Z ) ), true ) ] )
% 44.17/44.58 , clause( 9868, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.58 Y, implies( Z, T ) ) ), Z ), Z ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9870, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.58 ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9872, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 Z, implies( X, implies( Y, implies( Z, T ) ) ) ), implies( U, implies( X
% 44.17/44.58 , implies( Y, implies( Z, T ) ) ) ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 452, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.58 Y, implies( Z, T ) ) ), Z ), Z ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9870, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.58 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.58 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 , substitution( 1, [ :=( X, implies( X, implies( Y, implies( Z, T ) ) ) )
% 44.17/44.58 , :=( Y, Z ), :=( Z, Z ), :=( T, U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9873, [ =( true, 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.58 implies( Z, implies( X, T ) ) ) ), implies( U, implies( Y, implies( Z,
% 44.17/44.58 implies( X, T ) ) ) ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9872, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( Z, implies( X, implies( Y, implies( Z, T ) ) ) ), implies( U,
% 44.17/44.58 implies( X, implies( Y, implies( Z, T ) ) ) ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( X, implies( Y, implies( Z, implies( X, T ) ) ) ), implies( U,
% 44.17/44.58 implies( Y, implies( Z, implies( X, T ) ) ) ) ) ) ), :=( Z, true )] ),
% 44.17/44.58 substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T ), :=( U
% 44.17/44.58 , U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9874, [ =( 'is_a_theorem'( implies( implies( X, implies( Y, implies(
% 44.17/44.58 Z, implies( X, T ) ) ) ), implies( U, implies( Y, implies( Z, implies( X
% 44.17/44.58 , T ) ) ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9873, [ =( true, 'is_a_theorem'( implies( implies( X, implies( Y
% 44.17/44.58 , implies( Z, implies( X, T ) ) ) ), implies( U, implies( Y, implies( Z,
% 44.17/44.58 implies( X, T ) ) ) ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.58 :=( U, U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 474, [ =( 'is_a_theorem'( implies( implies( Z, implies( X, implies(
% 44.17/44.58 Y, implies( Z, T ) ) ) ), implies( U, implies( X, implies( Y, implies( Z
% 44.17/44.58 , T ) ) ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9874, [ =( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.58 implies( Z, implies( X, T ) ) ) ), implies( U, implies( Y, implies( Z,
% 44.17/44.58 implies( X, T ) ) ) ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T ), :=( U
% 44.17/44.58 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9876, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y )
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , clause( 431, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9878, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 X, implies( Y, implies( X, Z ) ) ), implies( Y, implies( X, Z ) ) ) ),
% 44.17/44.58 true ) ) ] )
% 44.17/44.58 , clause( 444, [ =( 'is_a_theorem'( implies( implies( Y, implies( X,
% 44.17/44.58 implies( Y, Z ) ) ), implies( T, implies( X, implies( Y, Z ) ) ) ) ),
% 44.17/44.58 true ) ] )
% 44.17/44.58 , 0, clause( 9876, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X
% 44.17/44.58 , Y ) ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T,
% 44.17/44.58 implies( X, implies( Y, implies( X, Z ) ) ) )] ), substitution( 1, [ :=(
% 44.17/44.58 X, implies( X, implies( Y, implies( X, Z ) ) ) ), :=( Y, implies( Y,
% 44.17/44.58 implies( X, Z ) ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9880, [ =( true, 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.58 implies( X, Z ) ) ), implies( Y, implies( X, Z ) ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9878, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( X, implies( Y, implies( X, Z ) ) ), implies( Y, implies( X, Z )
% 44.17/44.58 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( X, implies( Y, implies( X, Z ) ) ), implies( Y, implies( X, Z )
% 44.17/44.58 ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 44.17/44.58 :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9881, [ =( 'is_a_theorem'( implies( implies( X, implies( Y, implies(
% 44.17/44.58 X, Z ) ) ), implies( Y, implies( X, Z ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9880, [ =( true, 'is_a_theorem'( implies( implies( X, implies( Y
% 44.17/44.58 , implies( X, Z ) ) ), implies( Y, implies( X, Z ) ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 574, [ =( 'is_a_theorem'( implies( implies( X, implies( Y, implies(
% 44.17/44.58 X, Z ) ) ), implies( Y, implies( X, Z ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9881, [ =( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.58 implies( X, Z ) ) ), implies( Y, implies( X, Z ) ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9883, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U )
% 44.17/44.58 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.58 , clause( 9, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, Y ), Z ), implies( implies( Z, X ), implies( T, X ) ) ), U ) ), true,
% 44.17/44.58 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.58 :=( U, U )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9885, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 Z, X ), implies( implies( implies( X, Y ), Z ), X ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 574, [ =( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.58 implies( X, Z ) ) ), implies( Y, implies( X, Z ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9883, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), implies( implies( Z, X ), implies( T, X )
% 44.17/44.58 ) ), U ) ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, implies( implies( X, Y ), Z ) ), :=( Y,
% 44.17/44.58 implies( Z, X ) ), :=( Z, X )] ), substitution( 1, [ :=( X, X ), :=( Y, Y
% 44.17/44.58 ), :=( Z, Z ), :=( T, implies( implies( X, Y ), Z ) ), :=( U, implies(
% 44.17/44.58 implies( Z, X ), implies( implies( implies( X, Y ), Z ), X ) ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9887, [ =( true, 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.58 implies( implies( Y, Z ), X ), Y ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9885, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( Z, X ), implies( implies( implies( X, Y ), Z ), X ) ) ), true )
% 44.17/44.58 ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( X, Y ), implies( implies( implies( Y, Z ), X ), Y ) ) ) ), :=( Z
% 44.17/44.58 , true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9888, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.58 implies( implies( Y, Z ), X ), Y ) ) ), true ) ] )
% 44.17/44.58 , clause( 9887, [ =( true, 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.58 implies( implies( implies( Y, Z ), X ), Y ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 583, [ =( 'is_a_theorem'( implies( implies( Z, X ), implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), X ) ) ), true ) ] )
% 44.17/44.58 , clause( 9888, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.58 implies( implies( Y, Z ), X ), Y ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9890, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9892, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies( X
% 44.17/44.58 , implies( Y, implies( X, Z ) ) ) ), true, 'is_a_theorem'( implies( Y,
% 44.17/44.58 implies( X, Z ) ) ), true ), true ) ) ] )
% 44.17/44.58 , clause( 574, [ =( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.58 implies( X, Z ) ) ), implies( Y, implies( X, Z ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9890, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.58 substitution( 1, [ :=( X, implies( X, implies( Y, implies( X, Z ) ) ) ),
% 44.17/44.58 :=( Y, implies( Y, implies( X, Z ) ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9897, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( Y,
% 44.17/44.58 implies( X, Z ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( X, Z )
% 44.17/44.58 ) ), true ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9892, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( X, implies( Y, implies( X, Z ) ) ) ), true, 'is_a_theorem'(
% 44.17/44.58 implies( Y, implies( X, Z ) ) ), true ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( X, implies( Y, implies( X, Z ) ) ) ), true, 'is_a_theorem'(
% 44.17/44.58 implies( Y, implies( X, Z ) ) ), true ) ), :=( Z, true )] ),
% 44.17/44.58 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9898, [ =( ifeq( 'is_a_theorem'( implies( X, implies( Y, implies( X
% 44.17/44.58 , Z ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( X, Z ) ) ), true
% 44.17/44.58 ), true ) ] )
% 44.17/44.58 , clause( 9897, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( Y,
% 44.17/44.58 implies( X, Z ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( X, Z )
% 44.17/44.58 ) ), true ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 584, [ =( ifeq( 'is_a_theorem'( implies( X, implies( Y, implies( X
% 44.17/44.58 , Z ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( X, Z ) ) ), true
% 44.17/44.58 ), true ) ] )
% 44.17/44.58 , clause( 9898, [ =( ifeq( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.58 X, Z ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( X, Z ) ) ), true
% 44.17/44.58 ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9900, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.58 Y, implies( Z, X ) ) ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.58 , clause( 224, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.58 implies( Z, X ) ) ), T ) ), true, 'is_a_theorem'( T ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9902, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( Y, implies( Z, X ) ), T ), X ), implies( Y, implies( Z
% 44.17/44.58 , X ) ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 583, [ =( 'is_a_theorem'( implies( implies( Z, X ), implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), X ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9900, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.58 implies( Y, implies( Z, X ) ) ), T ) ), true, 'is_a_theorem'( T ), true )
% 44.17/44.58 ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, implies( Y, implies( Z, X ) ) ), :=( Y, T
% 44.17/44.58 ), :=( Z, X )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )
% 44.17/44.58 , :=( T, implies( implies( implies( implies( Y, implies( Z, X ) ), T ), X
% 44.17/44.58 ), implies( Y, implies( Z, X ) ) ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9904, [ =( true, 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, implies( Y, Z ) ), T ), Z ), implies( X, implies( Y, Z ) ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9902, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( Y, implies( Z, X ) ), T ), X ), implies( Y,
% 44.17/44.58 implies( Z, X ) ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( X, implies( Y, Z ) ), T ), Z ), implies( X,
% 44.17/44.58 implies( Y, Z ) ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z )
% 44.17/44.58 , :=( Y, X ), :=( Z, Y ), :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9905, [ =( 'is_a_theorem'( implies( implies( implies( implies( X,
% 44.17/44.58 implies( Y, Z ) ), T ), Z ), implies( X, implies( Y, Z ) ) ) ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 9904, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, implies( Y, Z ) ), T ), Z ), implies( X, implies( Y, Z ) ) )
% 44.17/44.58 ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 589, [ =( 'is_a_theorem'( implies( implies( implies( implies( Y,
% 44.17/44.58 implies( Z, X ) ), T ), X ), implies( Y, implies( Z, X ) ) ) ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 9905, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.58 , implies( Y, Z ) ), T ), Z ), implies( X, implies( Y, Z ) ) ) ), true )
% 44.17/44.58 ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9907, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, X ), Y ), implies( Z, Y ) ), T ) ), true, 'is_a_theorem'( T )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 31, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, X ), Y ), implies( Z, Y ) ), T ) ), true, 'is_a_theorem'( T ), true )
% 44.17/44.58 , true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9909, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( Z, Y ), T ), implies( implies( X, X ), Y ) ), implies(
% 44.17/44.58 Z, Y ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 583, [ =( 'is_a_theorem'( implies( implies( Z, X ), implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), X ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9907, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( X, X ), Y ), implies( Z, Y ) ), T ) ), true,
% 44.17/44.58 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, implies( Z, Y ) ), :=( Y, T ), :=( Z,
% 44.17/44.58 implies( implies( X, X ), Y ) )] ), substitution( 1, [ :=( X, X ), :=( Y
% 44.17/44.58 , Y ), :=( Z, Z ), :=( T, implies( implies( implies( implies( Z, Y ), T )
% 44.17/44.58 , implies( implies( X, X ), Y ) ), implies( Z, Y ) ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9911, [ =( true, 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, Y ), Z ), implies( implies( T, T ), Y ) ), implies( X, Y ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9909, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( Z, Y ), T ), implies( implies( X, X ), Y ) ),
% 44.17/44.58 implies( Z, Y ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( X, Y ), Z ), implies( implies( T, T ), Y ) ),
% 44.17/44.58 implies( X, Y ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, T ),
% 44.17/44.58 :=( Y, Y ), :=( Z, X ), :=( T, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9912, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.58 ), Z ), implies( implies( T, T ), Y ) ), implies( X, Y ) ) ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 9911, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( implies( T, T ), Y ) ), implies( X, Y ) )
% 44.17/44.58 ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 600, [ =( 'is_a_theorem'( implies( implies( implies( implies( Z, Y
% 44.17/44.58 ), T ), implies( implies( X, X ), Y ) ), implies( Z, Y ) ) ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 9912, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.58 , Y ), Z ), implies( implies( T, T ), Y ) ), implies( X, Y ) ) ), true )
% 44.17/44.58 ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, T ), :=( T, X )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9914, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), X ), implies( Z, X ) ), T ) ), true, 'is_a_theorem'( T )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 16, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, Y ), X ), implies( Z, X ) ), T ) ), true, 'is_a_theorem'( T ), true )
% 44.17/44.58 , true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9916, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( Z, X ), T ), implies( implies( X, Y ), X ) ), implies(
% 44.17/44.58 Z, X ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 583, [ =( 'is_a_theorem'( implies( implies( Z, X ), implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), X ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9914, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), X ), implies( Z, X ) ), T ) ), true,
% 44.17/44.58 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, implies( Z, X ) ), :=( Y, T ), :=( Z,
% 44.17/44.58 implies( implies( X, Y ), X ) )] ), substitution( 1, [ :=( X, X ), :=( Y
% 44.17/44.58 , Y ), :=( Z, Z ), :=( T, implies( implies( implies( implies( Z, X ), T )
% 44.17/44.58 , implies( implies( X, Y ), X ) ), implies( Z, X ) ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9918, [ =( true, 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 X, Y ), Z ), implies( implies( Y, T ), Y ) ), implies( X, Y ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9916, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( Z, X ), T ), implies( implies( X, Y ), X ) ),
% 44.17/44.58 implies( Z, X ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( X, Y ), Z ), implies( implies( Y, T ), Y ) ),
% 44.17/44.58 implies( X, Y ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ),
% 44.17/44.58 :=( Y, T ), :=( Z, X ), :=( T, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9919, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.58 ), Z ), implies( implies( Y, T ), Y ) ), implies( X, Y ) ) ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 9918, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( implies( Y, T ), Y ) ), implies( X, Y ) )
% 44.17/44.58 ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 601, [ =( 'is_a_theorem'( implies( implies( implies( implies( Z, X
% 44.17/44.58 ), T ), implies( implies( X, Y ), X ) ), implies( Z, X ) ) ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 9919, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.58 , Y ), Z ), implies( implies( Y, T ), Y ) ), implies( X, Y ) ) ), true )
% 44.17/44.58 ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, T ), :=( T, Y )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9921, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.58 ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9923, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( implies( Y, Z ), X ), Y ), X ), implies( T, X ) ) ),
% 44.17/44.58 true ) ) ] )
% 44.17/44.58 , clause( 583, [ =( 'is_a_theorem'( implies( implies( Z, X ), implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), X ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9921, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.58 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.58 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 44.17/44.58 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( implies(
% 44.17/44.58 implies( Y, Z ), X ), Y ) ), :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9925, [ =( true, 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), X ), Z ), implies( T, Z ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9923, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( implies( Y, Z ), X ), Y ), X ), implies( T, X
% 44.17/44.58 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( implies( X, Y ), Z ), X ), Z ), implies( T, Z
% 44.17/44.58 ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, X ),
% 44.17/44.58 :=( Z, Y ), :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9926, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), X ), Z ), implies( T, Z ) ) ), true ) ] )
% 44.17/44.58 , clause( 9925, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), X ), Z ), implies( T, Z ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 602, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( Y, Z ), X ), Y ), X ), implies( T, X ) ) ), true ) ] )
% 44.17/44.58 , clause( 9926, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), X ), Z ), implies( T, Z ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9928, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9930, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies( X
% 44.17/44.58 , Y ) ), true, 'is_a_theorem'( implies( implies( implies( Y, Z ), X ), Y
% 44.17/44.58 ) ), true ), true ) ) ] )
% 44.17/44.58 , clause( 583, [ =( 'is_a_theorem'( implies( implies( Z, X ), implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), X ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9928, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 44.17/44.58 substitution( 1, [ :=( X, implies( X, Y ) ), :=( Y, implies( implies(
% 44.17/44.58 implies( Y, Z ), X ), Y ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9935, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 'is_a_theorem'( implies( implies( implies( Y, Z ), X ), Y ) ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9930, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( X, Y ) ), true, 'is_a_theorem'( implies( implies( implies( Y, Z
% 44.17/44.58 ), X ), Y ) ), true ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( X, Y ) ), true, 'is_a_theorem'( implies( implies( implies( Y, Z
% 44.17/44.58 ), X ), Y ) ), true ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X )
% 44.17/44.58 , :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9936, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 'is_a_theorem'( implies( implies( implies( Y, Z ), X ), Y ) ), true ),
% 44.17/44.58 true ) ] )
% 44.17/44.58 , clause( 9935, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 'is_a_theorem'( implies( implies( implies( Y, Z ), X ), Y ) ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 603, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 'is_a_theorem'( implies( implies( implies( Y, Z ), X ), Y ) ), true ),
% 44.17/44.58 true ) ] )
% 44.17/44.58 , clause( 9936, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 'is_a_theorem'( implies( implies( implies( Y, Z ), X ), Y ) ), true ),
% 44.17/44.58 true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9938, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y )
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , clause( 431, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9940, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( implies( X, Y ), Z ), X ), Z ), Z ) ), true ) ) ] )
% 44.17/44.58 , clause( 602, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( Y, Z ), X ), Y ), X ), implies( T, X ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9938, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X
% 44.17/44.58 , Y ) ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T,
% 44.17/44.58 implies( implies( implies( implies( X, Y ), Z ), X ), Z ) )] ),
% 44.17/44.58 substitution( 1, [ :=( X, implies( implies( implies( implies( X, Y ), Z )
% 44.17/44.58 , X ), Z ) ), :=( Y, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9942, [ =( true, 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), X ), Z ), Z ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9940, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( implies( X, Y ), Z ), X ), Z ), Z ) ), true )
% 44.17/44.58 ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( implies( X, Y ), Z ), X ), Z ), Z ) ) ), :=( Z
% 44.17/44.58 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9943, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), X ), Z ), Z ) ), true ) ] )
% 44.17/44.58 , clause( 9942, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), X ), Z ), Z ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 623, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), X ), Z ), Z ) ), true ) ] )
% 44.17/44.58 , clause( 9943, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), X ), Z ), Z ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9945, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.58 , true ) ) ] )
% 44.17/44.58 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.58 ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9947, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 Z, implies( implies( implies( X, Y ), Z ), X ) ), implies( T, implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), X ) ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 623, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), X ), Z ), Z ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9945, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.58 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.58 ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.58 substitution( 1, [ :=( X, implies( implies( implies( X, Y ), Z ), X ) ),
% 44.17/44.58 :=( Y, Z ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9948, [ =( true, 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.58 implies( implies( Y, Z ), X ), Y ) ), implies( T, implies( implies(
% 44.17/44.58 implies( Y, Z ), X ), Y ) ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9947, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( Z, implies( implies( implies( X, Y ), Z ), X ) ), implies( T,
% 44.17/44.58 implies( implies( implies( X, Y ), Z ), X ) ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( X, implies( implies( implies( Y, Z ), X ), Y ) ), implies( T,
% 44.17/44.58 implies( implies( implies( Y, Z ), X ), Y ) ) ) ) ), :=( Z, true )] ),
% 44.17/44.58 substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9949, [ =( 'is_a_theorem'( implies( implies( X, implies( implies(
% 44.17/44.58 implies( Y, Z ), X ), Y ) ), implies( T, implies( implies( implies( Y, Z
% 44.17/44.58 ), X ), Y ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9948, [ =( true, 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.58 implies( implies( Y, Z ), X ), Y ) ), implies( T, implies( implies(
% 44.17/44.58 implies( Y, Z ), X ), Y ) ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 640, [ =( 'is_a_theorem'( implies( implies( Z, implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), X ) ), implies( T, implies( implies( implies( X, Y
% 44.17/44.58 ), Z ), X ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9949, [ =( 'is_a_theorem'( implies( implies( X, implies( implies(
% 44.17/44.58 implies( Y, Z ), X ), Y ) ), implies( T, implies( implies( implies( Y, Z
% 44.17/44.58 ), X ), Y ) ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9951, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 'is_a_theorem'( implies( implies( implies( Y, Z ), X ), Y ) ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 603, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 'is_a_theorem'( implies( implies( implies( Y, Z ), X ), Y ) ), true ),
% 44.17/44.58 true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9953, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( implies( X, Y ), implies( Z, Y ) ), T ), X ), implies(
