TSTP Solution File: LCL104-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL104-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n028.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 07:50:21 EDT 2022
% Result : Unsatisfiable 0.71s 1.09s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL104-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Mon Jul 4 04:03:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.71/1.09 *** allocated 10000 integers for termspace/termends
% 0.71/1.09 *** allocated 10000 integers for clauses
% 0.71/1.09 *** allocated 10000 integers for justifications
% 0.71/1.09 Bliksem 1.12
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 Automatic Strategy Selection
% 0.71/1.09
% 0.71/1.09 Clauses:
% 0.71/1.09 [
% 0.71/1.09 [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~( 'is_a_theorem'( X ) ),
% 0.71/1.09 'is_a_theorem'( Y ) ],
% 0.71/1.09 [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( Y, Z ), equivalent( Y, T ) ), equivalent( Z, T ) ), X ) ) ) ]
% 0.71/1.09 ,
% 0.71/1.09 [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Y, X ), Z ) ), Z ) ) ],
% 0.71/1.09 [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a, b ), c ),
% 0.71/1.09 equivalent( equivalent( e, b ), equivalent( equivalent( a, e ), c ) ) ) )
% 0.71/1.09 ) ]
% 0.71/1.09 ] .
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 percentage equality = 0.000000, percentage horn = 1.000000
% 0.71/1.09 This is a near-Horn, non-equality problem
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 Options Used:
% 0.71/1.09
% 0.71/1.09 useres = 1
% 0.71/1.09 useparamod = 0
% 0.71/1.09 useeqrefl = 0
% 0.71/1.09 useeqfact = 0
% 0.71/1.09 usefactor = 1
% 0.71/1.09 usesimpsplitting = 0
% 0.71/1.09 usesimpdemod = 0
% 0.71/1.09 usesimpres = 4
% 0.71/1.09
% 0.71/1.09 resimpinuse = 1000
% 0.71/1.09 resimpclauses = 20000
% 0.71/1.09 substype = standard
% 0.71/1.09 backwardsubs = 1
% 0.71/1.09 selectoldest = 5
% 0.71/1.09
% 0.71/1.09 litorderings [0] = split
% 0.71/1.09 litorderings [1] = liftord
% 0.71/1.09
% 0.71/1.09 termordering = none
% 0.71/1.09
% 0.71/1.09 litapriori = 1
% 0.71/1.09 termapriori = 0
% 0.71/1.09 litaposteriori = 0
% 0.71/1.09 termaposteriori = 0
% 0.71/1.09 demodaposteriori = 0
% 0.71/1.09 ordereqreflfact = 0
% 0.71/1.09
% 0.71/1.09 litselect = negative
% 0.71/1.09
% 0.71/1.09 maxweight = 30000
% 0.71/1.09 maxdepth = 30000
% 0.71/1.09 maxlength = 115
% 0.71/1.09 maxnrvars = 195
% 0.71/1.09 excuselevel = 0
% 0.71/1.09 increasemaxweight = 0
% 0.71/1.09
% 0.71/1.09 maxselected = 10000000
% 0.71/1.09 maxnrclauses = 10000000
% 0.71/1.09
% 0.71/1.09 showgenerated = 0
% 0.71/1.09 showkept = 0
% 0.71/1.09 showselected = 0
% 0.71/1.09 showdeleted = 0
% 0.71/1.09 showresimp = 1
% 0.71/1.09 showstatus = 2000
% 0.71/1.09
% 0.71/1.09 prologoutput = 1
% 0.71/1.09 nrgoals = 5000000
% 0.71/1.09 totalproof = 1
% 0.71/1.09
% 0.71/1.09 Symbols occurring in the translation:
% 0.71/1.09
% 0.71/1.09 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.71/1.09 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.71/1.09 ! [4, 1] (w:1, o:17, a:1, s:1, b:0),
% 0.71/1.09 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.09 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.09 equivalent [41, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.71/1.09 'is_a_theorem' [42, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.71/1.09 a [45, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.71/1.09 b [46, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.71/1.09 c [47, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.71/1.09 e [48, 0] (w:1, o:16, a:1, s:1, b:0).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 Starting Search:
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 Bliksems!, er is een bewijs:
% 0.71/1.09 % SZS status Unsatisfiable
% 0.71/1.09 % SZS output start Refutation
% 0.71/1.09
% 0.71/1.09 clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.71/1.09 , ~( 'is_a_theorem'( X ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 1, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 0.71/1.09 equivalent( equivalent( Y, Z ), equivalent( Y, T ) ), equivalent( Z, T )
% 0.71/1.09 ), X ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 2, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.09 equivalent( equivalent( Y, X ), Z ) ), Z ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 3, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a, b )
% 0.71/1.09 , c ), equivalent( equivalent( e, b ), equivalent( equivalent( a, e ), c
% 0.71/1.09 ) ) ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 4, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.71/1.09 equivalent( equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ), Z
