TSTP Solution File: LCL113-10 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL113-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 07:50:31 EDT 2022
% Result : Unsatisfiable 51.24s 51.66s
% Output : Refutation 51.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL113-10 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Mon Jul 4 10:47:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 51.24/51.66 *** allocated 10000 integers for termspace/termends
% 51.24/51.66 *** allocated 10000 integers for clauses
% 51.24/51.66 *** allocated 10000 integers for justifications
% 51.24/51.66 Bliksem 1.12
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Automatic Strategy Selection
% 51.24/51.66
% 51.24/51.66 Clauses:
% 51.24/51.66 [
% 51.24/51.66 [ =( ifeq( X, X, Y, Z ), Y ) ],
% 51.24/51.66 [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq( 'is_a_theorem'(
% 51.24/51.66 X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ],
% 51.24/51.66 [ =( 'is_a_theorem'( implies( X, implies( Y, X ) ) ), true ) ],
% 51.24/51.66 [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( implies( Y, Z )
% 51.24/51.66 , implies( X, Z ) ) ) ), true ) ],
% 51.24/51.66 [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Y ), implies(
% 51.24/51.66 implies( Y, X ), X ) ) ), true ) ],
% 51.24/51.66 [ =( 'is_a_theorem'( implies( implies( not( X ), not( Y ) ), implies( Y
% 51.24/51.66 , X ) ) ), true ) ],
% 51.24/51.66 [ ~( =( 'is_a_theorem'( implies( implies( not( a ), b ), implies( not( b
% 51.24/51.66 ), a ) ) ), true ) ) ]
% 51.24/51.66 ] .
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 percentage equality = 1.000000, percentage horn = 1.000000
% 51.24/51.66 This is a pure equality problem
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Options Used:
% 51.24/51.66
% 51.24/51.66 useres = 1
% 51.24/51.66 useparamod = 1
% 51.24/51.66 useeqrefl = 1
% 51.24/51.66 useeqfact = 1
% 51.24/51.66 usefactor = 1
% 51.24/51.66 usesimpsplitting = 0
% 51.24/51.66 usesimpdemod = 5
% 51.24/51.66 usesimpres = 3
% 51.24/51.66
% 51.24/51.66 resimpinuse = 1000
% 51.24/51.66 resimpclauses = 20000
% 51.24/51.66 substype = eqrewr
% 51.24/51.66 backwardsubs = 1
% 51.24/51.66 selectoldest = 5
% 51.24/51.66
% 51.24/51.66 litorderings [0] = split
% 51.24/51.66 litorderings [1] = extend the termordering, first sorting on arguments
% 51.24/51.66
% 51.24/51.66 termordering = kbo
% 51.24/51.66
% 51.24/51.66 litapriori = 0
% 51.24/51.66 termapriori = 1
% 51.24/51.66 litaposteriori = 0
% 51.24/51.66 termaposteriori = 0
% 51.24/51.66 demodaposteriori = 0
% 51.24/51.66 ordereqreflfact = 0
% 51.24/51.66
% 51.24/51.66 litselect = negord
% 51.24/51.66
% 51.24/51.66 maxweight = 15
% 51.24/51.66 maxdepth = 30000
% 51.24/51.66 maxlength = 115
% 51.24/51.66 maxnrvars = 195
% 51.24/51.66 excuselevel = 1
% 51.24/51.66 increasemaxweight = 1
% 51.24/51.66
% 51.24/51.66 maxselected = 10000000
% 51.24/51.66 maxnrclauses = 10000000
% 51.24/51.66
% 51.24/51.66 showgenerated = 0
% 51.24/51.66 showkept = 0
% 51.24/51.66 showselected = 0
% 51.24/51.66 showdeleted = 0
% 51.24/51.66 showresimp = 1
% 51.24/51.66 showstatus = 2000
% 51.24/51.66
% 51.24/51.66 prologoutput = 1
% 51.24/51.66 nrgoals = 5000000
% 51.24/51.66 totalproof = 1
% 51.24/51.66
% 51.24/51.66 Symbols occurring in the translation:
% 51.24/51.66
% 51.24/51.66 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 51.24/51.66 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 51.24/51.66 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 51.24/51.66 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 51.24/51.66 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 51.24/51.66 ifeq [42, 4] (w:1, o:51, a:1, s:1, b:0),
% 51.24/51.66 implies [45, 2] (w:1, o:50, a:1, s:1, b:0),
% 51.24/51.66 'is_a_theorem' [46, 1] (w:1, o:23, a:1, s:1, b:0),
% 51.24/51.66 true [47, 0] (w:1, o:14, a:1, s:1, b:0),
% 51.24/51.66 not [49, 1] (w:1, o:24, a:1, s:1, b:0),
% 51.24/51.66 a [50, 0] (w:1, o:16, a:1, s:1, b:0),
% 51.24/51.66 b [51, 0] (w:1, o:17, a:1, s:1, b:0).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Starting Search:
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66 Failed to find proof!
% 51.24/51.66 maxweight = 15
% 51.24/51.66 maxnrclauses = 10000000
% 51.24/51.66 Generated: 9874
% 51.24/51.66 Kept: 132
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 The strategy used was not complete!
% 51.24/51.66
% 51.24/51.66 Increased maxweight to 16
% 51.24/51.66
% 51.24/51.66 Starting Search:
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66 Failed to find proof!
% 51.24/51.66 maxweight = 16
% 51.24/51.66 maxnrclauses = 10000000
% 51.24/51.66 Generated: 114957
% 51.24/51.66 Kept: 466
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 The strategy used was not complete!
% 51.24/51.66
% 51.24/51.66 Increased maxweight to 17
% 51.24/51.66
% 51.24/51.66 Starting Search:
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Intermediate Status:
% 51.24/51.66 Generated: 87516
% 51.24/51.66 Kept: 2000
% 51.24/51.66 Inuse: 434
% 51.24/51.66 Deleted: 24
% 51.24/51.66 Deletedinuse: 4
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Intermediate Status:
% 51.24/51.66 Generated: 260734
% 51.24/51.66 Kept: 4005
% 51.24/51.66 Inuse: 834
% 51.24/51.66 Deleted: 28
% 51.24/51.66 Deletedinuse: 4
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Intermediate Status:
% 51.24/51.66 Generated: 543697
% 51.24/51.66 Kept: 6008
% 51.24/51.66 Inuse: 1271
% 51.24/51.66 Deleted: 32
% 51.24/51.66 Deletedinuse: 6
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Intermediate Status:
% 51.24/51.66 Generated: 1754662
% 51.24/51.66 Kept: 8014
% 51.24/51.66 Inuse: 2471
% 51.24/51.66 Deleted: 45
% 51.24/51.66 Deletedinuse: 7
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Intermediate Status:
% 51.24/51.66 Generated: 7151743
% 51.24/51.66 Kept: 10054
% 51.24/51.66 Inuse: 5470
% 51.24/51.66 Deleted: 68
% 51.24/51.66 Deletedinuse: 15
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66 Failed to find proof!
% 51.24/51.66 maxweight = 17
% 51.24/51.66 maxnrclauses = 10000000
% 51.24/51.66 Generated: 24972011
% 51.24/51.66 Kept: 10339
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 The strategy used was not complete!
% 51.24/51.66
% 51.24/51.66 Increased maxweight to 18
% 51.24/51.66
% 51.24/51.66 Starting Search:
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Intermediate Status:
% 51.24/51.66 Generated: 95016
% 51.24/51.66 Kept: 2003
% 51.24/51.66 Inuse: 432
% 51.24/51.66 Deleted: 24
% 51.24/51.66 Deletedinuse: 4
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Intermediate Status:
% 51.24/51.66 Generated: 178150
% 51.24/51.66 Kept: 4004
% 51.24/51.66 Inuse: 641
% 51.24/51.66 Deleted: 24
% 51.24/51.66 Deletedinuse: 4
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Intermediate Status:
% 51.24/51.66 Generated: 248633
% 51.24/51.66 Kept: 6004
% 51.24/51.66 Inuse: 780
% 51.24/51.66 Deleted: 27
% 51.24/51.66 Deletedinuse: 4
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Intermediate Status:
% 51.24/51.66 Generated: 377047
% 51.24/51.66 Kept: 8013
% 51.24/51.66 Inuse: 1010
% 51.24/51.66 Deleted: 27
% 51.24/51.66 Deletedinuse: 4
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Intermediate Status:
% 51.24/51.66 Generated: 481293
% 51.24/51.66 Kept: 10014
% 51.24/51.66 Inuse: 1186
% 51.24/51.66 Deleted: 29
% 51.24/51.66 Deletedinuse: 6
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Intermediate Status:
% 51.24/51.66 Generated: 675908
% 51.24/51.66 Kept: 12135
% 51.24/51.66 Inuse: 1411
% 51.24/51.66 Deleted: 30
% 51.24/51.66 Deletedinuse: 7
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Intermediate Status:
% 51.24/51.66 Generated: 1025189
% 51.24/51.66 Kept: 14164
% 51.24/51.66 Inuse: 1773
% 51.24/51.66 Deleted: 36
% 51.24/51.66 Deletedinuse: 8
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Intermediate Status:
% 51.24/51.66 Generated: 1763914
% 51.24/51.66 Kept: 16599
% 51.24/51.66 Inuse: 2371
% 51.24/51.66 Deleted: 46
% 51.24/51.66 Deletedinuse: 9
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66 Resimplifying inuse:
% 51.24/51.66 Done
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 Bliksems!, er is een bewijs:
% 51.24/51.66 % SZS status Unsatisfiable
% 51.24/51.66 % SZS output start Refutation
% 51.24/51.66
% 51.24/51.66 clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 51.24/51.66 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 .
% 51.24/51.66 clause( 2, [ =( 'is_a_theorem'( implies( X, implies( Y, X ) ) ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 .
