TSTP Solution File: LCL024-10 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL024-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 07:49:18 EDT 2022
% Result : Unsatisfiable 87.99s 88.46s
% Output : Refutation 87.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL024-10 : TPTP v8.1.0. Released v7.5.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Mon Jul 4 15:40:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 31.03/31.46 *** allocated 10000 integers for termspace/termends
% 31.03/31.46 *** allocated 10000 integers for clauses
% 31.03/31.46 *** allocated 10000 integers for justifications
% 31.03/31.46 Bliksem 1.12
% 31.03/31.46
% 31.03/31.46
% 31.03/31.46 Automatic Strategy Selection
% 31.03/31.46
% 31.03/31.46 Clauses:
% 31.03/31.46 [
% 31.03/31.46 [ =( ifeq( X, X, Y, Z ), Y ) ],
% 31.03/31.46 [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 31.03/31.46 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 31.03/31.46 ,
% 31.03/31.46 [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent( Y,
% 31.03/31.46 equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ), true ) ],
% 31.03/31.46 [ ~( =( 'is_a_theorem'( equivalent( equivalent( equivalent( a,
% 31.03/31.46 equivalent( b, c ) ), c ), equivalent( b, a ) ) ), true ) ) ]
% 31.03/31.46 ] .
% 31.03/31.46
% 31.03/31.46
% 31.03/31.46 percentage equality = 1.000000, percentage horn = 1.000000
% 31.03/31.46 This is a pure equality problem
% 31.03/31.46
% 31.03/31.46
% 31.03/31.46
% 31.03/31.46 Options Used:
% 31.03/31.46
% 31.03/31.46 useres = 1
% 31.03/31.46 useparamod = 1
% 31.03/31.46 useeqrefl = 1
% 31.03/31.46 useeqfact = 1
% 31.03/31.46 usefactor = 1
% 31.03/31.46 usesimpsplitting = 0
% 31.03/31.46 usesimpdemod = 5
% 31.03/31.46 usesimpres = 3
% 31.03/31.46
% 31.03/31.46 resimpinuse = 1000
% 31.03/31.46 resimpclauses = 20000
% 31.03/31.46 substype = eqrewr
% 31.03/31.46 backwardsubs = 1
% 31.03/31.46 selectoldest = 5
% 31.03/31.46
% 31.03/31.46 litorderings [0] = split
% 31.03/31.46 litorderings [1] = extend the termordering, first sorting on arguments
% 31.03/31.46
% 31.03/31.46 termordering = kbo
% 31.03/31.46
% 31.03/31.46 litapriori = 0
% 31.03/31.46 termapriori = 1
% 31.03/31.46 litaposteriori = 0
% 31.03/31.46 termaposteriori = 0
% 31.03/31.46 demodaposteriori = 0
% 31.03/31.46 ordereqreflfact = 0
% 31.03/31.46
% 31.03/31.46 litselect = negord
% 31.03/31.46
% 31.03/31.46 maxweight = 15
% 31.03/31.46 maxdepth = 30000
% 31.03/31.46 maxlength = 115
% 31.03/31.46 maxnrvars = 195
% 31.03/31.46 excuselevel = 1
% 31.03/31.46 increasemaxweight = 1
% 31.03/31.46
% 31.03/31.46 maxselected = 10000000
% 31.03/31.46 maxnrclauses = 10000000
% 31.03/31.46
% 31.03/31.46 showgenerated = 0
% 31.03/31.46 showkept = 0
% 31.03/31.46 showselected = 0
% 31.03/31.46 showdeleted = 0
% 31.03/31.46 showresimp = 1
% 31.03/31.46 showstatus = 2000
% 31.03/31.46
% 31.03/31.46 prologoutput = 1
% 31.03/31.46 nrgoals = 5000000
% 31.03/31.46 totalproof = 1
% 31.03/31.46
% 31.03/31.46 Symbols occurring in the translation:
% 31.03/31.46
% 31.03/31.46 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 31.03/31.46 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 31.03/31.46 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 31.03/31.46 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 31.03/31.46 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 31.03/31.46 ifeq [42, 4] (w:1, o:51, a:1, s:1, b:0),
% 31.03/31.46 equivalent [45, 2] (w:1, o:50, a:1, s:1, b:0),
% 31.03/31.46 'is_a_theorem' [46, 1] (w:1, o:24, a:1, s:1, b:0),
% 31.03/31.46 true [47, 0] (w:1, o:14, a:1, s:1, b:0),
% 31.03/31.46 a [49, 0] (w:1, o:16, a:1, s:1, b:0),
% 31.03/31.46 b [50, 0] (w:1, o:17, a:1, s:1, b:0),
% 31.03/31.46 c [51, 0] (w:1, o:18, a:1, s:1, b:0).
% 31.03/31.46
% 31.03/31.46
% 31.03/31.46 Starting Search:
% 31.03/31.46
% 31.03/31.46 Resimplifying inuse:
% 31.03/31.46 Done
% 31.03/31.46
% 31.03/31.46 Failed to find proof!
% 31.03/31.46 maxweight = 15
% 31.03/31.46 maxnrclauses = 10000000
% 31.03/31.46 Generated: 25
% 31.03/31.46 Kept: 7
% 31.03/31.46
% 31.03/31.46
% 31.03/31.46 The strategy used was not complete!
% 31.03/31.46
% 31.03/31.46 Increased maxweight to 16
% 31.03/31.46
% 31.03/31.46 Starting Search:
% 31.03/31.46
% 31.03/31.46 Resimplifying inuse:
% 31.03/31.46 Done
% 31.03/31.46
% 31.03/31.46 Failed to find proof!
% 31.03/31.46 maxweight = 16
% 31.03/31.46 maxnrclauses = 10000000
% 31.03/31.46 Generated: 25
% 31.03/31.46 Kept: 7
% 31.03/31.46
% 31.03/31.46
% 31.03/31.46 The strategy used was not complete!
% 31.03/31.46
% 31.03/31.46 Increased maxweight to 17
% 31.03/31.46
% 31.03/31.46 Starting Search:
% 31.03/31.46
% 31.03/31.46 Resimplifying inuse:
% 31.03/31.46 Done
% 31.03/31.46
% 31.03/31.46 Failed to find proof!
% 31.03/31.46 maxweight = 17
% 31.03/31.46 maxnrclauses = 10000000
% 31.03/31.46 Generated: 25
% 31.03/31.46 Kept: 7
% 31.03/31.46
% 31.03/31.46
% 31.03/31.46 The strategy used was not complete!
% 31.03/31.46
% 31.03/31.46 Increased maxweight to 18
% 31.03/31.46
% 31.03/31.46 Starting Search:
% 31.03/31.46
% 31.03/31.46 Resimplifying inuse:
% 31.03/31.46 Done
% 31.03/31.46
% 31.03/31.46 Failed to find proof!
% 31.03/31.46 maxweight = 18
% 31.03/31.46 maxnrclauses = 10000000
% 31.03/31.46 Generated: 25
% 31.03/31.46 Kept: 7
% 31.03/31.46
% 31.03/31.46
% 31.03/31.46 The strategy used was not complete!
% 31.03/31.46
% 31.03/31.46 Increased maxweight to 19
% 31.03/31.46
% 31.03/31.46 Starting Search:
% 31.03/31.46
% 31.03/31.46 Resimplifying inuse:
% 31.03/31.46 Done
% 31.03/31.46
% 31.03/31.46 Failed to find proof!
% 31.03/31.46 maxweight = 19
% 31.03/31.46 maxnrclauses = 10000000
% 31.03/31.46 Generated: 25
% 31.03/31.46 Kept: 7
% 31.03/31.46
% 31.03/31.46
% 31.03/31.46 The strategy used was not complete!
% 31.03/31.46
% 31.03/31.46 Increased maxweight to 20
% 31.03/31.46
% 31.03/31.46 Starting Search:
% 31.03/31.46
% 31.03/31.46 Resimplifying inuse:
% 31.03/31.46 Done
% 31.03/31.46
% 31.03/31.46 Failed to find proof!
% 31.03/31.46 maxweight = 20
% 31.03/31.46 maxnrclauses = 10000000
% 31.03/31.46 Generated: 25
% 31.03/31.46 Kept: 7
% 31.03/31.46
% 31.03/31.46
% 31.03/31.46 The strategy used was not complete!
% 31.03/31.46
% 31.03/31.46 Increased maxweight to 21
% 31.03/31.46
% 31.03/31.46 Starting Search:
% 31.03/31.46
% 31.03/31.46 Resimplifying inuse:
% 31.03/31.46 Done
% 31.03/31.46
% 31.03/31.46 Failed to find proof!
% 31.03/31.46 maxweight = 21
% 31.03/31.46 maxnrclauses = 10000000
% 31.03/31.46 Generated: 25
% 31.03/31.46 Kept: 7
% 31.03/31.46
% 31.03/31.46
% 31.03/31.46 The strategy used was not complete!
% 31.03/31.46
% 31.03/31.46 Increased maxweight to 22
% 31.03/31.46
% 31.03/31.46 Starting Search:
% 31.03/31.46
% 31.03/31.46 Resimplifying inuse:
% 31.03/31.46 Done
% 31.03/31.46
% 31.03/31.46
% 31.03/31.46 Intermediate Status:
% 31.03/31.46 Generated: 38199
% 31.03/31.46 Kept: 2021
% 31.03/31.46 Inuse: 342
% 31.03/31.46 Deleted: 42
% 31.03/31.46 Deletedinuse: 4
% 31.03/31.46
% 31.03/31.46 Resimplifying inuse:
% 31.03/31.46 Done
% 31.03/31.46
% 31.03/31.46 Resimplifying inuse:
% 31.03/31.46 Done
% 31.03/31.46
% 31.03/31.46
% 31.03/31.46 Intermediate Status:
% 31.03/31.46 Generated: 244792
% 31.03/31.46 Kept: 4029
% 31.03/31.46 Inuse: 820
% 31.03/31.46 Deleted: 71
% 31.03/31.46 Deletedinuse: 11
% 31.03/31.46
% 31.03/31.46 Resimplifying inuse:
% 31.03/31.46 Done
% 31.03/31.46
% 31.03/31.46 Resimplifying inuse:
% 31.03/31.46 Done
% 31.03/31.46
% 31.03/31.46
% 31.03/31.46 Intermediate Status:
% 42.10/42.50 Generated: 722923
% 42.10/42.50 Kept: 6029
% 42.10/42.50 Inuse: 1331
% 42.10/42.50 Deleted: 107
% 42.10/42.50 Deletedinuse: 16
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 2704180
% 42.10/42.50 Kept: 8030
% 42.10/42.50 Inuse: 2715
% 42.10/42.50 Deleted: 144
% 42.10/42.50 Deletedinuse: 16
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 3162298
% 42.10/42.50 Kept: 10153
% 42.10/42.50 Inuse: 2957
% 42.10/42.50 Deleted: 158
% 42.10/42.50 Deletedinuse: 17
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 3281041
% 42.10/42.50 Kept: 12290
% 42.10/42.50 Inuse: 3013
% 42.10/42.50 Deleted: 162
% 42.10/42.50 Deletedinuse: 17
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 3647453
% 42.10/42.50 Kept: 14350
% 42.10/42.50 Inuse: 3231
% 42.10/42.50 Deleted: 163
% 42.10/42.50 Deletedinuse: 17
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 4083437
% 42.10/42.50 Kept: 16556
% 42.10/42.50 Inuse: 3494
% 42.10/42.50 Deleted: 174
% 42.10/42.50 Deletedinuse: 20
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 4102508
% 42.10/42.50 Kept: 18851
% 42.10/42.50 Inuse: 3500
% 42.10/42.50 Deleted: 174
% 42.10/42.50 Deletedinuse: 20
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying clauses:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 4166807
% 42.10/42.50 Kept: 20996
% 42.10/42.50 Inuse: 3538
% 42.10/42.50 Deleted: 753
% 42.10/42.50 Deletedinuse: 20
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 4225188
% 42.10/42.50 Kept: 23162
% 42.10/42.50 Inuse: 3571
% 42.10/42.50 Deleted: 753
% 42.10/42.50 Deletedinuse: 20
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 4289134
% 42.10/42.50 Kept: 25547
% 42.10/42.50 Inuse: 3593
% 42.10/42.50 Deleted: 758
% 42.10/42.50 Deletedinuse: 25
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 4335870
% 42.10/42.50 Kept: 27572
% 42.10/42.50 Inuse: 3624
% 42.10/42.50 Deleted: 758
% 42.10/42.50 Deletedinuse: 25
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 4462798
% 42.10/42.50 Kept: 29587
% 42.10/42.50 Inuse: 3669
% 42.10/42.50 Deleted: 758
% 42.10/42.50 Deletedinuse: 25
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 4571367
% 42.10/42.50 Kept: 31622
% 42.10/42.50 Inuse: 3700
% 42.10/42.50 Deleted: 758
% 42.10/42.50 Deletedinuse: 25
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 4948162
% 42.10/42.50 Kept: 33641
% 42.10/42.50 Inuse: 3911
% 42.10/42.50 Deleted: 758
% 42.10/42.50 Deletedinuse: 25
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 5005259
% 42.10/42.50 Kept: 35729
% 42.10/42.50 Inuse: 3930
% 42.10/42.50 Deleted: 758
% 42.10/42.50 Deletedinuse: 25
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 5078139
% 42.10/42.50 Kept: 37735
% 42.10/42.50 Inuse: 3958
% 42.10/42.50 Deleted: 758
% 42.10/42.50 Deletedinuse: 25
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 5186253
% 42.10/42.50 Kept: 39749
% 42.10/42.50 Inuse: 4001
% 42.10/42.50 Deleted: 758
% 42.10/42.50 Deletedinuse: 25
% 42.10/42.50
% 42.10/42.50 Resimplifying clauses:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 5370163
% 42.10/42.50 Kept: 41820
% 42.10/42.50 Inuse: 4081
% 42.10/42.50 Deleted: 1528
% 42.10/42.50 Deletedinuse: 25
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 5407258
% 42.10/42.50 Kept: 44014
% 42.10/42.50 Inuse: 4101
% 42.10/42.50 Deleted: 1528
% 42.10/42.50 Deletedinuse: 25
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 5433653
% 42.10/42.50 Kept: 46188
% 42.10/42.50 Inuse: 4116
% 42.10/42.50 Deleted: 1528
% 42.10/42.50 Deletedinuse: 25
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 5474442
% 42.10/42.50 Kept: 48245
% 42.10/42.50 Inuse: 4138
% 42.10/42.50 Deleted: 1528
% 42.10/42.50 Deletedinuse: 25
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 5514136
% 42.10/42.50 Kept: 50373
% 42.10/42.50 Inuse: 4158
% 42.10/42.50 Deleted: 1528
% 42.10/42.50 Deletedinuse: 25
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 5560692
% 42.10/42.50 Kept: 52395
% 42.10/42.50 Inuse: 4174
% 42.10/42.50 Deleted: 1528
% 42.10/42.50 Deletedinuse: 25
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50 Resimplifying inuse:
% 42.10/42.50 Done
% 42.10/42.50
% 42.10/42.50
% 42.10/42.50 Intermediate Status:
% 42.10/42.50 Generated: 5629913
% 42.10/42.50 Kept: 54454
% 42.10/42.50 Inuse: 4190
% 42.10/42.50 Deleted: 1528
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 5659551
% 87.99/88.46 Kept: 56615
% 87.99/88.46 Inuse: 4206
% 87.99/88.46 Deleted: 1528
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 5687931
% 87.99/88.46 Kept: 58654
% 87.99/88.46 Inuse: 4223
% 87.99/88.46 Deleted: 1528
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying clauses:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 5733390
% 87.99/88.46 Kept: 60751
% 87.99/88.46 Inuse: 4239
% 87.99/88.46 Deleted: 2434
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 5766037
% 87.99/88.46 Kept: 62763
% 87.99/88.46 Inuse: 4256
% 87.99/88.46 Deleted: 2434
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 5791856
% 87.99/88.46 Kept: 64782
% 87.99/88.46 Inuse: 4273
% 87.99/88.46 Deleted: 2434
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 5807883
% 87.99/88.46 Kept: 66789
% 87.99/88.46 Inuse: 4281
% 87.99/88.46 Deleted: 2434
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 5831237
% 87.99/88.46 Kept: 68922
% 87.99/88.46 Inuse: 4286
% 87.99/88.46 Deleted: 2434
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 5910518
% 87.99/88.46 Kept: 71005
% 87.99/88.46 Inuse: 4304
% 87.99/88.46 Deleted: 2434
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 5972514
% 87.99/88.46 Kept: 73009
% 87.99/88.46 Inuse: 4318
% 87.99/88.46 Deleted: 2434
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 6045663
% 87.99/88.46 Kept: 75098
% 87.99/88.46 Inuse: 4334
% 87.99/88.46 Deleted: 2434
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 6113653
% 87.99/88.46 Kept: 77152
% 87.99/88.46 Inuse: 4349
% 87.99/88.46 Deleted: 2434
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 6177739
% 87.99/88.46 Kept: 79170
% 87.99/88.46 Inuse: 4365
% 87.99/88.46 Deleted: 2434
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying clauses:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 6257580
% 87.99/88.46 Kept: 81394
% 87.99/88.46 Inuse: 4385
% 87.99/88.46 Deleted: 3192
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 6340162
% 87.99/88.46 Kept: 83613
% 87.99/88.46 Inuse: 4405
% 87.99/88.46 Deleted: 3192
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 6425993
% 87.99/88.46 Kept: 85659
% 87.99/88.46 Inuse: 4428
% 87.99/88.46 Deleted: 3192
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 6591713
% 87.99/88.46 Kept: 87695
% 87.99/88.46 Inuse: 4515
% 87.99/88.46 Deleted: 3192
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 6727654
% 87.99/88.46 Kept: 89726
% 87.99/88.46 Inuse: 4586
% 87.99/88.46 Deleted: 3192
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 6750632
% 87.99/88.46 Kept: 91740
% 87.99/88.46 Inuse: 4598
% 87.99/88.46 Deleted: 3192
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 6774269
% 87.99/88.46 Kept: 93877
% 87.99/88.46 Inuse: 4611
% 87.99/88.46 Deleted: 3192
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 6795035
% 87.99/88.46 Kept: 95941
% 87.99/88.46 Inuse: 4623
% 87.99/88.46 Deleted: 3192
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 6815946
% 87.99/88.46 Kept: 98042
% 87.99/88.46 Inuse: 4628
% 87.99/88.46 Deleted: 3192
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 6850852
% 87.99/88.46 Kept: 100151
% 87.99/88.46 Inuse: 4635
% 87.99/88.46 Deleted: 3192
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying clauses:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 6928751
% 87.99/88.46 Kept: 102409
% 87.99/88.46 Inuse: 4653
% 87.99/88.46 Deleted: 3899
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 7018391
% 87.99/88.46 Kept: 104430
% 87.99/88.46 Inuse: 4686
% 87.99/88.46 Deleted: 3899
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 7131582
% 87.99/88.46 Kept: 106572
% 87.99/88.46 Inuse: 4745
% 87.99/88.46 Deleted: 3899
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 7281861
% 87.99/88.46 Kept: 108623
% 87.99/88.46 Inuse: 4815
% 87.99/88.46 Deleted: 3899
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 7381310
% 87.99/88.46 Kept: 110626
% 87.99/88.46 Inuse: 4860
% 87.99/88.46 Deleted: 3899
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 7533591
% 87.99/88.46 Kept: 112682
% 87.99/88.46 Inuse: 4936
% 87.99/88.46 Deleted: 3899
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 7611214
% 87.99/88.46 Kept: 114750
% 87.99/88.46 Inuse: 4968
% 87.99/88.46 Deleted: 3899
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 7718192
% 87.99/88.46 Kept: 116986
% 87.99/88.46 Inuse: 5015
% 87.99/88.46 Deleted: 3899
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 7820289
% 87.99/88.46 Kept: 119012
% 87.99/88.46 Inuse: 5059
% 87.99/88.46 Deleted: 3899
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying clauses:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 8037208
% 87.99/88.46 Kept: 121014
% 87.99/88.46 Inuse: 5156
% 87.99/88.46 Deleted: 4269
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 8256510
% 87.99/88.46 Kept: 123016
% 87.99/88.46 Inuse: 5256
% 87.99/88.46 Deleted: 4269
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 8540981
% 87.99/88.46 Kept: 125053
% 87.99/88.46 Inuse: 5374
% 87.99/88.46 Deleted: 4269
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 8778652
% 87.99/88.46 Kept: 127107
% 87.99/88.46 Inuse: 5464
% 87.99/88.46 Deleted: 4269
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 9050367
% 87.99/88.46 Kept: 129114
% 87.99/88.46 Inuse: 5569
% 87.99/88.46 Deleted: 4269
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 9512863
% 87.99/88.46 Kept: 131138
% 87.99/88.46 Inuse: 5748
% 87.99/88.46 Deleted: 4269
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 10192607
% 87.99/88.46 Kept: 133149
% 87.99/88.46 Inuse: 6004
% 87.99/88.46 Deleted: 4269
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 10417020
% 87.99/88.46 Kept: 135166
% 87.99/88.46 Inuse: 6093
% 87.99/88.46 Deleted: 4269
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 10568804
% 87.99/88.46 Kept: 137186
% 87.99/88.46 Inuse: 6161
% 87.99/88.46 Deleted: 4269
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 10767855
% 87.99/88.46 Kept: 139232
% 87.99/88.46 Inuse: 6235
% 87.99/88.46 Deleted: 4269
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying clauses:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 10954358
% 87.99/88.46 Kept: 141256
% 87.99/88.46 Inuse: 6311
% 87.99/88.46 Deleted: 4414
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 11157042
% 87.99/88.46 Kept: 143284
% 87.99/88.46 Inuse: 6393
% 87.99/88.46 Deleted: 4414
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 11391535
% 87.99/88.46 Kept: 145305
% 87.99/88.46 Inuse: 6475
% 87.99/88.46 Deleted: 4414
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 11628452
% 87.99/88.46 Kept: 147354
% 87.99/88.46 Inuse: 6573
% 87.99/88.46 Deleted: 4414
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46 Done
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 Intermediate Status:
% 87.99/88.46 Generated: 11816718
% 87.99/88.46 Kept: 149438
% 87.99/88.46 Inuse: 6645
% 87.99/88.46 Deleted: 4414
% 87.99/88.46 Deletedinuse: 25
% 87.99/88.46
% 87.99/88.46 Resimplifying inuse:
% 87.99/88.46
% 87.99/88.46 Bliksems!, er is een bewijs:
% 87.99/88.46 % SZS status Unsatisfiable
% 87.99/88.46 % SZS output start Refutation
% 87.99/88.46
% 87.99/88.46 clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.46 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.46 )
% 87.99/88.46 .
% 87.99/88.46 clause( 2, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent( Y,
% 87.99/88.46 equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 3, [ ~( =( 'is_a_theorem'( equivalent( equivalent( equivalent( a,
% 87.99/88.46 equivalent( b, c ) ), c ), equivalent( b, a ) ) ), true ) ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 4, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ), true ), true
% 87.99/88.46 ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 5, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ), T ) ), true
% 87.99/88.46 , 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 7, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( U,
% 87.99/88.46 equivalent( X, equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ) ) ), equivalent( U, T ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 9, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Z, T ) ), equivalent( Z, Y ) ), equivalent( T
% 87.99/88.46 , X ) ), X ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 10, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z, T ) ) ),
% 87.99/88.46 true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 11, [ =( 'is_a_theorem'( equivalent( Y, Y ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 14, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z,
% 87.99/88.46 equivalent( X, X ) ) ), equivalent( Z, Y ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 24, [ =( 'is_a_theorem'( equivalent( equivalent( X, X ), equivalent(
% 87.99/88.46 Y, Y ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 25, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Y,
% 87.99/88.46 X ) ), X ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 26, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( U,
% 87.99/88.46 equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 87.99/88.46 equivalent( Y, X ) ) ) ), equivalent( U, T ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 27, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 30, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( T,
% 87.99/88.46 equivalent( equivalent( X, X ), equivalent( Y, Y ) ) ) ), equivalent( T,
% 87.99/88.46 Z ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 39, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( T,
% 87.99/88.46 equivalent( equivalent( X, equivalent( X, Y ) ), Y ) ) ), equivalent( T,
% 87.99/88.46 Z ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 77, [ =( 'is_a_theorem'( equivalent( Y, equivalent( X, equivalent(
% 87.99/88.46 X, equivalent( Y, equivalent( Z, Z ) ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 117, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 87.99/88.46 , Y ) ), X ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 136, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( T
% 87.99/88.46 , equivalent( equivalent( X, equivalent( Y, Y ) ), X ) ) ), equivalent( T
% 87.99/88.46 , Z ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 138, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 X, equivalent( Y, Y ) ), X ), Z ) ), true, 'is_a_theorem'( Z ), true ),
% 87.99/88.46 true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 191, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y, Z
% 87.99/88.46 ), equivalent( equivalent( Z, equivalent( Y, equivalent( T, T ) ) ), X )
% 87.99/88.46 ), X ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 227, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent( X
% 87.99/88.46 , equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y ) ),
% 87.99/88.46 equivalent( T, Z ) ) ) ), equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 272, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 413, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.46 equivalent( Z, equivalent( Z, Y ) ), X ) ), X ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 414, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 442, [ =( 'is_a_theorem'( equivalent( Z, equivalent( X, equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Y, X ) ), equivalent( Z, equivalent( T, T ) )
% 87.99/88.46 ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 447, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( U
% 87.99/88.46 , equivalent( equivalent( X, equivalent( equivalent( Y, equivalent( Y, X
% 87.99/88.46 ) ), Z ) ), Z ) ) ), equivalent( U, T ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 448, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 488, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Y
% 87.99/88.46 , X ) ), equivalent( X, equivalent( Z, Z ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 496, [ =( 'is_a_theorem'( equivalent( Y, equivalent( X, equivalent(
% 87.99/88.46 X, Y ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 523, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( T
% 87.99/88.46 , equivalent( X, equivalent( Y, equivalent( Y, X ) ) ) ) ), equivalent( T
% 87.99/88.46 , Z ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 798, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( Z
% 87.99/88.46 , equivalent( Y, equivalent( Y, X ) ) ) ), equivalent( X, equivalent( T,
% 87.99/88.46 T ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 805, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( T
% 87.99/88.46 , Z ) ), equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ),
% 87.99/88.46 equivalent( Y, X ) ), equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 859, [ =( 'is_a_theorem'( equivalent( Z, equivalent( X, equivalent(
% 87.99/88.46 X, equivalent( Y, equivalent( Y, Z ) ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 866, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Y
% 87.99/88.46 , X ) ), equivalent( Z, equivalent( Z, X ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 876, [ =( 'is_a_theorem'( equivalent( Z, equivalent( T, equivalent(
% 87.99/88.46 T, equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) )
% 87.99/88.46 ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 897, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 X, equivalent( X, Y ) ), equivalent( Z, equivalent( Z, Y ) ) ), T ) ),
% 87.99/88.46 true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 1118, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Y
% 87.99/88.46 , X ) ), equivalent( equivalent( Z, equivalent( T, X ) ), equivalent( T,
% 87.99/88.46 Z ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 1216, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( Z, equivalent( T, equivalent( T, Z ) ) ) ) ) ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 2360, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( equivalent( Z, equivalent( T, T ) ), Z ) ) ) ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 3245, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.46 equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ), T ) ) )
% 87.99/88.46 , true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 3833, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 87.99/88.46 , equivalent( equivalent( Z, equivalent( T, Y ) ), equivalent( T, Z ) ) )
% 87.99/88.46 ), X ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 3836, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( equivalent( Z, equivalent( T, Y ) ), equivalent( T, Z ) ) ) )
% 87.99/88.46 ), true, 'is_a_theorem'( X ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 3881, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( Y
% 87.99/88.46 , equivalent( T, T ) ) ), equivalent( X, equivalent( X, equivalent( Y, Z
% 87.99/88.46 ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 6062, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Z,
% 87.99/88.46 equivalent( Z, T ) ), equivalent( T, Y ) ), equivalent( X, equivalent( X
% 87.99/88.46 , Y ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 6228, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( T
% 87.99/88.46 , Z ) ), equivalent( equivalent( X, equivalent( X, Y ) ), equivalent( Y,
% 87.99/88.46 Z ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 6240, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( T
% 87.99/88.46 , equivalent( Y, X ) ) ), equivalent( X, equivalent( Y, equivalent( Z, Z
% 87.99/88.46 ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 6264, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.46 equivalent( T, equivalent( T, Z ) ), Y ) ), equivalent( X, equivalent( X
% 87.99/88.46 , Y ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 6273, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( T
% 87.99/88.46 , Z ) ), equivalent( X, equivalent( X, equivalent( Y, equivalent( Y, Z )
% 87.99/88.46 ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 6333, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( X,
% 87.99/88.46 equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Z, equivalent(
% 87.99/88.46 Y, equivalent( T, T ) ) ) ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 6398, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 87.99/88.46 ), equivalent( X, equivalent( Z, Z ) ) ), equivalent( T, equivalent( T,
% 87.99/88.46 Y ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 6404, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( T
% 87.99/88.46 , Y ) ), equivalent( equivalent( X, Y ), equivalent( X, equivalent( Z, Z
% 87.99/88.46 ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 6430, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 equivalent( Z, Z ), equivalent( T, T ) ), Y ), equivalent( X, equivalent(
% 87.99/88.46 X, Y ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 6448, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.46 equivalent( equivalent( X, X ), equivalent( Y, Y ) ), equivalent( T, T )
% 87.99/88.46 ) ), Z ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 6512, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.46 equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ), equivalent( T, T )
% 87.99/88.46 ) ) ), true, 'is_a_theorem'( X ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 6809, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Y, X ) ), Z ), equivalent( X, equivalent( T, T
% 87.99/88.46 ) ) ), Z ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 6887, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 X, equivalent( X, Y ) ), Z ), equivalent( Y, equivalent( T, T ) ) ) ),
% 87.99/88.46 true, 'is_a_theorem'( Z ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 7060, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.46 equivalent( Z, equivalent( equivalent( T, equivalent( T, Z ) ), Y ) ), X
% 87.99/88.46 ) ), X ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 7138, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.46 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y ) ), X ) ), T
% 87.99/88.46 ) ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 7386, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.46 equivalent( Z, equivalent( Z, Y ) ), X ) ), equivalent( equivalent( T,
% 87.99/88.46 equivalent( U, X ) ), equivalent( U, T ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 8003, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Z,
% 87.99/88.46 equivalent( T, Y ) ), equivalent( T, Z ) ), equivalent( X, equivalent( X
% 87.99/88.46 , Y ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 8011, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y, X
% 87.99/88.46 ), equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( T, T ) )
% 87.99/88.46 ), Z ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 8015, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 87.99/88.46 ), equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ), equivalent( T
% 87.99/88.46 , T ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 8130, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.46 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 8141, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 87.99/88.46 , equivalent( Z, Z ) ) ), equivalent( equivalent( X, Y ), equivalent( T,
% 87.99/88.46 T ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 8171, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 8173, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.46 equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 87.99/88.46 equivalent( T, T ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 8177, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 87.99/88.46 ), equivalent( equivalent( Y, equivalent( X, Z ) ), equivalent( T, T ) )
% 87.99/88.46 ), equivalent( Z, equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 8243, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 87.99/88.46 , equivalent( Z, Z ) ) ), equivalent( equivalent( equivalent( X, Y ),
% 87.99/88.46 equivalent( T, T ) ), equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 8256, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 87.99/88.46 , equivalent( Z, Z ) ) ), equivalent( X, Y ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 8300, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( X, Y ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 8554, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 87.99/88.46 ), equivalent( T, T ) ), equivalent( X, equivalent( Y, equivalent( Z, Z
% 87.99/88.46 ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 8558, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.46 equivalent( Z, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.46 Y, equivalent( T, T ) ) ) ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 8667, [ =( 'is_a_theorem'( equivalent( Z, equivalent( equivalent( X
% 87.99/88.46 , Y ), equivalent( equivalent( Y, equivalent( X, Z ) ), equivalent( T, T
% 87.99/88.46 ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 8684, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Z, Z ) ), equivalent( Y, equivalent( X, Y ) ) ), equivalent(
% 87.99/88.46 T, T ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 8794, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 87.99/88.46 , Y ) ), equivalent( equivalent( Z, equivalent( X, Z ) ), equivalent( U,
% 87.99/88.46 U ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 9269, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( X
% 87.99/88.46 , Z ) ), equivalent( X, equivalent( Y, Y ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 10159, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 Y, X ) ), Y ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 10501, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.46 T, equivalent( equivalent( X, equivalent( Y, X ) ), Y ) ) ), equivalent(
% 87.99/88.46 T, Z ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 10502, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, X )
% 87.99/88.46 ) ), true, 'is_a_theorem'( Y ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 10505, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y,
% 87.99/88.46 equivalent( Y, X ) ), Z ), equivalent( X, Z ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 10520, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 87.99/88.46 equivalent( X, Y ) ), Z ), equivalent( equivalent( Y, Z ), equivalent( T
% 87.99/88.46 , T ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 10569, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( X, Y ) ), Z ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 11858, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Z ),
% 87.99/88.46 equivalent( equivalent( X, equivalent( X, Y ) ), Z ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 11926, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( equivalent( Z, equivalent( Z, X ) ), Y ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 15939, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.46 equivalent( Z, equivalent( Y, Z ) ), X ) ), X ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 16017, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.46 equivalent( Y, equivalent( X, Y ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 16039, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 87.99/88.46 Y ), equivalent( Y, X ) ), equivalent( Z, Z ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 16244, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.46 equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 16333, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.46 Z, equivalent( X, Y ) ) ), equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 16343, [ =( 'is_a_theorem'( equivalent( Y, equivalent( equivalent(
% 87.99/88.46 X, Y ), X ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 16553, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 16972, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, X ), Y ) ), true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 17802, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.46 equivalent( X, Y ), equivalent( Y, X ) ) ), Z ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 19956, [ =( 'is_a_theorem'( equivalent( equivalent( Z, Y ),
% 87.99/88.46 equivalent( X, equivalent( X, equivalent( Y, Z ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 20093, [ =( 'is_a_theorem'( equivalent( Z, equivalent( equivalent(
% 87.99/88.46 Y, X ), equivalent( X, equivalent( Y, Z ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 20454, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 87.99/88.46 T, X ) ), equivalent( equivalent( Y, Z ), equivalent( Z, equivalent( Y, X
% 87.99/88.46 ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 33534, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.46 X, equivalent( X, Y ) ) ), equivalent( Z, Y ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 33763, [ =( 'is_a_theorem'( equivalent( equivalent( X, Z ),
% 87.99/88.46 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 33903, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( X, equivalent( Z, equivalent( Z, Y ) ) ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 34470, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 Y, equivalent( Y, Z ) ) ), equivalent( T, equivalent( T, equivalent( X, Z
% 87.99/88.46 ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 34601, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 equivalent( Y, Z ), equivalent( Z, Y ) ) ), equivalent( T, equivalent( T
% 87.99/88.46 , X ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 35765, [ =( 'is_a_theorem'( equivalent( Z, equivalent( equivalent(
% 87.99/88.46 equivalent( X, Y ), equivalent( X, Z ) ), Y ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 35817, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 equivalent( Y, Z ), equivalent( Y, X ) ), Z ), X ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 35954, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 equivalent( X, Y ), equivalent( X, Z ) ), Y ), equivalent( T, equivalent(
% 87.99/88.46 T, Z ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 40576, [ =( 'is_a_theorem'( equivalent( Z, equivalent( equivalent(
% 87.99/88.46 X, Y ), equivalent( equivalent( Y, X ), Z ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 40636, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y,
% 87.99/88.46 Z ), equivalent( equivalent( Z, Y ), X ) ), X ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 40873, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.46 equivalent( equivalent( Y, X ), Z ) ) ), true, 'is_a_theorem'( Z ), true
% 87.99/88.46 ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 40876, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.46 equivalent( X, Y ), equivalent( X, Z ) ) ), Z ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 41075, [ =( 'is_a_theorem'( equivalent( Z, equivalent( X,
% 87.99/88.46 equivalent( equivalent( Y, X ), equivalent( Y, Z ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 41185, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.46 Y, X ) ), equivalent( Z, equivalent( X, Y ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 41228, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.46 Y, equivalent( X, Y ) ) ), equivalent( Z, X ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 41511, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, Z )
% 87.99/88.46 ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z, Y ) ) ), true )
% 87.99/88.46 , true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 42464, [ =( 'is_a_theorem'( equivalent( equivalent( X, Z ),
% 87.99/88.46 equivalent( X, equivalent( Y, equivalent( Z, Y ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 45627, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.46 equivalent( equivalent( Z, equivalent( Y, Z ) ), X ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 45630, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 Y, Z ) ), equivalent( equivalent( Z, Y ), X ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 45669, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 Y, equivalent( Y, Z ) ) ), equivalent( Z, X ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 46313, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, Z )
% 87.99/88.46 ) ), true, 'is_a_theorem'( equivalent( equivalent( Z, Y ), X ) ), true )
% 87.99/88.46 , true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 47133, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Z,
% 87.99/88.46 equivalent( Y, Z ) ), X ), equivalent( X, Y ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 47212, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, X ) ), Z ), equivalent( Y, Z ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 47357, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Z ),
% 87.99/88.46 equivalent( equivalent( X, equivalent( Y, X ) ), Z ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 48038, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.46 equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 48243, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 49039, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Z, X ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 72227, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.46 Z, equivalent( X, Z ) ) ), equivalent( T, equivalent( equivalent( X, Y )
% 87.99/88.46 , T ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 116409, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 equivalent( X, Y ), equivalent( Y, Z ) ) ), Z ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 116523, [ =( 'is_a_theorem'( equivalent( equivalent( T, Z ),
% 87.99/88.46 equivalent( X, equivalent( equivalent( X, Y ), equivalent( Y, equivalent(
% 87.99/88.46 Z, T ) ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 147068, [ =( 'is_a_theorem'( equivalent( equivalent( Z, T ),
% 87.99/88.46 equivalent( T, equivalent( equivalent( Y, X ), equivalent( X, equivalent(
% 87.99/88.46 Y, Z ) ) ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 148924, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.46 Y, X ) ), equivalent( X, equivalent( Y, Z ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 149096, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y
% 87.99/88.46 , X ), Z ), equivalent( X, equivalent( Y, Z ) ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 149411, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.46 , equivalent( Y, Z ) ), Z ), equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.46 .