% 0.71/1.09 ), T ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 5, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.71/1.09 X, equivalent( equivalent( equivalent( equivalent( Y, Z ), equivalent( Y
% 0.71/1.09 , T ) ), equivalent( Z, T ) ), X ) ), U ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, X ), equivalent( Z, Y ) ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 10, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ), equivalent(
% 0.71/1.09 X, T ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 11, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 0.71/1.09 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 12, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( equivalent( Z, X ), equivalent( Z, Y ) )
% 0.71/1.09 ), T ), T ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 17, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, X ), equivalent( Z, Y ) ) ), T ), T ), U ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 22, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 0.71/1.09 ), equivalent( X, equivalent( equivalent( T, Y ), equivalent( T, Z ) ) )
% 0.71/1.09 ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 23, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, equivalent( T, X ) ), equivalent( Z, equivalent( T, Y ) )
% 0.71/1.09 ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 28, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.71/1.09 equivalent( Z, T ) ) ), equivalent( X, equivalent( Y, equivalent(
% 0.71/1.09 equivalent( U, Z ), equivalent( U, T ) ) ) ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 30, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.71/1.09 equivalent( equivalent( Z, T ), equivalent( equivalent( T, Z ), U ) ) ) )
% 0.71/1.09 , equivalent( X, equivalent( Y, U ) ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 33, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, X ), equivalent( equivalent( T, Z ), equivalent( T, Y ) )
% 0.71/1.09 ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 37, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 0.71/1.09 ), equivalent( equivalent( T, X ), equivalent( T, equivalent( equivalent(
% 0.71/1.09 U, Y ), equivalent( U, Z ) ) ) ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 64, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( Y, Z ), T ) ), equivalent( equivalent( equivalent( Z, Y ), X
% 0.71/1.09 ), T ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 67, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.09 equivalent( X, Z ) ), equivalent( Y, Z ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 78, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 0.71/1.09 equivalent( Y, Z ) ), T ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 85, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( Y, Z ), equivalent( Y, T ) ) ), equivalent( X, equivalent(
% 0.71/1.09 equivalent( U, Z ), equivalent( U, T ) ) ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 121, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( U
% 0.71/1.09 , equivalent( Y, Z ) ), equivalent( U, T ) ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 125, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( equivalent( Y, Z ), equivalent( Y, T ) ), U ) ), equivalent(
% 0.71/1.09 X, equivalent( equivalent( Z, T ), U ) ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 169, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.09 Z ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T ), Z )
% 0.71/1.09 ) ) ) ] )
% 0.71/1.09 .
% 0.71/1.09 clause( 184, [] )
% 0.71/1.09 .
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 % SZS output end Refutation
% 0.71/1.09 found a proof!
% 0.71/1.09
% 0.71/1.09 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.71/1.09
% 0.71/1.09 initialclauses(
% 0.71/1.09 [ clause( 186, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~(
% 0.71/1.09 'is_a_theorem'( X ) ), 'is_a_theorem'( Y ) ] )
% 0.71/1.09 , clause( 187, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 0.71/1.09 equivalent( equivalent( Y, Z ), equivalent( Y, T ) ), equivalent( Z, T )
% 0.71/1.09 ), X ) ) ) ] )
% 0.71/1.09 , clause( 188, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.71/1.09 , equivalent( equivalent( Y, X ), Z ) ), Z ) ) ] )
% 0.71/1.09 , clause( 189, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a,
% 0.71/1.09 b ), c ), equivalent( equivalent( e, b ), equivalent( equivalent( a, e )
% 0.71/1.09 , c ) ) ) ) ) ] )
% 0.71/1.09 ] ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.71/1.09 , ~( 'is_a_theorem'( X ) ) ] )
% 0.71/1.09 , clause( 186, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~(
% 0.71/1.09 'is_a_theorem'( X ) ), 'is_a_theorem'( Y ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.09 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 1, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 0.71/1.09 equivalent( equivalent( Y, Z ), equivalent( Y, T ) ), equivalent( Z, T )
