TSTP Solution File: LCL022-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL022-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 07:49:17 EDT 2022
% Result : Unsatisfiable 0.71s 1.10s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL022-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Mon Jul 4 15:34:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.71/1.10 *** allocated 10000 integers for termspace/termends
% 0.71/1.10 *** allocated 10000 integers for clauses
% 0.71/1.10 *** allocated 10000 integers for justifications
% 0.71/1.10 Bliksem 1.12
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 Automatic Strategy Selection
% 0.71/1.10
% 0.71/1.10 Clauses:
% 0.71/1.10 [
% 0.71/1.10 [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~( 'is_a_theorem'( X ) ),
% 0.71/1.10 'is_a_theorem'( Y ) ],
% 0.71/1.10 [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( equivalent(
% 0.71/1.10 Z, Y ), equivalent( X, Z ) ) ) ) ],
% 0.71/1.10 [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a, b ),
% 0.71/1.10 equivalent( c, a ) ), equivalent( b, c ) ) ) ) ]
% 0.71/1.10 ] .
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 percentage equality = 0.000000, percentage horn = 1.000000
% 0.71/1.10 This is a near-Horn, non-equality problem
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 Options Used:
% 0.71/1.10
% 0.71/1.10 useres = 1
% 0.71/1.10 useparamod = 0
% 0.71/1.10 useeqrefl = 0
% 0.71/1.10 useeqfact = 0
% 0.71/1.10 usefactor = 1
% 0.71/1.10 usesimpsplitting = 0
% 0.71/1.10 usesimpdemod = 0
% 0.71/1.10 usesimpres = 4
% 0.71/1.10
% 0.71/1.10 resimpinuse = 1000
% 0.71/1.10 resimpclauses = 20000
% 0.71/1.10 substype = standard
% 0.71/1.10 backwardsubs = 1
% 0.71/1.10 selectoldest = 5
% 0.71/1.10
% 0.71/1.10 litorderings [0] = split
% 0.71/1.10 litorderings [1] = liftord
% 0.71/1.10
% 0.71/1.10 termordering = none
% 0.71/1.10
% 0.71/1.10 litapriori = 1
% 0.71/1.10 termapriori = 0
% 0.71/1.10 litaposteriori = 0
% 0.71/1.10 termaposteriori = 0
% 0.71/1.10 demodaposteriori = 0
% 0.71/1.10 ordereqreflfact = 0
% 0.71/1.10
% 0.71/1.10 litselect = negative
% 0.71/1.10
% 0.71/1.10 maxweight = 30000
% 0.71/1.10 maxdepth = 30000
% 0.71/1.10 maxlength = 115
% 0.71/1.10 maxnrvars = 195
% 0.71/1.10 excuselevel = 0
% 0.71/1.10 increasemaxweight = 0
% 0.71/1.10
% 0.71/1.10 maxselected = 10000000
% 0.71/1.10 maxnrclauses = 10000000
% 0.71/1.10
% 0.71/1.10 showgenerated = 0
% 0.71/1.10 showkept = 0
% 0.71/1.10 showselected = 0
% 0.71/1.10 showdeleted = 0
% 0.71/1.10 showresimp = 1
% 0.71/1.10 showstatus = 2000
% 0.71/1.10
% 0.71/1.10 prologoutput = 1
% 0.71/1.10 nrgoals = 5000000
% 0.71/1.10 totalproof = 1
% 0.71/1.10
% 0.71/1.10 Symbols occurring in the translation:
% 0.71/1.10
% 0.71/1.10 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.71/1.10 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.71/1.10 ! [4, 1] (w:1, o:15, a:1, s:1, b:0),
% 0.71/1.10 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.10 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.10 equivalent [41, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.71/1.10 'is_a_theorem' [42, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.71/1.10 a [44, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.71/1.10 b [45, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.71/1.10 c [46, 0] (w:1, o:14, a:1, s:1, b:0).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 Starting Search:
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 Bliksems!, er is een bewijs:
% 0.71/1.10 % SZS status Unsatisfiable
% 0.71/1.10 % SZS output start Refutation
% 0.71/1.10
% 0.71/1.10 clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.71/1.10 , ~( 'is_a_theorem'( X ) ) ] )
% 0.71/1.10 .
% 0.71/1.10 clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.10 equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.71/1.10 .
% 0.71/1.10 clause( 2, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a, b )
% 0.71/1.10 , equivalent( c, a ) ), equivalent( b, c ) ) ) ) ] )
% 0.71/1.10 .
