TSTP Solution File: LCL146-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL146-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 07:50:52 EDT 2022
% Result : Unsatisfiable 0.73s 1.51s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL146-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n013.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 : Sun Jul 3 18:28:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.73/1.51 *** allocated 10000 integers for termspace/termends
% 0.73/1.51 *** allocated 10000 integers for clauses
% 0.73/1.51 *** allocated 10000 integers for justifications
% 0.73/1.51 Bliksem 1.12
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 Automatic Strategy Selection
% 0.73/1.51
% 0.73/1.51 Clauses:
% 0.73/1.51 [
% 0.73/1.51 [ =( implies( truth, X ), X ) ],
% 0.73/1.51 [ =( implies( implies( X, Y ), implies( implies( Y, Z ), implies( X, Z )
% 0.73/1.51 ) ), truth ) ],
% 0.73/1.51 [ =( implies( implies( X, Y ), Y ), implies( implies( Y, X ), X ) ) ]
% 0.73/1.51 ,
% 0.73/1.51 [ =( implies( implies( not( X ), not( Y ) ), implies( Y, X ) ), truth )
% 0.73/1.51 ],
% 0.73/1.51 [ =( 'big_V'( X, Y ), implies( implies( X, Y ), Y ) ) ],
% 0.73/1.51 [ =( 'big_hat'( X, Y ), not( 'big_V'( not( X ), not( Y ) ) ) ) ],
% 0.73/1.51 [ ~( ordered( X, Y ) ), =( implies( X, Y ), truth ) ],
% 0.73/1.51 [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ],
% 0.73/1.51 [ ~( =( not( 'big_hat'( x, y ) ), 'big_V'( not( x ), not( y ) ) ) ) ]
% 0.73/1.51 ] .
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 percentage equality = 0.818182, percentage horn = 1.000000
% 0.73/1.51 This is a pure equality problem
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 Options Used:
% 0.73/1.51
% 0.73/1.51 useres = 1
% 0.73/1.51 useparamod = 1
% 0.73/1.51 useeqrefl = 1
% 0.73/1.51 useeqfact = 1
% 0.73/1.51 usefactor = 1
% 0.73/1.51 usesimpsplitting = 0
% 0.73/1.51 usesimpdemod = 5
% 0.73/1.51 usesimpres = 3
% 0.73/1.51
% 0.73/1.51 resimpinuse = 1000
% 0.73/1.51 resimpclauses = 20000
% 0.73/1.51 substype = eqrewr
% 0.73/1.51 backwardsubs = 1
% 0.73/1.51 selectoldest = 5
% 0.73/1.51
% 0.73/1.51 litorderings [0] = split
% 0.73/1.51 litorderings [1] = extend the termordering, first sorting on arguments
% 0.73/1.51
% 0.73/1.51 termordering = kbo
% 0.73/1.51
% 0.73/1.51 litapriori = 0
% 0.73/1.51 termapriori = 1
% 0.73/1.51 litaposteriori = 0
% 0.73/1.51 termaposteriori = 0
% 0.73/1.51 demodaposteriori = 0
% 0.73/1.51 ordereqreflfact = 0
% 0.73/1.51
% 0.73/1.51 litselect = negord
% 0.73/1.51
% 0.73/1.51 maxweight = 15
% 0.73/1.51 maxdepth = 30000
% 0.73/1.51 maxlength = 115
% 0.73/1.51 maxnrvars = 195
% 0.73/1.51 excuselevel = 1
% 0.73/1.51 increasemaxweight = 1
% 0.73/1.51
% 0.73/1.51 maxselected = 10000000
% 0.73/1.51 maxnrclauses = 10000000
% 0.73/1.51
% 0.73/1.51 showgenerated = 0
% 0.73/1.51 showkept = 0
% 0.73/1.51 showselected = 0
% 0.73/1.51 showdeleted = 0
% 0.73/1.51 showresimp = 1
% 0.73/1.51 showstatus = 2000
% 0.73/1.51
% 0.73/1.51 prologoutput = 1
% 0.73/1.51 nrgoals = 5000000
% 0.73/1.51 totalproof = 1
% 0.73/1.51
% 0.73/1.51 Symbols occurring in the translation:
% 0.73/1.51
% 0.73/1.51 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.73/1.51 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.73/1.51 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.73/1.51 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.51 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.51 truth [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.73/1.51 implies [41, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.73/1.51 not [44, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.73/1.51 'big_V' [45, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.73/1.51 'big_hat' [46, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.73/1.51 ordered [47, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.73/1.51 x [48, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.73/1.51 y [49, 0] (w:1, o:14, a:1, s:1, b:0).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 Starting Search:
% 0.73/1.51
% 0.73/1.51 Resimplifying inuse:
% 0.73/1.51 Done
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 Intermediate Status:
% 0.73/1.51 Generated: 19528
% 0.73/1.51 Kept: 2024
% 0.73/1.51 Inuse: 145
% 0.73/1.51 Deleted: 37
% 0.73/1.51 Deletedinuse: 5
% 0.73/1.51
% 0.73/1.51 Resimplifying inuse:
% 0.73/1.51 Done
% 0.73/1.51
% 0.73/1.51 Resimplifying inuse:
% 0.73/1.51 Done
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 Intermediate Status:
% 0.73/1.51 Generated: 35974
% 0.73/1.51 Kept: 4028
% 0.73/1.51 Inuse: 209
% 0.73/1.51 Deleted: 54
% 0.73/1.51 Deletedinuse: 7
% 0.73/1.51
% 0.73/1.51 Resimplifying inuse:
% 0.73/1.51
% 0.73/1.51 Bliksems!, er is een bewijs:
% 0.73/1.51 % SZS status Unsatisfiable
% 0.73/1.51 % SZS output start Refutation
% 0.73/1.51
% 0.73/1.51 clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 1, [ =( implies( implies( X, Y ), implies( implies( Y, Z ), implies(
% 0.73/1.51 X, Z ) ) ), truth ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 2, [ =( implies( implies( X, Y ), Y ), implies( implies( Y, X ), X
% 0.73/1.51 ) ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 3, [ =( implies( implies( not( X ), not( Y ) ), implies( Y, X ) ),
% 0.73/1.51 truth ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 4, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 5, [ =( not( 'big_V'( not( X ), not( Y ) ) ), 'big_hat'( X, Y ) ) ]
% 0.73/1.51 )
% 0.73/1.51 .
