TSTP Solution File: LCL034-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL034-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 07:49:27 EDT 2022
% Result : Unsatisfiable 0.78s 1.31s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LCL034-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.14 % Command : bliksem %s
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Sun Jul 3 22:35:14 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.78/1.31 *** allocated 10000 integers for termspace/termends
% 0.78/1.31 *** allocated 10000 integers for clauses
% 0.78/1.31 *** allocated 10000 integers for justifications
% 0.78/1.31 Bliksem 1.12
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 Automatic Strategy Selection
% 0.78/1.31
% 0.78/1.31 Clauses:
% 0.78/1.31 [
% 0.78/1.31 [ ~( 'is_a_theorem'( implies( X, Y ) ) ), ~( 'is_a_theorem'( X ) ),
% 0.78/1.31 'is_a_theorem'( Y ) ],
% 0.78/1.31 [ 'is_a_theorem'( implies( implies( implies( implies( implies( X, Y ),
% 0.78/1.31 implies( Z, falsehood ) ), T ), U ), implies( implies( U, X ), implies( Z
% 0.78/1.31 , X ) ) ) ) ],
% 0.78/1.31 [ ~( 'is_a_theorem'( implies( implies( implies( a, b ), a ), a ) ) ) ]
% 0.78/1.31 ] .
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 percentage equality = 0.000000, percentage horn = 1.000000
% 0.78/1.31 This is a near-Horn, non-equality problem
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 Options Used:
% 0.78/1.31
% 0.78/1.31 useres = 1
% 0.78/1.31 useparamod = 0
% 0.78/1.31 useeqrefl = 0
% 0.78/1.31 useeqfact = 0
% 0.78/1.31 usefactor = 1
% 0.78/1.31 usesimpsplitting = 0
% 0.78/1.31 usesimpdemod = 0
% 0.78/1.31 usesimpres = 4
% 0.78/1.31
% 0.78/1.31 resimpinuse = 1000
% 0.78/1.31 resimpclauses = 20000
% 0.78/1.31 substype = standard
% 0.78/1.31 backwardsubs = 1
% 0.78/1.31 selectoldest = 5
% 0.78/1.31
% 0.78/1.31 litorderings [0] = split
% 0.78/1.31 litorderings [1] = liftord
% 0.78/1.31
% 0.78/1.31 termordering = none
% 0.78/1.31
% 0.78/1.31 litapriori = 1
% 0.78/1.31 termapriori = 0
% 0.78/1.31 litaposteriori = 0
% 0.78/1.31 termaposteriori = 0
% 0.78/1.31 demodaposteriori = 0
% 0.78/1.31 ordereqreflfact = 0
% 0.78/1.31
% 0.78/1.31 litselect = negative
% 0.78/1.31
% 0.78/1.31 maxweight = 30000
% 0.78/1.31 maxdepth = 30000
% 0.78/1.31 maxlength = 115
% 0.78/1.31 maxnrvars = 195
% 0.78/1.31 excuselevel = 0
% 0.78/1.31 increasemaxweight = 0
% 0.78/1.31
% 0.78/1.31 maxselected = 10000000
% 0.78/1.31 maxnrclauses = 10000000
% 0.78/1.31
% 0.78/1.31 showgenerated = 0
% 0.78/1.31 showkept = 0
% 0.78/1.31 showselected = 0
% 0.78/1.31 showdeleted = 0
% 0.78/1.31 showresimp = 1
% 0.78/1.31 showstatus = 2000
% 0.78/1.31
% 0.78/1.31 prologoutput = 1
% 0.78/1.31 nrgoals = 5000000
% 0.78/1.31 totalproof = 1
% 0.78/1.31
% 0.78/1.31 Symbols occurring in the translation:
% 0.78/1.31
% 0.78/1.31 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.78/1.31 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.78/1.31 ! [4, 1] (w:1, o:17, a:1, s:1, b:0),
% 0.78/1.31 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.78/1.31 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.78/1.31 implies [41, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.78/1.31 'is_a_theorem' [42, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.78/1.31 falsehood [44, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.78/1.31 a [47, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.78/1.31 b [48, 0] (w:1, o:16, a:1, s:1, b:0).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 Starting Search:
% 0.78/1.31
% 0.78/1.31 Resimplifying inuse:
% 0.78/1.31 Done
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 Intermediate Status:
% 0.78/1.31 Generated: 20412
% 0.78/1.31 Kept: 2002
% 0.78/1.31 Inuse: 384
% 0.78/1.31 Deleted: 87
% 0.78/1.31 Deletedinuse: 23
% 0.78/1.31
% 0.78/1.31 Resimplifying inuse:
% 0.78/1.31 Done
% 0.78/1.31
% 0.78/1.31 Resimplifying inuse:
% 0.78/1.31 Done
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 Intermediate Status:
% 0.78/1.31 Generated: 42789
% 0.78/1.31 Kept: 4008
% 0.78/1.31 Inuse: 588
% 0.78/1.31 Deleted: 120
% 0.78/1.31 Deletedinuse: 28
% 0.78/1.31
% 0.78/1.31 Resimplifying inuse:
% 0.78/1.31 Done
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 Bliksems!, er is een bewijs:
% 0.78/1.31 % SZS status Unsatisfiable
% 0.78/1.31 % SZS output start Refutation
% 0.78/1.31
% 0.78/1.31 clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y ),
% 0.78/1.31 ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 1, [ 'is_a_theorem'( implies( implies( implies( implies( implies( X
% 0.78/1.31 , Y ), implies( Z, falsehood ) ), T ), U ), implies( implies( U, X ),
% 0.78/1.31 implies( Z, X ) ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 2, [ ~( 'is_a_theorem'( implies( implies( implies( a, b ), a ), a )
% 0.78/1.31 ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 3, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( implies( implies( X, Y ), implies( Z, falsehood ) ), T
% 0.78/1.31 ), U ), implies( implies( U, X ), implies( Z, X ) ) ), W ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 4, [ 'is_a_theorem'( implies( implies( implies( implies( X, Y ),
% 0.78/1.31 implies( Z, Y ) ), implies( Y, T ) ), implies( U, implies( Y, T ) ) ) ) ]
% 0.78/1.31 )
% 0.78/1.31 .
% 0.78/1.31 clause( 5, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( implies( X, Y ), implies( Z, Y ) ), implies( Y, T ) ),
% 0.78/1.31 implies( U, implies( Y, T ) ) ), W ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 7, [ 'is_a_theorem'( implies( implies( implies( X, implies(
% 0.78/1.31 falsehood, Y ) ), Z ), implies( T, Z ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 8, [ 'is_a_theorem'( implies( X, implies( Y, implies( falsehood, Z
% 0.78/1.31 ) ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 10, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, implies( falsehood, Y ) ), Z ), implies( T, Z ) ), U
% 0.78/1.31 ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 11, [ 'is_a_theorem'( implies( X, implies( falsehood, Y ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 14, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( implies( implies( X,
% 0.78/1.31 implies( falsehood, Y ) ), Z ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 21, [ 'is_a_theorem'( implies( implies( implies( falsehood, X ), Y
% 0.78/1.31 ), implies( Z, Y ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 22, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( falsehood, X ), Y ), implies( Z, Y ) ), T ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 26, [ 'is_a_theorem'( implies( X, implies( Y, implies( Z, Y ) ) ) )
% 0.78/1.31 ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 27, [ 'is_a_theorem'( implies( X, implies( Y, X ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 29, [ 'is_a_theorem'( implies( X, implies( implies( implies( Y,
% 0.78/1.31 implies( falsehood, Z ) ), T ), implies( U, T ) ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 33, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( implies( implies( X,
% 0.78/1.31 implies( Y, X ) ), Z ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 36, [ 'is_a_theorem'( implies( implies( implies( X, implies(
% 0.78/1.31 implies( implies( Y, Z ), implies( T, falsehood ) ), U ) ), Y ), implies(
% 0.78/1.31 T, Y ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 56, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( implies( implies( X,
% 0.78/1.31 implies( implies( implies( Y, implies( falsehood, Z ) ), T ), implies( U
% 0.78/1.31 , T ) ) ), W ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 102, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, implies( implies( implies( Y, Z ), implies( T,
% 0.78/1.31 falsehood ) ), U ) ), Y ), implies( T, Y ) ), W ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 124, [ 'is_a_theorem'( implies( X, implies( Y, implies( implies(
% 0.78/1.31 implies( Z, implies( falsehood, T ) ), U ), implies( W, U ) ) ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 126, [ 'is_a_theorem'( V0 ), ~( 'is_a_theorem'( implies( implies( X
% 0.78/1.31 , implies( Y, implies( implies( implies( Z, implies( falsehood, T ) ), U
% 0.78/1.31 ), implies( W, U ) ) ) ), V0 ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 170, [ 'is_a_theorem'( implies( X, implies( Y, implies( Z, implies(
% 0.78/1.31 implies( implies( T, implies( falsehood, U ) ), W ), implies( V0, W ) ) )
% 0.78/1.31 ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 172, [ 'is_a_theorem'( V1 ), ~( 'is_a_theorem'( implies( implies( X
% 0.78/1.31 , implies( Y, implies( Z, implies( implies( implies( T, implies(
% 0.78/1.31 falsehood, U ) ), W ), implies( V0, W ) ) ) ) ), V1 ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 254, [ 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 0.78/1.31 implies( implies( implies( Y, T ), implies( X, falsehood ) ), Z ) ) ) ]
% 0.78/1.31 )
% 0.78/1.31 .