% 51.24/51.66 clause( 3, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( implies(
% 51.24/51.66 Y, Z ), implies( X, Z ) ) ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 4, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Y ),
% 51.24/51.66 implies( implies( Y, X ), X ) ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 5, [ =( 'is_a_theorem'( implies( implies( not( X ), not( Y ) ),
% 51.24/51.66 implies( Y, X ) ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 6, [ ~( =( 'is_a_theorem'( implies( implies( not( a ), b ), implies(
% 51.24/51.66 not( b ), a ) ) ), true ) ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 7, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ),
% 51.24/51.66 true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 10, [ =( ifeq( 'is_a_theorem'( implies( not( X ), not( Y ) ) ),
% 51.24/51.66 true, 'is_a_theorem'( implies( Y, X ) ), true ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 11, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( not( X )
% 51.24/51.66 , not( Y ) ), implies( Y, X ) ), Z ) ), true, 'is_a_theorem'( Z ), true )
% 51.24/51.66 , true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 26, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 51.24/51.66 X, Y ), Y ), implies( implies( Y, X ), X ) ), Z ) ), true, 'is_a_theorem'(
% 51.24/51.66 Z ), true ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 35, [ =( 'is_a_theorem'( implies( implies( implies( implies( Y, Z )
% 51.24/51.66 , implies( X, Z ) ), T ), implies( implies( X, Y ), T ) ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 37, [ =( 'is_a_theorem'( implies( implies( implies( Y, X ), Z ),
% 51.24/51.66 implies( X, Z ) ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 40, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 51.24/51.66 true, 'is_a_theorem'( implies( Y, Z ) ), true ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 46, [ =( 'is_a_theorem'( implies( Y, implies( implies( Y, X ), X )
% 51.24/51.66 ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 48, [ =( 'is_a_theorem'( implies( not( Y ), implies( Y, X ) ) ),
% 51.24/51.66 true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 50, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 51.24/51.66 implies( not( X ), Z ) ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 62, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y )
% 51.24/51.66 , Y ), Z ), implies( X, Z ) ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 64, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( X, Y ), Y ) ), true ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 101, [ =( 'is_a_theorem'( implies( not( not( X ) ), implies( Y, X )
% 51.24/51.66 ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 105, [ =( 'is_a_theorem'( implies( implies( implies( Y, X ), Z ),
% 51.24/51.66 implies( not( not( X ) ), Z ) ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 135, [ =( 'is_a_theorem'( implies( implies( implies( X, implies( Y
% 51.24/51.66 , X ) ), Z ), Z ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 138, [ =( 'is_a_theorem'( implies( Z, Z ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 141, [ =( 'is_a_theorem'( implies( implies( implies( X, X ), Y ), Y
% 51.24/51.66 ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 159, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 51.24/51.66 X, X ), Y ), Y ), Z ) ), true, 'is_a_theorem'( Z ), true ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 247, [ =( 'is_a_theorem'( implies( not( not( Y ) ), implies(
% 51.24/51.66 implies( Y, X ), X ) ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 252, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 51.24/51.66 ), Y ), Z ), implies( not( not( X ) ), Z ) ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 272, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 51.24/51.66 Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 993, [ =( 'is_a_theorem'( implies( not( not( X ) ), X ) ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 .
% 51.24/51.66 clause( 1005, [ =( 'is_a_theorem'( implies( X, not( not( X ) ) ) ), true )
% 51.24/51.66 ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 1037, [ =( ifeq( 'is_a_theorem'( implies( implies( X, not( not( X )
% 51.24/51.66 ) ), Y ) ), true, 'is_a_theorem'( Y ), true ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 5835, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 51.24/51.66 implies( Z, X ), implies( Z, Y ) ) ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 11364, [ =( 'is_a_theorem'( implies( implies( Y, X ), implies( Y,
% 51.24/51.66 not( not( X ) ) ) ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 11460, [ =( 'is_a_theorem'( implies( implies( implies( X, not( not(
% 51.24/51.66 Y ) ) ), Z ), implies( implies( X, Y ), Z ) ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 18277, [ =( 'is_a_theorem'( implies( implies( not( X ), Y ),
% 51.24/51.66 implies( not( Y ), X ) ) ), true ) ] )
% 51.24/51.66 .
% 51.24/51.66 clause( 18280, [] )
% 51.24/51.66 .
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 % SZS output end Refutation
% 51.24/51.66 found a proof!
% 51.24/51.66
% 51.24/51.66 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 51.24/51.66
% 51.24/51.66 initialclauses(
% 51.24/51.66 [ clause( 18282, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , clause( 18283, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 51.24/51.66 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 18284, [ =( 'is_a_theorem'( implies( X, implies( Y, X ) ) ), true
% 51.24/51.66 ) ] )
% 51.24/51.66 , clause( 18285, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 51.24/51.66 implies( Y, Z ), implies( X, Z ) ) ) ), true ) ] )
% 51.24/51.66 , clause( 18286, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Y
% 51.24/51.66 ), implies( implies( Y, X ), X ) ) ), true ) ] )
% 51.24/51.66 , clause( 18287, [ =( 'is_a_theorem'( implies( implies( not( X ), not( Y )
% 51.24/51.66 ), implies( Y, X ) ) ), true ) ] )
% 51.24/51.66 , clause( 18288, [ ~( =( 'is_a_theorem'( implies( implies( not( a ), b ),
% 51.24/51.66 implies( not( b ), a ) ) ), true ) ) ] )
% 51.24/51.66 ] ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , clause( 18282, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.66 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 51.24/51.66 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 18283, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 51.24/51.66 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 51.24/51.66 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 2, [ =( 'is_a_theorem'( implies( X, implies( Y, X ) ) ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 18284, [ =( 'is_a_theorem'( implies( X, implies( Y, X ) ) ), true
% 51.24/51.66 ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 51.24/51.66 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 3, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( implies(
% 51.24/51.66 Y, Z ), implies( X, Z ) ) ) ), true ) ] )
% 51.24/51.66 , clause( 18285, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 51.24/51.66 implies( Y, Z ), implies( X, Z ) ) ) ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.66 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 4, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Y ),
% 51.24/51.66 implies( implies( Y, X ), X ) ) ), true ) ] )
% 51.24/51.66 , clause( 18286, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Y
% 51.24/51.66 ), implies( implies( Y, X ), X ) ) ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 51.24/51.66 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 5, [ =( 'is_a_theorem'( implies( implies( not( X ), not( Y ) ),
% 51.24/51.66 implies( Y, X ) ) ), true ) ] )
% 51.24/51.66 , clause( 18287, [ =( 'is_a_theorem'( implies( implies( not( X ), not( Y )
% 51.24/51.66 ), implies( Y, X ) ) ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 51.24/51.66 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 6, [ ~( =( 'is_a_theorem'( implies( implies( not( a ), b ), implies(
% 51.24/51.66 not( b ), a ) ) ), true ) ) ] )
% 51.24/51.66 , clause( 18288, [ ~( =( 'is_a_theorem'( implies( implies( not( a ), b ),
% 51.24/51.66 implies( not( b ), a ) ) ), true ) ) ] )
% 51.24/51.66 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18318, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 51.24/51.66 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18320, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 51.24/51.66 X, Y ) ), true, 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z )
% 51.24/51.66 ) ), true ), true ) ) ] )
% 51.24/51.66 , clause( 3, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 51.24/51.66 implies( Y, Z ), implies( X, Z ) ) ) ), true ) ] )
% 51.24/51.66 , 0, clause( 18318, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 51.24/51.66 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 51.24/51.66 ) ) ] )
% 51.24/51.66 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.66 substitution( 1, [ :=( X, implies( X, Y ) ), :=( Y, implies( implies( Y,
% 51.24/51.66 Z ), implies( X, Z ) ) )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18325, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ) ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18320, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 51.24/51.66 implies( X, Y ) ), true, 'is_a_theorem'( implies( implies( Y, Z ),
% 51.24/51.66 implies( X, Z ) ) ), true ), true ) ) ] )
% 51.24/51.66 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 51.24/51.66 implies( X, Y ) ), true, 'is_a_theorem'( implies( implies( Y, Z ),
% 51.24/51.66 implies( X, Z ) ) ), true ) ), :=( Z, true )] ), substitution( 1, [ :=( X
% 51.24/51.66 , X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18326, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ),
% 51.24/51.66 true ) ] )
% 51.24/51.66 , clause( 18325, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ) ) ]
% 51.24/51.66 )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 7, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ),
% 51.24/51.66 true ) ] )
% 51.24/51.66 , clause( 18326, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ),
% 51.24/51.66 true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.66 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18328, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 51.24/51.66 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18330, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 51.24/51.66 not( X ), not( Y ) ) ), true, 'is_a_theorem'( implies( Y, X ) ), true ),