% 87.99/88.46 clause( 149438, [] )
% 87.99/88.46 .
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 % SZS output end Refutation
% 87.99/88.46 found a proof!
% 87.99/88.46
% 87.99/88.46 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 87.99/88.46
% 87.99/88.46 initialclauses(
% 87.99/88.46 [ clause( 149440, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , clause( 149441, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.46 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ),
% 87.99/88.46 true ) ] )
% 87.99/88.46 , clause( 149442, [ =( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ), true ) ]
% 87.99/88.46 )
% 87.99/88.46 , clause( 149443, [ ~( =( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.46 equivalent( a, equivalent( b, c ) ), c ), equivalent( b, a ) ) ), true )
% 87.99/88.46 ) ] )
% 87.99/88.46 ] ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , clause( 149440, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.46 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.46 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.46 )
% 87.99/88.46 , clause( 149441, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.46 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ),
% 87.99/88.46 true ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 87.99/88.46 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 2, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent( Y,
% 87.99/88.46 equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ), true ) ] )
% 87.99/88.46 , clause( 149442, [ =( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ), true ) ]
% 87.99/88.46 )
% 87.99/88.46 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.46 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 3, [ ~( =( 'is_a_theorem'( equivalent( equivalent( equivalent( a,
% 87.99/88.46 equivalent( b, c ) ), c ), equivalent( b, a ) ) ), true ) ) ] )
% 87.99/88.46 , clause( 149443, [ ~( =( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.46 equivalent( a, equivalent( b, c ) ), c ), equivalent( b, a ) ) ), true )
% 87.99/88.46 ) ] )
% 87.99/88.46 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149455, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.46 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.46 ] )
% 87.99/88.46 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.46 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.46 )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149457, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( X ),
% 87.99/88.46 true, 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ), true ), true ) ) ] )
% 87.99/88.46 , clause( 2, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent( Y
% 87.99/88.46 , equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ), true ) ] )
% 87.99/88.46 , 0, clause( 149455, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.46 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.46 true ) ) ] )
% 87.99/88.46 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.46 substitution( 1, [ :=( X, X ), :=( Y, equivalent( equivalent( Y,
% 87.99/88.46 equivalent( Z, X ) ), equivalent( Z, Y ) ) )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149462, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 true ) ) ] )
% 87.99/88.46 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , 0, clause( 149457, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( X )
% 87.99/88.46 , true, 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ), true ), true ) ) ] )
% 87.99/88.46 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'( X )
% 87.99/88.46 , true, 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ), true ) ), :=( Z, true )] ), substitution( 1, [
% 87.99/88.46 :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149463, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 , clause( 149462, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ), true ) ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 4, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ), true ), true
% 87.99/88.46 ) ] )
% 87.99/88.46 , clause( 149463, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.46 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149465, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.46 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.46 ] )
% 87.99/88.46 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.46 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.46 )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149468, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.46 , equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) )
% 87.99/88.46 , T ) ), true, ifeq( true, true, 'is_a_theorem'( T ), true ), true ) ) ]
% 87.99/88.46 )
% 87.99/88.46 , clause( 2, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent( Y
% 87.99/88.46 , equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ), true ) ] )
% 87.99/88.46 , 0, clause( 149465, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.46 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.46 true ) ) ] )
% 87.99/88.46 , 0, 19, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.46 substitution( 1, [ :=( X, equivalent( X, equivalent( equivalent( Y,
% 87.99/88.46 equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ), :=( Y, T )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149470, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.46 , equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) )
% 87.99/88.46 , T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.46 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , 0, clause( 149468, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( X, equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ), T ) ), true, ifeq( true, true, 'is_a_theorem'( T
% 87.99/88.46 ), true ), true ) ) ] )
% 87.99/88.46 , 0, 18, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( T ) ),
% 87.99/88.46 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 87.99/88.46 :=( T, T )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149471, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.46 , clause( 149470, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.46 X, equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) )
% 87.99/88.46 ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.46 ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 5, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ), T ) ), true
% 87.99/88.46 , 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.46 , clause( 149471, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.46 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149473, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 true ) ) ] )
% 87.99/88.46 , clause( 4, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149475, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( T, equivalent( U, equivalent( X, equivalent( equivalent( Y,
% 87.99/88.46 equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ) ), equivalent( U, T ) ) )
% 87.99/88.46 , true ) ) ] )
% 87.99/88.46 , clause( 2, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent( Y
% 87.99/88.46 , equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ), true ) ] )
% 87.99/88.46 , 0, clause( 149473, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ), true ) ) ] )
% 87.99/88.46 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.46 substitution( 1, [ :=( X, equivalent( X, equivalent( equivalent( Y,
% 87.99/88.46 equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ), :=( Y, T ), :=( Z, U )] )
% 87.99/88.46 ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149476, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( Z, equivalent( equivalent( T, equivalent( U, Z
% 87.99/88.46 ) ), equivalent( U, T ) ) ) ) ), equivalent( Y, X ) ) ) ) ] )
% 87.99/88.46 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , 0, clause( 149475, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( T, equivalent( U, equivalent( X, equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ) ),
% 87.99/88.46 equivalent( U, T ) ) ), true ) ) ] )
% 87.99/88.46 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, equivalent( Z, equivalent( equivalent( T,
% 87.99/88.46 equivalent( U, Z ) ), equivalent( U, T ) ) ) ) ), equivalent( Y, X ) ) )
% 87.99/88.46 ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, T ), :=( Z, U
% 87.99/88.46 ), :=( T, X ), :=( U, Y )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149477, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 Y, equivalent( Z, equivalent( equivalent( T, equivalent( U, Z ) ),
% 87.99/88.46 equivalent( U, T ) ) ) ) ), equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.46 , clause( 149476, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( Z, equivalent( equivalent( T, equivalent( U, Z
% 87.99/88.46 ) ), equivalent( U, T ) ) ) ) ), equivalent( Y, X ) ) ) ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 87.99/88.46 :=( U, U )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 7, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( U,
% 87.99/88.46 equivalent( X, equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ) ) ), equivalent( U, T ) ) ), true ) ] )
% 87.99/88.46 , clause( 149477, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( Z, equivalent( equivalent( T, equivalent( U, Z
% 87.99/88.46 ) ), equivalent( U, T ) ) ) ) ), equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, T ), :=( Y, U ), :=( Z, X ), :=( T, Y ), :=( U
% 87.99/88.46 , Z )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149479, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.46 , equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) )
% 87.99/88.46 , T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.46 , clause( 5, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.46 ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149481, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( equivalent( equivalent( Y, equivalent( Z, T ) ), equivalent(
% 87.99/88.46 Z, Y ) ), equivalent( T, X ) ), X ) ), true ) ) ] )
% 87.99/88.46 , clause( 7, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( U
% 87.99/88.46 , equivalent( X, equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ) ) ), equivalent( U, T ) ) ), true ) ] )
% 87.99/88.46 , 0, clause( 149479, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( X, equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.46 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, Y ), :=( Z, Z ), :=( T, X ),
% 87.99/88.46 :=( U, equivalent( equivalent( equivalent( Y, equivalent( Z, T ) ),
% 87.99/88.46 equivalent( Z, Y ) ), equivalent( T, X ) ) )] ), substitution( 1, [ :=( X
% 87.99/88.46 , X ), :=( Y, equivalent( equivalent( Y, equivalent( Z, T ) ), equivalent(
% 87.99/88.46 Z, Y ) ) ), :=( Z, T ), :=( T, equivalent( equivalent( equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Z, T ) ), equivalent( Z, Y ) ), equivalent( T
% 87.99/88.46 , X ) ), X ) )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149483, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.46 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ),
% 87.99/88.46 equivalent( Z, T ) ), T ) ) ) ] )
% 87.99/88.46 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , 0, clause( 149481, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( equivalent( equivalent( Y, equivalent( Z, T ) ),
% 87.99/88.46 equivalent( Z, Y ) ), equivalent( T, X ) ), X ) ), true ) ) ] )
% 87.99/88.46 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent(
% 87.99/88.46 Y, X ) ), equivalent( Z, T ) ), T ) ) ), :=( Z, true )] ), substitution(
% 87.99/88.46 1, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149484, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z
% 87.99/88.46 , T ) ), T ) ), true ) ] )
% 87.99/88.46 , clause( 149483, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.46 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ),
% 87.99/88.46 equivalent( Z, T ) ), T ) ) ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.46 ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 9, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Z, T ) ), equivalent( Z, Y ) ), equivalent( T
% 87.99/88.46 , X ) ), X ) ), true ) ] )
% 87.99/88.46 , clause( 149484, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z
% 87.99/88.46 , T ) ), T ) ), true ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, X )] ),
% 87.99/88.46 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149486, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.46 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.46 ] )
% 87.99/88.46 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.46 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.46 )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149488, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent(
% 87.99/88.46 Y, X ) ), equivalent( Z, T ) ) ), true, 'is_a_theorem'( T ), true ), true
% 87.99/88.46 ) ) ] )
% 87.99/88.46 , clause( 9, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Z, T ) ), equivalent( Z, Y ) ), equivalent( T
% 87.99/88.46 , X ) ), X ) ), true ) ] )
% 87.99/88.46 , 0, clause( 149486, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.46 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.46 true ) ) ] )
% 87.99/88.46 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] )
% 87.99/88.46 , substitution( 1, [ :=( X, equivalent( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z, T ) ) ), :=( Y
% 87.99/88.46 , T )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149493, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z
% 87.99/88.46 , T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.46 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , 0, clause( 149488, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent(
% 87.99/88.46 Y, X ) ), equivalent( Z, T ) ) ), true, 'is_a_theorem'( T ), true ), true
% 87.99/88.46 ) ) ] )
% 87.99/88.46 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent(
% 87.99/88.46 Y, X ) ), equivalent( Z, T ) ) ), true, 'is_a_theorem'( T ), true ) ),
% 87.99/88.46 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 87.99/88.46 :=( T, T )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149494, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z
% 87.99/88.46 , T ) ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.46 , clause( 149493, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z
% 87.99/88.46 , T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.46 ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 10, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z, T ) ) ),
% 87.99/88.46 true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.46 , clause( 149494, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z
% 87.99/88.46 , T ) ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.46 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149496, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z
% 87.99/88.46 , T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.46 , clause( 10, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z, T ) ) ),
% 87.99/88.46 true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.46 ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149498, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( Y
% 87.99/88.46 , Y ) ), true ) ) ] )
% 87.99/88.46 , clause( 9, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Z, T ) ), equivalent( Z, Y ) ), equivalent( T
% 87.99/88.46 , X ) ), X ) ), true ) ] )
% 87.99/88.46 , 0, clause( 149496, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ),
% 87.99/88.46 equivalent( Z, T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.46 , 0, 3, substitution( 0, [ :=( X, equivalent( X, equivalent( Y, Y ) ) ),
% 87.99/88.46 :=( Y, X ), :=( Z, Y ), :=( T, Y )] ), substitution( 1, [ :=( X,
% 87.99/88.46 equivalent( X, equivalent( Y, Y ) ) ), :=( Y, Y ), :=( Z, X ), :=( T,
% 87.99/88.46 equivalent( Y, Y ) )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149500, [ =( true, 'is_a_theorem'( equivalent( X, X ) ) ) ] )
% 87.99/88.46 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , 0, clause( 149498, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.46 equivalent( Y, Y ) ), true ) ) ] )
% 87.99/88.46 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.46 X, X ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, X )] )
% 87.99/88.46 ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149501, [ =( 'is_a_theorem'( equivalent( X, X ) ), true ) ] )
% 87.99/88.46 , clause( 149500, [ =( true, 'is_a_theorem'( equivalent( X, X ) ) ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 11, [ =( 'is_a_theorem'( equivalent( Y, Y ) ), true ) ] )
% 87.99/88.46 , clause( 149501, [ =( 'is_a_theorem'( equivalent( X, X ) ), true ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, Y )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149503, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 true ) ) ] )
% 87.99/88.46 , clause( 4, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149505, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Z, equivalent( X, X ) ) ), equivalent( Z, Y )
% 87.99/88.46 ) ), true ) ) ] )
% 87.99/88.46 , clause( 11, [ =( 'is_a_theorem'( equivalent( Y, Y ) ), true ) ] )
% 87.99/88.46 , 0, clause( 149503, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ), true ) ) ] )
% 87.99/88.46 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, X )] ), substitution( 1, [
% 87.99/88.46 :=( X, equivalent( X, X ) ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149506, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( Y, X ) ) ) ) ] )
% 87.99/88.46 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , 0, clause( 149505, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, equivalent( X, X ) ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ), true ) ) ] )
% 87.99/88.46 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ), equivalent( Y, X )
% 87.99/88.46 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, X ), :=(
% 87.99/88.46 Z, Y )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149507, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 Y, equivalent( Z, Z ) ) ), equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.46 , clause( 149506, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( Y, X ) ) ) ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 14, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z,
% 87.99/88.46 equivalent( X, X ) ) ), equivalent( Z, Y ) ) ), true ) ] )
% 87.99/88.46 , clause( 149507, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( Y, X ) ) ), true ) ]
% 87.99/88.46 )
% 87.99/88.46 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 87.99/88.46 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149509, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z
% 87.99/88.46 , T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.46 , clause( 10, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.46 X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z, T ) ) ),
% 87.99/88.46 true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.46 ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149511, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( X, X ), equivalent( Y, Y ) ) ), true ) ) ] )
% 87.99/88.46 , clause( 14, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z
% 87.99/88.46 , equivalent( X, X ) ) ), equivalent( Z, Y ) ) ), true ) ] )
% 87.99/88.46 , 0, clause( 149509, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ),
% 87.99/88.46 equivalent( Z, T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.46 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, equivalent( equivalent( X, X
% 87.99/88.46 ), equivalent( Y, Y ) ) ), :=( Z, Y )] ), substitution( 1, [ :=( X,
% 87.99/88.46 equivalent( X, X ) ), :=( Y, Y ), :=( Z, Y ), :=( T, equivalent(
% 87.99/88.46 equivalent( X, X ), equivalent( Y, Y ) ) )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149513, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, X ),
% 87.99/88.46 equivalent( Y, Y ) ) ) ) ] )
% 87.99/88.46 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , 0, clause( 149511, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( X, X ), equivalent( Y, Y ) ) ), true ) ) ] )
% 87.99/88.46 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( X, X ), equivalent( Y, Y ) ) ) ), :=( Z, true )] ),
% 87.99/88.46 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149514, [ =( 'is_a_theorem'( equivalent( equivalent( X, X ),
% 87.99/88.46 equivalent( Y, Y ) ) ), true ) ] )
% 87.99/88.46 , clause( 149513, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, X )
% 87.99/88.46 , equivalent( Y, Y ) ) ) ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 24, [ =( 'is_a_theorem'( equivalent( equivalent( X, X ), equivalent(
% 87.99/88.46 Y, Y ) ) ), true ) ] )
% 87.99/88.46 , clause( 149514, [ =( 'is_a_theorem'( equivalent( equivalent( X, X ),
% 87.99/88.46 equivalent( Y, Y ) ) ), true ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 87.99/88.46 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149516, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.46 , equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) )
% 87.99/88.46 , T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.46 , clause( 5, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.46 ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149518, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( Y, equivalent( Y, X ) ), X ) ), true ) ) ] )
% 87.99/88.46 , clause( 14, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z
% 87.99/88.46 , equivalent( X, X ) ) ), equivalent( Z, Y ) ) ), true ) ] )
% 87.99/88.46 , 0, clause( 149516, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( X, equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.46 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, equivalent( Y,
% 87.99/88.46 equivalent( Y, X ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 87.99/88.46 :=( Z, Y ), :=( T, equivalent( equivalent( Y, equivalent( Y, X ) ), X ) )] )
% 87.99/88.46 ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149520, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( X, Y ) ), Y ) ) ) ] )
% 87.99/88.46 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , 0, clause( 149518, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Y, X ) ), X ) ), true ) ) ] )
% 87.99/88.46 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( X, equivalent( X, Y ) ), Y ) ) ), :=( Z, true )] ),
% 87.99/88.46 substitution( 1, [ :=( X, Y ), :=( Y, X )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149521, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 X, Y ) ), Y ) ), true ) ] )
% 87.99/88.46 , clause( 149520, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( X, Y ) ), Y ) ) ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 25, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Y,
% 87.99/88.46 X ) ), X ) ), true ) ] )
% 87.99/88.46 , clause( 149521, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( X, Y ) ), Y ) ), true ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 87.99/88.46 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149523, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 true ) ) ] )
% 87.99/88.46 , clause( 4, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149525, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( T, equivalent( U, equivalent( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( Z, Z ) ) ), equivalent( Y, X ) ) ) ), equivalent( U, T ) ) )
% 87.99/88.46 , true ) ) ] )
% 87.99/88.46 , clause( 14, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z
% 87.99/88.46 , equivalent( X, X ) ) ), equivalent( Z, Y ) ) ), true ) ] )
% 87.99/88.46 , 0, clause( 149523, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ), true ) ) ] )
% 87.99/88.46 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 87.99/88.46 substitution( 1, [ :=( X, equivalent( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( Z, Z ) ) ), equivalent( Y, X ) ) ), :=( Y, T ), :=( Z, U )] )
% 87.99/88.46 ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149527, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( equivalent( Z, equivalent( T, equivalent( U, U
% 87.99/88.46 ) ) ), equivalent( T, Z ) ) ) ), equivalent( Y, X ) ) ) ) ] )
% 87.99/88.46 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , 0, clause( 149525, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( T, equivalent( U, equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( Y, X ) ) ) ),
% 87.99/88.46 equivalent( U, T ) ) ), true ) ) ] )
% 87.99/88.46 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( T,
% 87.99/88.46 equivalent( U, U ) ) ), equivalent( T, Z ) ) ) ), equivalent( Y, X ) ) )
% 87.99/88.46 ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, T ), :=( Z, U
% 87.99/88.46 ), :=( T, X ), :=( U, Y )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149528, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 Y, equivalent( equivalent( Z, equivalent( T, equivalent( U, U ) ) ),
% 87.99/88.46 equivalent( T, Z ) ) ) ), equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.46 , clause( 149527, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( equivalent( Z, equivalent( T, equivalent( U, U
% 87.99/88.46 ) ) ), equivalent( T, Z ) ) ) ), equivalent( Y, X ) ) ) ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 87.99/88.46 :=( U, U )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 26, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( U,
% 87.99/88.46 equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 87.99/88.46 equivalent( Y, X ) ) ) ), equivalent( U, T ) ) ), true ) ] )
% 87.99/88.46 , clause( 149528, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( equivalent( Z, equivalent( T, equivalent( U, U
% 87.99/88.46 ) ) ), equivalent( T, Z ) ) ) ), equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, T ), :=( Y, U ), :=( Z, X ), :=( T, Y ), :=( U
% 87.99/88.46 , Z )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149530, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.46 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.46 ] )
% 87.99/88.46 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.46 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.46 )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149532, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.46 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ) ] )
% 87.99/88.46 , clause( 14, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z
% 87.99/88.46 , equivalent( X, X ) ) ), equivalent( Z, Y ) ) ), true ) ] )
% 87.99/88.46 , 0, clause( 149530, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.46 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.46 true ) ) ] )
% 87.99/88.46 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 87.99/88.46 substitution( 1, [ :=( X, equivalent( X, equivalent( Y, equivalent( Z, Z
% 87.99/88.46 ) ) ) ), :=( Y, equivalent( Y, X ) )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149537, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.46 Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.46 true ) ) ] )
% 87.99/88.46 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , 0, clause( 149532, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.46 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ) ] )
% 87.99/88.46 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.46 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( Y, X ) ), true ) ), :=( Z, true )] ),
% 87.99/88.46 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149538, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 , clause( 149537, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent(
% 87.99/88.46 Y, X ) ), true ) ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 27, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 , clause( 149538, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.46 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149540, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 true ) ) ] )
% 87.99/88.46 , clause( 4, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149542, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( Z, equivalent( T, equivalent( equivalent( X, X ), equivalent(
% 87.99/88.46 Y, Y ) ) ) ), equivalent( T, Z ) ) ), true ) ) ] )
% 87.99/88.46 , clause( 24, [ =( 'is_a_theorem'( equivalent( equivalent( X, X ),
% 87.99/88.46 equivalent( Y, Y ) ) ), true ) ] )
% 87.99/88.46 , 0, clause( 149540, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ), true ) ) ] )
% 87.99/88.46 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 87.99/88.46 :=( X, equivalent( equivalent( X, X ), equivalent( Y, Y ) ) ), :=( Y, Z )
% 87.99/88.46 , :=( Z, T )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149543, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ),
% 87.99/88.46 equivalent( Y, X ) ) ) ) ] )
% 87.99/88.46 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , 0, clause( 149542, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Z, equivalent( T, equivalent( equivalent( X, X )
% 87.99/88.46 , equivalent( Y, Y ) ) ) ), equivalent( T, Z ) ) ), true ) ) ] )
% 87.99/88.46 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, equivalent( equivalent( Z, Z ), equivalent(
% 87.99/88.46 T, T ) ) ) ), equivalent( Y, X ) ) ) ), :=( Z, true )] ), substitution( 1
% 87.99/88.46 , [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149544, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ), equivalent(
% 87.99/88.46 Y, X ) ) ), true ) ] )
% 87.99/88.46 , clause( 149543, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ),
% 87.99/88.46 equivalent( Y, X ) ) ) ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.46 ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 30, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( T,
% 87.99/88.46 equivalent( equivalent( X, X ), equivalent( Y, Y ) ) ) ), equivalent( T,
% 87.99/88.46 Z ) ) ), true ) ] )
% 87.99/88.46 , clause( 149544, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ),
% 87.99/88.46 equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y )] ),
% 87.99/88.46 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149546, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 true ) ) ] )
% 87.99/88.46 , clause( 4, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149548, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( Z, equivalent( T, equivalent( equivalent( X, equivalent( X, Y
% 87.99/88.46 ) ), Y ) ) ), equivalent( T, Z ) ) ), true ) ) ] )
% 87.99/88.46 , clause( 25, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Y
% 87.99/88.46 , X ) ), X ) ), true ) ] )
% 87.99/88.46 , 0, clause( 149546, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ), true ) ) ] )
% 87.99/88.46 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 87.99/88.46 :=( X, equivalent( equivalent( X, equivalent( X, Y ) ), Y ) ), :=( Y, Z )
% 87.99/88.46 , :=( Z, T )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149550, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ),
% 87.99/88.46 equivalent( Y, X ) ) ) ) ] )
% 87.99/88.46 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , 0, clause( 149548, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Z, equivalent( T, equivalent( equivalent( X,
% 87.99/88.46 equivalent( X, Y ) ), Y ) ) ), equivalent( T, Z ) ) ), true ) ) ] )
% 87.99/88.46 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( Z, T
% 87.99/88.46 ) ), T ) ) ), equivalent( Y, X ) ) ) ), :=( Z, true )] ), substitution(
% 87.99/88.46 1, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149551, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 Y, equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ), equivalent(
% 87.99/88.46 Y, X ) ) ), true ) ] )
% 87.99/88.46 , clause( 149550, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ),
% 87.99/88.46 equivalent( Y, X ) ) ) ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.46 ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 39, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( T,
% 87.99/88.46 equivalent( equivalent( X, equivalent( X, Y ) ), Y ) ) ), equivalent( T,
% 87.99/88.46 Z ) ) ), true ) ] )
% 87.99/88.46 , clause( 149551, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ),
% 87.99/88.46 equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y )] ),
% 87.99/88.46 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149553, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.46 Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.46 true ) ) ] )
% 87.99/88.46 , clause( 27, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149555, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( Y
% 87.99/88.46 , equivalent( X, equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ) )
% 87.99/88.46 ), true ) ) ] )
% 87.99/88.46 , clause( 25, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Y
% 87.99/88.46 , X ) ), X ) ), true ) ] )
% 87.99/88.46 , 0, clause( 149553, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent(
% 87.99/88.46 Y, X ) ), true ) ) ] )
% 87.99/88.46 , 0, 3, substitution( 0, [ :=( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 87.99/88.46 :=( Y, X )] ), substitution( 1, [ :=( X, equivalent( X, equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( Z, Z ) ) ) ) ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149557, [ =( true, 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ) ) ) ) ) ] )
% 87.99/88.46 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , 0, clause( 149555, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.46 equivalent( Y, equivalent( X, equivalent( X, equivalent( Y, equivalent( Z
% 87.99/88.46 , Z ) ) ) ) ) ), true ) ) ] )
% 87.99/88.46 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.46 X, equivalent( Y, equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ) )
% 87.99/88.46 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, X ), :=(
% 87.99/88.46 Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149558, [ =( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ) ) ) ), true ) ] )
% 87.99/88.46 , clause( 149557, [ =( true, 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ) ) ) ) ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 77, [ =( 'is_a_theorem'( equivalent( Y, equivalent( X, equivalent(
% 87.99/88.46 X, equivalent( Y, equivalent( Z, Z ) ) ) ) ) ), true ) ] )
% 87.99/88.46 , clause( 149558, [ =( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ) ) ) ), true ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 87.99/88.46 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149560, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.46 Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.46 true ) ) ] )
% 87.99/88.46 , clause( 27, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.46 equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149562, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, Y ) ), X ) ), true ) ) ] )
% 87.99/88.46 , clause( 77, [ =( 'is_a_theorem'( equivalent( Y, equivalent( X, equivalent(
% 87.99/88.46 X, equivalent( Y, equivalent( Z, Z ) ) ) ) ) ), true ) ] )
% 87.99/88.46 , 0, clause( 149560, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent(
% 87.99/88.46 Y, X ) ), true ) ) ] )
% 87.99/88.46 , 0, 3, substitution( 0, [ :=( X, equivalent( X, equivalent( Y, Y ) ) ),
% 87.99/88.46 :=( Y, X ), :=( Z, Y )] ), substitution( 1, [ :=( X, X ), :=( Y,
% 87.99/88.46 equivalent( X, equivalent( Y, Y ) ) ), :=( Z, equivalent( X, equivalent(
% 87.99/88.46 Y, Y ) ) )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149564, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, Y ) ), X ) ) ) ] )
% 87.99/88.46 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , 0, clause( 149562, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( X, equivalent( Y, Y ) ), X ) ), true ) ) ] )
% 87.99/88.46 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, Y ) ), X ) ) ), :=( Z, true )] ),
% 87.99/88.46 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149565, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 Y, Y ) ), X ) ), true ) ] )
% 87.99/88.46 , clause( 149564, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, Y ) ), X ) ) ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 117, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 87.99/88.46 , Y ) ), X ) ), true ) ] )
% 87.99/88.46 , clause( 149565, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, Y ) ), X ) ), true ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 87.99/88.46 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149567, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 true ) ) ] )
% 87.99/88.46 , clause( 4, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.46 true ), true ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149569, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( Z, equivalent( T, equivalent( equivalent( X, equivalent( Y, Y
% 87.99/88.46 ) ), X ) ) ), equivalent( T, Z ) ) ), true ) ) ] )
% 87.99/88.46 , clause( 117, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 Y, Y ) ), X ) ), true ) ] )
% 87.99/88.46 , 0, clause( 149567, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 87.99/88.46 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.46 equivalent( Z, Y ) ) ), true ) ) ] )
% 87.99/88.46 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 87.99/88.46 :=( X, equivalent( equivalent( X, equivalent( Y, Y ) ), X ) ), :=( Y, Z )
% 87.99/88.46 , :=( Z, T )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149570, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( equivalent( Z, equivalent( T, T ) ), Z ) ) ),
% 87.99/88.46 equivalent( Y, X ) ) ) ) ] )
% 87.99/88.46 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.46 , 0, clause( 149569, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.46 equivalent( equivalent( Z, equivalent( T, equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, Y ) ), X ) ) ), equivalent( T, Z ) ) ), true ) ) ] )
% 87.99/88.46 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( T, T
% 87.99/88.46 ) ), Z ) ) ), equivalent( Y, X ) ) ) ), :=( Z, true )] ), substitution(
% 87.99/88.46 1, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149571, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.46 Y, equivalent( equivalent( Z, equivalent( T, T ) ), Z ) ) ), equivalent(
% 87.99/88.46 Y, X ) ) ), true ) ] )
% 87.99/88.46 , clause( 149570, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( equivalent( Z, equivalent( T, T ) ), Z ) ) ),
% 87.99/88.46 equivalent( Y, X ) ) ) ) ] )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.46 ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 subsumption(
% 87.99/88.46 clause( 136, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( T
% 87.99/88.46 , equivalent( equivalent( X, equivalent( Y, Y ) ), X ) ) ), equivalent( T
% 87.99/88.46 , Z ) ) ), true ) ] )
% 87.99/88.46 , clause( 149571, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.46 equivalent( Y, equivalent( equivalent( Z, equivalent( T, T ) ), Z ) ) ),
% 87.99/88.46 equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.46 , substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y )] ),
% 87.99/88.46 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 eqswap(
% 87.99/88.46 clause( 149573, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.46 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.46 ] )
% 87.99/88.46 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.46 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.46 )
% 87.99/88.46 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.46
% 87.99/88.46
% 87.99/88.46 paramod(
% 87.99/88.46 clause( 149576, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.46 equivalent( X, equivalent( Y, Y ) ), X ), Z ) ), true, ifeq( true, true,
% 87.99/88.46 'is_a_theorem'( Z ), true ), true ) ) ] )
% 87.99/88.46 , clause( 117, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 Y, Y ) ), X ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149573, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.47 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 15, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 87.99/88.47 :=( X, equivalent( equivalent( X, equivalent( Y, Y ) ), X ) ), :=( Y, Z )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149578, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, Y ) ), X ), Z ) ), true, 'is_a_theorem'( Z
% 87.99/88.47 ), true ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149576, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, equivalent( Y, Y ) ), X ), Z ) ), true, ifeq(
% 87.99/88.47 true, true, 'is_a_theorem'( Z ), true ), true ) ) ] )
% 87.99/88.47 , 0, 14, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( Z ) ),
% 87.99/88.47 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149579, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, Y ) ), X ), Z ) ), true, 'is_a_theorem'( Z
% 87.99/88.47 ), true ), true ) ] )
% 87.99/88.47 , clause( 149578, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, Y ) ), X ), Z ) ), true, 'is_a_theorem'( Z
% 87.99/88.47 ), true ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 138, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 X, equivalent( Y, Y ) ), X ), Z ) ), true, 'is_a_theorem'( Z ), true ),
% 87.99/88.47 true ) ] )
% 87.99/88.47 , clause( 149579, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, Y ) ), X ), Z ) ), true, 'is_a_theorem'( Z
% 87.99/88.47 ), true ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149581, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.47 , equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) )
% 87.99/88.47 , T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , clause( 5, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.47 T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149583, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( Y, Z ), equivalent( equivalent( Z, equivalent( Y
% 87.99/88.47 , equivalent( T, T ) ) ), X ) ), X ) ), true ) ) ] )
% 87.99/88.47 , clause( 26, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( U
% 87.99/88.47 , equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 87.99/88.47 equivalent( Y, X ) ) ) ), equivalent( U, T ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149581, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.47 equivalent( Z, Y ) ) ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, T ), :=( T, X ),
% 87.99/88.47 :=( U, equivalent( equivalent( Y, Z ), equivalent( equivalent( Z,
% 87.99/88.47 equivalent( Y, equivalent( T, T ) ) ), X ) ) )] ), substitution( 1, [
% 87.99/88.47 :=( X, X ), :=( Y, equivalent( Y, Z ) ), :=( Z, equivalent( Z, equivalent(
% 87.99/88.47 Y, equivalent( T, T ) ) ) ), :=( T, equivalent( equivalent( equivalent( Y
% 87.99/88.47 , Z ), equivalent( equivalent( Z, equivalent( Y, equivalent( T, T ) ) ),
% 87.99/88.47 X ) ), X ) )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149585, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X, equivalent(
% 87.99/88.47 Z, Z ) ) ), T ) ), T ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149583, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( equivalent( Y, Z ), equivalent( equivalent( Z,
% 87.99/88.47 equivalent( Y, equivalent( T, T ) ) ), X ) ), X ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X
% 87.99/88.47 , equivalent( Z, Z ) ) ), T ) ), T ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149586, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.47 , Y ), equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ),
% 87.99/88.47 T ) ), T ) ), true ) ] )
% 87.99/88.47 , clause( 149585, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X, equivalent(
% 87.99/88.47 Z, Z ) ) ), T ) ), T ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 191, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y, Z
% 87.99/88.47 ), equivalent( equivalent( Z, equivalent( Y, equivalent( T, T ) ) ), X )
% 87.99/88.47 ), X ) ), true ) ] )
% 87.99/88.47 , clause( 149586, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 X, Y ), equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) )
% 87.99/88.47 , T ) ), T ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, X )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149588, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, Y ) ), X ), Z ) ), true, 'is_a_theorem'( Z
% 87.99/88.47 ), true ) ) ] )
% 87.99/88.47 , clause( 138, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, Y ) ), X ), Z ) ), true, 'is_a_theorem'( Z
% 87.99/88.47 ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149590, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( X
% 87.99/88.47 , equivalent( equivalent( X, equivalent( Y, equivalent( equivalent( Z,
% 87.99/88.47 equivalent( T, Y ) ), equivalent( T, Z ) ) ) ), equivalent( U, U ) ) ) )
% 87.99/88.47 , true ) ) ] )
% 87.99/88.47 , clause( 7, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( U
% 87.99/88.47 , equivalent( X, equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.47 equivalent( Z, Y ) ) ) ) ), equivalent( U, T ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149588, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, equivalent( Y, Y ) ), X ), Z ) ), true,
% 87.99/88.47 'is_a_theorem'( Z ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T,
% 87.99/88.47 equivalent( equivalent( X, equivalent( Y, equivalent( equivalent( Z,
% 87.99/88.47 equivalent( T, Y ) ), equivalent( T, Z ) ) ) ), equivalent( U, U ) ) ),
% 87.99/88.47 :=( U, X )] ), substitution( 1, [ :=( X, equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( T, Y ) ), equivalent( T, Z ) ) ) )
% 87.99/88.47 ), :=( Y, U ), :=( Z, equivalent( X, equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y ) ),
% 87.99/88.47 equivalent( T, Z ) ) ) ), equivalent( U, U ) ) ) )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149592, [ =( true, 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y
% 87.99/88.47 ) ), equivalent( T, Z ) ) ) ), equivalent( U, U ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149590, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( equivalent( X, equivalent( Y, equivalent(
% 87.99/88.47 equivalent( Z, equivalent( T, Y ) ), equivalent( T, Z ) ) ) ), equivalent(
% 87.99/88.47 U, U ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 X, equivalent( equivalent( X, equivalent( Y, equivalent( equivalent( Z,
% 87.99/88.47 equivalent( T, Y ) ), equivalent( T, Z ) ) ) ), equivalent( U, U ) ) ) )
% 87.99/88.47 ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z