% 0.78/1.31 clause( 270, [ 'is_a_theorem'( implies( implies( implies( X, Y ), implies(
% 0.78/1.31 implies( falsehood, Z ), falsehood ) ), implies( T, X ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 278, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, Y ), implies( implies( falsehood, Z ), falsehood ) )
% 0.78/1.31 , implies( T, X ) ), U ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 372, [ 'is_a_theorem'( implies( implies( implies( X, implies( Y, Z
% 0.78/1.31 ) ), Y ), implies( T, Y ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 373, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, implies( Y, Z ) ), Y ), implies( T, Y ) ), U ) ) ) ]
% 0.78/1.31 )
% 0.78/1.31 .
% 0.78/1.31 clause( 379, [ 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 0.78/1.31 implies( Y, Z ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 386, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, Y ), Z ), implies( Y, Z ) ), T ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 553, [ 'is_a_theorem'( implies( implies( implies( implies( X,
% 0.78/1.31 falsehood ), Y ), Z ), implies( X, Z ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 558, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( implies( X, falsehood ), Y ), Z ), implies( X, Z ) ), T
% 0.78/1.31 ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 1464, [ 'is_a_theorem'( implies( implies( implies( X, Y ), X ),
% 0.78/1.31 implies( Z, X ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 1466, [ 'is_a_theorem'( implies( X, implies( Y, Y ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 1468, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, Y ), X ), implies( Z, X ) ), T ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 1479, [ 'is_a_theorem'( implies( X, X ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 1481, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( implies( implies( X
% 0.78/1.31 , X ), Y ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 1494, [ 'is_a_theorem'( implies( X, implies( implies( X, falsehood
% 0.78/1.31 ), Y ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 1499, [ 'is_a_theorem'( implies( implies( implies( X, Y ), implies(
% 0.78/1.31 Z, falsehood ) ), implies( Z, X ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 1554, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( implies( implies( X
% 0.78/1.31 , implies( implies( X, falsehood ), Y ) ), Z ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 1785, [ 'is_a_theorem'( implies( X, implies( implies( implies(
% 0.78/1.31 implies( X, falsehood ), Y ), falsehood ), Z ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 1872, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies( X
% 0.78/1.31 , implies( implies( implies( implies( X, falsehood ), Y ), falsehood ), Z
% 0.78/1.31 ) ), T ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 3984, [ 'is_a_theorem'( implies( implies( implies( implies( implies(
% 0.78/1.31 X, Y ), falsehood ), Z ), falsehood ), X ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 4011, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( implies( implies( X, Y ), falsehood ), Z ), falsehood )
% 0.78/1.31 , X ), T ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 4258, [ 'is_a_theorem'( implies( implies( X, implies( X, Y ) ),
% 0.78/1.31 implies( Z, implies( X, Y ) ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 4265, [ 'is_a_theorem'( implies( X, implies( implies( implies( Y, Z
% 0.78/1.31 ), Y ), Y ) ) ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 4289, [ 'is_a_theorem'( implies( implies( implies( X, Y ), X ), X )
% 0.78/1.31 ) ] )
% 0.78/1.31 .
% 0.78/1.31 clause( 4292, [] )
% 0.78/1.31 .
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 % SZS output end Refutation
% 0.78/1.31 found a proof!
% 0.78/1.31
% 0.78/1.31 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.78/1.31
% 0.78/1.31 initialclauses(
% 0.78/1.31 [ clause( 4294, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), ~( 'is_a_theorem'(
% 0.78/1.31 X ) ), 'is_a_theorem'( Y ) ] )
% 0.78/1.31 , clause( 4295, [ 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), implies( Z, falsehood ) ), T ), U ), implies( implies( U
% 0.78/1.31 , X ), implies( Z, X ) ) ) ) ] )
% 0.78/1.31 , clause( 4296, [ ~( 'is_a_theorem'( implies( implies( implies( a, b ), a )
% 0.78/1.31 , a ) ) ) ] )
% 0.78/1.31 ] ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y ),
% 0.78/1.31 ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , clause( 4294, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), ~( 'is_a_theorem'(
% 0.78/1.31 X ) ), 'is_a_theorem'( Y ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.78/1.31 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 1, [ 'is_a_theorem'( implies( implies( implies( implies( implies( X
% 0.78/1.31 , Y ), implies( Z, falsehood ) ), T ), U ), implies( implies( U, X ),
% 0.78/1.31 implies( Z, X ) ) ) ) ] )
% 0.78/1.31 , clause( 4295, [ 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), implies( Z, falsehood ) ), T ), U ), implies( implies( U
% 0.78/1.31 , X ), implies( Z, X ) ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.78/1.31 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 2, [ ~( 'is_a_theorem'( implies( implies( implies( a, b ), a ), a )
% 0.78/1.31 ) ) ] )
% 0.78/1.31 , clause( 4296, [ ~( 'is_a_theorem'( implies( implies( implies( a, b ), a )
% 0.78/1.31 , a ) ) ) ] )
% 0.78/1.31 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4298, [ ~( 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( implies( X, Y ), implies( Z, falsehood ) ), T ), U ), implies(
% 0.78/1.31 implies( U, X ), implies( Z, X ) ) ), W ) ) ), 'is_a_theorem'( W ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 1, [ 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), implies( Z, falsehood ) ), T ), U ), implies( implies( U
% 0.78/1.31 , X ), implies( Z, X ) ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( implies( implies( implies( implies(
% 0.78/1.31 X, Y ), implies( Z, falsehood ) ), T ), U ), implies( implies( U, X ),
% 0.78/1.31 implies( Z, X ) ) ) ), :=( Y, W )] ), substitution( 1, [ :=( X, X ), :=(
% 0.78/1.31 Y, Y ), :=( Z, Z ), :=( T, T ), :=( U, U )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 3, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( implies( implies( X, Y ), implies( Z, falsehood ) ), T
% 0.78/1.31 ), U ), implies( implies( U, X ), implies( Z, X ) ) ), W ) ) ) ] )
% 0.78/1.31 , clause( 4298, [ ~( 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( implies( X, Y ), implies( Z, falsehood ) ), T ), U ), implies(
% 0.78/1.31 implies( U, X ), implies( Z, X ) ) ), W ) ) ), 'is_a_theorem'( W ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.78/1.31 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4299, [ 'is_a_theorem'( implies( implies( implies( implies( X, Y )
% 0.78/1.31 , implies( Z, Y ) ), implies( Y, T ) ), implies( U, implies( Y, T ) ) ) )
% 0.78/1.31 ] )
% 0.78/1.31 , clause( 3, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( implies( implies( X, Y ), implies( Z, falsehood ) ), T
% 0.78/1.31 ), U ), implies( implies( U, X ), implies( Z, X ) ) ), W ) ) ) ] )
% 0.78/1.31 , 1, clause( 1, [ 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), implies( Z, falsehood ) ), T ), U ), implies( implies( U
% 0.78/1.31 , X ), implies( Z, X ) ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, Y ), :=( Y, T ), :=( Z, Z ), :=( T, implies(
% 0.78/1.31 U, falsehood ) ), :=( U, X ), :=( W, implies( implies( implies( implies(
% 0.78/1.31 X, Y ), implies( Z, Y ) ), implies( Y, T ) ), implies( U, implies( Y, T )
% 0.78/1.31 ) ) )] ), substitution( 1, [ :=( X, implies( Y, T ) ), :=( Y, implies( Z
% 0.78/1.31 , falsehood ) ), :=( Z, U ), :=( T, X ), :=( U, implies( implies( X, Y )
% 0.78/1.31 , implies( Z, Y ) ) )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 4, [ 'is_a_theorem'( implies( implies( implies( implies( X, Y ),
