TSTP Solution File: LCL109-5 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL109-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.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 07:50:28 EDT 2022
% Result : Unsatisfiable 0.70s 1.09s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL109-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Sat Jul 2 09:41:00 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.70/1.08 *** allocated 10000 integers for termspace/termends
% 0.70/1.08 *** allocated 10000 integers for clauses
% 0.70/1.08 *** allocated 10000 integers for justifications
% 0.70/1.08 Bliksem 1.12
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 Automatic Strategy Selection
% 0.70/1.08
% 0.70/1.08 Clauses:
% 0.70/1.08 [
% 0.70/1.08 [ =( implies( truth, X ), X ) ],
% 0.70/1.08 [ =( implies( implies( X, Y ), implies( implies( Y, Z ), implies( X, Z )
% 0.70/1.08 ) ), truth ) ],
% 0.70/1.08 [ =( implies( implies( X, Y ), Y ), implies( implies( Y, X ), X ) ) ]
% 0.70/1.08 ,
% 0.70/1.08 [ =( implies( implies( not( X ), not( Y ) ), implies( Y, X ) ), truth )
% 0.70/1.08 ],
% 0.70/1.08 [ =( 'big_V'( X, Y ), implies( implies( X, Y ), Y ) ) ],
% 0.70/1.08 [ =( 'big_hat'( X, Y ), not( 'big_V'( not( X ), not( Y ) ) ) ) ],
% 0.70/1.08 [ ~( ordered( X, Y ) ), =( implies( X, Y ), truth ) ],
% 0.70/1.08 [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ],
% 0.70/1.08 [ ~( ordered( X, Y ) ), ordered( implies( X, Z ), implies( Y, Z ) ) ]
% 0.70/1.08 ,
% 0.70/1.08 [ ~( ordered( X, Y ) ), ordered( implies( Z, X ), implies( Z, Y ) ) ]
% 0.70/1.08 ,
% 0.70/1.08 [ ~( ordered( X, implies( Y, Z ) ) ), ordered( Y, implies( X, Z ) ) ]
% 0.70/1.08 ,
% 0.70/1.08 [ ~( ordered( X, implies( Y, Z ) ) ), ordered( Y, implies( X, Z ) ) ]
% 0.70/1.08 ,
% 0.70/1.08 [ =( not( 'big_V'( X, Y ) ), 'big_hat'( not( X ), not( Y ) ) ) ],
% 0.70/1.08 [ =( not( 'big_hat'( X, Y ) ), 'big_V'( not( X ), not( Y ) ) ) ],
% 0.70/1.08 [ =( implies( 'big_V'( X, Y ), Z ), 'big_hat'( implies( X, Z ), implies(
% 0.70/1.08 Y, Z ) ) ) ],
% 0.70/1.08 [ =( implies( X, 'big_hat'( Y, Z ) ), 'big_hat'( implies( X, Y ),
% 0.70/1.08 implies( X, Z ) ) ) ],
% 0.70/1.08 [ ~( =( 'big_V'( implies( x, y ), implies( y, x ) ), truth ) ) ]
% 0.70/1.08 ] .