% 0.73/1.51 clause( 6, [ ~( ordered( X, Y ) ), =( implies( X, Y ), truth ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 7, [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 8, [ ~( =( 'big_V'( not( x ), not( y ) ), not( 'big_hat'( x, y ) )
% 0.73/1.51 ) ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 12, [ =( truth, X ), ~( ordered( truth, X ) ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 22, [ =( implies( X, 'big_V'( X, Y ) ), truth ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 37, [ ordered( X, Y ), ~( ordered( truth, implies( X, Y ) ) ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 41, [ =( 'big_V'( X, Y ), 'big_V'( Y, X ) ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 44, [ ordered( X, 'big_V'( X, Y ) ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 48, [ =( implies( implies( 'big_V'( X, Y ), Z ), implies( X, Z ) )
% 0.73/1.51 , truth ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 51, [ =( 'big_V'( truth, X ), truth ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 52, [ ordered( X, 'big_V'( Y, X ) ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 56, [ =( 'big_V'( X, truth ), truth ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 59, [ ordered( implies( not( X ), not( Y ) ), implies( Y, X ) ) ]
% 0.73/1.51 )
% 0.73/1.51 .
% 0.73/1.51 clause( 75, [ ~( ordered( not( X ), not( Y ) ) ), =( implies( Y, X ), truth
% 0.73/1.51 ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 79, [ =( implies( X, truth ), truth ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 86, [ =( implies( Y, implies( X, Y ) ), truth ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 100, [ ~( ordered( X, Y ) ), =( 'big_V'( X, Y ), Y ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 102, [ =( implies( X, X ), truth ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 103, [ ordered( X, X ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 124, [ =( 'big_V'( X, implies( Y, X ) ), implies( Y, X ) ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 152, [ =( 'big_V'( Y, X ), Y ), ~( ordered( X, Y ) ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 168, [ ~( ordered( X, Y ) ), =( X, Y ), ~( ordered( Y, X ) ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 913, [ ordered( implies( 'big_V'( X, Y ), Z ), implies( X, Z ) ) ]
% 0.73/1.51 )
% 0.73/1.51 .
% 0.73/1.51 clause( 1054, [ ordered( implies( implies( Y, X ), Z ), implies( X, Z ) ) ]
% 0.73/1.51 )
% 0.73/1.51 .
% 0.73/1.51 clause( 1077, [ ordered( truth, implies( not( Y ), implies( Y, X ) ) ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 1088, [ ordered( not( X ), implies( X, Y ) ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 1117, [ ordered( not( implies( X, Y ) ), 'big_V'( X, Y ) ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 1118, [ ordered( not( truth ), X ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 1122, [ =( 'big_V'( X, not( truth ) ), X ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 1148, [ ordered( implies( not( X ), not( truth ) ), X ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 2231, [ ordered( not( implies( X, not( truth ) ) ), X ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 3427, [ ~( ordered( not( X ), not( Y ) ) ), ordered( Y, X ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 3461, [ ordered( X, implies( not( X ), not( truth ) ) ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 3484, [ =( implies( not( X ), not( truth ) ), X ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 3553, [ =( implies( X, not( truth ) ), not( X ) ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 3555, [ =( not( not( X ) ), X ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 3596, [ =( 'big_V'( not( X ), not( Y ) ), not( 'big_hat'( X, Y ) )
% 0.73/1.51 ) ] )
% 0.73/1.51 .
% 0.73/1.51 clause( 4040, [] )
% 0.73/1.51 .
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 % SZS output end Refutation
% 0.73/1.51 found a proof!
% 0.73/1.51
% 0.73/1.51 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.73/1.51
% 0.73/1.51 initialclauses(
% 0.73/1.51 [ clause( 4042, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 , clause( 4043, [ =( implies( implies( X, Y ), implies( implies( Y, Z ),
% 0.73/1.51 implies( X, Z ) ) ), truth ) ] )
% 0.73/1.51 , clause( 4044, [ =( implies( implies( X, Y ), Y ), implies( implies( Y, X
% 0.73/1.51 ), X ) ) ] )
% 0.73/1.51 , clause( 4045, [ =( implies( implies( not( X ), not( Y ) ), implies( Y, X
% 0.73/1.51 ) ), truth ) ] )
% 0.73/1.51 , clause( 4046, [ =( 'big_V'( X, Y ), implies( implies( X, Y ), Y ) ) ] )
% 0.73/1.51 , clause( 4047, [ =( 'big_hat'( X, Y ), not( 'big_V'( not( X ), not( Y ) )
% 0.73/1.51 ) ) ] )
% 0.73/1.51 , clause( 4048, [ ~( ordered( X, Y ) ), =( implies( X, Y ), truth ) ] )
% 0.73/1.51 , clause( 4049, [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ] )
% 0.73/1.51 , clause( 4050, [ ~( =( not( 'big_hat'( x, y ) ), 'big_V'( not( x ), not( y
% 0.73/1.51 ) ) ) ) ] )
% 0.73/1.51 ] ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 , clause( 4042, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 1, [ =( implies( implies( X, Y ), implies( implies( Y, Z ), implies(
% 0.73/1.51 X, Z ) ) ), truth ) ] )
% 0.73/1.51 , clause( 4043, [ =( implies( implies( X, Y ), implies( implies( Y, Z ),
% 0.73/1.51 implies( X, Z ) ) ), truth ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.51 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 2, [ =( implies( implies( X, Y ), Y ), implies( implies( Y, X ), X
% 0.73/1.51 ) ) ] )
% 0.73/1.51 , clause( 4044, [ =( implies( implies( X, Y ), Y ), implies( implies( Y, X
% 0.73/1.51 ), X ) ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 3, [ =( implies( implies( not( X ), not( Y ) ), implies( Y, X ) ),
% 0.73/1.51 truth ) ] )
% 0.73/1.51 , clause( 4045, [ =( implies( implies( not( X ), not( Y ) ), implies( Y, X
% 0.73/1.51 ) ), truth ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4062, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , clause( 4046, [ =( 'big_V'( X, Y ), implies( implies( X, Y ), Y ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 4, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , clause( 4062, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4067, [ =( not( 'big_V'( not( X ), not( Y ) ) ), 'big_hat'( X, Y )