% 0.78/1.31 implies( Z, Y ) ), implies( Y, T ) ), implies( U, implies( Y, T ) ) ) ) ]
% 0.78/1.31 )
% 0.78/1.31 , clause( 4299, [ 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 0.78/1.31 ), implies( Z, Y ) ), implies( Y, T ) ), implies( U, implies( Y, T ) ) )
% 0.78/1.31 ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.78/1.31 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4301, [ ~( 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), implies( Z, Y ) ), implies( Y, T ) ), implies( U,
% 0.78/1.31 implies( Y, T ) ) ), W ) ) ), 'is_a_theorem'( W ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 4, [ 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 0.78/1.31 ), implies( Z, Y ) ), implies( Y, T ) ), implies( U, implies( Y, T ) ) )
% 0.78/1.31 ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( implies( implies( implies( X, Y ),
% 0.78/1.31 implies( Z, Y ) ), implies( Y, T ) ), implies( U, implies( Y, T ) ) ) ),
% 0.78/1.31 :=( Y, W )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ),
% 0.78/1.31 :=( T, T ), :=( U, U )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 5, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( implies( X, Y ), implies( Z, Y ) ), implies( Y, T ) ),
% 0.78/1.31 implies( U, implies( Y, T ) ) ), W ) ) ) ] )
% 0.78/1.31 , clause( 4301, [ ~( 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), implies( Z, Y ) ), implies( Y, T ) ), implies( U,
% 0.78/1.31 implies( Y, T ) ) ), W ) ) ), 'is_a_theorem'( W ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.78/1.31 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4302, [ 'is_a_theorem'( implies( implies( implies( X, implies(
% 0.78/1.31 falsehood, Y ) ), Z ), implies( T, Z ) ) ) ] )
% 0.78/1.31 , clause( 5, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( implies( X, Y ), implies( Z, Y ) ), implies( Y, T ) ),
% 0.78/1.31 implies( U, implies( Y, T ) ) ), W ) ) ) ] )
% 0.78/1.31 , 1, clause( 1, [ 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), implies( Z, falsehood ) ), T ), U ), implies( implies( U
% 0.78/1.31 , X ), implies( Z, X ) ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, Z ), :=( Y, falsehood ), :=( Z, T ), :=( T,
% 0.78/1.31 Y ), :=( U, X ), :=( W, implies( implies( implies( X, implies( falsehood
% 0.78/1.31 , Y ) ), Z ), implies( T, Z ) ) )] ), substitution( 1, [ :=( X, Z ), :=(
% 0.78/1.31 Y, falsehood ), :=( Z, T ), :=( T, implies( falsehood, Y ) ), :=( U,
% 0.78/1.31 implies( X, implies( falsehood, Y ) ) )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 7, [ 'is_a_theorem'( implies( implies( implies( X, implies(
% 0.78/1.31 falsehood, Y ) ), Z ), implies( T, Z ) ) ) ] )
% 0.78/1.31 , clause( 4302, [ 'is_a_theorem'( implies( implies( implies( X, implies(
% 0.78/1.31 falsehood, Y ) ), Z ), implies( T, Z ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4303, [ 'is_a_theorem'( implies( X, implies( Y, implies( falsehood
% 0.78/1.31 , Z ) ) ) ) ] )
% 0.78/1.31 , clause( 5, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( implies( X, Y ), implies( Z, Y ) ), implies( Y, T ) ),
% 0.78/1.31 implies( U, implies( Y, T ) ) ), W ) ) ) ] )
% 0.78/1.31 , 1, clause( 7, [ 'is_a_theorem'( implies( implies( implies( X, implies(
% 0.78/1.31 falsehood, Y ) ), Z ), implies( T, Z ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, T ), :=( Y, falsehood ), :=( Z, U ), :=( T,
% 0.78/1.31 Z ), :=( U, Y ), :=( W, implies( X, implies( Y, implies( falsehood, Z ) )
% 0.78/1.31 ) )] ), substitution( 1, [ :=( X, implies( implies( T, falsehood ),
% 0.78/1.31 implies( U, falsehood ) ) ), :=( Y, Z ), :=( Z, implies( Y, implies(
% 0.78/1.31 falsehood, Z ) ) ), :=( T, X )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 8, [ 'is_a_theorem'( implies( X, implies( Y, implies( falsehood, Z
% 0.78/1.31 ) ) ) ) ] )
% 0.78/1.31 , clause( 4303, [ 'is_a_theorem'( implies( X, implies( Y, implies(
% 0.78/1.31 falsehood, Z ) ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4305, [ ~( 'is_a_theorem'( implies( implies( implies( implies( X,
% 0.78/1.31 implies( falsehood, Y ) ), Z ), implies( T, Z ) ), U ) ) ),
% 0.78/1.31 'is_a_theorem'( U ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 7, [ 'is_a_theorem'( implies( implies( implies( X, implies(
% 0.78/1.31 falsehood, Y ) ), Z ), implies( T, Z ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( implies( implies( X, implies(
% 0.78/1.31 falsehood, Y ) ), Z ), implies( T, Z ) ) ), :=( Y, U )] ), substitution(
% 0.78/1.31 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 10, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, implies( falsehood, Y ) ), Z ), implies( T, Z ) ), U
% 0.78/1.31 ) ) ) ] )
% 0.78/1.31 , clause( 4305, [ ~( 'is_a_theorem'( implies( implies( implies( implies( X
% 0.78/1.31 , implies( falsehood, Y ) ), Z ), implies( T, Z ) ), U ) ) ),
% 0.78/1.31 'is_a_theorem'( U ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.78/1.31 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4306, [ 'is_a_theorem'( implies( X, implies( falsehood, Y ) ) ) ]
% 0.78/1.31 )
% 0.78/1.31 , clause( 5, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( implies( X, Y ), implies( Z, Y ) ), implies( Y, T ) ),
% 0.78/1.31 implies( U, implies( Y, T ) ) ), W ) ) ) ] )
% 0.78/1.31 , 1, clause( 8, [ 'is_a_theorem'( implies( X, implies( Y, implies(
% 0.78/1.31 falsehood, Z ) ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, U ), :=( T, W ),
% 0.78/1.31 :=( U, V0 ), :=( W, implies( X, implies( falsehood, Y ) ) )] ),
% 0.78/1.31 substitution( 1, [ :=( X, implies( implies( implies( implies( Z, T ),
% 0.78/1.31 implies( U, T ) ), implies( T, W ) ), implies( V0, implies( T, W ) ) ) )
% 0.78/1.31 , :=( Y, X ), :=( Z, Y )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 11, [ 'is_a_theorem'( implies( X, implies( falsehood, Y ) ) ) ] )
% 0.78/1.31 , clause( 4306, [ 'is_a_theorem'( implies( X, implies( falsehood, Y ) ) ) ]
% 0.78/1.31 )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.78/1.31 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4308, [ ~( 'is_a_theorem'( implies( implies( X, implies( falsehood
% 0.78/1.31 , Y ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 11, [ 'is_a_theorem'( implies( X, implies( falsehood, Y ) ) )
% 0.78/1.31 ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( X, implies( falsehood, Y ) ) ),
% 0.78/1.31 :=( Y, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 14, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( implies( implies( X,
% 0.78/1.31 implies( falsehood, Y ) ), Z ) ) ) ] )
% 0.78/1.31 , clause( 4308, [ ~( 'is_a_theorem'( implies( implies( X, implies(
% 0.78/1.31 falsehood, Y ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4309, [ 'is_a_theorem'( implies( implies( implies( falsehood, X ),
% 0.78/1.31 Y ), implies( Z, Y ) ) ) ] )
% 0.78/1.31 , clause( 14, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( implies( implies( X
% 0.78/1.31 , implies( falsehood, Y ) ), Z ) ) ) ] )
% 0.78/1.31 , 1, clause( 1, [ 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), implies( Z, falsehood ) ), T ), U ), implies( implies( U
% 0.78/1.31 , X ), implies( Z, X ) ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( implies( implies( Y, T ), implies(
% 0.78/1.31 Z, falsehood ) ), U ) ), :=( Y, X ), :=( Z, implies( implies( implies(
% 0.78/1.31 falsehood, X ), Y ), implies( Z, Y ) ) )] ), substitution( 1, [ :=( X, Y
% 0.78/1.31 ), :=( Y, T ), :=( Z, Z ), :=( T, U ), :=( U, implies( falsehood, X ) )] )
% 0.78/1.31 ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 21, [ 'is_a_theorem'( implies( implies( implies( falsehood, X ), Y
% 0.78/1.31 ), implies( Z, Y ) ) ) ] )
% 0.78/1.31 , clause( 4309, [ 'is_a_theorem'( implies( implies( implies( falsehood, X )
% 0.78/1.31 , Y ), implies( Z, Y ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4311, [ ~( 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 falsehood, X ), Y ), implies( Z, Y ) ), T ) ) ), 'is_a_theorem'( T ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 21, [ 'is_a_theorem'( implies( implies( implies( falsehood, X