% 51.24/51.66 true ) ) ] )
% 51.24/51.66 , clause( 5, [ =( 'is_a_theorem'( implies( implies( not( X ), not( Y ) ),
% 51.24/51.66 implies( Y, X ) ) ), true ) ] )
% 51.24/51.66 , 0, clause( 18328, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 51.24/51.66 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 51.24/51.66 ) ) ] )
% 51.24/51.66 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 51.24/51.66 :=( X, implies( not( X ), not( Y ) ) ), :=( Y, implies( Y, X ) )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18335, [ =( true, ifeq( 'is_a_theorem'( implies( not( X ), not( Y )
% 51.24/51.66 ) ), true, 'is_a_theorem'( implies( Y, X ) ), true ) ) ] )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18330, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 51.24/51.66 implies( not( X ), not( Y ) ) ), true, 'is_a_theorem'( implies( Y, X ) )
% 51.24/51.66 , true ), true ) ) ] )
% 51.24/51.66 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 51.24/51.66 implies( not( X ), not( Y ) ) ), true, 'is_a_theorem'( implies( Y, X ) )
% 51.24/51.66 , true ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 51.24/51.66 ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18336, [ =( ifeq( 'is_a_theorem'( implies( not( X ), not( Y ) ) ),
% 51.24/51.66 true, 'is_a_theorem'( implies( Y, X ) ), true ), true ) ] )
% 51.24/51.66 , clause( 18335, [ =( true, ifeq( 'is_a_theorem'( implies( not( X ), not( Y
% 51.24/51.66 ) ) ), true, 'is_a_theorem'( implies( Y, X ) ), true ) ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 10, [ =( ifeq( 'is_a_theorem'( implies( not( X ), not( Y ) ) ),
% 51.24/51.66 true, 'is_a_theorem'( implies( Y, X ) ), true ), true ) ] )
% 51.24/51.66 , clause( 18336, [ =( ifeq( 'is_a_theorem'( implies( not( X ), not( Y ) ) )
% 51.24/51.66 , true, 'is_a_theorem'( implies( Y, X ) ), true ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 51.24/51.66 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18338, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 51.24/51.66 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18341, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.66 not( X ), not( Y ) ), implies( Y, X ) ), Z ) ), true, ifeq( true, true,
% 51.24/51.66 'is_a_theorem'( Z ), true ), true ) ) ] )
% 51.24/51.66 , clause( 5, [ =( 'is_a_theorem'( implies( implies( not( X ), not( Y ) ),
% 51.24/51.66 implies( Y, X ) ) ), true ) ] )
% 51.24/51.66 , 0, clause( 18338, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 51.24/51.66 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 51.24/51.66 ) ) ] )
% 51.24/51.66 , 0, 17, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 51.24/51.66 :=( X, implies( implies( not( X ), not( Y ) ), implies( Y, X ) ) ), :=( Y
% 51.24/51.66 , Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18343, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.66 not( X ), not( Y ) ), implies( Y, X ) ), Z ) ), true, 'is_a_theorem'( Z )
% 51.24/51.66 , true ) ) ] )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18341, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 51.24/51.66 implies( not( X ), not( Y ) ), implies( Y, X ) ), Z ) ), true, ifeq( true
% 51.24/51.66 , true, 'is_a_theorem'( Z ), true ), true ) ) ] )
% 51.24/51.66 , 0, 16, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( Z ) ),
% 51.24/51.66 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )
% 51.24/51.66 ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18344, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( not( X
% 51.24/51.66 ), not( Y ) ), implies( Y, X ) ), Z ) ), true, 'is_a_theorem'( Z ), true
% 51.24/51.66 ), true ) ] )
% 51.24/51.66 , clause( 18343, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.66 not( X ), not( Y ) ), implies( Y, X ) ), Z ) ), true, 'is_a_theorem'( Z )
% 51.24/51.66 , true ) ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 11, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( not( X )
% 51.24/51.66 , not( Y ) ), implies( Y, X ) ), Z ) ), true, 'is_a_theorem'( Z ), true )
% 51.24/51.66 , true ) ] )
% 51.24/51.66 , clause( 18344, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( not(
% 51.24/51.66 X ), not( Y ) ), implies( Y, X ) ), Z ) ), true, 'is_a_theorem'( Z ),
% 51.24/51.66 true ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.66 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18346, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 51.24/51.66 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18349, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.66 implies( X, Y ), Y ), implies( implies( Y, X ), X ) ), Z ) ), true, ifeq(
% 51.24/51.66 true, true, 'is_a_theorem'( Z ), true ), true ) ) ] )
% 51.24/51.66 , clause( 4, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Y ),
% 51.24/51.66 implies( implies( Y, X ), X ) ) ), true ) ] )
% 51.24/51.66 , 0, clause( 18346, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 51.24/51.66 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 51.24/51.66 ) ) ] )
% 51.24/51.66 , 0, 19, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 51.24/51.66 :=( X, implies( implies( implies( X, Y ), Y ), implies( implies( Y, X ),
% 51.24/51.66 X ) ) ), :=( Y, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18351, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.66 implies( X, Y ), Y ), implies( implies( Y, X ), X ) ), Z ) ), true,
% 51.24/51.66 'is_a_theorem'( Z ), true ) ) ] )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18349, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 51.24/51.66 implies( implies( X, Y ), Y ), implies( implies( Y, X ), X ) ), Z ) ),
% 51.24/51.66 true, ifeq( true, true, 'is_a_theorem'( Z ), true ), true ) ) ] )
% 51.24/51.66 , 0, 18, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( Z ) ),
% 51.24/51.66 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )
% 51.24/51.66 ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18352, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.66 implies( X, Y ), Y ), implies( implies( Y, X ), X ) ), Z ) ), true,
% 51.24/51.66 'is_a_theorem'( Z ), true ), true ) ] )
% 51.24/51.66 , clause( 18351, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.66 implies( X, Y ), Y ), implies( implies( Y, X ), X ) ), Z ) ), true,
% 51.24/51.66 'is_a_theorem'( Z ), true ) ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 26, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 51.24/51.66 X, Y ), Y ), implies( implies( Y, X ), X ) ), Z ) ), true, 'is_a_theorem'(
% 51.24/51.66 Z ), true ), true ) ] )
% 51.24/51.66 , clause( 18352, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.66 implies( X, Y ), Y ), implies( implies( Y, X ), X ) ), Z ) ), true,
% 51.24/51.66 'is_a_theorem'( Z ), true ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.66 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18354, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ) ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 7, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ),
% 51.24/51.66 true ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18356, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( implies( Y, Z ), implies( X, Z ) ), T ), implies(
% 51.24/51.66 implies( X, Y ), T ) ) ), true ) ) ] )
% 51.24/51.66 , clause( 3, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 51.24/51.66 implies( Y, Z ), implies( X, Z ) ) ) ), true ) ] )
% 51.24/51.66 , 0, clause( 18354, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 51.24/51.66 true, 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true
% 51.24/51.66 ) ) ] )
% 51.24/51.66 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.66 substitution( 1, [ :=( X, implies( X, Y ) ), :=( Y, implies( implies( Y,
% 51.24/51.66 Z ), implies( X, Z ) ) ), :=( Z, T )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18358, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 51.24/51.66 implies( X, Y ), implies( Z, Y ) ), T ), implies( implies( Z, X ), T ) )
% 51.24/51.66 ) ) ] )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18356, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( implies( Y, Z ), implies( X, Z ) ), T ), implies(
% 51.24/51.66 implies( X, Y ), T ) ) ), true ) ) ] )
% 51.24/51.66 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( implies( X, Y ), implies( Z, Y ) ), T ), implies(
% 51.24/51.66 implies( Z, X ), T ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Z
% 51.24/51.66 ), :=( Y, X ), :=( Z, Y ), :=( T, T )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18359, [ =( 'is_a_theorem'( implies( implies( implies( implies( X,
% 51.24/51.66 Y ), implies( Z, Y ) ), T ), implies( implies( Z, X ), T ) ) ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 18358, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 51.24/51.66 implies( X, Y ), implies( Z, Y ) ), T ), implies( implies( Z, X ), T ) )
% 51.24/51.66 ) ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 51.24/51.66 ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 35, [ =( 'is_a_theorem'( implies( implies( implies( implies( Y, Z )
% 51.24/51.66 , implies( X, Z ) ), T ), implies( implies( X, Y ), T ) ) ), true ) ] )
% 51.24/51.66 , clause( 18359, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 51.24/51.66 , Y ), implies( Z, Y ) ), T ), implies( implies( Z, X ), T ) ) ), true )
% 51.24/51.66 ] )
% 51.24/51.66 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T )] ),
% 51.24/51.66 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18361, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ) ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 7, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ),
% 51.24/51.66 true ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18363, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( Y, X ), Z ), implies( X, Z ) ) ), true ) ) ] )
% 51.24/51.66 , clause( 2, [ =( 'is_a_theorem'( implies( X, implies( Y, X ) ) ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 , 0, clause( 18361, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 51.24/51.66 true, 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true
% 51.24/51.66 ) ) ] )
% 51.24/51.66 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 51.24/51.66 :=( X, X ), :=( Y, implies( Y, X ) ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18364, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y )
% 51.24/51.66 , Z ), implies( Y, Z ) ) ) ) ] )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18363, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( Y, X ), Z ), implies( X, Z ) ) ), true ) ) ] )