% 87.99/88.47 ), :=( T, T ), :=( U, U )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149593, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 87.99/88.47 X, equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y ) ),
% 87.99/88.47 equivalent( T, Z ) ) ) ), equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149592, [ =( true, 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y
% 87.99/88.47 ) ), equivalent( T, Z ) ) ) ), equivalent( U, U ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 87.99/88.47 :=( U, U )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 227, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent( X
% 87.99/88.47 , equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y ) ),
% 87.99/88.47 equivalent( T, Z ) ) ) ), equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149593, [ =( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y
% 87.99/88.47 ) ), equivalent( T, Z ) ) ) ), equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 87.99/88.47 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149595, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.47 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.47 ] )
% 87.99/88.47 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.47 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149597, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, Z ), equivalent(
% 87.99/88.47 T, T ) ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ), true ), true
% 87.99/88.47 ) ) ] )
% 87.99/88.47 , clause( 30, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( T
% 87.99/88.47 , equivalent( equivalent( X, X ), equivalent( Y, Y ) ) ) ), equivalent( T
% 87.99/88.47 , Z ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149595, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.47 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y )] )
% 87.99/88.47 , substitution( 1, [ :=( X, equivalent( X, equivalent( Y, equivalent(
% 87.99/88.47 equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), :=( Y, equivalent( Y, X )
% 87.99/88.47 )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149602, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149597, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, Z ), equivalent(
% 87.99/88.47 T, T ) ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ), true ), true
% 87.99/88.47 ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, Z ), equivalent(
% 87.99/88.47 T, T ) ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ),
% 87.99/88.47 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 87.99/88.47 :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149603, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , clause( 149602, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 272, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , clause( 149603, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149605, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.47 , equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) )
% 87.99/88.47 , T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , clause( 5, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.47 T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149607, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y ) ), X ) ), X
% 87.99/88.47 ) ), true ) ) ] )
% 87.99/88.47 , clause( 39, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( T
% 87.99/88.47 , equivalent( equivalent( X, equivalent( X, Y ) ), Y ) ) ), equivalent( T
% 87.99/88.47 , Z ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149605, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.47 equivalent( Z, Y ) ) ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X ), :=( T,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y ) ), X ) ) )] )
% 87.99/88.47 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, equivalent( Z,
% 87.99/88.47 equivalent( Z, Y ) ) ), :=( T, equivalent( equivalent( Y, equivalent(
% 87.99/88.47 equivalent( Z, equivalent( Z, Y ) ), X ) ), X ) )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149609, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ), Z ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149607, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y )
% 87.99/88.47 ), X ) ), X ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ), Z
% 87.99/88.47 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, X ), :=(
% 87.99/88.47 Z, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149610, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ), Z ) ), true ) ] )
% 87.99/88.47 , clause( 149609, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ), Z ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 413, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.47 equivalent( Z, equivalent( Z, Y ) ), X ) ), X ) ), true ) ] )
% 87.99/88.47 , clause( 149610, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ), Z ) ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149612, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.47 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.47 ] )
% 87.99/88.47 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.47 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149614, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( Z, T
% 87.99/88.47 ) ), T ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ), true ), true
% 87.99/88.47 ) ) ] )
% 87.99/88.47 , clause( 39, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( T
% 87.99/88.47 , equivalent( equivalent( X, equivalent( X, Y ) ), Y ) ) ), equivalent( T
% 87.99/88.47 , Z ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149612, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.47 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y )] )
% 87.99/88.47 , substitution( 1, [ :=( X, equivalent( X, equivalent( Y, equivalent(
% 87.99/88.47 equivalent( Z, equivalent( Z, T ) ), T ) ) ) ), :=( Y, equivalent( Y, X )
% 87.99/88.47 )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149619, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149614, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( Z, T
% 87.99/88.47 ) ), T ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ), true ), true
% 87.99/88.47 ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( Z, T
% 87.99/88.47 ) ), T ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ),
% 87.99/88.47 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 87.99/88.47 :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149620, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , clause( 149619, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 414, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , clause( 149620, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149622, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , clause( 27, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149624, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( Z
% 87.99/88.47 , equivalent( X, equivalent( equivalent( Y, equivalent( Y, X ) ),
% 87.99/88.47 equivalent( Z, equivalent( T, T ) ) ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 413, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.47 equivalent( Z, equivalent( Z, Y ) ), X ) ), X ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149622, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent(
% 87.99/88.47 Y, X ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, equivalent( Z, equivalent( T, T ) ) ),
% 87.99/88.47 :=( Y, X ), :=( Z, Y )] ), substitution( 1, [ :=( X, equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), equivalent( Z,
% 87.99/88.47 equivalent( T, T ) ) ) ) ), :=( Y, Z ), :=( Z, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149626, [ =( true, 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( Z, Y ) ), equivalent( X,
% 87.99/88.47 equivalent( T, T ) ) ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149624, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( Z, equivalent( X, equivalent( equivalent( Y, equivalent( Y, X
% 87.99/88.47 ) ), equivalent( Z, equivalent( T, T ) ) ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 X, equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y ) ),
% 87.99/88.47 equivalent( X, equivalent( T, T ) ) ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149627, [ =( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( Z, Y ) ), equivalent( X,
% 87.99/88.47 equivalent( T, T ) ) ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149626, [ =( true, 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( Z, Y ) ), equivalent( X,
% 87.99/88.47 equivalent( T, T ) ) ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 442, [ =( 'is_a_theorem'( equivalent( Z, equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), equivalent( Z, equivalent( T, T ) )
% 87.99/88.47 ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149627, [ =( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( Z, Y ) ), equivalent( X,
% 87.99/88.47 equivalent( T, T ) ) ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149629, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , clause( 4, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149631, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( T, equivalent( U, equivalent( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ), Z ) ) ), equivalent( U, T ) )
% 87.99/88.47 ), true ) ) ] )
% 87.99/88.47 , clause( 413, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.47 equivalent( Z, equivalent( Z, Y ) ), X ) ), X ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149629, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.47 equivalent( Z, Y ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 87.99/88.47 substitution( 1, [ :=( X, equivalent( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ), Z ) ), :=( Y, T ), :=( Z, U )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149633, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( equivalent( T,
% 87.99/88.47 equivalent( T, Z ) ), U ) ), U ) ) ), equivalent( Y, X ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149631, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( T, equivalent( U, equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ), Z ) ) ),
% 87.99/88.47 equivalent( U, T ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent(
% 87.99/88.47 equivalent( T, equivalent( T, Z ) ), U ) ), U ) ) ), equivalent( Y, X ) )
% 87.99/88.47 ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, T ), :=( Z
% 87.99/88.47 , U ), :=( T, X ), :=( U, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149634, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( equivalent( Z, equivalent( equivalent( T, equivalent( T, Z
% 87.99/88.47 ) ), U ) ), U ) ) ), equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.47 , clause( 149633, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( equivalent( T,
% 87.99/88.47 equivalent( T, Z ) ), U ) ), U ) ) ), equivalent( Y, X ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 87.99/88.47 :=( U, U )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 447, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( U
% 87.99/88.47 , equivalent( equivalent( X, equivalent( equivalent( Y, equivalent( Y, X
% 87.99/88.47 ) ), Z ) ), Z ) ) ), equivalent( U, T ) ) ), true ) ] )
% 87.99/88.47 , clause( 149634, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( equivalent( T,
% 87.99/88.47 equivalent( T, Z ) ), U ) ), U ) ) ), equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, T ), :=( Y, U ), :=( Z, X ), :=( T, Y ), :=( U
% 87.99/88.47 , Z )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149636, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.47 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.47 ] )
% 87.99/88.47 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.47 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149638, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ) ),
% 87.99/88.47 true, 'is_a_theorem'( Z ), true ), true ) ) ] )
% 87.99/88.47 , clause( 413, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.47 equivalent( Z, equivalent( Z, Y ) ), X ) ), X ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149636, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.47 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 87.99/88.47 substitution( 1, [ :=( X, equivalent( X, equivalent( equivalent( Y,
% 87.99/88.47 equivalent( Y, X ) ), Z ) ) ), :=( Y, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149643, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149638, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ) ),
% 87.99/88.47 true, 'is_a_theorem'( Z ), true ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ) ),
% 87.99/88.47 true, 'is_a_theorem'( Z ), true ) ), :=( Z, true )] ), substitution( 1, [
% 87.99/88.47 :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149644, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , clause( 149643, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true,
% 87.99/88.47 'is_a_theorem'( Z ), true ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 448, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , clause( 149644, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149646, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , clause( 448, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149648, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), equivalent( X, equivalent( Z, Z ) )
% 87.99/88.47 ) ), true ) ) ] )
% 87.99/88.47 , clause( 77, [ =( 'is_a_theorem'( equivalent( Y, equivalent( X, equivalent(
% 87.99/88.47 X, equivalent( Y, equivalent( Z, Z ) ) ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149646, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true,
% 87.99/88.47 'is_a_theorem'( Z ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, equivalent( Y, equivalent( Y, X ) ) ),
% 87.99/88.47 :=( Y, X ), :=( Z, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 87.99/88.47 :=( Z, equivalent( equivalent( Y, equivalent( Y, X ) ), equivalent( X,
% 87.99/88.47 equivalent( Z, Z ) ) ) )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149650, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( Y, equivalent( Z, Z ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149648, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), equivalent( X,
% 87.99/88.47 equivalent( Z, Z ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), equivalent( Y, equivalent( Z, Z ) )
% 87.99/88.47 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, X ), :=(
% 87.99/88.47 Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149651, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 X, Y ) ), equivalent( Y, equivalent( Z, Z ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149650, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( Y, equivalent( Z, Z ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 488, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Y
% 87.99/88.47 , X ) ), equivalent( X, equivalent( Z, Z ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149651, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( Y, equivalent( Z, Z ) ) ) ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149653, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , clause( 27, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149655, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( Y
% 87.99/88.47 , equivalent( X, equivalent( X, Y ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 488, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.47 Y, X ) ), equivalent( X, equivalent( Z, Z ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149653, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent(
% 87.99/88.47 Y, X ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 87.99/88.47 substitution( 1, [ :=( X, equivalent( X, equivalent( X, Y ) ) ), :=( Y, Y
% 87.99/88.47 ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149657, [ =( true, 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Y, X ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149655, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( Y, equivalent( X, equivalent( X, Y ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 X, equivalent( Y, equivalent( Y, X ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, Y ), :=( Y, X )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149658, [ =( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Y, X ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149657, [ =( true, 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Y, X ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 496, [ =( 'is_a_theorem'( equivalent( Y, equivalent( X, equivalent(
% 87.99/88.47 X, Y ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149658, [ =( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Y, X ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 87.99/88.47 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149660, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , clause( 4, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149662, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( Z, equivalent( T, equivalent( X, equivalent( Y, equivalent( Y
% 87.99/88.47 , X ) ) ) ) ), equivalent( T, Z ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 496, [ =( 'is_a_theorem'( equivalent( Y, equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149660, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.47 equivalent( Z, Y ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 87.99/88.47 :=( X, equivalent( X, equivalent( Y, equivalent( Y, X ) ) ) ), :=( Y, Z )
% 87.99/88.47 , :=( Z, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149663, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, equivalent( T, equivalent( T, Z ) ) ) ) ),
% 87.99/88.47 equivalent( Y, X ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149662, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( Z, equivalent( T, equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Y, X ) ) ) ) ), equivalent( T, Z ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Z, equivalent( T, equivalent( T
% 87.99/88.47 , Z ) ) ) ) ), equivalent( Y, X ) ) ) ), :=( Z, true )] ), substitution(
% 87.99/88.47 1, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149664, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( Z, equivalent( T, equivalent( T, Z ) ) ) ) ), equivalent(
% 87.99/88.47 Y, X ) ) ), true ) ] )
% 87.99/88.47 , clause( 149663, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, equivalent( T, equivalent( T, Z ) ) ) ) ),
% 87.99/88.47 equivalent( Y, X ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 523, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( T
% 87.99/88.47 , equivalent( X, equivalent( Y, equivalent( Y, X ) ) ) ) ), equivalent( T
% 87.99/88.47 , Z ) ) ), true ) ] )
% 87.99/88.47 , clause( 149664, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, equivalent( T, equivalent( T, Z ) ) ) ) ),
% 87.99/88.47 equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149666, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , clause( 448, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149668, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( Z, equivalent( Z, equivalent( Y, equivalent( Y, X ) ) ) ),
% 87.99/88.47 equivalent( X, equivalent( T, T ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 442, [ =( 'is_a_theorem'( equivalent( Z, equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), equivalent( Z,
% 87.99/88.47 equivalent( T, T ) ) ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149666, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true,
% 87.99/88.47 'is_a_theorem'( Z ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, equivalent( Y, equivalent( Y, X ) ) ),
% 87.99/88.47 :=( Y, Z ), :=( Z, X ), :=( T, T )] ), substitution( 1, [ :=( X, X ),
% 87.99/88.47 :=( Y, Y ), :=( Z, equivalent( equivalent( Z, equivalent( Z, equivalent(
% 87.99/88.47 Y, equivalent( Y, X ) ) ) ), equivalent( X, equivalent( T, T ) ) ) )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149670, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ) ), equivalent( Z,
% 87.99/88.47 equivalent( T, T ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149668, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( Z, equivalent( Z, equivalent( Y, equivalent( Y, X
% 87.99/88.47 ) ) ) ), equivalent( X, equivalent( T, T ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ) ),
% 87.99/88.47 equivalent( Z, equivalent( T, T ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, Z ), :=( Y, Y ), :=( Z, X ), :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149671, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 X, equivalent( Y, equivalent( Y, Z ) ) ) ), equivalent( Z, equivalent( T
% 87.99/88.47 , T ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149670, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ) ), equivalent( Z,
% 87.99/88.47 equivalent( T, T ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 798, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( Z
% 87.99/88.47 , equivalent( Y, equivalent( Y, X ) ) ) ), equivalent( X, equivalent( T,
% 87.99/88.47 T ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149671, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ) ), equivalent( Z,
% 87.99/88.47 equivalent( T, T ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149673, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z
% 87.99/88.47 , T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , clause( 10, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z, T ) ) ),
% 87.99/88.47 true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149675, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( T, equivalent( T, Z ) ), equivalent( equivalent( equivalent(
% 87.99/88.47 X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( U, U ) ) ) ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , clause( 442, [ =( 'is_a_theorem'( equivalent( Z, equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), equivalent( Z,
% 87.99/88.47 equivalent( T, T ) ) ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149673, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ),
% 87.99/88.47 equivalent( Z, T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ) ), :=( T, U )] )
% 87.99/88.47 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 87.99/88.47 equivalent( equivalent( T, equivalent( T, Z ) ), equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( U
% 87.99/88.47 , U ) ) ) )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149677, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( equivalent( equivalent( Z, equivalent(
% 87.99/88.47 T, Y ) ), equivalent( T, Z ) ), equivalent( U, U ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149675, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( T, equivalent( T, Z ) ), equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( U
% 87.99/88.47 , U ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), equivalent( equivalent( equivalent(
% 87.99/88.47 Z, equivalent( T, Y ) ), equivalent( T, Z ) ), equivalent( U, U ) ) ) ) )
% 87.99/88.47 , :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, T ), :=( Z, Y )
% 87.99/88.47 , :=( T, X ), :=( U, U )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149678, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 X, Y ) ), equivalent( equivalent( equivalent( Z, equivalent( T, Y ) ),
% 87.99/88.47 equivalent( T, Z ) ), equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149677, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( equivalent( equivalent( Z, equivalent(
% 87.99/88.47 T, Y ) ), equivalent( T, Z ) ), equivalent( U, U ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 87.99/88.47 :=( U, U )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 805, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( T
% 87.99/88.47 , Z ) ), equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ),
% 87.99/88.47 equivalent( Y, X ) ), equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149678, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( equivalent( equivalent( Z, equivalent(
% 87.99/88.47 T, Y ) ), equivalent( T, Z ) ), equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, T ), :=( Y, Z ), :=( Z, X ), :=( T, Y ), :=( U
% 87.99/88.47 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149680, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , clause( 27, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149682, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( Z
% 87.99/88.47 , equivalent( X, equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ) ) )
% 87.99/88.47 ), true ) ) ] )
% 87.99/88.47 , clause( 798, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.47 Z, equivalent( Y, equivalent( Y, X ) ) ) ), equivalent( X, equivalent( T
% 87.99/88.47 , T ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149680, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent(
% 87.99/88.47 Y, X ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X ), :=( T, T )] )
% 87.99/88.47 , substitution( 1, [ :=( X, equivalent( X, equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Y, Z ) ) ) ) ), :=( Y, Z ), :=( Z, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149684, [ =( true, 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Y, equivalent( Z, equivalent( Z, X ) ) ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149682, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( Z, equivalent( X, equivalent( X, equivalent( Y, equivalent( Y
% 87.99/88.47 , Z ) ) ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 X, equivalent( Y, equivalent( Y, equivalent( Z, equivalent( Z, X ) ) ) )
% 87.99/88.47 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=(
% 87.99/88.47 Z, X )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149685, [ =( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Y, equivalent( Z, equivalent( Z, X ) ) ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149684, [ =( true, 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Y, equivalent( Z, equivalent( Z, X ) ) ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 859, [ =( 'is_a_theorem'( equivalent( Z, equivalent( X, equivalent(
% 87.99/88.47 X, equivalent( Y, equivalent( Y, Z ) ) ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149685, [ =( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Y, equivalent( Z, equivalent( Z, X ) ) ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149687, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , clause( 448, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149689, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), equivalent( Z, equivalent( Z, X ) )
% 87.99/88.47 ) ), true ) ) ] )
% 87.99/88.47 , clause( 859, [ =( 'is_a_theorem'( equivalent( Z, equivalent( X,
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149687, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true,
% 87.99/88.47 'is_a_theorem'( Z ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, equivalent( Y, equivalent( Y, X ) ) ),
% 87.99/88.47 :=( Y, Z ), :=( Z, X )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 87.99/88.47 :=( Z, equivalent( equivalent( Y, equivalent( Y, X ) ), equivalent( Z,
% 87.99/88.47 equivalent( Z, X ) ) ) )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149691, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( Z, equivalent( Z, Y ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149689, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), equivalent( Z,
% 87.99/88.47 equivalent( Z, X ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), equivalent( Z, equivalent( Z, Y ) )
% 87.99/88.47 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, X ), :=(
% 87.99/88.47 Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149692, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 X, Y ) ), equivalent( Z, equivalent( Z, Y ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149691, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( Z, equivalent( Z, Y ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 866, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Y
% 87.99/88.47 , X ) ), equivalent( Z, equivalent( Z, X ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149692, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( Z, equivalent( Z, Y ) ) ) ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149694, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z
% 87.99/88.47 , T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , clause( 10, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z, T ) ) ),
% 87.99/88.47 true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149696, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( Z
% 87.99/88.47 , equivalent( T, equivalent( T, equivalent( equivalent( X, equivalent( Y
% 87.99/88.47 , Z ) ), equivalent( Y, X ) ) ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 859, [ =( 'is_a_theorem'( equivalent( Z, equivalent( X,
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149694, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ),
% 87.99/88.47 equivalent( Z, T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ) )] ),
% 87.99/88.47 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, equivalent(
% 87.99/88.47 Z, equivalent( T, equivalent( T, equivalent( equivalent( X, equivalent( Y
% 87.99/88.47 , Z ) ), equivalent( Y, X ) ) ) ) ) )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149698, [ =( true, 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( T, X ) ),
% 87.99/88.47 equivalent( T, Z ) ) ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149696, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( Z, equivalent( T, equivalent( T, equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, Z ) ), equivalent( Y, X ) ) ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 X, equivalent( Y, equivalent( Y, equivalent( equivalent( Z, equivalent( T
% 87.99/88.47 , X ) ), equivalent( T, Z ) ) ) ) ) ) ), :=( Z, true )] ), substitution(
% 87.99/88.47 1, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149699, [ =( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( T, X ) ),
% 87.99/88.47 equivalent( T, Z ) ) ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149698, [ =( true, 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( T, X ) ),
% 87.99/88.47 equivalent( T, Z ) ) ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 876, [ =( 'is_a_theorem'( equivalent( Z, equivalent( T, equivalent(
% 87.99/88.47 T, equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) )
% 87.99/88.47 ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149699, [ =( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( T, X ) ),
% 87.99/88.47 equivalent( T, Z ) ) ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149701, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.47 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.47 ] )
% 87.99/88.47 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.47 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149704, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), equivalent( Z, equivalent( Z, Y ) )
% 87.99/88.47 ), T ) ), true, ifeq( true, true, 'is_a_theorem'( T ), true ), true ) )
% 87.99/88.47 ] )
% 87.99/88.47 , clause( 866, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.47 Y, X ) ), equivalent( Z, equivalent( Z, X ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149701, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.47 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 19, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 87.99/88.47 substitution( 1, [ :=( X, equivalent( equivalent( X, equivalent( X, Y ) )
% 87.99/88.47 , equivalent( Z, equivalent( Z, Y ) ) ) ), :=( Y, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149706, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), equivalent( Z, equivalent( Z, Y ) )
% 87.99/88.47 ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149704, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, equivalent( X, Y ) ), equivalent( Z,
% 87.99/88.47 equivalent( Z, Y ) ) ), T ) ), true, ifeq( true, true, 'is_a_theorem'( T
% 87.99/88.47 ), true ), true ) ) ] )
% 87.99/88.47 , 0, 18, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( T ) ),
% 87.99/88.47 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 87.99/88.47 :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149707, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), equivalent( Z, equivalent( Z, Y ) )
% 87.99/88.47 ), T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , clause( 149706, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), equivalent( Z, equivalent( Z, Y ) )
% 87.99/88.47 ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 897, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 X, equivalent( X, Y ) ), equivalent( Z, equivalent( Z, Y ) ) ), T ) ),
% 87.99/88.47 true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , clause( 149707, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), equivalent( Z, equivalent( Z, Y ) )
% 87.99/88.47 ), T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149709, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , clause( 448, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149711, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), equivalent( equivalent( Z,
% 87.99/88.47 equivalent( T, X ) ), equivalent( T, Z ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 876, [ =( 'is_a_theorem'( equivalent( Z, equivalent( T,
% 87.99/88.47 equivalent( T, equivalent( equivalent( X, equivalent( Y, Z ) ),
% 87.99/88.47 equivalent( Y, X ) ) ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149709, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true,
% 87.99/88.47 'is_a_theorem'( Z ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T,
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ) )] ), substitution( 1, [ :=( X, X ),
% 87.99/88.47 :=( Y, Y ), :=( Z, equivalent( equivalent( Y, equivalent( Y, X ) ),
% 87.99/88.47 equivalent( equivalent( Z, equivalent( T, X ) ), equivalent( T, Z ) ) ) )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149713, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( equivalent( Z, equivalent( T, Y ) ),
% 87.99/88.47 equivalent( T, Z ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149711, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), equivalent( equivalent(
% 87.99/88.47 Z, equivalent( T, X ) ), equivalent( T, Z ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), equivalent( equivalent( Z,
% 87.99/88.47 equivalent( T, Y ) ), equivalent( T, Z ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149714, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 X, Y ) ), equivalent( equivalent( Z, equivalent( T, Y ) ), equivalent( T
% 87.99/88.47 , Z ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149713, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( equivalent( Z, equivalent( T, Y ) ),
% 87.99/88.47 equivalent( T, Z ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 1118, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Y
% 87.99/88.47 , X ) ), equivalent( equivalent( Z, equivalent( T, X ) ), equivalent( T,
% 87.99/88.47 Z ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149714, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( equivalent( Z, equivalent( T, Y ) ),
% 87.99/88.47 equivalent( T, Z ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149716, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.47 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.47 ] )
% 87.99/88.47 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.47 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149718, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Z, equivalent( T, equivalent( T
% 87.99/88.47 , Z ) ) ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ), true ), true
% 87.99/88.47 ) ) ] )
% 87.99/88.47 , clause( 523, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.47 T, equivalent( X, equivalent( Y, equivalent( Y, X ) ) ) ) ), equivalent(
% 87.99/88.47 T, Z ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149716, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.47 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y )] )
% 87.99/88.47 , substitution( 1, [ :=( X, equivalent( X, equivalent( Y, equivalent( Z,
% 87.99/88.47 equivalent( T, equivalent( T, Z ) ) ) ) ) ), :=( Y, equivalent( Y, X ) )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149723, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( Z, equivalent( T, equivalent( T, Z ) ) ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149718, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Z, equivalent( T, equivalent( T
% 87.99/88.47 , Z ) ) ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ), true ), true
% 87.99/88.47 ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Z, equivalent( T, equivalent( T
% 87.99/88.47 , Z ) ) ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ),
% 87.99/88.47 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 87.99/88.47 :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149724, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Z, equivalent( T, equivalent( T, Z ) ) ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , clause( 149723, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, equivalent( T, equivalent( T, Z ) ) ) ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 1216, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Z, equivalent( T, equivalent( T, Z ) ) ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , clause( 149724, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Z, equivalent( T, equivalent( T, Z ) ) ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149726, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.47 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.47 ] )
% 87.99/88.47 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.47 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149728, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( T, T
% 87.99/88.47 ) ), Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ), true ), true
% 87.99/88.47 ) ) ] )
% 87.99/88.47 , clause( 136, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.47 T, equivalent( equivalent( X, equivalent( Y, Y ) ), X ) ) ), equivalent(
% 87.99/88.47 T, Z ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149726, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.47 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y )] )
% 87.99/88.47 , substitution( 1, [ :=( X, equivalent( X, equivalent( Y, equivalent(
% 87.99/88.47 equivalent( Z, equivalent( T, T ) ), Z ) ) ) ), :=( Y, equivalent( Y, X )
% 87.99/88.47 )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149733, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( equivalent( Z, equivalent( T, T ) ), Z ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149728, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( T, T
% 87.99/88.47 ) ), Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ), true ), true
% 87.99/88.47 ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( T, T
% 87.99/88.47 ) ), Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ),
% 87.99/88.47 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 87.99/88.47 :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149734, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( T, T ) ), Z ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , clause( 149733, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( T, T ) ), Z ) ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 2360, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( T, T ) ), Z ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , clause( 149734, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( T, T ) ), Z ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149736, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.47 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.47 ] )
% 87.99/88.47 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.47 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149738, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X
% 87.99/88.47 , equivalent( Z, Z ) ) ), T ) ) ), true, 'is_a_theorem'( T ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , clause( 191, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y,
% 87.99/88.47 Z ), equivalent( equivalent( Z, equivalent( Y, equivalent( T, T ) ) ), X
% 87.99/88.47 ) ), X ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149736, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.47 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] )
% 87.99/88.47 , substitution( 1, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 87.99/88.47 equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ), T ) ) ), :=( Y, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149743, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.47 , Y ), equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ),
% 87.99/88.47 T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149738, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X
% 87.99/88.47 , equivalent( Z, Z ) ) ), T ) ) ), true, 'is_a_theorem'( T ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X
% 87.99/88.47 , equivalent( Z, Z ) ) ), T ) ) ), true, 'is_a_theorem'( T ), true ) ),
% 87.99/88.47 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 87.99/88.47 :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149744, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ), T ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , clause( 149743, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 X, Y ), equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) )
% 87.99/88.47 , T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 3245, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ), T ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , clause( 149744, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y )
% 87.99/88.47 , equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ), T ) )
% 87.99/88.47 ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149746, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , clause( 27, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Y, X ) ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149748, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y
% 87.99/88.47 ) ), equivalent( T, Z ) ) ) ), X ) ), true ) ) ] )
% 87.99/88.47 , clause( 227, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 87.99/88.47 X, equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y ) ),
% 87.99/88.47 equivalent( T, Z ) ) ) ), equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149746, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent(
% 87.99/88.47 Y, X ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 87.99/88.47 :=( U, U )] ), substitution( 1, [ :=( X, X ), :=( Y, equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y ) ),
% 87.99/88.47 equivalent( T, Z ) ) ) ) ), :=( Z, U )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149750, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y ) ),
% 87.99/88.47 equivalent( T, Z ) ) ) ), X ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149748, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( X, equivalent( Y, equivalent( equivalent( Z,
% 87.99/88.47 equivalent( T, Y ) ), equivalent( T, Z ) ) ) ), X ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y
% 87.99/88.47 ) ), equivalent( T, Z ) ) ) ), X ) ) ), :=( Z, true )] ), substitution(
% 87.99/88.47 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149751, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( equivalent( Z, equivalent( T, Y ) ), equivalent( T, Z ) )
% 87.99/88.47 ) ), X ) ), true ) ] )
% 87.99/88.47 , clause( 149750, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y ) ),
% 87.99/88.47 equivalent( T, Z ) ) ) ), X ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 3833, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 87.99/88.47 , equivalent( equivalent( Z, equivalent( T, Y ) ), equivalent( T, Z ) ) )
% 87.99/88.47 ), X ) ), true ) ] )
% 87.99/88.47 , clause( 149751, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y ) ),
% 87.99/88.47 equivalent( T, Z ) ) ) ), X ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149753, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.47 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.47 ] )
% 87.99/88.47 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.47 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149755, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y
% 87.99/88.47 ) ), equivalent( T, Z ) ) ) ) ), true, 'is_a_theorem'( X ), true ), true
% 87.99/88.47 ) ) ] )
% 87.99/88.47 , clause( 3833, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( equivalent( Z, equivalent( T, Y ) ), equivalent( T, Z ) )
% 87.99/88.47 ) ), X ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149753, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.47 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 , substitution( 1, [ :=( X, equivalent( X, equivalent( Y, equivalent(
% 87.99/88.47 equivalent( Z, equivalent( T, Y ) ), equivalent( T, Z ) ) ) ) ), :=( Y, X
% 87.99/88.47 )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149760, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( equivalent( Z, equivalent( T, Y ) ), equivalent( T, Z ) )
% 87.99/88.47 ) ) ), true, 'is_a_theorem'( X ), true ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149755, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y
% 87.99/88.47 ) ), equivalent( T, Z ) ) ) ) ), true, 'is_a_theorem'( X ), true ), true
% 87.99/88.47 ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y
% 87.99/88.47 ) ), equivalent( T, Z ) ) ) ) ), true, 'is_a_theorem'( X ), true ) ),
% 87.99/88.47 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 87.99/88.47 :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149761, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( T, Y ) ), equivalent( T, Z ) ) ) )
% 87.99/88.47 ), true, 'is_a_theorem'( X ), true ), true ) ] )
% 87.99/88.47 , clause( 149760, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y ) ),
% 87.99/88.47 equivalent( T, Z ) ) ) ) ), true, 'is_a_theorem'( X ), true ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 3836, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( T, Y ) ), equivalent( T, Z ) ) ) )
% 87.99/88.47 ), true, 'is_a_theorem'( X ), true ), true ) ] )
% 87.99/88.47 , clause( 149761, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( T, Y ) ), equivalent( T, Z ) ) ) )