% 0.78/1.31 ), Y ), implies( Z, Y ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( implies( implies( falsehood, X ), Y
% 0.78/1.31 ), implies( Z, Y ) ) ), :=( Y, T )] ), substitution( 1, [ :=( X, X ),
% 0.78/1.31 :=( Y, Y ), :=( Z, Z )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 22, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( falsehood, X ), Y ), implies( Z, Y ) ), T ) ) ) ] )
% 0.78/1.31 , clause( 4311, [ ~( 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 falsehood, X ), Y ), implies( Z, Y ) ), T ) ) ), 'is_a_theorem'( T ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4312, [ 'is_a_theorem'( implies( X, implies( Y, implies( Z, Y ) ) )
% 0.78/1.31 ) ] )
% 0.78/1.31 , clause( 22, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( falsehood, X ), Y ), implies( Z, Y ) ), T ) ) ) ] )
% 0.78/1.31 , 1, clause( 4, [ 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 0.78/1.31 ), implies( Z, Y ) ), implies( Y, T ) ), implies( U, implies( Y, T ) ) )
% 0.78/1.31 ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, Y ), :=( Y, implies( Z, Y ) ), :=( Z, Y ),
% 0.78/1.31 :=( T, implies( X, implies( Y, implies( Z, Y ) ) ) )] ), substitution( 1
% 0.78/1.31 , [ :=( X, falsehood ), :=( Y, Y ), :=( Z, Z ), :=( T, implies( Z, Y ) )
% 0.78/1.31 , :=( U, X )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 26, [ 'is_a_theorem'( implies( X, implies( Y, implies( Z, Y ) ) ) )
% 0.78/1.31 ] )
% 0.78/1.31 , clause( 4312, [ 'is_a_theorem'( implies( X, implies( Y, implies( Z, Y ) )
% 0.78/1.31 ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4313, [ 'is_a_theorem'( implies( X, implies( Y, X ) ) ) ] )
% 0.78/1.31 , clause( 22, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( falsehood, X ), Y ), implies( Z, Y ) ), T ) ) ) ] )
% 0.78/1.31 , 1, clause( 26, [ 'is_a_theorem'( implies( X, implies( Y, implies( Z, Y )
% 0.78/1.31 ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, U ), :=( T, implies(
% 0.78/1.31 X, implies( Y, X ) ) )] ), substitution( 1, [ :=( X, implies( implies(
% 0.78/1.31 implies( falsehood, Z ), T ), implies( U, T ) ) ), :=( Y, X ), :=( Z, Y )] )
% 0.78/1.31 ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 27, [ 'is_a_theorem'( implies( X, implies( Y, X ) ) ) ] )
% 0.78/1.31 , clause( 4313, [ 'is_a_theorem'( implies( X, implies( Y, X ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.78/1.31 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4314, [ 'is_a_theorem'( implies( X, implies( implies( implies( Y,
% 0.78/1.31 implies( falsehood, Z ) ), T ), implies( U, T ) ) ) ) ] )
% 0.78/1.31 , clause( 10, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, implies( falsehood, Y ) ), Z ), implies( T, Z ) ), U
% 0.78/1.31 ) ) ) ] )
% 0.78/1.31 , 1, clause( 27, [ 'is_a_theorem'( implies( X, implies( Y, X ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, U ),
% 0.78/1.31 :=( U, implies( X, implies( implies( implies( Y, implies( falsehood, Z )
% 0.78/1.31 ), T ), implies( U, T ) ) ) )] ), substitution( 1, [ :=( X, implies(
% 0.78/1.31 implies( implies( Y, implies( falsehood, Z ) ), T ), implies( U, T ) ) )
% 0.78/1.31 , :=( Y, X )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 29, [ 'is_a_theorem'( implies( X, implies( implies( implies( Y,
% 0.78/1.31 implies( falsehood, Z ) ), T ), implies( U, T ) ) ) ) ] )
% 0.78/1.31 , clause( 4314, [ 'is_a_theorem'( implies( X, implies( implies( implies( Y
% 0.78/1.31 , implies( falsehood, Z ) ), T ), implies( U, T ) ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.78/1.31 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4316, [ ~( 'is_a_theorem'( implies( implies( X, implies( Y, X ) ),
% 0.78/1.31 Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 27, [ 'is_a_theorem'( implies( X, implies( Y, X ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( X, implies( Y, X ) ) ), :=( Y, Z )] )
% 0.78/1.31 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 33, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( implies( implies( X,
% 0.78/1.31 implies( Y, X ) ), Z ) ) ) ] )
% 0.78/1.31 , clause( 4316, [ ~( 'is_a_theorem'( implies( implies( X, implies( Y, X ) )
% 0.78/1.31 , Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4317, [ 'is_a_theorem'( implies( implies( implies( X, implies(
% 0.78/1.31 implies( implies( Y, Z ), implies( T, falsehood ) ), U ) ), Y ), implies(
% 0.78/1.31 T, Y ) ) ) ] )
% 0.78/1.31 , clause( 33, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( implies( implies( X
% 0.78/1.31 , implies( Y, X ) ), Z ) ) ) ] )
% 0.78/1.31 , 1, clause( 1, [ 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), implies( Z, falsehood ) ), T ), U ), implies( implies( U
% 0.78/1.31 , X ), implies( Z, X ) ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( implies( implies( Y, Z ), implies(
% 0.78/1.31 T, falsehood ) ), U ) ), :=( Y, X ), :=( Z, implies( implies( implies( X
% 0.78/1.31 , implies( implies( implies( Y, Z ), implies( T, falsehood ) ), U ) ), Y
% 0.78/1.31 ), implies( T, Y ) ) )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z ),
% 0.78/1.31 :=( Z, T ), :=( T, U ), :=( U, implies( X, implies( implies( implies( Y,
% 0.78/1.31 Z ), implies( T, falsehood ) ), U ) ) )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 36, [ 'is_a_theorem'( implies( implies( implies( X, implies(
% 0.78/1.31 implies( implies( Y, Z ), implies( T, falsehood ) ), U ) ), Y ), implies(
% 0.78/1.31 T, Y ) ) ) ] )
% 0.78/1.31 , clause( 4317, [ 'is_a_theorem'( implies( implies( implies( X, implies(
% 0.78/1.31 implies( implies( Y, Z ), implies( T, falsehood ) ), U ) ), Y ), implies(
% 0.78/1.31 T, Y ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.78/1.31 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4319, [ ~( 'is_a_theorem'( implies( implies( X, implies( implies(
% 0.78/1.31 implies( Y, implies( falsehood, Z ) ), T ), implies( U, T ) ) ), W ) ) )
% 0.78/1.31 , 'is_a_theorem'( W ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 29, [ 'is_a_theorem'( implies( X, implies( implies( implies( Y
% 0.78/1.31 , implies( falsehood, Z ) ), T ), implies( U, T ) ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( X, implies( implies( implies( Y,
% 0.78/1.31 implies( falsehood, Z ) ), T ), implies( U, T ) ) ) ), :=( Y, W )] ),
% 0.78/1.31 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.78/1.31 , U )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 56, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( implies( implies( X,
% 0.78/1.31 implies( implies( implies( Y, implies( falsehood, Z ) ), T ), implies( U
% 0.78/1.31 , T ) ) ), W ) ) ) ] )
% 0.78/1.31 , clause( 4319, [ ~( 'is_a_theorem'( implies( implies( X, implies( implies(
% 0.78/1.31 implies( Y, implies( falsehood, Z ) ), T ), implies( U, T ) ) ), W ) ) )
% 0.78/1.31 , 'is_a_theorem'( W ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.78/1.31 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4321, [ ~( 'is_a_theorem'( implies( implies( implies( implies( X,
% 0.78/1.31 implies( implies( implies( Y, Z ), implies( T, falsehood ) ), U ) ), Y )
% 0.78/1.31 , implies( T, Y ) ), W ) ) ), 'is_a_theorem'( W ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 36, [ 'is_a_theorem'( implies( implies( implies( X, implies(
% 0.78/1.31 implies( implies( Y, Z ), implies( T, falsehood ) ), U ) ), Y ), implies(
% 0.78/1.31 T, Y ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( implies( implies( X, implies(
% 0.78/1.31 implies( implies( Y, Z ), implies( T, falsehood ) ), U ) ), Y ), implies(
% 0.78/1.31 T, Y ) ) ), :=( Y, W )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 0.78/1.31 :=( Z, Z ), :=( T, T ), :=( U, U )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 102, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, implies( implies( implies( Y, Z ), implies( T,
% 0.78/1.31 falsehood ) ), U ) ), Y ), implies( T, Y ) ), W ) ) ) ] )
% 0.78/1.31 , clause( 4321, [ ~( 'is_a_theorem'( implies( implies( implies( implies( X