% 51.24/51.66 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( X, Y ), Z ), implies( Y, Z ) ) ) ), :=( Z, true )] ),
% 51.24/51.66 substitution( 1, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18365, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z )
% 51.24/51.66 , implies( Y, Z ) ) ), true ) ] )
% 51.24/51.66 , clause( 18364, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y
% 51.24/51.66 ), Z ), implies( Y, Z ) ) ) ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 37, [ =( 'is_a_theorem'( implies( implies( implies( Y, X ), Z ),
% 51.24/51.66 implies( X, Z ) ) ), true ) ] )
% 51.24/51.66 , clause( 18365, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z
% 51.24/51.66 ), implies( Y, Z ) ) ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 51.24/51.66 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18367, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 51.24/51.66 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18369, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 51.24/51.66 implies( X, Y ), Z ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ),
% 51.24/51.66 true ) ) ] )
% 51.24/51.66 , clause( 37, [ =( 'is_a_theorem'( implies( implies( implies( Y, X ), Z ),
% 51.24/51.66 implies( X, Z ) ) ), true ) ] )
% 51.24/51.66 , 0, clause( 18367, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 51.24/51.66 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 51.24/51.66 ) ) ] )
% 51.24/51.66 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 51.24/51.66 substitution( 1, [ :=( X, implies( implies( X, Y ), Z ) ), :=( Y, implies(
% 51.24/51.66 Y, Z ) )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18374, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 51.24/51.66 ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ) ) ] )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18369, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 51.24/51.66 implies( implies( X, Y ), Z ) ), true, 'is_a_theorem'( implies( Y, Z ) )
% 51.24/51.66 , true ), true ) ) ] )
% 51.24/51.66 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 51.24/51.66 implies( implies( X, Y ), Z ) ), true, 'is_a_theorem'( implies( Y, Z ) )
% 51.24/51.66 , true ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 51.24/51.66 :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18375, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 51.24/51.66 true, 'is_a_theorem'( implies( Y, Z ) ), true ), true ) ] )
% 51.24/51.66 , clause( 18374, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y )
% 51.24/51.66 , Z ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ) ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 40, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 51.24/51.66 true, 'is_a_theorem'( implies( Y, Z ) ), true ), true ) ] )
% 51.24/51.66 , clause( 18375, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) )
% 51.24/51.66 , true, 'is_a_theorem'( implies( Y, Z ) ), true ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.66 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18377, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 51.24/51.66 ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ) ) ] )
% 51.24/51.66 , clause( 40, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 51.24/51.66 true, 'is_a_theorem'( implies( Y, Z ) ), true ), true ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18379, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Y,
% 51.24/51.66 implies( implies( Y, X ), X ) ) ), true ) ) ] )
% 51.24/51.66 , clause( 4, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Y ),
% 51.24/51.66 implies( implies( Y, X ), X ) ) ), true ) ] )
% 51.24/51.66 , 0, clause( 18377, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 51.24/51.66 ), Z ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ) ) ] )
% 51.24/51.66 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 51.24/51.66 :=( X, implies( X, Y ) ), :=( Y, Y ), :=( Z, implies( implies( Y, X ), X
% 51.24/51.66 ) )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18381, [ =( true, 'is_a_theorem'( implies( X, implies( implies( X,
% 51.24/51.66 Y ), Y ) ) ) ) ] )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18379, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Y
% 51.24/51.66 , implies( implies( Y, X ), X ) ) ), true ) ) ] )
% 51.24/51.66 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 51.24/51.66 , implies( implies( X, Y ), Y ) ) ) ), :=( Z, true )] ), substitution( 1
% 51.24/51.66 , [ :=( X, Y ), :=( Y, X )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18382, [ =( 'is_a_theorem'( implies( X, implies( implies( X, Y ), Y
% 51.24/51.66 ) ) ), true ) ] )
% 51.24/51.66 , clause( 18381, [ =( true, 'is_a_theorem'( implies( X, implies( implies( X
% 51.24/51.66 , Y ), Y ) ) ) ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 46, [ =( 'is_a_theorem'( implies( Y, implies( implies( Y, X ), X )
% 51.24/51.66 ) ), true ) ] )
% 51.24/51.66 , clause( 18382, [ =( 'is_a_theorem'( implies( X, implies( implies( X, Y )
% 51.24/51.66 , Y ) ) ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 51.24/51.66 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18384, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 51.24/51.66 ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ) ) ] )
% 51.24/51.66 , clause( 40, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 51.24/51.66 true, 'is_a_theorem'( implies( Y, Z ) ), true ), true ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18386, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( not( Y
% 51.24/51.66 ), implies( Y, X ) ) ), true ) ) ] )
% 51.24/51.66 , clause( 5, [ =( 'is_a_theorem'( implies( implies( not( X ), not( Y ) ),
% 51.24/51.66 implies( Y, X ) ) ), true ) ] )
% 51.24/51.66 , 0, clause( 18384, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 51.24/51.66 ), Z ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ) ) ] )
% 51.24/51.66 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 51.24/51.66 :=( X, not( X ) ), :=( Y, not( Y ) ), :=( Z, implies( Y, X ) )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18388, [ =( true, 'is_a_theorem'( implies( not( X ), implies( X, Y
% 51.24/51.66 ) ) ) ) ] )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18386, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.66 not( Y ), implies( Y, X ) ) ), true ) ) ] )
% 51.24/51.66 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 51.24/51.66 not( X ), implies( X, Y ) ) ) ), :=( Z, true )] ), substitution( 1, [
% 51.24/51.66 :=( X, Y ), :=( Y, X )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18389, [ =( 'is_a_theorem'( implies( not( X ), implies( X, Y ) ) )
% 51.24/51.66 , true ) ] )
% 51.24/51.66 , clause( 18388, [ =( true, 'is_a_theorem'( implies( not( X ), implies( X,
% 51.24/51.66 Y ) ) ) ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 48, [ =( 'is_a_theorem'( implies( not( Y ), implies( Y, X ) ) ),
% 51.24/51.66 true ) ] )
% 51.24/51.66 , clause( 18389, [ =( 'is_a_theorem'( implies( not( X ), implies( X, Y ) )
% 51.24/51.66 ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 51.24/51.66 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18391, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ) ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 7, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ),
% 51.24/51.66 true ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18393, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( X, Y ), Z ), implies( not( X ), Z ) ) ), true ) ) ] )
% 51.24/51.66 , clause( 48, [ =( 'is_a_theorem'( implies( not( Y ), implies( Y, X ) ) ),
% 51.24/51.66 true ) ] )
% 51.24/51.66 , 0, clause( 18391, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 51.24/51.66 true, 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true
% 51.24/51.66 ) ) ] )
% 51.24/51.66 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 51.24/51.66 :=( X, not( X ) ), :=( Y, implies( X, Y ) ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18394, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y )
% 51.24/51.66 , Z ), implies( not( X ), Z ) ) ) ) ] )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18393, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( X, Y ), Z ), implies( not( X ), Z ) ) ), true ) ) ] )
% 51.24/51.66 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( X, Y ), Z ), implies( not( X ), Z ) ) ) ), :=( Z, true
% 51.24/51.66 )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18395, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z )
% 51.24/51.66 , implies( not( X ), Z ) ) ), true ) ] )
% 51.24/51.66 , clause( 18394, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y
% 51.24/51.66 ), Z ), implies( not( X ), Z ) ) ) ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 50, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 51.24/51.66 implies( not( X ), Z ) ) ), true ) ] )
% 51.24/51.66 , clause( 18395, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z
% 51.24/51.66 ), implies( not( X ), Z ) ) ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.66 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18397, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ) ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 7, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ),
% 51.24/51.66 true ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18399, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( implies( X, Y ), Y ), Z ), implies( X, Z ) ) ), true )
% 51.24/51.66 ) ] )
% 51.24/51.66 , clause( 46, [ =( 'is_a_theorem'( implies( Y, implies( implies( Y, X ), X
% 51.24/51.66 ) ) ), true ) ] )
% 51.24/51.66 , 0, clause( 18397, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 51.24/51.66 true, 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true
% 51.24/51.66 ) ) ] )
% 51.24/51.66 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 51.24/51.66 :=( X, X ), :=( Y, implies( implies( X, Y ), Y ) ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18401, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 51.24/51.66 implies( X, Y ), Y ), Z ), implies( X, Z ) ) ) ) ] )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18399, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( implies( X, Y ), Y ), Z ), implies( X, Z ) ) ), true )
% 51.24/51.66 ) ] )
% 51.24/51.66 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( implies( X, Y ), Y ), Z ), implies( X, Z ) ) ) ), :=( Z
% 51.24/51.66 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )
% 51.24/51.66 ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18402, [ =( 'is_a_theorem'( implies( implies( implies( implies( X,
% 51.24/51.66 Y ), Y ), Z ), implies( X, Z ) ) ), true ) ] )
% 51.24/51.66 , clause( 18401, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 51.24/51.66 implies( X, Y ), Y ), Z ), implies( X, Z ) ) ) ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 62, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y )
% 51.24/51.66 , Y ), Z ), implies( X, Z ) ) ), true ) ] )
% 51.24/51.66 , clause( 18402, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 51.24/51.66 , Y ), Y ), Z ), implies( X, Z ) ) ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.66 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18404, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 51.24/51.66 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18406, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( X ), true
% 51.24/51.66 , 'is_a_theorem'( implies( implies( X, Y ), Y ) ), true ), true ) ) ] )
% 51.24/51.66 , clause( 46, [ =( 'is_a_theorem'( implies( Y, implies( implies( Y, X ), X
% 51.24/51.66 ) ) ), true ) ] )
% 51.24/51.66 , 0, clause( 18404, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 51.24/51.66 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 51.24/51.66 ) ) ] )
% 51.24/51.66 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 51.24/51.66 :=( X, X ), :=( Y, implies( implies( X, Y ), Y ) )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18411, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 51.24/51.66 implies( implies( X, Y ), Y ) ), true ) ) ] )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18406, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( X )
% 51.24/51.66 , true, 'is_a_theorem'( implies( implies( X, Y ), Y ) ), true ), true ) )
% 51.24/51.66 ] )
% 51.24/51.66 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'( X )
% 51.24/51.66 , true, 'is_a_theorem'( implies( implies( X, Y ), Y ) ), true ) ), :=( Z
% 51.24/51.66 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18412, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 51.24/51.66 implies( implies( X, Y ), Y ) ), true ), true ) ] )
% 51.24/51.66 , clause( 18411, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 51.24/51.66 implies( implies( X, Y ), Y ) ), true ) ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 64, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( X, Y ), Y ) ), true ), true ) ] )
% 51.24/51.66 , clause( 18412, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 51.24/51.66 implies( implies( X, Y ), Y ) ), true ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 51.24/51.66 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18414, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.66 not( X ), not( Y ) ), implies( Y, X ) ), Z ) ), true, 'is_a_theorem'( Z )
% 51.24/51.66 , true ) ) ] )
% 51.24/51.66 , clause( 11, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( not( X
% 51.24/51.66 ), not( Y ) ), implies( Y, X ) ), Z ) ), true, 'is_a_theorem'( Z ), true
% 51.24/51.66 ), true ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18416, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( not(
% 51.24/51.66 not( X ) ), implies( Y, X ) ) ), true ) ) ] )
% 51.24/51.66 , clause( 50, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 51.24/51.66 implies( not( X ), Z ) ) ), true ) ] )
% 51.24/51.66 , 0, clause( 18414, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 51.24/51.66 implies( not( X ), not( Y ) ), implies( Y, X ) ), Z ) ), true,
% 51.24/51.66 'is_a_theorem'( Z ), true ) ) ] )
% 51.24/51.66 , 0, 3, substitution( 0, [ :=( X, not( X ) ), :=( Y, not( Y ) ), :=( Z,
% 51.24/51.66 implies( Y, X ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z,
% 51.24/51.66 implies( not( not( X ) ), implies( Y, X ) ) )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18418, [ =( true, 'is_a_theorem'( implies( not( not( X ) ), implies(
% 51.24/51.66 Y, X ) ) ) ) ] )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18416, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.66 not( not( X ) ), implies( Y, X ) ) ), true ) ) ] )
% 51.24/51.66 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 51.24/51.66 not( not( X ) ), implies( Y, X ) ) ) ), :=( Z, true )] ), substitution( 1
% 51.24/51.66 , [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18419, [ =( 'is_a_theorem'( implies( not( not( X ) ), implies( Y, X
% 51.24/51.66 ) ) ), true ) ] )
% 51.24/51.66 , clause( 18418, [ =( true, 'is_a_theorem'( implies( not( not( X ) ),
% 51.24/51.66 implies( Y, X ) ) ) ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 101, [ =( 'is_a_theorem'( implies( not( not( X ) ), implies( Y, X )
% 51.24/51.66 ) ), true ) ] )
% 51.24/51.66 , clause( 18419, [ =( 'is_a_theorem'( implies( not( not( X ) ), implies( Y
% 51.24/51.66 , X ) ) ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 51.24/51.66 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18421, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ) ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 7, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ),
% 51.24/51.66 true ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18423, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( Y, X ), Z ), implies( not( not( X ) ), Z ) ) ), true )
% 51.24/51.66 ) ] )
% 51.24/51.66 , clause( 101, [ =( 'is_a_theorem'( implies( not( not( X ) ), implies( Y, X
% 51.24/51.66 ) ) ), true ) ] )
% 51.24/51.66 , 0, clause( 18421, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 51.24/51.66 true, 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true
% 51.24/51.66 ) ) ] )
% 51.24/51.66 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 51.24/51.66 :=( X, not( not( X ) ) ), :=( Y, implies( Y, X ) ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18424, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y )
% 51.24/51.66 , Z ), implies( not( not( Y ) ), Z ) ) ) ) ] )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18423, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( Y, X ), Z ), implies( not( not( X ) ), Z ) ) ), true )
% 51.24/51.66 ) ] )
% 51.24/51.66 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( X, Y ), Z ), implies( not( not( Y ) ), Z ) ) ) ), :=( Z
% 51.24/51.66 , true )] ), substitution( 1, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] )
% 51.24/51.66 ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18425, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z )
% 51.24/51.66 , implies( not( not( Y ) ), Z ) ) ), true ) ] )
% 51.24/51.66 , clause( 18424, [ =( true, 'is_a_theorem'( implies( implies( implies( X, Y
% 51.24/51.66 ), Z ), implies( not( not( Y ) ), Z ) ) ) ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 105, [ =( 'is_a_theorem'( implies( implies( implies( Y, X ), Z ),
% 51.24/51.66 implies( not( not( X ) ), Z ) ) ), true ) ] )
% 51.24/51.66 , clause( 18425, [ =( 'is_a_theorem'( implies( implies( implies( X, Y ), Z
% 51.24/51.66 ), implies( not( not( Y ) ), Z ) ) ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 51.24/51.66 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18427, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 51.24/51.66 implies( implies( X, Y ), Y ) ), true ) ) ] )
% 51.24/51.66 , clause( 64, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( X, Y ), Y ) ), true ), true ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18429, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( X, implies( Y, X ) ), Z ), Z ) ), true ) ) ] )
% 51.24/51.66 , clause( 2, [ =( 'is_a_theorem'( implies( X, implies( Y, X ) ) ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 , 0, clause( 18427, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( X, Y ), Y ) ), true ) ) ] )
% 51.24/51.66 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 51.24/51.66 :=( X, implies( X, implies( Y, X ) ) ), :=( Y, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18430, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 51.24/51.66 implies( Y, X ) ), Z ), Z ) ) ) ] )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18429, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( X, implies( Y, X ) ), Z ), Z ) ), true ) ) ] )
% 51.24/51.66 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( X, implies( Y, X ) ), Z ), Z ) ) ), :=( Z, true )] ),
% 51.24/51.66 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18431, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 51.24/51.66 Y, X ) ), Z ), Z ) ), true ) ] )
% 51.24/51.66 , clause( 18430, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 51.24/51.66 implies( Y, X ) ), Z ), Z ) ) ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 135, [ =( 'is_a_theorem'( implies( implies( implies( X, implies( Y
% 51.24/51.66 , X ) ), Z ), Z ) ), true ) ] )
% 51.24/51.66 , clause( 18431, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 51.24/51.66 Y, X ) ), Z ), Z ) ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.66 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18433, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z
% 51.24/51.66 ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ) ) ] )
% 51.24/51.66 , clause( 40, [ =( ifeq( 'is_a_theorem'( implies( implies( X, Y ), Z ) ),
% 51.24/51.66 true, 'is_a_theorem'( implies( Y, Z ) ), true ), true ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18435, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Z, Z )
% 51.24/51.66 ), true ) ) ] )
% 51.24/51.66 , clause( 135, [ =( 'is_a_theorem'( implies( implies( implies( X, implies(
% 51.24/51.66 Y, X ) ), Z ), Z ) ), true ) ] )
% 51.24/51.66 , 0, clause( 18433, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, Y
% 51.24/51.66 ), Z ) ), true, 'is_a_theorem'( implies( Y, Z ) ), true ) ) ] )
% 51.24/51.66 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.66 substitution( 1, [ :=( X, implies( X, implies( Y, X ) ) ), :=( Y, Z ),
% 51.24/51.66 :=( Z, Z )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18437, [ =( true, 'is_a_theorem'( implies( X, X ) ) ) ] )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18435, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( Z
% 51.24/51.66 , Z ) ), true ) ) ] )
% 51.24/51.66 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 51.24/51.66 , X ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ),
% 51.24/51.66 :=( Z, X )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18438, [ =( 'is_a_theorem'( implies( X, X ) ), true ) ] )