% 87.99/88.47 ), true, 'is_a_theorem'( X ), true ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149763, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), equivalent( Z, equivalent( Z, Y ) )
% 87.99/88.47 ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , clause( 897, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), equivalent( Z, equivalent( Z, Y ) )
% 87.99/88.47 ), T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149765, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( Z, equivalent( Y, equivalent( T, T ) ) ), equivalent( X,
% 87.99/88.47 equivalent( X, equivalent( Y, Z ) ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 26, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( U
% 87.99/88.47 , equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 87.99/88.47 equivalent( Y, X ) ) ) ), equivalent( U, T ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149763, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, equivalent( X, Y ) ), equivalent( Z,
% 87.99/88.47 equivalent( Z, Y ) ) ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, T ), :=( T,
% 87.99/88.47 equivalent( X, equivalent( X, equivalent( Y, Z ) ) ) ), :=( U, equivalent(
% 87.99/88.47 Z, equivalent( Y, equivalent( T, T ) ) ) )] ), substitution( 1, [ :=( X,
% 87.99/88.47 X ), :=( Y, equivalent( Y, Z ) ), :=( Z, equivalent( Z, equivalent( Y,
% 87.99/88.47 equivalent( T, T ) ) ) ), :=( T, equivalent( equivalent( Z, equivalent( Y
% 87.99/88.47 , equivalent( T, T ) ) ), equivalent( X, equivalent( X, equivalent( Y, Z
% 87.99/88.47 ) ) ) ) )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149767, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( T, equivalent( T,
% 87.99/88.47 equivalent( Y, X ) ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149765, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( Z, equivalent( Y, equivalent( T, T ) ) ),
% 87.99/88.47 equivalent( X, equivalent( X, equivalent( Y, Z ) ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ), equivalent( T,
% 87.99/88.47 equivalent( T, equivalent( Y, X ) ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, T ), :=( Y, Y ), :=( Z, X ), :=( T, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149768, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( Z, Z ) ) ), equivalent( T, equivalent( T, equivalent( Y, X
% 87.99/88.47 ) ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149767, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( T, equivalent( T,
% 87.99/88.47 equivalent( Y, X ) ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 3881, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( Y
% 87.99/88.47 , equivalent( T, T ) ) ), equivalent( X, equivalent( X, equivalent( Y, Z
% 87.99/88.47 ) ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149768, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( T, equivalent( T,
% 87.99/88.47 equivalent( Y, X ) ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, T ), :=( T, X )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149770, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( Z, equivalent( T, equivalent( T, Z ) ) ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , clause( 1216, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Z, equivalent( T, equivalent( T, Z ) ) ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149772, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( Z, equivalent( Z, T ) ), equivalent( T, Y ) ),
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 1118, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.47 Y, X ) ), equivalent( equivalent( Z, equivalent( T, X ) ), equivalent( T
% 87.99/88.47 , Z ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149770, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, equivalent( T, equivalent( T, Z ) ) ) ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, equivalent( Z,
% 87.99/88.47 equivalent( Z, T ) ) ), :=( T, T )] ), substitution( 1, [ :=( X,
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ) ), :=( Y, equivalent( equivalent( Z,
% 87.99/88.47 equivalent( Z, T ) ), equivalent( T, Y ) ) ), :=( Z, T ), :=( T, Z )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149774, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), equivalent( Y, Z ) ), equivalent( T
% 87.99/88.47 , equivalent( T, Z ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149772, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( equivalent( Z, equivalent( Z, T ) ), equivalent(
% 87.99/88.47 T, Y ) ), equivalent( X, equivalent( X, Y ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, equivalent( X, Y ) ), equivalent( Y, Z ) ),
% 87.99/88.47 equivalent( T, equivalent( T, Z ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, T ), :=( Y, Z ), :=( Z, X ), :=( T, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149775, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.47 , equivalent( X, Y ) ), equivalent( Y, Z ) ), equivalent( T, equivalent(
% 87.99/88.47 T, Z ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149774, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), equivalent( Y, Z ) ), equivalent( T
% 87.99/88.47 , equivalent( T, Z ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 6062, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Z,
% 87.99/88.47 equivalent( Z, T ) ), equivalent( T, Y ) ), equivalent( X, equivalent( X
% 87.99/88.47 , Y ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149775, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 X, equivalent( X, Y ) ), equivalent( Y, Z ) ), equivalent( T, equivalent(
% 87.99/88.47 T, Z ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, Y ), :=( T, X )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149777, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , clause( 414, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149779, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( T, equivalent( T, Z ) ), equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( Y, Z ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 6062, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Z
% 87.99/88.47 , equivalent( Z, T ) ), equivalent( T, Y ) ), equivalent( X, equivalent(
% 87.99/88.47 X, Y ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149777, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, equivalent( T, equivalent( T, Z ) ) ),
% 87.99/88.47 :=( Y, Z ), :=( Z, X ), :=( T, Y )] ), substitution( 1, [ :=( X,
% 87.99/88.47 equivalent( equivalent( X, equivalent( X, Y ) ), equivalent( Y, Z ) ) ),
% 87.99/88.47 :=( Y, equivalent( T, equivalent( T, Z ) ) ), :=( Z, T ), :=( T, Z )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149781, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( equivalent( Z, equivalent( Z, T ) ),
% 87.99/88.47 equivalent( T, Y ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149779, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( T, equivalent( T, Z ) ), equivalent( equivalent(
% 87.99/88.47 X, equivalent( X, Y ) ), equivalent( Y, Z ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), equivalent( equivalent( Z,
% 87.99/88.47 equivalent( Z, T ) ), equivalent( T, Y ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, Z ), :=( Y, T ), :=( Z, Y ), :=( T, X )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149782, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 X, Y ) ), equivalent( equivalent( Z, equivalent( Z, T ) ), equivalent( T
% 87.99/88.47 , Y ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149781, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( equivalent( Z, equivalent( Z, T ) ),
% 87.99/88.47 equivalent( T, Y ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 6228, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( T
% 87.99/88.47 , Z ) ), equivalent( equivalent( X, equivalent( X, Y ) ), equivalent( Y,
% 87.99/88.47 Z ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149782, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( equivalent( Z, equivalent( Z, T ) ),
% 87.99/88.47 equivalent( T, Y ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, T ), :=( Y, Z ), :=( Z, X ), :=( T, Y )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149784, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , clause( 414, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149786, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( T, equivalent( T, equivalent( Y, X ) ) ), equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, Z ) ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 3881, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.47 Y, equivalent( T, T ) ) ), equivalent( X, equivalent( X, equivalent( Y, Z
% 87.99/88.47 ) ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149784, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, equivalent( T, equivalent( T, equivalent(
% 87.99/88.47 Y, X ) ) ) ), :=( Y, Y ), :=( Z, X ), :=( T, Z )] ), substitution( 1, [
% 87.99/88.47 :=( X, equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ), :=( Y,
% 87.99/88.47 equivalent( T, equivalent( T, equivalent( Y, X ) ) ) ), :=( Z, T ), :=( T
% 87.99/88.47 , equivalent( Y, X ) )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149788, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, equivalent( Y, Z ) ) ), equivalent( Z, equivalent( Y,
% 87.99/88.47 equivalent( T, T ) ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149786, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( T, equivalent( T, equivalent( Y, X ) ) ),
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, equivalent( Y, Z ) ) ), equivalent( Z,
% 87.99/88.47 equivalent( Y, equivalent( T, T ) ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, Z ), :=( Y, Y ), :=( Z, T ), :=( T, X )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149789, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 X, equivalent( Y, Z ) ) ), equivalent( Z, equivalent( Y, equivalent( T, T
% 87.99/88.47 ) ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149788, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, equivalent( Y, Z ) ) ), equivalent( Z, equivalent( Y,
% 87.99/88.47 equivalent( T, T ) ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 6240, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( T
% 87.99/88.47 , equivalent( Y, X ) ) ), equivalent( X, equivalent( Y, equivalent( Z, Z
% 87.99/88.47 ) ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149789, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, equivalent( Y, Z ) ) ), equivalent( Z, equivalent( Y,
% 87.99/88.47 equivalent( T, T ) ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, T ), :=( Y, Y ), :=( Z, X ), :=( T, Z )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149791, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , clause( 414, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149793, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( Z, equivalent( equivalent( T, equivalent( T, Z ) ), Y ) ),
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 1118, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.47 Y, X ) ), equivalent( equivalent( Z, equivalent( T, X ) ), equivalent( T
% 87.99/88.47 , Z ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149791, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T,
% 87.99/88.47 equivalent( T, equivalent( T, Z ) ) )] ), substitution( 1, [ :=( X,
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ) ), :=( Y, equivalent( Z, equivalent(
% 87.99/88.47 equivalent( T, equivalent( T, Z ) ), Y ) ) ), :=( Z, T ), :=( T, Z )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149795, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ), equivalent( T,
% 87.99/88.47 equivalent( T, Z ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149793, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( Z, equivalent( equivalent( T, equivalent( T, Z )
% 87.99/88.47 ), Y ) ), equivalent( X, equivalent( X, Y ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ),
% 87.99/88.47 equivalent( T, equivalent( T, Z ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, T ), :=( Y, Z ), :=( Z, X ), :=( T, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149796, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ), equivalent( T, equivalent( T
% 87.99/88.47 , Z ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149795, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ), equivalent( T,
% 87.99/88.47 equivalent( T, Z ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 6264, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.47 equivalent( T, equivalent( T, Z ) ), Y ) ), equivalent( X, equivalent( X
% 87.99/88.47 , Y ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149796, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ), equivalent( T,
% 87.99/88.47 equivalent( T, Z ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, Y ), :=( T, X )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149798, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( Z, equivalent( T, equivalent( T, Z ) ) ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , clause( 1216, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( Z, equivalent( T, equivalent( T, Z ) ) ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149800, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( T, equivalent( T, Z ) ), equivalent( X, equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Y, Z ) ) ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 6228, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 87.99/88.47 T, Z ) ), equivalent( equivalent( X, equivalent( X, Y ) ), equivalent( Y
% 87.99/88.47 , Z ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149798, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, equivalent( T, equivalent( T, Z ) ) ) ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, Z ), :=( Z, equivalent( Y,
% 87.99/88.47 equivalent( Y, Z ) ) ), :=( T, X )] ), substitution( 1, [ :=( X,
% 87.99/88.47 equivalent( X, equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ) ) ),
% 87.99/88.47 :=( Y, equivalent( T, equivalent( T, Z ) ) ), :=( Z, Z ), :=( T, Y )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149802, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( Z, equivalent( Z, equivalent( T,
% 87.99/88.47 equivalent( T, Y ) ) ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149800, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( T, equivalent( T, Z ) ), equivalent( X,
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), equivalent( Z, equivalent( Z,
% 87.99/88.47 equivalent( T, equivalent( T, Y ) ) ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, Z ), :=( Y, T ), :=( Z, Y ), :=( T, X )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149803, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 X, Y ) ), equivalent( Z, equivalent( Z, equivalent( T, equivalent( T, Y )
% 87.99/88.47 ) ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149802, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( Z, equivalent( Z, equivalent( T,
% 87.99/88.47 equivalent( T, Y ) ) ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 6273, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( T
% 87.99/88.47 , Z ) ), equivalent( X, equivalent( X, equivalent( Y, equivalent( Y, Z )
% 87.99/88.47 ) ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149803, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( Z, equivalent( Z, equivalent( T,
% 87.99/88.47 equivalent( T, Y ) ) ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, T ), :=( Y, Z ), :=( Z, X ), :=( T, Y )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149805, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.47 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.47 ] )
% 87.99/88.47 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.47 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149807, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( X, equivalent( Y, Z ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Z, equivalent( Y, equivalent( T, T ) ) ) ),
% 87.99/88.47 true ), true ) ) ] )
% 87.99/88.47 , clause( 6240, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 87.99/88.47 T, equivalent( Y, X ) ) ), equivalent( X, equivalent( Y, equivalent( Z, Z
% 87.99/88.47 ) ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149805, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.47 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, T ), :=( T, X )] )
% 87.99/88.47 , substitution( 1, [ :=( X, equivalent( X, equivalent( X, equivalent( Y,
% 87.99/88.47 Z ) ) ) ), :=( Y, equivalent( Z, equivalent( Y, equivalent( T, T ) ) ) )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149812, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 X, equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Z,
% 87.99/88.47 equivalent( Y, equivalent( T, T ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149807, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( X, equivalent( Y, Z ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Z, equivalent( Y, equivalent( T, T ) ) ) ),
% 87.99/88.47 true ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( X, equivalent( Y, Z ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Z, equivalent( Y, equivalent( T, T ) ) ) ),
% 87.99/88.47 true ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 87.99/88.47 :=( Z, Z ), :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149813, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( X,
% 87.99/88.47 equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Z, equivalent(
% 87.99/88.47 Y, equivalent( T, T ) ) ) ), true ), true ) ] )
% 87.99/88.47 , clause( 149812, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( X, equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent(
% 87.99/88.47 Z, equivalent( Y, equivalent( T, T ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 6333, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( X,
% 87.99/88.47 equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Z, equivalent(
% 87.99/88.47 Y, equivalent( T, T ) ) ) ), true ), true ) ] )
% 87.99/88.47 , clause( 149813, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( X,
% 87.99/88.47 equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Z, equivalent(
% 87.99/88.47 Y, equivalent( T, T ) ) ) ), true ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149815, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.47 , Y ), equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ),
% 87.99/88.47 T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , clause( 3245, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ), T ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149817, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, Y ), equivalent( X, equivalent( Z, Z ) ) ),
% 87.99/88.47 equivalent( T, equivalent( T, Y ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 6273, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 87.99/88.47 T, Z ) ), equivalent( X, equivalent( X, equivalent( Y, equivalent( Y, Z )
% 87.99/88.47 ) ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149815, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X, equivalent(
% 87.99/88.47 Z, Z ) ) ), T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( X, equivalent( Z, Z ) ) ) ), :=( Y, T ), :=( Z, Y ), :=( T, X
% 87.99/88.47 )] ), substitution( 1, [ :=( X, X ), :=( Y, equivalent( X, Y ) ), :=( Z
% 87.99/88.47 , Z ), :=( T, equivalent( equivalent( equivalent( X, Y ), equivalent( X,
% 87.99/88.47 equivalent( Z, Z ) ) ), equivalent( T, equivalent( T, Y ) ) ) )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149819, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( X, equivalent( Z, Z ) ) ), equivalent( T
% 87.99/88.47 , equivalent( T, Y ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149817, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( equivalent( X, Y ), equivalent( X, equivalent( Z
% 87.99/88.47 , Z ) ) ), equivalent( T, equivalent( T, Y ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, Y ), equivalent( X, equivalent( Z, Z ) ) ),
% 87.99/88.47 equivalent( T, equivalent( T, Y ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149820, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.47 , Y ), equivalent( X, equivalent( Z, Z ) ) ), equivalent( T, equivalent(
% 87.99/88.47 T, Y ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149819, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( X, equivalent( Z, Z ) ) ), equivalent( T
% 87.99/88.47 , equivalent( T, Y ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 6398, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 87.99/88.47 ), equivalent( X, equivalent( Z, Z ) ) ), equivalent( T, equivalent( T,
% 87.99/88.47 Y ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149820, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 X, Y ), equivalent( X, equivalent( Z, Z ) ) ), equivalent( T, equivalent(
% 87.99/88.47 T, Y ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149822, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , clause( 414, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149824, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( T, equivalent( T, Y ) ), equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( X, equivalent( Z, Z ) ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 6398, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.47 , Y ), equivalent( X, equivalent( Z, Z ) ) ), equivalent( T, equivalent(
% 87.99/88.47 T, Y ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149822, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, T ) ), T ) ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 87.99/88.47 equivalent( T, equivalent( T, Y ) ) )] ), substitution( 1, [ :=( X,
% 87.99/88.47 equivalent( equivalent( X, Y ), equivalent( X, equivalent( Z, Z ) ) ) ),
% 87.99/88.47 :=( Y, equivalent( T, equivalent( T, Y ) ) ), :=( Z, T ), :=( T, Y )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149826, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( equivalent( Z, Y ), equivalent( Z,
% 87.99/88.47 equivalent( T, T ) ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149824, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( T, equivalent( T, Y ) ), equivalent( equivalent(
% 87.99/88.47 X, Y ), equivalent( X, equivalent( Z, Z ) ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), equivalent( equivalent( Z, Y ),
% 87.99/88.47 equivalent( Z, equivalent( T, T ) ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, Z ), :=( Y, Y ), :=( Z, T ), :=( T, X )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149827, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 X, Y ) ), equivalent( equivalent( Z, Y ), equivalent( Z, equivalent( T, T
% 87.99/88.47 ) ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149826, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( equivalent( Z, Y ), equivalent( Z,
% 87.99/88.47 equivalent( T, T ) ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 6404, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent( T
% 87.99/88.47 , Y ) ), equivalent( equivalent( X, Y ), equivalent( X, equivalent( Z, Z
% 87.99/88.47 ) ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149827, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), equivalent( equivalent( Z, Y ), equivalent( Z,
% 87.99/88.47 equivalent( T, T ) ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, T ), :=( Y, Y ), :=( Z, X ), :=( T, Z )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149829, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( equivalent( Z, equivalent( T, T ) ), Z ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , clause( 2360, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( T, T ) ), Z ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149831, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( equivalent( Z, Z ), equivalent( T, T ) ), Y ),
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 6404, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 87.99/88.47 T, Y ) ), equivalent( equivalent( X, Y ), equivalent( X, equivalent( Z, Z
% 87.99/88.47 ) ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149829, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( T, T ) ), Z ) ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, equivalent( equivalent( Z, Z ),
% 87.99/88.47 equivalent( T, T ) ) ), :=( Y, Y ), :=( Z, Z ), :=( T, X )] ),
% 87.99/88.47 substitution( 1, [ :=( X, equivalent( X, equivalent( X, Y ) ) ), :=( Y,
% 87.99/88.47 equivalent( equivalent( equivalent( Z, Z ), equivalent( T, T ) ), Y ) ),
% 87.99/88.47 :=( Z, equivalent( Z, Z ) ), :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149833, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( equivalent( X, X ), equivalent( Y, Y ) ), Z ), equivalent( T
% 87.99/88.47 , equivalent( T, Z ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149831, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( equivalent( equivalent( Z, Z ), equivalent( T, T
% 87.99/88.47 ) ), Y ), equivalent( X, equivalent( X, Y ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( equivalent( X, X ), equivalent( Y, Y ) ), Z ),
% 87.99/88.47 equivalent( T, equivalent( T, Z ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, T ), :=( Y, Z ), :=( Z, X ), :=( T, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149834, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 equivalent( X, X ), equivalent( Y, Y ) ), Z ), equivalent( T, equivalent(
% 87.99/88.47 T, Z ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149833, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( equivalent( X, X ), equivalent( Y, Y ) ), Z ), equivalent( T
% 87.99/88.47 , equivalent( T, Z ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 6430, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 equivalent( Z, Z ), equivalent( T, T ) ), Y ), equivalent( X, equivalent(
% 87.99/88.47 X, Y ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149834, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 equivalent( X, X ), equivalent( Y, Y ) ), Z ), equivalent( T, equivalent(
% 87.99/88.47 T, Z ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, Y ), :=( T, X )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149836, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.47 , Y ), equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ),
% 87.99/88.47 T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , clause( 3245, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ), T ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149838, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( Z, equivalent( equivalent( equivalent( X, X ), equivalent( Y
% 87.99/88.47 , Y ) ), equivalent( T, T ) ) ), Z ) ), true ) ) ] )
% 87.99/88.47 , clause( 6430, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 equivalent( Z, Z ), equivalent( T, T ) ), Y ), equivalent( X, equivalent(
% 87.99/88.47 X, Y ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149836, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X, equivalent(
% 87.99/88.47 Z, Z ) ) ), T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, equivalent( Z, equivalent( equivalent(
% 87.99/88.47 equivalent( X, X ), equivalent( Y, Y ) ), equivalent( T, T ) ) ) ), :=( Y
% 87.99/88.47 , Z ), :=( Z, X ), :=( T, Y )] ), substitution( 1, [ :=( X, equivalent(
% 87.99/88.47 equivalent( X, X ), equivalent( Y, Y ) ) ), :=( Y, Z ), :=( Z, T ), :=( T
% 87.99/88.47 , equivalent( equivalent( Z, equivalent( equivalent( equivalent( X, X ),
% 87.99/88.47 equivalent( Y, Y ) ), equivalent( T, T ) ) ), Z ) )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149840, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ),
% 87.99/88.47 equivalent( T, T ) ) ), X ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149838, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( Z, equivalent( equivalent( equivalent( X, X ),
% 87.99/88.47 equivalent( Y, Y ) ), equivalent( T, T ) ) ), Z ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( equivalent( equivalent( Y, Y ), equivalent( Z
% 87.99/88.47 , Z ) ), equivalent( T, T ) ) ), X ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149841, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ), equivalent( T, T )
% 87.99/88.47 ) ), X ) ), true ) ] )
% 87.99/88.47 , clause( 149840, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ),
% 87.99/88.47 equivalent( T, T ) ) ), X ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 6448, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.47 equivalent( equivalent( X, X ), equivalent( Y, Y ) ), equivalent( T, T )
% 87.99/88.47 ) ), Z ) ), true ) ] )
% 87.99/88.47 , clause( 149841, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ),
% 87.99/88.47 equivalent( T, T ) ) ), X ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149843, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.47 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.47 ] )
% 87.99/88.47 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.47 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149845, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( equivalent( equivalent( Y, Y ), equivalent( Z
% 87.99/88.47 , Z ) ), equivalent( T, T ) ) ) ), true, 'is_a_theorem'( X ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , clause( 6448, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.47 equivalent( equivalent( X, X ), equivalent( Y, Y ) ), equivalent( T, T )
% 87.99/88.47 ) ), Z ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149843, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.47 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T )] )
% 87.99/88.47 , substitution( 1, [ :=( X, equivalent( X, equivalent( equivalent(
% 87.99/88.47 equivalent( Y, Y ), equivalent( Z, Z ) ), equivalent( T, T ) ) ) ), :=( Y
% 87.99/88.47 , X )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149850, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ), equivalent( T, T )
% 87.99/88.47 ) ) ), true, 'is_a_theorem'( X ), true ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149845, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( equivalent( equivalent( Y, Y ), equivalent( Z
% 87.99/88.47 , Z ) ), equivalent( T, T ) ) ) ), true, 'is_a_theorem'( X ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( equivalent( equivalent( Y, Y ), equivalent( Z
% 87.99/88.47 , Z ) ), equivalent( T, T ) ) ) ), true, 'is_a_theorem'( X ), true ) ),
% 87.99/88.47 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 87.99/88.47 :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149851, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ), equivalent( T, T )
% 87.99/88.47 ) ) ), true, 'is_a_theorem'( X ), true ), true ) ] )
% 87.99/88.47 , clause( 149850, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ),
% 87.99/88.47 equivalent( T, T ) ) ) ), true, 'is_a_theorem'( X ), true ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 6512, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ), equivalent( T, T )
% 87.99/88.47 ) ) ), true, 'is_a_theorem'( X ), true ), true ) ] )
% 87.99/88.47 , clause( 149851, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ), equivalent( T, T )
% 87.99/88.47 ) ) ), true, 'is_a_theorem'( X ), true ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149853, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.47 , Y ), equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ),
% 87.99/88.47 T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , clause( 3245, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ), T ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149855, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( equivalent( Y, equivalent( Y, X ) ), Z ),
% 87.99/88.47 equivalent( X, equivalent( T, T ) ) ), Z ) ), true ) ) ] )
% 87.99/88.47 , clause( 6264, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.47 equivalent( T, equivalent( T, Z ) ), Y ) ), equivalent( X, equivalent( X
% 87.99/88.47 , Y ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149853, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X, equivalent(
% 87.99/88.47 Z, Z ) ) ), T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( Y,
% 87.99/88.47 equivalent( Y, X ) ), Z ), equivalent( X, equivalent( T, T ) ) ) ), :=( Y
% 87.99/88.47 , Z ), :=( Z, X ), :=( T, Y )] ), substitution( 1, [ :=( X, X ), :=( Y,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ), :=( Z, T ), :=( T
% 87.99/88.47 , equivalent( equivalent( equivalent( equivalent( Y, equivalent( Y, X ) )
% 87.99/88.47 , Z ), equivalent( X, equivalent( T, T ) ) ), Z ) )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149857, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( equivalent( X, equivalent( X, Y ) ), Z ), equivalent( Y,
% 87.99/88.47 equivalent( T, T ) ) ), Z ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149855, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( equivalent( equivalent( Y, equivalent( Y, X ) ),
% 87.99/88.47 Z ), equivalent( X, equivalent( T, T ) ) ), Z ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( equivalent( X, equivalent( X, Y ) ), Z ),
% 87.99/88.47 equivalent( Y, equivalent( T, T ) ) ), Z ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149858, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), Z ), equivalent( Y, equivalent( T, T
% 87.99/88.47 ) ) ), Z ) ), true ) ] )
% 87.99/88.47 , clause( 149857, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( equivalent( X, equivalent( X, Y ) ), Z ), equivalent( Y,
% 87.99/88.47 equivalent( T, T ) ) ), Z ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 6809, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ), equivalent( X, equivalent( T, T
% 87.99/88.47 ) ) ), Z ) ), true ) ] )
% 87.99/88.47 , clause( 149858, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), Z ), equivalent( Y, equivalent( T, T
% 87.99/88.47 ) ) ), Z ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149860, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.47 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.47 ] )
% 87.99/88.47 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.47 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149862, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( equivalent( X, equivalent( X, Y ) ), Z ),
% 87.99/88.47 equivalent( Y, equivalent( T, T ) ) ) ), true, 'is_a_theorem'( Z ), true
% 87.99/88.47 ), true ) ) ] )
% 87.99/88.47 , clause( 6809, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ), equivalent( X, equivalent( T, T
% 87.99/88.47 ) ) ), Z ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149860, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.47 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 , substitution( 1, [ :=( X, equivalent( equivalent( equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ), Z ), equivalent( Y, equivalent( T, T ) ) ) ), :=( Y
% 87.99/88.47 , Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149867, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), Z ), equivalent( Y, equivalent( T, T
% 87.99/88.47 ) ) ) ), true, 'is_a_theorem'( Z ), true ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149862, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( equivalent( X, equivalent( X, Y ) ), Z ),
% 87.99/88.47 equivalent( Y, equivalent( T, T ) ) ) ), true, 'is_a_theorem'( Z ), true
% 87.99/88.47 ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( equivalent( X, equivalent( X, Y ) ), Z ),
% 87.99/88.47 equivalent( Y, equivalent( T, T ) ) ) ), true, 'is_a_theorem'( Z ), true
% 87.99/88.47 ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z
% 87.99/88.47 , Z ), :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149868, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), Z ), equivalent( Y, equivalent( T, T
% 87.99/88.47 ) ) ) ), true, 'is_a_theorem'( Z ), true ), true ) ] )
% 87.99/88.47 , clause( 149867, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), Z ), equivalent( Y, equivalent( T, T
% 87.99/88.47 ) ) ) ), true, 'is_a_theorem'( Z ), true ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 6887, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 X, equivalent( X, Y ) ), Z ), equivalent( Y, equivalent( T, T ) ) ) ),
% 87.99/88.47 true, 'is_a_theorem'( Z ), true ), true ) ] )
% 87.99/88.47 , clause( 149868, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), Z ), equivalent( Y, equivalent( T, T
% 87.99/88.47 ) ) ) ), true, 'is_a_theorem'( Z ), true ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149870, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.47 , equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) )
% 87.99/88.47 , T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , clause( 5, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.47 T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149872, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( equivalent( T,
% 87.99/88.47 equivalent( T, Z ) ), Y ) ), X ) ), X ) ), true ) ) ] )
% 87.99/88.47 , clause( 447, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 87.99/88.47 U, equivalent( equivalent( X, equivalent( equivalent( Y, equivalent( Y, X
% 87.99/88.47 ) ), Z ) ), Z ) ) ), equivalent( U, T ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149870, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.47 equivalent( Z, Y ) ) ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, Y ), :=( T, X ),
% 87.99/88.47 :=( U, equivalent( Y, equivalent( equivalent( Z, equivalent( equivalent(
% 87.99/88.47 T, equivalent( T, Z ) ), Y ) ), X ) ) )] ), substitution( 1, [ :=( X, X )
% 87.99/88.47 , :=( Y, Y ), :=( Z, equivalent( Z, equivalent( equivalent( T, equivalent(
% 87.99/88.47 T, Z ) ), Y ) ) ), :=( T, equivalent( equivalent( Y, equivalent(
% 87.99/88.47 equivalent( Z, equivalent( equivalent( T, equivalent( T, Z ) ), Y ) ), X
% 87.99/88.47 ) ), X ) )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149874, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y )
% 87.99/88.47 ), X ) ), T ) ), T ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149872, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( Y, equivalent( equivalent( Z, equivalent(
% 87.99/88.47 equivalent( T, equivalent( T, Z ) ), Y ) ), X ) ), X ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( equivalent( Y, equivalent( equivalent( Z,
% 87.99/88.47 equivalent( Z, Y ) ), X ) ), T ) ), T ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149875, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y ) ), X ) ), T
% 87.99/88.47 ) ), T ) ), true ) ] )
% 87.99/88.47 , clause( 149874, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y )
% 87.99/88.47 ), X ) ), T ) ), T ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 7060, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.47 equivalent( Z, equivalent( equivalent( T, equivalent( T, Z ) ), Y ) ), X
% 87.99/88.47 ) ), X ) ), true ) ] )
% 87.99/88.47 , clause( 149875, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y )
% 87.99/88.47 ), X ) ), T ) ), T ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, X )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149877, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.47 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.47 ] )
% 87.99/88.47 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.47 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149879, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( equivalent( Y, equivalent( equivalent( Z,
% 87.99/88.47 equivalent( Z, Y ) ), X ) ), T ) ) ), true, 'is_a_theorem'( T ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , clause( 7060, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.47 equivalent( Z, equivalent( equivalent( T, equivalent( T, Z ) ), Y ) ), X
% 87.99/88.47 ) ), X ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149877, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.47 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] )
% 87.99/88.47 , substitution( 1, [ :=( X, equivalent( X, equivalent( equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, equivalent( Z, Y ) ), X ) ), T ) ) ), :=( Y, T
% 87.99/88.47 )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149884, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y ) ), X ) ), T
% 87.99/88.47 ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149879, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( equivalent( Y, equivalent( equivalent( Z,
% 87.99/88.47 equivalent( Z, Y ) ), X ) ), T ) ) ), true, 'is_a_theorem'( T ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, equivalent( equivalent( Y, equivalent( equivalent( Z,
% 87.99/88.47 equivalent( Z, Y ) ), X ) ), T ) ) ), true, 'is_a_theorem'( T ), true ) )
% 87.99/88.47 , :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )
% 87.99/88.47 , :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149885, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y ) ), X ) ), T
% 87.99/88.47 ) ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , clause( 149884, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y )
% 87.99/88.47 ), X ) ), T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 7138, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y ) ), X ) ), T
% 87.99/88.47 ) ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , clause( 149885, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y ) ), X ) ), T
% 87.99/88.47 ) ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149887, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y ) ), X ) ), T
% 87.99/88.47 ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , clause( 7138, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y ) ), X ) ), T
% 87.99/88.47 ) ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149889, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y ) ), X ) ),
% 87.99/88.47 equivalent( equivalent( T, equivalent( U, X ) ), equivalent( U, T ) ) ) )
% 87.99/88.47 , true ) ) ] )
% 87.99/88.47 , clause( 876, [ =( 'is_a_theorem'( equivalent( Z, equivalent( T,
% 87.99/88.47 equivalent( T, equivalent( equivalent( X, equivalent( Y, Z ) ),
% 87.99/88.47 equivalent( Y, X ) ) ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149887, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y )
% 87.99/88.47 ), X ) ), T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, T ), :=( Y, U ), :=( Z, X ), :=( T,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y ) ), X ) ) )] )
% 87.99/88.47 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y )
% 87.99/88.47 ), X ) ), equivalent( equivalent( T, equivalent( U, X ) ), equivalent( U
% 87.99/88.47 , T ) ) ) )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149891, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ), equivalent(
% 87.99/88.47 equivalent( T, equivalent( U, Z ) ), equivalent( U, T ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149889, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( Y, equivalent( equivalent( Z, equivalent( Z, Y )
% 87.99/88.47 ), X ) ), equivalent( equivalent( T, equivalent( U, X ) ), equivalent( U
% 87.99/88.47 , T ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ),
% 87.99/88.47 equivalent( equivalent( T, equivalent( U, Z ) ), equivalent( U, T ) ) ) )
% 87.99/88.47 ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, X ), :=( Z, Y
% 87.99/88.47 ), :=( T, T ), :=( U, U )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149892, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 equivalent( Y, equivalent( Y, X ) ), Z ) ), equivalent( equivalent( T,
% 87.99/88.47 equivalent( U, Z ) ), equivalent( U, T ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149891, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ), equivalent(
% 87.99/88.47 equivalent( T, equivalent( U, Z ) ), equivalent( U, T ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 87.99/88.47 :=( U, U )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 7386, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.47 equivalent( Z, equivalent( Z, Y ) ), X ) ), equivalent( equivalent( T,
% 87.99/88.47 equivalent( U, X ) ), equivalent( U, T ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149892, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ), equivalent(
% 87.99/88.47 equivalent( T, equivalent( U, Z ) ), equivalent( U, T ) ) ) ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T ), :=( U
% 87.99/88.47 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149894, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , clause( 272, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.47 equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149896, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( Z, equivalent( T, Y ) ), equivalent( T, Z ) ),
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 805, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 87.99/88.47 T, Z ) ), equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ),
% 87.99/88.47 equivalent( Y, X ) ), equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149894, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, Y ), :=( T, X ),
% 87.99/88.47 :=( U, equivalent( U, U ) )] ), substitution( 1, [ :=( X, equivalent( X,
% 87.99/88.47 equivalent( X, Y ) ) ), :=( Y, equivalent( equivalent( Z, equivalent( T,
% 87.99/88.47 Y ) ), equivalent( T, Z ) ) ), :=( Z, U ), :=( T, U )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149898, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( T
% 87.99/88.47 , equivalent( T, Z ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149896, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( equivalent( Z, equivalent( T, Y ) ), equivalent(
% 87.99/88.47 T, Z ) ), equivalent( X, equivalent( X, Y ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ),
% 87.99/88.47 equivalent( T, equivalent( T, Z ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, T ), :=( Y, Z ), :=( Z, X ), :=( T, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149899, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.47 , equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( T, equivalent(
% 87.99/88.47 T, Z ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149898, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( T
% 87.99/88.47 , equivalent( T, Z ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 8003, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Z,
% 87.99/88.47 equivalent( T, Y ) ), equivalent( T, Z ) ), equivalent( X, equivalent( X
% 87.99/88.47 , Y ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149899, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( T, equivalent(
% 87.99/88.47 T, Z ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, Y ), :=( T, X )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149901, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.47 , Y ), equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ),