% 0.73/1.51 ) ] )
% 0.73/1.51 , clause( 4047, [ =( 'big_hat'( X, Y ), not( 'big_V'( not( X ), not( Y ) )
% 0.73/1.51 ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 5, [ =( not( 'big_V'( not( X ), not( Y ) ) ), 'big_hat'( X, Y ) ) ]
% 0.73/1.51 )
% 0.73/1.51 , clause( 4067, [ =( not( 'big_V'( not( X ), not( Y ) ) ), 'big_hat'( X, Y
% 0.73/1.51 ) ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 6, [ ~( ordered( X, Y ) ), =( implies( X, Y ), truth ) ] )
% 0.73/1.51 , clause( 4048, [ ~( ordered( X, Y ) ), =( implies( X, Y ), truth ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 ), ==>( 1, 1 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 7, [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ] )
% 0.73/1.51 , clause( 4049, [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 ), ==>( 1, 1 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4088, [ ~( =( 'big_V'( not( x ), not( y ) ), not( 'big_hat'( x, y )
% 0.73/1.51 ) ) ) ] )
% 0.73/1.51 , clause( 4050, [ ~( =( not( 'big_hat'( x, y ) ), 'big_V'( not( x ), not( y
% 0.73/1.51 ) ) ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 8, [ ~( =( 'big_V'( not( x ), not( y ) ), not( 'big_hat'( x, y ) )
% 0.73/1.51 ) ) ] )
% 0.73/1.51 , clause( 4088, [ ~( =( 'big_V'( not( x ), not( y ) ), not( 'big_hat'( x, y
% 0.73/1.51 ) ) ) ) ] )
% 0.73/1.51 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4089, [ =( truth, implies( X, Y ) ), ~( ordered( X, Y ) ) ] )
% 0.73/1.51 , clause( 6, [ ~( ordered( X, Y ) ), =( implies( X, Y ), truth ) ] )
% 0.73/1.51 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4091, [ =( truth, X ), ~( ordered( truth, X ) ) ] )
% 0.73/1.51 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 , 0, clause( 4089, [ =( truth, implies( X, Y ) ), ~( ordered( X, Y ) ) ] )
% 0.73/1.51 , 0, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, truth )
% 0.73/1.51 , :=( Y, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 12, [ =( truth, X ), ~( ordered( truth, X ) ) ] )
% 0.73/1.51 , clause( 4091, [ =( truth, X ), ~( ordered( truth, X ) ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.73/1.51 1 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4094, [ =( truth, implies( implies( X, Y ), implies( implies( Y, Z
% 0.73/1.51 ), implies( X, Z ) ) ) ) ] )
% 0.73/1.51 , clause( 1, [ =( implies( implies( X, Y ), implies( implies( Y, Z ),
% 0.73/1.51 implies( X, Z ) ) ), truth ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4099, [ =( truth, implies( implies( truth, X ), implies( implies( X
% 0.73/1.51 , Y ), Y ) ) ) ] )
% 0.73/1.51 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 , 0, clause( 4094, [ =( truth, implies( implies( X, Y ), implies( implies(
% 0.73/1.51 Y, Z ), implies( X, Z ) ) ) ) ] )
% 0.73/1.51 , 0, 10, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, truth
% 0.73/1.51 ), :=( Y, X ), :=( Z, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4101, [ =( truth, implies( X, implies( implies( X, Y ), Y ) ) ) ]
% 0.73/1.51 )
% 0.73/1.51 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 , 0, clause( 4099, [ =( truth, implies( implies( truth, X ), implies(
% 0.73/1.51 implies( X, Y ), Y ) ) ) ] )
% 0.73/1.51 , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.73/1.51 :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4102, [ =( truth, implies( X, 'big_V'( X, Y ) ) ) ] )
% 0.73/1.51 , clause( 4, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , 0, clause( 4101, [ =( truth, implies( X, implies( implies( X, Y ), Y ) )
% 0.73/1.51 ) ] )
% 0.73/1.51 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.73/1.51 :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4103, [ =( implies( X, 'big_V'( X, Y ) ), truth ) ] )
% 0.73/1.51 , clause( 4102, [ =( truth, implies( X, 'big_V'( X, Y ) ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 22, [ =( implies( X, 'big_V'( X, Y ) ), truth ) ] )
% 0.73/1.51 , clause( 4103, [ =( implies( X, 'big_V'( X, Y ) ), truth ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4104, [ =( X, truth ), ~( ordered( truth, X ) ) ] )
% 0.73/1.51 , clause( 12, [ =( truth, X ), ~( ordered( truth, X ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4105, [ ~( =( truth, implies( X, Y ) ) ), ordered( X, Y ) ] )
% 0.73/1.51 , clause( 7, [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4107, [ ~( =( truth, truth ) ), ~( ordered( truth, implies( X, Y )
% 0.73/1.51 ) ), ordered( X, Y ) ] )
% 0.73/1.51 , clause( 4104, [ =( X, truth ), ~( ordered( truth, X ) ) ] )
% 0.73/1.51 , 0, clause( 4105, [ ~( =( truth, implies( X, Y ) ) ), ordered( X, Y ) ] )
% 0.73/1.51 , 0, 3, substitution( 0, [ :=( X, implies( X, Y ) )] ), substitution( 1, [
% 0.73/1.51 :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqrefl(
% 0.73/1.51 clause( 4118, [ ~( ordered( truth, implies( X, Y ) ) ), ordered( X, Y ) ]
% 0.73/1.51 )
% 0.73/1.51 , clause( 4107, [ ~( =( truth, truth ) ), ~( ordered( truth, implies( X, Y
% 0.73/1.51 ) ) ), ordered( X, Y ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 37, [ ordered( X, Y ), ~( ordered( truth, implies( X, Y ) ) ) ] )
% 0.73/1.51 , clause( 4118, [ ~( ordered( truth, implies( X, Y ) ) ), ordered( X, Y ) ]
% 0.73/1.51 )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 0.73/1.51 ), ==>( 1, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4122, [ =( implies( implies( X, Y ), Y ), 'big_V'( Y, X ) ) ] )
% 0.73/1.51 , clause( 4, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , 0, clause( 2, [ =( implies( implies( X, Y ), Y ), implies( implies( Y, X
% 0.73/1.51 ), X ) ) ] )
% 0.73/1.51 , 0, 6, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 0.73/1.51 :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4124, [ =( 'big_V'( X, Y ), 'big_V'( Y, X ) ) ] )
% 0.73/1.51 , clause( 4, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , 0, clause( 4122, [ =( implies( implies( X, Y ), Y ), 'big_V'( Y, X ) ) ]
% 0.73/1.51 )
% 0.73/1.51 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.73/1.51 :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 41, [ =( 'big_V'( X, Y ), 'big_V'( Y, X ) ) ] )