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 percentage equality = 0.619048, percentage horn = 1.000000
% 0.70/1.08 This is a problem with some equality
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 Options Used:
% 0.70/1.08
% 0.70/1.08 useres = 1
% 0.70/1.08 useparamod = 1
% 0.70/1.08 useeqrefl = 1
% 0.70/1.08 useeqfact = 1
% 0.70/1.08 usefactor = 1
% 0.70/1.08 usesimpsplitting = 0
% 0.70/1.08 usesimpdemod = 5
% 0.70/1.08 usesimpres = 3
% 0.70/1.08
% 0.70/1.08 resimpinuse = 1000
% 0.70/1.08 resimpclauses = 20000
% 0.70/1.08 substype = eqrewr
% 0.70/1.08 backwardsubs = 1
% 0.70/1.08 selectoldest = 5
% 0.70/1.08
% 0.70/1.08 litorderings [0] = split
% 0.70/1.08 litorderings [1] = extend the termordering, first sorting on arguments
% 0.70/1.08
% 0.70/1.08 termordering = kbo
% 0.70/1.08
% 0.70/1.08 litapriori = 0
% 0.70/1.08 termapriori = 1
% 0.70/1.08 litaposteriori = 0
% 0.70/1.08 termaposteriori = 0
% 0.70/1.09 demodaposteriori = 0
% 0.70/1.09 ordereqreflfact = 0
% 0.70/1.09
% 0.70/1.09 litselect = negord
% 0.70/1.09
% 0.70/1.09 maxweight = 15
% 0.70/1.09 maxdepth = 30000
% 0.70/1.09 maxlength = 115
% 0.70/1.09 maxnrvars = 195
% 0.70/1.09 excuselevel = 1
% 0.70/1.09 increasemaxweight = 1
% 0.70/1.09
% 0.70/1.09 maxselected = 10000000
% 0.70/1.09 maxnrclauses = 10000000
% 0.70/1.09
% 0.70/1.09 showgenerated = 0
% 0.70/1.09 showkept = 0
% 0.70/1.09 showselected = 0
% 0.70/1.09 showdeleted = 0
% 0.70/1.09 showresimp = 1
% 0.70/1.09 showstatus = 2000
% 0.70/1.09
% 0.70/1.09 prologoutput = 1
% 0.70/1.09 nrgoals = 5000000
% 0.70/1.09 totalproof = 1
% 0.70/1.09
% 0.70/1.09 Symbols occurring in the translation:
% 0.70/1.09
% 0.70/1.09 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.70/1.09 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.70/1.09 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.70/1.09 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.09 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.09 truth [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.70/1.09 implies [41, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.70/1.09 not [44, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.70/1.09 'big_V' [45, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.70/1.09 'big_hat' [46, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.70/1.09 ordered [47, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.70/1.09 x [48, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.70/1.09 y [49, 0] (w:1, o:14, a:1, s:1, b:0).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 Starting Search:
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 Bliksems!, er is een bewijs:
% 0.70/1.09 % SZS status Unsatisfiable
% 0.70/1.09 % SZS output start Refutation
% 0.70/1.09
% 0.70/1.09 clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 1, [ =( implies( implies( X, Y ), implies( implies( Y, Z ), implies(
% 0.70/1.09 X, Z ) ) ), truth ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 2, [ =( implies( implies( X, Y ), Y ), implies( implies( Y, X ), X
% 0.70/1.09 ) ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 4, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 6, [ ~( ordered( X, Y ) ), =( implies( X, Y ), truth ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 7, [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 8, [ ~( ordered( X, Y ) ), ordered( implies( X, Z ), implies( Y, Z
% 0.70/1.09 ) ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 15, [ ~( =( 'big_V'( implies( x, y ), implies( y, x ) ), truth ) )
% 0.70/1.09 ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 19, [ =( truth, X ), ~( ordered( truth, X ) ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 29, [ =( implies( X, 'big_V'( X, Y ) ), truth ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 48, [ =( 'big_V'( X, Y ), 'big_V'( Y, X ) ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 51, [ ordered( X, 'big_V'( X, Y ) ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 58, [ =( 'big_V'( truth, X ), truth ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 59, [ ordered( X, 'big_V'( Y, X ) ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 63, [ =( 'big_V'( X, truth ), truth ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 85, [ ordered( X, truth ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 109, [ =( implies( X, X ), truth ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 125, [ ordered( implies( X, Y ), Y ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 143, [ ordered( truth, X ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 145, [ =( truth, X ) ] )
% 0.70/1.09 .
% 0.70/1.09 clause( 148, [] )
% 0.70/1.09 .
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 % SZS output end Refutation
% 0.70/1.09 found a proof!