% 44.17/44.58 implies( X, Y ), implies( Z, Y ) ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 264, [ =( 'is_a_theorem'( implies( Z, implies( implies( Z, X ),
% 44.17/44.58 implies( T, X ) ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9951, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , 'is_a_theorem'( implies( implies( implies( Y, Z ), X ), Y ) ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, U ), :=( Z, X ), :=( T, Z )] )
% 44.17/44.58 , substitution( 1, [ :=( X, X ), :=( Y, implies( implies( X, Y ), implies(
% 44.17/44.58 Z, Y ) ) ), :=( Z, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9954, [ =( true, 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), implies( Z, Y ) ), T ), X ), implies( implies( X, Y ),
% 44.17/44.58 implies( Z, Y ) ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9953, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( implies( X, Y ), implies( Z, Y ) ), T ), X ),
% 44.17/44.58 implies( implies( X, Y ), implies( Z, Y ) ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( implies( X, Y ), implies( Z, Y ) ), T ), X ),
% 44.17/44.58 implies( implies( X, Y ), implies( Z, Y ) ) ) ) ), :=( Z, true )] ),
% 44.17/44.58 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9955, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), implies( Z, Y ) ), T ), X ), implies( implies( X, Y ),
% 44.17/44.58 implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9954, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), implies( Z, Y ) ), T ), X ), implies( implies(
% 44.17/44.58 X, Y ), implies( Z, Y ) ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 671, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), implies( Z, Y ) ), T ), X ), implies( implies( X, Y ),
% 44.17/44.58 implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.58 , clause( 9955, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), implies( Z, Y ) ), T ), X ), implies( implies( X, Y ),
% 44.17/44.58 implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9957, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9959, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), implies( implies( T, T ), Y ) ) ), true,
% 44.17/44.58 'is_a_theorem'( implies( X, Y ) ), true ), true ) ) ] )
% 44.17/44.58 , clause( 600, [ =( 'is_a_theorem'( implies( implies( implies( implies( Z,
% 44.17/44.58 Y ), T ), implies( implies( X, X ), Y ) ), implies( Z, Y ) ) ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, clause( 9957, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, Y ), :=( Z, X ), :=( T, Z )] )
% 44.17/44.58 , substitution( 1, [ :=( X, implies( implies( implies( X, Y ), Z ),
% 44.17/44.58 implies( implies( T, T ), Y ) ) ), :=( Y, implies( X, Y ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9964, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies( X
% 44.17/44.58 , Y ), Z ), implies( implies( T, T ), Y ) ) ), true, 'is_a_theorem'(
% 44.17/44.58 implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9959, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( implies( implies( X, Y ), Z ), implies( implies( T, T ), Y ) ) )
% 44.17/44.58 , true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( implies( implies( X, Y ), Z ), implies( implies( T, T ), Y ) ) )
% 44.17/44.58 , true, 'is_a_theorem'( implies( X, Y ) ), true ) ), :=( Z, true )] ),
% 44.17/44.58 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9965, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.58 , Z ), implies( implies( T, T ), Y ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.58 X, Y ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9964, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 X, Y ), Z ), implies( implies( T, T ), Y ) ) ), true, 'is_a_theorem'(
% 44.17/44.58 implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 702, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.58 Z ), implies( implies( T, T ), Y ) ) ), true, 'is_a_theorem'( implies( X
% 44.17/44.58 , Y ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9965, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.58 ), Z ), implies( implies( T, T ), Y ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.58 X, Y ) ), true ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9967, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9969, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), implies( implies( Y, T ), Y ) ) ), true,
% 44.17/44.58 'is_a_theorem'( implies( X, Y ) ), true ), true ) ) ] )
% 44.17/44.58 , clause( 601, [ =( 'is_a_theorem'( implies( implies( implies( implies( Z,
% 44.17/44.58 X ), T ), implies( implies( X, Y ), X ) ), implies( Z, X ) ) ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, clause( 9967, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, T ), :=( Z, X ), :=( T, Z )] )
% 44.17/44.58 , substitution( 1, [ :=( X, implies( implies( implies( X, Y ), Z ),
% 44.17/44.58 implies( implies( Y, T ), Y ) ) ), :=( Y, implies( X, Y ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9974, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies( X
% 44.17/44.58 , Y ), Z ), implies( implies( Y, T ), Y ) ) ), true, 'is_a_theorem'(
% 44.17/44.58 implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9969, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( implies( implies( X, Y ), Z ), implies( implies( Y, T ), Y ) ) )
% 44.17/44.58 , true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( implies( implies( X, Y ), Z ), implies( implies( Y, T ), Y ) ) )
% 44.17/44.58 , true, 'is_a_theorem'( implies( X, Y ) ), true ) ), :=( Z, true )] ),
% 44.17/44.58 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9975, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.58 , Z ), implies( implies( Y, T ), Y ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.58 X, Y ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9974, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 X, Y ), Z ), implies( implies( Y, T ), Y ) ) ), true, 'is_a_theorem'(
% 44.17/44.58 implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 705, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.58 Z ), implies( implies( Y, T ), Y ) ) ), true, 'is_a_theorem'( implies( X
% 44.17/44.58 , Y ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9975, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.58 ), Z ), implies( implies( Y, T ), Y ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.58 X, Y ) ), true ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9977, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y )
% 44.17/44.58 ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , clause( 431, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.58 true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9979, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( implies( X, Y ), Z ), implies( T, Z ) ), X ), X ) ),
% 44.17/44.58 true ) ) ] )
% 44.17/44.58 , clause( 269, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( T, Z ) ), X ), implies( U, X ) ) ), true )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, clause( 9977, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X
% 44.17/44.58 , Y ) ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.58 :=( U, implies( implies( implies( implies( X, Y ), Z ), implies( T, Z ) )
% 44.17/44.58 , X ) )] ), substitution( 1, [ :=( X, implies( implies( implies( implies(
% 44.17/44.58 X, Y ), Z ), implies( T, Z ) ), X ) ), :=( Y, X )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9981, [ =( true, 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( T, Z ) ), X ), X ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9979, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( implies( X, Y ), Z ), implies( T, Z ) ), X ),
% 44.17/44.58 X ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( implies( X, Y ), Z ), implies( T, Z ) ), X ),
% 44.17/44.58 X ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 44.17/44.58 :=( Z, Z ), :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9982, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( T, Z ) ), X ), X ) ), true ) ] )
% 44.17/44.58 , clause( 9981, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), implies( T, Z ) ), X ), X ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 723, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( T, Z ) ), X ), X ) ), true ) ] )
% 44.17/44.58 , clause( 9982, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( T, Z ) ), X ), X ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9984, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.58 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.58 )
% 44.17/44.58 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.58 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9986, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( X, implies( Y, Z ) ), T ), Z ) ), true, 'is_a_theorem'(
% 44.17/44.58 implies( X, implies( Y, Z ) ) ), true ), true ) ) ] )
% 44.17/44.58 , clause( 589, [ =( 'is_a_theorem'( implies( implies( implies( implies( Y,
% 44.17/44.58 implies( Z, X ) ), T ), X ), implies( Y, implies( Z, X ) ) ) ), true ) ]
% 44.17/44.58 )
% 44.17/44.58 , 0, clause( 9984, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true
% 44.17/44.58 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 44.17/44.58 ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T )] )
% 44.17/44.58 , substitution( 1, [ :=( X, implies( implies( implies( X, implies( Y, Z )
% 44.17/44.58 ), T ), Z ) ), :=( Y, implies( X, implies( Y, Z ) ) )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9991, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies( X
% 44.17/44.58 , implies( Y, Z ) ), T ), Z ) ), true, 'is_a_theorem'( implies( X,
% 44.17/44.58 implies( Y, Z ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9986, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( implies( implies( X, implies( Y, Z ) ), T ), Z ) ), true,
% 44.17/44.58 'is_a_theorem'( implies( X, implies( Y, Z ) ) ), true ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.58 implies( implies( implies( X, implies( Y, Z ) ), T ), Z ) ), true,
% 44.17/44.58 'is_a_theorem'( implies( X, implies( Y, Z ) ) ), true ) ), :=( Z, true )] )
% 44.17/44.58 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9992, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( Y, Z ) ), T ), Z ) ), true, 'is_a_theorem'( implies( X, implies(
% 44.17/44.58 Y, Z ) ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9991, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 X, implies( Y, Z ) ), T ), Z ) ), true, 'is_a_theorem'( implies( X,
% 44.17/44.58 implies( Y, Z ) ) ), true ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 756, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( Y, Z ) ), T ), Z ) ), true, 'is_a_theorem'( implies( X, implies(
% 44.17/44.58 Y, Z ) ) ), true ), true ) ] )
% 44.17/44.58 , clause( 9992, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.58 implies( Y, Z ) ), T ), Z ) ), true, 'is_a_theorem'( implies( X, implies(
% 44.17/44.58 Y, Z ) ) ), true ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9994, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies( X
% 44.17/44.58 , Y ), Z ), implies( implies( Y, T ), Y ) ) ), true, 'is_a_theorem'(
% 44.17/44.58 implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , clause( 705, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.58 , Z ), implies( implies( Y, T ), Y ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.58 X, Y ) ), true ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9996, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( implies( implies( implies( X, Y ), Z ), implies( X, Y ) ), T ),
% 44.17/44.58 Y ), implies( X, Y ) ) ), true ) ) ] )
% 44.17/44.58 , clause( 723, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( T, Z ) ), X ), X ) ), true ) ] )
% 44.17/44.58 , 0, clause( 9994, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( implies( Y, T ), Y ) ) ), true,
% 44.17/44.58 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, implies( implies( implies( X, Y ), Z ),
% 44.17/44.58 implies( X, Y ) ) ), :=( Y, T ), :=( Z, Y ), :=( T, X )] ),
% 44.17/44.58 substitution( 1, [ :=( X, implies( implies( implies( implies( implies( X
% 44.17/44.58 , Y ), Z ), implies( X, Y ) ), T ), Y ) ), :=( Y, implies( X, Y ) ), :=(
% 44.17/44.58 Z, implies( implies( implies( X, Y ), Z ), implies( X, Y ) ) ), :=( T, Z
% 44.17/44.58 )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 9998, [ =( true, 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), implies( X, Y ) ), T ), Y ), implies( X, Y
% 44.17/44.58 ) ) ) ) ] )
% 44.17/44.58 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.58 , 0, clause( 9996, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( implies( implies( X, Y ), Z ), implies( X, Y )
% 44.17/44.58 ), T ), Y ), implies( X, Y ) ) ), true ) ) ] )
% 44.17/44.58 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( implies( implies( X, Y ), Z ), implies( X, Y )
% 44.17/44.58 ), T ), Y ), implies( X, Y ) ) ) ), :=( Z, true )] ), substitution( 1, [
% 44.17/44.58 :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 9999, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), implies( X, Y ) ), T ), Y ), implies( X, Y
% 44.17/44.58 ) ) ), true ) ] )
% 44.17/44.58 , clause( 9998, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( implies( implies( X, Y ), Z ), implies( X, Y ) ), T ), Y ),
% 44.17/44.58 implies( X, Y ) ) ) ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 subsumption(
% 44.17/44.58 clause( 1210, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), implies( X, Y ) ), T ), Y ), implies( X, Y
% 44.17/44.58 ) ) ), true ) ] )
% 44.17/44.58 , clause( 9999, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), implies( X, Y ) ), T ), Y ), implies( X, Y
% 44.17/44.58 ) ) ), true ) ] )
% 44.17/44.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 eqswap(
% 44.17/44.58 clause( 10001, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 X, Y ), Z ), implies( implies( Y, T ), Y ) ) ), true, 'is_a_theorem'(
% 44.17/44.58 implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , clause( 705, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.58 , Z ), implies( implies( Y, T ), Y ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.58 X, Y ) ), true ), true ) ] )
% 44.17/44.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.58 ).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 10003, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.58 implies( implies( implies( implies( X, Y ), X ), Z ), implies( implies( X
% 44.17/44.58 , Y ), X ) ), X ) ), true ) ) ] )
% 44.17/44.58 , clause( 1210, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), Z ), implies( X, Y ) ), T ), Y ), implies( X, Y
% 44.17/44.58 ) ) ), true ) ] )
% 44.17/44.58 , 0, clause( 10001, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.58 implies( X, Y ), Z ), implies( implies( Y, T ), Y ) ) ), true,
% 44.17/44.58 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.58 , 0, 3, substitution( 0, [ :=( X, implies( X, Y ) ), :=( Y, X ), :=( Z, Z )
% 44.17/44.58 , :=( T, X )] ), substitution( 1, [ :=( X, implies( implies( implies(
% 44.17/44.58 implies( X, Y ), X ), Z ), implies( implies( X, Y ), X ) ) ), :=( Y, X )
% 44.17/44.58 , :=( Z, X ), :=( T, Y )] )).
% 44.17/44.58
% 44.17/44.58
% 44.17/44.58 paramod(
% 44.17/44.58 clause( 10005, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.58 implies( implies( X, Y ), X ), Z ), implies( implies( X, Y ), X ) ), X )
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10003, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( implies( X, Y ), X ), Z ), implies( implies( X
% 44.17/44.59 , Y ), X ) ), X ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( implies( X, Y ), X ), Z ), implies( implies( X
% 44.17/44.59 , Y ), X ) ), X ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ),
% 44.17/44.59 :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10006, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), X ), Z ), implies( implies( X, Y ), X ) ), X ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , clause( 10005, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( implies( X, Y ), X ), Z ), implies( implies( X, Y ), X ) ), X )
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 1211, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), X ), Z ), implies( implies( X, Y ), X ) ), X ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , clause( 10006, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), X ), Z ), implies( implies( X, Y ), X ) ), X ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10008, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.59 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.59 , true ) ) ] )
% 44.17/44.59 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.59 ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10010, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, implies( implies( implies( X, Y ), X ), Z ) ), implies( T,
% 44.17/44.59 implies( implies( implies( X, Y ), X ), Z ) ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 1211, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), X ), Z ), implies( implies( X, Y ), X ) ), X ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, clause( 10008, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.59 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 substitution( 1, [ :=( X, implies( implies( implies( X, Y ), X ), Z ) ),
% 44.17/44.59 :=( Y, implies( implies( X, Y ), X ) ), :=( Z, X ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10011, [ =( true, 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.59 implies( implies( X, Y ), X ), Z ) ), implies( T, implies( implies(
% 44.17/44.59 implies( X, Y ), X ), Z ) ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10010, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, implies( implies( implies( X, Y ), X ), Z ) ), implies( T,
% 44.17/44.59 implies( implies( implies( X, Y ), X ), Z ) ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, implies( implies( implies( X, Y ), X ), Z ) ), implies( T,
% 44.17/44.59 implies( implies( implies( X, Y ), X ), Z ) ) ) ) ), :=( Z, true )] ),
% 44.17/44.59 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10012, [ =( 'is_a_theorem'( implies( implies( X, implies( implies(
% 44.17/44.59 implies( X, Y ), X ), Z ) ), implies( T, implies( implies( implies( X, Y
% 44.17/44.59 ), X ), Z ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10011, [ =( true, 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.59 implies( implies( X, Y ), X ), Z ) ), implies( T, implies( implies(
% 44.17/44.59 implies( X, Y ), X ), Z ) ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 1219, [ =( 'is_a_theorem'( implies( implies( X, implies( implies(
% 44.17/44.59 implies( X, Y ), X ), Z ) ), implies( T, implies( implies( implies( X, Y
% 44.17/44.59 ), X ), Z ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10012, [ =( 'is_a_theorem'( implies( implies( X, implies( implies(
% 44.17/44.59 implies( X, Y ), X ), Z ) ), implies( T, implies( implies( implies( X, Y
% 44.17/44.59 ), X ), Z ) ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10014, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 X, Y ), Z ), implies( implies( T, T ), Y ) ) ), true, 'is_a_theorem'(
% 44.17/44.59 implies( X, Y ) ), true ) ) ] )
% 44.17/44.59 , clause( 702, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.59 , Z ), implies( implies( T, T ), Y ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.59 X, Y ) ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10016, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( implies( X, X ), Y ), Z ), implies( implies( X
% 44.17/44.59 , X ), Y ) ), Y ) ), true ) ) ] )
% 44.17/44.59 , clause( 1211, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), X ), Z ), implies( implies( X, Y ), X ) ), X ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, clause( 10014, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.59 implies( X, Y ), Z ), implies( implies( T, T ), Y ) ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, implies( implies( X, X ), Y ) ), :=( Y, Z
% 44.17/44.59 ), :=( Z, Y )] ), substitution( 1, [ :=( X, implies( implies( implies(
% 44.17/44.59 implies( X, X ), Y ), Z ), implies( implies( X, X ), Y ) ) ), :=( Y, Y )
% 44.17/44.59 , :=( Z, implies( implies( implies( implies( X, X ), Y ), Z ), implies(
% 44.17/44.59 implies( X, X ), Y ) ) ), :=( T, X )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10018, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( implies( X, X ), Y ), Z ), implies( implies( X, X ), Y ) ), Y )
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10016, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( implies( X, X ), Y ), Z ), implies( implies( X
% 44.17/44.59 , X ), Y ) ), Y ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( implies( X, X ), Y ), Z ), implies( implies( X
% 44.17/44.59 , X ), Y ) ), Y ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ),
% 44.17/44.59 :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10019, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( X, X ), Y ), Z ), implies( implies( X, X ), Y ) ), Y ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , clause( 10018, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( implies( X, X ), Y ), Z ), implies( implies( X, X ), Y ) ), Y )
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 1223, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( X, X ), Y ), Z ), implies( implies( X, X ), Y ) ), Y ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , clause( 10019, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( X, X ), Y ), Z ), implies( implies( X, X ), Y ) ), Y ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10021, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.59 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.59 , true ) ) ] )
% 44.17/44.59 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.59 ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10023, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( Y, implies( implies( implies( X, X ), Y ), Z ) ), implies( T,
% 44.17/44.59 implies( implies( implies( X, X ), Y ), Z ) ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 1223, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( X, X ), Y ), Z ), implies( implies( X, X ), Y ) ), Y ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, clause( 10021, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.59 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 substitution( 1, [ :=( X, implies( implies( implies( X, X ), Y ), Z ) ),
% 44.17/44.59 :=( Y, implies( implies( X, X ), Y ) ), :=( Z, Y ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10024, [ =( true, 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Y ), X ), Z ) ), implies( T, implies( implies(
% 44.17/44.59 implies( Y, Y ), X ), Z ) ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10023, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( Y, implies( implies( implies( X, X ), Y ), Z ) ), implies( T,
% 44.17/44.59 implies( implies( implies( X, X ), Y ), Z ) ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Y ), X ), Z ) ), implies( T,
% 44.17/44.59 implies( implies( implies( Y, Y ), X ), Z ) ) ) ) ), :=( Z, true )] ),
% 44.17/44.59 substitution( 1, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10025, [ =( 'is_a_theorem'( implies( implies( X, implies( implies(
% 44.17/44.59 implies( Y, Y ), X ), Z ) ), implies( T, implies( implies( implies( Y, Y
% 44.17/44.59 ), X ), Z ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10024, [ =( true, 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Y ), X ), Z ) ), implies( T, implies( implies(
% 44.17/44.59 implies( Y, Y ), X ), Z ) ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 1264, [ =( 'is_a_theorem'( implies( implies( Y, implies( implies(
% 44.17/44.59 implies( X, X ), Y ), Z ) ), implies( T, implies( implies( implies( X, X
% 44.17/44.59 ), Y ), Z ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10025, [ =( 'is_a_theorem'( implies( implies( X, implies( implies(
% 44.17/44.59 implies( Y, Y ), X ), Z ) ), implies( T, implies( implies( implies( Y, Y
% 44.17/44.59 ), X ), Z ) ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10027, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y )
% 44.17/44.59 ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.59 , clause( 431, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10029, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, implies( Y, implies( Z, implies( X, T ) ) ) ), implies( Y,
% 44.17/44.59 implies( Z, implies( X, T ) ) ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 474, [ =( 'is_a_theorem'( implies( implies( Z, implies( X,
% 44.17/44.59 implies( Y, implies( Z, T ) ) ) ), implies( U, implies( X, implies( Y,
% 44.17/44.59 implies( Z, T ) ) ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10027, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X
% 44.17/44.59 , Y ) ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T ),
% 44.17/44.59 :=( U, implies( X, implies( Y, implies( Z, implies( X, T ) ) ) ) )] ),
% 44.17/44.59 substitution( 1, [ :=( X, implies( X, implies( Y, implies( Z, implies( X
% 44.17/44.59 , T ) ) ) ) ), :=( Y, implies( Y, implies( Z, implies( X, T ) ) ) )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10031, [ =( true, 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.59 implies( Z, implies( X, T ) ) ) ), implies( Y, implies( Z, implies( X, T
% 44.17/44.59 ) ) ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10029, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, implies( Y, implies( Z, implies( X, T ) ) ) ), implies( Y,
% 44.17/44.59 implies( Z, implies( X, T ) ) ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, implies( Y, implies( Z, implies( X, T ) ) ) ), implies( Y,
% 44.17/44.59 implies( Z, implies( X, T ) ) ) ) ) ), :=( Z, true )] ), substitution( 1
% 44.17/44.59 , [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10032, [ =( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.59 implies( Z, implies( X, T ) ) ) ), implies( Y, implies( Z, implies( X, T