% 0.71/1.09 ), X ) ) ) ] )
% 0.71/1.09 , clause( 187, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 0.71/1.09 equivalent( equivalent( Y, Z ), equivalent( Y, T ) ), equivalent( Z, T )
% 0.71/1.09 ), X ) ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.71/1.09 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 2, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.09 equivalent( equivalent( Y, X ), Z ) ), Z ) ) ] )
% 0.71/1.09 , clause( 188, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.71/1.09 , equivalent( equivalent( Y, X ), Z ) ), Z ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.71/1.09 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 3, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a, b )
% 0.71/1.09 , c ), equivalent( equivalent( e, b ), equivalent( equivalent( a, e ), c
% 0.71/1.09 ) ) ) ) ) ] )
% 0.71/1.09 , clause( 189, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a,
% 0.71/1.09 b ), c ), equivalent( equivalent( e, b ), equivalent( equivalent( a, e )
% 0.71/1.09 , c ) ) ) ) ) ] )
% 0.71/1.09 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 191, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ), Z ), T ) ) ),
% 0.71/1.09 'is_a_theorem'( T ) ] )
% 0.71/1.09 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.71/1.09 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.71/1.09 , 2, clause( 2, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.71/1.09 ), equivalent( equivalent( Y, X ), Z ) ), Z ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.09 equivalent( equivalent( Y, X ), Z ) ), Z ) ), :=( Y, T )] ),
% 0.71/1.09 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 4, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.71/1.09 equivalent( equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ), Z
% 0.71/1.09 ), T ) ) ) ] )
% 0.71/1.09 , clause( 191, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( equivalent( Y, X ), Z ) ), Z ), T ) ) ),
% 0.71/1.09 'is_a_theorem'( T ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.71/1.09 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 193, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( equivalent( equivalent( Y, Z ), equivalent( Y, T ) ),
% 0.71/1.09 equivalent( Z, T ) ), X ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.71/1.09 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.71/1.09 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.71/1.09 , 2, clause( 1, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent(
% 0.71/1.09 equivalent( equivalent( Y, Z ), equivalent( Y, T ) ), equivalent( Z, T )
% 0.71/1.09 ), X ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( equivalent(
% 0.71/1.09 equivalent( equivalent( Y, Z ), equivalent( Y, T ) ), equivalent( Z, T )
% 0.71/1.09 ), X ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 0.71/1.09 :=( Z, Z ), :=( T, T )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 5, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.71/1.09 X, equivalent( equivalent( equivalent( equivalent( Y, Z ), equivalent( Y
% 0.71/1.09 , T ) ), equivalent( Z, T ) ), X ) ), U ) ) ) ] )
% 0.71/1.09 , clause( 193, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( equivalent( equivalent( Y, Z ), equivalent( Y, T ) ),
% 0.71/1.09 equivalent( Z, T ) ), X ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.71/1.09 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 194, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, X ), equivalent( Z, Y ) ) ) ) ] )
% 0.71/1.09 , clause( 5, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( X, equivalent( equivalent( equivalent( equivalent( Y, Z ),
% 0.71/1.09 equivalent( Y, T ) ), equivalent( Z, T ) ), X ) ), U ) ) ) ] )
% 0.71/1.09 , 1, clause( 2, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.71/1.09 ), equivalent( equivalent( Y, X ), Z ) ), Z ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, X ), equivalent( Z, Y ) ) ) ), :=( Y, Z ), :=( Z, X ),
% 0.71/1.09 :=( T, Y ), :=( U, equivalent( equivalent( X, Y ), equivalent( equivalent(
% 0.71/1.09 Z, X ), equivalent( Z, Y ) ) ) )] ), substitution( 1, [ :=( X, equivalent(
% 0.71/1.09 X, Y ) ), :=( Y, equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ),
% 0.71/1.09 :=( Z, equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 0.71/1.09 equivalent( Z, Y ) ) ) )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, X ), equivalent( Z, Y ) ) ) ) ] )
% 0.71/1.09 , clause( 194, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, X ), equivalent( Z, Y ) ) ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.71/1.09 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 195, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ), equivalent(
% 0.71/1.09 X, T ) ) ) ] )
% 0.71/1.09 , clause( 4, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( equivalent( X, Y ), equivalent( equivalent( Y, X