% 0.70/1.09
% 0.70/1.09 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.70/1.09
% 0.70/1.09 initialclauses(
% 0.70/1.09 [ clause( 150, [ =( implies( truth, X ), X ) ] )
% 0.70/1.09 , clause( 151, [ =( implies( implies( X, Y ), implies( implies( Y, Z ),
% 0.70/1.09 implies( X, Z ) ) ), truth ) ] )
% 0.70/1.09 , clause( 152, [ =( implies( implies( X, Y ), Y ), implies( implies( Y, X )
% 0.70/1.09 , X ) ) ] )
% 0.70/1.09 , clause( 153, [ =( implies( implies( not( X ), not( Y ) ), implies( Y, X )
% 0.70/1.09 ), truth ) ] )
% 0.70/1.09 , clause( 154, [ =( 'big_V'( X, Y ), implies( implies( X, Y ), Y ) ) ] )
% 0.70/1.09 , clause( 155, [ =( 'big_hat'( X, Y ), not( 'big_V'( not( X ), not( Y ) ) )
% 0.70/1.09 ) ] )
% 0.70/1.09 , clause( 156, [ ~( ordered( X, Y ) ), =( implies( X, Y ), truth ) ] )
% 0.70/1.09 , clause( 157, [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ] )
% 0.70/1.09 , clause( 158, [ ~( ordered( X, Y ) ), ordered( implies( X, Z ), implies( Y
% 0.70/1.09 , Z ) ) ] )
% 0.70/1.09 , clause( 159, [ ~( ordered( X, Y ) ), ordered( implies( Z, X ), implies( Z
% 0.70/1.09 , Y ) ) ] )
% 0.70/1.09 , clause( 160, [ ~( ordered( X, implies( Y, Z ) ) ), ordered( Y, implies( X
% 0.70/1.09 , Z ) ) ] )
% 0.70/1.09 , clause( 161, [ ~( ordered( X, implies( Y, Z ) ) ), ordered( Y, implies( X
% 0.70/1.09 , Z ) ) ] )
% 0.70/1.09 , clause( 162, [ =( not( 'big_V'( X, Y ) ), 'big_hat'( not( X ), not( Y ) )
% 0.70/1.09 ) ] )
% 0.70/1.09 , clause( 163, [ =( not( 'big_hat'( X, Y ) ), 'big_V'( not( X ), not( Y ) )
% 0.70/1.09 ) ] )
% 0.70/1.09 , clause( 164, [ =( implies( 'big_V'( X, Y ), Z ), 'big_hat'( implies( X, Z
% 0.70/1.09 ), implies( Y, Z ) ) ) ] )
% 0.70/1.09 , clause( 165, [ =( implies( X, 'big_hat'( Y, Z ) ), 'big_hat'( implies( X
% 0.70/1.09 , Y ), implies( X, Z ) ) ) ] )
% 0.70/1.09 , clause( 166, [ ~( =( 'big_V'( implies( x, y ), implies( y, x ) ), truth )
% 0.70/1.09 ) ] )
% 0.70/1.09 ] ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.70/1.09 , clause( 150, [ =( implies( truth, X ), X ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 1, [ =( implies( implies( X, Y ), implies( implies( Y, Z ), implies(
% 0.70/1.09 X, Z ) ) ), truth ) ] )
% 0.70/1.09 , clause( 151, [ =( implies( implies( X, Y ), implies( implies( Y, Z ),
% 0.70/1.09 implies( X, Z ) ) ), truth ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.70/1.09 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 2, [ =( implies( implies( X, Y ), Y ), implies( implies( Y, X ), X
% 0.70/1.09 ) ) ] )
% 0.70/1.09 , clause( 152, [ =( implies( implies( X, Y ), Y ), implies( implies( Y, X )
% 0.70/1.09 , X ) ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.70/1.09 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 eqswap(
% 0.70/1.09 clause( 175, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.70/1.09 , clause( 154, [ =( 'big_V'( X, Y ), implies( implies( X, Y ), Y ) ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 4, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.70/1.09 , clause( 175, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.70/1.09 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 6, [ ~( ordered( X, Y ) ), =( implies( X, Y ), truth ) ] )
% 0.70/1.09 , clause( 156, [ ~( ordered( X, Y ) ), =( implies( X, Y ), truth ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.70/1.09 ), ==>( 1, 1 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 7, [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ] )