% 0.78/1.31 , implies( implies( implies( Y, Z ), implies( T, falsehood ) ), U ) ), Y
% 0.78/1.31 ), implies( T, Y ) ), W ) ) ), 'is_a_theorem'( W ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.78/1.31 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4322, [ 'is_a_theorem'( implies( X, implies( Y, implies( implies(
% 0.78/1.31 implies( Z, implies( falsehood, T ) ), U ), implies( W, U ) ) ) ) ) ] )
% 0.78/1.31 , clause( 56, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( implies( implies( X
% 0.78/1.31 , implies( implies( implies( Y, implies( falsehood, Z ) ), T ), implies(
% 0.78/1.31 U, T ) ) ), W ) ) ) ] )
% 0.78/1.31 , 1, clause( 27, [ 'is_a_theorem'( implies( X, implies( Y, X ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, U ),
% 0.78/1.31 :=( U, W ), :=( W, implies( X, implies( Y, implies( implies( implies( Z,
% 0.78/1.31 implies( falsehood, T ) ), U ), implies( W, U ) ) ) ) )] ),
% 0.78/1.31 substitution( 1, [ :=( X, implies( Y, implies( implies( implies( Z,
% 0.78/1.31 implies( falsehood, T ) ), U ), implies( W, U ) ) ) ), :=( Y, X )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 124, [ 'is_a_theorem'( implies( X, implies( Y, implies( implies(
% 0.78/1.31 implies( Z, implies( falsehood, T ) ), U ), implies( W, U ) ) ) ) ) ] )
% 0.78/1.31 , clause( 4322, [ 'is_a_theorem'( implies( X, implies( Y, implies( implies(
% 0.78/1.31 implies( Z, implies( falsehood, T ) ), U ), implies( W, U ) ) ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.78/1.31 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4324, [ ~( 'is_a_theorem'( implies( implies( X, implies( Y, implies(
% 0.78/1.31 implies( implies( Z, implies( falsehood, T ) ), U ), implies( W, U ) ) )
% 0.78/1.31 ), V0 ) ) ), 'is_a_theorem'( V0 ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 124, [ 'is_a_theorem'( implies( X, implies( Y, implies(
% 0.78/1.31 implies( implies( Z, implies( falsehood, T ) ), U ), implies( W, U ) ) )
% 0.78/1.31 ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( X, implies( Y, implies( implies(
% 0.78/1.31 implies( Z, implies( falsehood, T ) ), U ), implies( W, U ) ) ) ) ), :=(
% 0.78/1.31 Y, V0 )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T
% 0.78/1.31 , T ), :=( U, U ), :=( W, W )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 126, [ 'is_a_theorem'( V0 ), ~( 'is_a_theorem'( implies( implies( X
% 0.78/1.31 , implies( Y, implies( implies( implies( Z, implies( falsehood, T ) ), U
% 0.78/1.31 ), implies( W, U ) ) ) ), V0 ) ) ) ] )
% 0.78/1.31 , clause( 4324, [ ~( 'is_a_theorem'( implies( implies( X, implies( Y,
% 0.78/1.31 implies( implies( implies( Z, implies( falsehood, T ) ), U ), implies( W
% 0.78/1.31 , U ) ) ) ), V0 ) ) ), 'is_a_theorem'( V0 ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.78/1.31 , U ), :=( W, W ), :=( V0, V0 )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1
% 0.78/1.31 , 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4325, [ 'is_a_theorem'( implies( X, implies( Y, implies( Z, implies(
% 0.78/1.31 implies( implies( T, implies( falsehood, U ) ), W ), implies( V0, W ) ) )
% 0.78/1.31 ) ) ) ] )
% 0.78/1.31 , clause( 126, [ 'is_a_theorem'( V0 ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 X, implies( Y, implies( implies( implies( Z, implies( falsehood, T ) ), U
% 0.78/1.31 ), implies( W, U ) ) ) ), V0 ) ) ) ] )
% 0.78/1.31 , 1, clause( 27, [ 'is_a_theorem'( implies( X, implies( Y, X ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, U ),
% 0.78/1.31 :=( U, W ), :=( W, V0 ), :=( V0, implies( X, implies( Y, implies( Z,
% 0.78/1.31 implies( implies( implies( T, implies( falsehood, U ) ), W ), implies( V0
% 0.78/1.31 , W ) ) ) ) ) )] ), substitution( 1, [ :=( X, implies( Y, implies( Z,
% 0.78/1.31 implies( implies( implies( T, implies( falsehood, U ) ), W ), implies( V0
% 0.78/1.31 , W ) ) ) ) ), :=( Y, X )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 170, [ 'is_a_theorem'( implies( X, implies( Y, implies( Z, implies(
% 0.78/1.31 implies( implies( T, implies( falsehood, U ) ), W ), implies( V0, W ) ) )
% 0.78/1.31 ) ) ) ] )
% 0.78/1.31 , clause( 4325, [ 'is_a_theorem'( implies( X, implies( Y, implies( Z,
% 0.78/1.31 implies( implies( implies( T, implies( falsehood, U ) ), W ), implies( V0
% 0.78/1.31 , W ) ) ) ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.78/1.31 , U ), :=( W, W ), :=( V0, V0 )] ), permutation( 0, [ ==>( 0, 0 )] )
% 0.78/1.31 ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4327, [ ~( 'is_a_theorem'( implies( implies( X, implies( Y, implies(
% 0.78/1.31 Z, implies( implies( implies( T, implies( falsehood, U ) ), W ), implies(
% 0.78/1.31 V0, W ) ) ) ) ), V1 ) ) ), 'is_a_theorem'( V1 ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 170, [ 'is_a_theorem'( implies( X, implies( Y, implies( Z,
% 0.78/1.31 implies( implies( implies( T, implies( falsehood, U ) ), W ), implies( V0
% 0.78/1.31 , W ) ) ) ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( X, implies( Y, implies( Z, implies(
% 0.78/1.31 implies( implies( T, implies( falsehood, U ) ), W ), implies( V0, W ) ) )
% 0.78/1.31 ) ) ), :=( Y, V1 )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z
% 0.78/1.31 , Z ), :=( T, T ), :=( U, U ), :=( W, W ), :=( V0, V0 )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 172, [ 'is_a_theorem'( V1 ), ~( 'is_a_theorem'( implies( implies( X
% 0.78/1.31 , implies( Y, implies( Z, implies( implies( implies( T, implies(
% 0.78/1.31 falsehood, U ) ), W ), implies( V0, W ) ) ) ) ), V1 ) ) ) ] )
% 0.78/1.31 , clause( 4327, [ ~( 'is_a_theorem'( implies( implies( X, implies( Y,
% 0.78/1.31 implies( Z, implies( implies( implies( T, implies( falsehood, U ) ), W )
% 0.78/1.31 , implies( V0, W ) ) ) ) ), V1 ) ) ), 'is_a_theorem'( V1 ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.78/1.31 , U ), :=( W, W ), :=( V0, V0 ), :=( V1, V1 )] ), permutation( 0, [ ==>(
% 0.78/1.31 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4328, [ 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 0.78/1.31 implies( implies( implies( Y, T ), implies( X, falsehood ) ), Z ) ) ) ]
% 0.78/1.31 )
% 0.78/1.31 , clause( 102, [ 'is_a_theorem'( W ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, implies( implies( implies( Y, Z ), implies( T,
% 0.78/1.31 falsehood ) ), U ) ), Y ), implies( T, Y ) ), W ) ) ) ] )
% 0.78/1.31 , 1, clause( 1, [ 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), implies( Z, falsehood ) ), T ), U ), implies( implies( U
% 0.78/1.31 , X ), implies( Z, X ) ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( Z, U ) ), :=( Y, Y ), :=( Z, T ),
% 0.78/1.31 :=( T, X ), :=( U, falsehood ), :=( W, implies( implies( implies( X, Y )
% 0.78/1.31 , Z ), implies( implies( implies( Y, T ), implies( X, falsehood ) ), Z )
% 0.78/1.31 ) )] ), substitution( 1, [ :=( X, Z ), :=( Y, U ), :=( Z, implies(
% 0.78/1.31 implies( Y, T ), implies( X, falsehood ) ) ), :=( T, Y ), :=( U, implies(
% 0.78/1.31 X, Y ) )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 254, [ 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 0.78/1.31 implies( implies( implies( Y, T ), implies( X, falsehood ) ), Z ) ) ) ]
% 0.78/1.31 )
% 0.78/1.31 , clause( 4328, [ 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 0.78/1.31 implies( implies( implies( Y, T ), implies( X, falsehood ) ), Z ) ) ) ]
% 0.78/1.31 )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4329, [ 'is_a_theorem'( implies( implies( implies( X, Y ), implies(
% 0.78/1.31 implies( falsehood, Z ), falsehood ) ), implies( T, X ) ) ) ] )
% 0.78/1.31 , clause( 22, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( falsehood, X ), Y ), implies( Z, Y ) ), T ) ) ) ] )
% 0.78/1.31 , 1, clause( 254, [ 'is_a_theorem'( implies( implies( implies( X, Y ), Z )
% 0.78/1.31 , implies( implies( implies( Y, T ), implies( X, falsehood ) ), Z ) ) ) ]
% 0.78/1.31 )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, T ), :=( T, implies(
% 0.78/1.31 implies( implies( X, Y ), implies( implies( falsehood, Z ), falsehood ) )