% 0.71/1.09 ), Z ) ), Z ), T ) ) ) ] )
% 0.71/1.09 , 1, clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.71/1.09 equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T,
% 0.71/1.09 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), equivalent(
% 0.71/1.09 equivalent( Z, Y ), T ) ) ), equivalent( X, T ) ) )] ), substitution( 1
% 0.71/1.09 , [ :=( X, equivalent( equivalent( Y, Z ), equivalent( equivalent( Z, Y )
% 0.71/1.09 , T ) ) ), :=( Y, T ), :=( Z, X )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 10, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ), equivalent(
% 0.71/1.09 X, T ) ) ) ] )
% 0.71/1.09 , clause( 195, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ), equivalent(
% 0.71/1.09 X, T ) ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.71/1.09 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 197, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.71/1.09 ), equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ), T ) ) ),
% 0.71/1.09 'is_a_theorem'( T ) ] )
% 0.71/1.09 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.71/1.09 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.71/1.09 , 2, clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.71/1.09 equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, X ), equivalent( Z, Y ) ) ) ), :=( Y, T )] ),
% 0.71/1.09 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 11, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 0.71/1.09 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 0.71/1.09 , clause( 197, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.71/1.09 Y ), equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ), T ) ) ),
% 0.71/1.09 'is_a_theorem'( T ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.71/1.09 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 198, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( equivalent( Z, X ), equivalent( Z, Y ) )
% 0.71/1.09 ), T ), T ) ) ] )
% 0.71/1.09 , clause( 5, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( X, equivalent( equivalent( equivalent( equivalent( Y, Z ),
% 0.71/1.09 equivalent( Y, T ) ), equivalent( Z, T ) ), X ) ), U ) ) ) ] )
% 0.71/1.09 , 1, clause( 10, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( Y, Z ), equivalent( equivalent( Z, Y ), T ) ) ), equivalent(
% 0.71/1.09 X, T ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.09 equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) ), T ) ), :=( Y, Z )
% 0.71/1.09 , :=( Z, X ), :=( T, Y ), :=( U, equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( equivalent( Z, X ), equivalent( Z, Y ) )
% 0.71/1.09 ), T ), T ) )] ), substitution( 1, [ :=( X, equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( equivalent( Z, X ), equivalent( Z, Y ) )
% 0.71/1.09 ), T ) ), :=( Y, equivalent( equivalent( Z, X ), equivalent( Z, Y ) ) )
% 0.71/1.09 , :=( Z, equivalent( X, Y ) ), :=( T, T )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 12, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( equivalent( Z, X ), equivalent( Z, Y ) )
% 0.71/1.09 ), T ), T ) ) ] )
% 0.71/1.09 , clause( 198, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( equivalent( Z, X ), equivalent( Z, Y ) )
% 0.71/1.09 ), T ), T ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.71/1.09 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 200, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 0.71/1.09 equivalent( Z, Y ) ) ), T ), T ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.71/1.09 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.71/1.09 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.71/1.09 , 2, clause( 12, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( equivalent( Z, X ), equivalent( Z, Y ) )
% 0.71/1.09 ), T ), T ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( equivalent( Z, X ), equivalent( Z, Y ) )
% 0.71/1.09 ), T ), T ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )
% 0.71/1.09 , :=( Z, Z ), :=( T, T )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 17, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, X ), equivalent( Z, Y ) ) ), T ), T ), U ) ) ) ] )
% 0.71/1.09 , clause( 200, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 0.71/1.09 equivalent( Z, Y ) ) ), T ), T ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.71/1.09 , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 201, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.71/1.09 ) ), equivalent( X, equivalent( equivalent( T, Y ), equivalent( T, Z ) )
% 0.71/1.09 ) ) ) ] )
% 0.71/1.09 , clause( 11, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 0.71/1.09 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 0.71/1.09 , 1, clause( 12, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( equivalent( Z, X ), equivalent( Z, Y ) )