% 44.17/44.59 ) ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10031, [ =( true, 'is_a_theorem'( implies( implies( X, implies( Y
% 44.17/44.59 , implies( Z, implies( X, T ) ) ) ), implies( Y, implies( Z, implies( X,
% 44.17/44.59 T ) ) ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 1302, [ =( 'is_a_theorem'( implies( implies( X, implies( Y, implies(
% 44.17/44.59 Z, implies( X, T ) ) ) ), implies( Y, implies( Z, implies( X, T ) ) ) ) )
% 44.17/44.59 , true ) ] )
% 44.17/44.59 , clause( 10032, [ =( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.59 implies( Z, implies( X, T ) ) ) ), implies( Y, implies( Z, implies( X, T
% 44.17/44.59 ) ) ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10034, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.59 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10036, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.59 X, implies( Y, implies( Z, implies( X, T ) ) ) ) ), true, 'is_a_theorem'(
% 44.17/44.59 implies( Y, implies( Z, implies( X, T ) ) ) ), true ), true ) ) ] )
% 44.17/44.59 , clause( 1302, [ =( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.59 implies( Z, implies( X, T ) ) ) ), implies( Y, implies( Z, implies( X, T
% 44.17/44.59 ) ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10034, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 , substitution( 1, [ :=( X, implies( X, implies( Y, implies( Z, implies(
% 44.17/44.59 X, T ) ) ) ) ), :=( Y, implies( Y, implies( Z, implies( X, T ) ) ) )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10041, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( Y,
% 44.17/44.59 implies( Z, implies( X, T ) ) ) ) ), true, 'is_a_theorem'( implies( Y,
% 44.17/44.59 implies( Z, implies( X, T ) ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10036, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( X, implies( Y, implies( Z, implies( X, T ) ) ) ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( Y, implies( Z, implies( X, T ) ) ) ), true ),
% 44.17/44.59 true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( X, implies( Y, implies( Z, implies( X, T ) ) ) ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( Y, implies( Z, implies( X, T ) ) ) ), true ) ),
% 44.17/44.59 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.59 :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10042, [ =( ifeq( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 Z, implies( X, T ) ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( Z
% 44.17/44.59 , implies( X, T ) ) ) ), true ), true ) ] )
% 44.17/44.59 , clause( 10041, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( Y,
% 44.17/44.59 implies( Z, implies( X, T ) ) ) ) ), true, 'is_a_theorem'( implies( Y,
% 44.17/44.59 implies( Z, implies( X, T ) ) ) ), true ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 1304, [ =( ifeq( 'is_a_theorem'( implies( X, implies( Y, implies( Z
% 44.17/44.59 , implies( X, T ) ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( Z,
% 44.17/44.59 implies( X, T ) ) ) ), true ), true ) ] )
% 44.17/44.59 , clause( 10042, [ =( ifeq( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 Z, implies( X, T ) ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( Z
% 44.17/44.59 , implies( X, T ) ) ) ), true ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10044, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.59 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.59 , true ) ) ] )
% 44.17/44.59 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.59 ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10046, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( T, implies( implies( implies( Y, Y ), X ), Z ) ), X ),
% 44.17/44.59 implies( U, X ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 1264, [ =( 'is_a_theorem'( implies( implies( Y, implies( implies(
% 44.17/44.59 implies( X, X ), Y ), Z ) ), implies( T, implies( implies( implies( X, X
% 44.17/44.59 ), Y ), Z ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10044, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.59 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 , substitution( 1, [ :=( X, X ), :=( Y, implies( implies( implies( Y, Y )
% 44.17/44.59 , X ), Z ) ), :=( Z, implies( T, implies( implies( implies( Y, Y ), X ),
% 44.17/44.59 Z ) ) ), :=( T, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10048, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.59 implies( implies( implies( Y, Y ), Z ), T ) ), Z ), implies( U, Z ) ) ) )
% 44.17/44.59 ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10046, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( T, implies( implies( implies( Y, Y ), X ), Z ) ), X ),
% 44.17/44.59 implies( U, X ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Y ), Z ), T ) ), Z ),
% 44.17/44.59 implies( U, Z ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ),
% 44.17/44.59 :=( Y, Y ), :=( Z, T ), :=( T, X ), :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10049, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Y ), Z ), T ) ), Z ), implies( U, Z ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 10048, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.59 implies( implies( implies( Y, Y ), Z ), T ) ), Z ), implies( U, Z ) ) ) )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.59 :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 1324, [ =( 'is_a_theorem'( implies( implies( implies( T, implies(
% 44.17/44.59 implies( implies( Y, Y ), X ), Z ) ), X ), implies( U, X ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 10049, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Y ), Z ), T ) ), Z ), implies( U, Z ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , substitution( 0, [ :=( X, T ), :=( Y, Y ), :=( Z, X ), :=( T, Z ), :=( U
% 44.17/44.59 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10051, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y )
% 44.17/44.59 ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.59 , clause( 431, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10053, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Y ), Z ), T ) ), Z ),
% 44.17/44.59 Z ) ), true ) ) ] )
% 44.17/44.59 , clause( 1324, [ =( 'is_a_theorem'( implies( implies( implies( T, implies(
% 44.17/44.59 implies( implies( Y, Y ), X ), Z ) ), X ), implies( U, X ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, clause( 10051, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X
% 44.17/44.59 , Y ) ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, T ), :=( T, X ),
% 44.17/44.59 :=( U, implies( implies( X, implies( implies( implies( Y, Y ), Z ), T ) )
% 44.17/44.59 , Z ) )] ), substitution( 1, [ :=( X, implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Y ), Z ), T ) ), Z ) ), :=( Y, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10055, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.59 implies( implies( implies( Y, Y ), Z ), T ) ), Z ), Z ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10053, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Y ), Z ), T ) ), Z ),
% 44.17/44.59 Z ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Y ), Z ), T ) ), Z ),
% 44.17/44.59 Z ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 44.17/44.59 :=( Z, Z ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10056, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Y ), Z ), T ) ), Z ), Z ) ), true ) ] )
% 44.17/44.59 , clause( 10055, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.59 implies( implies( implies( Y, Y ), Z ), T ) ), Z ), Z ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 1369, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Y ), Z ), T ) ), Z ), Z ) ), true ) ] )
% 44.17/44.59 , clause( 10056, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Y ), Z ), T ) ), Z ), Z ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10058, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.59 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10061, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Y ), Z ), T ) ), Z ), Z ), U )
% 44.17/44.59 ), true, ifeq( true, true, 'is_a_theorem'( U ), true ), true ) ) ] )
% 44.17/44.59 , clause( 1369, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Y ), Z ), T ) ), Z ), Z ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10058, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 21, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 , substitution( 1, [ :=( X, implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Y ), Z ), T ) ), Z ), Z ) ), :=( Y, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10063, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Y ), Z ), T ) ), Z ), Z ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10061, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Y ), Z ), T ) ), Z ),
% 44.17/44.59 Z ), U ) ), true, ifeq( true, true, 'is_a_theorem'( U ), true ), true ) )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, 20, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( U ) ),
% 44.17/44.59 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.59 :=( T, T ), :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10064, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Y ), Z ), T ) ), Z ), Z ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.59 , clause( 10063, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Y ), Z ), T ) ), Z ), Z ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.59 :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 1379, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 X, implies( implies( implies( Y, Y ), Z ), T ) ), Z ), Z ), U ) ), true,
% 44.17/44.59 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.59 , clause( 10064, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Y ), Z ), T ) ), Z ), Z ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 44.17/44.59 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10066, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.59 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.59 , true ) ) ] )
% 44.17/44.59 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.59 ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10068, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( T, implies( implies( implies( X, Y ), X ), Z ) ), X ),
% 44.17/44.59 implies( U, X ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 1219, [ =( 'is_a_theorem'( implies( implies( X, implies( implies(
% 44.17/44.59 implies( X, Y ), X ), Z ) ), implies( T, implies( implies( implies( X, Y
% 44.17/44.59 ), X ), Z ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10066, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.59 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 , substitution( 1, [ :=( X, X ), :=( Y, implies( implies( implies( X, Y )
% 44.17/44.59 , X ), Z ) ), :=( Z, implies( T, implies( implies( implies( X, Y ), X ),
% 44.17/44.59 Z ) ) ), :=( T, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10070, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.59 implies( implies( implies( Y, Z ), Y ), T ) ), Y ), implies( U, Y ) ) ) )
% 44.17/44.59 ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10068, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( T, implies( implies( implies( X, Y ), X ), Z ) ), X ),
% 44.17/44.59 implies( U, X ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Z ), Y ), T ) ), Y ),
% 44.17/44.59 implies( U, Y ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ),
% 44.17/44.59 :=( Y, Z ), :=( Z, T ), :=( T, X ), :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10071, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Z ), Y ), T ) ), Y ), implies( U, Y ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 10070, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.59 implies( implies( implies( Y, Z ), Y ), T ) ), Y ), implies( U, Y ) ) ) )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.59 :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 1492, [ =( 'is_a_theorem'( implies( implies( implies( T, implies(
% 44.17/44.59 implies( implies( X, Y ), X ), Z ) ), X ), implies( U, X ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 10071, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Z ), Y ), T ) ), Y ), implies( U, Y ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z ), :=( U
% 44.17/44.59 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10073, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y )
% 44.17/44.59 ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.59 , clause( 431, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10075, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Z ), Y ), T ) ), Y ),
% 44.17/44.59 Y ) ), true ) ) ] )
% 44.17/44.59 , clause( 1492, [ =( 'is_a_theorem'( implies( implies( implies( T, implies(
% 44.17/44.59 implies( implies( X, Y ), X ), Z ) ), X ), implies( U, X ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, clause( 10073, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X
% 44.17/44.59 , Y ) ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, X ),
% 44.17/44.59 :=( U, implies( implies( X, implies( implies( implies( Y, Z ), Y ), T ) )
% 44.17/44.59 , Y ) )] ), substitution( 1, [ :=( X, implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Z ), Y ), T ) ), Y ) ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10077, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.59 implies( implies( implies( Y, Z ), Y ), T ) ), Y ), Y ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10075, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Z ), Y ), T ) ), Y ),
% 44.17/44.59 Y ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Z ), Y ), T ) ), Y ),
% 44.17/44.59 Y ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 44.17/44.59 :=( Z, Z ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10078, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Z ), Y ), T ) ), Y ), Y ) ), true ) ] )
% 44.17/44.59 , clause( 10077, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.59 implies( implies( implies( Y, Z ), Y ), T ) ), Y ), Y ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 1510, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Z ), Y ), T ) ), Y ), Y ) ), true ) ] )
% 44.17/44.59 , clause( 10078, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Z ), Y ), T ) ), Y ), Y ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10080, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.59 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10083, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Z ), Y ), T ) ), Y ), Y ), U )
% 44.17/44.59 ), true, ifeq( true, true, 'is_a_theorem'( U ), true ), true ) ) ] )
% 44.17/44.59 , clause( 1510, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Z ), Y ), T ) ), Y ), Y ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10080, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 21, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 , substitution( 1, [ :=( X, implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Z ), Y ), T ) ), Y ), Y ) ), :=( Y, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10085, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Z ), Y ), T ) ), Y ), Y ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10083, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Z ), Y ), T ) ), Y ),
% 44.17/44.59 Y ), U ) ), true, ifeq( true, true, 'is_a_theorem'( U ), true ), true ) )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, 20, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( U ) ),
% 44.17/44.59 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.59 :=( T, T ), :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10086, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Z ), Y ), T ) ), Y ), Y ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.59 , clause( 10085, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Z ), Y ), T ) ), Y ), Y ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.59 :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 1520, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 X, implies( implies( implies( Y, Z ), Y ), T ) ), Y ), Y ), U ) ), true,
% 44.17/44.59 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.59 , clause( 10086, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Z ), Y ), T ) ), Y ), Y ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 44.17/44.59 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10088, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.59 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.59 , true ) ) ] )
% 44.17/44.59 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.59 ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10090, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( T, implies( implies( implies( Y, Z ), X ), Y ) ), X ),
% 44.17/44.59 implies( U, X ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 640, [ =( 'is_a_theorem'( implies( implies( Z, implies( implies(
% 44.17/44.59 implies( X, Y ), Z ), X ) ), implies( T, implies( implies( implies( X, Y
% 44.17/44.59 ), Z ), X ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10088, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.59 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T )] )
% 44.17/44.59 , substitution( 1, [ :=( X, X ), :=( Y, implies( implies( implies( Y, Z )
% 44.17/44.59 , X ), Y ) ), :=( Z, implies( T, implies( implies( implies( Y, Z ), X ),
% 44.17/44.59 Y ) ) ), :=( T, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10092, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.59 implies( implies( implies( Y, Z ), T ), Y ) ), T ), implies( U, T ) ) ) )
% 44.17/44.59 ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10090, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( T, implies( implies( implies( Y, Z ), X ), Y ) ), X ),
% 44.17/44.59 implies( U, X ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Z ), T ), Y ) ), T ),
% 44.17/44.59 implies( U, T ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, T ),
% 44.17/44.59 :=( Y, Y ), :=( Z, Z ), :=( T, X ), :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10093, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Z ), T ), Y ) ), T ), implies( U, T ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 10092, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.59 implies( implies( implies( Y, Z ), T ), Y ) ), T ), implies( U, T ) ) ) )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.59 :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 1596, [ =( 'is_a_theorem'( implies( implies( implies( T, implies(
% 44.17/44.59 implies( implies( Y, Z ), X ), Y ) ), X ), implies( U, X ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 10093, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Z ), T ), Y ) ), T ), implies( U, T ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , substitution( 0, [ :=( X, T ), :=( Y, Y ), :=( Z, Z ), :=( T, X ), :=( U
% 44.17/44.59 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10095, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y )
% 44.17/44.59 ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.59 , clause( 431, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10097, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Z ), T ), Y ) ), T ),
% 44.17/44.59 T ) ), true ) ) ] )
% 44.17/44.59 , clause( 1596, [ =( 'is_a_theorem'( implies( implies( implies( T, implies(
% 44.17/44.59 implies( implies( Y, Z ), X ), Y ) ), X ), implies( U, X ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, clause( 10095, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X
% 44.17/44.59 , Y ) ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, Y ), :=( Z, Z ), :=( T, X ),
% 44.17/44.59 :=( U, implies( implies( X, implies( implies( implies( Y, Z ), T ), Y ) )
% 44.17/44.59 , T ) )] ), substitution( 1, [ :=( X, implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Z ), T ), Y ) ), T ) ), :=( Y, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10099, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.59 implies( implies( implies( Y, Z ), T ), Y ) ), T ), T ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10097, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Z ), T ), Y ) ), T ),
% 44.17/44.59 T ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Z ), T ), Y ) ), T ),
% 44.17/44.59 T ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 44.17/44.59 :=( Z, Z ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10100, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Z ), T ), Y ) ), T ), T ) ), true ) ] )
% 44.17/44.59 , clause( 10099, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.59 implies( implies( implies( Y, Z ), T ), Y ) ), T ), T ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 1597, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Z ), T ), Y ) ), T ), T ) ), true ) ] )
% 44.17/44.59 , clause( 10100, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Z ), T ), Y ) ), T ), T ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10102, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.59 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10105, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Z ), T ), Y ) ), T ), T ), U )
% 44.17/44.59 ), true, ifeq( true, true, 'is_a_theorem'( U ), true ), true ) ) ] )
% 44.17/44.59 , clause( 1597, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Z ), T ), Y ) ), T ), T ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10102, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 21, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 , substitution( 1, [ :=( X, implies( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, Z ), T ), Y ) ), T ), T ) ), :=( Y, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10107, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Z ), T ), Y ) ), T ), T ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10105, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Z ), T ), Y ) ), T ),
% 44.17/44.59 T ), U ) ), true, ifeq( true, true, 'is_a_theorem'( U ), true ), true ) )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, 20, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( U ) ),
% 44.17/44.59 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.59 :=( T, T ), :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10108, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Z ), T ), Y ) ), T ), T ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.59 , clause( 10107, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Z ), T ), Y ) ), T ), T ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.59 :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 1607, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 X, implies( implies( implies( Y, Z ), T ), Y ) ), T ), T ), U ) ), true,
% 44.17/44.59 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.59 , clause( 10108, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Z ), T ), Y ) ), T ), T ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 44.17/44.59 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10110, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Y ), Z ), T ) ), Z ), Z ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.59 , clause( 1379, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Y ), Z ), T ) ), Z ), Z ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.59 :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10112, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, Y ), implies( implies( implies( Z, Z ), X ), Y ) ) ), true )
% 44.17/44.59 ) ] )
% 44.17/44.59 , clause( 671, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), implies( Z, Y ) ), T ), X ), implies( implies( X, Y ),
% 44.17/44.59 implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10110, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Y ), Z ), T ) ), Z ),
% 44.17/44.59 Z ), U ) ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( implies(
% 44.17/44.59 Z, Z ), X ) ), :=( T, X )] ), substitution( 1, [ :=( X, implies( X, Y ) )
% 44.17/44.59 , :=( Y, Z ), :=( Z, X ), :=( T, Y ), :=( U, implies( implies( X, Y ),
% 44.17/44.59 implies( implies( implies( Z, Z ), X ), Y ) ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10114, [ =( true, 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.59 implies( implies( Z, Z ), X ), Y ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10112, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, Y ), implies( implies( implies( Z, Z ), X ), Y ) ) ), true )
% 44.17/44.59 ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, Y ), implies( implies( implies( Z, Z ), X ), Y ) ) ) ), :=( Z
% 44.17/44.59 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10115, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.59 implies( implies( Z, Z ), X ), Y ) ) ), true ) ] )
% 44.17/44.59 , clause( 10114, [ =( true, 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.59 implies( implies( implies( Z, Z ), X ), Y ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2102, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.59 implies( implies( Z, Z ), X ), Y ) ) ), true ) ] )
% 44.17/44.59 , clause( 10115, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.59 implies( implies( Z, Z ), X ), Y ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10117, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Z ), implies( Y, Z ) ), T ) ), true, 'is_a_theorem'( T )
% 44.17/44.59 , true ) ) ] )
% 44.17/44.59 , clause( 266, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Z ), implies( Y, Z ) ), T ) ), true, 'is_a_theorem'( T )
% 44.17/44.59 , true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10119, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( T, T ), implies( implies( X, Y ), Z ) ), implies( Y, Z
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 2102, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.59 implies( implies( Z, Z ), X ), Y ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10117, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.59 implies( implies( X, Y ), Z ), implies( Y, Z ) ), T ) ), true,