% 87.99/88.47 T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , clause( 3245, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ), T ) ) )
% 87.99/88.47 , true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149903, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( Y, X ), equivalent( equivalent( X, equivalent( Y
% 87.99/88.47 , Z ) ), equivalent( T, T ) ) ), Z ) ), true ) ) ] )
% 87.99/88.47 , clause( 8003, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Z
% 87.99/88.47 , equivalent( T, Y ) ), equivalent( T, Z ) ), equivalent( X, equivalent(
% 87.99/88.47 X, Y ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149901, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X, equivalent(
% 87.99/88.47 Z, Z ) ) ), T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, equivalent( equivalent( Y, X ),
% 87.99/88.47 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( T, T ) ) ) )
% 87.99/88.47 , :=( Y, Z ), :=( Z, X ), :=( T, Y )] ), substitution( 1, [ :=( X,
% 87.99/88.47 equivalent( X, equivalent( Y, Z ) ) ), :=( Y, equivalent( Y, X ) ), :=( Z
% 87.99/88.47 , T ), :=( T, equivalent( equivalent( equivalent( Y, X ), equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, Z ) ), equivalent( T, T ) ) ), Z ) )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149905, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X, Z ) ),
% 87.99/88.47 equivalent( T, T ) ) ), Z ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149903, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( equivalent( Y, X ), equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, Z ) ), equivalent( T, T ) ) ), Z ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X
% 87.99/88.47 , Z ) ), equivalent( T, T ) ) ), Z ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149906, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.47 , Y ), equivalent( equivalent( Y, equivalent( X, Z ) ), equivalent( T, T
% 87.99/88.47 ) ) ), Z ) ), true ) ] )
% 87.99/88.47 , clause( 149905, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X, Z ) ),
% 87.99/88.47 equivalent( T, T ) ) ), Z ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 8011, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y, X
% 87.99/88.47 ), equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( T, T ) )
% 87.99/88.47 ), Z ) ), true ) ] )
% 87.99/88.47 , clause( 149906, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 X, Y ), equivalent( equivalent( Y, equivalent( X, Z ) ), equivalent( T, T
% 87.99/88.47 ) ) ), Z ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149908, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), Z ), equivalent( Y, equivalent( T, T
% 87.99/88.47 ) ) ) ), true, 'is_a_theorem'( Z ), true ) ) ] )
% 87.99/88.47 , clause( 6887, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, equivalent( X, Y ) ), Z ), equivalent( Y, equivalent( T, T
% 87.99/88.47 ) ) ) ), true, 'is_a_theorem'( Z ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149910, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, Y ), equivalent( X, equivalent( Y, equivalent(
% 87.99/88.47 Z, Z ) ) ) ), equivalent( T, T ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 8011, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y
% 87.99/88.47 , X ), equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( T, T
% 87.99/88.47 ) ) ), Z ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149908, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, equivalent( X, Y ) ), Z ), equivalent( Y,
% 87.99/88.47 equivalent( T, T ) ) ) ), true, 'is_a_theorem'( Z ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, equivalent( X, Y ) ), :=( Y, X ), :=( Z,
% 87.99/88.47 equivalent( Y, equivalent( Z, Z ) ) ), :=( T, T )] ), substitution( 1, [
% 87.99/88.47 :=( X, X ), :=( Y, Y ), :=( Z, equivalent( equivalent( equivalent( X, Y )
% 87.99/88.47 , equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ), equivalent( T,
% 87.99/88.47 T ) ) ), :=( T, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149912, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( X, equivalent( Y, equivalent( Z, Z ) ) )
% 87.99/88.47 ), equivalent( T, T ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149910, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( equivalent( X, Y ), equivalent( X, equivalent( Y
% 87.99/88.47 , equivalent( Z, Z ) ) ) ), equivalent( T, T ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, Y ), equivalent( X, equivalent( Y, equivalent(
% 87.99/88.47 Z, Z ) ) ) ), equivalent( T, T ) ) ) ), :=( Z, true )] ), substitution( 1
% 87.99/88.47 , [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149913, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.47 , Y ), equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ), equivalent(
% 87.99/88.47 T, T ) ) ), true ) ] )
% 87.99/88.47 , clause( 149912, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( X, equivalent( Y, equivalent( Z, Z ) ) )
% 87.99/88.47 ), equivalent( T, T ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 8015, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 87.99/88.47 ), equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ), equivalent( T
% 87.99/88.47 , T ) ) ), true ) ] )
% 87.99/88.47 , clause( 149913, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.47 X, Y ), equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ),
% 87.99/88.47 equivalent( T, T ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149915, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ), equivalent( T, T )
% 87.99/88.47 ) ) ), true, 'is_a_theorem'( X ), true ) ) ] )
% 87.99/88.47 , clause( 6512, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ), equivalent( T, T )
% 87.99/88.47 ) ) ), true, 'is_a_theorem'( X ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149917, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( X, equivalent( Y, equivalent( Z, Z ) ) )
% 87.99/88.47 ) ), true ) ) ] )
% 87.99/88.47 , clause( 8015, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.47 , Y ), equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ), equivalent(
% 87.99/88.47 T, T ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149915, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( equivalent( equivalent( Y, Y ), equivalent( Z, Z ) ),
% 87.99/88.47 equivalent( T, T ) ) ) ), true, 'is_a_theorem'( X ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 87.99/88.47 equivalent( equivalent( T, T ), equivalent( T, T ) ) )] ), substitution(
% 87.99/88.47 1, [ :=( X, equivalent( equivalent( X, Y ), equivalent( X, equivalent( Y
% 87.99/88.47 , equivalent( Z, Z ) ) ) ) ), :=( Y, T ), :=( Z, T ), :=( T, equivalent(
% 87.99/88.47 T, T ) )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149919, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149917, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( X, Y ), equivalent( X, equivalent( Y, equivalent(
% 87.99/88.47 Z, Z ) ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( X, equivalent( Y, equivalent( Z, Z ) ) )
% 87.99/88.47 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=(
% 87.99/88.47 Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149920, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149919, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y )
% 87.99/88.47 , equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 8130, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149920, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149922, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.47 X, equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Z,
% 87.99/88.47 equivalent( Y, equivalent( T, T ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 6333, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( X,
% 87.99/88.47 equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Z, equivalent(
% 87.99/88.47 Y, equivalent( T, T ) ) ) ), true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149924, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ), equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( T, T ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 8015, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.47 , Y ), equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ), equivalent(
% 87.99/88.47 T, T ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149922, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.47 equivalent( X, equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent(
% 87.99/88.47 Z, equivalent( Y, equivalent( T, T ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 87.99/88.47 equivalent( equivalent( X, Y ), equivalent( X, equivalent( Y, equivalent(
% 87.99/88.47 Z, Z ) ) ) ) )] ), substitution( 1, [ :=( X, equivalent( equivalent( X, Y
% 87.99/88.47 ), equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ) ), :=( Y,
% 87.99/88.47 equivalent( X, Y ) ), :=( Z, equivalent( X, equivalent( Y, equivalent( Z
% 87.99/88.47 , Z ) ) ) ), :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149926, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( T, T ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149924, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 87.99/88.47 equivalent( equivalent( X, Y ), equivalent( T, T ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ), equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( T, T ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.47 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149927, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.47 Y, equivalent( Z, Z ) ) ), equivalent( equivalent( X, Y ), equivalent( T
% 87.99/88.47 , T ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149926, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( T, T ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 8141, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 87.99/88.47 , equivalent( Z, Z ) ) ), equivalent( equivalent( X, Y ), equivalent( T,
% 87.99/88.47 T ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149927, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( T, T ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149929, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.47 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.47 ] )
% 87.99/88.47 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.47 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.47 )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149931, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Y
% 87.99/88.47 , equivalent( Z, Z ) ) ) ), true ), true ) ) ] )
% 87.99/88.47 , clause( 8130, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149929, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.47 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.47 true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.47 substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, Z ) ) ) )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149936, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.47 , 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) )
% 87.99/88.47 , true ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149931, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Y
% 87.99/88.47 , equivalent( Z, Z ) ) ) ), true ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.47 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Y
% 87.99/88.47 , equivalent( Z, Z ) ) ) ), true ) ), :=( Z, true )] ), substitution( 1
% 87.99/88.47 , [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149937, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , clause( 149936, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 87.99/88.47 true, 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z ) )
% 87.99/88.47 ) ), true ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 8171, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , clause( 149937, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149939, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.47 , 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) )
% 87.99/88.47 , true ) ) ] )
% 87.99/88.47 , clause( 8171, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149941, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( equivalent( X, equivalent( Y, equivalent(
% 87.99/88.47 Z, Z ) ) ), equivalent( T, T ) ) ) ), true ) ) ] )
% 87.99/88.47 , clause( 8130, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149939, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.47 , true, 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z )
% 87.99/88.47 ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.47 substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, equivalent( X,
% 87.99/88.47 equivalent( Y, equivalent( Z, Z ) ) ) ), :=( Z, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149943, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 87.99/88.47 equivalent( T, T ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149941, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( X, Y ), equivalent( equivalent( X, equivalent( Y
% 87.99/88.47 , equivalent( Z, Z ) ) ), equivalent( T, T ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( equivalent( X, equivalent( Y, equivalent(
% 87.99/88.47 Z, Z ) ) ), equivalent( T, T ) ) ) ) ), :=( Z, true )] ), substitution( 1
% 87.99/88.47 , [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149944, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 87.99/88.47 equivalent( T, T ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149943, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y )
% 87.99/88.47 , equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 87.99/88.47 equivalent( T, T ) ) ) ) ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 subsumption(
% 87.99/88.47 clause( 8173, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 87.99/88.47 equivalent( T, T ) ) ) ), true ) ] )
% 87.99/88.47 , clause( 149944, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.47 equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 87.99/88.47 equivalent( T, T ) ) ) ), true ) ] )
% 87.99/88.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 eqswap(
% 87.99/88.47 clause( 149946, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.47 , 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) )
% 87.99/88.47 , true ) ) ] )
% 87.99/88.47 , clause( 8171, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.47 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ),
% 87.99/88.47 true ), true ) ] )
% 87.99/88.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149948, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X
% 87.99/88.47 , Z ) ), equivalent( T, T ) ) ), equivalent( Z, equivalent( U, U ) ) ) )
% 87.99/88.47 , true ) ) ] )
% 87.99/88.47 , clause( 8011, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y
% 87.99/88.47 , X ), equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( T, T
% 87.99/88.47 ) ) ), Z ) ), true ) ] )
% 87.99/88.47 , 0, clause( 149946, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.47 , true, 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z )
% 87.99/88.47 ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.47 , substitution( 1, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 87.99/88.47 equivalent( Y, equivalent( X, Z ) ), equivalent( T, T ) ) ) ), :=( Y, Z )
% 87.99/88.47 , :=( Z, U )] )).
% 87.99/88.47
% 87.99/88.47
% 87.99/88.47 paramod(
% 87.99/88.47 clause( 149950, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.47 equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X, Z ) ),
% 87.99/88.47 equivalent( T, T ) ) ), equivalent( Z, equivalent( U, U ) ) ) ) ) ] )
% 87.99/88.47 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.47 , 0, clause( 149948, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.47 equivalent( equivalent( equivalent( X, Y ), equivalent( equivalent( Y,
% 87.99/88.47 equivalent( X, Z ) ), equivalent( T, T ) ) ), equivalent( Z, equivalent(
% 87.99/88.47 U, U ) ) ) ), true ) ) ] )
% 87.99/88.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.47 equivalent( equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X
% 87.99/88.47 , Z ) ), equivalent( T, T ) ) ), equivalent( Z, equivalent( U, U ) ) ) )
% 87.99/88.48 ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z
% 87.99/88.48 ), :=( T, T ), :=( U, U )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 149951, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.48 , Y ), equivalent( equivalent( Y, equivalent( X, Z ) ), equivalent( T, T
% 87.99/88.48 ) ) ), equivalent( Z, equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 149950, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.48 equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X, Z ) ),
% 87.99/88.48 equivalent( T, T ) ) ), equivalent( Z, equivalent( U, U ) ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 87.99/88.48 :=( U, U )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 8177, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 87.99/88.48 ), equivalent( equivalent( Y, equivalent( X, Z ) ), equivalent( T, T ) )
% 87.99/88.48 ), equivalent( Z, equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 149951, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.48 X, Y ), equivalent( equivalent( Y, equivalent( X, Z ) ), equivalent( T, T
% 87.99/88.48 ) ) ), equivalent( Z, equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 87.99/88.48 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 149953, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) )
% 87.99/88.48 , true ) ) ] )
% 87.99/88.48 , clause( 8171, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 149955, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ), equivalent(
% 87.99/88.48 equivalent( equivalent( X, Y ), equivalent( T, T ) ), equivalent( U, U )
% 87.99/88.48 ) ) ), true ) ) ] )
% 87.99/88.48 , clause( 8141, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( Z, Z ) ) ), equivalent( equivalent( X, Y ), equivalent( T
% 87.99/88.48 , T ) ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 149953, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.48 , true, 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z )
% 87.99/88.48 ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 , substitution( 1, [ :=( X, equivalent( X, equivalent( Y, equivalent( Z,
% 87.99/88.48 Z ) ) ) ), :=( Y, equivalent( equivalent( X, Y ), equivalent( T, T ) ) )
% 87.99/88.48 , :=( Z, U )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 149957, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( equivalent( equivalent(
% 87.99/88.48 X, Y ), equivalent( T, T ) ), equivalent( U, U ) ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 149955, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 87.99/88.48 equivalent( equivalent( equivalent( X, Y ), equivalent( T, T ) ),
% 87.99/88.48 equivalent( U, U ) ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ), equivalent(
% 87.99/88.48 equivalent( equivalent( X, Y ), equivalent( T, T ) ), equivalent( U, U )
% 87.99/88.48 ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 87.99/88.48 :=( Z, Z ), :=( T, T ), :=( U, U )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 149958, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( Z, Z ) ) ), equivalent( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( T, T ) ), equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 149957, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( equivalent( equivalent(
% 87.99/88.48 X, Y ), equivalent( T, T ) ), equivalent( U, U ) ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 87.99/88.48 :=( U, U )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 8243, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 87.99/88.48 , equivalent( Z, Z ) ) ), equivalent( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( T, T ) ), equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 149958, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( equivalent( equivalent(
% 87.99/88.48 X, Y ), equivalent( T, T ) ), equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 87.99/88.48 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 149960, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.48 , clause( 272, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.48 equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 149962, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ), equivalent( X, Y )
% 87.99/88.48 ) ), true ) ) ] )
% 87.99/88.48 , clause( 8173, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 87.99/88.48 equivalent( T, T ) ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 149960, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) )
% 87.99/88.48 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 87.99/88.48 equivalent( T, T ) )] ), substitution( 1, [ :=( X, equivalent( X, Y ) ),
% 87.99/88.48 :=( Y, equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ), :=( Z, T )
% 87.99/88.48 , :=( T, T )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 149964, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( X, Y ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 149962, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ),
% 87.99/88.48 equivalent( X, Y ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ), equivalent( X, Y )
% 87.99/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=(
% 87.99/88.48 Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 149965, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( Z, Z ) ) ), equivalent( X, Y ) ) ), true ) ] )
% 87.99/88.48 , clause( 149964, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( X, Y ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 8256, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 87.99/88.48 , equivalent( Z, Z ) ) ), equivalent( X, Y ) ) ), true ) ] )
% 87.99/88.48 , clause( 149965, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( Z, Z ) ) ), equivalent( X, Y ) ) ), true ) ]
% 87.99/88.48 )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 149967, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.48 ] )
% 87.99/88.48 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.48 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.48 )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 149969, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( X, Y ) ), true ), true ) ) ] )
% 87.99/88.48 , clause( 8256, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( Z, Z ) ) ), equivalent( X, Y ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 149967, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.48 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.48 true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.48 substitution( 1, [ :=( X, equivalent( X, equivalent( Y, equivalent( Z, Z
% 87.99/88.48 ) ) ) ), :=( Y, equivalent( X, Y ) )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 149974, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( X, Y ) ),
% 87.99/88.48 true ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 149969, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( X, Y ) ), true ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( X, Y ) ), true ) ), :=( Z, true )] ),
% 87.99/88.48 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 149975, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.48 equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( X, Y ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , clause( 149974, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent(
% 87.99/88.48 X, Y ) ), true ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 8300, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.48 equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( X, Y ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , clause( 149975, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.48 equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( X, Y ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 149977, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.48 , clause( 272, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.48 equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 149979, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( equivalent( X, Y ), equivalent( T, T ) ), equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( Z, Z ) ) ) ) ), true ) ) ] )
% 87.99/88.48 , clause( 8243, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( Z, Z ) ) ), equivalent( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( T, T ) ), equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 149977, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) )
% 87.99/88.48 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 87.99/88.48 :=( U, equivalent( U, U ) )] ), substitution( 1, [ :=( X, equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( Z, Z ) ) ) ), :=( Y, equivalent( equivalent( X
% 87.99/88.48 , Y ), equivalent( T, T ) ) ), :=( Z, U ), :=( T, U )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 149981, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.48 equivalent( X, Y ), equivalent( Z, Z ) ), equivalent( X, equivalent( Y,
% 87.99/88.48 equivalent( T, T ) ) ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 149979, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( equivalent( X, Y ), equivalent( T, T ) ),
% 87.99/88.48 equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( equivalent( X, Y ), equivalent( Z, Z ) ), equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( T, T ) ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.48 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 149982, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.48 , Y ), equivalent( Z, Z ) ), equivalent( X, equivalent( Y, equivalent( T
% 87.99/88.48 , T ) ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 149981, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.48 equivalent( X, Y ), equivalent( Z, Z ) ), equivalent( X, equivalent( Y,
% 87.99/88.48 equivalent( T, T ) ) ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 8554, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 87.99/88.48 ), equivalent( T, T ) ), equivalent( X, equivalent( Y, equivalent( Z, Z
% 87.99/88.48 ) ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 149982, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.48 X, Y ), equivalent( Z, Z ) ), equivalent( X, equivalent( Y, equivalent( T
% 87.99/88.48 , T ) ) ) ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T, Z )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 149984, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.48 ] )
% 87.99/88.48 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.48 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.48 )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 149986, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( X, Y ), equivalent( Z, Z ) ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( T, T ) ) ) ),
% 87.99/88.48 true ), true ) ) ] )
% 87.99/88.48 , clause( 8554, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.48 , Y ), equivalent( T, T ) ), equivalent( X, equivalent( Y, equivalent( Z
% 87.99/88.48 , Z ) ) ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 149984, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.48 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.48 true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T, Z )] )
% 87.99/88.48 , substitution( 1, [ :=( X, equivalent( equivalent( X, Y ), equivalent( Z
% 87.99/88.48 , Z ) ) ), :=( Y, equivalent( X, equivalent( Y, equivalent( T, T ) ) ) )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 149991, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.48 , Y ), equivalent( Z, Z ) ) ), true, 'is_a_theorem'( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( T, T ) ) ) ), true ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 149986, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( X, Y ), equivalent( Z, Z ) ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( T, T ) ) ) ),
% 87.99/88.48 true ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( X, Y ), equivalent( Z, Z ) ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( T, T ) ) ) ),
% 87.99/88.48 true ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 87.99/88.48 :=( Z, Z ), :=( T, T )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 149992, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( Z, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( T, T ) ) ) ), true ), true ) ] )
% 87.99/88.48 , clause( 149991, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.48 X, Y ), equivalent( Z, Z ) ) ), true, 'is_a_theorem'( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( T, T ) ) ) ), true ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 8558, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( Z, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( T, T ) ) ) ), true ), true ) ] )
% 87.99/88.48 , clause( 149992, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y )
% 87.99/88.48 , equivalent( Z, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( T, T ) ) ) ), true ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 149994, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.48 , clause( 272, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.48 equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 149996, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( Z
% 87.99/88.48 , equivalent( equivalent( X, Y ), equivalent( equivalent( Y, equivalent(
% 87.99/88.48 X, Z ) ), equivalent( T, T ) ) ) ) ), true ) ) ] )
% 87.99/88.48 , clause( 8177, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.48 , Y ), equivalent( equivalent( Y, equivalent( X, Z ) ), equivalent( T, T
% 87.99/88.48 ) ) ), equivalent( Z, equivalent( U, U ) ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 149994, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) )
% 87.99/88.48 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 87.99/88.48 :=( U, equivalent( U, U ) )] ), substitution( 1, [ :=( X, equivalent(
% 87.99/88.48 equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X, Z ) ),
% 87.99/88.48 equivalent( T, T ) ) ) ), :=( Y, Z ), :=( Z, U ), :=( T, U )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 149998, [ =( true, 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, Z ), equivalent( equivalent( Z, equivalent( Y, X ) ),
% 87.99/88.48 equivalent( T, T ) ) ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 149996, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( Z, equivalent( equivalent( X, Y ), equivalent( equivalent( Y
% 87.99/88.48 , equivalent( X, Z ) ), equivalent( T, T ) ) ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 X, equivalent( equivalent( Y, Z ), equivalent( equivalent( Z, equivalent(
% 87.99/88.48 Y, X ) ), equivalent( T, T ) ) ) ) ) ), :=( Z, true )] ), substitution( 1
% 87.99/88.48 , [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 149999, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 87.99/88.48 Y, Z ), equivalent( equivalent( Z, equivalent( Y, X ) ), equivalent( T, T
% 87.99/88.48 ) ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 149998, [ =( true, 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, Z ), equivalent( equivalent( Z, equivalent( Y, X ) ),
% 87.99/88.48 equivalent( T, T ) ) ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 8667, [ =( 'is_a_theorem'( equivalent( Z, equivalent( equivalent( X
% 87.99/88.48 , Y ), equivalent( equivalent( Y, equivalent( X, Z ) ), equivalent( T, T
% 87.99/88.48 ) ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 149999, [ =( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, Z ), equivalent( equivalent( Z, equivalent( Y, X ) ),
% 87.99/88.48 equivalent( T, T ) ) ) ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150001, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.48 , Y ), equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ),
% 87.99/88.48 T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.48 , clause( 3245, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( equivalent( Y, equivalent( X, equivalent( Z, Z ) ) ), T ) ) )
% 87.99/88.48 , true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150003, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( equivalent( X, equivalent( Z, Z ) ), equivalent( Y,
% 87.99/88.48 equivalent( X, Y ) ) ), equivalent( T, T ) ) ), true ) ) ] )
% 87.99/88.48 , clause( 8667, [ =( 'is_a_theorem'( equivalent( Z, equivalent( equivalent(
% 87.99/88.48 X, Y ), equivalent( equivalent( Y, equivalent( X, Z ) ), equivalent( T, T
% 87.99/88.48 ) ) ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150001, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, Y ), equivalent( equivalent( Y, equivalent( X, equivalent(
% 87.99/88.48 Z, Z ) ) ), T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, equivalent( X, equivalent( Z
% 87.99/88.48 , Z ) ) ), :=( Z, equivalent( X, Y ) ), :=( T, T )] ), substitution( 1, [
% 87.99/88.48 :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, equivalent( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Z, Z ) ), equivalent( Y, equivalent( X, Y ) )
% 87.99/88.48 ), equivalent( T, T ) ) )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150005, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Y, Y ) ), equivalent( Z, equivalent( X, Z ) )
% 87.99/88.48 ), equivalent( T, T ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150003, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( equivalent( X, equivalent( Z, Z ) ), equivalent(
% 87.99/88.48 Y, equivalent( X, Y ) ) ), equivalent( T, T ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( equivalent( X, equivalent( Y, Y ) ), equivalent( Z,
% 87.99/88.48 equivalent( X, Z ) ) ), equivalent( T, T ) ) ) ), :=( Z, true )] ),
% 87.99/88.48 substitution( 1, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T, T )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150006, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.48 , equivalent( Y, Y ) ), equivalent( Z, equivalent( X, Z ) ) ), equivalent(
% 87.99/88.48 T, T ) ) ), true ) ] )
% 87.99/88.48 , clause( 150005, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Y, Y ) ), equivalent( Z, equivalent( X, Z ) )
% 87.99/88.48 ), equivalent( T, T ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 8684, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Z, Z ) ), equivalent( Y, equivalent( X, Y ) ) ), equivalent(
% 87.99/88.48 T, T ) ) ), true ) ] )
% 87.99/88.48 , clause( 150006, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.48 X, equivalent( Y, Y ) ), equivalent( Z, equivalent( X, Z ) ) ),
% 87.99/88.48 equivalent( T, T ) ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T, T )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150008, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.48 , Y ), equivalent( Z, Z ) ) ), true, 'is_a_theorem'( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( T, T ) ) ) ), true ) ) ] )
% 87.99/88.48 , clause( 8558, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( Z, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( T, T ) ) ) ), true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150010, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Y, Y ) ), equivalent( equivalent( Z,
% 87.99/88.48 equivalent( X, Z ) ), equivalent( U, U ) ) ) ), true ) ) ] )
% 87.99/88.48 , clause( 8684, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.48 , equivalent( Z, Z ) ), equivalent( Y, equivalent( X, Y ) ) ), equivalent(
% 87.99/88.48 T, T ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150008, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, Y ), equivalent( Z, Z ) ) ), true, 'is_a_theorem'(
% 87.99/88.48 equivalent( X, equivalent( Y, equivalent( T, T ) ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T, T )] )
% 87.99/88.48 , substitution( 1, [ :=( X, equivalent( X, equivalent( Y, Y ) ) ), :=( Y
% 87.99/88.48 , equivalent( Z, equivalent( X, Z ) ) ), :=( Z, T ), :=( T, U )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150012, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, Y ) ), equivalent( equivalent( Z, equivalent( X, Z ) ),
% 87.99/88.48 equivalent( T, T ) ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150010, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( X, equivalent( Y, Y ) ), equivalent( equivalent(
% 87.99/88.48 Z, equivalent( X, Z ) ), equivalent( U, U ) ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Y, Y ) ), equivalent( equivalent( Z,
% 87.99/88.48 equivalent( X, Z ) ), equivalent( T, T ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.48 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, U ), :=( U
% 87.99/88.48 , T )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150013, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 Y, Y ) ), equivalent( equivalent( Z, equivalent( X, Z ) ), equivalent( T
% 87.99/88.48 , T ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 150012, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, Y ) ), equivalent( equivalent( Z, equivalent( X, Z ) ),
% 87.99/88.48 equivalent( T, T ) ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 8794, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 87.99/88.48 , Y ) ), equivalent( equivalent( Z, equivalent( X, Z ) ), equivalent( U,
% 87.99/88.48 U ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 150013, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, Y ) ), equivalent( equivalent( Z, equivalent( X, Z ) ),
% 87.99/88.48 equivalent( T, T ) ) ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, U )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150015, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.48 , clause( 272, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.48 equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150017, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( Z, equivalent( X, Z ) ), equivalent( X, equivalent( Y, Y ) )
% 87.99/88.48 ) ), true ) ) ] )
% 87.99/88.48 , clause( 8794, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 Y, Y ) ), equivalent( equivalent( Z, equivalent( X, Z ) ), equivalent( U
% 87.99/88.48 , U ) ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150015, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) )
% 87.99/88.48 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, U ),
% 87.99/88.48 :=( U, equivalent( T, T ) )] ), substitution( 1, [ :=( X, equivalent( X,
% 87.99/88.48 equivalent( Y, Y ) ) ), :=( Y, equivalent( Z, equivalent( X, Z ) ) ),
% 87.99/88.48 :=( Z, T ), :=( T, T )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150019, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, X ) ), equivalent( Y, equivalent( Z, Z ) ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150017, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( Z, equivalent( X, Z ) ), equivalent( X,
% 87.99/88.48 equivalent( Y, Y ) ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Y, X ) ), equivalent( Y, equivalent( Z, Z ) )
% 87.99/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=(
% 87.99/88.48 Z, X )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150020, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 Y, X ) ), equivalent( Y, equivalent( Z, Z ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 150019, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, X ) ), equivalent( Y, equivalent( Z, Z ) ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 9269, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent( X
% 87.99/88.48 , Z ) ), equivalent( X, equivalent( Y, Y ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 150020, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, X ) ), equivalent( Y, equivalent( Z, Z ) ) ) ), true ) ]
% 87.99/88.48 )
% 87.99/88.48 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150022, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( X, Y ) ),
% 87.99/88.48 true ) ) ] )
% 87.99/88.48 , clause( 8300, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.48 equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent( X, Y ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150024, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Y, X ) ), Y ) ), true ) ) ] )
% 87.99/88.48 , clause( 9269, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.48 X, Z ) ), equivalent( X, equivalent( Y, Y ) ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150022, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( Z, Z ) ) ) ), true, 'is_a_theorem'( equivalent(
% 87.99/88.48 X, Y ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 87.99/88.48 substitution( 1, [ :=( X, equivalent( X, equivalent( Y, X ) ) ), :=( Y, Y
% 87.99/88.48 ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150026, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, X ) ), Y ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150024, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( X, equivalent( Y, X ) ), Y ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Y, X ) ), Y ) ) ), :=( Z, true )] ),
% 87.99/88.48 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150027, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 Y, X ) ), Y ) ), true ) ] )
% 87.99/88.48 , clause( 150026, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, X ) ), Y ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 10159, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 Y, X ) ), Y ) ), true ) ] )
% 87.99/88.48 , clause( 150027, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, X ) ), Y ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 87.99/88.48 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150029, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.48 true ) ) ] )
% 87.99/88.48 , clause( 4, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150031, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( Z, equivalent( T, equivalent( equivalent( X, equivalent( Y, X
% 87.99/88.48 ) ), Y ) ) ), equivalent( T, Z ) ) ), true ) ) ] )
% 87.99/88.48 , clause( 10159, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 Y, X ) ), Y ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150029, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.48 equivalent( Z, Y ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 87.99/88.48 :=( X, equivalent( equivalent( X, equivalent( Y, X ) ), Y ) ), :=( Y, Z )
% 87.99/88.48 , :=( Z, T )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150032, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( equivalent( Z, equivalent( T, Z ) ), T ) ) ),
% 87.99/88.48 equivalent( Y, X ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150031, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( Z, equivalent( T, equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, X ) ), Y ) ) ), equivalent( T, Z ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Y, equivalent( equivalent( Z, equivalent( T, Z
% 87.99/88.48 ) ), T ) ) ), equivalent( Y, X ) ) ) ), :=( Z, true )] ), substitution(
% 87.99/88.48 1, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150033, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( equivalent( Z, equivalent( T, Z ) ), T ) ) ), equivalent(
% 87.99/88.48 Y, X ) ) ), true ) ] )
% 87.99/88.48 , clause( 150032, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( equivalent( Z, equivalent( T, Z ) ), T ) ) ),
% 87.99/88.48 equivalent( Y, X ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 10501, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.48 T, equivalent( equivalent( X, equivalent( Y, X ) ), Y ) ) ), equivalent(
% 87.99/88.48 T, Z ) ) ), true ) ] )
% 87.99/88.48 , clause( 150033, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( equivalent( Z, equivalent( T, Z ) ), T ) ) ),
% 87.99/88.48 equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, X ), :=( T, Y )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150035, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.48 ] )
% 87.99/88.48 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.48 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.48 )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150037, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, equivalent( Y, X ) ) ), true, 'is_a_theorem'( Y ), true )
% 87.99/88.48 , true ) ) ] )
% 87.99/88.48 , clause( 10159, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 Y, X ) ), Y ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150035, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.48 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.48 true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 87.99/88.48 :=( X, equivalent( X, equivalent( Y, X ) ) ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150042, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 Y, X ) ) ), true, 'is_a_theorem'( Y ), true ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150037, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, equivalent( Y, X ) ) ), true, 'is_a_theorem'( Y ), true )
% 87.99/88.48 , true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, equivalent( Y, X ) ) ), true, 'is_a_theorem'( Y ), true )
% 87.99/88.48 ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150043, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, X
% 87.99/88.48 ) ) ), true, 'is_a_theorem'( Y ), true ), true ) ] )
% 87.99/88.48 , clause( 150042, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.48 equivalent( Y, X ) ) ), true, 'is_a_theorem'( Y ), true ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 10502, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, X )
% 87.99/88.48 ) ), true, 'is_a_theorem'( Y ), true ), true ) ] )
% 87.99/88.48 , clause( 150043, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.48 X ) ) ), true, 'is_a_theorem'( Y ), true ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 87.99/88.48 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150045, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 Y, X ) ) ), true, 'is_a_theorem'( Y ), true ) ) ] )
% 87.99/88.48 , clause( 10502, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, X
% 87.99/88.48 ) ) ), true, 'is_a_theorem'( Y ), true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150047, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ), equivalent( X, Z )
% 87.99/88.48 ) ), true ) ) ] )
% 87.99/88.48 , clause( 7386, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.48 equivalent( Z, equivalent( Z, Y ) ), X ) ), equivalent( equivalent( T,