% 0.71/1.10 clause( 3, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.71/1.10 equivalent( X, Y ), equivalent( equivalent( Z, Y ), equivalent( X, Z ) )
% 0.71/1.10 ), T ) ) ) ] )
% 0.71/1.10 .
% 0.71/1.10 clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.10 equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent( equivalent( T, Z
% 0.71/1.10 ), X ) ) ) ] )
% 0.71/1.10 .
% 0.71/1.10 clause( 5, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( X
% 0.71/1.10 , Y ) ) ) ] )
% 0.71/1.10 .
% 0.71/1.10 clause( 7, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.71/1.10 equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 0.71/1.10 .
% 0.71/1.10 clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 0.71/1.10 ), equivalent( equivalent( Y, Z ), X ) ) ) ] )
% 0.71/1.10 .
% 0.71/1.10 clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.10 equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ] )
% 0.71/1.10 .
% 0.71/1.10 clause( 11, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 0.71/1.10 .
% 0.71/1.10 clause( 13, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.10 equivalent( X, X ), Y ) ) ) ] )
% 0.71/1.10 .
% 0.71/1.10 clause( 17, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( Y
% 0.71/1.10 , X ) ) ) ] )
% 0.71/1.10 .
% 0.71/1.10 clause( 18, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.10 equivalent( equivalent( X, Y ), equivalent( Y, X ) ), Z ) ) ) ] )
% 0.71/1.10 .
% 0.71/1.10 clause( 19, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.10 equivalent( X, Z ), equivalent( Z, Y ) ) ) ) ] )
% 0.71/1.10 .
% 0.71/1.10 clause( 21, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), Z
% 0.71/1.10 ), equivalent( Z, equivalent( Y, X ) ) ) ) ] )
% 0.71/1.10 .
% 0.71/1.10 clause( 25, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.10 equivalent( Z, X ) ), equivalent( Y, Z ) ) ) ] )
% 0.71/1.10 .
% 0.71/1.10 clause( 27, [] )
% 0.71/1.10 .
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 % SZS output end Refutation
% 0.71/1.10 found a proof!
% 0.71/1.10
% 0.71/1.10 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.71/1.10
% 0.71/1.10 initialclauses(
% 0.71/1.10 [ clause( 29, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~(
% 0.71/1.10 'is_a_theorem'( X ) ), 'is_a_theorem'( Y ) ] )
% 0.71/1.10 , clause( 30, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.10 equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.71/1.10 , clause( 31, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a, b
% 0.71/1.10 ), equivalent( c, a ) ), equivalent( b, c ) ) ) ) ] )
% 0.71/1.10 ] ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.71/1.10 , ~( 'is_a_theorem'( X ) ) ] )
% 0.71/1.10 , clause( 29, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~(
% 0.71/1.10 'is_a_theorem'( X ) ), 'is_a_theorem'( Y ) ] )
% 0.71/1.10 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.10 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.10 equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.71/1.10 , clause( 30, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.10 equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.71/1.10 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.71/1.10 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 2, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a, b )
% 0.71/1.10 , equivalent( c, a ) ), equivalent( b, c ) ) ) ) ] )
% 0.71/1.10 , clause( 31, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a, b
% 0.71/1.10 ), equivalent( c, a ) ), equivalent( b, c ) ) ) ) ] )
% 0.71/1.10 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 resolution(
% 0.71/1.10 clause( 33, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.71/1.10 , equivalent( equivalent( Z, Y ), equivalent( X, Z ) ) ), T ) ) ),
% 0.71/1.10 'is_a_theorem'( T ) ] )
% 0.71/1.10 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.71/1.10 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.71/1.10 , 2, clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.71/1.10 equivalent( equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.71/1.10 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.10 equivalent( Z, Y ), equivalent( X, Z ) ) ) ), :=( Y, T )] ),
% 0.71/1.10 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 3, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.71/1.10 equivalent( X, Y ), equivalent( equivalent( Z, Y ), equivalent( X, Z ) )
% 0.71/1.10 ), T ) ) ) ] )
% 0.71/1.10 , clause( 33, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.71/1.10 ), equivalent( equivalent( Z, Y ), equivalent( X, Z ) ) ), T ) ) ),
% 0.71/1.10 'is_a_theorem'( T ) ] )
% 0.71/1.10 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.71/1.10 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 resolution(