% 0.78/1.31 , implies( T, X ) ) )] ), substitution( 1, [ :=( X, implies( falsehood, Z
% 0.78/1.31 ) ), :=( Y, X ), :=( Z, implies( T, X ) ), :=( T, Y )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 270, [ 'is_a_theorem'( implies( implies( implies( X, Y ), implies(
% 0.78/1.31 implies( falsehood, Z ), falsehood ) ), implies( T, X ) ) ) ] )
% 0.78/1.31 , clause( 4329, [ 'is_a_theorem'( implies( implies( implies( X, Y ),
% 0.78/1.31 implies( implies( falsehood, Z ), falsehood ) ), implies( T, X ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4331, [ ~( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 0.78/1.31 ), implies( implies( falsehood, Z ), falsehood ) ), implies( T, X ) ), U
% 0.78/1.31 ) ) ), 'is_a_theorem'( U ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 270, [ 'is_a_theorem'( implies( implies( implies( X, Y ),
% 0.78/1.31 implies( implies( falsehood, Z ), falsehood ) ), implies( T, X ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( implies( implies( X, Y ), implies(
% 0.78/1.31 implies( falsehood, Z ), falsehood ) ), implies( T, X ) ) ), :=( Y, U )] )
% 0.78/1.31 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 0.78/1.31 ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 278, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, Y ), implies( implies( falsehood, Z ), falsehood ) )
% 0.78/1.31 , implies( T, X ) ), U ) ) ) ] )
% 0.78/1.31 , clause( 4331, [ ~( 'is_a_theorem'( implies( implies( implies( implies( X
% 0.78/1.31 , Y ), implies( implies( falsehood, Z ), falsehood ) ), implies( T, X ) )
% 0.78/1.31 , U ) ) ), 'is_a_theorem'( U ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.78/1.31 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4332, [ 'is_a_theorem'( implies( implies( implies( X, implies( Y, Z
% 0.78/1.31 ) ), Y ), implies( T, Y ) ) ) ] )
% 0.78/1.31 , clause( 278, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, Y ), implies( implies( falsehood, Z ), falsehood ) )
% 0.78/1.31 , implies( T, X ) ), U ) ) ) ] )
% 0.78/1.31 , 1, clause( 1, [ 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), implies( Z, falsehood ) ), T ), U ), implies( implies( U
% 0.78/1.31 , X ), implies( Z, X ) ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( Y, Z ) ), :=( Y, implies( T,
% 0.78/1.31 falsehood ) ), :=( Z, U ), :=( T, X ), :=( U, implies( implies( implies(
% 0.78/1.31 X, implies( Y, Z ) ), Y ), implies( T, Y ) ) )] ), substitution( 1, [
% 0.78/1.31 :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, implies( implies( falsehood, U
% 0.78/1.31 ), falsehood ) ), :=( U, implies( X, implies( Y, Z ) ) )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 372, [ 'is_a_theorem'( implies( implies( implies( X, implies( Y, Z
% 0.78/1.31 ) ), Y ), implies( T, Y ) ) ) ] )
% 0.78/1.31 , clause( 4332, [ 'is_a_theorem'( implies( implies( implies( X, implies( Y
% 0.78/1.31 , Z ) ), Y ), implies( T, Y ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4334, [ ~( 'is_a_theorem'( implies( implies( implies( implies( X,
% 0.78/1.31 implies( Y, Z ) ), Y ), implies( T, Y ) ), U ) ) ), 'is_a_theorem'( U ) ]
% 0.78/1.31 )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 372, [ 'is_a_theorem'( implies( implies( implies( X, implies(
% 0.78/1.31 Y, Z ) ), Y ), implies( T, Y ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( implies( implies( X, implies( Y, Z
% 0.78/1.31 ) ), Y ), implies( T, Y ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X,
% 0.78/1.31 X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 373, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, implies( Y, Z ) ), Y ), implies( T, Y ) ), U ) ) ) ]
% 0.78/1.31 )
% 0.78/1.31 , clause( 4334, [ ~( 'is_a_theorem'( implies( implies( implies( implies( X
% 0.78/1.31 , implies( Y, Z ) ), Y ), implies( T, Y ) ), U ) ) ), 'is_a_theorem'( U )
% 0.78/1.31 ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.78/1.31 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4335, [ 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 0.78/1.31 implies( Y, Z ) ) ) ] )
% 0.78/1.31 , clause( 373, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, implies( Y, Z ) ), Y ), implies( T, Y ) ), U ) ) ) ]
% 0.78/1.31 )
% 0.78/1.31 , 1, clause( 1, [ 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), implies( Z, falsehood ) ), T ), U ), implies( implies( U
% 0.78/1.31 , X ), implies( Z, X ) ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( Z, T ) ), :=( Y, Y ), :=( Z,
% 0.78/1.31 falsehood ), :=( T, X ), :=( U, implies( implies( implies( X, Y ), Z ),
% 0.78/1.31 implies( Y, Z ) ) )] ), substitution( 1, [ :=( X, Z ), :=( Y, T ), :=( Z
% 0.78/1.31 , Y ), :=( T, Y ), :=( U, implies( X, Y ) )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 379, [ 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 0.78/1.31 implies( Y, Z ) ) ) ] )
% 0.78/1.31 , clause( 4335, [ 'is_a_theorem'( implies( implies( implies( X, Y ), Z ),
% 0.78/1.31 implies( Y, Z ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4337, [ ~( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 0.78/1.31 ), Z ), implies( Y, Z ) ), T ) ) ), 'is_a_theorem'( T ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 379, [ 'is_a_theorem'( implies( implies( implies( X, Y ), Z )
% 0.78/1.31 , implies( Y, Z ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( implies( implies( X, Y ), Z ),
% 0.78/1.31 implies( Y, Z ) ) ), :=( Y, T )] ), substitution( 1, [ :=( X, X ), :=( Y
% 0.78/1.31 , Y ), :=( Z, Z )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 386, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, Y ), Z ), implies( Y, Z ) ), T ) ) ) ] )
% 0.78/1.31 , clause( 4337, [ ~( 'is_a_theorem'( implies( implies( implies( implies( X
% 0.78/1.31 , Y ), Z ), implies( Y, Z ) ), T ) ) ), 'is_a_theorem'( T ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4338, [ 'is_a_theorem'( implies( implies( implies( implies( X,
% 0.78/1.31 falsehood ), Y ), Z ), implies( X, Z ) ) ) ] )
% 0.78/1.31 , clause( 386, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, Y ), Z ), implies( Y, Z ) ), T ) ) ) ] )
% 0.78/1.31 , 1, clause( 1, [ 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), implies( Z, falsehood ) ), T ), U ), implies( implies( U
% 0.78/1.31 , X ), implies( Z, X ) ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( Z, T ) ), :=( Y, implies( X,
% 0.78/1.31 falsehood ) ), :=( Z, Y ), :=( T, implies( implies( implies( implies( X,
% 0.78/1.31 falsehood ), Y ), Z ), implies( X, Z ) ) )] ), substitution( 1, [ :=( X,
% 0.78/1.31 Z ), :=( Y, T ), :=( Z, X ), :=( T, Y ), :=( U, implies( implies( X,
% 0.78/1.31 falsehood ), Y ) )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 553, [ 'is_a_theorem'( implies( implies( implies( implies( X,
% 0.78/1.31 falsehood ), Y ), Z ), implies( X, Z ) ) ) ] )
% 0.78/1.31 , clause( 4338, [ 'is_a_theorem'( implies( implies( implies( implies( X,
% 0.78/1.31 falsehood ), Y ), Z ), implies( X, Z ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4340, [ ~( 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, falsehood ), Y ), Z ), implies( X, Z ) ), T ) ) ),
% 0.78/1.31 'is_a_theorem'( T ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 553, [ 'is_a_theorem'( implies( implies( implies( implies( X,
% 0.78/1.31 falsehood ), Y ), Z ), implies( X, Z ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( implies( implies( implies( X,
% 0.78/1.31 falsehood ), Y ), Z ), implies( X, Z ) ) ), :=( Y, T )] ), substitution(
% 0.78/1.31 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 558, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( implies( X, falsehood ), Y ), Z ), implies( X, Z ) ), T
% 0.78/1.31 ) ) ) ] )
% 0.78/1.31 , clause( 4340, [ ~( 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, falsehood ), Y ), Z ), implies( X, Z ) ), T ) ) ),
% 0.78/1.31 'is_a_theorem'( T ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4341, [ 'is_a_theorem'( implies( implies( implies( X, Y ), X ),