% 0.70/1.09 , clause( 157, [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.70/1.09 ), ==>( 1, 1 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 8, [ ~( ordered( X, Y ) ), ordered( implies( X, Z ), implies( Y, Z
% 0.70/1.09 ) ) ] )
% 0.70/1.09 , clause( 158, [ ~( ordered( X, Y ) ), ordered( implies( X, Z ), implies( Y
% 0.70/1.09 , Z ) ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.70/1.09 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 15, [ ~( =( 'big_V'( implies( x, y ), implies( y, x ) ), truth ) )
% 0.70/1.09 ] )
% 0.70/1.09 , clause( 166, [ ~( =( 'big_V'( implies( x, y ), implies( y, x ) ), truth )
% 0.70/1.09 ) ] )
% 0.70/1.09 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 eqswap(
% 0.70/1.09 clause( 208, [ =( truth, implies( X, Y ) ), ~( ordered( X, Y ) ) ] )
% 0.70/1.09 , clause( 6, [ ~( ordered( X, Y ) ), =( implies( X, Y ), truth ) ] )
% 0.70/1.09 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 paramod(
% 0.70/1.09 clause( 210, [ =( truth, X ), ~( ordered( truth, X ) ) ] )
% 0.70/1.09 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.70/1.09 , 0, clause( 208, [ =( truth, implies( X, Y ) ), ~( ordered( X, Y ) ) ] )
% 0.70/1.09 , 0, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, truth )
% 0.70/1.09 , :=( Y, X )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 19, [ =( truth, X ), ~( ordered( truth, X ) ) ] )
% 0.70/1.09 , clause( 210, [ =( truth, X ), ~( ordered( truth, X ) ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.70/1.09 1 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 eqswap(
% 0.70/1.09 clause( 213, [ =( truth, implies( implies( X, Y ), implies( implies( Y, Z )
% 0.70/1.09 , implies( X, Z ) ) ) ) ] )
% 0.70/1.09 , clause( 1, [ =( implies( implies( X, Y ), implies( implies( Y, Z ),
% 0.70/1.09 implies( X, Z ) ) ), truth ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 paramod(
% 0.70/1.09 clause( 218, [ =( truth, implies( implies( truth, X ), implies( implies( X
% 0.70/1.09 , Y ), Y ) ) ) ] )
% 0.70/1.09 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.70/1.09 , 0, clause( 213, [ =( truth, implies( implies( X, Y ), implies( implies( Y
% 0.70/1.09 , Z ), implies( X, Z ) ) ) ) ] )
% 0.70/1.09 , 0, 10, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, truth
% 0.70/1.09 ), :=( Y, X ), :=( Z, Y )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 paramod(
% 0.70/1.09 clause( 220, [ =( truth, implies( X, implies( implies( X, Y ), Y ) ) ) ] )
% 0.70/1.09 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.70/1.09 , 0, clause( 218, [ =( truth, implies( implies( truth, X ), implies(
% 0.70/1.09 implies( X, Y ), Y ) ) ) ] )
% 0.70/1.09 , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.70/1.09 :=( Y, Y )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 paramod(
% 0.70/1.09 clause( 221, [ =( truth, implies( X, 'big_V'( X, Y ) ) ) ] )
% 0.70/1.09 , clause( 4, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.70/1.09 , 0, clause( 220, [ =( truth, implies( X, implies( implies( X, Y ), Y ) ) )
% 0.70/1.09 ] )
% 0.70/1.09 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.70/1.09 :=( X, X ), :=( Y, Y )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 eqswap(
% 0.70/1.09 clause( 222, [ =( implies( X, 'big_V'( X, Y ) ), truth ) ] )
% 0.70/1.09 , clause( 221, [ =( truth, implies( X, 'big_V'( X, Y ) ) ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 29, [ =( implies( X, 'big_V'( X, Y ) ), truth ) ] )
% 0.70/1.09 , clause( 222, [ =( implies( X, 'big_V'( X, Y ) ), truth ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.70/1.09 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 paramod(