% 0.71/1.09 ), T ), T ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, equivalent( Y, Z ) ), :=( Y, equivalent(
% 0.71/1.09 equivalent( T, Y ), equivalent( T, Z ) ) ), :=( Z, X ), :=( T, equivalent(
% 0.71/1.09 equivalent( X, equivalent( Y, Z ) ), equivalent( X, equivalent(
% 0.71/1.09 equivalent( T, Y ), equivalent( T, Z ) ) ) ) )] ), substitution( 1, [
% 0.71/1.09 :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, equivalent( equivalent( X,
% 0.71/1.09 equivalent( Y, Z ) ), equivalent( X, equivalent( equivalent( T, Y ),
% 0.71/1.09 equivalent( T, Z ) ) ) ) )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 22, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 0.71/1.09 ), equivalent( X, equivalent( equivalent( T, Y ), equivalent( T, Z ) ) )
% 0.71/1.09 ) ) ] )
% 0.71/1.09 , clause( 201, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.71/1.09 Z ) ), equivalent( X, equivalent( equivalent( T, Y ), equivalent( T, Z )
% 0.71/1.09 ) ) ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.71/1.09 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 202, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, equivalent( T, X ) ), equivalent( Z, equivalent( T, Y ) )
% 0.71/1.09 ) ) ) ] )
% 0.71/1.09 , clause( 11, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 0.71/1.09 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 0.71/1.09 , 1, clause( 22, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.71/1.09 , Z ) ), equivalent( X, equivalent( equivalent( T, Y ), equivalent( T, Z
% 0.71/1.09 ) ) ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T,
% 0.71/1.09 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, equivalent( T
% 0.71/1.09 , X ) ), equivalent( Z, equivalent( T, Y ) ) ) ) )] ), substitution( 1, [
% 0.71/1.09 :=( X, equivalent( X, Y ) ), :=( Y, equivalent( T, X ) ), :=( Z,
% 0.71/1.09 equivalent( T, Y ) ), :=( T, Z )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 23, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, equivalent( T, X ) ), equivalent( Z, equivalent( T, Y ) )
% 0.71/1.09 ) ) ) ] )
% 0.71/1.09 , clause( 202, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, equivalent( T, X ) ), equivalent( Z, equivalent( T, Y ) )
% 0.71/1.09 ) ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.71/1.09 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 203, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.71/1.09 equivalent( Z, T ) ) ), equivalent( X, equivalent( Y, equivalent(
% 0.71/1.09 equivalent( U, Z ), equivalent( U, T ) ) ) ) ) ) ] )
% 0.71/1.09 , clause( 11, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 0.71/1.09 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 0.71/1.09 , 1, clause( 23, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.71/1.09 equivalent( equivalent( Z, equivalent( T, X ) ), equivalent( Z,
% 0.71/1.09 equivalent( T, Y ) ) ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, U ), :=( T,
% 0.71/1.09 equivalent( equivalent( X, equivalent( Y, equivalent( Z, T ) ) ),
% 0.71/1.09 equivalent( X, equivalent( Y, equivalent( equivalent( U, Z ), equivalent(
% 0.71/1.09 U, T ) ) ) ) ) )] ), substitution( 1, [ :=( X, equivalent( Z, T ) ), :=(
% 0.71/1.09 Y, equivalent( equivalent( U, Z ), equivalent( U, T ) ) ), :=( Z, X ),
% 0.71/1.09 :=( T, Y )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 28, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.71/1.09 equivalent( Z, T ) ) ), equivalent( X, equivalent( Y, equivalent(
% 0.71/1.09 equivalent( U, Z ), equivalent( U, T ) ) ) ) ) ) ] )
% 0.71/1.09 , clause( 203, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.71/1.09 equivalent( Z, T ) ) ), equivalent( X, equivalent( Y, equivalent(
% 0.71/1.09 equivalent( U, Z ), equivalent( U, T ) ) ) ) ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.71/1.09 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 204, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.71/1.09 equivalent( equivalent( Z, T ), equivalent( equivalent( T, Z ), U ) ) ) )
% 0.71/1.09 , equivalent( X, equivalent( Y, U ) ) ) ) ] )
% 0.71/1.09 , clause( 4, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( equivalent( X, Y ), equivalent( equivalent( Y, X
% 0.71/1.09 ), Z ) ), Z ), T ) ) ) ] )
% 0.71/1.09 , 1, clause( 23, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.71/1.09 equivalent( equivalent( Z, equivalent( T, X ) ), equivalent( Z,
% 0.71/1.09 equivalent( T, Y ) ) ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, U ), :=( T,
% 0.71/1.09 equivalent( equivalent( X, equivalent( Y, equivalent( equivalent( Z, T )
% 0.71/1.09 , equivalent( equivalent( T, Z ), U ) ) ) ), equivalent( X, equivalent( Y
% 0.71/1.09 , U ) ) ) )] ), substitution( 1, [ :=( X, equivalent( equivalent( Z, T )
% 0.71/1.09 , equivalent( equivalent( T, Z ), U ) ) ), :=( Y, U ), :=( Z, X ), :=( T