% 0.73/1.51 , clause( 4124, [ =( 'big_V'( X, Y ), 'big_V'( Y, X ) ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4125, [ =( truth, implies( X, 'big_V'( X, Y ) ) ) ] )
% 0.73/1.51 , clause( 22, [ =( implies( X, 'big_V'( X, Y ) ), truth ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4126, [ ~( =( truth, implies( X, Y ) ) ), ordered( X, Y ) ] )
% 0.73/1.51 , clause( 7, [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 resolution(
% 0.73/1.51 clause( 4127, [ ordered( X, 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , clause( 4126, [ ~( =( truth, implies( X, Y ) ) ), ordered( X, Y ) ] )
% 0.73/1.51 , 0, clause( 4125, [ =( truth, implies( X, 'big_V'( X, Y ) ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'big_V'( X, Y ) )] ),
% 0.73/1.51 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 44, [ ordered( X, 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , clause( 4127, [ ordered( X, 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4129, [ =( truth, implies( implies( X, Y ), implies( implies( Y, Z
% 0.73/1.51 ), implies( X, Z ) ) ) ) ] )
% 0.73/1.51 , clause( 1, [ =( implies( implies( X, Y ), implies( implies( Y, Z ),
% 0.73/1.51 implies( X, Z ) ) ), truth ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4131, [ =( truth, implies( truth, implies( implies( 'big_V'( X, Y )
% 0.73/1.51 , Z ), implies( X, Z ) ) ) ) ] )
% 0.73/1.51 , clause( 22, [ =( implies( X, 'big_V'( X, Y ) ), truth ) ] )
% 0.73/1.51 , 0, clause( 4129, [ =( truth, implies( implies( X, Y ), implies( implies(
% 0.73/1.51 Y, Z ), implies( X, Z ) ) ) ) ] )
% 0.73/1.51 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.73/1.51 :=( X, X ), :=( Y, 'big_V'( X, Y ) ), :=( Z, Z )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4136, [ =( truth, implies( implies( 'big_V'( X, Y ), Z ), implies(
% 0.73/1.51 X, Z ) ) ) ] )
% 0.73/1.51 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 , 0, clause( 4131, [ =( truth, implies( truth, implies( implies( 'big_V'( X
% 0.73/1.51 , Y ), Z ), implies( X, Z ) ) ) ) ] )
% 0.73/1.51 , 0, 2, substitution( 0, [ :=( X, implies( implies( 'big_V'( X, Y ), Z ),
% 0.73/1.51 implies( X, Z ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z
% 0.73/1.51 , Z )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4137, [ =( implies( implies( 'big_V'( X, Y ), Z ), implies( X, Z )
% 0.73/1.51 ), truth ) ] )
% 0.73/1.51 , clause( 4136, [ =( truth, implies( implies( 'big_V'( X, Y ), Z ), implies(
% 0.73/1.51 X, Z ) ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 48, [ =( implies( implies( 'big_V'( X, Y ), Z ), implies( X, Z ) )
% 0.73/1.51 , truth ) ] )
% 0.73/1.51 , clause( 4137, [ =( implies( implies( 'big_V'( X, Y ), Z ), implies( X, Z
% 0.73/1.51 ) ), truth ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.51 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4138, [ =( truth, implies( X, 'big_V'( X, Y ) ) ) ] )
% 0.73/1.51 , clause( 22, [ =( implies( X, 'big_V'( X, Y ) ), truth ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4140, [ =( truth, 'big_V'( truth, X ) ) ] )
% 0.73/1.51 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 , 0, clause( 4138, [ =( truth, implies( X, 'big_V'( X, Y ) ) ) ] )
% 0.73/1.51 , 0, 2, substitution( 0, [ :=( X, 'big_V'( truth, X ) )] ), substitution( 1
% 0.73/1.51 , [ :=( X, truth ), :=( Y, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4141, [ =( 'big_V'( truth, X ), truth ) ] )
% 0.73/1.51 , clause( 4140, [ =( truth, 'big_V'( truth, X ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 51, [ =( 'big_V'( truth, X ), truth ) ] )
% 0.73/1.51 , clause( 4141, [ =( 'big_V'( truth, X ), truth ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4142, [ ordered( X, 'big_V'( Y, X ) ) ] )
% 0.73/1.51 , clause( 41, [ =( 'big_V'( X, Y ), 'big_V'( Y, X ) ) ] )
% 0.73/1.51 , 0, clause( 44, [ ordered( X, 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.73/1.51 :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 52, [ ordered( X, 'big_V'( Y, X ) ) ] )
% 0.73/1.51 , clause( 4142, [ ordered( X, 'big_V'( Y, X ) ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4144, [ =( X, truth ), ~( ordered( truth, X ) ) ] )
% 0.73/1.51 , clause( 12, [ =( truth, X ), ~( ordered( truth, X ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 resolution(
% 0.73/1.51 clause( 4145, [ =( 'big_V'( X, truth ), truth ) ] )
% 0.73/1.51 , clause( 4144, [ =( X, truth ), ~( ordered( truth, X ) ) ] )
% 0.73/1.51 , 1, clause( 52, [ ordered( X, 'big_V'( Y, X ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, 'big_V'( X, truth ) )] ), substitution( 1, [
% 0.73/1.51 :=( X, truth ), :=( Y, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 56, [ =( 'big_V'( X, truth ), truth ) ] )
% 0.73/1.51 , clause( 4145, [ =( 'big_V'( X, truth ), truth ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4147, [ =( truth, implies( implies( not( X ), not( Y ) ), implies(
% 0.73/1.51 Y, X ) ) ) ] )
% 0.73/1.51 , clause( 3, [ =( implies( implies( not( X ), not( Y ) ), implies( Y, X ) )
% 0.73/1.51 , truth ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4148, [ ~( =( truth, implies( X, Y ) ) ), ordered( X, Y ) ] )
% 0.73/1.51 , clause( 7, [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 resolution(
% 0.73/1.51 clause( 4149, [ ordered( implies( not( X ), not( Y ) ), implies( Y, X ) ) ]
% 0.73/1.51 )
% 0.73/1.51 , clause( 4148, [ ~( =( truth, implies( X, Y ) ) ), ordered( X, Y ) ] )
% 0.73/1.51 , 0, clause( 4147, [ =( truth, implies( implies( not( X ), not( Y ) ),
% 0.73/1.51 implies( Y, X ) ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, implies( not( X ), not( Y ) ) ), :=( Y,
% 0.73/1.51 implies( Y, X ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 59, [ ordered( implies( not( X ), not( Y ) ), implies( Y, X ) ) ]
% 0.73/1.51 )
% 0.73/1.51 , clause( 4149, [ ordered( implies( not( X ), not( Y ) ), implies( Y, X ) )
% 0.73/1.51 ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4151, [ =( truth, implies( implies( not( X ), not( Y ) ), implies(
% 0.73/1.51 Y, X ) ) ) ] )
% 0.73/1.51 , clause( 3, [ =( implies( implies( not( X ), not( Y ) ), implies( Y, X ) )