% 0.70/1.09 clause( 226, [ =( implies( implies( X, Y ), Y ), 'big_V'( Y, X ) ) ] )
% 0.70/1.09 , clause( 4, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.70/1.09 , 0, clause( 2, [ =( implies( implies( X, Y ), Y ), implies( implies( Y, X
% 0.70/1.09 ), X ) ) ] )
% 0.70/1.09 , 0, 6, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 0.70/1.09 :=( X, X ), :=( Y, Y )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 paramod(
% 0.70/1.09 clause( 228, [ =( 'big_V'( X, Y ), 'big_V'( Y, X ) ) ] )
% 0.70/1.09 , clause( 4, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.70/1.09 , 0, clause( 226, [ =( implies( implies( X, Y ), Y ), 'big_V'( Y, X ) ) ]
% 0.70/1.09 )
% 0.70/1.09 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.70/1.09 :=( X, X ), :=( Y, Y )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 48, [ =( 'big_V'( X, Y ), 'big_V'( Y, X ) ) ] )
% 0.70/1.09 , clause( 228, [ =( 'big_V'( X, Y ), 'big_V'( Y, X ) ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.70/1.09 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 eqswap(
% 0.70/1.09 clause( 229, [ =( truth, implies( X, 'big_V'( X, Y ) ) ) ] )
% 0.70/1.09 , clause( 29, [ =( implies( X, 'big_V'( X, Y ) ), truth ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 eqswap(
% 0.70/1.09 clause( 230, [ ~( =( truth, implies( X, Y ) ) ), ordered( X, Y ) ] )
% 0.70/1.09 , clause( 7, [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 resolution(
% 0.70/1.09 clause( 231, [ ordered( X, 'big_V'( X, Y ) ) ] )
% 0.70/1.09 , clause( 230, [ ~( =( truth, implies( X, Y ) ) ), ordered( X, Y ) ] )
% 0.70/1.09 , 0, clause( 229, [ =( truth, implies( X, 'big_V'( X, Y ) ) ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'big_V'( X, Y ) )] ),
% 0.70/1.09 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 51, [ ordered( X, 'big_V'( X, Y ) ) ] )
% 0.70/1.09 , clause( 231, [ ordered( X, 'big_V'( X, Y ) ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.70/1.09 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 eqswap(
% 0.70/1.09 clause( 232, [ =( truth, implies( X, 'big_V'( X, Y ) ) ) ] )
% 0.70/1.09 , clause( 29, [ =( implies( X, 'big_V'( X, Y ) ), truth ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 paramod(
% 0.70/1.09 clause( 234, [ =( truth, 'big_V'( truth, X ) ) ] )
% 0.70/1.09 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.70/1.09 , 0, clause( 232, [ =( truth, implies( X, 'big_V'( X, Y ) ) ) ] )
% 0.70/1.09 , 0, 2, substitution( 0, [ :=( X, 'big_V'( truth, X ) )] ), substitution( 1
% 0.70/1.09 , [ :=( X, truth ), :=( Y, X )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 eqswap(
% 0.70/1.09 clause( 235, [ =( 'big_V'( truth, X ), truth ) ] )
% 0.70/1.09 , clause( 234, [ =( truth, 'big_V'( truth, X ) ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, X )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 58, [ =( 'big_V'( truth, X ), truth ) ] )
% 0.70/1.09 , clause( 235, [ =( 'big_V'( truth, X ), truth ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 paramod(
% 0.70/1.09 clause( 236, [ ordered( X, 'big_V'( Y, X ) ) ] )
% 0.70/1.09 , clause( 48, [ =( 'big_V'( X, Y ), 'big_V'( Y, X ) ) ] )
% 0.70/1.09 , 0, clause( 51, [ ordered( X, 'big_V'( X, Y ) ) ] )
% 0.70/1.09 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.70/1.09 :=( X, X ), :=( Y, Y )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 59, [ ordered( X, 'big_V'( Y, X ) ) ] )