% 44.17/44.59 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, implies( implies( X, Y ), Z ) ), :=( Y,
% 44.17/44.59 implies( Y, Z ) ), :=( Z, T )] ), substitution( 1, [ :=( X, X ), :=( Y, Y
% 44.17/44.59 ), :=( Z, Z ), :=( T, implies( implies( implies( T, T ), implies(
% 44.17/44.59 implies( X, Y ), Z ) ), implies( Y, Z ) ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10121, [ =( true, 'is_a_theorem'( implies( implies( implies( X, X )
% 44.17/44.59 , implies( implies( Y, Z ), T ) ), implies( Z, T ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10119, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( T, T ), implies( implies( X, Y ), Z ) ), implies( Y, Z
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, X ), implies( implies( Y, Z ), T ) ), implies( Z, T
% 44.17/44.59 ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ),
% 44.17/44.59 :=( Z, T ), :=( T, X )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10122, [ =( 'is_a_theorem'( implies( implies( implies( X, X ),
% 44.17/44.59 implies( implies( Y, Z ), T ) ), implies( Z, T ) ) ), true ) ] )
% 44.17/44.59 , clause( 10121, [ =( true, 'is_a_theorem'( implies( implies( implies( X, X
% 44.17/44.59 ), implies( implies( Y, Z ), T ) ), implies( Z, T ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2134, [ =( 'is_a_theorem'( implies( implies( implies( T, T ),
% 44.17/44.59 implies( implies( X, Y ), Z ) ), implies( Y, Z ) ) ), true ) ] )
% 44.17/44.59 , clause( 10122, [ =( 'is_a_theorem'( implies( implies( implies( X, X ),
% 44.17/44.59 implies( implies( Y, Z ), T ) ), implies( Z, T ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10124, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.59 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10126, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, X ), implies( implies( Y, Z ), T ) ) ), true, 'is_a_theorem'(
% 44.17/44.59 implies( Z, T ) ), true ), true ) ) ] )
% 44.17/44.59 , clause( 2134, [ =( 'is_a_theorem'( implies( implies( implies( T, T ),
% 44.17/44.59 implies( implies( X, Y ), Z ) ), implies( Y, Z ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10124, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, X )] )
% 44.17/44.59 , substitution( 1, [ :=( X, implies( implies( X, X ), implies( implies( Y
% 44.17/44.59 , Z ), T ) ) ), :=( Y, implies( Z, T ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10131, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X ),
% 44.17/44.59 implies( implies( Y, Z ), T ) ) ), true, 'is_a_theorem'( implies( Z, T )
% 44.17/44.59 ), true ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10126, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( implies( X, X ), implies( implies( Y, Z ), T ) ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( Z, T ) ), true ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( implies( X, X ), implies( implies( Y, Z ), T ) ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( Z, T ) ), true ) ), :=( Z, true )] ),
% 44.17/44.59 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10132, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ), implies(
% 44.17/44.59 implies( Y, Z ), T ) ) ), true, 'is_a_theorem'( implies( Z, T ) ), true )
% 44.17/44.59 , true ) ] )
% 44.17/44.59 , clause( 10131, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X )
% 44.17/44.59 , implies( implies( Y, Z ), T ) ) ), true, 'is_a_theorem'( implies( Z, T
% 44.17/44.59 ) ), true ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2161, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ), implies(
% 44.17/44.59 implies( Y, Z ), T ) ) ), true, 'is_a_theorem'( implies( Z, T ) ), true )
% 44.17/44.59 , true ) ] )
% 44.17/44.59 , clause( 10132, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ),
% 44.17/44.59 implies( implies( Y, Z ), T ) ) ), true, 'is_a_theorem'( implies( Z, T )
% 44.17/44.59 ), true ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10134, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Z ), Y ), T ) ), Y ), Y ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.59 , clause( 1520, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Z ), Y ), T ) ), Y ), Y ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.59 :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10136, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, Y ), implies( implies( implies( X, Z ), X ), Y ) ) ), true )
% 44.17/44.59 ) ] )
% 44.17/44.59 , clause( 671, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), implies( Z, Y ) ), T ), X ), implies( implies( X, Y ),
% 44.17/44.59 implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10134, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Z ), Y ), T ) ), Y ),
% 44.17/44.59 Y ), U ) ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( implies(
% 44.17/44.59 X, Z ), X ) ), :=( T, X )] ), substitution( 1, [ :=( X, implies( X, Y ) )
% 44.17/44.59 , :=( Y, X ), :=( Z, Z ), :=( T, Y ), :=( U, implies( implies( X, Y ),
% 44.17/44.59 implies( implies( implies( X, Z ), X ), Y ) ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10138, [ =( true, 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.59 implies( implies( X, Z ), X ), Y ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10136, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, Y ), implies( implies( implies( X, Z ), X ), Y ) ) ), true )
% 44.17/44.59 ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, Y ), implies( implies( implies( X, Z ), X ), Y ) ) ) ), :=( Z
% 44.17/44.59 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10139, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.59 implies( implies( X, Z ), X ), Y ) ) ), true ) ] )
% 44.17/44.59 , clause( 10138, [ =( true, 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.59 implies( implies( implies( X, Z ), X ), Y ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2341, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.59 implies( implies( X, Z ), X ), Y ) ) ), true ) ] )
% 44.17/44.59 , clause( 10139, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.59 implies( implies( X, Z ), X ), Y ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10141, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.59 implies( implies( X, Y ), implies( Z, Y ) ) ), T ) ), true,
% 44.17/44.59 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.59 , clause( 271, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.59 implies( X, Y ), implies( Z, Y ) ) ), T ) ), true, 'is_a_theorem'( T ),
% 44.17/44.59 true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10143, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, T ), X ), implies( implies( X, Y ), implies( Z, Y )
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 2341, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.59 implies( implies( X, Z ), X ), Y ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10141, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.59 implies( implies( X, Y ), implies( Z, Y ) ) ), T ) ), true,
% 44.17/44.59 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, implies( implies( X, Y ),
% 44.17/44.59 implies( Z, Y ) ) ), :=( Z, T )] ), substitution( 1, [ :=( X, X ), :=( Y
% 44.17/44.59 , Y ), :=( Z, Z ), :=( T, implies( implies( implies( X, T ), X ), implies(
% 44.17/44.59 implies( X, Y ), implies( Z, Y ) ) ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10145, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.59 , X ), implies( implies( X, Z ), implies( T, Z ) ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10143, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, T ), X ), implies( implies( X, Y ), implies( Z, Y )
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, Y ), X ), implies( implies( X, Z ), implies( T, Z )
% 44.17/44.59 ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Z ),
% 44.17/44.59 :=( Z, T ), :=( T, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10146, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X )
% 44.17/44.59 , implies( implies( X, Z ), implies( T, Z ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10145, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.59 ), X ), implies( implies( X, Z ), implies( T, Z ) ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2352, [ =( 'is_a_theorem'( implies( implies( implies( X, T ), X ),
% 44.17/44.59 implies( implies( X, Y ), implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10146, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X
% 44.17/44.59 ), implies( implies( X, Z ), implies( T, Z ) ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, T ), :=( Z, Y ), :=( T, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10148, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.59 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10150, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.59 X, Y ) ), true, 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y
% 44.17/44.59 ) ), true ), true ) ) ] )
% 44.17/44.59 , clause( 2341, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.59 implies( implies( X, Z ), X ), Y ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10148, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 substitution( 1, [ :=( X, implies( X, Y ) ), :=( Y, implies( implies(
% 44.17/44.59 implies( X, Z ), X ), Y ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10155, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10150, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( X, Y ) ), true, 'is_a_theorem'( implies( implies( implies( X, Z
% 44.17/44.59 ), X ), Y ) ), true ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( X, Y ) ), true, 'is_a_theorem'( implies( implies( implies( X, Z
% 44.17/44.59 ), X ), Y ) ), true ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X )
% 44.17/44.59 , :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10156, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true ),
% 44.17/44.59 true ) ] )
% 44.17/44.59 , clause( 10155, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2359, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true ),
% 44.17/44.59 true ) ] )
% 44.17/44.59 , clause( 10156, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true ),
% 44.17/44.59 true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10158, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 X, implies( Y, Z ) ), T ), Z ) ), true, 'is_a_theorem'( implies( X,
% 44.17/44.59 implies( Y, Z ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 756, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.59 implies( Y, Z ) ), T ), Z ) ), true, 'is_a_theorem'( implies( X, implies(
% 44.17/44.59 Y, Z ) ) ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10160, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X,
% 44.17/44.59 implies( Y, implies( implies( X, Z ), implies( T, Z ) ) ) ) ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 2352, [ =( 'is_a_theorem'( implies( implies( implies( X, T ), X )
% 44.17/44.59 , implies( implies( X, Y ), implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10158, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.59 implies( X, implies( Y, Z ) ), T ), Z ) ), true, 'is_a_theorem'( implies(
% 44.17/44.59 X, implies( Y, Z ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, T ), :=( T,
% 44.17/44.59 implies( Y, implies( implies( X, Z ), implies( T, Z ) ) ) )] ),
% 44.17/44.59 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( implies( X, Z
% 44.17/44.59 ), implies( T, Z ) ) ), :=( T, X )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10162, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( X, Z ), implies( T, Z ) ) ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10160, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X
% 44.17/44.59 , implies( Y, implies( implies( X, Z ), implies( T, Z ) ) ) ) ), true ) )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.59 , implies( Y, implies( implies( X, Z ), implies( T, Z ) ) ) ) ) ), :=( Z
% 44.17/44.59 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T
% 44.17/44.59 , T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10163, [ =( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( X, Z ), implies( T, Z ) ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10162, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( X, Z ), implies( T, Z ) ) ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2362, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( implies(
% 44.17/44.59 X, Z ), implies( T, Z ) ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10163, [ =( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( X, Z ), implies( T, Z ) ) ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10165, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.59 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.59 , true ) ) ] )
% 44.17/44.59 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.59 ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10167, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Z ), implies( T, Z ) ), implies( X, Y ) ),
% 44.17/44.59 implies( U, implies( X, Y ) ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 2352, [ =( 'is_a_theorem'( implies( implies( implies( X, T ), X )
% 44.17/44.59 , implies( implies( X, Y ), implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10165, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.59 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, T ), :=( T, Y )] )
% 44.17/44.59 , substitution( 1, [ :=( X, implies( X, Y ) ), :=( Y, X ), :=( Z, implies(
% 44.17/44.59 implies( X, Z ), implies( T, Z ) ) ), :=( T, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10169, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), implies( Z, Y ) ), implies( X, T ) ), implies( U,
% 44.17/44.59 implies( X, T ) ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10167, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Z ), implies( T, Z ) ), implies( X, Y ) ),
% 44.17/44.59 implies( U, implies( X, Y ) ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), implies( Z, Y ) ), implies( X, T ) ),
% 44.17/44.59 implies( U, implies( X, T ) ) ) ) ), :=( Z, true )] ), substitution( 1, [
% 44.17/44.59 :=( X, X ), :=( Y, T ), :=( Z, Y ), :=( T, Z ), :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10170, [ =( 'is_a_theorem'( implies( implies( implies( implies( X,
% 44.17/44.59 Y ), implies( Z, Y ) ), implies( X, T ) ), implies( U, implies( X, T ) )
% 44.17/44.59 ) ), true ) ] )
% 44.17/44.59 , clause( 10169, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), implies( Z, Y ) ), implies( X, T ) ), implies( U,
% 44.17/44.59 implies( X, T ) ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.59 :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2366, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Z
% 44.17/44.59 ), implies( T, Z ) ), implies( X, Y ) ), implies( U, implies( X, Y ) ) )
% 44.17/44.59 ), true ) ] )
% 44.17/44.59 , clause( 10170, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.59 , Y ), implies( Z, Y ) ), implies( X, T ) ), implies( U, implies( X, T )
% 44.17/44.59 ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, T ), :=( T, Y ), :=( U
% 44.17/44.59 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10172, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 2359, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true ),
% 44.17/44.59 true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10174, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, U ), X ), implies( Y, implies( implies( X, Z ),
% 44.17/44.59 implies( T, Z ) ) ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 2362, [ =( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( X, Z ), implies( T, Z ) ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10172, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 , substitution( 1, [ :=( X, X ), :=( Y, implies( Y, implies( implies( X,
% 44.17/44.59 Z ), implies( T, Z ) ) ) ), :=( Z, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10176, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.59 , X ), implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10174, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, U ), X ), implies( Y, implies( implies( X, Z ),
% 44.17/44.59 implies( T, Z ) ) ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, Y ), X ), implies( Z, implies( implies( X, T ),
% 44.17/44.59 implies( U, T ) ) ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X
% 44.17/44.59 ), :=( Y, Z ), :=( Z, T ), :=( T, U ), :=( U, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10177, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X )
% 44.17/44.59 , implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 10176, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.59 ), X ), implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) ) )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.59 :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2398, [ =( 'is_a_theorem'( implies( implies( implies( X, U ), X ),
% 44.17/44.59 implies( Y, implies( implies( X, Z ), implies( T, Z ) ) ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 10177, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X
% 44.17/44.59 ), implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, U ), :=( Z, Y ), :=( T, Z ), :=( U
% 44.17/44.59 , T )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10179, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 X, implies( Y, Z ) ), T ), Z ) ), true, 'is_a_theorem'( implies( X,
% 44.17/44.59 implies( Y, Z ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 756, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.59 implies( Y, Z ) ), T ), Z ) ), true, 'is_a_theorem'( implies( X, implies(
% 44.17/44.59 Y, Z ) ) ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10181, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X,
% 44.17/44.59 implies( Y, implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) )
% 44.17/44.59 ), true ) ) ] )
% 44.17/44.59 , clause( 2398, [ =( 'is_a_theorem'( implies( implies( implies( X, U ), X )
% 44.17/44.59 , implies( Y, implies( implies( X, Z ), implies( T, Z ) ) ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, clause( 10179, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.59 implies( X, implies( Y, Z ) ), T ), Z ) ), true, 'is_a_theorem'( implies(
% 44.17/44.59 X, implies( Y, Z ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, T ), :=( T, U ),
% 44.17/44.59 :=( U, implies( Y, implies( Z, implies( implies( X, T ), implies( U, T )
% 44.17/44.59 ) ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( Z
% 44.17/44.59 , implies( implies( X, T ), implies( U, T ) ) ) ), :=( T, X )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10183, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 Z, implies( implies( X, T ), implies( U, T ) ) ) ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10181, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X
% 44.17/44.59 , implies( Y, implies( Z, implies( implies( X, T ), implies( U, T ) ) ) )
% 44.17/44.59 ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.59 , implies( Y, implies( Z, implies( implies( X, T ), implies( U, T ) ) ) )
% 44.17/44.59 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=(
% 44.17/44.59 Z, Z ), :=( T, T ), :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10184, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z,
% 44.17/44.59 implies( implies( X, T ), implies( U, T ) ) ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10183, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 Z, implies( implies( X, T ), implies( U, T ) ) ) ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.59 :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2403, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z,
% 44.17/44.59 implies( implies( X, T ), implies( U, T ) ) ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10184, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z,
% 44.17/44.59 implies( implies( X, T ), implies( U, T ) ) ) ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 44.17/44.59 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10186, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.59 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10189, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.59 implies( Y, implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) )
% 44.17/44.59 , W ) ), true, ifeq( true, true, 'is_a_theorem'( W ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 2403, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( Z,
% 44.17/44.59 implies( implies( X, T ), implies( U, T ) ) ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10186, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 21, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )
% 44.17/44.59 , :=( U, U )] ), substitution( 1, [ :=( X, implies( X, implies( Y,
% 44.17/44.59 implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) ) ), :=( Y, W
% 44.17/44.59 )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10191, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.59 implies( Y, implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) )
% 44.17/44.59 , W ) ), true, 'is_a_theorem'( W ), true ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10189, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.59 implies( Y, implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) )
% 44.17/44.59 , W ) ), true, ifeq( true, true, 'is_a_theorem'( W ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, 20, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( W ) ),
% 44.17/44.59 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.59 :=( T, T ), :=( U, U ), :=( W, W )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10192, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.59 implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) ), W ) ),
% 44.17/44.59 true, 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.59 , clause( 10191, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.59 implies( Y, implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) )
% 44.17/44.59 , W ) ), true, 'is_a_theorem'( W ), true ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.59 :=( U, U ), :=( W, W )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2422, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.59 implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) ), W ) ),
% 44.17/44.59 true, 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.59 , clause( 10192, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y
% 44.17/44.59 , implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) ), W ) ),
% 44.17/44.59 true, 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 44.17/44.59 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10194, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 X, implies( X, Y ) ), implies( Z, implies( X, Y ) ) ), T ) ), true,
% 44.17/44.59 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.59 , clause( 191, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.59 implies( X, Y ) ), implies( Z, implies( X, Y ) ) ), T ) ), true,
% 44.17/44.59 'is_a_theorem'( T ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10196, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Z,
% 44.17/44.59 implies( X, implies( implies( X, Y ), Y ) ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 2366, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.59 , Z ), implies( T, Z ) ), implies( X, Y ) ), implies( U, implies( X, Y )
% 44.17/44.59 ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10194, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.59 implies( X, implies( X, Y ) ), implies( Z, implies( X, Y ) ) ), T ) ),
% 44.17/44.59 true, 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, implies( implies( X, Y ), Y )
% 44.17/44.59 ), :=( Z, Y ), :=( T, implies( X, Y ) ), :=( U, Z )] ), substitution( 1
% 44.17/44.59 , [ :=( X, implies( X, Y ) ), :=( Y, Y ), :=( Z, X ), :=( T, implies( Z,
% 44.17/44.59 implies( X, implies( implies( X, Y ), Y ) ) ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10198, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( Y, Z ), Z ) ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10196, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Z
% 44.17/44.59 , implies( X, implies( implies( X, Y ), Y ) ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.59 , implies( Y, implies( implies( Y, Z ), Z ) ) ) ) ), :=( Z, true )] ),
% 44.17/44.59 substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10199, [ =( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( Y, Z ), Z ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10198, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( Y, Z ), Z ) ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2467, [ =( 'is_a_theorem'( implies( Z, implies( X, implies( implies(
% 44.17/44.59 X, Y ), Y ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10199, [ =( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( Y, Z ), Z ) ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10201, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y )
% 44.17/44.59 ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.59 , clause( 431, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10203, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), implies( Z, Y ) ), implies( X, T ) ),
% 44.17/44.59 implies( X, T ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 2366, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.59 , Z ), implies( T, Z ) ), implies( X, Y ) ), implies( U, implies( X, Y )
% 44.17/44.59 ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10201, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X
% 44.17/44.59 , Y ) ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, T ), :=( Z, Y ), :=( T, Z ),
% 44.17/44.59 :=( U, implies( implies( implies( X, Y ), implies( Z, Y ) ), implies( X,
% 44.17/44.59 T ) ) )] ), substitution( 1, [ :=( X, implies( implies( implies( X, Y ),
% 44.17/44.59 implies( Z, Y ) ), implies( X, T ) ) ), :=( Y, implies( X, T ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10205, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), implies( Z, Y ) ), implies( X, T ) ), implies( X, T ) )