% 0.78/1.31 implies( Z, X ) ) ) ] )
% 0.78/1.31 , clause( 558, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( implies( X, falsehood ), Y ), Z ), implies( X, Z ) ), T
% 0.78/1.31 ) ) ) ] )
% 0.78/1.31 , 1, clause( 1, [ 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), implies( Z, falsehood ) ), T ), U ), implies( implies( U
% 0.78/1.31 , X ), implies( Z, X ) ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, X ), :=( Y, implies( Z, falsehood ) ), :=( Z
% 0.78/1.31 , Y ), :=( T, implies( implies( implies( X, Y ), X ), implies( Z, X ) ) )] )
% 0.78/1.31 , substitution( 1, [ :=( X, X ), :=( Y, falsehood ), :=( Z, Z ), :=( T, Y
% 0.78/1.31 ), :=( U, implies( X, Y ) )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 1464, [ 'is_a_theorem'( implies( implies( implies( X, Y ), X ),
% 0.78/1.31 implies( Z, X ) ) ) ] )
% 0.78/1.31 , clause( 4341, [ 'is_a_theorem'( implies( implies( implies( X, Y ), X ),
% 0.78/1.31 implies( Z, X ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4342, [ 'is_a_theorem'( implies( X, implies( Y, Y ) ) ) ] )
% 0.78/1.31 , clause( 386, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, Y ), Z ), implies( Y, Z ) ), T ) ) ) ] )
% 0.78/1.31 , 1, clause( 1464, [ 'is_a_theorem'( implies( implies( implies( X, Y ), X )
% 0.78/1.31 , implies( Z, X ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Y ), :=( Z, Y ), :=( T, implies(
% 0.78/1.31 X, implies( Y, Y ) ) )] ), substitution( 1, [ :=( X, implies( Y, Y ) ),
% 0.78/1.31 :=( Y, Y ), :=( Z, X )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 1466, [ 'is_a_theorem'( implies( X, implies( Y, Y ) ) ) ] )
% 0.78/1.31 , clause( 4342, [ 'is_a_theorem'( implies( X, implies( Y, Y ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.78/1.31 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4344, [ ~( 'is_a_theorem'( implies( implies( implies( implies( X, Y
% 0.78/1.31 ), X ), implies( Z, X ) ), T ) ) ), 'is_a_theorem'( T ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 1464, [ 'is_a_theorem'( implies( implies( implies( X, Y ), X )
% 0.78/1.31 , implies( Z, X ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( implies( implies( X, Y ), X ),
% 0.78/1.31 implies( Z, X ) ) ), :=( Y, T )] ), substitution( 1, [ :=( X, X ), :=( Y
% 0.78/1.31 , Y ), :=( Z, Z )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 1468, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, Y ), X ), implies( Z, X ) ), T ) ) ) ] )
% 0.78/1.31 , clause( 4344, [ ~( 'is_a_theorem'( implies( implies( implies( implies( X
% 0.78/1.31 , Y ), X ), implies( Z, X ) ), T ) ) ), 'is_a_theorem'( T ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4345, [ 'is_a_theorem'( implies( X, X ) ) ] )
% 0.78/1.31 , clause( 172, [ 'is_a_theorem'( V1 ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 X, implies( Y, implies( Z, implies( implies( implies( T, implies(
% 0.78/1.31 falsehood, U ) ), W ), implies( V0, W ) ) ) ) ), V1 ) ) ) ] )
% 0.78/1.31 , 1, clause( 1466, [ 'is_a_theorem'( implies( X, implies( Y, Y ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, U ),
% 0.78/1.31 :=( U, W ), :=( W, V0 ), :=( V0, V1 ), :=( V1, implies( X, X ) )] ),
% 0.78/1.31 substitution( 1, [ :=( X, implies( Y, implies( Z, implies( T, implies(
% 0.78/1.31 implies( implies( U, implies( falsehood, W ) ), V0 ), implies( V1, V0 ) )
% 0.78/1.31 ) ) ) ), :=( Y, X )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 1479, [ 'is_a_theorem'( implies( X, X ) ) ] )
% 0.78/1.31 , clause( 4345, [ 'is_a_theorem'( implies( X, X ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4347, [ ~( 'is_a_theorem'( implies( implies( X, X ), Y ) ) ),
% 0.78/1.31 'is_a_theorem'( Y ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 1479, [ 'is_a_theorem'( implies( X, X ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( X, X ) ), :=( Y, Y )] ),
% 0.78/1.31 substitution( 1, [ :=( X, X )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 1481, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( implies( implies( X
% 0.78/1.31 , X ), Y ) ) ) ] )
% 0.78/1.31 , clause( 4347, [ ~( 'is_a_theorem'( implies( implies( X, X ), Y ) ) ),
% 0.78/1.31 'is_a_theorem'( Y ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 0.78/1.31 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4348, [ 'is_a_theorem'( implies( X, implies( implies( X, falsehood
% 0.78/1.31 ), Y ) ) ) ] )
% 0.78/1.31 , clause( 1481, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 X, X ), Y ) ) ) ] )
% 0.78/1.31 , 1, clause( 553, [ 'is_a_theorem'( implies( implies( implies( implies( X,
% 0.78/1.31 falsehood ), Y ), Z ), implies( X, Z ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( implies( X, falsehood ), Y ) ),
% 0.78/1.31 :=( Y, implies( X, implies( implies( X, falsehood ), Y ) ) )] ),
% 0.78/1.31 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( implies( X,
% 0.78/1.31 falsehood ), Y ) )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 1494, [ 'is_a_theorem'( implies( X, implies( implies( X, falsehood
% 0.78/1.31 ), Y ) ) ) ] )
% 0.78/1.31 , clause( 4348, [ 'is_a_theorem'( implies( X, implies( implies( X,
% 0.78/1.31 falsehood ), Y ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.78/1.31 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4349, [ 'is_a_theorem'( implies( implies( implies( X, Y ), implies(
% 0.78/1.31 Z, falsehood ) ), implies( Z, X ) ) ) ] )
% 0.78/1.31 , clause( 1481, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 X, X ), Y ) ) ) ] )
% 0.78/1.31 , 1, clause( 254, [ 'is_a_theorem'( implies( implies( implies( X, Y ), Z )
% 0.78/1.31 , implies( implies( implies( Y, T ), implies( X, falsehood ) ), Z ) ) ) ]
% 0.78/1.31 )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( Z, X ) ), :=( Y, implies( implies(
% 0.78/1.31 implies( X, Y ), implies( Z, falsehood ) ), implies( Z, X ) ) )] ),
% 0.78/1.31 substitution( 1, [ :=( X, Z ), :=( Y, X ), :=( Z, implies( Z, X ) ), :=(
% 0.78/1.31 T, Y )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 1499, [ 'is_a_theorem'( implies( implies( implies( X, Y ), implies(
% 0.78/1.31 Z, falsehood ) ), implies( Z, X ) ) ) ] )
% 0.78/1.31 , clause( 4349, [ 'is_a_theorem'( implies( implies( implies( X, Y ),
% 0.78/1.31 implies( Z, falsehood ) ), implies( Z, X ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4351, [ ~( 'is_a_theorem'( implies( implies( X, implies( implies( X
% 0.78/1.31 , falsehood ), Y ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 1494, [ 'is_a_theorem'( implies( X, implies( implies( X,
% 0.78/1.31 falsehood ), Y ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( X, implies( implies( X, falsehood )
% 0.78/1.31 , Y ) ) ), :=( Y, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 0.78/1.31 ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 1554, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( implies( implies( X
% 0.78/1.31 , implies( implies( X, falsehood ), Y ) ), Z ) ) ) ] )
% 0.78/1.31 , clause( 4351, [ ~( 'is_a_theorem'( implies( implies( X, implies( implies(
% 0.78/1.31 X, falsehood ), Y ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4352, [ 'is_a_theorem'( implies( X, implies( implies( implies(
% 0.78/1.31 implies( X, falsehood ), Y ), falsehood ), Z ) ) ) ] )
% 0.78/1.31 , clause( 1554, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 X, implies( implies( X, falsehood ), Y ) ), Z ) ) ) ] )
% 0.78/1.31 , 1, clause( 553, [ 'is_a_theorem'( implies( implies( implies( implies( X,
% 0.78/1.31 falsehood ), Y ), Z ), implies( X, Z ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( implies( X, falsehood ), Y ) ),
% 0.78/1.31 :=( Y, Z ), :=( Z, implies( X, implies( implies( implies( implies( X,
% 0.78/1.31 falsehood ), Y ), falsehood ), Z ) ) )] ), substitution( 1, [ :=( X, X )
% 0.78/1.31 , :=( Y, Y ), :=( Z, implies( implies( implies( implies( X, falsehood ),
% 0.78/1.31 Y ), falsehood ), Z ) )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 1785, [ 'is_a_theorem'( implies( X, implies( implies( implies(
% 0.78/1.31 implies( X, falsehood ), Y ), falsehood ), Z ) ) ) ] )