% 0.71/1.09 , Y )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 30, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.71/1.09 equivalent( equivalent( Z, T ), equivalent( equivalent( T, Z ), U ) ) ) )
% 0.71/1.09 , equivalent( X, equivalent( Y, U ) ) ) ) ] )
% 0.71/1.09 , clause( 204, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.71/1.09 equivalent( equivalent( Z, T ), equivalent( equivalent( T, Z ), U ) ) ) )
% 0.71/1.09 , equivalent( X, equivalent( Y, U ) ) ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.71/1.09 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 205, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, X ), equivalent( equivalent( T, Z ), equivalent( T, Y ) )
% 0.71/1.09 ) ) ) ] )
% 0.71/1.09 , clause( 11, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 0.71/1.09 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 0.71/1.09 , 1, clause( 28, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.71/1.09 , equivalent( Z, T ) ) ), equivalent( X, equivalent( Y, equivalent(
% 0.71/1.09 equivalent( U, Z ), equivalent( U, T ) ) ) ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 0.71/1.09 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 0.71/1.09 equivalent( equivalent( T, Z ), equivalent( T, Y ) ) ) ) )] ),
% 0.71/1.09 substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y, equivalent( Z, X )
% 0.71/1.09 ), :=( Z, Z ), :=( T, Y ), :=( U, T )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 33, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, X ), equivalent( equivalent( T, Z ), equivalent( T, Y ) )
% 0.71/1.09 ) ) ) ] )
% 0.71/1.09 , clause( 205, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, X ), equivalent( equivalent( T, Z ), equivalent( T, Y ) )
% 0.71/1.09 ) ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.71/1.09 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 206, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.71/1.09 ) ), equivalent( equivalent( T, X ), equivalent( T, equivalent(
% 0.71/1.09 equivalent( U, Y ), equivalent( U, Z ) ) ) ) ) ) ] )
% 0.71/1.09 , clause( 11, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 0.71/1.09 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 0.71/1.09 , 1, clause( 33, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.71/1.09 equivalent( equivalent( Z, X ), equivalent( equivalent( T, Z ),
% 0.71/1.09 equivalent( T, Y ) ) ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, U ), :=( T,
% 0.71/1.09 equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( equivalent(
% 0.71/1.09 T, X ), equivalent( T, equivalent( equivalent( U, Y ), equivalent( U, Z )
% 0.71/1.09 ) ) ) ) )] ), substitution( 1, [ :=( X, equivalent( Y, Z ) ), :=( Y,
% 0.71/1.09 equivalent( equivalent( U, Y ), equivalent( U, Z ) ) ), :=( Z, X ), :=( T
% 0.71/1.09 , T )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 37, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 0.71/1.09 ), equivalent( equivalent( T, X ), equivalent( T, equivalent( equivalent(
% 0.71/1.09 U, Y ), equivalent( U, Z ) ) ) ) ) ) ] )
% 0.71/1.09 , clause( 206, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y,
% 0.71/1.09 Z ) ), equivalent( equivalent( T, X ), equivalent( T, equivalent(
% 0.71/1.09 equivalent( U, Y ), equivalent( U, Z ) ) ) ) ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.71/1.09 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 207, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( Y, Z ), T ) ), equivalent( equivalent( equivalent( Z, Y ), X
% 0.71/1.09 ), T ) ) ) ] )
% 0.71/1.09 , clause( 11, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 0.71/1.09 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 0.71/1.09 , 1, clause( 30, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.71/1.09 , equivalent( equivalent( Z, T ), equivalent( equivalent( T, Z ), U ) ) )
% 0.71/1.09 ), equivalent( X, equivalent( Y, U ) ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, X ), :=( Y, equivalent( equivalent( Y, Z ),
% 0.71/1.09 T ) ), :=( Z, equivalent( Z, Y ) ), :=( T, equivalent( equivalent( X,
% 0.71/1.09 equivalent( equivalent( Y, Z ), T ) ), equivalent( equivalent( equivalent(
% 0.71/1.09 Z, Y ), X ), T ) ) )] ), substitution( 1, [ :=( X, equivalent( X,
% 0.71/1.09 equivalent( equivalent( Y, Z ), T ) ) ), :=( Y, equivalent( equivalent( Z
% 0.71/1.09 , Y ), X ) ), :=( Z, Z ), :=( T, Y ), :=( U, T )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 64, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( Y, Z ), T ) ), equivalent( equivalent( equivalent( Z, Y ), X
% 0.71/1.09 ), T ) ) ) ] )
% 0.71/1.09 , clause( 207, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( Y, Z ), T ) ), equivalent( equivalent( equivalent( Z, Y ), X