% 0.73/1.51 , truth ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4155, [ =( truth, implies( truth, implies( Y, X ) ) ), ~( ordered(
% 0.73/1.51 not( X ), not( Y ) ) ) ] )
% 0.73/1.51 , clause( 6, [ ~( ordered( X, Y ) ), =( implies( X, Y ), truth ) ] )
% 0.73/1.51 , 1, clause( 4151, [ =( truth, implies( implies( not( X ), not( Y ) ),
% 0.73/1.51 implies( Y, X ) ) ) ] )
% 0.73/1.51 , 0, 3, substitution( 0, [ :=( X, not( X ) ), :=( Y, not( Y ) )] ),
% 0.73/1.51 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4163, [ =( truth, implies( X, Y ) ), ~( ordered( not( Y ), not( X )
% 0.73/1.51 ) ) ] )
% 0.73/1.51 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 , 0, clause( 4155, [ =( truth, implies( truth, implies( Y, X ) ) ), ~(
% 0.73/1.51 ordered( not( X ), not( Y ) ) ) ] )
% 0.73/1.51 , 0, 2, substitution( 0, [ :=( X, implies( X, Y ) )] ), substitution( 1, [
% 0.73/1.51 :=( X, Y ), :=( Y, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4164, [ =( implies( X, Y ), truth ), ~( ordered( not( Y ), not( X )
% 0.73/1.51 ) ) ] )
% 0.73/1.51 , clause( 4163, [ =( truth, implies( X, Y ) ), ~( ordered( not( Y ), not( X
% 0.73/1.51 ) ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 75, [ ~( ordered( not( X ), not( Y ) ) ), =( implies( Y, X ), truth
% 0.73/1.51 ) ] )
% 0.73/1.51 , clause( 4164, [ =( implies( X, Y ), truth ), ~( ordered( not( Y ), not( X
% 0.73/1.51 ) ) ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 1
% 0.73/1.51 ), ==>( 1, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4166, [ =( truth, implies( X, 'big_V'( X, Y ) ) ) ] )
% 0.73/1.51 , clause( 22, [ =( implies( X, 'big_V'( X, Y ) ), truth ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4167, [ =( truth, implies( X, truth ) ) ] )
% 0.73/1.51 , clause( 56, [ =( 'big_V'( X, truth ), truth ) ] )
% 0.73/1.51 , 0, clause( 4166, [ =( truth, implies( X, 'big_V'( X, Y ) ) ) ] )
% 0.73/1.51 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.73/1.51 :=( Y, truth )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4168, [ =( implies( X, truth ), truth ) ] )
% 0.73/1.51 , clause( 4167, [ =( truth, implies( X, truth ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 79, [ =( implies( X, truth ), truth ) ] )
% 0.73/1.51 , clause( 4168, [ =( implies( X, truth ), truth ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4170, [ =( truth, implies( implies( X, Y ), implies( implies( Y, Z
% 0.73/1.51 ), implies( X, Z ) ) ) ) ] )
% 0.73/1.51 , clause( 1, [ =( implies( implies( X, Y ), implies( implies( Y, Z ),
% 0.73/1.51 implies( X, Z ) ) ), truth ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4173, [ =( truth, implies( truth, implies( implies( truth, Y ),
% 0.73/1.51 implies( X, Y ) ) ) ) ] )
% 0.73/1.51 , clause( 79, [ =( implies( X, truth ), truth ) ] )
% 0.73/1.51 , 0, clause( 4170, [ =( truth, implies( implies( X, Y ), implies( implies(
% 0.73/1.51 Y, Z ), implies( X, Z ) ) ) ) ] )
% 0.73/1.51 , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.73/1.51 :=( Y, truth ), :=( Z, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4182, [ =( truth, implies( truth, implies( X, implies( Y, X ) ) ) )
% 0.73/1.51 ] )
% 0.73/1.51 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 , 0, clause( 4173, [ =( truth, implies( truth, implies( implies( truth, Y )
% 0.73/1.51 , implies( X, Y ) ) ) ) ] )
% 0.73/1.51 , 0, 5, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, Y ),
% 0.73/1.51 :=( Y, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4184, [ =( truth, implies( X, implies( Y, X ) ) ) ] )
% 0.73/1.51 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 , 0, clause( 4182, [ =( truth, implies( truth, implies( X, implies( Y, X )
% 0.73/1.51 ) ) ) ] )
% 0.73/1.51 , 0, 2, substitution( 0, [ :=( X, implies( X, implies( Y, X ) ) )] ),
% 0.73/1.51 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4185, [ =( implies( X, implies( Y, X ) ), truth ) ] )
% 0.73/1.51 , clause( 4184, [ =( truth, implies( X, implies( Y, X ) ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 86, [ =( implies( Y, implies( X, Y ) ), truth ) ] )
% 0.73/1.51 , clause( 4185, [ =( implies( X, implies( Y, X ) ), truth ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4187, [ =( 'big_V'( X, Y ), implies( implies( X, Y ), Y ) ) ] )
% 0.73/1.51 , clause( 4, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4191, [ =( 'big_V'( X, Y ), implies( truth, Y ) ), ~( ordered( X, Y
% 0.73/1.51 ) ) ] )
% 0.73/1.51 , clause( 6, [ ~( ordered( X, Y ) ), =( implies( X, Y ), truth ) ] )
% 0.73/1.51 , 1, clause( 4187, [ =( 'big_V'( X, Y ), implies( implies( X, Y ), Y ) ) ]
% 0.73/1.51 )
% 0.73/1.51 , 0, 5, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.73/1.51 :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4194, [ =( 'big_V'( X, Y ), Y ), ~( ordered( X, Y ) ) ] )
% 0.73/1.51 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 , 0, clause( 4191, [ =( 'big_V'( X, Y ), implies( truth, Y ) ), ~( ordered(
% 0.73/1.51 X, Y ) ) ] )
% 0.73/1.51 , 0, 4, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.73/1.51 :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 100, [ ~( ordered( X, Y ) ), =( 'big_V'( X, Y ), Y ) ] )
% 0.73/1.51 , clause( 4194, [ =( 'big_V'( X, Y ), Y ), ~( ordered( X, Y ) ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 0.73/1.51 ), ==>( 1, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4197, [ =( 'big_V'( X, Y ), implies( implies( X, Y ), Y ) ) ] )
% 0.73/1.51 , clause( 4, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4199, [ =( 'big_V'( truth, X ), implies( X, X ) ) ] )
% 0.73/1.51 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 , 0, clause( 4197, [ =( 'big_V'( X, Y ), implies( implies( X, Y ), Y ) ) ]
% 0.73/1.51 )
% 0.73/1.51 , 0, 5, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, truth )
% 0.73/1.51 , :=( Y, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4200, [ =( truth, implies( X, X ) ) ] )
% 0.73/1.51 , clause( 51, [ =( 'big_V'( truth, X ), truth ) ] )
% 0.73/1.51 , 0, clause( 4199, [ =( 'big_V'( truth, X ), implies( X, X ) ) ] )
% 0.73/1.51 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.73/1.51 ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4201, [ =( implies( X, X ), truth ) ] )