% 87.99/88.48 equivalent( U, X ) ), equivalent( U, T ) ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150045, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.48 equivalent( Y, X ) ) ), true, 'is_a_theorem'( Y ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T,
% 87.99/88.48 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ), :=( U, X )] ),
% 87.99/88.48 substitution( 1, [ :=( X, equivalent( X, equivalent( equivalent( Y,
% 87.99/88.48 equivalent( Y, X ) ), Z ) ) ), :=( Y, equivalent( equivalent( equivalent(
% 87.99/88.48 Y, equivalent( Y, X ) ), Z ), equivalent( X, Z ) ) )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150049, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.48 equivalent( X, equivalent( X, Y ) ), Z ), equivalent( Y, Z ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150047, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( equivalent( Y, equivalent( Y, X ) ), Z ),
% 87.99/88.48 equivalent( X, Z ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( equivalent( X, equivalent( X, Y ) ), Z ), equivalent( Y, Z )
% 87.99/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, X ), :=(
% 87.99/88.48 Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150050, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.48 , equivalent( X, Y ) ), Z ), equivalent( Y, Z ) ) ), true ) ] )
% 87.99/88.48 , clause( 150049, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.48 equivalent( X, equivalent( X, Y ) ), Z ), equivalent( Y, Z ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 10505, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y,
% 87.99/88.48 equivalent( Y, X ) ), Z ), equivalent( X, Z ) ) ), true ) ] )
% 87.99/88.48 , clause( 150050, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.48 X, equivalent( X, Y ) ), Z ), equivalent( Y, Z ) ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150052, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) )
% 87.99/88.48 , true ) ) ] )
% 87.99/88.48 , clause( 8171, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z ) ) ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150054, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( equivalent( X, equivalent( X, Y ) ), Z ), equivalent(
% 87.99/88.48 equivalent( Y, Z ), equivalent( T, T ) ) ) ), true ) ) ] )
% 87.99/88.48 , clause( 10505, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y
% 87.99/88.48 , equivalent( Y, X ) ), Z ), equivalent( X, Z ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150052, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.48 , true, 'is_a_theorem'( equivalent( X, equivalent( Y, equivalent( Z, Z )
% 87.99/88.48 ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 87.99/88.48 substitution( 1, [ :=( X, equivalent( equivalent( X, equivalent( X, Y ) )
% 87.99/88.48 , Z ) ), :=( Y, equivalent( Y, Z ) ), :=( Z, T )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150056, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.48 equivalent( X, equivalent( X, Y ) ), Z ), equivalent( equivalent( Y, Z )
% 87.99/88.48 , equivalent( T, T ) ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150054, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( equivalent( X, equivalent( X, Y ) ), Z ),
% 87.99/88.48 equivalent( equivalent( Y, Z ), equivalent( T, T ) ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( equivalent( X, equivalent( X, Y ) ), Z ), equivalent(
% 87.99/88.48 equivalent( Y, Z ), equivalent( T, T ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.48 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150057, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.48 , equivalent( X, Y ) ), Z ), equivalent( equivalent( Y, Z ), equivalent(
% 87.99/88.48 T, T ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 150056, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.48 equivalent( X, equivalent( X, Y ) ), Z ), equivalent( equivalent( Y, Z )
% 87.99/88.48 , equivalent( T, T ) ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 10520, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 87.99/88.48 equivalent( X, Y ) ), Z ), equivalent( equivalent( Y, Z ), equivalent( T
% 87.99/88.48 , T ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 150057, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.48 X, equivalent( X, Y ) ), Z ), equivalent( equivalent( Y, Z ), equivalent(
% 87.99/88.48 T, T ) ) ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150059, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.48 ] )
% 87.99/88.48 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.48 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.48 )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150061, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( X, equivalent( X, Y ) ), Z ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, Z ) ), true ), true ) ) ] )
% 87.99/88.48 , clause( 10505, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y
% 87.99/88.48 , equivalent( Y, X ) ), Z ), equivalent( X, Z ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150059, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.48 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.48 true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 87.99/88.48 substitution( 1, [ :=( X, equivalent( equivalent( X, equivalent( X, Y ) )
% 87.99/88.48 , Z ) ), :=( Y, equivalent( Y, Z ) )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150066, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.48 , equivalent( X, Y ) ), Z ) ), true, 'is_a_theorem'( equivalent( Y, Z ) )
% 87.99/88.48 , true ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150061, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( X, equivalent( X, Y ) ), Z ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, Z ) ), true ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( X, equivalent( X, Y ) ), Z ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, Z ) ), true ) ), :=( Z, true )] ),
% 87.99/88.48 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150067, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( X, Y ) ), Z ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , clause( 150066, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.48 X, equivalent( X, Y ) ), Z ) ), true, 'is_a_theorem'( equivalent( Y, Z )
% 87.99/88.48 ), true ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 10569, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( X, Y ) ), Z ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , clause( 150067, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( X, Y ) ), Z ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150069, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.48 , clause( 272, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 87.99/88.48 equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150071, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( Y, Z ), equivalent( equivalent( X, equivalent( X, Y ) ), Z )
% 87.99/88.48 ) ), true ) ) ] )
% 87.99/88.48 , clause( 10520, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.48 , equivalent( X, Y ) ), Z ), equivalent( equivalent( Y, Z ), equivalent(
% 87.99/88.48 T, T ) ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150069, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( equivalent( Z, Z ), equivalent( T, T ) ) ) ) )
% 87.99/88.48 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 87.99/88.48 equivalent( T, T ) )] ), substitution( 1, [ :=( X, equivalent( equivalent(
% 87.99/88.48 X, equivalent( X, Y ) ), Z ) ), :=( Y, equivalent( Y, Z ) ), :=( Z, T ),
% 87.99/88.48 :=( T, T )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150073, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( equivalent( Z, equivalent( Z, X ) ), Y ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150071, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( Y, Z ), equivalent( equivalent( X, equivalent( X
% 87.99/88.48 , Y ) ), Z ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, Y ), equivalent( equivalent( Z, equivalent( Z, X ) ), Y )
% 87.99/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, X ), :=(
% 87.99/88.48 Z, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150074, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( equivalent( Z, equivalent( Z, X ) ), Y ) ) ), true ) ] )
% 87.99/88.48 , clause( 150073, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y )
% 87.99/88.48 , equivalent( equivalent( Z, equivalent( Z, X ) ), Y ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 11858, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Z ),
% 87.99/88.48 equivalent( equivalent( X, equivalent( X, Y ) ), Z ) ) ), true ) ] )
% 87.99/88.48 , clause( 150074, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( equivalent( Z, equivalent( Z, X ) ), Y ) ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150076, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.48 ] )
% 87.99/88.48 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.48 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.48 )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150078, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( equivalent( Z,
% 87.99/88.48 equivalent( Z, X ) ), Y ) ), true ), true ) ) ] )
% 87.99/88.48 , clause( 11858, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Z ),
% 87.99/88.48 equivalent( equivalent( X, equivalent( X, Y ) ), Z ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150076, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.48 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.48 true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 87.99/88.48 substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, equivalent(
% 87.99/88.48 equivalent( Z, equivalent( Z, X ) ), Y ) )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150083, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , 'is_a_theorem'( equivalent( equivalent( Z, equivalent( Z, X ) ), Y ) )
% 87.99/88.48 , true ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150078, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( equivalent( Z,
% 87.99/88.48 equivalent( Z, X ) ), Y ) ), true ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( equivalent( Z,
% 87.99/88.48 equivalent( Z, X ) ), Y ) ), true ) ), :=( Z, true )] ), substitution( 1
% 87.99/88.48 , [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150084, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( equivalent( Z, equivalent( Z, X ) ), Y ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , clause( 150083, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 87.99/88.48 true, 'is_a_theorem'( equivalent( equivalent( Z, equivalent( Z, X ) ), Y
% 87.99/88.48 ) ), true ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 11926, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( equivalent( Z, equivalent( Z, X ) ), Y ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , clause( 150084, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( equivalent( Z, equivalent( Z, X ) ), Y ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150086, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.48 , equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) )
% 87.99/88.48 , T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.48 , clause( 5, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( equivalent( Y, equivalent( Z, X ) ), equivalent( Z, Y ) ) ),
% 87.99/88.48 T ) ), true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150088, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( Y, equivalent( equivalent( Z, equivalent( Y, Z ) ), X ) ), X
% 87.99/88.48 ) ), true ) ) ] )
% 87.99/88.48 , clause( 10501, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.48 T, equivalent( equivalent( X, equivalent( Y, X ) ), Y ) ) ), equivalent(
% 87.99/88.48 T, Z ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150086, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( equivalent( Y, equivalent( Z, X ) ),
% 87.99/88.48 equivalent( Z, Y ) ) ), T ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X ), :=( T,
% 87.99/88.48 equivalent( Y, equivalent( equivalent( Z, equivalent( Y, Z ) ), X ) ) )] )
% 87.99/88.48 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, equivalent( Z,
% 87.99/88.48 equivalent( Y, Z ) ) ), :=( T, equivalent( equivalent( Y, equivalent(
% 87.99/88.48 equivalent( Z, equivalent( Y, Z ) ), X ) ), X ) )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150090, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( equivalent( Y, equivalent( X, Y ) ), Z ) ), Z ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150088, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( Y, equivalent( equivalent( Z, equivalent( Y, Z )
% 87.99/88.48 ), X ) ), X ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( equivalent( Y, equivalent( X, Y ) ), Z ) ), Z
% 87.99/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, X ), :=(
% 87.99/88.48 Z, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150091, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, equivalent( X, Y ) ), Z ) ), Z ) ), true ) ] )
% 87.99/88.48 , clause( 150090, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( equivalent( Y, equivalent( X, Y ) ), Z ) ), Z ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 15939, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.48 equivalent( Z, equivalent( Y, Z ) ), X ) ), X ) ), true ) ] )
% 87.99/88.48 , clause( 150091, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( equivalent( Y, equivalent( X, Y ) ), Z ) ), Z ) ), true ) ]
% 87.99/88.48 )
% 87.99/88.48 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150093, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.48 ] )
% 87.99/88.48 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.48 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.48 )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150095, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, equivalent( equivalent( Y, equivalent( X, Y ) ), Z ) ) ),
% 87.99/88.48 true, 'is_a_theorem'( Z ), true ), true ) ) ] )
% 87.99/88.48 , clause( 15939, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 87.99/88.48 equivalent( Z, equivalent( Y, Z ) ), X ) ), X ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150093, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.48 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.48 true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 87.99/88.48 substitution( 1, [ :=( X, equivalent( X, equivalent( equivalent( Y,
% 87.99/88.48 equivalent( X, Y ) ), Z ) ) ), :=( Y, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150100, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, equivalent( X, Y ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.48 true ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150095, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, equivalent( equivalent( Y, equivalent( X, Y ) ), Z ) ) ),
% 87.99/88.48 true, 'is_a_theorem'( Z ), true ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, equivalent( equivalent( Y, equivalent( X, Y ) ), Z ) ) ),
% 87.99/88.48 true, 'is_a_theorem'( Z ), true ) ), :=( Z, true )] ), substitution( 1, [
% 87.99/88.48 :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150101, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, equivalent( X, Y ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , clause( 150100, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.48 equivalent( equivalent( Y, equivalent( X, Y ) ), Z ) ) ), true,
% 87.99/88.48 'is_a_theorem'( Z ), true ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 16017, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, equivalent( X, Y ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , clause( 150101, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, equivalent( X, Y ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150103, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, equivalent( X, Y ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.48 true ) ) ] )
% 87.99/88.48 , clause( 16017, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, equivalent( X, Y ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150105, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( equivalent( X, Y ), equivalent( Y, X ) ), equivalent( Z, Z )
% 87.99/88.48 ) ), true ) ) ] )
% 87.99/88.48 , clause( 8667, [ =( 'is_a_theorem'( equivalent( Z, equivalent( equivalent(
% 87.99/88.48 X, Y ), equivalent( equivalent( Y, equivalent( X, Z ) ), equivalent( T, T
% 87.99/88.48 ) ) ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150103, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.48 equivalent( equivalent( Y, equivalent( X, Y ) ), Z ) ) ), true,
% 87.99/88.48 'is_a_theorem'( Z ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, equivalent( X, Y ) ), :=( Z,
% 87.99/88.48 X ), :=( T, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z,
% 87.99/88.48 equivalent( equivalent( equivalent( X, Y ), equivalent( Y, X ) ),
% 87.99/88.48 equivalent( Z, Z ) ) )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150107, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.48 equivalent( X, Y ), equivalent( Y, X ) ), equivalent( Z, Z ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150105, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( equivalent( X, Y ), equivalent( Y, X ) ),
% 87.99/88.48 equivalent( Z, Z ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( equivalent( X, Y ), equivalent( Y, X ) ), equivalent( Z, Z )
% 87.99/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=(
% 87.99/88.48 Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150108, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.48 , Y ), equivalent( Y, X ) ), equivalent( Z, Z ) ) ), true ) ] )
% 87.99/88.48 , clause( 150107, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.48 equivalent( X, Y ), equivalent( Y, X ) ), equivalent( Z, Z ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 16039, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 87.99/88.48 Y ), equivalent( Y, X ) ), equivalent( Z, Z ) ) ), true ) ] )
% 87.99/88.48 , clause( 150108, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.48 X, Y ), equivalent( Y, X ) ), equivalent( Z, Z ) ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150110, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 Y, X ) ) ), true, 'is_a_theorem'( Y ), true ) ) ] )
% 87.99/88.48 , clause( 10502, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, X
% 87.99/88.48 ) ) ), true, 'is_a_theorem'( Y ), true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150112, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, Y ), equivalent( Y, X ) ) ), true ) ) ] )
% 87.99/88.48 , clause( 16039, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 87.99/88.48 , Y ), equivalent( Y, X ) ), equivalent( Z, Z ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150110, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.48 equivalent( Y, X ) ) ), true, 'is_a_theorem'( Y ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, equivalent(
% 87.99/88.48 equivalent( X, Y ), equivalent( Y, X ) ) )] ), substitution( 1, [ :=( X,
% 87.99/88.48 equivalent( equivalent( X, Y ), equivalent( Y, X ) ) ), :=( Y, equivalent(
% 87.99/88.48 equivalent( X, Y ), equivalent( Y, X ) ) )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150114, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( Y, X ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150112, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( X, Y ), equivalent( Y, X ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, Y ), equivalent( Y, X ) ) ) ), :=( Z, true )] ),
% 87.99/88.48 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150115, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.48 , clause( 150114, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y )
% 87.99/88.48 , equivalent( Y, X ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 16244, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.48 , clause( 150115, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 87.99/88.48 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150117, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , 'is_a_theorem'( equivalent( equivalent( Z, equivalent( Z, X ) ), Y ) )
% 87.99/88.48 , true ) ) ] )
% 87.99/88.48 , clause( 11926, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( equivalent( Z, equivalent( Z, X ) ), Y ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150119, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( Z, equivalent( Z, equivalent( X, Y ) ) ), equivalent( Y, X )
% 87.99/88.48 ) ), true ) ) ] )
% 87.99/88.48 , clause( 16244, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150117, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.48 , true, 'is_a_theorem'( equivalent( equivalent( Z, equivalent( Z, X ) ),
% 87.99/88.48 Y ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 87.99/88.48 :=( X, equivalent( X, Y ) ), :=( Y, equivalent( Y, X ) ), :=( Z, Z )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150121, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( X, equivalent( Y, Z ) ) ), equivalent( Z, Y ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150119, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( Z, equivalent( Z, equivalent( X, Y ) ) ),
% 87.99/88.48 equivalent( Y, X ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( X, equivalent( Y, Z ) ) ), equivalent( Z, Y )
% 87.99/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=(
% 87.99/88.48 Z, X )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150122, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 X, equivalent( Y, Z ) ) ), equivalent( Z, Y ) ) ), true ) ] )
% 87.99/88.48 , clause( 150121, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( X, equivalent( Y, Z ) ) ), equivalent( Z, Y ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 16333, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.48 Z, equivalent( X, Y ) ) ), equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.48 , clause( 150122, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( X, equivalent( Y, Z ) ) ), equivalent( Z, Y ) ) ), true ) ]
% 87.99/88.48 )
% 87.99/88.48 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150124, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 87.99/88.48 , equivalent( X, Y ) ), Z ) ), true, 'is_a_theorem'( equivalent( Y, Z ) )
% 87.99/88.48 , true ) ) ] )
% 87.99/88.48 , clause( 10569, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( X, Y ) ), Z ) ), true, 'is_a_theorem'( equivalent( Y, Z ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150126, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( Y
% 87.99/88.48 , equivalent( equivalent( X, Y ), X ) ) ), true ) ) ] )
% 87.99/88.48 , clause( 16244, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150124, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( X, Y ) ), Z ) ), true, 'is_a_theorem'(
% 87.99/88.48 equivalent( Y, Z ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, equivalent( X, Y ) )] ),
% 87.99/88.48 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, equivalent( equivalent(
% 87.99/88.48 X, Y ), X ) )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150128, [ =( true, 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, X ), Y ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150126, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( Y, equivalent( equivalent( X, Y ), X ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 X, equivalent( equivalent( Y, X ), Y ) ) ) ), :=( Z, true )] ),
% 87.99/88.48 substitution( 1, [ :=( X, Y ), :=( Y, X )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150129, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 87.99/88.48 Y, X ), Y ) ) ), true ) ] )
% 87.99/88.48 , clause( 150128, [ =( true, 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, X ), Y ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 16343, [ =( 'is_a_theorem'( equivalent( Y, equivalent( equivalent(
% 87.99/88.48 X, Y ), X ) ) ), true ) ] )
% 87.99/88.48 , clause( 150129, [ =( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, X ), Y ) ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 87.99/88.48 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150131, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.48 ] )
% 87.99/88.48 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.48 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.48 )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150133, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( Y, X ) ), true )
% 87.99/88.48 , true ) ) ] )
% 87.99/88.48 , clause( 16244, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150131, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.48 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.48 true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 87.99/88.48 :=( X, equivalent( X, Y ) ), :=( Y, equivalent( Y, X ) )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150138, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150133, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( Y, X ) ), true )
% 87.99/88.48 , true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( Y, X ) ), true )
% 87.99/88.48 ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150139, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.48 , clause( 150138, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 87.99/88.48 true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 16553, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.48 , clause( 150139, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 87.99/88.48 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150141, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.48 ] )
% 87.99/88.48 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.48 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.48 )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150143, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( X ),
% 87.99/88.48 true, 'is_a_theorem'( equivalent( equivalent( Y, X ), Y ) ), true ), true
% 87.99/88.48 ) ) ] )
% 87.99/88.48 , clause( 16343, [ =( 'is_a_theorem'( equivalent( Y, equivalent( equivalent(
% 87.99/88.48 X, Y ), X ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150141, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.48 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.48 true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 87.99/88.48 :=( X, X ), :=( Y, equivalent( equivalent( Y, X ), Y ) )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150148, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( Y, X ), Y ) ), true ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150143, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( X )
% 87.99/88.48 , true, 'is_a_theorem'( equivalent( equivalent( Y, X ), Y ) ), true ),
% 87.99/88.48 true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'( X )
% 87.99/88.48 , true, 'is_a_theorem'( equivalent( equivalent( Y, X ), Y ) ), true ) ),
% 87.99/88.48 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150149, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( Y, X ), Y ) ), true ), true ) ] )
% 87.99/88.48 , clause( 150148, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( equivalent( Y, X ), Y ) ), true ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 16972, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( Y, X ), Y ) ), true ), true ) ] )
% 87.99/88.48 , clause( 150149, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( Y, X ), Y ) ), true ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 87.99/88.48 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150151, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( Y, X ), Y ) ), true ) ) ] )
% 87.99/88.48 , clause( 16972, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( Y, X ), Y ) ), true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150153, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( Z, equivalent( equivalent( X, Y ), equivalent( Y, X ) ) ), Z
% 87.99/88.48 ) ), true ) ) ] )
% 87.99/88.48 , clause( 16244, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150151, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( equivalent( Y, X ), Y ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 87.99/88.48 :=( X, equivalent( equivalent( X, Y ), equivalent( Y, X ) ) ), :=( Y, Z )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150154, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( equivalent( Y, Z ), equivalent( Z, Y ) ) ), X ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150153, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( Z, equivalent( equivalent( X, Y ), equivalent( Y
% 87.99/88.48 , X ) ) ), Z ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( equivalent( Y, Z ), equivalent( Z, Y ) ) ), X
% 87.99/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=(
% 87.99/88.48 Z, X )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150155, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, Z ), equivalent( Z, Y ) ) ), X ) ), true ) ] )
% 87.99/88.48 , clause( 150154, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( equivalent( Y, Z ), equivalent( Z, Y ) ) ), X ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 17802, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.48 equivalent( X, Y ), equivalent( Y, X ) ) ), Z ) ), true ) ] )
% 87.99/88.48 , clause( 150155, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( equivalent( Y, Z ), equivalent( Z, Y ) ) ), X ) ), true ) ]
% 87.99/88.48 )
% 87.99/88.48 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150157, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.48 , clause( 16553, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150159, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( Z, Y ), equivalent( X, equivalent( X, equivalent( Y, Z ) ) )
% 87.99/88.48 ) ), true ) ) ] )
% 87.99/88.48 , clause( 16333, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.48 Z, equivalent( X, Y ) ) ), equivalent( Y, X ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150157, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.48 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 87.99/88.48 substitution( 1, [ :=( X, equivalent( X, equivalent( X, equivalent( Y, Z
% 87.99/88.48 ) ) ) ), :=( Y, equivalent( Z, Y ) )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150161, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( Z, equivalent( Z, equivalent( Y, X ) ) ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150159, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( Z, Y ), equivalent( X, equivalent( X, equivalent(
% 87.99/88.48 Y, Z ) ) ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, Y ), equivalent( Z, equivalent( Z, equivalent( Y, X ) ) )
% 87.99/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, Y ), :=(
% 87.99/88.48 Z, X )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150162, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( Z, equivalent( Z, equivalent( Y, X ) ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 150161, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y )
% 87.99/88.48 , equivalent( Z, equivalent( Z, equivalent( Y, X ) ) ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 19956, [ =( 'is_a_theorem'( equivalent( equivalent( Z, Y ),
% 87.99/88.48 equivalent( X, equivalent( X, equivalent( Y, Z ) ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 150162, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( Z, equivalent( Z, equivalent( Y, X ) ) ) ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150164, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z
% 87.99/88.48 , T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.48 , clause( 10, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 87.99/88.48 X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z, T ) ) ),
% 87.99/88.48 true, 'is_a_theorem'( T ), true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150166, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( Z
% 87.99/88.48 , equivalent( equivalent( Y, X ), equivalent( X, equivalent( Y, Z ) ) ) )
% 87.99/88.48 ), true ) ) ] )
% 87.99/88.48 , clause( 19956, [ =( 'is_a_theorem'( equivalent( equivalent( Z, Y ),
% 87.99/88.48 equivalent( X, equivalent( X, equivalent( Y, Z ) ) ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150164, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ),
% 87.99/88.48 equivalent( Z, T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, equivalent( Y, X ) ), :=( Z,
% 87.99/88.48 equivalent( X, equivalent( Y, Z ) ) )] ), substitution( 1, [ :=( X, X ),
% 87.99/88.48 :=( Y, Y ), :=( Z, Z ), :=( T, equivalent( Z, equivalent( equivalent( Y,
% 87.99/88.48 X ), equivalent( X, equivalent( Y, Z ) ) ) ) )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150168, [ =( true, 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, Z ), equivalent( Z, equivalent( Y, X ) ) ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150166, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( Z, equivalent( equivalent( Y, X ), equivalent( X, equivalent(
% 87.99/88.48 Y, Z ) ) ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 X, equivalent( equivalent( Y, Z ), equivalent( Z, equivalent( Y, X ) ) )
% 87.99/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, Y ), :=(
% 87.99/88.48 Z, X )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150169, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 87.99/88.48 Y, Z ), equivalent( Z, equivalent( Y, X ) ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 150168, [ =( true, 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, Z ), equivalent( Z, equivalent( Y, X ) ) ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 20093, [ =( 'is_a_theorem'( equivalent( Z, equivalent( equivalent(
% 87.99/88.48 Y, X ), equivalent( X, equivalent( Y, Z ) ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 150169, [ =( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, Z ), equivalent( Z, equivalent( Y, X ) ) ) ) ), true ) ]
% 87.99/88.48 )
% 87.99/88.48 , substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150171, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , 'is_a_theorem'( equivalent( equivalent( Z, equivalent( Z, X ) ), Y ) )
% 87.99/88.48 , true ) ) ] )
% 87.99/88.48 , clause( 11926, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( equivalent( Z, equivalent( Z, X ) ), Y ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150173, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( T, equivalent( T, X ) ), equivalent( equivalent( Y, Z ),
% 87.99/88.48 equivalent( Z, equivalent( Y, X ) ) ) ) ), true ) ) ] )
% 87.99/88.48 , clause( 20093, [ =( 'is_a_theorem'( equivalent( Z, equivalent( equivalent(
% 87.99/88.48 Y, X ), equivalent( X, equivalent( Y, Z ) ) ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150171, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.48 , true, 'is_a_theorem'( equivalent( equivalent( Z, equivalent( Z, X ) ),
% 87.99/88.48 Y ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 87.99/88.48 substitution( 1, [ :=( X, X ), :=( Y, equivalent( equivalent( Y, Z ),
% 87.99/88.48 equivalent( Z, equivalent( Y, X ) ) ) ), :=( Z, T )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150175, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( X, Y ) ), equivalent( equivalent( Z, T ), equivalent( T,
% 87.99/88.48 equivalent( Z, Y ) ) ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150173, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( T, equivalent( T, X ) ), equivalent( equivalent(
% 87.99/88.48 Y, Z ), equivalent( Z, equivalent( Y, X ) ) ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( X, Y ) ), equivalent( equivalent( Z, T ),
% 87.99/88.48 equivalent( T, equivalent( Z, Y ) ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.48 substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, X )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150176, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 X, Y ) ), equivalent( equivalent( Z, T ), equivalent( T, equivalent( Z, Y
% 87.99/88.48 ) ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 150175, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( X, Y ) ), equivalent( equivalent( Z, T ), equivalent( T,
% 87.99/88.48 equivalent( Z, Y ) ) ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 87.99/88.48 ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 20454, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 87.99/88.48 T, X ) ), equivalent( equivalent( Y, Z ), equivalent( Z, equivalent( Y, X
% 87.99/88.48 ) ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 150176, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( X, Y ) ), equivalent( equivalent( Z, T ), equivalent( T,
% 87.99/88.48 equivalent( Z, Y ) ) ) ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150178, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.48 true ) ) ] )
% 87.99/88.48 , clause( 448, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 87.99/88.48 equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150180, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( Z, equivalent( X, equivalent( X, Y ) ) ), equivalent( Z, Y )
% 87.99/88.48 ) ), true ) ) ] )
% 87.99/88.48 , clause( 20454, [ =( 'is_a_theorem'( equivalent( equivalent( T, equivalent(
% 87.99/88.48 T, X ) ), equivalent( equivalent( Y, Z ), equivalent( Z, equivalent( Y, X
% 87.99/88.48 ) ) ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150178, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 87.99/88.48 equivalent( equivalent( Y, equivalent( Y, X ) ), Z ) ) ), true,
% 87.99/88.48 'is_a_theorem'( Z ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, equivalent( Z,
% 87.99/88.48 equivalent( X, equivalent( X, Y ) ) ) ), :=( T, X )] ), substitution( 1
% 87.99/88.48 , [ :=( X, equivalent( X, equivalent( X, Y ) ) ), :=( Y, Z ), :=( Z,
% 87.99/88.48 equivalent( equivalent( Z, equivalent( X, equivalent( X, Y ) ) ),
% 87.99/88.48 equivalent( Z, Y ) ) )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150182, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( Y, Z ) ) ), equivalent( X, Z ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150180, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( Z, equivalent( X, equivalent( X, Y ) ) ),
% 87.99/88.48 equivalent( Z, Y ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ), equivalent( X, Z )
% 87.99/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=(
% 87.99/88.48 Z, X )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150183, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( Y, Z ) ) ), equivalent( X, Z ) ) ), true ) ] )
% 87.99/88.48 , clause( 150182, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( Y, Z ) ) ), equivalent( X, Z ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 33534, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.48 X, equivalent( X, Y ) ) ), equivalent( Z, Y ) ) ), true ) ] )
% 87.99/88.48 , clause( 150183, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( Y, Z ) ) ), equivalent( X, Z ) ) ), true ) ]
% 87.99/88.48 )
% 87.99/88.48 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150185, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.48 , clause( 16553, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150187, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, Z ), equivalent( X, equivalent( Y, equivalent( Y, Z ) ) )
% 87.99/88.48 ) ), true ) ) ] )
% 87.99/88.48 , clause( 33534, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.48 X, equivalent( X, Y ) ) ), equivalent( Z, Y ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150185, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.48 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 87.99/88.48 substitution( 1, [ :=( X, equivalent( X, equivalent( Y, equivalent( Y, Z
% 87.99/88.48 ) ) ) ), :=( Y, equivalent( X, Z ) )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150189, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( X, equivalent( Z, equivalent( Z, Y ) ) ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150187, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( X, Z ), equivalent( X, equivalent( Y, equivalent(
% 87.99/88.48 Y, Z ) ) ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, Y ), equivalent( X, equivalent( Z, equivalent( Z, Y ) ) )
% 87.99/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Z ), :=(
% 87.99/88.48 Z, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150190, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( X, equivalent( Z, equivalent( Z, Y ) ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 150189, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y )
% 87.99/88.48 , equivalent( X, equivalent( Z, equivalent( Z, Y ) ) ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 33763, [ =( 'is_a_theorem'( equivalent( equivalent( X, Z ),
% 87.99/88.48 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 150190, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 87.99/88.48 equivalent( X, equivalent( Z, equivalent( Z, Y ) ) ) ) ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150192, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 87.99/88.48 ] )
% 87.99/88.48 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 87.99/88.48 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 87.99/88.48 )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150194, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z
% 87.99/88.48 , equivalent( Z, Y ) ) ) ), true ), true ) ) ] )
% 87.99/88.48 , clause( 33763, [ =( 'is_a_theorem'( equivalent( equivalent( X, Z ),
% 87.99/88.48 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150192, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.48 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 87.99/88.48 true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 87.99/88.48 substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, equivalent( X,
% 87.99/88.48 equivalent( Z, equivalent( Z, Y ) ) ) )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150199, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , 'is_a_theorem'( equivalent( X, equivalent( Z, equivalent( Z, Y ) ) ) )
% 87.99/88.48 , true ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150194, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z
% 87.99/88.48 , equivalent( Z, Y ) ) ) ), true ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 87.99/88.48 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z
% 87.99/88.48 , equivalent( Z, Y ) ) ) ), true ) ), :=( Z, true )] ), substitution( 1
% 87.99/88.48 , [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150200, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( X, equivalent( Z, equivalent( Z, Y ) ) ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , clause( 150199, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 87.99/88.48 true, 'is_a_theorem'( equivalent( X, equivalent( Z, equivalent( Z, Y ) )
% 87.99/88.48 ) ), true ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 subsumption(
% 87.99/88.48 clause( 33903, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( X, equivalent( Z, equivalent( Z, Y ) ) ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , clause( 150200, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( X, equivalent( Z, equivalent( Z, Y ) ) ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 87.99/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150202, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 87.99/88.48 , 'is_a_theorem'( equivalent( X, equivalent( Z, equivalent( Z, Y ) ) ) )
% 87.99/88.48 , true ) ) ] )
% 87.99/88.48 , clause( 33903, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 87.99/88.48 'is_a_theorem'( equivalent( X, equivalent( Z, equivalent( Z, Y ) ) ) ),
% 87.99/88.48 true ), true ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150204, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ), equivalent( T,
% 87.99/88.48 equivalent( T, equivalent( X, Z ) ) ) ) ), true ) ) ] )
% 87.99/88.48 , clause( 33534, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 87.99/88.48 X, equivalent( X, Y ) ) ), equivalent( Z, Y ) ) ), true ) ] )
% 87.99/88.48 , 0, clause( 150202, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 87.99/88.48 , true, 'is_a_theorem'( equivalent( X, equivalent( Z, equivalent( Z, Y )
% 87.99/88.48 ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 87.99/88.48 substitution( 1, [ :=( X, equivalent( X, equivalent( Y, equivalent( Y, Z
% 87.99/88.48 ) ) ) ), :=( Y, equivalent( X, Z ) ), :=( Z, T )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 paramod(
% 87.99/88.48 clause( 150206, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( Y, Z ) ) ), equivalent( T, equivalent( T,
% 87.99/88.48 equivalent( X, Z ) ) ) ) ) ) ] )
% 87.99/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 87.99/88.48 , 0, clause( 150204, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 87.99/88.48 equivalent( equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ),
% 87.99/88.48 equivalent( T, equivalent( T, equivalent( X, Z ) ) ) ) ), true ) ) ] )
% 87.99/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 87.99/88.48 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ), equivalent( T,
% 87.99/88.48 equivalent( T, equivalent( X, Z ) ) ) ) ) ), :=( Z, true )] ),
% 87.99/88.48 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 87.99/88.48
% 87.99/88.48
% 87.99/88.48 eqswap(
% 87.99/88.48 clause( 150207, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 87.99/88.48 Y, equivalent( Y, Z ) ) ), equivalent( T, equivalent( T, equivalent( X, Z
% 87.99/88.48 ) ) ) ) ), true ) ] )
% 87.99/88.48 , clause( 150206, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 87.99/88.48 equivalent( Y, equivalent( Y, Z ) ) ), equivalent( T, equivalent( T,
% 87.99/88.48 equivalent( X, Z ) ) ) ) ) ) ] )
% 87.99/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 88.08/88.48 ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 34470, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.48 Y, equivalent( Y, Z ) ) ), equivalent( T, equivalent( T, equivalent( X, Z
% 88.08/88.48 ) ) ) ) ), true ) ] )
% 88.08/88.48 , clause( 150207, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( Y, equivalent( Y, Z ) ) ), equivalent( T, equivalent( T,
% 88.08/88.48 equivalent( X, Z ) ) ) ) ), true ) ] )
% 88.08/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150209, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 88.08/88.48 , 'is_a_theorem'( equivalent( X, equivalent( Z, equivalent( Z, Y ) ) ) )
% 88.08/88.48 , true ) ) ] )
% 88.08/88.48 , clause( 33903, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 88.08/88.48 'is_a_theorem'( equivalent( X, equivalent( Z, equivalent( Z, Y ) ) ) ),