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10203, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), implies( Z, Y ) ), implies( X, T ) ),
% 44.17/44.59 implies( X, T ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), implies( Z, Y ) ), implies( X, T ) ),
% 44.17/44.59 implies( X, T ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ),
% 44.17/44.59 :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10206, [ =( 'is_a_theorem'( implies( implies( implies( implies( X,
% 44.17/44.59 Y ), implies( Z, Y ) ), implies( X, T ) ), implies( X, T ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 10205, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), implies( Z, Y ) ), implies( X, T ) ), implies( X, T ) )
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2468, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.59 ), implies( Z, Y ) ), implies( X, T ) ), implies( X, T ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 10206, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.59 , Y ), implies( Z, Y ) ), implies( X, T ) ), implies( X, T ) ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10208, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Z ), T ), Y ) ), T ), T ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.59 , clause( 1607, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Z ), T ), Y ) ), T ), T ), U )
% 44.17/44.59 ), true, 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.59 :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10210, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( U,
% 44.17/44.59 implies( implies( U, W ), W ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 2467, [ =( 'is_a_theorem'( implies( Z, implies( X, implies(
% 44.17/44.59 implies( X, Y ), Y ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10208, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.59 implies( implies( X, implies( implies( implies( Y, Z ), T ), Y ) ), T ),
% 44.17/44.59 T ), U ) ), true, 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, U ), :=( Y, W ), :=( Z, implies( implies(
% 44.17/44.59 implies( X, implies( implies( implies( Y, Z ), T ), Y ) ), T ), T ) )] )
% 44.17/44.59 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=(
% 44.17/44.59 U, implies( U, implies( implies( U, W ), W ) ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10212, [ =( true, 'is_a_theorem'( implies( X, implies( implies( X,
% 44.17/44.59 Y ), Y ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10210, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( U
% 44.17/44.59 , implies( implies( U, W ), W ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.59 , implies( implies( X, Y ), Y ) ) ) ), :=( Z, true )] ), substitution( 1
% 44.17/44.59 , [ :=( X, Z ), :=( Y, T ), :=( Z, U ), :=( T, W ), :=( U, X ), :=( W, Y
% 44.17/44.59 )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10213, [ =( 'is_a_theorem'( implies( X, implies( implies( X, Y ), Y
% 44.17/44.59 ) ) ), true ) ] )
% 44.17/44.59 , clause( 10212, [ =( true, 'is_a_theorem'( implies( X, implies( implies( X
% 44.17/44.59 , Y ), Y ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2474, [ =( 'is_a_theorem'( implies( U, implies( implies( U, W ), W
% 44.17/44.59 ) ) ), true ) ] )
% 44.17/44.59 , clause( 10213, [ =( 'is_a_theorem'( implies( X, implies( implies( X, Y )
% 44.17/44.59 , Y ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, U ), :=( Y, W )] ), permutation( 0, [ ==>( 0, 0
% 44.17/44.59 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10215, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X ),
% 44.17/44.59 implies( implies( Y, Z ), T ) ) ), true, 'is_a_theorem'( implies( Z, T )
% 44.17/44.59 ), true ) ) ] )
% 44.17/44.59 , clause( 2161, [ =( ifeq( 'is_a_theorem'( implies( implies( X, X ),
% 44.17/44.59 implies( implies( Y, Z ), T ) ) ), true, 'is_a_theorem'( implies( Z, T )
% 44.17/44.59 ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10217, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Z,
% 44.17/44.59 implies( implies( implies( Y, Z ), T ), T ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 2467, [ =( 'is_a_theorem'( implies( Z, implies( X, implies(
% 44.17/44.59 implies( X, Y ), Y ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10215, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, X
% 44.17/44.59 ), implies( implies( Y, Z ), T ) ) ), true, 'is_a_theorem'( implies( Z,
% 44.17/44.59 T ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, implies( Y, Z ) ), :=( Y, T ), :=( Z,
% 44.17/44.59 implies( X, X ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z
% 44.17/44.59 ), :=( T, implies( implies( implies( Y, Z ), T ), T ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10219, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.59 implies( Y, X ), Z ), Z ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10217, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Z
% 44.17/44.59 , implies( implies( implies( Y, Z ), T ), T ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.59 , implies( implies( implies( Y, X ), Z ), Z ) ) ) ), :=( Z, true )] ),
% 44.17/44.59 substitution( 1, [ :=( X, T ), :=( Y, Y ), :=( Z, X ), :=( T, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10220, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.59 Y, X ), Z ), Z ) ) ), true ) ] )
% 44.17/44.59 , clause( 10219, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.59 implies( Y, X ), Z ), Z ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2477, [ =( 'is_a_theorem'( implies( Z, implies( implies( implies( Y
% 44.17/44.59 , Z ), T ), T ) ) ), true ) ] )
% 44.17/44.59 , clause( 10220, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.59 Y, X ), Z ), Z ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10222, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 2359, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true ),
% 44.17/44.59 true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10224, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, Z ), X ), implies( implies( X, Y ), Y ) ) ), true )
% 44.17/44.59 ) ] )
% 44.17/44.59 , clause( 2474, [ =( 'is_a_theorem'( implies( U, implies( implies( U, W ),
% 44.17/44.59 W ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10222, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, U ), :=( Z, W ), :=( T, V0 )
% 44.17/44.59 , :=( U, X ), :=( W, Y )] ), substitution( 1, [ :=( X, X ), :=( Y,
% 44.17/44.59 implies( implies( X, Y ), Y ) ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10226, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.59 , X ), implies( implies( X, Z ), Z ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10224, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, Z ), X ), implies( implies( X, Y ), Y ) ) ), true )
% 44.17/44.59 ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, Y ), X ), implies( implies( X, Z ), Z ) ) ) ), :=( Z
% 44.17/44.59 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10227, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X )
% 44.17/44.59 , implies( implies( X, Z ), Z ) ) ), true ) ] )
% 44.17/44.59 , clause( 10226, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.59 ), X ), implies( implies( X, Z ), Z ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2489, [ =( 'is_a_theorem'( implies( implies( implies( X, Z ), X ),
% 44.17/44.59 implies( implies( X, Y ), Y ) ) ), true ) ] )
% 44.17/44.59 , clause( 10227, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X
% 44.17/44.59 ), implies( implies( X, Z ), Z ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10229, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( implies( Y, Z ), X ), Y ) ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 603, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( implies( Y, Z ), X ), Y ) ), true ),
% 44.17/44.59 true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10231, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( implies( X, Y ), Y ), Z ), X ), implies(
% 44.17/44.59 implies( X, Y ), Y ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 2474, [ =( 'is_a_theorem'( implies( U, implies( implies( U, W ),
% 44.17/44.59 W ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10229, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( implies( implies( Y, Z ), X ), Y ) ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, U ), :=( Z, W ), :=( T, V0 )
% 44.17/44.59 , :=( U, X ), :=( W, Y )] ), substitution( 1, [ :=( X, X ), :=( Y,
% 44.17/44.59 implies( implies( X, Y ), Y ) ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10232, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( implies( X, Y ), Y ), Z ), X ), implies( implies( X, Y ), Y ) )
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10231, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( implies( X, Y ), Y ), Z ), X ), implies(
% 44.17/44.59 implies( X, Y ), Y ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( implies( X, Y ), Y ), Z ), X ), implies(
% 44.17/44.59 implies( X, Y ), Y ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X
% 44.17/44.59 ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10233, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ), X ), implies( implies( X, Y ), Y ) ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , clause( 10232, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( implies( X, Y ), Y ), Z ), X ), implies( implies( X, Y ), Y ) )
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2496, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ), X ), implies( implies( X, Y ), Y ) ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , clause( 10233, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ), X ), implies( implies( X, Y ), Y ) ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10235, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.59 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10238, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.59 implies( implies( implies( Y, X ), Z ), Z ) ), T ) ), true, ifeq( true,
% 44.17/44.59 true, 'is_a_theorem'( T ), true ), true ) ) ] )
% 44.17/44.59 , clause( 2477, [ =( 'is_a_theorem'( implies( Z, implies( implies( implies(
% 44.17/44.59 Y, Z ), T ), T ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10235, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 17, substitution( 0, [ :=( X, U ), :=( Y, Y ), :=( Z, X ), :=( T, Z )] )
% 44.17/44.59 , substitution( 1, [ :=( X, implies( X, implies( implies( implies( Y, X )
% 44.17/44.59 , Z ), Z ) ) ), :=( Y, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10240, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.59 implies( implies( implies( Y, X ), Z ), Z ) ), T ) ), true,
% 44.17/44.59 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10238, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.59 implies( implies( implies( Y, X ), Z ), Z ) ), T ) ), true, ifeq( true,
% 44.17/44.59 true, 'is_a_theorem'( T ), true ), true ) ) ] )
% 44.17/44.59 , 0, 16, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( T ) ),
% 44.17/44.59 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.59 :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10241, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, X ), Z ), Z ) ), T ) ), true, 'is_a_theorem'( T ),
% 44.17/44.59 true ), true ) ] )
% 44.17/44.59 , clause( 10240, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.59 implies( implies( implies( Y, X ), Z ), Z ) ), T ) ), true,
% 44.17/44.59 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2606, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, X ), Z ), Z ) ), T ) ), true, 'is_a_theorem'( T ),
% 44.17/44.59 true ), true ) ] )
% 44.17/44.59 , clause( 10241, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.59 implies( implies( Y, X ), Z ), Z ) ), T ) ), true, 'is_a_theorem'( T ),
% 44.17/44.59 true ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10243, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 X, implies( Y, Z ) ), T ), Z ) ), true, 'is_a_theorem'( implies( X,
% 44.17/44.59 implies( Y, Z ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 756, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.59 implies( Y, Z ) ), T ), Z ) ), true, 'is_a_theorem'( implies( X, implies(
% 44.17/44.59 Y, Z ) ) ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10245, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X,
% 44.17/44.59 implies( Y, implies( implies( X, Z ), Z ) ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 2489, [ =( 'is_a_theorem'( implies( implies( implies( X, Z ), X )
% 44.17/44.59 , implies( implies( X, Y ), Y ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10243, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.59 implies( X, implies( Y, Z ) ), T ), Z ) ), true, 'is_a_theorem'( implies(
% 44.17/44.59 X, implies( Y, Z ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, implies( Y,
% 44.17/44.59 implies( implies( X, Z ), Z ) ) )] ), substitution( 1, [ :=( X, X ), :=(
% 44.17/44.59 Y, Y ), :=( Z, implies( implies( X, Z ), Z ) ), :=( T, X )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10247, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( X, Z ), Z ) ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10245, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X
% 44.17/44.59 , implies( Y, implies( implies( X, Z ), Z ) ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.59 , implies( Y, implies( implies( X, Z ), Z ) ) ) ) ), :=( Z, true )] ),
% 44.17/44.59 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10248, [ =( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( X, Z ), Z ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10247, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( X, Z ), Z ) ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2791, [ =( 'is_a_theorem'( implies( X, implies( Y, implies( implies(
% 44.17/44.59 X, Z ), Z ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10248, [ =( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( X, Z ), Z ) ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10250, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.59 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.59 , true ) ) ] )
% 44.17/44.59 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.59 ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10252, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Z ), Z ), implies( X, Y ) ), implies( T,
% 44.17/44.59 implies( X, Y ) ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 2489, [ =( 'is_a_theorem'( implies( implies( implies( X, Z ), X )
% 44.17/44.59 , implies( implies( X, Y ), Y ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10250, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.59 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 44.17/44.59 substitution( 1, [ :=( X, implies( X, Y ) ), :=( Y, X ), :=( Z, implies(
% 44.17/44.59 implies( X, Z ), Z ) ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10254, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), implies( X, Z ) ), implies( T, implies( X, Z ) ) )
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10252, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Z ), Z ), implies( X, Y ) ), implies( T,
% 44.17/44.59 implies( X, Y ) ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), implies( X, Z ) ), implies( T,
% 44.17/44.59 implies( X, Z ) ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X )
% 44.17/44.59 , :=( Y, Z ), :=( Z, Y ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10255, [ =( 'is_a_theorem'( implies( implies( implies( implies( X,
% 44.17/44.59 Y ), Y ), implies( X, Z ) ), implies( T, implies( X, Z ) ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 10254, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), implies( X, Z ) ), implies( T, implies( X, Z ) ) )
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2799, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Z
% 44.17/44.59 ), Z ), implies( X, Y ) ), implies( T, implies( X, Y ) ) ) ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 10255, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.59 , Y ), Y ), implies( X, Z ) ), implies( T, implies( X, Z ) ) ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10257, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.59 ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ) ) ] )
% 44.17/44.59 , clause( 265, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( Y, Z ) ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10259, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Y,
% 44.17/44.59 implies( Z, implies( implies( implies( X, Y ), T ), T ) ) ) ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 2791, [ =( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( X, Z ), Z ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10257, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.59 ), Z ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, implies( X, Y ) ), :=( Y, Z ), :=( Z, T )] )
% 44.17/44.59 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( Z, implies(
% 44.17/44.59 implies( implies( X, Y ), T ), T ) ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10261, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( implies( Z, X ), T ), T ) ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10259, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Y
% 44.17/44.59 , implies( Z, implies( implies( implies( X, Y ), T ), T ) ) ) ), true ) )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.59 , implies( Y, implies( implies( implies( Z, X ), T ), T ) ) ) ) ), :=( Z
% 44.17/44.59 , true )] ), substitution( 1, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T
% 44.17/44.59 , T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10262, [ =( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( implies( Z, X ), T ), T ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10261, [ =( true, 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( implies( Z, X ), T ), T ) ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2822, [ =( 'is_a_theorem'( implies( Y, implies( Z, implies( implies(
% 44.17/44.59 implies( X, Y ), T ), T ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10262, [ =( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( implies( Z, X ), T ), T ) ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10264, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.59 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10267, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.59 implies( Y, implies( implies( implies( Z, X ), T ), T ) ) ), U ) ), true
% 44.17/44.59 , ifeq( true, true, 'is_a_theorem'( U ), true ), true ) ) ] )
% 44.17/44.59 , clause( 2822, [ =( 'is_a_theorem'( implies( Y, implies( Z, implies(
% 44.17/44.59 implies( implies( X, Y ), T ), T ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10264, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 19, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T )] )
% 44.17/44.59 , substitution( 1, [ :=( X, implies( X, implies( Y, implies( implies(
% 44.17/44.59 implies( Z, X ), T ), T ) ) ) ), :=( Y, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10269, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.59 implies( Y, implies( implies( implies( Z, X ), T ), T ) ) ), U ) ), true
% 44.17/44.59 , 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10267, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.59 implies( Y, implies( implies( implies( Z, X ), T ), T ) ) ), U ) ), true
% 44.17/44.59 , ifeq( true, true, 'is_a_theorem'( U ), true ), true ) ) ] )
% 44.17/44.59 , 0, 18, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( U ) ),
% 44.17/44.59 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 44.17/44.59 :=( T, T ), :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10270, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.59 implies( implies( implies( Z, X ), T ), T ) ) ), U ) ), true,
% 44.17/44.59 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.59 , clause( 10269, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.59 implies( Y, implies( implies( implies( Z, X ), T ), T ) ) ), U ) ), true
% 44.17/44.59 , 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.59 :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 2855, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.59 implies( implies( implies( Z, X ), T ), T ) ) ), U ) ), true,
% 44.17/44.59 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.59 , clause( 10270, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y
% 44.17/44.59 , implies( implies( implies( Z, X ), T ), T ) ) ), U ) ), true,
% 44.17/44.59 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 44.17/44.59 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10272, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y )
% 44.17/44.59 ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.59 , clause( 431, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10274, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), implies( X, Z ) ), implies( X, Z
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 2799, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.59 , Z ), Z ), implies( X, Y ) ), implies( T, implies( X, Y ) ) ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, clause( 10272, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X
% 44.17/44.59 , Y ) ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T,
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), implies( X, Z ) ) )] ),
% 44.17/44.59 substitution( 1, [ :=( X, implies( implies( implies( X, Y ), Y ), implies(
% 44.17/44.59 X, Z ) ) ), :=( Y, implies( X, Z ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10276, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), implies( X, Z ) ), implies( X, Z ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10274, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), implies( X, Z ) ), implies( X, Z
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), implies( X, Z ) ), implies( X, Z
% 44.17/44.59 ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 44.17/44.59 :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10277, [ =( 'is_a_theorem'( implies( implies( implies( implies( X,
% 44.17/44.59 Y ), Y ), implies( X, Z ) ), implies( X, Z ) ) ), true ) ] )
% 44.17/44.59 , clause( 10276, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), implies( X, Z ) ), implies( X, Z ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 3239, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.59 ), Y ), implies( X, Z ) ), implies( X, Z ) ) ), true ) ] )
% 44.17/44.59 , clause( 10277, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.59 , Y ), Y ), implies( X, Z ) ), implies( X, Z ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10279, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 44.17/44.59 ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) )
% 44.17/44.59 , true ) ) ] )
% 44.17/44.59 , clause( 8, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X ) ) ), true
% 44.17/44.59 ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10281, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, Z ), implies( implies( X, Y ), Y ) ), implies( T,
% 44.17/44.59 implies( implies( X, Y ), Y ) ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 3239, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.59 , Y ), Y ), implies( X, Z ) ), implies( X, Z ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10279, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.59 ), Z ) ), true, 'is_a_theorem'( implies( implies( Z, X ), implies( T, X
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 substitution( 1, [ :=( X, implies( implies( X, Y ), Y ) ), :=( Y, implies(
% 44.17/44.59 X, Z ) ), :=( Z, implies( X, Z ) ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10282, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.59 , implies( implies( X, Z ), Z ) ), implies( T, implies( implies( X, Z ),
% 44.17/44.59 Z ) ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10281, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, Z ), implies( implies( X, Y ), Y ) ), implies( T,
% 44.17/44.59 implies( implies( X, Y ), Y ) ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, Y ), implies( implies( X, Z ), Z ) ), implies( T,
% 44.17/44.59 implies( implies( X, Z ), Z ) ) ) ) ), :=( Z, true )] ), substitution( 1
% 44.17/44.59 , [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10283, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.59 implies( implies( X, Z ), Z ) ), implies( T, implies( implies( X, Z ), Z
% 44.17/44.59 ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10282, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.59 ), implies( implies( X, Z ), Z ) ), implies( T, implies( implies( X, Z )
% 44.17/44.59 , Z ) ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 3253, [ =( 'is_a_theorem'( implies( implies( implies( X, Z ),
% 44.17/44.59 implies( implies( X, Y ), Y ) ), implies( T, implies( implies( X, Y ), Y
% 44.17/44.59 ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10283, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.59 implies( implies( X, Z ), Z ) ), implies( T, implies( implies( X, Z ), Z
% 44.17/44.59 ) ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10285, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.59 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10287, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, Y ), Y ), implies( X, Z ) ) ), true, 'is_a_theorem'(
% 44.17/44.59 implies( X, Z ) ), true ), true ) ) ] )
% 44.17/44.59 , clause( 3239, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.59 , Y ), Y ), implies( X, Z ) ), implies( X, Z ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10285, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 substitution( 1, [ :=( X, implies( implies( implies( X, Y ), Y ), implies(