% 51.24/51.66 , clause( 18437, [ =( true, 'is_a_theorem'( implies( X, X ) ) ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 138, [ =( 'is_a_theorem'( implies( Z, Z ) ), true ) ] )
% 51.24/51.66 , clause( 18438, [ =( 'is_a_theorem'( implies( X, X ) ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, Z )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18440, [ =( true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'(
% 51.24/51.66 implies( implies( X, Y ), Y ) ), true ) ) ] )
% 51.24/51.66 , clause( 64, [ =( ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( X, Y ), Y ) ), true ), true ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18442, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( X, X ), Y ), Y ) ), true ) ) ] )
% 51.24/51.66 , clause( 138, [ =( 'is_a_theorem'( implies( Z, Z ) ), true ) ] )
% 51.24/51.66 , 0, clause( 18440, [ =( true, ifeq( 'is_a_theorem'( X ), true,
% 51.24/51.66 'is_a_theorem'( implies( implies( X, Y ), Y ) ), true ) ) ] )
% 51.24/51.66 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, X )] ),
% 51.24/51.66 substitution( 1, [ :=( X, implies( X, X ) ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18443, [ =( true, 'is_a_theorem'( implies( implies( implies( X, X )
% 51.24/51.66 , Y ), Y ) ) ) ] )
% 51.24/51.66 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.66 , 0, clause( 18442, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( X, X ), Y ), Y ) ), true ) ) ] )
% 51.24/51.66 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 51.24/51.66 implies( implies( X, X ), Y ), Y ) ) ), :=( Z, true )] ), substitution( 1
% 51.24/51.66 , [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18444, [ =( 'is_a_theorem'( implies( implies( implies( X, X ), Y )
% 51.24/51.66 , Y ) ), true ) ] )
% 51.24/51.66 , clause( 18443, [ =( true, 'is_a_theorem'( implies( implies( implies( X, X
% 51.24/51.66 ), Y ), Y ) ) ) ] )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 subsumption(
% 51.24/51.66 clause( 141, [ =( 'is_a_theorem'( implies( implies( implies( X, X ), Y ), Y
% 51.24/51.66 ) ), true ) ] )
% 51.24/51.66 , clause( 18444, [ =( 'is_a_theorem'( implies( implies( implies( X, X ), Y
% 51.24/51.66 ), Y ) ), true ) ] )
% 51.24/51.66 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 51.24/51.66 )] ) ).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 eqswap(
% 51.24/51.66 clause( 18446, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.66 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 51.24/51.66 )
% 51.24/51.66 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 51.24/51.66 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 51.24/51.66 )
% 51.24/51.66 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.66
% 51.24/51.66
% 51.24/51.66 paramod(
% 51.24/51.66 clause( 18449, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.66 implies( X, X ), Y ), Y ), Z ) ), true, ifeq( true, true, 'is_a_theorem'(
% 51.24/51.66 Z ), true ), true ) ) ] )
% 51.24/51.66 , clause( 141, [ =( 'is_a_theorem'( implies( implies( implies( X, X ), Y )
% 51.24/51.66 , Y ) ), true ) ] )
% 51.24/51.66 , 0, clause( 18446, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 51.24/51.66 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 51.24/51.67 ) ) ] )
% 51.24/51.67 , 0, 15, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 51.24/51.67 :=( X, implies( implies( implies( X, X ), Y ), Y ) ), :=( Y, Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18451, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.67 implies( X, X ), Y ), Y ), Z ) ), true, 'is_a_theorem'( Z ), true ) ) ]
% 51.24/51.67 )
% 51.24/51.67 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.67 , 0, clause( 18449, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 51.24/51.67 implies( implies( X, X ), Y ), Y ), Z ) ), true, ifeq( true, true,
% 51.24/51.67 'is_a_theorem'( Z ), true ), true ) ) ] )
% 51.24/51.67 , 0, 14, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( Z ) ),
% 51.24/51.67 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )
% 51.24/51.67 ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18452, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.67 implies( X, X ), Y ), Y ), Z ) ), true, 'is_a_theorem'( Z ), true ), true
% 51.24/51.67 ) ] )
% 51.24/51.67 , clause( 18451, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.67 implies( X, X ), Y ), Y ), Z ) ), true, 'is_a_theorem'( Z ), true ) ) ]
% 51.24/51.67 )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 subsumption(
% 51.24/51.67 clause( 159, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 51.24/51.67 X, X ), Y ), Y ), Z ) ), true, 'is_a_theorem'( Z ), true ), true ) ] )
% 51.24/51.67 , clause( 18452, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.67 implies( X, X ), Y ), Y ), Z ) ), true, 'is_a_theorem'( Z ), true ), true
% 51.24/51.67 ) ] )
% 51.24/51.67 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.67 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18454, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.67 implies( X, Y ), Y ), implies( implies( Y, X ), X ) ), Z ) ), true,
% 51.24/51.67 'is_a_theorem'( Z ), true ) ) ] )
% 51.24/51.67 , clause( 26, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( implies(
% 51.24/51.67 X, Y ), Y ), implies( implies( Y, X ), X ) ), Z ) ), true, 'is_a_theorem'(
% 51.24/51.67 Z ), true ), true ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18456, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( not(
% 51.24/51.67 not( Y ) ), implies( implies( Y, X ), X ) ) ), true ) ) ] )
% 51.24/51.67 , clause( 105, [ =( 'is_a_theorem'( implies( implies( implies( Y, X ), Z )
% 51.24/51.67 , implies( not( not( X ) ), Z ) ) ), true ) ] )
% 51.24/51.67 , 0, clause( 18454, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 51.24/51.67 implies( implies( X, Y ), Y ), implies( implies( Y, X ), X ) ), Z ) ),
% 51.24/51.67 true, 'is_a_theorem'( Z ), true ) ) ] )
% 51.24/51.67 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, implies( X, Y ) ), :=( Z,
% 51.24/51.67 implies( implies( Y, X ), X ) )] ), substitution( 1, [ :=( X, X ), :=( Y
% 51.24/51.67 , Y ), :=( Z, implies( not( not( Y ) ), implies( implies( Y, X ), X ) ) )] )
% 51.24/51.67 ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18458, [ =( true, 'is_a_theorem'( implies( not( not( X ) ), implies(
% 51.24/51.67 implies( X, Y ), Y ) ) ) ) ] )
% 51.24/51.67 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.67 , 0, clause( 18456, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.67 not( not( Y ) ), implies( implies( Y, X ), X ) ) ), true ) ) ] )
% 51.24/51.67 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 51.24/51.67 not( not( X ) ), implies( implies( X, Y ), Y ) ) ) ), :=( Z, true )] ),
% 51.24/51.67 substitution( 1, [ :=( X, Y ), :=( Y, X )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18459, [ =( 'is_a_theorem'( implies( not( not( X ) ), implies(
% 51.24/51.67 implies( X, Y ), Y ) ) ), true ) ] )
% 51.24/51.67 , clause( 18458, [ =( true, 'is_a_theorem'( implies( not( not( X ) ),
% 51.24/51.67 implies( implies( X, Y ), Y ) ) ) ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 subsumption(
% 51.24/51.67 clause( 247, [ =( 'is_a_theorem'( implies( not( not( Y ) ), implies(
% 51.24/51.67 implies( Y, X ), X ) ) ), true ) ] )
% 51.24/51.67 , clause( 18459, [ =( 'is_a_theorem'( implies( not( not( X ) ), implies(
% 51.24/51.67 implies( X, Y ), Y ) ) ), true ) ] )
% 51.24/51.67 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 51.24/51.67 )] ) ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18461, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.67 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ) ) ]
% 51.24/51.67 )
% 51.24/51.67 , clause( 7, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.67 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ),
% 51.24/51.67 true ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18463, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.67 implies( implies( implies( X, Y ), Y ), Z ), implies( not( not( X ) ), Z
% 51.24/51.67 ) ) ), true ) ) ] )
% 51.24/51.67 , clause( 247, [ =( 'is_a_theorem'( implies( not( not( Y ) ), implies(
% 51.24/51.67 implies( Y, X ), X ) ) ), true ) ] )
% 51.24/51.67 , 0, clause( 18461, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 51.24/51.67 true, 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true
% 51.24/51.67 ) ) ] )
% 51.24/51.67 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 51.24/51.67 :=( X, not( not( X ) ) ), :=( Y, implies( implies( X, Y ), Y ) ), :=( Z,
% 51.24/51.67 Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18464, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 51.24/51.67 implies( X, Y ), Y ), Z ), implies( not( not( X ) ), Z ) ) ) ) ] )
% 51.24/51.67 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.67 , 0, clause( 18463, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.67 implies( implies( implies( X, Y ), Y ), Z ), implies( not( not( X ) ), Z
% 51.24/51.67 ) ) ), true ) ) ] )
% 51.24/51.67 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 51.24/51.67 implies( implies( implies( X, Y ), Y ), Z ), implies( not( not( X ) ), Z
% 51.24/51.67 ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 51.24/51.67 :=( Z, Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18465, [ =( 'is_a_theorem'( implies( implies( implies( implies( X,
% 51.24/51.67 Y ), Y ), Z ), implies( not( not( X ) ), Z ) ) ), true ) ] )
% 51.24/51.67 , clause( 18464, [ =( true, 'is_a_theorem'( implies( implies( implies(
% 51.24/51.67 implies( X, Y ), Y ), Z ), implies( not( not( X ) ), Z ) ) ) ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 subsumption(
% 51.24/51.67 clause( 252, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 51.24/51.67 ), Y ), Z ), implies( not( not( X ) ), Z ) ) ), true ) ] )
% 51.24/51.67 , clause( 18465, [ =( 'is_a_theorem'( implies( implies( implies( implies( X
% 51.24/51.67 , Y ), Y ), Z ), implies( not( not( X ) ), Z ) ) ), true ) ] )
% 51.24/51.67 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.67 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18467, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.67 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 51.24/51.67 )
% 51.24/51.67 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 51.24/51.67 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 51.24/51.67 )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18469, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'( implies(
% 51.24/51.67 implies( implies( X, Y ), Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z
% 51.24/51.67 ) ), true ), true ) ) ] )