% 0.71/1.09 ), T ) ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.71/1.09 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 208, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.09 equivalent( X, Z ) ), equivalent( Y, Z ) ) ) ] )
% 0.71/1.09 , clause( 11, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 0.71/1.09 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 0.71/1.09 , 1, clause( 64, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( Y, Z ), T ) ), equivalent( equivalent( equivalent( Z, Y ), X
% 0.71/1.09 ), T ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T,
% 0.71/1.09 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 0.71/1.09 equivalent( Y, Z ) ) )] ), substitution( 1, [ :=( X, equivalent( X, Z ) )
% 0.71/1.09 , :=( Y, Y ), :=( Z, X ), :=( T, equivalent( Y, Z ) )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 67, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.09 equivalent( X, Z ) ), equivalent( Y, Z ) ) ) ] )
% 0.71/1.09 , clause( 208, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.71/1.09 , equivalent( X, Z ) ), equivalent( Y, Z ) ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.71/1.09 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 210, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ), T ) ) ),
% 0.71/1.09 'is_a_theorem'( T ) ] )
% 0.71/1.09 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.71/1.09 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.71/1.09 , 2, clause( 67, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.71/1.09 ), equivalent( X, Z ) ), equivalent( Y, Z ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.09 equivalent( X, Z ) ), equivalent( Y, Z ) ) ), :=( Y, T )] ),
% 0.71/1.09 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 78, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 0.71/1.09 equivalent( Y, Z ) ), T ) ) ) ] )
% 0.71/1.09 , clause( 210, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( X, Z ) ), equivalent( Y, Z ) ), T ) ) ),
% 0.71/1.09 'is_a_theorem'( T ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.71/1.09 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 211, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( Y, Z ), equivalent( Y, T ) ) ), equivalent( X, equivalent(
% 0.71/1.09 equivalent( U, Z ), equivalent( U, T ) ) ) ) ) ] )
% 0.71/1.09 , clause( 78, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z ) ),
% 0.71/1.09 equivalent( Y, Z ) ), T ) ) ) ] )
% 0.71/1.09 , 1, clause( 37, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.71/1.09 , Z ) ), equivalent( equivalent( T, X ), equivalent( T, equivalent(
% 0.71/1.09 equivalent( U, Y ), equivalent( U, Z ) ) ) ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T,
% 0.71/1.09 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), equivalent( Y
% 0.71/1.09 , T ) ) ), equivalent( X, equivalent( equivalent( U, Z ), equivalent( U,
% 0.71/1.09 T ) ) ) ) )] ), substitution( 1, [ :=( X, equivalent( equivalent( Y, Z )
% 0.71/1.09 , equivalent( Y, T ) ) ), :=( Y, Z ), :=( Z, T ), :=( T, X ), :=( U, U )] )
% 0.71/1.09 ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 85, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( Y, Z ), equivalent( Y, T ) ) ), equivalent( X, equivalent(
% 0.71/1.09 equivalent( U, Z ), equivalent( U, T ) ) ) ) ) ] )
% 0.71/1.09 , clause( 211, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( Y, Z ), equivalent( Y, T ) ) ), equivalent( X, equivalent(
% 0.71/1.09 equivalent( U, Z ), equivalent( U, T ) ) ) ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.71/1.09 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 212, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( U
% 0.71/1.09 , equivalent( Y, Z ) ), equivalent( U, T ) ) ) ) ] )
% 0.71/1.09 , clause( 5, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( X, equivalent( equivalent( equivalent( equivalent( Y, Z ),
% 0.71/1.09 equivalent( Y, T ) ), equivalent( Z, T ) ), X ) ), U ) ) ) ] )
% 0.71/1.09 , 1, clause( 85, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( Y, Z ), equivalent( Y, T ) ) ), equivalent( X, equivalent(
% 0.71/1.09 equivalent( U, Z ), equivalent( U, T ) ) ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.09 equivalent( X, Z ) ), T ) ), :=( Y, X ), :=( Z, Y ), :=( T, Z ), :=( U,
% 0.71/1.09 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent( X, Z
% 0.71/1.09 ) ), T ), equivalent( equivalent( U, equivalent( Y, Z ) ), equivalent( U
% 0.71/1.09 , T ) ) ) )] ), substitution( 1, [ :=( X, equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( X, Z ) ), T ) ), :=( Y, equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( X, Z ) ) ), :=( Z, equivalent( Y, Z ) ),
% 0.71/1.09 :=( T, T ), :=( U, U )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 121, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( U
% 0.71/1.09 , equivalent( Y, Z ) ), equivalent( U, T ) ) ) ) ] )
% 0.71/1.09 , clause( 212, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( U