% 0.73/1.51 , clause( 4200, [ =( truth, implies( X, X ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 102, [ =( implies( X, X ), truth ) ] )
% 0.73/1.51 , clause( 4201, [ =( implies( X, X ), truth ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4202, [ =( truth, implies( X, X ) ) ] )
% 0.73/1.51 , clause( 102, [ =( implies( X, X ), truth ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4203, [ ~( =( truth, implies( X, Y ) ) ), ordered( X, Y ) ] )
% 0.73/1.51 , clause( 7, [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 resolution(
% 0.73/1.51 clause( 4204, [ ordered( X, X ) ] )
% 0.73/1.51 , clause( 4203, [ ~( =( truth, implies( X, Y ) ) ), ordered( X, Y ) ] )
% 0.73/1.51 , 0, clause( 4202, [ =( truth, implies( X, X ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, X )] ), substitution( 1, [ :=( X
% 0.73/1.51 , X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 103, [ ordered( X, X ) ] )
% 0.73/1.51 , clause( 4204, [ ordered( X, X ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4206, [ =( 'big_V'( X, Y ), implies( implies( X, Y ), Y ) ) ] )
% 0.73/1.51 , clause( 4, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4209, [ =( 'big_V'( X, implies( Y, X ) ), implies( truth, implies(
% 0.73/1.51 Y, X ) ) ) ] )
% 0.73/1.51 , clause( 86, [ =( implies( Y, implies( X, Y ) ), truth ) ] )
% 0.73/1.51 , 0, clause( 4206, [ =( 'big_V'( X, Y ), implies( implies( X, Y ), Y ) ) ]
% 0.73/1.51 )
% 0.73/1.51 , 0, 7, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 0.73/1.51 :=( X, X ), :=( Y, implies( Y, X ) )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4210, [ =( 'big_V'( X, implies( Y, X ) ), implies( Y, X ) ) ] )
% 0.73/1.51 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 , 0, clause( 4209, [ =( 'big_V'( X, implies( Y, X ) ), implies( truth,
% 0.73/1.51 implies( Y, X ) ) ) ] )
% 0.73/1.51 , 0, 6, substitution( 0, [ :=( X, implies( Y, X ) )] ), substitution( 1, [
% 0.73/1.51 :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 124, [ =( 'big_V'( X, implies( Y, X ) ), implies( Y, X ) ) ] )
% 0.73/1.51 , clause( 4210, [ =( 'big_V'( X, implies( Y, X ) ), implies( Y, X ) ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4212, [ =( Y, 'big_V'( X, Y ) ), ~( ordered( X, Y ) ) ] )
% 0.73/1.51 , clause( 100, [ ~( ordered( X, Y ) ), =( 'big_V'( X, Y ), Y ) ] )
% 0.73/1.51 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4213, [ =( X, 'big_V'( X, Y ) ), ~( ordered( Y, X ) ) ] )
% 0.73/1.51 , clause( 41, [ =( 'big_V'( X, Y ), 'big_V'( Y, X ) ) ] )
% 0.73/1.51 , 0, clause( 4212, [ =( Y, 'big_V'( X, Y ) ), ~( ordered( X, Y ) ) ] )
% 0.73/1.51 , 0, 2, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 0.73/1.51 :=( X, Y ), :=( Y, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4216, [ =( 'big_V'( X, Y ), X ), ~( ordered( Y, X ) ) ] )
% 0.73/1.51 , clause( 4213, [ =( X, 'big_V'( X, Y ) ), ~( ordered( Y, X ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 152, [ =( 'big_V'( Y, X ), Y ), ~( ordered( X, Y ) ) ] )
% 0.73/1.51 , clause( 4216, [ =( 'big_V'( X, Y ), X ), ~( ordered( Y, X ) ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 ), ==>( 1, 1 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4217, [ =( X, 'big_V'( X, Y ) ), ~( ordered( Y, X ) ) ] )
% 0.73/1.51 , clause( 152, [ =( 'big_V'( Y, X ), Y ), ~( ordered( X, Y ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4219, [ =( X, Y ), ~( ordered( X, Y ) ), ~( ordered( Y, X ) ) ] )
% 0.73/1.51 , clause( 100, [ ~( ordered( X, Y ) ), =( 'big_V'( X, Y ), Y ) ] )
% 0.73/1.51 , 1, clause( 4217, [ =( X, 'big_V'( X, Y ) ), ~( ordered( Y, X ) ) ] )
% 0.73/1.51 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.73/1.51 :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 168, [ ~( ordered( X, Y ) ), =( X, Y ), ~( ordered( Y, X ) ) ] )
% 0.73/1.51 , clause( 4219, [ =( X, Y ), ~( ordered( X, Y ) ), ~( ordered( Y, X ) ) ]
% 0.73/1.51 )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 0.73/1.51 ), ==>( 1, 0 ), ==>( 2, 2 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4221, [ =( truth, implies( implies( 'big_V'( X, Y ), Z ), implies(
% 0.73/1.51 X, Z ) ) ) ] )
% 0.73/1.51 , clause( 48, [ =( implies( implies( 'big_V'( X, Y ), Z ), implies( X, Z )
% 0.73/1.51 ), truth ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4222, [ ~( =( truth, implies( X, Y ) ) ), ordered( X, Y ) ] )
% 0.73/1.51 , clause( 7, [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 resolution(
% 0.73/1.51 clause( 4223, [ ordered( implies( 'big_V'( X, Y ), Z ), implies( X, Z ) ) ]
% 0.73/1.51 )
% 0.73/1.51 , clause( 4222, [ ~( =( truth, implies( X, Y ) ) ), ordered( X, Y ) ] )
% 0.73/1.51 , 0, clause( 4221, [ =( truth, implies( implies( 'big_V'( X, Y ), Z ),
% 0.73/1.51 implies( X, Z ) ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, implies( 'big_V'( X, Y ), Z ) ), :=( Y,
% 0.73/1.51 implies( X, Z ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z
% 0.73/1.51 )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 913, [ ordered( implies( 'big_V'( X, Y ), Z ), implies( X, Z ) ) ]
% 0.73/1.51 )
% 0.73/1.51 , clause( 4223, [ ordered( implies( 'big_V'( X, Y ), Z ), implies( X, Z ) )
% 0.73/1.51 ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.51 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4225, [ ordered( implies( implies( Y, X ), Z ), implies( X, Z ) ) ]
% 0.73/1.51 )
% 0.73/1.51 , clause( 124, [ =( 'big_V'( X, implies( Y, X ) ), implies( Y, X ) ) ] )
% 0.73/1.51 , 0, clause( 913, [ ordered( implies( 'big_V'( X, Y ), Z ), implies( X, Z )
% 0.73/1.51 ) ] )
% 0.73/1.51 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.73/1.51 :=( X, X ), :=( Y, implies( Y, X ) ), :=( Z, Z )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 1054, [ ordered( implies( implies( Y, X ), Z ), implies( X, Z ) ) ]
% 0.73/1.51 )
% 0.73/1.51 , clause( 4225, [ ordered( implies( implies( Y, X ), Z ), implies( X, Z ) )
% 0.73/1.51 ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.51 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4227, [ ordered( truth, implies( not( Y ), implies( Y, X ) ) ) ] )
% 0.73/1.51 , clause( 3, [ =( implies( implies( not( X ), not( Y ) ), implies( Y, X ) )
% 0.73/1.51 , truth ) ] )