% 0.70/1.09 , clause( 236, [ ordered( X, 'big_V'( Y, X ) ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.70/1.09 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 eqswap(
% 0.70/1.09 clause( 238, [ =( X, truth ), ~( ordered( truth, X ) ) ] )
% 0.70/1.09 , clause( 19, [ =( truth, X ), ~( ordered( truth, X ) ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, X )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 resolution(
% 0.70/1.09 clause( 239, [ =( 'big_V'( X, truth ), truth ) ] )
% 0.70/1.09 , clause( 238, [ =( X, truth ), ~( ordered( truth, X ) ) ] )
% 0.70/1.09 , 1, clause( 59, [ ordered( X, 'big_V'( Y, X ) ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, 'big_V'( X, truth ) )] ), substitution( 1, [
% 0.70/1.09 :=( X, truth ), :=( Y, X )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 63, [ =( 'big_V'( X, truth ), truth ) ] )
% 0.70/1.09 , clause( 239, [ =( 'big_V'( X, truth ), truth ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 paramod(
% 0.70/1.09 clause( 242, [ ordered( X, truth ) ] )
% 0.70/1.09 , clause( 63, [ =( 'big_V'( X, truth ), truth ) ] )
% 0.70/1.09 , 0, clause( 51, [ ordered( X, 'big_V'( X, Y ) ) ] )
% 0.70/1.09 , 0, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.70/1.09 :=( Y, truth )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 85, [ ordered( X, truth ) ] )
% 0.70/1.09 , clause( 242, [ ordered( X, truth ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 eqswap(
% 0.70/1.09 clause( 244, [ =( 'big_V'( X, Y ), implies( implies( X, Y ), Y ) ) ] )
% 0.70/1.09 , clause( 4, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 paramod(
% 0.70/1.09 clause( 246, [ =( 'big_V'( truth, X ), implies( X, X ) ) ] )
% 0.70/1.09 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.70/1.09 , 0, clause( 244, [ =( 'big_V'( X, Y ), implies( implies( X, Y ), Y ) ) ]
% 0.70/1.09 )
% 0.70/1.09 , 0, 5, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, truth )
% 0.70/1.09 , :=( Y, X )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 paramod(
% 0.70/1.09 clause( 247, [ =( truth, implies( X, X ) ) ] )
% 0.70/1.09 , clause( 58, [ =( 'big_V'( truth, X ), truth ) ] )
% 0.70/1.09 , 0, clause( 246, [ =( 'big_V'( truth, X ), implies( X, X ) ) ] )
% 0.70/1.09 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.70/1.09 ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 eqswap(
% 0.70/1.09 clause( 248, [ =( implies( X, X ), truth ) ] )
% 0.70/1.09 , clause( 247, [ =( truth, implies( X, X ) ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, X )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 109, [ =( implies( X, X ), truth ) ] )
% 0.70/1.09 , clause( 248, [ =( implies( X, X ), truth ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 resolution(
% 0.70/1.09 clause( 250, [ ordered( implies( X, Y ), implies( truth, Y ) ) ] )
% 0.70/1.09 , clause( 8, [ ~( ordered( X, Y ) ), ordered( implies( X, Z ), implies( Y,
% 0.70/1.09 Z ) ) ] )
% 0.70/1.09 , 0, clause( 85, [ ordered( X, truth ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, X ), :=( Y, truth ), :=( Z, Y )] ),
% 0.70/1.09 substitution( 1, [ :=( X, X )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 paramod(
% 0.70/1.09 clause( 251, [ ordered( implies( X, Y ), Y ) ] )
% 0.70/1.09 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.70/1.09 , 0, clause( 250, [ ordered( implies( X, Y ), implies( truth, Y ) ) ] )
% 0.70/1.09 , 0, 4, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.70/1.09 :=( Y, Y )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 125, [ ordered( implies( X, Y ), Y ) ] )