% 44.17/44.59 X, Z ) ) ), :=( Y, implies( X, Z ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10292, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 X, Y ), Y ), implies( X, Z ) ) ), true, 'is_a_theorem'( implies( X, Z ) )
% 44.17/44.59 , true ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10287, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), implies( X, Z ) ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( X, Z ) ), true ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), implies( X, Z ) ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( X, Z ) ), true ) ), :=( Z, true )] ),
% 44.17/44.59 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10293, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.59 , Y ), implies( X, Z ) ) ), true, 'is_a_theorem'( implies( X, Z ) ), true
% 44.17/44.59 ), true ) ] )
% 44.17/44.59 , clause( 10292, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 X, Y ), Y ), implies( X, Z ) ) ), true, 'is_a_theorem'( implies( X, Z ) )
% 44.17/44.59 , true ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 3254, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.59 , Y ), implies( X, Z ) ) ), true, 'is_a_theorem'( implies( X, Z ) ), true
% 44.17/44.59 ), true ) ] )
% 44.17/44.59 , clause( 10293, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.59 ), Y ), implies( X, Z ) ) ), true, 'is_a_theorem'( implies( X, Z ) ),
% 44.17/44.59 true ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10295, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.59 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10297, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, Y ), implies( Z, Y ) ), implies( X, T ) ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( X, T ) ), true ), true ) ) ] )
% 44.17/44.59 , clause( 2468, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.59 , Y ), implies( Z, Y ) ), implies( X, T ) ), implies( X, T ) ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, clause( 10295, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 , substitution( 1, [ :=( X, implies( implies( implies( X, Y ), implies( Z
% 44.17/44.59 , Y ) ), implies( X, T ) ) ), :=( Y, implies( X, T ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10302, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 X, Y ), implies( Z, Y ) ), implies( X, T ) ) ), true, 'is_a_theorem'(
% 44.17/44.59 implies( X, T ) ), true ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10297, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( implies( implies( X, Y ), implies( Z, Y ) ), implies( X, T ) ) )
% 44.17/44.59 , true, 'is_a_theorem'( implies( X, T ) ), true ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( implies( implies( X, Y ), implies( Z, Y ) ), implies( X, T ) ) )
% 44.17/44.59 , true, 'is_a_theorem'( implies( X, T ) ), true ) ), :=( Z, true )] ),
% 44.17/44.59 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10303, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.59 , implies( Z, Y ) ), implies( X, T ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.59 X, T ) ), true ), true ) ] )
% 44.17/44.59 , clause( 10302, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 X, Y ), implies( Z, Y ) ), implies( X, T ) ) ), true, 'is_a_theorem'(
% 44.17/44.59 implies( X, T ) ), true ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 3277, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.59 , implies( Z, Y ) ), implies( X, T ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.59 X, T ) ), true ), true ) ] )
% 44.17/44.59 , clause( 10303, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.59 ), implies( Z, Y ) ), implies( X, T ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.59 X, T ) ), true ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10305, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.59 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10307, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), Z ), X ) ), true, 'is_a_theorem'(
% 44.17/44.59 implies( implies( X, Y ), Y ) ), true ), true ) ) ] )
% 44.17/44.59 , clause( 2496, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ), X ), implies( implies( X, Y ), Y ) ) ), true )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, clause( 10305, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 substitution( 1, [ :=( X, implies( implies( implies( implies( X, Y ), Y )
% 44.17/44.59 , Z ), X ) ), :=( Y, implies( implies( X, Y ), Y ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10312, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ), X ) ), true, 'is_a_theorem'( implies( implies(
% 44.17/44.59 X, Y ), Y ) ), true ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10307, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( implies( implies( implies( X, Y ), Y ), Z ), X ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( X, Y ), Y ) ), true ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( implies( implies( implies( X, Y ), Y ), Z ), X ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( X, Y ), Y ) ), true ) ), :=( Z, true )] )
% 44.17/44.59 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10313, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ), X ) ), true, 'is_a_theorem'( implies( implies(
% 44.17/44.59 X, Y ), Y ) ), true ), true ) ] )
% 44.17/44.59 , clause( 10312, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ), X ) ), true, 'is_a_theorem'( implies( implies(
% 44.17/44.59 X, Y ), Y ) ), true ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 3323, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 X, Y ), Y ), Z ), X ) ), true, 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.59 Y ) ), true ), true ) ] )
% 44.17/44.59 , clause( 10313, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ), X ) ), true, 'is_a_theorem'( implies( implies(
% 44.17/44.59 X, Y ), Y ) ), true ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10315, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 X, Y ), Y ), implies( X, Z ) ) ), true, 'is_a_theorem'( implies( X, Z ) )
% 44.17/44.59 , true ) ) ] )
% 44.17/44.59 , clause( 3254, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.59 ), Y ), implies( X, Z ) ) ), true, 'is_a_theorem'( implies( X, Z ) ),
% 44.17/44.59 true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10317, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X,
% 44.17/44.59 implies( implies( implies( implies( X, Y ), Y ), Z ), implies( T, Z ) ) )
% 44.17/44.59 ), true ) ) ] )
% 44.17/44.59 , clause( 2362, [ =( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 implies( X, Z ), implies( T, Z ) ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10315, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), implies( X, Z ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.59 X, Z ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, implies( implies( X, Y ), Y ) ), :=( Y, X
% 44.17/44.59 ), :=( Z, Z ), :=( T, T )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )
% 44.17/44.59 , :=( Z, implies( implies( implies( implies( X, Y ), Y ), Z ), implies( T
% 44.17/44.59 , Z ) ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10319, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.59 implies( implies( X, Y ), Y ), Z ), implies( T, Z ) ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10317, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X
% 44.17/44.59 , implies( implies( implies( implies( X, Y ), Y ), Z ), implies( T, Z ) )
% 44.17/44.59 ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.59 , implies( implies( implies( implies( X, Y ), Y ), Z ), implies( T, Z ) )
% 44.17/44.59 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=(
% 44.17/44.59 Z, Z ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10320, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ), implies( T, Z ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10319, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.59 implies( implies( X, Y ), Y ), Z ), implies( T, Z ) ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 3494, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ), implies( T, Z ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10320, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ), implies( T, Z ) ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10322, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( Y,
% 44.17/44.59 implies( X, Z ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( X, Z )
% 44.17/44.59 ) ), true ) ) ] )
% 44.17/44.59 , clause( 584, [ =( ifeq( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.59 X, Z ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( X, Z ) ) ), true
% 44.17/44.59 ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10324, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), Z ), implies( X, Z ) ) ), true )
% 44.17/44.59 ) ] )
% 44.17/44.59 , clause( 3494, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ), implies( T, Z ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10322, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( Y
% 44.17/44.59 , implies( X, Z ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( X, Z
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, X )] )
% 44.17/44.59 , substitution( 1, [ :=( X, X ), :=( Y, implies( implies( implies( X, Y )
% 44.17/44.59 , Y ), Z ) ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10326, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ), implies( X, Z ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10324, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), Z ), implies( X, Z ) ) ), true )
% 44.17/44.59 ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), Z ), implies( X, Z ) ) ) ), :=( Z
% 44.17/44.59 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10327, [ =( 'is_a_theorem'( implies( implies( implies( implies( X,
% 44.17/44.59 Y ), Y ), Z ), implies( X, Z ) ) ), true ) ] )
% 44.17/44.59 , clause( 10326, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ), implies( X, Z ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 3544, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.59 ), Y ), Z ), implies( X, Z ) ) ), true ) ] )
% 44.17/44.59 , clause( 10327, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.59 , Y ), Y ), Z ), implies( X, Z ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10329, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 44.17/44.59 implies( implies( X, Y ), implies( Z, Y ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 270, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 44.17/44.59 implies( implies( X, Y ), implies( Z, Y ) ) ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10331, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( implies( implies( X, Y ), Y ), Z ), implies( X
% 44.17/44.59 , Z ) ), T ), implies( U, T ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 3544, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.59 , Y ), Y ), Z ), implies( X, Z ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10329, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( X, Y ), implies( Z, Y ) ) ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 substitution( 1, [ :=( X, implies( implies( implies( implies( X, Y ), Y )
% 44.17/44.59 , Z ), implies( X, Z ) ) ), :=( Y, T ), :=( Z, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10333, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), Z ), implies( X, Z ) ), T ),
% 44.17/44.59 implies( U, T ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10331, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( implies( implies( X, Y ), Y ), Z ), implies( X
% 44.17/44.59 , Z ) ), T ), implies( U, T ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( implies( implies( X, Y ), Y ), Z ), implies( X
% 44.17/44.59 , Z ) ), T ), implies( U, T ) ) ) ), :=( Z, true )] ), substitution( 1, [
% 44.17/44.59 :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10334, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( implies( X, Y ), Y ), Z ), implies( X, Z ) ), T ), implies( U, T
% 44.17/44.59 ) ) ), true ) ] )
% 44.17/44.59 , clause( 10333, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), Z ), implies( X, Z ) ), T ),
% 44.17/44.59 implies( U, T ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.59 :=( U, U )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 3572, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( implies( X, Y ), Y ), Z ), implies( X, Z ) ), T ), implies( U, T
% 44.17/44.59 ) ) ), true ) ] )
% 44.17/44.59 , clause( 10334, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( implies( X, Y ), Y ), Z ), implies( X, Z ) ), T ), implies( U, T
% 44.17/44.59 ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 44.17/44.59 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10336, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.59 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10338, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, Y ), Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z
% 44.17/44.59 ) ), true ), true ) ) ] )
% 44.17/44.59 , clause( 3544, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.59 , Y ), Y ), Z ), implies( X, Z ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10336, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 substitution( 1, [ :=( X, implies( implies( implies( X, Y ), Y ), Z ) ),
% 44.17/44.59 :=( Y, implies( X, Z ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10343, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 X, Y ), Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10338, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), Z ) ), true, 'is_a_theorem'(
% 44.17/44.59 implies( X, Z ) ), true ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), Z ) ), true, 'is_a_theorem'(
% 44.17/44.59 implies( X, Z ) ), true ) ), :=( Z, true )] ), substitution( 1, [ :=( X,
% 44.17/44.59 X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10344, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.59 , Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 10343, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 X, Y ), Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 3574, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.59 , Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 10344, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.59 ), Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10346, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X, Y )
% 44.17/44.59 ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.59 , clause( 431, [ =( ifeq( 'is_a_theorem'( implies( X, implies( X, Y ) ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( X, Y ) ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10348, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, Y ), implies( implies( X, Z ), Z ) ), implies(
% 44.17/44.59 implies( X, Z ), Z ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 3253, [ =( 'is_a_theorem'( implies( implies( implies( X, Z ),
% 44.17/44.59 implies( implies( X, Y ), Y ) ), implies( T, implies( implies( X, Y ), Y
% 44.17/44.59 ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10346, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( X
% 44.17/44.59 , Y ) ) ), true, 'is_a_theorem'( implies( X, Y ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T,
% 44.17/44.59 implies( implies( X, Y ), implies( implies( X, Z ), Z ) ) )] ),
% 44.17/44.59 substitution( 1, [ :=( X, implies( implies( X, Y ), implies( implies( X,
% 44.17/44.59 Z ), Z ) ) ), :=( Y, implies( implies( X, Z ), Z ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10350, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.59 , implies( implies( X, Z ), Z ) ), implies( implies( X, Z ), Z ) ) ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10348, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, Y ), implies( implies( X, Z ), Z ) ), implies(
% 44.17/44.59 implies( X, Z ), Z ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( X, Y ), implies( implies( X, Z ), Z ) ), implies(
% 44.17/44.59 implies( X, Z ), Z ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X
% 44.17/44.59 ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10351, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.59 implies( implies( X, Z ), Z ) ), implies( implies( X, Z ), Z ) ) ), true
% 44.17/44.59 ) ] )
% 44.17/44.59 , clause( 10350, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.59 ), implies( implies( X, Z ), Z ) ), implies( implies( X, Z ), Z ) ) ) )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 4554, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.59 implies( implies( X, Z ), Z ) ), implies( implies( X, Z ), Z ) ) ), true
% 44.17/44.59 ) ] )
% 44.17/44.59 , clause( 10351, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.59 implies( implies( X, Z ), Z ) ), implies( implies( X, Z ), Z ) ) ), true
% 44.17/44.59 ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10353, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.59 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10355, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, Y ), implies( implies( X, Z ), Z ) ) ), true, 'is_a_theorem'(
% 44.17/44.59 implies( implies( X, Z ), Z ) ), true ), true ) ) ] )
% 44.17/44.59 , clause( 4554, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 44.17/44.59 implies( implies( X, Z ), Z ) ), implies( implies( X, Z ), Z ) ) ), true
% 44.17/44.59 ) ] )
% 44.17/44.59 , 0, clause( 10353, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 substitution( 1, [ :=( X, implies( implies( X, Y ), implies( implies( X,
% 44.17/44.59 Z ), Z ) ) ), :=( Y, implies( implies( X, Z ), Z ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10360, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.59 implies( implies( X, Z ), Z ) ) ), true, 'is_a_theorem'( implies( implies(
% 44.17/44.59 X, Z ), Z ) ), true ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10355, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( implies( X, Y ), implies( implies( X, Z ), Z ) ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( X, Z ), Z ) ), true ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( implies( X, Y ), implies( implies( X, Z ), Z ) ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( X, Z ), Z ) ), true ) ), :=( Z, true )] )
% 44.17/44.59 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10361, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.59 implies( X, Z ), Z ) ) ), true, 'is_a_theorem'( implies( implies( X, Z )
% 44.17/44.59 , Z ) ), true ), true ) ] )
% 44.17/44.59 , clause( 10360, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y )
% 44.17/44.59 , implies( implies( X, Z ), Z ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, Z ), Z ) ), true ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 4560, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.59 implies( X, Z ), Z ) ) ), true, 'is_a_theorem'( implies( implies( X, Z )
% 44.17/44.59 , Z ) ), true ), true ) ] )
% 44.17/44.59 , clause( 10361, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.59 implies( implies( X, Z ), Z ) ) ), true, 'is_a_theorem'( implies( implies(
% 44.17/44.59 X, Z ), Z ) ), true ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10363, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 X, Y ), Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 3574, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.59 ), Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10365, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), Z ), implies( T, implies( X, Z )
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 3572, [ =( 'is_a_theorem'( implies( implies( implies( implies(
% 44.17/44.59 implies( implies( X, Y ), Y ), Z ), implies( X, Z ) ), T ), implies( U, T
% 44.17/44.59 ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10363, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ),
% 44.17/44.59 true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 44.17/44.59 implies( X, Z ) ), :=( U, T )] ), substitution( 1, [ :=( X, implies(
% 44.17/44.59 implies( implies( X, Y ), Y ), Z ) ), :=( Y, implies( X, Z ) ), :=( Z,
% 44.17/44.59 implies( T, implies( X, Z ) ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10367, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ), implies( T, implies( X, Z ) ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10365, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), Z ), implies( T, implies( X, Z )
% 44.17/44.59 ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), Y ), Z ), implies( T, implies( X, Z )
% 44.17/44.59 ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 44.17/44.59 :=( Z, Z ), :=( T, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10368, [ =( 'is_a_theorem'( implies( implies( implies( implies( X,
% 44.17/44.59 Y ), Y ), Z ), implies( T, implies( X, Z ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10367, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 implies( X, Y ), Y ), Z ), implies( T, implies( X, Z ) ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 4878, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.59 ), Y ), Z ), implies( T, implies( X, Z ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10368, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.59 , Y ), Y ), Z ), implies( T, implies( X, Z ) ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10370, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 X, Y ), implies( Z, Y ) ), implies( X, T ) ) ), true, 'is_a_theorem'(
% 44.17/44.59 implies( X, T ) ), true ) ) ] )
% 44.17/44.59 , clause( 3277, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.59 ), implies( Z, Y ) ), implies( X, T ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.59 X, T ) ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10372, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, Y ), implies( X, implies( Z, Y ) ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 4878, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.59 , Y ), Y ), Z ), implies( T, implies( X, Z ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10370, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.59 implies( X, Y ), implies( Z, Y ) ), implies( X, T ) ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( X, T ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( Z, Y ) )
% 44.17/44.59 , :=( T, implies( X, Y ) )] ), substitution( 1, [ :=( X, implies( X, Y )
% 44.17/44.59 ), :=( Y, Y ), :=( Z, Z ), :=( T, implies( X, implies( Z, Y ) ) )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10374, [ =( true, 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.59 X, implies( Z, Y ) ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10372, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, Y ), implies( X, implies( Z, Y ) ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, Y ), implies( X, implies( Z, Y ) ) ) ) ), :=( Z, true )] ),
% 44.17/44.59 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10375, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( X,
% 44.17/44.59 implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10374, [ =( true, 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.59 implies( X, implies( Z, Y ) ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 5198, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( X,
% 44.17/44.59 implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10375, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( X
% 44.17/44.59 , implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10377, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.59 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.59 )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10379, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.59 X, Y ) ), true, 'is_a_theorem'( implies( X, implies( Z, Y ) ) ), true ),
% 44.17/44.59 true ) ) ] )
% 44.17/44.59 , clause( 5198, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( X,
% 44.17/44.59 implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10377, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 44.17/44.59 ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 substitution( 1, [ :=( X, implies( X, Y ) ), :=( Y, implies( X, implies(
% 44.17/44.59 Z, Y ) ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10384, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( X, implies( Z, Y ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10379, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( X, Y ) ), true, 'is_a_theorem'( implies( X, implies( Z, Y ) ) )
% 44.17/44.59 , true ), true ) ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.59 implies( X, Y ) ), true, 'is_a_theorem'( implies( X, implies( Z, Y ) ) )
% 44.17/44.59 , true ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 44.17/44.59 :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10385, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( X, implies( Z, Y ) ) ), true ), true ) ] )
% 44.17/44.59 , clause( 10384, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( X, implies( Z, Y ) ) ), true ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 5272, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( X, implies( Z, Y ) ) ), true ), true ) ] )
% 44.17/44.59 , clause( 10385, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( X, implies( Z, Y ) ) ), true ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10387, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( X, implies( Z, Y ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 5272, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( X, implies( Z, Y ) ) ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10389, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, Y ), implies( T, implies( X, implies( Z, Y ) ) ) ) ), true )
% 44.17/44.59 ) ] )
% 44.17/44.59 , clause( 5198, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( X,
% 44.17/44.59 implies( Z, Y ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10387, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( X, implies( Z, Y ) ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.59 substitution( 1, [ :=( X, implies( X, Y ) ), :=( Y, implies( X, implies(