% 0.73/1.51 , 0, clause( 1054, [ ordered( implies( implies( Y, X ), Z ), implies( X, Z
% 0.73/1.51 ) ) ] )
% 0.73/1.51 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.73/1.51 :=( X, not( Y ) ), :=( Y, not( X ) ), :=( Z, implies( Y, X ) )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 1077, [ ordered( truth, implies( not( Y ), implies( Y, X ) ) ) ] )
% 0.73/1.51 , clause( 4227, [ ordered( truth, implies( not( Y ), implies( Y, X ) ) ) ]
% 0.73/1.51 )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 resolution(
% 0.73/1.51 clause( 4230, [ ordered( not( X ), implies( X, Y ) ) ] )
% 0.73/1.51 , clause( 37, [ ordered( X, Y ), ~( ordered( truth, implies( X, Y ) ) ) ]
% 0.73/1.51 )
% 0.73/1.51 , 1, clause( 1077, [ ordered( truth, implies( not( Y ), implies( Y, X ) ) )
% 0.73/1.51 ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, not( X ) ), :=( Y, implies( X, Y ) )] ),
% 0.73/1.51 substitution( 1, [ :=( X, Y ), :=( Y, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 1088, [ ordered( not( X ), implies( X, Y ) ) ] )
% 0.73/1.51 , clause( 4230, [ ordered( not( X ), implies( X, Y ) ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4232, [ ordered( not( implies( X, Y ) ), 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , clause( 4, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , 0, clause( 1088, [ ordered( not( X ), implies( X, Y ) ) ] )
% 0.73/1.51 , 0, 5, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.73/1.51 :=( X, implies( X, Y ) ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 1117, [ ordered( not( implies( X, Y ) ), 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , clause( 4232, [ ordered( not( implies( X, Y ) ), 'big_V'( X, Y ) ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.51 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4234, [ ordered( not( truth ), X ) ] )
% 0.73/1.51 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 , 0, clause( 1088, [ ordered( not( X ), implies( X, Y ) ) ] )
% 0.73/1.51 , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, truth )
% 0.73/1.51 , :=( Y, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 1118, [ ordered( not( truth ), X ) ] )
% 0.73/1.51 , clause( 4234, [ ordered( not( truth ), X ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4235, [ =( X, 'big_V'( X, Y ) ), ~( ordered( Y, X ) ) ] )
% 0.73/1.51 , clause( 152, [ =( 'big_V'( Y, X ), Y ), ~( ordered( X, Y ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 resolution(
% 0.73/1.51 clause( 4236, [ =( X, 'big_V'( X, not( truth ) ) ) ] )
% 0.73/1.51 , clause( 4235, [ =( X, 'big_V'( X, Y ) ), ~( ordered( Y, X ) ) ] )
% 0.73/1.51 , 1, clause( 1118, [ ordered( not( truth ), X ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, not( truth ) )] ),
% 0.73/1.51 substitution( 1, [ :=( X, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4237, [ =( 'big_V'( X, not( truth ) ), X ) ] )
% 0.73/1.51 , clause( 4236, [ =( X, 'big_V'( X, not( truth ) ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 1122, [ =( 'big_V'( X, not( truth ) ), X ) ] )
% 0.73/1.51 , clause( 4237, [ =( 'big_V'( X, not( truth ) ), X ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4239, [ ordered( implies( not( X ), not( truth ) ), X ) ] )
% 0.73/1.51 , clause( 0, [ =( implies( truth, X ), X ) ] )
% 0.73/1.51 , 0, clause( 59, [ ordered( implies( not( X ), not( Y ) ), implies( Y, X )
% 0.73/1.51 ) ] )
% 0.73/1.51 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.73/1.51 :=( Y, truth )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 1148, [ ordered( implies( not( X ), not( truth ) ), X ) ] )
% 0.73/1.51 , clause( 4239, [ ordered( implies( not( X ), not( truth ) ), X ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 paramod(
% 0.73/1.51 clause( 4241, [ ordered( not( implies( X, not( truth ) ) ), X ) ] )
% 0.73/1.51 , clause( 1122, [ =( 'big_V'( X, not( truth ) ), X ) ] )
% 0.73/1.51 , 0, clause( 1117, [ ordered( not( implies( X, Y ) ), 'big_V'( X, Y ) ) ]
% 0.73/1.51 )
% 0.73/1.51 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.73/1.51 :=( Y, not( truth ) )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 2231, [ ordered( not( implies( X, not( truth ) ) ), X ) ] )
% 0.73/1.51 , clause( 4241, [ ordered( not( implies( X, not( truth ) ) ), X ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4242, [ =( truth, implies( X, Y ) ), ~( ordered( not( Y ), not( X )
% 0.73/1.51 ) ) ] )
% 0.73/1.51 , clause( 75, [ ~( ordered( not( X ), not( Y ) ) ), =( implies( Y, X ),
% 0.73/1.51 truth ) ] )
% 0.73/1.51 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4243, [ ~( =( truth, implies( X, Y ) ) ), ordered( X, Y ) ] )
% 0.73/1.51 , clause( 7, [ ~( =( implies( X, Y ), truth ) ), ordered( X, Y ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 resolution(
% 0.73/1.51 clause( 4248, [ ordered( X, Y ), ~( ordered( not( Y ), not( X ) ) ) ] )
% 0.73/1.51 , clause( 4243, [ ~( =( truth, implies( X, Y ) ) ), ordered( X, Y ) ] )
% 0.73/1.51 , 0, clause( 4242, [ =( truth, implies( X, Y ) ), ~( ordered( not( Y ), not(
% 0.73/1.51 X ) ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 0.73/1.51 , X ), :=( Y, Y )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 3427, [ ~( ordered( not( X ), not( Y ) ) ), ordered( Y, X ) ] )
% 0.73/1.51 , clause( 4248, [ ordered( X, Y ), ~( ordered( not( Y ), not( X ) ) ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 1
% 0.73/1.51 ), ==>( 1, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 resolution(
% 0.73/1.51 clause( 4249, [ ordered( X, implies( not( X ), not( truth ) ) ) ] )
% 0.73/1.51 , clause( 3427, [ ~( ordered( not( X ), not( Y ) ) ), ordered( Y, X ) ] )
% 0.73/1.51 , 0, clause( 2231, [ ordered( not( implies( X, not( truth ) ) ), X ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, implies( not( X ), not( truth ) ) ), :=( Y,
% 0.73/1.51 X )] ), substitution( 1, [ :=( X, not( X ) )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 3461, [ ordered( X, implies( not( X ), not( truth ) ) ) ] )
% 0.73/1.51 , clause( 4249, [ ordered( X, implies( not( X ), not( truth ) ) ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 resolution(
% 0.73/1.51 clause( 4250, [ =( X, implies( not( X ), not( truth ) ) ), ~( ordered(