% 0.71/1.10 clause( 34, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.10 equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent( equivalent( T, Z
% 0.71/1.10 ), X ) ) ) ] )
% 0.71/1.10 , clause( 3, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.10 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, Y ),
% 0.71/1.10 equivalent( X, Z ) ) ), T ) ) ) ] )
% 0.71/1.10 , 1, clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.71/1.10 equivalent( equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.71/1.10 , 0, substitution( 0, [ :=( X, T ), :=( Y, Z ), :=( Z, Y ), :=( T,
% 0.71/1.10 equivalent( equivalent( X, equivalent( equivalent( Y, Z ), equivalent( T
% 0.71/1.10 , Y ) ) ), equivalent( equivalent( T, Z ), X ) ) )] ), substitution( 1, [
% 0.71/1.10 :=( X, equivalent( T, Z ) ), :=( Y, equivalent( equivalent( Y, Z ),
% 0.71/1.10 equivalent( T, Y ) ) ), :=( Z, X )] )).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.10 equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent( equivalent( T, Z
% 0.71/1.10 ), X ) ) ) ] )
% 0.71/1.10 , clause( 34, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.10 equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent( equivalent( T, Z
% 0.71/1.10 ), X ) ) ) ] )
% 0.71/1.10 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.71/1.10 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 resolution(
% 0.71/1.10 clause( 35, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( X
% 0.71/1.10 , Y ) ) ) ] )
% 0.71/1.10 , clause( 3, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.10 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, Y ),
% 0.71/1.10 equivalent( X, Z ) ) ), T ) ) ) ] )
% 0.71/1.10 , 1, clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.10 equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent( equivalent( T, Z
% 0.71/1.10 ), X ) ) ) ] )
% 0.71/1.10 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 0.71/1.10 equivalent( equivalent( X, Y ), equivalent( X, Y ) ) )] ), substitution(
% 0.71/1.10 1, [ :=( X, equivalent( X, Y ) ), :=( Y, Z ), :=( Z, Y ), :=( T, X )] )
% 0.71/1.10 ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 5, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( X
% 0.71/1.10 , Y ) ) ) ] )
% 0.71/1.10 , clause( 35, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.10 X, Y ) ) ) ] )
% 0.71/1.10 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.10 )] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 resolution(
% 0.71/1.10 clause( 37, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.71/1.10 , equivalent( X, Y ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.71/1.10 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.71/1.10 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.71/1.10 , 2, clause( 5, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.71/1.10 equivalent( X, Y ) ) ) ] )
% 0.71/1.10 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.10 X, Y ) ) ), :=( Y, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 0.71/1.10 ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 7, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent( equivalent(
% 0.71/1.10 equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 0.71/1.10 , clause( 37, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.71/1.10 ), equivalent( X, Y ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.71/1.10 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.71/1.10 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 resolution(
% 0.71/1.10 clause( 38, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 0.71/1.10 ), equivalent( equivalent( Y, Z ), X ) ) ) ] )
% 0.71/1.10 , clause( 7, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.10 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 0.71/1.10 , 1, clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.71/1.10 equivalent( equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.71/1.10 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, equivalent(
% 0.71/1.10 equivalent( X, equivalent( Y, Z ) ), equivalent( equivalent( Y, Z ), X )
% 0.71/1.10 ) )] ), substitution( 1, [ :=( X, equivalent( Y, Z ) ), :=( Y,
% 0.71/1.10 equivalent( Y, Z ) ), :=( Z, X )] )).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 0.71/1.10 ), equivalent( equivalent( Y, Z ), X ) ) ) ] )
% 0.71/1.10 , clause( 38, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.71/1.10 ) ), equivalent( equivalent( Y, Z ), X ) ) ) ] )
% 0.71/1.10 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.71/1.10 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 resolution(
% 0.71/1.10 clause( 39, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.10 equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ] )
% 0.71/1.10 , clause( 3, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.10 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, Y ),