% 44.17/44.59 Z, Y ) ) ), :=( Z, T )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10391, [ =( true, 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.59 Z, implies( X, implies( T, Y ) ) ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10389, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, Y ), implies( T, implies( X, implies( Z, Y ) ) ) ) ), true )
% 44.17/44.59 ) ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.59 implies( X, Y ), implies( Z, implies( X, implies( T, Y ) ) ) ) ) ), :=( Z
% 44.17/44.59 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T
% 44.17/44.59 , Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10392, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( Z,
% 44.17/44.59 implies( X, implies( T, Y ) ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10391, [ =( true, 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.59 implies( Z, implies( X, implies( T, Y ) ) ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 5275, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( T,
% 44.17/44.59 implies( X, implies( Z, Y ) ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10392, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( Z
% 44.17/44.59 , implies( X, implies( T, Y ) ) ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10394, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.59 X, Y ), implies( Z, Y ) ), implies( X, T ) ) ), true, 'is_a_theorem'(
% 44.17/44.59 implies( X, T ) ), true ) ) ] )
% 44.17/44.59 , clause( 3277, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.59 ), implies( Z, Y ) ), implies( X, T ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.59 X, T ) ), true ), true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10396, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X,
% 44.17/44.59 implies( implies( X, Y ), implies( T, implies( Z, Y ) ) ) ) ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 5275, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( T,
% 44.17/44.59 implies( X, implies( Z, Y ) ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10394, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.59 implies( X, Y ), implies( Z, Y ) ), implies( X, T ) ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( X, T ) ), true ) ) ] )
% 44.17/44.59 , 0, 3, substitution( 0, [ :=( X, implies( X, Y ) ), :=( Y, implies( Z, Y )
% 44.17/44.59 ), :=( Z, T ), :=( T, X )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )
% 44.17/44.59 , :=( Z, Z ), :=( T, implies( implies( X, Y ), implies( T, implies( Z, Y
% 44.17/44.59 ) ) ) )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10398, [ =( true, 'is_a_theorem'( implies( X, implies( implies( X,
% 44.17/44.59 Y ), implies( Z, implies( T, Y ) ) ) ) ) ) ] )
% 44.17/44.59 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.59 , 0, clause( 10396, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X
% 44.17/44.59 , implies( implies( X, Y ), implies( T, implies( Z, Y ) ) ) ) ), true ) )
% 44.17/44.59 ] )
% 44.17/44.59 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.59 , implies( implies( X, Y ), implies( Z, implies( T, Y ) ) ) ) ) ), :=( Z
% 44.17/44.59 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T
% 44.17/44.59 , Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10399, [ =( 'is_a_theorem'( implies( X, implies( implies( X, Y ),
% 44.17/44.59 implies( Z, implies( T, Y ) ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10398, [ =( true, 'is_a_theorem'( implies( X, implies( implies( X
% 44.17/44.59 , Y ), implies( Z, implies( T, Y ) ) ) ) ) ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.59 ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 subsumption(
% 44.17/44.59 clause( 5654, [ =( 'is_a_theorem'( implies( X, implies( implies( X, Y ),
% 44.17/44.59 implies( T, implies( Z, Y ) ) ) ) ), true ) ] )
% 44.17/44.59 , clause( 10399, [ =( 'is_a_theorem'( implies( X, implies( implies( X, Y )
% 44.17/44.59 , implies( Z, implies( T, Y ) ) ) ) ), true ) ] )
% 44.17/44.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T, Z )] ),
% 44.17/44.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 eqswap(
% 44.17/44.59 clause( 10401, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true ) ) ]
% 44.17/44.59 )
% 44.17/44.59 , clause( 2359, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.59 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true ),
% 44.17/44.59 true ) ] )
% 44.17/44.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.59
% 44.17/44.59
% 44.17/44.59 paramod(
% 44.17/44.59 clause( 10403, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.59 implies( implies( implies( X, Y ), U ), implies( X, Y ) ), implies( Z,
% 44.17/44.59 implies( X, implies( T, Y ) ) ) ) ), true ) ) ] )
% 44.17/44.59 , clause( 5275, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( T,
% 44.17/44.59 implies( X, implies( Z, Y ) ) ) ) ), true ) ] )
% 44.17/44.59 , 0, clause( 10401, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.59 true, 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true
% 44.17/44.60 ) ) ] )
% 44.17/44.60 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T, Z )] )
% 44.17/44.60 , substitution( 1, [ :=( X, implies( X, Y ) ), :=( Y, implies( Z, implies(
% 44.17/44.60 X, implies( T, Y ) ) ) ), :=( Z, U )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10405, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.60 implies( X, Y ), Z ), implies( X, Y ) ), implies( T, implies( X, implies(
% 44.17/44.60 U, Y ) ) ) ) ) ) ] )
% 44.17/44.60 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.60 , 0, clause( 10403, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( implies( X, Y ), U ), implies( X, Y ) ), implies( Z,
% 44.17/44.60 implies( X, implies( T, Y ) ) ) ) ), true ) ) ] )
% 44.17/44.60 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( implies( X, Y ), Z ), implies( X, Y ) ), implies( T,
% 44.17/44.60 implies( X, implies( U, Y ) ) ) ) ) ), :=( Z, true )] ), substitution( 1
% 44.17/44.60 , [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T, U ), :=( U, Z )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10406, [ =( 'is_a_theorem'( implies( implies( implies( implies( X,
% 44.17/44.60 Y ), Z ), implies( X, Y ) ), implies( T, implies( X, implies( U, Y ) ) )
% 44.17/44.60 ) ), true ) ] )
% 44.17/44.60 , clause( 10405, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.60 implies( X, Y ), Z ), implies( X, Y ) ), implies( T, implies( X, implies(
% 44.17/44.60 U, Y ) ) ) ) ) ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.60 :=( U, U )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 5667, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.60 ), U ), implies( X, Y ) ), implies( Z, implies( X, implies( T, Y ) ) ) )
% 44.17/44.60 ), true ) ] )
% 44.17/44.60 , clause( 10406, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.60 , Y ), Z ), implies( X, Y ) ), implies( T, implies( X, implies( U, Y ) )
% 44.17/44.60 ) ) ), true ) ] )
% 44.17/44.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, U ), :=( T, Z ), :=( U
% 44.17/44.60 , T )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10408, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.60 X, Y ), Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ) ) ]
% 44.17/44.60 )
% 44.17/44.60 , clause( 3574, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.60 ), Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ), true ) ]
% 44.17/44.60 )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10410, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X,
% 44.17/44.60 implies( implies( implies( implies( X, Y ), Y ), Z ), implies( T, implies(
% 44.17/44.60 U, Z ) ) ) ) ), true ) ) ] )
% 44.17/44.60 , clause( 5654, [ =( 'is_a_theorem'( implies( X, implies( implies( X, Y ),
% 44.17/44.60 implies( T, implies( Z, Y ) ) ) ) ), true ) ] )
% 44.17/44.60 , 0, clause( 10408, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.60 implies( X, Y ), Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ),
% 44.17/44.60 true ) ) ] )
% 44.17/44.60 , 0, 3, substitution( 0, [ :=( X, implies( implies( X, Y ), Y ) ), :=( Y, Z
% 44.17/44.60 ), :=( Z, U ), :=( T, T )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )
% 44.17/44.60 , :=( Z, implies( implies( implies( implies( X, Y ), Y ), Z ), implies( T
% 44.17/44.60 , implies( U, Z ) ) ) )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10412, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.60 implies( implies( X, Y ), Y ), Z ), implies( T, implies( U, Z ) ) ) ) ) )
% 44.17/44.60 ] )
% 44.17/44.60 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.60 , 0, clause( 10410, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X
% 44.17/44.60 , implies( implies( implies( implies( X, Y ), Y ), Z ), implies( T,
% 44.17/44.60 implies( U, Z ) ) ) ) ), true ) ) ] )
% 44.17/44.60 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.60 , implies( implies( implies( implies( X, Y ), Y ), Z ), implies( T,
% 44.17/44.60 implies( U, Z ) ) ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X
% 44.17/44.60 ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U, U )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10413, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.60 implies( X, Y ), Y ), Z ), implies( T, implies( U, Z ) ) ) ) ), true ) ]
% 44.17/44.60 )
% 44.17/44.60 , clause( 10412, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.60 implies( implies( X, Y ), Y ), Z ), implies( T, implies( U, Z ) ) ) ) ) )
% 44.17/44.60 ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.60 :=( U, U )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 5697, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.60 implies( X, Y ), Y ), Z ), implies( T, implies( U, Z ) ) ) ) ), true ) ]
% 44.17/44.60 )
% 44.17/44.60 , clause( 10413, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.60 implies( X, Y ), Y ), Z ), implies( T, implies( U, Z ) ) ) ) ), true ) ]
% 44.17/44.60 )
% 44.17/44.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 44.17/44.60 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10415, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( Y,
% 44.17/44.60 implies( X, Z ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( X, Z )
% 44.17/44.60 ) ), true ) ) ] )
% 44.17/44.60 , clause( 584, [ =( ifeq( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.60 X, Z ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( X, Z ) ) ), true
% 44.17/44.60 ), true ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10417, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( implies( X, Y ), Y ), Z ), implies( X, implies( T, Z )
% 44.17/44.60 ) ) ), true ) ) ] )
% 44.17/44.60 , clause( 5697, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.60 implies( X, Y ), Y ), Z ), implies( T, implies( U, Z ) ) ) ) ), true ) ]
% 44.17/44.60 )
% 44.17/44.60 , 0, clause( 10415, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( Y
% 44.17/44.60 , implies( X, Z ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( X, Z
% 44.17/44.60 ) ) ), true ) ) ] )
% 44.17/44.60 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, X ),
% 44.17/44.60 :=( U, T )] ), substitution( 1, [ :=( X, X ), :=( Y, implies( implies(
% 44.17/44.60 implies( X, Y ), Y ), Z ) ), :=( Z, implies( T, Z ) )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10419, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.60 implies( X, Y ), Y ), Z ), implies( X, implies( T, Z ) ) ) ) ) ] )
% 44.17/44.60 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.60 , 0, clause( 10417, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( implies( X, Y ), Y ), Z ), implies( X, implies( T, Z )
% 44.17/44.60 ) ) ), true ) ) ] )
% 44.17/44.60 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( implies( X, Y ), Y ), Z ), implies( X, implies( T, Z )
% 44.17/44.60 ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 44.17/44.60 :=( Z, Z ), :=( T, T )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10420, [ =( 'is_a_theorem'( implies( implies( implies( implies( X,
% 44.17/44.60 Y ), Y ), Z ), implies( X, implies( T, Z ) ) ) ), true ) ] )
% 44.17/44.60 , clause( 10419, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.60 implies( X, Y ), Y ), Z ), implies( X, implies( T, Z ) ) ) ) ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.60 ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 6223, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.60 ), Y ), Z ), implies( X, implies( T, Z ) ) ) ), true ) ] )
% 44.17/44.60 , clause( 10420, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.60 , Y ), Y ), Z ), implies( X, implies( T, Z ) ) ) ), true ) ] )
% 44.17/44.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10422, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.60 'is_a_theorem'( implies( X, implies( Z, Y ) ) ), true ) ) ] )
% 44.17/44.60 , clause( 5272, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.60 'is_a_theorem'( implies( X, implies( Z, Y ) ) ), true ), true ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10424, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( implies( X, Y ), Y ), Z ), implies( U, implies( X,
% 44.17/44.60 implies( T, Z ) ) ) ) ), true ) ) ] )
% 44.17/44.60 , clause( 6223, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.60 , Y ), Y ), Z ), implies( X, implies( T, Z ) ) ) ), true ) ] )
% 44.17/44.60 , 0, clause( 10422, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.60 true, 'is_a_theorem'( implies( X, implies( Z, Y ) ) ), true ) ) ] )
% 44.17/44.60 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.60 , substitution( 1, [ :=( X, implies( implies( implies( X, Y ), Y ), Z ) )
% 44.17/44.60 , :=( Y, implies( X, implies( T, Z ) ) ), :=( Z, U )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10426, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.60 implies( X, Y ), Y ), Z ), implies( T, implies( X, implies( U, Z ) ) ) )
% 44.17/44.60 ) ) ] )
% 44.17/44.60 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.60 , 0, clause( 10424, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( implies( X, Y ), Y ), Z ), implies( U, implies( X,
% 44.17/44.60 implies( T, Z ) ) ) ) ), true ) ) ] )
% 44.17/44.60 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( implies( X, Y ), Y ), Z ), implies( T, implies( X,
% 44.17/44.60 implies( U, Z ) ) ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X
% 44.17/44.60 ), :=( Y, Y ), :=( Z, Z ), :=( T, U ), :=( U, T )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10427, [ =( 'is_a_theorem'( implies( implies( implies( implies( X,
% 44.17/44.60 Y ), Y ), Z ), implies( T, implies( X, implies( U, Z ) ) ) ) ), true ) ]
% 44.17/44.60 )
% 44.17/44.60 , clause( 10426, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.60 implies( X, Y ), Y ), Z ), implies( T, implies( X, implies( U, Z ) ) ) )
% 44.17/44.60 ) ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.60 :=( U, U )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 6228, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.60 ), Y ), Z ), implies( U, implies( X, implies( T, Z ) ) ) ) ), true ) ]
% 44.17/44.60 )
% 44.17/44.60 , clause( 10427, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.60 , Y ), Y ), Z ), implies( T, implies( X, implies( U, Z ) ) ) ) ), true )
% 44.17/44.60 ] )
% 44.17/44.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, U ), :=( U
% 44.17/44.60 , T )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10429, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.60 X, Y ), implies( Z, Y ) ), implies( X, T ) ) ), true, 'is_a_theorem'(
% 44.17/44.60 implies( X, T ) ), true ) ) ] )
% 44.17/44.60 , clause( 3277, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.60 ), implies( Z, Y ) ), implies( X, T ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.60 X, T ) ), true ), true ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.60 ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10431, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( X, Y ), implies( X, implies( T, implies( Z, Y ) ) ) ) ), true )
% 44.17/44.60 ) ] )
% 44.17/44.60 , clause( 6228, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.60 , Y ), Y ), Z ), implies( U, implies( X, implies( T, Z ) ) ) ) ), true )
% 44.17/44.60 ] )
% 44.17/44.60 , 0, clause( 10429, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.60 implies( X, Y ), implies( Z, Y ) ), implies( X, T ) ) ), true,
% 44.17/44.60 'is_a_theorem'( implies( X, T ) ), true ) ) ] )
% 44.17/44.60 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( Z, Y ) )
% 44.17/44.60 , :=( T, T ), :=( U, implies( X, Y ) )] ), substitution( 1, [ :=( X,
% 44.17/44.60 implies( X, Y ) ), :=( Y, Y ), :=( Z, Z ), :=( T, implies( X, implies( T
% 44.17/44.60 , implies( Z, Y ) ) ) )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10433, [ =( true, 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.60 X, implies( Z, implies( T, Y ) ) ) ) ) ) ] )
% 44.17/44.60 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.60 , 0, clause( 10431, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( X, Y ), implies( X, implies( T, implies( Z, Y ) ) ) ) ), true )
% 44.17/44.60 ) ] )
% 44.17/44.60 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.60 implies( X, Y ), implies( X, implies( Z, implies( T, Y ) ) ) ) ) ), :=( Z
% 44.17/44.60 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T
% 44.17/44.60 , Z )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10434, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( X,
% 44.17/44.60 implies( Z, implies( T, Y ) ) ) ) ), true ) ] )
% 44.17/44.60 , clause( 10433, [ =( true, 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.60 implies( X, implies( Z, implies( T, Y ) ) ) ) ) ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.60 ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 6241, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( X,
% 44.17/44.60 implies( T, implies( Z, Y ) ) ) ) ), true ) ] )
% 44.17/44.60 , clause( 10434, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( X
% 44.17/44.60 , implies( Z, implies( T, Y ) ) ) ) ), true ) ] )
% 44.17/44.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T, Z )] ),
% 44.17/44.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10436, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.60 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 44.17/44.60 )
% 44.17/44.60 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 44.17/44.60 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 44.17/44.60 )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10438, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 44.17/44.60 X, Y ) ), true, 'is_a_theorem'( implies( X, implies( Z, implies( T, Y ) )
% 44.17/44.60 ) ), true ), true ) ) ] )
% 44.17/44.60 , clause( 6241, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( X,
% 44.17/44.60 implies( T, implies( Z, Y ) ) ) ) ), true ) ] )
% 44.17/44.60 , 0, clause( 10436, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.60 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 44.17/44.60 ) ) ] )
% 44.17/44.60 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T, Z )] )
% 44.17/44.60 , substitution( 1, [ :=( X, implies( X, Y ) ), :=( Y, implies( X, implies(
% 44.17/44.60 Z, implies( T, Y ) ) ) )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10443, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.60 'is_a_theorem'( implies( X, implies( Z, implies( T, Y ) ) ) ), true ) ) ]
% 44.17/44.60 )
% 44.17/44.60 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.60 , 0, clause( 10438, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 44.17/44.60 implies( X, Y ) ), true, 'is_a_theorem'( implies( X, implies( Z, implies(
% 44.17/44.60 T, Y ) ) ) ), true ), true ) ) ] )
% 44.17/44.60 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 44.17/44.60 implies( X, Y ) ), true, 'is_a_theorem'( implies( X, implies( Z, implies(
% 44.17/44.60 T, Y ) ) ) ), true ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ),
% 44.17/44.60 :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10444, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.60 'is_a_theorem'( implies( X, implies( Z, implies( T, Y ) ) ) ), true ),
% 44.17/44.60 true ) ] )
% 44.17/44.60 , clause( 10443, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.60 'is_a_theorem'( implies( X, implies( Z, implies( T, Y ) ) ) ), true ) ) ]
% 44.17/44.60 )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.60 ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 6270, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.60 'is_a_theorem'( implies( X, implies( Z, implies( T, Y ) ) ) ), true ),
% 44.17/44.60 true ) ] )
% 44.17/44.60 , clause( 10444, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.60 'is_a_theorem'( implies( X, implies( Z, implies( T, Y ) ) ) ), true ),
% 44.17/44.60 true ) ] )
% 44.17/44.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10446, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.60 implies( implies( X, Z ), Z ) ) ), true, 'is_a_theorem'( implies( implies(
% 44.17/44.60 X, Z ), Z ) ), true ) ) ] )
% 44.17/44.60 , clause( 4560, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.60 implies( implies( X, Z ), Z ) ) ), true, 'is_a_theorem'( implies( implies(
% 44.17/44.60 X, Z ), Z ) ), true ), true ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10448, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( implies( X, Y ), Z ), implies( X, implies( T, Y ) ) ),
% 44.17/44.60 implies( X, implies( T, Y ) ) ) ), true ) ) ] )
% 44.17/44.60 , clause( 5667, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.60 , Y ), U ), implies( X, Y ) ), implies( Z, implies( X, implies( T, Y ) )
% 44.17/44.60 ) ) ), true ) ] )
% 44.17/44.60 , 0, clause( 10446, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.60 ), implies( implies( X, Z ), Z ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( X, Z ), Z ) ), true ) ) ] )
% 44.17/44.60 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( implies(
% 44.17/44.60 implies( X, Y ), Z ), implies( X, implies( T, Y ) ) ) ), :=( T, T ), :=(
% 44.17/44.60 U, Z )] ), substitution( 1, [ :=( X, implies( implies( X, Y ), Z ) ),
% 44.17/44.60 :=( Y, implies( X, Y ) ), :=( Z, implies( X, implies( T, Y ) ) )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10449, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.60 implies( X, Y ), Z ), implies( X, implies( T, Y ) ) ), implies( X,
% 44.17/44.60 implies( T, Y ) ) ) ) ) ] )
% 44.17/44.60 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.60 , 0, clause( 10448, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( implies( X, Y ), Z ), implies( X, implies( T, Y ) ) ),
% 44.17/44.60 implies( X, implies( T, Y ) ) ) ), true ) ) ] )
% 44.17/44.60 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( implies( X, Y ), Z ), implies( X, implies( T, Y ) ) ),
% 44.17/44.60 implies( X, implies( T, Y ) ) ) ) ), :=( Z, true )] ), substitution( 1, [
% 44.17/44.60 :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10450, [ =( 'is_a_theorem'( implies( implies( implies( implies( X,
% 44.17/44.60 Y ), Z ), implies( X, implies( T, Y ) ) ), implies( X, implies( T, Y ) )
% 44.17/44.60 ) ), true ) ] )
% 44.17/44.60 , clause( 10449, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 44.17/44.60 implies( X, Y ), Z ), implies( X, implies( T, Y ) ) ), implies( X,
% 44.17/44.60 implies( T, Y ) ) ) ) ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.60 ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 7778, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 44.17/44.60 ), Z ), implies( X, implies( T, Y ) ) ), implies( X, implies( T, Y ) ) )
% 44.17/44.60 ), true ) ] )
% 44.17/44.60 , clause( 10450, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.60 , Y ), Z ), implies( X, implies( T, Y ) ) ), implies( X, implies( T, Y )
% 44.17/44.60 ) ) ), true ) ] )
% 44.17/44.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10452, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.60 implies( Y, implies( implies( implies( Z, X ), T ), T ) ) ), U ) ), true
% 44.17/44.60 , 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.60 , clause( 2855, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y
% 44.17/44.60 , implies( implies( implies( Z, X ), T ), T ) ) ), U ) ), true,
% 44.17/44.60 'is_a_theorem'( U ), true ), true ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.60 :=( U, U )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10454, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X,
% 44.17/44.60 implies( implies( implies( T, implies( implies( X, Y ), Z ) ), Y ), Y ) )
% 44.17/44.60 ), true ) ) ] )
% 44.17/44.60 , clause( 7778, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 44.17/44.60 , Y ), Z ), implies( X, implies( T, Y ) ) ), implies( X, implies( T, Y )
% 44.17/44.60 ) ) ), true ) ] )
% 44.17/44.60 , 0, clause( 10452, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.60 implies( Y, implies( implies( implies( Z, X ), T ), T ) ) ), U ) ), true
% 44.17/44.60 , 'is_a_theorem'( U ), true ) ) ] )
% 44.17/44.60 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 44.17/44.60 implies( implies( T, implies( implies( X, Y ), Z ) ), Y ) )] ),
% 44.17/44.60 substitution( 1, [ :=( X, implies( implies( X, Y ), Z ) ), :=( Y, X ),
% 44.17/44.60 :=( Z, T ), :=( T, Y ), :=( U, implies( X, implies( implies( implies( T,
% 44.17/44.60 implies( implies( X, Y ), Z ) ), Y ), Y ) ) )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10456, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.60 implies( Y, implies( implies( X, Z ), T ) ), Z ), Z ) ) ) ) ] )
% 44.17/44.60 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.60 , 0, clause( 10454, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X
% 44.17/44.60 , implies( implies( implies( T, implies( implies( X, Y ), Z ) ), Y ), Y )
% 44.17/44.60 ) ), true ) ) ] )
% 44.17/44.60 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.60 , implies( implies( implies( Y, implies( implies( X, Z ), T ) ), Z ), Z )
% 44.17/44.60 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Z ), :=(