% 88.08/88.48 true ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150211, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( X, equivalent( equivalent( Y, Z ), equivalent( Z, Y ) ) ),
% 88.08/88.48 equivalent( T, equivalent( T, X ) ) ) ), true ) ) ] )
% 88.08/88.48 , clause( 17802, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( Y, X ) ) ), Z ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150209, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 88.08/88.48 , true, 'is_a_theorem'( equivalent( X, equivalent( Z, equivalent( Z, Y )
% 88.08/88.48 ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 88.08/88.48 substitution( 1, [ :=( X, equivalent( X, equivalent( equivalent( Y, Z ),
% 88.08/88.48 equivalent( Z, Y ) ) ) ), :=( Y, X ), :=( Z, T )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150213, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( equivalent( Y, Z ), equivalent( Z, Y ) ) ), equivalent( T,
% 88.08/88.48 equivalent( T, X ) ) ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150211, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), equivalent( Z
% 88.08/88.48 , Y ) ) ), equivalent( T, equivalent( T, X ) ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( X, equivalent( equivalent( Y, Z ), equivalent( Z, Y ) ) ),
% 88.08/88.48 equivalent( T, equivalent( T, X ) ) ) ) ), :=( Z, true )] ),
% 88.08/88.48 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150214, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.48 equivalent( Y, Z ), equivalent( Z, Y ) ) ), equivalent( T, equivalent( T
% 88.08/88.48 , X ) ) ) ), true ) ] )
% 88.08/88.48 , clause( 150213, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( equivalent( Y, Z ), equivalent( Z, Y ) ) ), equivalent( T,
% 88.08/88.48 equivalent( T, X ) ) ) ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 88.08/88.48 ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 34601, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.48 equivalent( Y, Z ), equivalent( Z, Y ) ) ), equivalent( T, equivalent( T
% 88.08/88.48 , X ) ) ) ), true ) ] )
% 88.08/88.48 , clause( 150214, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( equivalent( Y, Z ), equivalent( Z, Y ) ) ), equivalent( T,
% 88.08/88.48 equivalent( T, X ) ) ) ), true ) ] )
% 88.08/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150216, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.48 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z
% 88.08/88.48 , T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 88.08/88.48 , clause( 10, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.48 X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z, T ) ) ),
% 88.08/88.48 true, 'is_a_theorem'( T ), true ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 88.08/88.48 ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150218, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( Z
% 88.08/88.48 , equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), Y ) )
% 88.08/88.48 ), true ) ) ] )
% 88.08/88.48 , clause( 34470, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.48 Y, equivalent( Y, Z ) ) ), equivalent( T, equivalent( T, equivalent( X, Z
% 88.08/88.48 ) ) ) ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150216, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ),
% 88.08/88.48 equivalent( Z, T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ),
% 88.08/88.48 equivalent( X, Z ) ) ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] ),
% 88.08/88.48 substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, X ), :=( Z, Z ),
% 88.08/88.48 :=( T, equivalent( Z, equivalent( equivalent( equivalent( X, Y ),
% 88.08/88.48 equivalent( X, Z ) ), Y ) ) )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150220, [ =( true, 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 equivalent( equivalent( Y, Z ), equivalent( Y, X ) ), Z ) ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150218, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( Z, equivalent( equivalent( equivalent( X, Y ), equivalent( X
% 88.08/88.48 , Z ) ), Y ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.48 X, equivalent( equivalent( equivalent( Y, Z ), equivalent( Y, X ) ), Z )
% 88.08/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=(
% 88.08/88.48 Z, X )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150221, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 88.08/88.48 equivalent( Y, Z ), equivalent( Y, X ) ), Z ) ) ), true ) ] )
% 88.08/88.48 , clause( 150220, [ =( true, 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 equivalent( equivalent( Y, Z ), equivalent( Y, X ) ), Z ) ) ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 35765, [ =( 'is_a_theorem'( equivalent( Z, equivalent( equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( X, Z ) ), Y ) ) ), true ) ] )
% 88.08/88.48 , clause( 150221, [ =( 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 equivalent( equivalent( Y, Z ), equivalent( Y, X ) ), Z ) ) ), true ) ]
% 88.08/88.48 )
% 88.08/88.48 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150223, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 88.08/88.48 , 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 88.08/88.48 , clause( 16553, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 88.08/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150225, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( equivalent( equivalent( Y, Z ), equivalent( Y, X ) ), Z ), X
% 88.08/88.48 ) ), true ) ) ] )
% 88.08/88.48 , clause( 35765, [ =( 'is_a_theorem'( equivalent( Z, equivalent( equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( X, Z ) ), Y ) ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150223, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 88.08/88.48 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 88.08/88.48 substitution( 1, [ :=( X, X ), :=( Y, equivalent( equivalent( equivalent(
% 88.08/88.48 Y, Z ), equivalent( Y, X ) ), Z ) )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150227, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.48 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), Y ), Z ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150225, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( equivalent( equivalent( Y, Z ), equivalent( Y, X
% 88.08/88.48 ) ), Z ), X ) ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), Y ), Z
% 88.08/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, X ), :=(
% 88.08/88.48 Z, Y )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150228, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( X, Z ) ), Y ), Z ) ), true ) ] )
% 88.08/88.48 , clause( 150227, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.48 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), Y ), Z ) ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 35817, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.48 equivalent( Y, Z ), equivalent( Y, X ) ), Z ), X ) ), true ) ] )
% 88.08/88.48 , clause( 150228, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( X, Z ) ), Y ), Z ) ), true ) ] )
% 88.08/88.48 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150230, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 88.08/88.48 , 'is_a_theorem'( equivalent( X, equivalent( Z, equivalent( Z, Y ) ) ) )
% 88.08/88.48 , true ) ) ] )
% 88.08/88.48 , clause( 33903, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 88.08/88.48 'is_a_theorem'( equivalent( X, equivalent( Z, equivalent( Z, Y ) ) ) ),
% 88.08/88.48 true ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150232, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), Y ),
% 88.08/88.48 equivalent( T, equivalent( T, Z ) ) ) ), true ) ) ] )
% 88.08/88.48 , clause( 35817, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.48 equivalent( Y, Z ), equivalent( Y, X ) ), Z ), X ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150230, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 88.08/88.48 , true, 'is_a_theorem'( equivalent( X, equivalent( Z, equivalent( Z, Y )
% 88.08/88.48 ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 88.08/88.48 substitution( 1, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 88.08/88.48 equivalent( X, Z ) ), Y ) ), :=( Y, Z ), :=( Z, T )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150234, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.48 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), Y ), equivalent( T
% 88.08/88.48 , equivalent( T, Z ) ) ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150232, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 88.08/88.48 ) ), Y ), equivalent( T, equivalent( T, Z ) ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ), Y ),
% 88.08/88.48 equivalent( T, equivalent( T, Z ) ) ) ) ), :=( Z, true )] ),
% 88.08/88.48 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150235, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( X, Z ) ), Y ), equivalent( T, equivalent(
% 88.08/88.48 T, Z ) ) ) ), true ) ] )
% 88.08/88.48 , clause( 150234, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.48 equivalent( equivalent( X, Y ), equivalent( X, Z ) ), Y ), equivalent( T
% 88.08/88.48 , equivalent( T, Z ) ) ) ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 88.08/88.48 ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 35954, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( X, Z ) ), Y ), equivalent( T, equivalent(
% 88.08/88.48 T, Z ) ) ) ), true ) ] )
% 88.08/88.48 , clause( 150235, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( X, Z ) ), Y ), equivalent( T, equivalent(
% 88.08/88.48 T, Z ) ) ) ), true ) ] )
% 88.08/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150237, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.48 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z
% 88.08/88.48 , T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 88.08/88.48 , clause( 10, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.48 X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z, T ) ) ),
% 88.08/88.48 true, 'is_a_theorem'( T ), true ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 88.08/88.48 ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150239, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( Z
% 88.08/88.48 , equivalent( equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ) )
% 88.08/88.48 ), true ) ) ] )
% 88.08/88.48 , clause( 34601, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.48 equivalent( Y, Z ), equivalent( Z, Y ) ) ), equivalent( T, equivalent( T
% 88.08/88.48 , X ) ) ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150237, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ),
% 88.08/88.48 equivalent( Z, T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ),
% 88.08/88.48 equivalent( equivalent( Y, X ), Z ) ) ), :=( Y, Y ), :=( Z, X ), :=( T, Z
% 88.08/88.48 )] ), substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, equivalent(
% 88.08/88.48 Y, X ) ), :=( Z, Z ), :=( T, equivalent( Z, equivalent( equivalent( X, Y
% 88.08/88.48 ), equivalent( equivalent( Y, X ), Z ) ) ) )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150241, [ =( true, 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), X ) ) ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150239, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( Z, equivalent( equivalent( X, Y ), equivalent( equivalent( Y
% 88.08/88.48 , X ), Z ) ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.48 X, equivalent( equivalent( Y, Z ), equivalent( equivalent( Z, Y ), X ) )
% 88.08/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=(
% 88.08/88.48 Z, X )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150242, [ =( 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 88.08/88.48 Y, Z ), equivalent( equivalent( Z, Y ), X ) ) ) ), true ) ] )
% 88.08/88.48 , clause( 150241, [ =( true, 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), X ) ) ) ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 40576, [ =( 'is_a_theorem'( equivalent( Z, equivalent( equivalent(
% 88.08/88.48 X, Y ), equivalent( equivalent( Y, X ), Z ) ) ) ), true ) ] )
% 88.08/88.48 , clause( 150242, [ =( 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), X ) ) ) ), true ) ]
% 88.08/88.48 )
% 88.08/88.48 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150244, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 88.08/88.48 , 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 88.08/88.48 , clause( 16553, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 88.08/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150246, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( equivalent( Y, Z ), equivalent( equivalent( Z, Y ), X ) ), X
% 88.08/88.48 ) ), true ) ) ] )
% 88.08/88.48 , clause( 40576, [ =( 'is_a_theorem'( equivalent( Z, equivalent( equivalent(
% 88.08/88.48 X, Y ), equivalent( equivalent( Y, X ), Z ) ) ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150244, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 88.08/88.48 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 88.08/88.48 substitution( 1, [ :=( X, X ), :=( Y, equivalent( equivalent( Y, Z ),
% 88.08/88.48 equivalent( equivalent( Z, Y ), X ) ) )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150248, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ), Z ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150246, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( equivalent( Y, Z ), equivalent( equivalent( Z, Y
% 88.08/88.48 ), X ) ), X ) ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ), Z
% 88.08/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, X ), :=(
% 88.08/88.48 Z, Y )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150249, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 88.08/88.48 , Y ), equivalent( equivalent( Y, X ), Z ) ), Z ) ), true ) ] )
% 88.08/88.48 , clause( 150248, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ), Z ) ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 40636, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y,
% 88.08/88.48 Z ), equivalent( equivalent( Z, Y ), X ) ), X ) ), true ) ] )
% 88.08/88.48 , clause( 150249, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.48 X, Y ), equivalent( equivalent( Y, X ), Z ) ), Z ) ), true ) ] )
% 88.08/88.48 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150251, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 88.08/88.48 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 88.08/88.48 ] )
% 88.08/88.48 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 88.08/88.48 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 88.08/88.48 )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150253, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ) ),
% 88.08/88.48 true, 'is_a_theorem'( Z ), true ), true ) ) ] )
% 88.08/88.48 , clause( 40636, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y
% 88.08/88.48 , Z ), equivalent( equivalent( Z, Y ), X ) ), X ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150251, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 88.08/88.48 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 88.08/88.48 true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 88.08/88.48 substitution( 1, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 88.08/88.48 equivalent( Y, X ), Z ) ) ), :=( Y, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150258, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 88.08/88.48 , Y ), equivalent( equivalent( Y, X ), Z ) ) ), true, 'is_a_theorem'( Z )
% 88.08/88.48 , true ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150253, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ) ),
% 88.08/88.48 true, 'is_a_theorem'( Z ), true ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ) ),
% 88.08/88.48 true, 'is_a_theorem'( Z ), true ) ), :=( Z, true )] ), substitution( 1, [
% 88.08/88.48 :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150259, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.48 equivalent( equivalent( Y, X ), Z ) ) ), true, 'is_a_theorem'( Z ), true
% 88.08/88.48 ), true ) ] )
% 88.08/88.48 , clause( 150258, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.48 X, Y ), equivalent( equivalent( Y, X ), Z ) ) ), true, 'is_a_theorem'( Z
% 88.08/88.48 ), true ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 40873, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.48 equivalent( equivalent( Y, X ), Z ) ) ), true, 'is_a_theorem'( Z ), true
% 88.08/88.48 ), true ) ] )
% 88.08/88.48 , clause( 150259, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y )
% 88.08/88.48 , equivalent( equivalent( Y, X ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 88.08/88.48 true ), true ) ] )
% 88.08/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150261, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 88.08/88.48 , Y ), equivalent( equivalent( Y, X ), Z ) ) ), true, 'is_a_theorem'( Z )
% 88.08/88.48 , true ) ) ] )
% 88.08/88.48 , clause( 40873, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y )
% 88.08/88.48 , equivalent( equivalent( Y, X ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 88.08/88.48 true ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150263, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( Y, equivalent( equivalent( X, Y ), equivalent( X, Z ) ) ), Z
% 88.08/88.48 ) ), true ) ) ] )
% 88.08/88.48 , clause( 35954, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( X, Z ) ), Y ), equivalent( T, equivalent(
% 88.08/88.48 T, Z ) ) ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150261, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ) ), true,
% 88.08/88.48 'is_a_theorem'( Z ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 88.08/88.48 equivalent( Y, equivalent( equivalent( X, Y ), equivalent( X, Z ) ) ) )] )
% 88.08/88.48 , substitution( 1, [ :=( X, equivalent( equivalent( X, Y ), equivalent( X
% 88.08/88.48 , Z ) ) ), :=( Y, Y ), :=( Z, equivalent( equivalent( Y, equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( X, Z ) ) ), Z ) )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150265, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( equivalent( Y, X ), equivalent( Y, Z ) ) ), Z ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150263, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( Y, equivalent( equivalent( X, Y ), equivalent( X
% 88.08/88.48 , Z ) ) ), Z ) ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( X, equivalent( equivalent( Y, X ), equivalent( Y, Z ) ) ), Z
% 88.08/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, X ), :=(
% 88.08/88.48 Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150266, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.48 equivalent( Y, X ), equivalent( Y, Z ) ) ), Z ) ), true ) ] )
% 88.08/88.48 , clause( 150265, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( equivalent( Y, X ), equivalent( Y, Z ) ) ), Z ) ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 40876, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( X, Z ) ) ), Z ) ), true ) ] )
% 88.08/88.48 , clause( 150266, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( equivalent( Y, X ), equivalent( Y, Z ) ) ), Z ) ), true ) ]
% 88.08/88.48 )
% 88.08/88.48 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150268, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 88.08/88.48 , 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 88.08/88.48 , clause( 16553, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 88.08/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150270, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent( Z
% 88.08/88.48 , equivalent( X, equivalent( equivalent( Y, X ), equivalent( Y, Z ) ) ) )
% 88.08/88.48 ), true ) ) ] )
% 88.08/88.48 , clause( 40876, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( X, Z ) ) ), Z ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150268, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 88.08/88.48 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 88.08/88.48 substitution( 1, [ :=( X, equivalent( X, equivalent( equivalent( Y, X ),
% 88.08/88.48 equivalent( Y, Z ) ) ) ), :=( Y, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150272, [ =( true, 'is_a_theorem'( equivalent( X, equivalent( Y,
% 88.08/88.48 equivalent( equivalent( Z, Y ), equivalent( Z, X ) ) ) ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150270, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( Z, equivalent( X, equivalent( equivalent( Y, X ), equivalent(
% 88.08/88.48 Y, Z ) ) ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.48 X, equivalent( Y, equivalent( equivalent( Z, Y ), equivalent( Z, X ) ) )
% 88.08/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=(
% 88.08/88.48 Z, X )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150273, [ =( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 88.08/88.48 equivalent( equivalent( Z, Y ), equivalent( Z, X ) ) ) ) ), true ) ] )
% 88.08/88.48 , clause( 150272, [ =( true, 'is_a_theorem'( equivalent( X, equivalent( Y,
% 88.08/88.48 equivalent( equivalent( Z, Y ), equivalent( Z, X ) ) ) ) ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 41075, [ =( 'is_a_theorem'( equivalent( Z, equivalent( X,
% 88.08/88.48 equivalent( equivalent( Y, X ), equivalent( Y, Z ) ) ) ) ), true ) ] )
% 88.08/88.48 , clause( 150273, [ =( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 88.08/88.48 equivalent( equivalent( Z, Y ), equivalent( Z, X ) ) ) ) ), true ) ] )
% 88.08/88.48 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150275, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent( X
% 88.08/88.48 , Y ), equivalent( equivalent( Y, X ), Z ) ) ), true, 'is_a_theorem'( Z )
% 88.08/88.48 , true ) ) ] )
% 88.08/88.48 , clause( 40873, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( X, Y )
% 88.08/88.48 , equivalent( equivalent( Y, X ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 88.08/88.48 true ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150277, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( Z, equivalent( Y, X ) ), equivalent( Z, equivalent( X, Y ) )
% 88.08/88.48 ) ), true ) ) ] )
% 88.08/88.48 , clause( 41075, [ =( 'is_a_theorem'( equivalent( Z, equivalent( X,
% 88.08/88.48 equivalent( equivalent( Y, X ), equivalent( Y, Z ) ) ) ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150275, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ) ), true,
% 88.08/88.48 'is_a_theorem'( Z ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, equivalent( Y, X ) ), :=( Y, Z ), :=( Z,
% 88.08/88.48 equivalent( X, Y ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z
% 88.08/88.48 , equivalent( equivalent( Z, equivalent( Y, X ) ), equivalent( Z,
% 88.08/88.48 equivalent( X, Y ) ) ) )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150279, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( Y, Z ) ), equivalent( X, equivalent( Z, Y ) ) ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150277, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( Z, equivalent( Y, X ) ), equivalent( Z,
% 88.08/88.48 equivalent( X, Y ) ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( X, equivalent( Y, Z ) ), equivalent( X, equivalent( Z, Y ) )
% 88.08/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, Y ), :=(
% 88.08/88.48 Z, X )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150280, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.48 Y, Z ) ), equivalent( X, equivalent( Z, Y ) ) ) ), true ) ] )
% 88.08/88.48 , clause( 150279, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( Y, Z ) ), equivalent( X, equivalent( Z, Y ) ) ) ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 41185, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 88.08/88.48 Y, X ) ), equivalent( Z, equivalent( X, Y ) ) ) ), true ) ] )
% 88.08/88.48 , clause( 150280, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( Y, Z ) ), equivalent( X, equivalent( Z, Y ) ) ) ), true ) ]
% 88.08/88.48 )
% 88.08/88.48 , substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150282, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 equivalent( Y, equivalent( X, Y ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 88.08/88.48 true ) ) ] )
% 88.08/88.48 , clause( 16017, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 equivalent( Y, equivalent( X, Y ) ), Z ) ) ), true, 'is_a_theorem'( Z ),
% 88.08/88.48 true ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150284, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( Z, equivalent( Y, equivalent( X, Y ) ) ), equivalent( Z, X )
% 88.08/88.48 ) ), true ) ) ] )
% 88.08/88.48 , clause( 41075, [ =( 'is_a_theorem'( equivalent( Z, equivalent( X,
% 88.08/88.48 equivalent( equivalent( Y, X ), equivalent( Y, Z ) ) ) ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150282, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 88.08/88.48 equivalent( equivalent( Y, equivalent( X, Y ) ), Z ) ) ), true,
% 88.08/88.48 'is_a_theorem'( Z ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, equivalent( Y, equivalent( X, Y ) ) ),
% 88.08/88.48 :=( Y, Z ), :=( Z, X )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 88.08/88.48 :=( Z, equivalent( equivalent( Z, equivalent( Y, equivalent( X, Y ) ) ),
% 88.08/88.48 equivalent( Z, X ) ) )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150286, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( Y, equivalent( Z, Y ) ) ), equivalent( X, Z ) ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150284, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( Z, equivalent( Y, equivalent( X, Y ) ) ),
% 88.08/88.48 equivalent( Z, X ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( X, equivalent( Y, equivalent( Z, Y ) ) ), equivalent( X, Z )
% 88.08/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, Y ), :=(
% 88.08/88.48 Z, X )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150287, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.48 Y, equivalent( Z, Y ) ) ), equivalent( X, Z ) ) ), true ) ] )
% 88.08/88.48 , clause( 150286, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( Y, equivalent( Z, Y ) ) ), equivalent( X, Z ) ) ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 41228, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 88.08/88.48 Y, equivalent( X, Y ) ) ), equivalent( Z, X ) ) ), true ) ] )
% 88.08/88.48 , clause( 150287, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( Y, equivalent( Z, Y ) ) ), equivalent( X, Z ) ) ), true ) ]
% 88.08/88.48 )
% 88.08/88.48 , substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150289, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 88.08/88.48 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 88.08/88.48 ] )
% 88.08/88.48 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 88.08/88.48 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 88.08/88.48 )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150291, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 88.08/88.48 equivalent( X, equivalent( Y, Z ) ) ), true, 'is_a_theorem'( equivalent(
% 88.08/88.48 X, equivalent( Z, Y ) ) ), true ), true ) ) ] )
% 88.08/88.48 , clause( 41185, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 88.08/88.48 Y, X ) ), equivalent( Z, equivalent( X, Y ) ) ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150289, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 88.08/88.48 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 88.08/88.48 true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 88.08/88.48 substitution( 1, [ :=( X, equivalent( X, equivalent( Y, Z ) ) ), :=( Y,
% 88.08/88.48 equivalent( X, equivalent( Z, Y ) ) )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150296, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 Y, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z, Y ) ) ),
% 88.08/88.48 true ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150291, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 88.08/88.48 equivalent( X, equivalent( Y, Z ) ) ), true, 'is_a_theorem'( equivalent(
% 88.08/88.48 X, equivalent( Z, Y ) ) ), true ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 88.08/88.48 equivalent( X, equivalent( Y, Z ) ) ), true, 'is_a_theorem'( equivalent(
% 88.08/88.48 X, equivalent( Z, Y ) ) ), true ) ), :=( Z, true )] ), substitution( 1, [
% 88.08/88.48 :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150297, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, Z
% 88.08/88.48 ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z, Y ) ) ), true
% 88.08/88.48 ), true ) ] )
% 88.08/88.48 , clause( 150296, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 88.08/88.48 equivalent( Y, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 Z, Y ) ) ), true ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 41511, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, Z )
% 88.08/88.48 ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z, Y ) ) ), true )
% 88.08/88.48 , true ) ] )
% 88.08/88.48 , clause( 150297, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 88.08/88.48 Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z, Y ) ) ),
% 88.08/88.48 true ), true ) ] )
% 88.08/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150299, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 88.08/88.48 , 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 88.08/88.48 , clause( 16553, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 88.08/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150301, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( X, Z ), equivalent( X, equivalent( Y, equivalent( Z, Y ) ) )
% 88.08/88.48 ) ), true ) ) ] )
% 88.08/88.48 , clause( 41228, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 88.08/88.48 Y, equivalent( X, Y ) ) ), equivalent( Z, X ) ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150299, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 88.08/88.48 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 88.08/88.48 substitution( 1, [ :=( X, equivalent( X, equivalent( Y, equivalent( Z, Y
% 88.08/88.48 ) ) ) ), :=( Y, equivalent( X, Z ) )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150303, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.48 equivalent( X, equivalent( Z, equivalent( Y, Z ) ) ) ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150301, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( X, Z ), equivalent( X, equivalent( Y, equivalent(
% 88.08/88.48 Z, Y ) ) ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( X, equivalent( Z, equivalent( Y, Z ) ) )
% 88.08/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Z ), :=(
% 88.08/88.48 Z, Y )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150304, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.48 equivalent( X, equivalent( Z, equivalent( Y, Z ) ) ) ) ), true ) ] )
% 88.08/88.48 , clause( 150303, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y )
% 88.08/88.48 , equivalent( X, equivalent( Z, equivalent( Y, Z ) ) ) ) ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 42464, [ =( 'is_a_theorem'( equivalent( equivalent( X, Z ),
% 88.08/88.48 equivalent( X, equivalent( Y, equivalent( Z, Y ) ) ) ) ), true ) ] )
% 88.08/88.48 , clause( 150304, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.48 equivalent( X, equivalent( Z, equivalent( Y, Z ) ) ) ) ), true ) ] )
% 88.08/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150306, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 Y, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z, Y ) ) ),
% 88.08/88.48 true ) ) ] )
% 88.08/88.48 , clause( 41511, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, Z
% 88.08/88.48 ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z, Y ) ) ), true
% 88.08/88.48 ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150308, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( equivalent( Z, equivalent( Y, Z ) ), X )
% 88.08/88.48 ) ), true ) ) ] )
% 88.08/88.48 , clause( 42464, [ =( 'is_a_theorem'( equivalent( equivalent( X, Z ),
% 88.08/88.48 equivalent( X, equivalent( Y, equivalent( Z, Y ) ) ) ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150306, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 88.08/88.48 equivalent( Y, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 Z, Y ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 88.08/88.48 substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, X ), :=( Z,
% 88.08/88.48 equivalent( Z, equivalent( Y, Z ) ) )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150310, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.48 equivalent( equivalent( Z, equivalent( Y, Z ) ), X ) ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150308, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, equivalent( Y
% 88.08/88.48 , Z ) ), X ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( X, Y ), equivalent( equivalent( Z, equivalent( Y, Z ) ), X )
% 88.08/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=(
% 88.08/88.48 Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150311, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.48 equivalent( equivalent( Z, equivalent( Y, Z ) ), X ) ) ), true ) ] )
% 88.08/88.48 , clause( 150310, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y )
% 88.08/88.48 , equivalent( equivalent( Z, equivalent( Y, Z ) ), X ) ) ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 45627, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.48 equivalent( equivalent( Z, equivalent( Y, Z ) ), X ) ) ), true ) ] )
% 88.08/88.48 , clause( 150311, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.48 equivalent( equivalent( Z, equivalent( Y, Z ) ), X ) ) ), true ) ] )
% 88.08/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150313, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 Y, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z, Y ) ) ),
% 88.08/88.48 true ) ) ] )
% 88.08/88.48 , clause( 41511, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, Z
% 88.08/88.48 ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z, Y ) ) ), true
% 88.08/88.48 ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150315, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( X, equivalent( Y, Z ) ), equivalent( equivalent( Z, Y ), X )
% 88.08/88.48 ) ), true ) ) ] )
% 88.08/88.48 , clause( 41185, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 88.08/88.48 Y, X ) ), equivalent( Z, equivalent( X, Y ) ) ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150313, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 88.08/88.48 equivalent( Y, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 Z, Y ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 88.08/88.48 substitution( 1, [ :=( X, equivalent( X, equivalent( Y, Z ) ) ), :=( Y, X
% 88.08/88.48 ), :=( Z, equivalent( Z, Y ) )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150317, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( Y, Z ) ), equivalent( equivalent( Z, Y ), X ) ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150315, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( equivalent(
% 88.08/88.48 Z, Y ), X ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( X, equivalent( Y, Z ) ), equivalent( equivalent( Z, Y ), X )
% 88.08/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=(
% 88.08/88.48 Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150318, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.48 Y, Z ) ), equivalent( equivalent( Z, Y ), X ) ) ), true ) ] )
% 88.08/88.48 , clause( 150317, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( Y, Z ) ), equivalent( equivalent( Z, Y ), X ) ) ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 45630, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.48 Y, Z ) ), equivalent( equivalent( Z, Y ), X ) ) ), true ) ] )
% 88.08/88.48 , clause( 150318, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( Y, Z ) ), equivalent( equivalent( Z, Y ), X ) ) ), true ) ]
% 88.08/88.48 )
% 88.08/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150320, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 Y, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z, Y ) ) ),
% 88.08/88.48 true ) ) ] )
% 88.08/88.48 , clause( 41511, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, Z
% 88.08/88.48 ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z, Y ) ) ), true
% 88.08/88.48 ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150322, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ), equivalent( Z, X )
% 88.08/88.48 ) ), true ) ) ] )
% 88.08/88.48 , clause( 33534, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 88.08/88.48 X, equivalent( X, Y ) ) ), equivalent( Z, Y ) ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150320, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 88.08/88.48 equivalent( Y, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 Z, Y ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 88.08/88.48 substitution( 1, [ :=( X, equivalent( X, equivalent( Y, equivalent( Y, Z
% 88.08/88.48 ) ) ) ), :=( Y, X ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150324, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( Y, equivalent( Y, Z ) ) ), equivalent( Z, X ) ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150322, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ),
% 88.08/88.48 equivalent( Z, X ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ), equivalent( Z, X )
% 88.08/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=(
% 88.08/88.48 Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150325, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.48 Y, equivalent( Y, Z ) ) ), equivalent( Z, X ) ) ), true ) ] )
% 88.08/88.48 , clause( 150324, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( Y, equivalent( Y, Z ) ) ), equivalent( Z, X ) ) ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 45669, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.48 Y, equivalent( Y, Z ) ) ), equivalent( Z, X ) ) ), true ) ] )
% 88.08/88.48 , clause( 150325, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.48 equivalent( Y, equivalent( Y, Z ) ) ), equivalent( Z, X ) ) ), true ) ]
% 88.08/88.48 )
% 88.08/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150327, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 88.08/88.48 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 88.08/88.48 ] )
% 88.08/88.48 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 88.08/88.48 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 88.08/88.48 )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150329, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 88.08/88.48 equivalent( X, equivalent( Y, Z ) ) ), true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( Z, Y ), X ) ), true ), true ) ) ] )
% 88.08/88.48 , clause( 45630, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.48 Y, Z ) ), equivalent( equivalent( Z, Y ), X ) ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150327, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 88.08/88.48 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 88.08/88.48 true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.48 substitution( 1, [ :=( X, equivalent( X, equivalent( Y, Z ) ) ), :=( Y,
% 88.08/88.48 equivalent( equivalent( Z, Y ), X ) )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150334, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 Y, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent( Z, Y ), X ) ),
% 88.08/88.48 true ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150329, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 88.08/88.48 equivalent( X, equivalent( Y, Z ) ) ), true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( Z, Y ), X ) ), true ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 88.08/88.48 equivalent( X, equivalent( Y, Z ) ) ), true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( Z, Y ), X ) ), true ) ), :=( Z, true )] ), substitution( 1, [
% 88.08/88.48 :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150335, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, Z
% 88.08/88.48 ) ) ), true, 'is_a_theorem'( equivalent( equivalent( Z, Y ), X ) ), true
% 88.08/88.48 ), true ) ] )
% 88.08/88.48 , clause( 150334, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 88.08/88.48 equivalent( Y, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent( Z,
% 88.08/88.48 Y ), X ) ), true ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 46313, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, Z )
% 88.08/88.48 ) ), true, 'is_a_theorem'( equivalent( equivalent( Z, Y ), X ) ), true )
% 88.08/88.48 , true ) ] )
% 88.08/88.48 , clause( 150335, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 88.08/88.48 Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent( Z, Y ), X ) ),
% 88.08/88.48 true ), true ) ] )
% 88.08/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150337, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 88.08/88.48 , 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 88.08/88.48 , clause( 16553, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 88.08/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150339, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( equivalent( Z, equivalent( Y, Z ) ), X ), equivalent( X, Y )
% 88.08/88.48 ) ), true ) ) ] )
% 88.08/88.48 , clause( 45627, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.48 equivalent( equivalent( Z, equivalent( Y, Z ) ), X ) ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150337, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 88.08/88.48 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.48 substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, equivalent(
% 88.08/88.48 equivalent( Z, equivalent( Y, Z ) ), X ) )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150341, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.48 equivalent( X, equivalent( Y, X ) ), Z ), equivalent( Z, Y ) ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150339, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( equivalent( Z, equivalent( Y, Z ) ), X ),
% 88.08/88.48 equivalent( X, Y ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( equivalent( X, equivalent( Y, X ) ), Z ), equivalent( Z, Y )
% 88.08/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, Y ), :=(
% 88.08/88.48 Z, X )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150342, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 88.08/88.48 , equivalent( Y, X ) ), Z ), equivalent( Z, Y ) ) ), true ) ] )
% 88.08/88.48 , clause( 150341, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.48 equivalent( X, equivalent( Y, X ) ), Z ), equivalent( Z, Y ) ) ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 47133, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Z,
% 88.08/88.48 equivalent( Y, Z ) ), X ), equivalent( X, Y ) ) ), true ) ] )
% 88.08/88.48 , clause( 150342, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.48 X, equivalent( Y, X ) ), Z ), equivalent( Z, Y ) ) ), true ) ] )
% 88.08/88.48 , substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150344, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 Y, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z, Y ) ) ),
% 88.08/88.48 true ) ) ] )
% 88.08/88.48 , clause( 41511, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, Z
% 88.08/88.48 ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z, Y ) ) ), true
% 88.08/88.48 ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150346, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( equivalent( X, equivalent( Y, X ) ), Z ), equivalent( Y, Z )
% 88.08/88.48 ) ), true ) ) ] )
% 88.08/88.48 , clause( 47133, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Z
% 88.08/88.48 , equivalent( Y, Z ) ), X ), equivalent( X, Y ) ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150344, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 88.08/88.48 equivalent( Y, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.48 Z, Y ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 88.08/88.48 substitution( 1, [ :=( X, equivalent( equivalent( X, equivalent( Y, X ) )
% 88.08/88.48 , Z ) ), :=( Y, Z ), :=( Z, Y )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150348, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.48 equivalent( X, equivalent( Y, X ) ), Z ), equivalent( Y, Z ) ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150346, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( equivalent( X, equivalent( Y, X ) ), Z ),
% 88.08/88.48 equivalent( Y, Z ) ) ), true ) ) ] )
% 88.08/88.48 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( equivalent( X, equivalent( Y, X ) ), Z ), equivalent( Y, Z )
% 88.08/88.48 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=(
% 88.08/88.48 Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150349, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 88.08/88.48 , equivalent( Y, X ) ), Z ), equivalent( Y, Z ) ) ), true ) ] )
% 88.08/88.48 , clause( 150348, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.48 equivalent( X, equivalent( Y, X ) ), Z ), equivalent( Y, Z ) ) ) ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 subsumption(
% 88.08/88.48 clause( 47212, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 88.08/88.48 equivalent( Y, X ) ), Z ), equivalent( Y, Z ) ) ), true ) ] )
% 88.08/88.48 , clause( 150349, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.48 X, equivalent( Y, X ) ), Z ), equivalent( Y, Z ) ) ), true ) ] )
% 88.08/88.48 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.48 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 eqswap(
% 88.08/88.48 clause( 150351, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 88.08/88.48 , 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 88.08/88.48 , clause( 16553, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 88.08/88.48 'is_a_theorem'( equivalent( Y, X ) ), true ), true ) ] )
% 88.08/88.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150353, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.48 equivalent( Y, Z ), equivalent( equivalent( X, equivalent( Y, X ) ), Z )
% 88.08/88.48 ) ), true ) ) ] )
% 88.08/88.48 , clause( 47212, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 88.08/88.48 , equivalent( Y, X ) ), Z ), equivalent( Y, Z ) ) ), true ) ] )
% 88.08/88.48 , 0, clause( 150351, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 88.08/88.48 , true, 'is_a_theorem'( equivalent( Y, X ) ), true ) ) ] )
% 88.08/88.48 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.48 substitution( 1, [ :=( X, equivalent( equivalent( X, equivalent( Y, X ) )
% 88.08/88.48 , Z ) ), :=( Y, equivalent( Y, Z ) )] )).