% 0.71/1.10 equivalent( X, Z ) ) ), T ) ) ) ] )
% 0.71/1.10 , 1, clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.71/1.10 , Z ) ), equivalent( equivalent( Y, Z ), X ) ) ) ] )
% 0.71/1.10 , 0, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X ), :=( T,
% 0.71/1.10 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, X ) ),
% 0.71/1.10 equivalent( Z, Y ) ) )] ), substitution( 1, [ :=( X, equivalent( Z, Y ) )
% 0.71/1.10 , :=( Y, equivalent( X, Y ) ), :=( Z, equivalent( Z, X ) )] )).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.10 equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ] )
% 0.71/1.10 , clause( 39, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.71/1.10 , equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ] )
% 0.71/1.10 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.71/1.10 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 resolution(
% 0.71/1.10 clause( 40, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 0.71/1.10 , clause( 7, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.10 equivalent( equivalent( X, Y ), equivalent( X, Y ) ), Z ) ) ) ] )
% 0.71/1.10 , 1, clause( 9, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.71/1.10 ), equivalent( Z, X ) ), equivalent( Z, Y ) ) ) ] )
% 0.71/1.10 , 0, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, equivalent( X, X ) )] )
% 0.71/1.10 , substitution( 1, [ :=( X, X ), :=( Y, X ), :=( Z, X )] )).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 11, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 0.71/1.10 , clause( 40, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 0.71/1.10 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 resolution(
% 0.71/1.10 clause( 42, [ ~( 'is_a_theorem'( equivalent( equivalent( X, X ), Y ) ) ),
% 0.71/1.10 'is_a_theorem'( Y ) ] )
% 0.71/1.10 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.71/1.10 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.71/1.10 , 2, clause( 11, [ 'is_a_theorem'( equivalent( X, X ) ) ] )
% 0.71/1.10 , 0, substitution( 0, [ :=( X, equivalent( X, X ) ), :=( Y, Y )] ),
% 0.71/1.10 substitution( 1, [ :=( X, X )] )).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 13, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.10 equivalent( X, X ), Y ) ) ) ] )
% 0.71/1.10 , clause( 42, [ ~( 'is_a_theorem'( equivalent( equivalent( X, X ), Y ) ) )
% 0.71/1.10 , 'is_a_theorem'( Y ) ] )
% 0.71/1.10 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 0.71/1.10 ), ==>( 1, 0 )] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 resolution(
% 0.71/1.10 clause( 43, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( Y
% 0.71/1.10 , X ) ) ) ] )
% 0.71/1.10 , clause( 13, [ 'is_a_theorem'( Y ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.10 equivalent( X, X ), Y ) ) ) ] )
% 0.71/1.10 , 1, clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.71/1.10 equivalent( equivalent( Z, Y ), equivalent( X, Z ) ) ) ) ] )
% 0.71/1.10 , 0, substitution( 0, [ :=( X, Y ), :=( Y, equivalent( equivalent( X, Y ),
% 0.71/1.10 equivalent( Y, X ) ) )] ), substitution( 1, [ :=( X, Y ), :=( Y, Y ),
% 0.71/1.10 :=( Z, X )] )).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 17, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( Y
% 0.71/1.10 , X ) ) ) ] )
% 0.71/1.10 , clause( 43, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.10 Y, X ) ) ) ] )
% 0.71/1.10 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.10 )] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 resolution(
% 0.71/1.10 clause( 45, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.71/1.10 , equivalent( Y, X ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.71/1.10 , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.71/1.10 ), ~( 'is_a_theorem'( X ) ) ] )
% 0.71/1.10 , 2, clause( 17, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.71/1.10 equivalent( Y, X ) ) ) ] )
% 0.71/1.10 , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.10 Y, X ) ) ), :=( Y, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 0.71/1.10 ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 18, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.10 equivalent( equivalent( X, Y ), equivalent( Y, X ) ), Z ) ) ) ] )
% 0.71/1.10 , clause( 45, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.71/1.10 ), equivalent( Y, X ) ), Z ) ) ), 'is_a_theorem'( Z ) ] )
% 0.71/1.10 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.71/1.10 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 resolution(
% 0.71/1.10 clause( 46, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.10 equivalent( X, Z ), equivalent( Z, Y ) ) ) ) ] )
% 0.71/1.10 , clause( 18, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.10 equivalent( equivalent( X, Y ), equivalent( Y, X ) ), Z ) ) ) ] )