% 51.24/51.67 , clause( 62, [ =( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 51.24/51.67 ), Y ), Z ), implies( X, Z ) ) ), true ) ] )
% 51.24/51.67 , 0, clause( 18467, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 51.24/51.67 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 51.24/51.67 ) ) ] )
% 51.24/51.67 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.67 substitution( 1, [ :=( X, implies( implies( implies( X, Y ), Y ), Z ) ),
% 51.24/51.67 :=( Y, implies( X, Z ) )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18474, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.67 X, Y ), Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ) ) ]
% 51.24/51.67 )
% 51.24/51.67 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.67 , 0, clause( 18469, [ =( true, ifeq( true, true, ifeq( 'is_a_theorem'(
% 51.24/51.67 implies( implies( implies( X, Y ), Y ), Z ) ), true, 'is_a_theorem'(
% 51.24/51.67 implies( X, Z ) ), true ), true ) ) ] )
% 51.24/51.67 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( 'is_a_theorem'(
% 51.24/51.67 implies( implies( implies( X, Y ), Y ), Z ) ), true, 'is_a_theorem'(
% 51.24/51.67 implies( X, Z ) ), true ) ), :=( Z, true )] ), substitution( 1, [ :=( X,
% 51.24/51.67 X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18475, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 51.24/51.67 , Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ), true ) ]
% 51.24/51.67 )
% 51.24/51.67 , clause( 18474, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.67 X, Y ), Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ) ) ]
% 51.24/51.67 )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 subsumption(
% 51.24/51.67 clause( 272, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y ),
% 51.24/51.67 Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ), true ) ] )
% 51.24/51.67 , clause( 18475, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y
% 51.24/51.67 ), Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ), true ) ]
% 51.24/51.67 )
% 51.24/51.67 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.67 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18477, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.67 implies( X, X ), Y ), Y ), Z ) ), true, 'is_a_theorem'( Z ), true ) ) ]
% 51.24/51.67 )
% 51.24/51.67 , clause( 159, [ =( ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.67 implies( X, X ), Y ), Y ), Z ) ), true, 'is_a_theorem'( Z ), true ), true
% 51.24/51.67 ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18479, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( not(
% 51.24/51.67 not( X ) ), X ) ), true ) ) ] )
% 51.24/51.67 , clause( 252, [ =( 'is_a_theorem'( implies( implies( implies( implies( X,
% 51.24/51.67 Y ), Y ), Z ), implies( not( not( X ) ), Z ) ) ), true ) ] )
% 51.24/51.67 , 0, clause( 18477, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 51.24/51.67 implies( implies( X, X ), Y ), Y ), Z ) ), true, 'is_a_theorem'( Z ),
% 51.24/51.67 true ) ) ] )
% 51.24/51.67 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, X )] ),
% 51.24/51.67 substitution( 1, [ :=( X, X ), :=( Y, X ), :=( Z, implies( not( not( X )
% 51.24/51.67 ), X ) )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18481, [ =( true, 'is_a_theorem'( implies( not( not( X ) ), X ) ) )
% 51.24/51.67 ] )
% 51.24/51.67 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.67 , 0, clause( 18479, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.67 not( not( X ) ), X ) ), true ) ) ] )
% 51.24/51.67 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 51.24/51.67 not( not( X ) ), X ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X )] )
% 51.24/51.67 ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18482, [ =( 'is_a_theorem'( implies( not( not( X ) ), X ) ), true )
% 51.24/51.67 ] )
% 51.24/51.67 , clause( 18481, [ =( true, 'is_a_theorem'( implies( not( not( X ) ), X ) )
% 51.24/51.67 ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 subsumption(
% 51.24/51.67 clause( 993, [ =( 'is_a_theorem'( implies( not( not( X ) ), X ) ), true ) ]
% 51.24/51.67 )
% 51.24/51.67 , clause( 18482, [ =( 'is_a_theorem'( implies( not( not( X ) ), X ) ), true
% 51.24/51.67 ) ] )
% 51.24/51.67 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18484, [ =( true, ifeq( 'is_a_theorem'( implies( not( X ), not( Y )
% 51.24/51.67 ) ), true, 'is_a_theorem'( implies( Y, X ) ), true ) ) ] )
% 51.24/51.67 , clause( 10, [ =( ifeq( 'is_a_theorem'( implies( not( X ), not( Y ) ) ),
% 51.24/51.67 true, 'is_a_theorem'( implies( Y, X ) ), true ), true ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18486, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X, not(
% 51.24/51.67 not( X ) ) ) ), true ) ) ] )
% 51.24/51.67 , clause( 993, [ =( 'is_a_theorem'( implies( not( not( X ) ), X ) ), true )
% 51.24/51.67 ] )
% 51.24/51.67 , 0, clause( 18484, [ =( true, ifeq( 'is_a_theorem'( implies( not( X ), not(
% 51.24/51.67 Y ) ) ), true, 'is_a_theorem'( implies( Y, X ) ), true ) ) ] )
% 51.24/51.67 , 0, 3, substitution( 0, [ :=( X, not( X ) )] ), substitution( 1, [ :=( X,
% 51.24/51.67 not( not( X ) ) ), :=( Y, X )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18488, [ =( true, 'is_a_theorem'( implies( X, not( not( X ) ) ) ) )
% 51.24/51.67 ] )
% 51.24/51.67 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.67 , 0, clause( 18486, [ =( true, ifeq( true, true, 'is_a_theorem'( implies( X
% 51.24/51.67 , not( not( X ) ) ) ), true ) ) ] )
% 51.24/51.67 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies( X
% 51.24/51.67 , not( not( X ) ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X )] )
% 51.24/51.67 ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18489, [ =( 'is_a_theorem'( implies( X, not( not( X ) ) ) ), true )
% 51.24/51.67 ] )
% 51.24/51.67 , clause( 18488, [ =( true, 'is_a_theorem'( implies( X, not( not( X ) ) ) )
% 51.24/51.67 ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 subsumption(
% 51.24/51.67 clause( 1005, [ =( 'is_a_theorem'( implies( X, not( not( X ) ) ) ), true )
% 51.24/51.67 ] )
% 51.24/51.67 , clause( 18489, [ =( 'is_a_theorem'( implies( X, not( not( X ) ) ) ), true
% 51.24/51.67 ) ] )
% 51.24/51.67 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18491, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.67 ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ) ) ]
% 51.24/51.67 )
% 51.24/51.67 , clause( 1, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true, ifeq(
% 51.24/51.67 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true ), true ) ]
% 51.24/51.67 )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18494, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, not(
% 51.24/51.67 not( X ) ) ), Y ) ), true, ifeq( true, true, 'is_a_theorem'( Y ), true )
% 51.24/51.67 , true ) ) ] )
% 51.24/51.67 , clause( 1005, [ =( 'is_a_theorem'( implies( X, not( not( X ) ) ) ), true
% 51.24/51.67 ) ] )
% 51.24/51.67 , 0, clause( 18491, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 51.24/51.67 true, ifeq( 'is_a_theorem'( X ), true, 'is_a_theorem'( Y ), true ), true
% 51.24/51.67 ) ) ] )
% 51.24/51.67 , 0, 13, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 51.24/51.67 implies( X, not( not( X ) ) ) ), :=( Y, Y )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18496, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, not(
% 51.24/51.67 not( X ) ) ), Y ) ), true, 'is_a_theorem'( Y ), true ) ) ] )
% 51.24/51.67 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.67 , 0, clause( 18494, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 51.24/51.67 not( not( X ) ) ), Y ) ), true, ifeq( true, true, 'is_a_theorem'( Y ),
% 51.24/51.67 true ), true ) ) ] )
% 51.24/51.67 , 0, 12, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( Y ) ),
% 51.24/51.67 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18497, [ =( ifeq( 'is_a_theorem'( implies( implies( X, not( not( X
% 51.24/51.67 ) ) ), Y ) ), true, 'is_a_theorem'( Y ), true ), true ) ] )
% 51.24/51.67 , clause( 18496, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, not(
% 51.24/51.67 not( X ) ) ), Y ) ), true, 'is_a_theorem'( Y ), true ) ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 subsumption(
% 51.24/51.67 clause( 1037, [ =( ifeq( 'is_a_theorem'( implies( implies( X, not( not( X )
% 51.24/51.67 ) ), Y ) ), true, 'is_a_theorem'( Y ), true ), true ) ] )
% 51.24/51.67 , clause( 18497, [ =( ifeq( 'is_a_theorem'( implies( implies( X, not( not(
% 51.24/51.67 X ) ) ), Y ) ), true, 'is_a_theorem'( Y ), true ), true ) ] )
% 51.24/51.67 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 51.24/51.67 )] ) ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18499, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.67 X, Y ), Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ) ) ]
% 51.24/51.67 )
% 51.24/51.67 , clause( 272, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( X, Y )
% 51.24/51.67 , Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ), true ), true ) ]
% 51.24/51.67 )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18501, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.67 implies( X, Y ), implies( implies( Z, X ), implies( Z, Y ) ) ) ), true )
% 51.24/51.67 ) ] )
% 51.24/51.67 , clause( 35, [ =( 'is_a_theorem'( implies( implies( implies( implies( Y, Z
% 51.24/51.67 ), implies( X, Z ) ), T ), implies( implies( X, Y ), T ) ) ), true ) ]
% 51.24/51.67 )
% 51.24/51.67 , 0, clause( 18499, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 51.24/51.67 implies( X, Y ), Y ), Z ) ), true, 'is_a_theorem'( implies( X, Z ) ),
% 51.24/51.67 true ) ) ] )
% 51.24/51.67 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T,
% 51.24/51.67 implies( Z, Y ) )] ), substitution( 1, [ :=( X, implies( X, Y ) ), :=( Y
% 51.24/51.67 , implies( Z, Y ) ), :=( Z, implies( implies( Z, X ), implies( Z, Y ) ) )] )
% 51.24/51.67 ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18503, [ =( true, 'is_a_theorem'( implies( implies( X, Y ), implies(
% 51.24/51.67 implies( Z, X ), implies( Z, Y ) ) ) ) ) ] )
% 51.24/51.67 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.67 , 0, clause( 18501, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.67 implies( X, Y ), implies( implies( Z, X ), implies( Z, Y ) ) ) ), true )
% 51.24/51.67 ) ] )
% 51.24/51.67 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 51.24/51.67 implies( X, Y ), implies( implies( Z, X ), implies( Z, Y ) ) ) ) ), :=( Z
% 51.24/51.67 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )
% 51.24/51.67 ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18504, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 51.24/51.67 implies( Z, X ), implies( Z, Y ) ) ) ), true ) ] )
% 51.24/51.67 , clause( 18503, [ =( true, 'is_a_theorem'( implies( implies( X, Y ),
% 51.24/51.67 implies( implies( Z, X ), implies( Z, Y ) ) ) ) ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 subsumption(
% 51.24/51.67 clause( 5835, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 51.24/51.67 implies( Z, X ), implies( Z, Y ) ) ) ), true ) ] )
% 51.24/51.67 , clause( 18504, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 51.24/51.67 implies( Z, X ), implies( Z, Y ) ) ) ), true ) ] )
% 51.24/51.67 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.67 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18506, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X, not(
% 51.24/51.67 not( X ) ) ), Y ) ), true, 'is_a_theorem'( Y ), true ) ) ] )
% 51.24/51.67 , clause( 1037, [ =( ifeq( 'is_a_theorem'( implies( implies( X, not( not( X
% 51.24/51.67 ) ) ), Y ) ), true, 'is_a_theorem'( Y ), true ), true ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18508, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.67 implies( Y, X ), implies( Y, not( not( X ) ) ) ) ), true ) ) ] )
% 51.24/51.67 , clause( 5835, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies(
% 51.24/51.67 implies( Z, X ), implies( Z, Y ) ) ) ), true ) ] )
% 51.24/51.67 , 0, clause( 18506, [ =( true, ifeq( 'is_a_theorem'( implies( implies( X,
% 51.24/51.67 not( not( X ) ) ), Y ) ), true, 'is_a_theorem'( Y ), true ) ) ] )
% 51.24/51.67 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, not( not( X ) ) ), :=( Z, Y )] )
% 51.24/51.67 , substitution( 1, [ :=( X, X ), :=( Y, implies( implies( Y, X ), implies(
% 51.24/51.67 Y, not( not( X ) ) ) ) )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18510, [ =( true, 'is_a_theorem'( implies( implies( X, Y ), implies(
% 51.24/51.67 X, not( not( Y ) ) ) ) ) ) ] )
% 51.24/51.67 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.67 , 0, clause( 18508, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.67 implies( Y, X ), implies( Y, not( not( X ) ) ) ) ), true ) ) ] )
% 51.24/51.67 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 51.24/51.67 implies( X, Y ), implies( X, not( not( Y ) ) ) ) ) ), :=( Z, true )] ),
% 51.24/51.67 substitution( 1, [ :=( X, Y ), :=( Y, X )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18511, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( X,
% 51.24/51.67 not( not( Y ) ) ) ) ), true ) ] )
% 51.24/51.67 , clause( 18510, [ =( true, 'is_a_theorem'( implies( implies( X, Y ),
% 51.24/51.67 implies( X, not( not( Y ) ) ) ) ) ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 subsumption(
% 51.24/51.67 clause( 11364, [ =( 'is_a_theorem'( implies( implies( Y, X ), implies( Y,
% 51.24/51.67 not( not( X ) ) ) ) ), true ) ] )
% 51.24/51.67 , clause( 18511, [ =( 'is_a_theorem'( implies( implies( X, Y ), implies( X
% 51.24/51.67 , not( not( Y ) ) ) ) ), true ) ] )
% 51.24/51.67 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 51.24/51.67 )] ) ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18513, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.67 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ) ) ]
% 51.24/51.67 )
% 51.24/51.67 , clause( 7, [ =( ifeq( 'is_a_theorem'( implies( X, Y ) ), true,
% 51.24/51.67 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true ),
% 51.24/51.67 true ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18515, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.67 implies( implies( X, not( not( Y ) ) ), Z ), implies( implies( X, Y ), Z
% 51.24/51.67 ) ) ), true ) ) ] )
% 51.24/51.67 , clause( 11364, [ =( 'is_a_theorem'( implies( implies( Y, X ), implies( Y
% 51.24/51.67 , not( not( X ) ) ) ) ), true ) ] )
% 51.24/51.67 , 0, clause( 18513, [ =( true, ifeq( 'is_a_theorem'( implies( X, Y ) ),
% 51.24/51.67 true, 'is_a_theorem'( implies( implies( Y, Z ), implies( X, Z ) ) ), true
% 51.24/51.67 ) ) ] )
% 51.24/51.67 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 51.24/51.67 :=( X, implies( X, Y ) ), :=( Y, implies( X, not( not( Y ) ) ) ), :=( Z,
% 51.24/51.67 Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18516, [ =( true, 'is_a_theorem'( implies( implies( implies( X, not(
% 51.24/51.67 not( Y ) ) ), Z ), implies( implies( X, Y ), Z ) ) ) ) ] )
% 51.24/51.67 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.67 , 0, clause( 18515, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.67 implies( implies( X, not( not( Y ) ) ), Z ), implies( implies( X, Y ), Z
% 51.24/51.67 ) ) ), true ) ) ] )
% 51.24/51.67 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 51.24/51.67 implies( implies( X, not( not( Y ) ) ), Z ), implies( implies( X, Y ), Z
% 51.24/51.67 ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 51.24/51.67 :=( Z, Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18517, [ =( 'is_a_theorem'( implies( implies( implies( X, not( not(
% 51.24/51.67 Y ) ) ), Z ), implies( implies( X, Y ), Z ) ) ), true ) ] )
% 51.24/51.67 , clause( 18516, [ =( true, 'is_a_theorem'( implies( implies( implies( X,
% 51.24/51.67 not( not( Y ) ) ), Z ), implies( implies( X, Y ), Z ) ) ) ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 subsumption(
% 51.24/51.67 clause( 11460, [ =( 'is_a_theorem'( implies( implies( implies( X, not( not(
% 51.24/51.67 Y ) ) ), Z ), implies( implies( X, Y ), Z ) ) ), true ) ] )
% 51.24/51.67 , clause( 18517, [ =( 'is_a_theorem'( implies( implies( implies( X, not(
% 51.24/51.67 not( Y ) ) ), Z ), implies( implies( X, Y ), Z ) ) ), true ) ] )
% 51.24/51.67 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 51.24/51.67 permutation( 0, [ ==>( 0, 0 )] ) ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18519, [ =( true, ifeq( 'is_a_theorem'( implies( implies( implies(
% 51.24/51.67 not( X ), not( Y ) ), implies( Y, X ) ), Z ) ), true, 'is_a_theorem'( Z )
% 51.24/51.67 , true ) ) ] )
% 51.24/51.67 , clause( 11, [ =( ifeq( 'is_a_theorem'( implies( implies( implies( not( X
% 51.24/51.67 ), not( Y ) ), implies( Y, X ) ), Z ) ), true, 'is_a_theorem'( Z ), true
% 51.24/51.67 ), true ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18521, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.67 implies( not( X ), Y ), implies( not( Y ), X ) ) ), true ) ) ] )
% 51.24/51.67 , clause( 11460, [ =( 'is_a_theorem'( implies( implies( implies( X, not(
% 51.24/51.67 not( Y ) ) ), Z ), implies( implies( X, Y ), Z ) ) ), true ) ] )
% 51.24/51.67 , 0, clause( 18519, [ =( true, ifeq( 'is_a_theorem'( implies( implies(
% 51.24/51.67 implies( not( X ), not( Y ) ), implies( Y, X ) ), Z ) ), true,
% 51.24/51.67 'is_a_theorem'( Z ), true ) ) ] )
% 51.24/51.67 , 0, 3, substitution( 0, [ :=( X, not( X ) ), :=( Y, Y ), :=( Z, implies(
% 51.24/51.67 not( Y ), X ) )] ), substitution( 1, [ :=( X, X ), :=( Y, not( Y ) ),
% 51.24/51.67 :=( Z, implies( implies( not( X ), Y ), implies( not( Y ), X ) ) )] )
% 51.24/51.67 ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 paramod(
% 51.24/51.67 clause( 18523, [ =( true, 'is_a_theorem'( implies( implies( not( X ), Y ),
% 51.24/51.67 implies( not( Y ), X ) ) ) ) ] )
% 51.24/51.67 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 51.24/51.67 , 0, clause( 18521, [ =( true, ifeq( true, true, 'is_a_theorem'( implies(
% 51.24/51.67 implies( not( X ), Y ), implies( not( Y ), X ) ) ), true ) ) ] )
% 51.24/51.67 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, 'is_a_theorem'( implies(
% 51.24/51.67 implies( not( X ), Y ), implies( not( Y ), X ) ) ) ), :=( Z, true )] ),
% 51.24/51.67 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18524, [ =( 'is_a_theorem'( implies( implies( not( X ), Y ),
% 51.24/51.67 implies( not( Y ), X ) ) ), true ) ] )
% 51.24/51.67 , clause( 18523, [ =( true, 'is_a_theorem'( implies( implies( not( X ), Y )
% 51.24/51.67 , implies( not( Y ), X ) ) ) ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 subsumption(
% 51.24/51.67 clause( 18277, [ =( 'is_a_theorem'( implies( implies( not( X ), Y ),
% 51.24/51.67 implies( not( Y ), X ) ) ), true ) ] )
% 51.24/51.67 , clause( 18524, [ =( 'is_a_theorem'( implies( implies( not( X ), Y ),
% 51.24/51.67 implies( not( Y ), X ) ) ), true ) ] )
% 51.24/51.67 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 51.24/51.67 )] ) ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18525, [ =( true, 'is_a_theorem'( implies( implies( not( X ), Y ),
% 51.24/51.67 implies( not( Y ), X ) ) ) ) ] )
% 51.24/51.67 , clause( 18277, [ =( 'is_a_theorem'( implies( implies( not( X ), Y ),
% 51.24/51.67 implies( not( Y ), X ) ) ), true ) ] )
% 51.24/51.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 eqswap(
% 51.24/51.67 clause( 18526, [ ~( =( true, 'is_a_theorem'( implies( implies( not( a ), b
% 51.24/51.67 ), implies( not( b ), a ) ) ) ) ) ] )
% 51.24/51.67 , clause( 6, [ ~( =( 'is_a_theorem'( implies( implies( not( a ), b ),
% 51.24/51.67 implies( not( b ), a ) ) ), true ) ) ] )
% 51.24/51.67 , 0, substitution( 0, [] )).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 resolution(
% 51.24/51.67 clause( 18527, [] )
% 51.24/51.67 , clause( 18526, [ ~( =( true, 'is_a_theorem'( implies( implies( not( a ),
% 51.24/51.67 b ), implies( not( b ), a ) ) ) ) ) ] )
% 51.24/51.67 , 0, clause( 18525, [ =( true, 'is_a_theorem'( implies( implies( not( X ),
% 51.24/51.67 Y ), implies( not( Y ), X ) ) ) ) ] )
% 51.24/51.67 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, b )] )
% 51.24/51.67 ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 subsumption(
% 51.24/51.67 clause( 18280, [] )
% 51.24/51.67 , clause( 18527, [] )
% 51.24/51.67 , substitution( 0, [] ), permutation( 0, [] ) ).
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 end.
% 51.24/51.67
% 51.24/51.67 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 51.24/51.67
% 51.24/51.67 Memory use:
% 51.24/51.67
% 51.24/51.67 space for terms: 312123
% 51.24/51.67 space for clauses: 1955778
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 clauses generated: 2446891
% 51.24/51.67 clauses kept: 18281
% 51.24/51.67 clauses selected: 2812
% 51.24/51.67 clauses deleted: 51
% 51.24/51.67 clauses inuse deleted: 10
% 51.24/51.67
% 51.24/51.67 subsentry: 612
% 51.24/51.67 literals s-matched: 251
% 51.24/51.67 literals matched: 251
% 51.24/51.67 full subsumption: 0
% 51.24/51.67
% 51.24/51.67 checksum: -656297981
% 51.24/51.67
% 51.24/51.67
% 51.24/51.67 Bliksem ended
%------------------------------------------------------------------------------