% 0.78/1.31 , clause( 4352, [ 'is_a_theorem'( implies( X, implies( implies( implies(
% 0.78/1.31 implies( X, falsehood ), Y ), falsehood ), Z ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4354, [ ~( 'is_a_theorem'( implies( implies( X, implies( implies(
% 0.78/1.31 implies( implies( X, falsehood ), Y ), falsehood ), Z ) ), T ) ) ),
% 0.78/1.31 'is_a_theorem'( T ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 1785, [ 'is_a_theorem'( implies( X, implies( implies( implies(
% 0.78/1.31 implies( X, falsehood ), Y ), falsehood ), Z ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( X, implies( implies( implies(
% 0.78/1.31 implies( X, falsehood ), Y ), falsehood ), Z ) ) ), :=( Y, T )] ),
% 0.78/1.31 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 1872, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies( X
% 0.78/1.31 , implies( implies( implies( implies( X, falsehood ), Y ), falsehood ), Z
% 0.78/1.31 ) ), T ) ) ) ] )
% 0.78/1.31 , clause( 4354, [ ~( 'is_a_theorem'( implies( implies( X, implies( implies(
% 0.78/1.31 implies( implies( X, falsehood ), Y ), falsehood ), Z ) ), T ) ) ),
% 0.78/1.31 'is_a_theorem'( T ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4355, [ 'is_a_theorem'( implies( implies( implies( implies( implies(
% 0.78/1.31 X, Y ), falsehood ), Z ), falsehood ), X ) ) ] )
% 0.78/1.31 , clause( 1872, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 X, implies( implies( implies( implies( X, falsehood ), Y ), falsehood ),
% 0.78/1.31 Z ) ), T ) ) ) ] )
% 0.78/1.31 , 1, clause( 1499, [ 'is_a_theorem'( implies( implies( implies( X, Y ),
% 0.78/1.31 implies( Z, falsehood ) ), implies( Z, X ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( X, Y ) ), :=( Y, Z ), :=( Z,
% 0.78/1.31 falsehood ), :=( T, implies( implies( implies( implies( implies( X, Y ),
% 0.78/1.31 falsehood ), Z ), falsehood ), X ) )] ), substitution( 1, [ :=( X, X ),
% 0.78/1.31 :=( Y, Y ), :=( Z, implies( implies( implies( implies( X, Y ), falsehood
% 0.78/1.31 ), Z ), falsehood ) )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 3984, [ 'is_a_theorem'( implies( implies( implies( implies( implies(
% 0.78/1.31 X, Y ), falsehood ), Z ), falsehood ), X ) ) ] )
% 0.78/1.31 , clause( 4355, [ 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), falsehood ), Z ), falsehood ), X ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4357, [ ~( 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( implies( X, Y ), falsehood ), Z ), falsehood ), X ), T ) ) ),
% 0.78/1.31 'is_a_theorem'( T ) ] )
% 0.78/1.31 , clause( 0, [ ~( 'is_a_theorem'( implies( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.78/1.31 , ~( 'is_a_theorem'( X ) ) ] )
% 0.78/1.31 , 2, clause( 3984, [ 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), falsehood ), Z ), falsehood ), X ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, implies( implies( implies( implies( implies(
% 0.78/1.31 X, Y ), falsehood ), Z ), falsehood ), X ) ), :=( Y, T )] ),
% 0.78/1.31 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 4011, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( implies( implies( X, Y ), falsehood ), Z ), falsehood )
% 0.78/1.31 , X ), T ) ) ) ] )
% 0.78/1.31 , clause( 4357, [ ~( 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( implies( X, Y ), falsehood ), Z ), falsehood ), X ), T ) ) ),
% 0.78/1.31 'is_a_theorem'( T ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4358, [ 'is_a_theorem'( implies( implies( X, implies( X, Y ) ),
% 0.78/1.31 implies( Z, implies( X, Y ) ) ) ) ] )
% 0.78/1.31 , clause( 4011, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( implies( implies( X, Y ), falsehood ), Z ), falsehood )
% 0.78/1.31 , X ), T ) ) ) ] )
% 0.78/1.31 , 1, clause( 1, [ 'is_a_theorem'( implies( implies( implies( implies(
% 0.78/1.31 implies( X, Y ), implies( Z, falsehood ) ), T ), U ), implies( implies( U
% 0.78/1.31 , X ), implies( Z, X ) ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( Z,
% 0.78/1.31 falsehood ) ), :=( T, implies( implies( X, implies( X, Y ) ), implies( Z
% 0.78/1.31 , implies( X, Y ) ) ) )] ), substitution( 1, [ :=( X, implies( X, Y ) ),
% 0.78/1.31 :=( Y, falsehood ), :=( Z, Z ), :=( T, falsehood ), :=( U, X )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 4258, [ 'is_a_theorem'( implies( implies( X, implies( X, Y ) ),
% 0.78/1.31 implies( Z, implies( X, Y ) ) ) ) ] )
% 0.78/1.31 , clause( 4358, [ 'is_a_theorem'( implies( implies( X, implies( X, Y ) ),
% 0.78/1.31 implies( Z, implies( X, Y ) ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4359, [ 'is_a_theorem'( implies( X, implies( implies( implies( Y, Z
% 0.78/1.31 ), Y ), Y ) ) ) ] )
% 0.78/1.31 , clause( 1468, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( X, Y ), X ), implies( Z, X ) ), T ) ) ) ] )
% 0.78/1.31 , 1, clause( 4258, [ 'is_a_theorem'( implies( implies( X, implies( X, Y ) )
% 0.78/1.31 , implies( Z, implies( X, Y ) ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, implies( implies( Y
% 0.78/1.31 , Z ), Y ) ), :=( T, implies( X, implies( implies( implies( Y, Z ), Y ),
% 0.78/1.31 Y ) ) )] ), substitution( 1, [ :=( X, implies( implies( Y, Z ), Y ) ),
% 0.78/1.31 :=( Y, Y ), :=( Z, X )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 4265, [ 'is_a_theorem'( implies( X, implies( implies( implies( Y, Z
% 0.78/1.31 ), Y ), Y ) ) ) ] )
% 0.78/1.31 , clause( 4359, [ 'is_a_theorem'( implies( X, implies( implies( implies( Y
% 0.78/1.31 , Z ), Y ), Y ) ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.78/1.31 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4360, [ 'is_a_theorem'( implies( implies( implies( X, Y ), X ), X )
% 0.78/1.31 ) ] )
% 0.78/1.31 , clause( 4011, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( implies( implies(
% 0.78/1.31 implies( implies( implies( implies( X, Y ), falsehood ), Z ), falsehood )
% 0.78/1.31 , X ), T ) ) ) ] )
% 0.78/1.31 , 1, clause( 4265, [ 'is_a_theorem'( implies( X, implies( implies( implies(
% 0.78/1.31 Y, Z ), Y ), Y ) ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, U ), :=( T, implies(
% 0.78/1.31 implies( implies( X, Y ), X ), X ) )] ), substitution( 1, [ :=( X,
% 0.78/1.31 implies( implies( implies( implies( implies( Z, T ), falsehood ), U ),
% 0.78/1.31 falsehood ), Z ) ), :=( Y, X ), :=( Z, Y )] )).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 4289, [ 'is_a_theorem'( implies( implies( implies( X, Y ), X ), X )
% 0.78/1.31 ) ] )
% 0.78/1.31 , clause( 4360, [ 'is_a_theorem'( implies( implies( implies( X, Y ), X ), X
% 0.78/1.31 ) ) ] )
% 0.78/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.78/1.31 )] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 resolution(
% 0.78/1.31 clause( 4361, [] )
% 0.78/1.31 , clause( 2, [ ~( 'is_a_theorem'( implies( implies( implies( a, b ), a ), a
% 0.78/1.31 ) ) ) ] )
% 0.78/1.31 , 0, clause( 4289, [ 'is_a_theorem'( implies( implies( implies( X, Y ), X )
% 0.78/1.31 , X ) ) ] )
% 0.78/1.31 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, b )] )
% 0.78/1.31 ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 subsumption(
% 0.78/1.31 clause( 4292, [] )
% 0.78/1.31 , clause( 4361, [] )
% 0.78/1.31 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 end.
% 0.78/1.31
% 0.78/1.31 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.78/1.31
% 0.78/1.31 Memory use:
% 0.78/1.31
% 0.78/1.31 space for terms: 100906
% 0.78/1.31 space for clauses: 478582
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 clauses generated: 44309
% 0.78/1.31 clauses kept: 4293
% 0.78/1.31 clauses selected: 603
% 0.78/1.31 clauses deleted: 120
% 0.78/1.31 clauses inuse deleted: 28
% 0.78/1.31
% 0.78/1.31 subsentry: 41175
% 0.78/1.31 literals s-matched: 40137
% 0.78/1.31 literals matched: 40137
% 0.78/1.31 full subsumption: 0
% 0.78/1.31
% 0.78/1.31 checksum: -1254507716
% 0.78/1.31
% 0.78/1.31
% 0.78/1.31 Bliksem ended
%------------------------------------------------------------------------------