% 88.08/88.48
% 88.08/88.48
% 88.08/88.48 paramod(
% 88.08/88.48 clause( 150355, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.48 equivalent( equivalent( Z, equivalent( X, Z ) ), Y ) ) ) ) ] )
% 88.08/88.48 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.48 , 0, clause( 150353, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.48 equivalent( equivalent( Y, Z ), equivalent( equivalent( X, equivalent( Y
% 88.08/88.48 , X ) ), Z ) ) ), true ) ) ] )
% 88.08/88.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( X, Y ), equivalent( equivalent( Z, equivalent( X, Z ) ), Y )
% 88.08/88.49 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, X ), :=(
% 88.08/88.49 Z, Y )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150356, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.49 equivalent( equivalent( Z, equivalent( X, Z ) ), Y ) ) ), true ) ] )
% 88.08/88.49 , clause( 150355, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y )
% 88.08/88.49 , equivalent( equivalent( Z, equivalent( X, Z ) ), Y ) ) ) ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 subsumption(
% 88.08/88.49 clause( 47357, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Z ),
% 88.08/88.49 equivalent( equivalent( X, equivalent( Y, X ) ), Z ) ) ), true ) ] )
% 88.08/88.49 , clause( 150356, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.49 equivalent( equivalent( Z, equivalent( X, Z ) ), Y ) ) ), true ) ] )
% 88.08/88.49 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 88.08/88.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150358, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.49 Y, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z, Y ) ) ),
% 88.08/88.49 true ) ) ] )
% 88.08/88.49 , clause( 41511, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, Z
% 88.08/88.49 ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent( Z, Y ) ) ), true
% 88.08/88.49 ), true ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150360, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( X, Y ), equivalent( Y, equivalent( Z, equivalent( X, Z ) ) )
% 88.08/88.49 ) ), true ) ) ] )
% 88.08/88.49 , clause( 47357, [ =( 'is_a_theorem'( equivalent( equivalent( Y, Z ),
% 88.08/88.49 equivalent( equivalent( X, equivalent( Y, X ) ), Z ) ) ), true ) ] )
% 88.08/88.49 , 0, clause( 150358, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 88.08/88.49 equivalent( Y, Z ) ) ), true, 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.49 Z, Y ) ) ), true ) ) ] )
% 88.08/88.49 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 88.08/88.49 substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, equivalent( Z,
% 88.08/88.49 equivalent( X, Z ) ) ), :=( Z, Y )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150362, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.49 equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ) ) ) ) ] )
% 88.08/88.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.49 , 0, clause( 150360, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.49 equivalent( equivalent( X, Y ), equivalent( Y, equivalent( Z, equivalent(
% 88.08/88.49 X, Z ) ) ) ) ), true ) ) ] )
% 88.08/88.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( X, Y ), equivalent( Y, equivalent( Z, equivalent( X, Z ) ) )
% 88.08/88.49 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=(
% 88.08/88.49 Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150363, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.49 equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ) ) ), true ) ] )
% 88.08/88.49 , clause( 150362, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y )
% 88.08/88.49 , equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ) ) ) ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 subsumption(
% 88.08/88.49 clause( 48038, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.49 equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ) ) ), true ) ] )
% 88.08/88.49 , clause( 150363, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.49 equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ) ) ), true ) ] )
% 88.08/88.49 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150365, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 88.08/88.49 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 88.08/88.49 ] )
% 88.08/88.49 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 88.08/88.49 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 88.08/88.49 )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150367, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 88.08/88.49 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( Y, equivalent( Z
% 88.08/88.49 , equivalent( X, Z ) ) ) ), true ), true ) ) ] )
% 88.08/88.49 , clause( 48038, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.49 equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ) ) ), true ) ] )
% 88.08/88.49 , 0, clause( 150365, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 88.08/88.49 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 88.08/88.49 true ) ) ] )
% 88.08/88.49 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.49 substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, equivalent( Y,
% 88.08/88.49 equivalent( Z, equivalent( X, Z ) ) ) )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150372, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 88.08/88.49 , 'is_a_theorem'( equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ) )
% 88.08/88.49 , true ) ) ] )
% 88.08/88.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.49 , 0, clause( 150367, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 88.08/88.49 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( Y, equivalent( Z
% 88.08/88.49 , equivalent( X, Z ) ) ) ), true ), true ) ) ] )
% 88.08/88.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 88.08/88.49 equivalent( X, Y ) ), true, 'is_a_theorem'( equivalent( Y, equivalent( Z
% 88.08/88.49 , equivalent( X, Z ) ) ) ), true ) ), :=( Z, true )] ), substitution( 1
% 88.08/88.49 , [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150373, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 88.08/88.49 'is_a_theorem'( equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ) ),
% 88.08/88.49 true ), true ) ] )
% 88.08/88.49 , clause( 150372, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ),
% 88.08/88.49 true, 'is_a_theorem'( equivalent( Y, equivalent( Z, equivalent( X, Z ) )
% 88.08/88.49 ) ), true ) ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 subsumption(
% 88.08/88.49 clause( 48243, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 88.08/88.49 'is_a_theorem'( equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ) ),
% 88.08/88.49 true ), true ) ] )
% 88.08/88.49 , clause( 150373, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 88.08/88.49 'is_a_theorem'( equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ) ),
% 88.08/88.49 true ), true ) ] )
% 88.08/88.49 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150375, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 88.08/88.49 , ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) )
% 88.08/88.49 ] )
% 88.08/88.49 , clause( 1, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true, ifeq(
% 88.08/88.49 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 88.08/88.49 )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150377, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 88.08/88.49 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ) ), true,
% 88.08/88.49 'is_a_theorem'( equivalent( Z, X ) ), true ), true ) ) ] )
% 88.08/88.49 , clause( 45669, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.49 Y, equivalent( Y, Z ) ) ), equivalent( Z, X ) ) ), true ) ] )
% 88.08/88.49 , 0, clause( 150375, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 88.08/88.49 , true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ),
% 88.08/88.49 true ) ) ] )
% 88.08/88.49 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.49 substitution( 1, [ :=( X, equivalent( X, equivalent( Y, equivalent( Y, Z
% 88.08/88.49 ) ) ) ), :=( Y, equivalent( Z, X ) )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150382, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.49 Y, equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Z, X ) ),
% 88.08/88.49 true ) ) ] )
% 88.08/88.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.49 , 0, clause( 150377, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 88.08/88.49 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ) ), true,
% 88.08/88.49 'is_a_theorem'( equivalent( Z, X ) ), true ), true ) ) ] )
% 88.08/88.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 88.08/88.49 equivalent( X, equivalent( Y, equivalent( Y, Z ) ) ) ), true,
% 88.08/88.49 'is_a_theorem'( equivalent( Z, X ) ), true ) ), :=( Z, true )] ),
% 88.08/88.49 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150383, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 88.08/88.49 equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Z, X ) ),
% 88.08/88.49 true ), true ) ] )
% 88.08/88.49 , clause( 150382, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 88.08/88.49 equivalent( Y, equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent(
% 88.08/88.49 Z, X ) ), true ) ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 subsumption(
% 88.08/88.49 clause( 49039, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 88.08/88.49 equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Z, X ) ),
% 88.08/88.49 true ), true ) ] )
% 88.08/88.49 , clause( 150383, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 88.08/88.49 equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Z, X ) ),
% 88.08/88.49 true ), true ) ] )
% 88.08/88.49 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150385, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true
% 88.08/88.49 , 'is_a_theorem'( equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ) )
% 88.08/88.49 , true ) ) ] )
% 88.08/88.49 , clause( 48243, [ =( ifeq( 'is_a_theorem'( equivalent( X, Y ) ), true,
% 88.08/88.49 'is_a_theorem'( equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ) ),
% 88.08/88.49 true ), true ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150387, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ), equivalent( T,
% 88.08/88.49 equivalent( equivalent( X, Y ), T ) ) ) ), true ) ) ] )
% 88.08/88.49 , clause( 48038, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.49 equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ) ) ), true ) ] )
% 88.08/88.49 , 0, clause( 150385, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, Y ) )
% 88.08/88.49 , true, 'is_a_theorem'( equivalent( Y, equivalent( Z, equivalent( X, Z )
% 88.08/88.49 ) ) ), true ) ) ] )
% 88.08/88.49 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.49 substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, equivalent( Y,
% 88.08/88.49 equivalent( Z, equivalent( X, Z ) ) ) ), :=( Z, T )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150389, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.49 equivalent( Y, equivalent( Z, Y ) ) ), equivalent( T, equivalent(
% 88.08/88.49 equivalent( Z, X ), T ) ) ) ) ) ] )
% 88.08/88.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.49 , 0, clause( 150387, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.49 equivalent( equivalent( Y, equivalent( Z, equivalent( X, Z ) ) ),
% 88.08/88.49 equivalent( T, equivalent( equivalent( X, Y ), T ) ) ) ), true ) ) ] )
% 88.08/88.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( X, equivalent( Y, equivalent( Z, Y ) ) ), equivalent( T,
% 88.08/88.49 equivalent( equivalent( Z, X ), T ) ) ) ) ), :=( Z, true )] ),
% 88.08/88.49 substitution( 1, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150390, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.49 Y, equivalent( Z, Y ) ) ), equivalent( T, equivalent( equivalent( Z, X )
% 88.08/88.49 , T ) ) ) ), true ) ] )
% 88.08/88.49 , clause( 150389, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.49 equivalent( Y, equivalent( Z, Y ) ) ), equivalent( T, equivalent(
% 88.08/88.49 equivalent( Z, X ), T ) ) ) ) ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 88.08/88.49 ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 subsumption(
% 88.08/88.49 clause( 72227, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 88.08/88.49 Z, equivalent( X, Z ) ) ), equivalent( T, equivalent( equivalent( X, Y )
% 88.08/88.49 , T ) ) ) ), true ) ] )
% 88.08/88.49 , clause( 150390, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.49 equivalent( Y, equivalent( Z, Y ) ) ), equivalent( T, equivalent(
% 88.08/88.49 equivalent( Z, X ), T ) ) ) ), true ) ] )
% 88.08/88.49 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T )] ),
% 88.08/88.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150392, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.49 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z
% 88.08/88.49 , T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 88.08/88.49 , clause( 10, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.49 X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z, T ) ) ),
% 88.08/88.49 true, 'is_a_theorem'( T ), true ), true ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 88.08/88.49 ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150394, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( X, equivalent( equivalent( X, Y ), equivalent( Y, Z ) ) ), Z
% 88.08/88.49 ) ), true ) ) ] )
% 88.08/88.49 , clause( 72227, [ =( 'is_a_theorem'( equivalent( equivalent( Y, equivalent(
% 88.08/88.49 Z, equivalent( X, Z ) ) ), equivalent( T, equivalent( equivalent( X, Y )
% 88.08/88.49 , T ) ) ) ), true ) ] )
% 88.08/88.49 , 0, clause( 150392, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ),
% 88.08/88.49 equivalent( Z, T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 88.08/88.49 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, equivalent( equivalent( X, Y
% 88.08/88.49 ), equivalent( Y, Z ) ) ), :=( Z, Y ), :=( T, Z )] ), substitution( 1, [
% 88.08/88.49 :=( X, equivalent( X, Y ) ), :=( Y, Y ), :=( Z, Z ), :=( T, equivalent(
% 88.08/88.49 equivalent( X, equivalent( equivalent( X, Y ), equivalent( Y, Z ) ) ), Z
% 88.08/88.49 ) )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150396, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.49 equivalent( equivalent( X, Y ), equivalent( Y, Z ) ) ), Z ) ) ) ] )
% 88.08/88.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.49 , 0, clause( 150394, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.49 equivalent( equivalent( X, equivalent( equivalent( X, Y ), equivalent( Y
% 88.08/88.49 , Z ) ) ), Z ) ), true ) ) ] )
% 88.08/88.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( X, equivalent( equivalent( X, Y ), equivalent( Y, Z ) ) ), Z
% 88.08/88.49 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=(
% 88.08/88.49 Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150397, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.49 equivalent( X, Y ), equivalent( Y, Z ) ) ), Z ) ), true ) ] )
% 88.08/88.49 , clause( 150396, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.49 equivalent( equivalent( X, Y ), equivalent( Y, Z ) ) ), Z ) ) ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 subsumption(
% 88.08/88.49 clause( 116409, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.49 equivalent( X, Y ), equivalent( Y, Z ) ) ), Z ) ), true ) ] )
% 88.08/88.49 , clause( 150397, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.49 equivalent( equivalent( X, Y ), equivalent( Y, Z ) ) ), Z ) ), true ) ]
% 88.08/88.49 )
% 88.08/88.49 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150399, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.49 Y, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent( Z, Y ), X ) ),
% 88.08/88.49 true ) ) ] )
% 88.08/88.49 , clause( 46313, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, Z
% 88.08/88.49 ) ) ), true, 'is_a_theorem'( equivalent( equivalent( Z, Y ), X ) ), true
% 88.08/88.49 ), true ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150401, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( T, Z ), equivalent( X, equivalent( equivalent( X, Y ),
% 88.08/88.49 equivalent( Y, equivalent( Z, T ) ) ) ) ) ), true ) ) ] )
% 88.08/88.49 , clause( 116409, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.49 equivalent( equivalent( X, Y ), equivalent( Y, Z ) ) ), Z ) ), true ) ]
% 88.08/88.49 )
% 88.08/88.49 , 0, clause( 150399, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 88.08/88.49 equivalent( Y, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent( Z,
% 88.08/88.49 Y ), X ) ), true ) ) ] )
% 88.08/88.49 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, equivalent( Z, T
% 88.08/88.49 ) )] ), substitution( 1, [ :=( X, equivalent( X, equivalent( equivalent(
% 88.08/88.49 X, Y ), equivalent( Y, equivalent( Z, T ) ) ) ) ), :=( Y, Z ), :=( Z, T )] )
% 88.08/88.49 ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150403, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.49 equivalent( Z, equivalent( equivalent( Z, T ), equivalent( T, equivalent(
% 88.08/88.49 Y, X ) ) ) ) ) ) ) ] )
% 88.08/88.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.49 , 0, clause( 150401, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.49 equivalent( equivalent( T, Z ), equivalent( X, equivalent( equivalent( X
% 88.08/88.49 , Y ), equivalent( Y, equivalent( Z, T ) ) ) ) ) ), true ) ) ] )
% 88.08/88.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( X, Y ), equivalent( Z, equivalent( equivalent( Z, T ),
% 88.08/88.49 equivalent( T, equivalent( Y, X ) ) ) ) ) ) ), :=( Z, true )] ),
% 88.08/88.49 substitution( 1, [ :=( X, Z ), :=( Y, T ), :=( Z, Y ), :=( T, X )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150404, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.49 equivalent( Z, equivalent( equivalent( Z, T ), equivalent( T, equivalent(
% 88.08/88.49 Y, X ) ) ) ) ) ), true ) ] )
% 88.08/88.49 , clause( 150403, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y )
% 88.08/88.49 , equivalent( Z, equivalent( equivalent( Z, T ), equivalent( T,
% 88.08/88.49 equivalent( Y, X ) ) ) ) ) ) ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 88.08/88.49 ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 subsumption(
% 88.08/88.49 clause( 116523, [ =( 'is_a_theorem'( equivalent( equivalent( T, Z ),
% 88.08/88.49 equivalent( X, equivalent( equivalent( X, Y ), equivalent( Y, equivalent(
% 88.08/88.49 Z, T ) ) ) ) ) ), true ) ] )
% 88.08/88.49 , clause( 150404, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.49 equivalent( Z, equivalent( equivalent( Z, T ), equivalent( T, equivalent(
% 88.08/88.49 Y, X ) ) ) ) ) ), true ) ] )
% 88.08/88.49 , substitution( 0, [ :=( X, T ), :=( Y, Z ), :=( Z, X ), :=( T, Y )] ),
% 88.08/88.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150406, [ =( true, ifeq( 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.49 equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z
% 88.08/88.49 , T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 88.08/88.49 , clause( 10, [ =( ifeq( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.49 X, equivalent( Y, Z ) ), equivalent( Y, X ) ), equivalent( Z, T ) ) ),
% 88.08/88.49 true, 'is_a_theorem'( T ), true ), true ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 88.08/88.49 ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150408, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( Z, T ), equivalent( T, equivalent( equivalent( Y, X ),
% 88.08/88.49 equivalent( X, equivalent( Y, Z ) ) ) ) ) ), true ) ) ] )
% 88.08/88.49 , clause( 116523, [ =( 'is_a_theorem'( equivalent( equivalent( T, Z ),
% 88.08/88.49 equivalent( X, equivalent( equivalent( X, Y ), equivalent( Y, equivalent(
% 88.08/88.49 Z, T ) ) ) ) ) ), true ) ] )
% 88.08/88.49 , 0, clause( 150406, [ =( true, ifeq( 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( Y, X ) ),
% 88.08/88.49 equivalent( Z, T ) ) ), true, 'is_a_theorem'( T ), true ) ) ] )
% 88.08/88.49 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, equivalent( Y, X
% 88.08/88.49 ) ), :=( T, equivalent( X, equivalent( Y, Z ) ) )] ), substitution( 1, [
% 88.08/88.49 :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, equivalent( equivalent( Z, T
% 88.08/88.49 ), equivalent( T, equivalent( equivalent( Y, X ), equivalent( X,
% 88.08/88.49 equivalent( Y, Z ) ) ) ) ) )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150410, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.49 equivalent( Y, equivalent( equivalent( Z, T ), equivalent( T, equivalent(
% 88.08/88.49 Z, X ) ) ) ) ) ) ) ] )
% 88.08/88.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.49 , 0, clause( 150408, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.49 equivalent( equivalent( Z, T ), equivalent( T, equivalent( equivalent( Y
% 88.08/88.49 , X ), equivalent( X, equivalent( Y, Z ) ) ) ) ) ), true ) ) ] )
% 88.08/88.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( X, Y ), equivalent( Y, equivalent( equivalent( Z, T ),
% 88.08/88.49 equivalent( T, equivalent( Z, X ) ) ) ) ) ) ), :=( Z, true )] ),
% 88.08/88.49 substitution( 1, [ :=( X, T ), :=( Y, Z ), :=( Z, X ), :=( T, Y )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150411, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.49 equivalent( Y, equivalent( equivalent( Z, T ), equivalent( T, equivalent(
% 88.08/88.49 Z, X ) ) ) ) ) ), true ) ] )
% 88.08/88.49 , clause( 150410, [ =( true, 'is_a_theorem'( equivalent( equivalent( X, Y )
% 88.08/88.49 , equivalent( Y, equivalent( equivalent( Z, T ), equivalent( T,
% 88.08/88.49 equivalent( Z, X ) ) ) ) ) ) ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 88.08/88.49 ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 subsumption(
% 88.08/88.49 clause( 147068, [ =( 'is_a_theorem'( equivalent( equivalent( Z, T ),
% 88.08/88.49 equivalent( T, equivalent( equivalent( Y, X ), equivalent( X, equivalent(
% 88.08/88.49 Y, Z ) ) ) ) ) ), true ) ] )
% 88.08/88.49 , clause( 150411, [ =( 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 88.08/88.49 equivalent( Y, equivalent( equivalent( Z, T ), equivalent( T, equivalent(
% 88.08/88.49 Z, X ) ) ) ) ) ), true ) ] )
% 88.08/88.49 , substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, Y ), :=( T, X )] ),
% 88.08/88.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150413, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.49 Y, equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Z, X ) ),
% 88.08/88.49 true ) ) ] )
% 88.08/88.49 , clause( 49039, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 88.08/88.49 equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent( Z, X ) ),
% 88.08/88.49 true ), true ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150415, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( Z, equivalent( Y, X ) ), equivalent( X, equivalent( Y, Z ) )
% 88.08/88.49 ) ), true ) ) ] )
% 88.08/88.49 , clause( 147068, [ =( 'is_a_theorem'( equivalent( equivalent( Z, T ),
% 88.08/88.49 equivalent( T, equivalent( equivalent( Y, X ), equivalent( X, equivalent(
% 88.08/88.49 Y, Z ) ) ) ) ) ), true ) ] )
% 88.08/88.49 , 0, clause( 150413, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 88.08/88.49 equivalent( Y, equivalent( Y, Z ) ) ) ), true, 'is_a_theorem'( equivalent(
% 88.08/88.49 Z, X ) ), true ) ) ] )
% 88.08/88.49 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X ), :=( T,
% 88.08/88.49 equivalent( Y, Z ) )] ), substitution( 1, [ :=( X, equivalent( X,
% 88.08/88.49 equivalent( Y, Z ) ) ), :=( Y, equivalent( Y, Z ) ), :=( Z, equivalent( Z
% 88.08/88.49 , equivalent( Y, X ) ) )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150417, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.49 equivalent( Y, Z ) ), equivalent( Z, equivalent( Y, X ) ) ) ) ) ] )
% 88.08/88.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.49 , 0, clause( 150415, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.49 equivalent( equivalent( Z, equivalent( Y, X ) ), equivalent( X,
% 88.08/88.49 equivalent( Y, Z ) ) ) ), true ) ) ] )
% 88.08/88.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( X, equivalent( Y, Z ) ), equivalent( Z, equivalent( Y, X ) )
% 88.08/88.49 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z ), :=( Y, Y ), :=(
% 88.08/88.49 Z, X )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150418, [ =( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 88.08/88.49 Y, Z ) ), equivalent( Z, equivalent( Y, X ) ) ) ), true ) ] )
% 88.08/88.49 , clause( 150417, [ =( true, 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.49 equivalent( Y, Z ) ), equivalent( Z, equivalent( Y, X ) ) ) ) ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 subsumption(
% 88.08/88.49 clause( 148924, [ =( 'is_a_theorem'( equivalent( equivalent( Z, equivalent(
% 88.08/88.49 Y, X ) ), equivalent( X, equivalent( Y, Z ) ) ) ), true ) ] )
% 88.08/88.49 , clause( 150418, [ =( 'is_a_theorem'( equivalent( equivalent( X,
% 88.08/88.49 equivalent( Y, Z ) ), equivalent( Z, equivalent( Y, X ) ) ) ), true ) ]
% 88.08/88.49 )
% 88.08/88.49 , substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 88.08/88.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150420, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.49 Y, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent( Z, Y ), X ) ),
% 88.08/88.49 true ) ) ] )
% 88.08/88.49 , clause( 46313, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y, Z
% 88.08/88.49 ) ) ), true, 'is_a_theorem'( equivalent( equivalent( Z, Y ), X ) ), true
% 88.08/88.49 ), true ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150422, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( equivalent( Y, X ), Z ), equivalent( X, equivalent( Y, Z ) )
% 88.08/88.49 ) ), true ) ) ] )
% 88.08/88.49 , clause( 148924, [ =( 'is_a_theorem'( equivalent( equivalent( Z,
% 88.08/88.49 equivalent( Y, X ) ), equivalent( X, equivalent( Y, Z ) ) ) ), true ) ]
% 88.08/88.49 )
% 88.08/88.49 , 0, clause( 150420, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 88.08/88.49 equivalent( Y, Z ) ) ), true, 'is_a_theorem'( equivalent( equivalent( Z,
% 88.08/88.49 Y ), X ) ), true ) ) ] )
% 88.08/88.49 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 88.08/88.49 substitution( 1, [ :=( X, equivalent( X, equivalent( Y, Z ) ) ), :=( Y, Z
% 88.08/88.49 ), :=( Z, equivalent( Y, X ) )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150424, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.49 equivalent( X, Y ), Z ), equivalent( Y, equivalent( X, Z ) ) ) ) ) ] )
% 88.08/88.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.49 , 0, clause( 150422, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.49 equivalent( equivalent( equivalent( Y, X ), Z ), equivalent( X,
% 88.08/88.49 equivalent( Y, Z ) ) ) ), true ) ) ] )
% 88.08/88.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( equivalent( X, Y ), Z ), equivalent( Y, equivalent( X, Z ) )
% 88.08/88.49 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, X ), :=(
% 88.08/88.49 Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150425, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 88.08/88.49 , Y ), Z ), equivalent( Y, equivalent( X, Z ) ) ) ), true ) ] )
% 88.08/88.49 , clause( 150424, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.49 equivalent( X, Y ), Z ), equivalent( Y, equivalent( X, Z ) ) ) ) ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 subsumption(
% 88.08/88.49 clause( 149096, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( Y
% 88.08/88.49 , X ), Z ), equivalent( X, equivalent( Y, Z ) ) ) ), true ) ] )
% 88.08/88.49 , clause( 150425, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.49 X, Y ), Z ), equivalent( Y, equivalent( X, Z ) ) ) ), true ) ] )
% 88.08/88.49 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 88.08/88.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150427, [ =( true, ifeq( 'is_a_theorem'( equivalent( X, equivalent(
% 88.08/88.49 Y, equivalent( equivalent( Z, equivalent( T, Y ) ), equivalent( T, Z ) )
% 88.08/88.49 ) ) ), true, 'is_a_theorem'( X ), true ) ) ] )
% 88.08/88.49 , clause( 3836, [ =( ifeq( 'is_a_theorem'( equivalent( X, equivalent( Y,
% 88.08/88.49 equivalent( equivalent( Z, equivalent( T, Y ) ), equivalent( T, Z ) ) ) )
% 88.08/88.49 ), true, 'is_a_theorem'( X ), true ), true ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 88.08/88.49 ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150429, [ =( true, ifeq( true, true, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( equivalent( X, equivalent( Y, Z ) ), Z ), equivalent( Y, X )
% 88.08/88.49 ) ), true ) ) ] )
% 88.08/88.49 , clause( 149096, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.49 Y, X ), Z ), equivalent( X, equivalent( Y, Z ) ) ) ), true ) ] )
% 88.08/88.49 , 0, clause( 150427, [ =( true, ifeq( 'is_a_theorem'( equivalent( X,
% 88.08/88.49 equivalent( Y, equivalent( equivalent( Z, equivalent( T, Y ) ),
% 88.08/88.49 equivalent( T, Z ) ) ) ) ), true, 'is_a_theorem'( X ), true ) ) ] )
% 88.08/88.49 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, equivalent( X, equivalent( Y
% 88.08/88.49 , Z ) ) ), :=( Z, equivalent( Y, X ) )] ), substitution( 1, [ :=( X,
% 88.08/88.49 equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ), Z ),
% 88.08/88.49 equivalent( Y, X ) ) ), :=( Y, Z ), :=( Z, X ), :=( T, Y )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150431, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.49 equivalent( X, equivalent( Y, Z ) ), Z ), equivalent( Y, X ) ) ) ) ] )
% 88.08/88.49 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 88.08/88.49 , 0, clause( 150429, [ =( true, ifeq( true, true, 'is_a_theorem'(
% 88.08/88.49 equivalent( equivalent( equivalent( X, equivalent( Y, Z ) ), Z ),
% 88.08/88.49 equivalent( Y, X ) ) ), true ) ) ] )
% 88.08/88.49 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( equivalent(
% 88.08/88.49 equivalent( equivalent( X, equivalent( Y, Z ) ), Z ), equivalent( Y, X )
% 88.08/88.49 ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=(
% 88.08/88.49 Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqswap(
% 88.08/88.49 clause( 150432, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 88.08/88.49 , equivalent( Y, Z ) ), Z ), equivalent( Y, X ) ) ), true ) ] )
% 88.08/88.49 , clause( 150431, [ =( true, 'is_a_theorem'( equivalent( equivalent(
% 88.08/88.49 equivalent( X, equivalent( Y, Z ) ), Z ), equivalent( Y, X ) ) ) ) ] )
% 88.08/88.49 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 subsumption(
% 88.08/88.49 clause( 149411, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 88.08/88.49 , equivalent( Y, Z ) ), Z ), equivalent( Y, X ) ) ), true ) ] )
% 88.08/88.49 , clause( 150432, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.49 X, equivalent( Y, Z ) ), Z ), equivalent( Y, X ) ) ), true ) ] )
% 88.08/88.49 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 88.08/88.49 permutation( 0, [ ==>( 0, 0 )] ) ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 paramod(
% 88.08/88.49 clause( 150435, [ ~( =( true, true ) ) ] )
% 88.08/88.49 , clause( 149411, [ =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.49 X, equivalent( Y, Z ) ), Z ), equivalent( Y, X ) ) ), true ) ] )
% 88.08/88.49 , 0, clause( 3, [ ~( =( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 88.08/88.49 a, equivalent( b, c ) ), c ), equivalent( b, a ) ) ), true ) ) ] )
% 88.08/88.49 , 0, 2, substitution( 0, [ :=( X, a ), :=( Y, b ), :=( Z, c )] ),
% 88.08/88.49 substitution( 1, [] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 eqrefl(
% 88.08/88.49 clause( 150436, [] )
% 88.08/88.49 , clause( 150435, [ ~( =( true, true ) ) ] )
% 88.08/88.49 , 0, substitution( 0, [] )).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 subsumption(
% 88.08/88.49 clause( 149438, [] )
% 88.08/88.49 , clause( 150436, [] )
% 88.08/88.49 , substitution( 0, [] ), permutation( 0, [] ) ).
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 end.
% 88.08/88.49
% 88.08/88.49 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 88.08/88.49
% 88.08/88.49 Memory use:
% 88.08/88.49
% 88.08/88.49 space for terms: 3235836
% 88.08/88.49 space for clauses: 17222957
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 clauses generated: 11816719
% 88.08/88.49 clauses kept: 149439
% 88.08/88.49 clauses selected: 6645
% 88.08/88.49 clauses deleted: 4415
% 88.08/88.49 clauses inuse deleted: 26
% 88.08/88.49
% 88.08/88.49 subsentry: 1874
% 88.08/88.49 literals s-matched: 573
% 88.08/88.49 literals matched: 573
% 88.08/88.49 full subsumption: 0
% 88.08/88.49
% 88.08/88.49 checksum: 489766484
% 88.08/88.49
% 88.08/88.49
% 88.08/88.49 Bliksem ended
%------------------------------------------------------------------------------