% 0.71/1.10 , 1, clause( 4, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent(
% 0.71/1.10 equivalent( Y, Z ), equivalent( T, Y ) ) ), equivalent( equivalent( T, Z
% 0.71/1.10 ), X ) ) ) ] )
% 0.71/1.10 , 0, substitution( 0, [ :=( X, equivalent( X, Z ) ), :=( Y, equivalent( Z,
% 0.71/1.10 Y ) ), :=( Z, equivalent( equivalent( X, Y ), equivalent( equivalent( X,
% 0.71/1.10 Z ), equivalent( Z, Y ) ) ) )] ), substitution( 1, [ :=( X, equivalent(
% 0.71/1.10 equivalent( X, Z ), equivalent( Z, Y ) ) ), :=( Y, Z ), :=( Z, Y ), :=( T
% 0.71/1.10 , X )] )).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 19, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.10 equivalent( X, Z ), equivalent( Z, Y ) ) ) ) ] )
% 0.71/1.10 , clause( 46, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent(
% 0.71/1.10 equivalent( X, Z ), equivalent( Z, Y ) ) ) ) ] )
% 0.71/1.10 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.71/1.10 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 resolution(
% 0.71/1.10 clause( 47, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), Z
% 0.71/1.10 ), equivalent( Z, equivalent( Y, X ) ) ) ) ] )
% 0.71/1.10 , clause( 18, [ 'is_a_theorem'( Z ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.10 equivalent( equivalent( X, Y ), equivalent( Y, X ) ), Z ) ) ) ] )
% 0.71/1.10 , 1, clause( 19, [ 'is_a_theorem'( equivalent( equivalent( X, Y ),
% 0.71/1.10 equivalent( equivalent( X, Z ), equivalent( Z, Y ) ) ) ) ] )
% 0.71/1.10 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, equivalent(
% 0.71/1.10 equivalent( equivalent( X, Y ), Z ), equivalent( Z, equivalent( Y, X ) )
% 0.71/1.10 ) )] ), substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y,
% 0.71/1.10 equivalent( Y, X ) ), :=( Z, Z )] )).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 21, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), Z
% 0.71/1.10 ), equivalent( Z, equivalent( Y, X ) ) ) ) ] )
% 0.71/1.10 , clause( 47, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.71/1.10 , Z ), equivalent( Z, equivalent( Y, X ) ) ) ) ] )
% 0.71/1.10 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.71/1.10 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 resolution(
% 0.71/1.10 clause( 48, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.10 equivalent( Z, X ) ), equivalent( Y, Z ) ) ) ] )
% 0.71/1.10 , clause( 3, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent(
% 0.71/1.10 equivalent( equivalent( X, Y ), equivalent( equivalent( Z, Y ),
% 0.71/1.10 equivalent( X, Z ) ) ), T ) ) ) ] )
% 0.71/1.10 , 1, clause( 21, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.71/1.10 ), Z ), equivalent( Z, equivalent( Y, X ) ) ) ) ] )
% 0.71/1.10 , 0, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X ), :=( T,
% 0.71/1.10 equivalent( equivalent( equivalent( X, Y ), equivalent( Z, X ) ),
% 0.71/1.10 equivalent( Y, Z ) ) )] ), substitution( 1, [ :=( X, Z ), :=( Y, Y ),
% 0.71/1.10 :=( Z, equivalent( equivalent( X, Y ), equivalent( Z, X ) ) )] )).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 25, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ),
% 0.71/1.10 equivalent( Z, X ) ), equivalent( Y, Z ) ) ) ] )
% 0.71/1.10 , clause( 48, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.71/1.10 , equivalent( Z, X ) ), equivalent( Y, Z ) ) ) ] )
% 0.71/1.10 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.71/1.10 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 resolution(
% 0.71/1.10 clause( 49, [] )
% 0.71/1.10 , clause( 2, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a, b
% 0.71/1.10 ), equivalent( c, a ) ), equivalent( b, c ) ) ) ) ] )
% 0.71/1.10 , 0, clause( 25, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.71/1.10 ), equivalent( Z, X ) ), equivalent( Y, Z ) ) ) ] )
% 0.71/1.10 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, b ), :=(
% 0.71/1.10 Z, c )] )).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 subsumption(
% 0.71/1.10 clause( 27, [] )
% 0.71/1.10 , clause( 49, [] )
% 0.71/1.10 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 end.
% 0.71/1.10
% 0.71/1.10 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.71/1.10
% 0.71/1.10 Memory use:
% 0.71/1.10
% 0.71/1.10 space for terms: 465
% 0.71/1.10 space for clauses: 2584
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 clauses generated: 61
% 0.71/1.10 clauses kept: 28
% 0.71/1.10 clauses selected: 17
% 0.71/1.10 clauses deleted: 1
% 0.71/1.10 clauses inuse deleted: 0
% 0.71/1.10
% 0.71/1.10 subsentry: 53
% 0.71/1.10 literals s-matched: 35
% 0.71/1.10 literals matched: 35
% 0.71/1.10 full subsumption: 0
% 0.71/1.10
% 0.71/1.10 checksum: 1085811587
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 Bliksem ended
%------------------------------------------------------------------------------