% 0.71/1.09 , equivalent( Y, Z ) ), equivalent( U, T ) ) ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.71/1.09 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 213, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( equivalent( Y, Z ), equivalent( Y, T ) ), U ) ), equivalent(
% 0.71/1.09 X, equivalent( equivalent( Z, T ), U ) ) ) ) ] )
% 0.71/1.09 , clause( 17, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.09 equivalent( Z, X ), equivalent( Z, Y ) ) ), T ), T ), U ) ) ) ] )
% 0.71/1.09 , 1, clause( 121, [ 'is_a_theorem'( equivalent( equivalent( equivalent(
% 0.71/1.09 equivalent( X, Y ), equivalent( X, Z ) ), T ), equivalent( equivalent( U
% 0.71/1.09 , equivalent( Y, Z ) ), equivalent( U, T ) ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, Z ), :=( Y, T ), :=( Z, Y ), :=( T,
% 0.71/1.09 equivalent( equivalent( Z, T ), U ) ), :=( U, equivalent( equivalent( X,
% 0.71/1.09 equivalent( equivalent( equivalent( Y, Z ), equivalent( Y, T ) ), U ) ),
% 0.71/1.09 equivalent( X, equivalent( equivalent( Z, T ), U ) ) ) )] ),
% 0.71/1.09 substitution( 1, [ :=( X, equivalent( Z, T ) ), :=( Y, equivalent(
% 0.71/1.09 equivalent( Y, Z ), equivalent( Y, T ) ) ), :=( Z, U ), :=( T, equivalent(
% 0.71/1.09 equivalent( Z, T ), U ) ), :=( U, X )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 125, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( equivalent( Y, Z ), equivalent( Y, T ) ), U ) ), equivalent(
% 0.71/1.09 X, equivalent( equivalent( Z, T ), U ) ) ) ) ] )
% 0.71/1.09 , clause( 213, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( equivalent( Y, Z ), equivalent( Y, T ) ), U ) ), equivalent(
% 0.71/1.09 X, equivalent( equivalent( Z, T ), U ) ) ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.71/1.09 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 214, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.09 Z ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T ), Z )
% 0.71/1.09 ) ) ) ] )
% 0.71/1.09 , clause( 11, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.09 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, X ),
% 0.71/1.09 equivalent( Z, Y ) ) ), T ) ) ) ] )
% 0.71/1.09 , 1, clause( 125, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.09 equivalent( equivalent( Y, Z ), equivalent( Y, T ) ), U ) ), equivalent(
% 0.71/1.09 X, equivalent( equivalent( Z, T ), U ) ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [ :=( X, equivalent( X, Y ) ), :=( Y, Z ), :=( Z,
% 0.71/1.09 equivalent( X, T ) ), :=( T, equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.09 Z ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T ), Z )
% 0.71/1.09 ) ) )] ), substitution( 1, [ :=( X, equivalent( equivalent( X, Y ), Z )
% 0.71/1.09 ), :=( Y, X ), :=( Z, T ), :=( T, Y ), :=( U, equivalent( equivalent( X
% 0.71/1.09 , T ), Z ) )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 169, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.09 Z ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T ), Z )
% 0.71/1.09 ) ) ) ] )
% 0.71/1.09 , clause( 214, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.71/1.09 , Z ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T ), Z
% 0.71/1.09 ) ) ) ) ] )
% 0.71/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.71/1.09 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 resolution(
% 0.71/1.09 clause( 215, [] )
% 0.71/1.09 , clause( 3, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a, b
% 0.71/1.09 ), c ), equivalent( equivalent( e, b ), equivalent( equivalent( a, e ),
% 0.71/1.09 c ) ) ) ) ) ] )
% 0.71/1.09 , 0, clause( 169, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X,
% 0.71/1.09 Y ), Z ), equivalent( equivalent( T, Y ), equivalent( equivalent( X, T )
% 0.71/1.09 , Z ) ) ) ) ] )
% 0.71/1.09 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, b ), :=(
% 0.71/1.09 Z, c ), :=( T, e )] )).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 subsumption(
% 0.71/1.09 clause( 184, [] )
% 0.71/1.09 , clause( 215, [] )
% 0.71/1.09 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 end.
% 0.71/1.09
% 0.71/1.09 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.71/1.09
% 0.71/1.09 Memory use:
% 0.71/1.09
% 0.71/1.09 space for terms: 4385
% 0.71/1.09 space for clauses: 23333
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 clauses generated: 334
% 0.71/1.09 clauses kept: 185
% 0.71/1.09 clauses selected: 57
% 0.71/1.09 clauses deleted: 0
% 0.71/1.09 clauses inuse deleted: 0
% 0.71/1.09
% 0.71/1.09 subsentry: 208
% 0.71/1.09 literals s-matched: 149
% 0.71/1.09 literals matched: 149
% 0.71/1.09 full subsumption: 0
% 0.71/1.09
% 0.71/1.09 checksum: -1410880884
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 Bliksem ended
%------------------------------------------------------------------------------