% 44.17/44.60 Z, T ), :=( T, Y )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10457, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.60 Y, implies( implies( X, Z ), T ) ), Z ), Z ) ) ), true ) ] )
% 44.17/44.60 , clause( 10456, [ =( true, 'is_a_theorem'( implies( X, implies( implies(
% 44.17/44.60 implies( Y, implies( implies( X, Z ), T ) ), Z ), Z ) ) ) ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.60 ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 8141, [ =( 'is_a_theorem'( implies( X, implies( implies( implies( T
% 44.17/44.60 , implies( implies( X, Y ), Z ) ), Y ), Y ) ) ), true ) ] )
% 44.17/44.60 , clause( 10457, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.60 Y, implies( implies( X, Z ), T ) ), Z ), Z ) ) ), true ) ] )
% 44.17/44.60 , substitution( 0, [ :=( X, X ), :=( Y, T ), :=( Z, Y ), :=( T, Z )] ),
% 44.17/44.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10459, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.60 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true ) ) ]
% 44.17/44.60 )
% 44.17/44.60 , clause( 2359, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.60 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true ),
% 44.17/44.60 true ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10461, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( X, U ), X ), implies( implies( implies( Y, implies(
% 44.17/44.60 implies( X, Z ), T ) ), Z ), Z ) ) ), true ) ) ] )
% 44.17/44.60 , clause( 8141, [ =( 'is_a_theorem'( implies( X, implies( implies( implies(
% 44.17/44.60 T, implies( implies( X, Y ), Z ) ), Y ), Y ) ) ), true ) ] )
% 44.17/44.60 , 0, clause( 10459, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.60 true, 'is_a_theorem'( implies( implies( implies( X, Z ), X ), Y ) ), true
% 44.17/44.60 ) ) ] )
% 44.17/44.60 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, T ), :=( T, Y )] )
% 44.17/44.60 , substitution( 1, [ :=( X, X ), :=( Y, implies( implies( implies( Y,
% 44.17/44.60 implies( implies( X, Z ), T ) ), Z ), Z ) ), :=( Z, U )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10463, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y )
% 44.17/44.60 , X ), implies( implies( implies( Z, implies( implies( X, T ), U ) ), T )
% 44.17/44.60 , T ) ) ) ) ] )
% 44.17/44.60 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.60 , 0, clause( 10461, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( X, U ), X ), implies( implies( implies( Y, implies(
% 44.17/44.60 implies( X, Z ), T ) ), Z ), Z ) ) ), true ) ) ] )
% 44.17/44.60 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( X, Y ), X ), implies( implies( implies( Z, implies(
% 44.17/44.60 implies( X, T ), U ) ), T ), T ) ) ) ), :=( Z, true )] ), substitution( 1
% 44.17/44.60 , [ :=( X, X ), :=( Y, Z ), :=( Z, T ), :=( T, U ), :=( U, Y )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10464, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X )
% 44.17/44.60 , implies( implies( implies( Z, implies( implies( X, T ), U ) ), T ), T )
% 44.17/44.60 ) ), true ) ] )
% 44.17/44.60 , clause( 10463, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y
% 44.17/44.60 ), X ), implies( implies( implies( Z, implies( implies( X, T ), U ) ), T
% 44.17/44.60 ), T ) ) ) ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.60 :=( U, U )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 8180, [ =( 'is_a_theorem'( implies( implies( implies( X, U ), X ),
% 44.17/44.60 implies( implies( implies( Y, implies( implies( X, Z ), T ) ), Z ), Z ) )
% 44.17/44.60 ), true ) ] )
% 44.17/44.60 , clause( 10464, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), X
% 44.17/44.60 ), implies( implies( implies( Z, implies( implies( X, T ), U ) ), T ), T
% 44.17/44.60 ) ) ), true ) ] )
% 44.17/44.60 , substitution( 0, [ :=( X, X ), :=( Y, U ), :=( Z, Y ), :=( T, Z ), :=( U
% 44.17/44.60 , T )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10466, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.60 implies( implies( X, Z ), Z ) ) ), true, 'is_a_theorem'( implies( implies(
% 44.17/44.60 X, Z ), Z ) ), true ) ) ] )
% 44.17/44.60 , clause( 4560, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.60 implies( implies( X, Z ), Z ) ) ), true, 'is_a_theorem'( implies( implies(
% 44.17/44.60 X, Z ), Z ) ), true ), true ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10468, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( X, implies( implies( X, Y ), Z ) ), Y ), Y ) ), true )
% 44.17/44.60 ) ] )
% 44.17/44.60 , clause( 8180, [ =( 'is_a_theorem'( implies( implies( implies( X, U ), X )
% 44.17/44.60 , implies( implies( implies( Y, implies( implies( X, Z ), T ) ), Z ), Z )
% 44.17/44.60 ) ), true ) ] )
% 44.17/44.60 , 0, clause( 10466, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.60 ), implies( implies( X, Z ), Z ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( X, Z ), Z ) ), true ) ) ] )
% 44.17/44.60 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, Y ), :=( T, Z ),
% 44.17/44.60 :=( U, implies( implies( X, Y ), Z ) )] ), substitution( 1, [ :=( X,
% 44.17/44.60 implies( X, implies( implies( X, Y ), Z ) ) ), :=( Y, X ), :=( Z, Y )] )
% 44.17/44.60 ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10469, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.60 implies( implies( X, Y ), Z ) ), Y ), Y ) ) ) ] )
% 44.17/44.60 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.60 , 0, clause( 10468, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( X, implies( implies( X, Y ), Z ) ), Y ), Y ) ), true )
% 44.17/44.60 ) ] )
% 44.17/44.60 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( X, implies( implies( X, Y ), Z ) ), Y ), Y ) ) ), :=( Z
% 44.17/44.60 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )
% 44.17/44.60 ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10470, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.60 implies( X, Y ), Z ) ), Y ), Y ) ), true ) ] )
% 44.17/44.60 , clause( 10469, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.60 implies( implies( X, Y ), Z ) ), Y ), Y ) ) ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 8230, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.60 implies( X, Y ), Z ) ), Y ), Y ) ), true ) ] )
% 44.17/44.60 , clause( 10470, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.60 implies( X, Y ), Z ) ), Y ), Y ) ), true ) ] )
% 44.17/44.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10472, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.60 'is_a_theorem'( implies( X, implies( Z, implies( T, Y ) ) ) ), true ) ) ]
% 44.17/44.60 )
% 44.17/44.60 , clause( 6270, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 44.17/44.60 'is_a_theorem'( implies( X, implies( Z, implies( T, Y ) ) ) ), true ),
% 44.17/44.60 true ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.60 ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10474, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( X, implies( implies( X, Y ), Z ) ), Y ), implies( T,
% 44.17/44.60 implies( U, Y ) ) ) ), true ) ) ] )
% 44.17/44.60 , clause( 8230, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.60 implies( X, Y ), Z ) ), Y ), Y ) ), true ) ] )
% 44.17/44.60 , 0, clause( 10472, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 44.17/44.60 true, 'is_a_theorem'( implies( X, implies( Z, implies( T, Y ) ) ) ), true
% 44.17/44.60 ) ) ] )
% 44.17/44.60 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.60 substitution( 1, [ :=( X, implies( implies( X, implies( implies( X, Y ),
% 44.17/44.60 Z ) ), Y ) ), :=( Y, Y ), :=( Z, T ), :=( T, U )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10476, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.60 implies( implies( X, Y ), Z ) ), Y ), implies( T, implies( U, Y ) ) ) ) )
% 44.17/44.60 ] )
% 44.17/44.60 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.60 , 0, clause( 10474, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( X, implies( implies( X, Y ), Z ) ), Y ), implies( T,
% 44.17/44.60 implies( U, Y ) ) ) ), true ) ) ] )
% 44.17/44.60 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( X, implies( implies( X, Y ), Z ) ), Y ), implies( T,
% 44.17/44.60 implies( U, Y ) ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X )
% 44.17/44.60 , :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U, U )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10477, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.60 implies( X, Y ), Z ) ), Y ), implies( T, implies( U, Y ) ) ) ), true ) ]
% 44.17/44.60 )
% 44.17/44.60 , clause( 10476, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.60 implies( implies( X, Y ), Z ) ), Y ), implies( T, implies( U, Y ) ) ) ) )
% 44.17/44.60 ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.60 :=( U, U )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 8244, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.60 implies( X, Y ), Z ) ), Y ), implies( T, implies( U, Y ) ) ) ), true ) ]
% 44.17/44.60 )
% 44.17/44.60 , clause( 10477, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.60 implies( X, Y ), Z ) ), Y ), implies( T, implies( U, Y ) ) ) ), true ) ]
% 44.17/44.60 )
% 44.17/44.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 44.17/44.60 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10479, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.60 implies( implies( X, Z ), Z ) ) ), true, 'is_a_theorem'( implies( implies(
% 44.17/44.60 X, Z ), Z ) ), true ) ) ] )
% 44.17/44.60 , clause( 4560, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.60 implies( implies( X, Z ), Z ) ) ), true, 'is_a_theorem'( implies( implies(
% 44.17/44.60 X, Z ), Z ) ), true ), true ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10481, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( X, implies( implies( X, Y ), Z ) ), implies( T, Y ) ),
% 44.17/44.60 implies( T, Y ) ) ), true ) ) ] )
% 44.17/44.60 , clause( 8244, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.60 implies( X, Y ), Z ) ), Y ), implies( T, implies( U, Y ) ) ) ), true ) ]
% 44.17/44.60 )
% 44.17/44.60 , 0, clause( 10479, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 44.17/44.60 ), implies( implies( X, Z ), Z ) ) ), true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( X, Z ), Z ) ), true ) ) ] )
% 44.17/44.60 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 44.17/44.60 implies( implies( X, implies( implies( X, Y ), Z ) ), implies( T, Y ) ) )
% 44.17/44.60 , :=( U, T )] ), substitution( 1, [ :=( X, implies( X, implies( implies(
% 44.17/44.60 X, Y ), Z ) ) ), :=( Y, Y ), :=( Z, implies( T, Y ) )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10482, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.60 implies( implies( X, Y ), Z ) ), implies( T, Y ) ), implies( T, Y ) ) ) )
% 44.17/44.60 ] )
% 44.17/44.60 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.60 , 0, clause( 10481, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( X, implies( implies( X, Y ), Z ) ), implies( T, Y ) ),
% 44.17/44.60 implies( T, Y ) ) ), true ) ) ] )
% 44.17/44.60 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( X, implies( implies( X, Y ), Z ) ), implies( T, Y ) ),
% 44.17/44.60 implies( T, Y ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ),
% 44.17/44.60 :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10483, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.60 implies( X, Y ), Z ) ), implies( T, Y ) ), implies( T, Y ) ) ), true ) ]
% 44.17/44.60 )
% 44.17/44.60 , clause( 10482, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.60 implies( implies( X, Y ), Z ) ), implies( T, Y ) ), implies( T, Y ) ) ) )
% 44.17/44.60 ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.60 ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 8282, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.60 implies( X, Y ), Z ) ), implies( T, Y ) ), implies( T, Y ) ) ), true ) ]
% 44.17/44.60 )
% 44.17/44.60 , clause( 10483, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.60 implies( X, Y ), Z ) ), implies( T, Y ) ), implies( T, Y ) ) ), true ) ]
% 44.17/44.60 )
% 44.17/44.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10485, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.60 implies( implies( implies( Y, X ), Z ), Z ) ), T ) ), true,
% 44.17/44.60 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.60 , clause( 2606, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies(
% 44.17/44.60 implies( implies( Y, X ), Z ), Z ) ), T ) ), true, 'is_a_theorem'( T ),
% 44.17/44.60 true ), true ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.60 ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10487, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( T, implies( X, implies( implies( X, Y ), Z ) ) ), Y ),
% 44.17/44.60 Y ) ), true ) ) ] )
% 44.17/44.60 , clause( 8282, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.60 implies( X, Y ), Z ) ), implies( T, Y ) ), implies( T, Y ) ) ), true ) ]
% 44.17/44.60 )
% 44.17/44.60 , 0, clause( 10485, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.60 implies( implies( implies( Y, X ), Z ), Z ) ), T ) ), true,
% 44.17/44.60 'is_a_theorem'( T ), true ) ) ] )
% 44.17/44.60 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 44.17/44.60 implies( implies( T, implies( X, implies( implies( X, Y ), Z ) ) ), Y ) )] )
% 44.17/44.60 , substitution( 1, [ :=( X, implies( X, implies( implies( X, Y ), Z ) ) )
% 44.17/44.60 , :=( Y, T ), :=( Z, Y ), :=( T, implies( implies( implies( T, implies( X
% 44.17/44.60 , implies( implies( X, Y ), Z ) ) ), Y ), Y ) )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10489, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.60 implies( Y, implies( implies( Y, Z ), T ) ) ), Z ), Z ) ) ) ] )
% 44.17/44.60 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.60 , 0, clause( 10487, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( T, implies( X, implies( implies( X, Y ), Z ) ) ), Y ),
% 44.17/44.60 Y ) ), true ) ) ] )
% 44.17/44.60 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.60 implies( implies( X, implies( Y, implies( implies( Y, Z ), T ) ) ), Z ),
% 44.17/44.60 Z ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ),
% 44.17/44.60 :=( Z, T ), :=( T, X )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10490, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.60 Y, implies( implies( Y, Z ), T ) ) ), Z ), Z ) ), true ) ] )
% 44.17/44.60 , clause( 10489, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 44.17/44.60 implies( Y, implies( implies( Y, Z ), T ) ) ), Z ), Z ) ) ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.60 ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 8291, [ =( 'is_a_theorem'( implies( implies( implies( T, implies( X
% 44.17/44.60 , implies( implies( X, Y ), Z ) ) ), Y ), Y ) ), true ) ] )
% 44.17/44.60 , clause( 10490, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 44.17/44.60 Y, implies( implies( Y, Z ), T ) ) ), Z ), Z ) ), true ) ] )
% 44.17/44.60 , substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] ),
% 44.17/44.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10492, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.60 implies( X, Y ), Y ), Z ), X ) ), true, 'is_a_theorem'( implies( implies(
% 44.17/44.60 X, Y ), Y ) ), true ) ) ] )
% 44.17/44.60 , clause( 3323, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 44.17/44.60 implies( X, Y ), Y ), Z ), X ) ), true, 'is_a_theorem'( implies( implies(
% 44.17/44.60 X, Y ), Y ) ), true ), true ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10494, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( X, implies( Y, implies( implies( Y, X ), Z ) ) ), implies( Y,
% 44.17/44.60 implies( implies( Y, X ), Z ) ) ) ), true ) ) ] )
% 44.17/44.60 , clause( 8291, [ =( 'is_a_theorem'( implies( implies( implies( T, implies(
% 44.17/44.60 X, implies( implies( X, Y ), Z ) ) ), Y ), Y ) ), true ) ] )
% 44.17/44.60 , 0, clause( 10492, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 44.17/44.60 implies( implies( X, Y ), Y ), Z ), X ) ), true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( X, Y ), Y ) ), true ) ) ] )
% 44.17/44.60 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T,
% 44.17/44.60 implies( X, implies( Y, implies( implies( Y, X ), Z ) ) ) )] ),
% 44.17/44.60 substitution( 1, [ :=( X, X ), :=( Y, implies( Y, implies( implies( Y, X
% 44.17/44.60 ), Z ) ) ), :=( Z, X )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10496, [ =( true, 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.60 implies( implies( Y, X ), Z ) ) ), implies( Y, implies( implies( Y, X ),
% 44.17/44.60 Z ) ) ) ) ) ] )
% 44.17/44.60 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.60 , 0, clause( 10494, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( X, implies( Y, implies( implies( Y, X ), Z ) ) ), implies( Y,
% 44.17/44.60 implies( implies( Y, X ), Z ) ) ) ), true ) ) ] )
% 44.17/44.60 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.60 implies( X, implies( Y, implies( implies( Y, X ), Z ) ) ), implies( Y,
% 44.17/44.60 implies( implies( Y, X ), Z ) ) ) ) ), :=( Z, true )] ), substitution( 1
% 44.17/44.60 , [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10497, [ =( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.60 implies( implies( Y, X ), Z ) ) ), implies( Y, implies( implies( Y, X ),
% 44.17/44.60 Z ) ) ) ), true ) ] )
% 44.17/44.60 , clause( 10496, [ =( true, 'is_a_theorem'( implies( implies( X, implies( Y
% 44.17/44.60 , implies( implies( Y, X ), Z ) ) ), implies( Y, implies( implies( Y, X )
% 44.17/44.60 , Z ) ) ) ) ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 8302, [ =( 'is_a_theorem'( implies( implies( X, implies( Y, implies(
% 44.17/44.60 implies( Y, X ), Z ) ) ), implies( Y, implies( implies( Y, X ), Z ) ) ) )
% 44.17/44.60 , true ) ] )
% 44.17/44.60 , clause( 10497, [ =( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.60 implies( implies( Y, X ), Z ) ) ), implies( Y, implies( implies( Y, X ),
% 44.17/44.60 Z ) ) ) ), true ) ] )
% 44.17/44.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10499, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.60 implies( Y, implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) )
% 44.17/44.60 , W ) ), true, 'is_a_theorem'( W ), true ) ) ] )
% 44.17/44.60 , clause( 2422, [ =( ifeq( 'is_a_theorem'( implies( implies( X, implies( Y
% 44.17/44.60 , implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) ), W ) ),
% 44.17/44.60 true, 'is_a_theorem'( W ), true ), true ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 44.17/44.60 :=( U, U ), :=( W, W )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10501, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Y,
% 44.17/44.60 implies( implies( Y, X ), implies( implies( X, Z ), implies( T, Z ) ) ) )
% 44.17/44.60 ), true ) ) ] )
% 44.17/44.60 , clause( 8302, [ =( 'is_a_theorem'( implies( implies( X, implies( Y,
% 44.17/44.60 implies( implies( Y, X ), Z ) ) ), implies( Y, implies( implies( Y, X ),
% 44.17/44.60 Z ) ) ) ), true ) ] )
% 44.17/44.60 , 0, clause( 10499, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 44.17/44.60 implies( Y, implies( Z, implies( implies( X, T ), implies( U, T ) ) ) ) )
% 44.17/44.60 , W ) ), true, 'is_a_theorem'( W ), true ) ) ] )
% 44.17/44.60 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( implies(
% 44.17/44.60 X, Z ), implies( T, Z ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )
% 44.17/44.60 , :=( Z, implies( Y, X ) ), :=( T, Z ), :=( U, T ), :=( W, implies( Y,
% 44.17/44.60 implies( implies( Y, X ), implies( implies( X, Z ), implies( T, Z ) ) ) )
% 44.17/44.60 )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10503, [ =( true, 'is_a_theorem'( implies( X, implies( implies( X,
% 44.17/44.60 Y ), implies( implies( Y, Z ), implies( T, Z ) ) ) ) ) ) ] )
% 44.17/44.60 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.60 , 0, clause( 10501, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Y
% 44.17/44.60 , implies( implies( Y, X ), implies( implies( X, Z ), implies( T, Z ) ) )
% 44.17/44.60 ) ), true ) ) ] )
% 44.17/44.60 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 44.17/44.60 , implies( implies( X, Y ), implies( implies( Y, Z ), implies( T, Z ) ) )
% 44.17/44.60 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, X ), :=(
% 44.17/44.60 Z, Z ), :=( T, T )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10504, [ =( 'is_a_theorem'( implies( X, implies( implies( X, Y ),
% 44.17/44.60 implies( implies( Y, Z ), implies( T, Z ) ) ) ) ), true ) ] )
% 44.17/44.60 , clause( 10503, [ =( true, 'is_a_theorem'( implies( X, implies( implies( X
% 44.17/44.60 , Y ), implies( implies( Y, Z ), implies( T, Z ) ) ) ) ) ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.60 ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 8358, [ =( 'is_a_theorem'( implies( Y, implies( implies( Y, X ),
% 44.17/44.60 implies( implies( X, Z ), implies( T, Z ) ) ) ) ), true ) ] )
% 44.17/44.60 , clause( 10504, [ =( 'is_a_theorem'( implies( X, implies( implies( X, Y )
% 44.17/44.60 , implies( implies( Y, Z ), implies( T, Z ) ) ) ) ), true ) ] )
% 44.17/44.60 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T, T )] ),
% 44.17/44.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10506, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( Y,
% 44.17/44.60 implies( Z, implies( X, T ) ) ) ) ), true, 'is_a_theorem'( implies( Y,
% 44.17/44.60 implies( Z, implies( X, T ) ) ) ), true ) ) ] )
% 44.17/44.60 , clause( 1304, [ =( ifeq( 'is_a_theorem'( implies( X, implies( Y, implies(
% 44.17/44.60 Z, implies( X, T ) ) ) ) ), true, 'is_a_theorem'( implies( Y, implies( Z
% 44.17/44.60 , implies( X, T ) ) ) ), true ), true ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 44.17/44.60 ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10508, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( X, Y ), implies( implies( Y, Z ), implies( X, Z ) ) ) ), true )
% 44.17/44.60 ) ] )
% 44.17/44.60 , clause( 8358, [ =( 'is_a_theorem'( implies( Y, implies( implies( Y, X ),
% 44.17/44.60 implies( implies( X, Z ), implies( T, Z ) ) ) ) ), true ) ] )
% 44.17/44.60 , 0, clause( 10506, [ =( true, ifeq( 'is_a_theorem'( implies( X, implies( Y
% 44.17/44.60 , implies( Z, implies( X, T ) ) ) ) ), true, 'is_a_theorem'( implies( Y,
% 44.17/44.60 implies( Z, implies( X, T ) ) ) ), true ) ) ] )
% 44.17/44.60 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T, X )] )
% 44.17/44.60 , substitution( 1, [ :=( X, X ), :=( Y, implies( X, Y ) ), :=( Z, implies(
% 44.17/44.60 Y, Z ) ), :=( T, Z )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 paramod(
% 44.17/44.60 clause( 10510, [ =( true, 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.60 implies( Y, Z ), implies( X, Z ) ) ) ) ) ] )
% 44.17/44.60 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 44.17/44.60 , 0, clause( 10508, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 44.17/44.60 implies( X, Y ), implies( implies( Y, Z ), implies( X, Z ) ) ) ), true )
% 44.17/44.60 ) ] )
% 44.17/44.60 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 44.17/44.60 implies( X, Y ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) ), :=( Z
% 44.17/44.60 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )
% 44.17/44.60 ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10511, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.60 implies( Y, Z ), implies( X, Z ) ) ) ), true ) ] )
% 44.17/44.60 , clause( 10510, [ =( true, 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.60 implies( implies( Y, Z ), implies( X, Z ) ) ) ) ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 9344, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.60 implies( Y, Z ), implies( X, Z ) ) ) ), true ) ] )
% 44.17/44.60 , clause( 10511, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.60 implies( Y, Z ), implies( X, Z ) ) ) ), true ) ] )
% 44.17/44.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 44.17/44.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10512, [ =( true, 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.60 implies( Y, Z ), implies( X, Z ) ) ) ) ) ] )
% 44.17/44.60 , clause( 9344, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 44.17/44.60 implies( Y, Z ), implies( X, Z ) ) ) ), true ) ] )
% 44.17/44.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 eqswap(
% 44.17/44.60 clause( 10513, [ ~( =( true, 'is_a_theorem'( implies( implies( a, b ),
% 44.17/44.60 implies( implies( b, c ), implies( a, c ) ) ) ) ) ) ] )
% 44.17/44.60 , clause( 4, [ ~( =( 'is_a_theorem'( implies( implies( a, b ), implies(
% 44.17/44.60 implies( b, c ), implies( a, c ) ) ) ), true ) ) ] )
% 44.17/44.60 , 0, substitution( 0, [] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 resolution(
% 44.17/44.60 clause( 10514, [] )
% 44.17/44.60 , clause( 10513, [ ~( =( true, 'is_a_theorem'( implies( implies( a, b ),
% 44.17/44.60 implies( implies( b, c ), implies( a, c ) ) ) ) ) ) ] )
% 44.17/44.60 , 0, clause( 10512, [ =( true, 'is_a_theorem'( implies( implies( X, Y ),
% 44.17/44.60 implies( implies( Y, Z ), implies( X, Z ) ) ) ) ) ] )
% 44.17/44.60 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, b ), :=(
% 44.17/44.60 Z, c )] )).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 subsumption(
% 44.17/44.60 clause( 9389, [] )
% 44.17/44.60 , clause( 10514, [] )
% 44.17/44.60 , substitution( 0, [] ), permutation( 0, [] ) ).
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 end.
% 44.17/44.60
% 44.17/44.60 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 44.17/44.60
% 44.17/44.60 Memory use:
% 44.17/44.60
% 44.17/44.60 space for terms: 197461
% 44.17/44.60 space for clauses: 1142842
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 clauses generated: 13382200
% 44.17/44.60 clauses kept: 9390
% 44.17/44.60 clauses selected: 4456
% 44.17/44.60 clauses deleted: 68
% 44.17/44.60 clauses inuse deleted: 36
% 44.17/44.60
% 44.17/44.60 subsentry: 2207
% 44.17/44.60 literals s-matched: 721
% 44.17/44.60 literals matched: 721
% 44.17/44.60 full subsumption: 0
% 44.17/44.60
% 44.17/44.60 checksum: 1972789010
% 44.17/44.60
% 44.17/44.60
% 44.17/44.60 Bliksem ended
%------------------------------------------------------------------------------