% 0.70/1.09 , clause( 251, [ ordered( implies( X, Y ), Y ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.70/1.09 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 paramod(
% 0.70/1.09 clause( 253, [ ordered( truth, X ) ] )
% 0.70/1.09 , clause( 109, [ =( implies( X, X ), truth ) ] )
% 0.70/1.09 , 0, clause( 125, [ ordered( implies( X, Y ), Y ) ] )
% 0.70/1.09 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.70/1.09 :=( Y, X )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 143, [ ordered( truth, X ) ] )
% 0.70/1.09 , clause( 253, [ ordered( truth, X ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 eqswap(
% 0.70/1.09 clause( 254, [ =( X, truth ), ~( ordered( truth, X ) ) ] )
% 0.70/1.09 , clause( 19, [ =( truth, X ), ~( ordered( truth, X ) ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, X )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 resolution(
% 0.70/1.09 clause( 255, [ =( X, truth ) ] )
% 0.70/1.09 , clause( 254, [ =( X, truth ), ~( ordered( truth, X ) ) ] )
% 0.70/1.09 , 1, clause( 143, [ ordered( truth, X ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.70/1.09 ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 eqswap(
% 0.70/1.09 clause( 256, [ =( truth, X ) ] )
% 0.70/1.09 , clause( 255, [ =( X, truth ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, X )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 145, [ =( truth, X ) ] )
% 0.70/1.09 , clause( 256, [ =( truth, X ) ] )
% 0.70/1.09 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 eqswap(
% 0.70/1.09 clause( 257, [ =( X, truth ) ] )
% 0.70/1.09 , clause( 145, [ =( truth, X ) ] )
% 0.70/1.09 , 0, substitution( 0, [ :=( X, X )] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 eqswap(
% 0.70/1.09 clause( 258, [ ~( =( truth, 'big_V'( implies( x, y ), implies( y, x ) ) ) )
% 0.70/1.09 ] )
% 0.70/1.09 , clause( 15, [ ~( =( 'big_V'( implies( x, y ), implies( y, x ) ), truth )
% 0.70/1.09 ) ] )
% 0.70/1.09 , 0, substitution( 0, [] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 paramod(
% 0.70/1.09 clause( 260, [ ~( =( truth, truth ) ) ] )
% 0.70/1.09 , clause( 257, [ =( X, truth ) ] )
% 0.70/1.09 , 0, clause( 258, [ ~( =( truth, 'big_V'( implies( x, y ), implies( y, x )
% 0.70/1.09 ) ) ) ] )
% 0.70/1.09 , 0, 3, substitution( 0, [ :=( X, 'big_V'( implies( x, y ), implies( y, x )
% 0.70/1.09 ) )] ), substitution( 1, [] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 eqrefl(
% 0.70/1.09 clause( 279, [] )
% 0.70/1.09 , clause( 260, [ ~( =( truth, truth ) ) ] )
% 0.70/1.09 , 0, substitution( 0, [] )).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 subsumption(
% 0.70/1.09 clause( 148, [] )
% 0.70/1.09 , clause( 279, [] )
% 0.70/1.09 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 end.
% 0.70/1.09
% 0.70/1.09 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.70/1.09
% 0.70/1.09 Memory use:
% 0.70/1.09
% 0.70/1.09 space for terms: 1982
% 0.70/1.09 space for clauses: 11629
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 clauses generated: 694
% 0.70/1.09 clauses kept: 149
% 0.70/1.09 clauses selected: 34
% 0.70/1.09 clauses deleted: 32
% 0.70/1.09 clauses inuse deleted: 0
% 0.70/1.09
% 0.70/1.09 subsentry: 1527
% 0.70/1.09 literals s-matched: 822
% 0.70/1.09 literals matched: 772
% 0.70/1.09 full subsumption: 11
% 0.70/1.09
% 0.70/1.09 checksum: -16365657
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 Bliksem ended
%------------------------------------------------------------------------------