% 0.73/1.51 implies( not( X ), not( truth ) ), X ) ) ] )
% 0.73/1.51 , clause( 168, [ ~( ordered( X, Y ) ), =( X, Y ), ~( ordered( Y, X ) ) ] )
% 0.73/1.51 , 0, clause( 3461, [ ordered( X, implies( not( X ), not( truth ) ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, implies( not( X ), not( truth )
% 0.73/1.51 ) )] ), substitution( 1, [ :=( X, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 resolution(
% 0.73/1.51 clause( 4252, [ =( X, implies( not( X ), not( truth ) ) ) ] )
% 0.73/1.51 , clause( 4250, [ =( X, implies( not( X ), not( truth ) ) ), ~( ordered(
% 0.73/1.51 implies( not( X ), not( truth ) ), X ) ) ] )
% 0.73/1.51 , 1, clause( 1148, [ ordered( implies( not( X ), not( truth ) ), X ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.73/1.51 ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4253, [ =( implies( not( X ), not( truth ) ), X ) ] )
% 0.73/1.51 , clause( 4252, [ =( X, implies( not( X ), not( truth ) ) ) ] )
% 0.73/1.51 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 subsumption(
% 0.73/1.51 clause( 3484, [ =( implies( not( X ), not( truth ) ), X ) ] )
% 0.73/1.51 , clause( 4253, [ =( implies( not( X ), not( truth ) ), X ) ] )
% 0.73/1.51 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.51
% 0.73/1.51
% 0.73/1.51 eqswap(
% 0.73/1.51 clause( 4255, [ =( 'big_V'( X, Y ), implies( implies( X, Y ), Y ) ) ] )
% 0.73/1.51 , clause( 4, [ =( implies( implies( X, Y ), Y ), 'big_V'( X, Y ) ) ] )
% 0.73/1.52 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 paramod(
% 0.73/1.52 clause( 4257, [ =( 'big_V'( not( X ), not( truth ) ), implies( X, not(
% 0.73/1.52 truth ) ) ) ] )
% 0.73/1.52 , clause( 3484, [ =( implies( not( X ), not( truth ) ), X ) ] )
% 0.73/1.52 , 0, clause( 4255, [ =( 'big_V'( X, Y ), implies( implies( X, Y ), Y ) ) ]
% 0.73/1.52 )
% 0.73/1.52 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, not( X
% 0.73/1.52 ) ), :=( Y, not( truth ) )] )).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 paramod(
% 0.73/1.52 clause( 4258, [ =( not( X ), implies( X, not( truth ) ) ) ] )
% 0.73/1.52 , clause( 1122, [ =( 'big_V'( X, not( truth ) ), X ) ] )
% 0.73/1.52 , 0, clause( 4257, [ =( 'big_V'( not( X ), not( truth ) ), implies( X, not(
% 0.73/1.52 truth ) ) ) ] )
% 0.73/1.52 , 0, 1, substitution( 0, [ :=( X, not( X ) )] ), substitution( 1, [ :=( X,
% 0.73/1.52 X )] )).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 eqswap(
% 0.73/1.52 clause( 4259, [ =( implies( X, not( truth ) ), not( X ) ) ] )
% 0.73/1.52 , clause( 4258, [ =( not( X ), implies( X, not( truth ) ) ) ] )
% 0.73/1.52 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 subsumption(
% 0.73/1.52 clause( 3553, [ =( implies( X, not( truth ) ), not( X ) ) ] )
% 0.73/1.52 , clause( 4259, [ =( implies( X, not( truth ) ), not( X ) ) ] )
% 0.73/1.52 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 eqswap(
% 0.73/1.52 clause( 4260, [ =( X, truth ), ~( ordered( truth, X ) ) ] )
% 0.73/1.52 , clause( 12, [ =( truth, X ), ~( ordered( truth, X ) ) ] )
% 0.73/1.52 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 eqswap(
% 0.73/1.52 clause( 4261, [ =( X, implies( not( X ), not( truth ) ) ) ] )
% 0.73/1.52 , clause( 3484, [ =( implies( not( X ), not( truth ) ), X ) ] )
% 0.73/1.52 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 paramod(
% 0.73/1.52 clause( 4266, [ =( X, implies( not( X ), not( truth ) ) ), ~( ordered(
% 0.73/1.52 truth, truth ) ) ] )
% 0.73/1.52 , clause( 4260, [ =( X, truth ), ~( ordered( truth, X ) ) ] )
% 0.73/1.52 , 0, clause( 4261, [ =( X, implies( not( X ), not( truth ) ) ) ] )
% 0.73/1.52 , 0, 6, substitution( 0, [ :=( X, truth )] ), substitution( 1, [ :=( X, X )] )
% 0.73/1.52 ).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 paramod(
% 0.73/1.52 clause( 4307, [ =( X, not( not( X ) ) ), ~( ordered( truth, truth ) ) ] )
% 0.73/1.52 , clause( 3553, [ =( implies( X, not( truth ) ), not( X ) ) ] )
% 0.73/1.52 , 0, clause( 4266, [ =( X, implies( not( X ), not( truth ) ) ), ~( ordered(
% 0.73/1.52 truth, truth ) ) ] )
% 0.73/1.52 , 0, 2, substitution( 0, [ :=( X, not( X ) )] ), substitution( 1, [ :=( X,
% 0.73/1.52 X )] )).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 resolution(
% 0.73/1.52 clause( 4308, [ =( X, not( not( X ) ) ) ] )
% 0.73/1.52 , clause( 4307, [ =( X, not( not( X ) ) ), ~( ordered( truth, truth ) ) ]
% 0.73/1.52 )
% 0.73/1.52 , 1, clause( 103, [ ordered( X, X ) ] )
% 0.73/1.52 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, truth )] )
% 0.73/1.52 ).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 eqswap(
% 0.73/1.52 clause( 4309, [ =( not( not( X ) ), X ) ] )
% 0.73/1.52 , clause( 4308, [ =( X, not( not( X ) ) ) ] )
% 0.73/1.52 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 subsumption(
% 0.73/1.52 clause( 3555, [ =( not( not( X ) ), X ) ] )
% 0.73/1.52 , clause( 4309, [ =( not( not( X ) ), X ) ] )
% 0.73/1.52 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 eqswap(
% 0.73/1.52 clause( 4311, [ =( X, not( not( X ) ) ) ] )
% 0.73/1.52 , clause( 3555, [ =( not( not( X ) ), X ) ] )
% 0.73/1.52 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 paramod(
% 0.73/1.52 clause( 4316, [ =( 'big_V'( not( X ), not( Y ) ), not( 'big_hat'( X, Y ) )
% 0.73/1.52 ) ] )
% 0.73/1.52 , clause( 5, [ =( not( 'big_V'( not( X ), not( Y ) ) ), 'big_hat'( X, Y ) )
% 0.73/1.52 ] )
% 0.73/1.52 , 0, clause( 4311, [ =( X, not( not( X ) ) ) ] )
% 0.73/1.52 , 0, 7, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.73/1.52 :=( X, 'big_V'( not( X ), not( Y ) ) )] )).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 subsumption(
% 0.73/1.52 clause( 3596, [ =( 'big_V'( not( X ), not( Y ) ), not( 'big_hat'( X, Y ) )
% 0.73/1.52 ) ] )
% 0.73/1.52 , clause( 4316, [ =( 'big_V'( not( X ), not( Y ) ), not( 'big_hat'( X, Y )
% 0.73/1.52 ) ) ] )
% 0.73/1.52 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.52 )] ) ).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 paramod(
% 0.73/1.52 clause( 4320, [ ~( =( not( 'big_hat'( x, y ) ), not( 'big_hat'( x, y ) ) )
% 0.73/1.52 ) ] )
% 0.73/1.52 , clause( 3596, [ =( 'big_V'( not( X ), not( Y ) ), not( 'big_hat'( X, Y )
% 0.73/1.52 ) ) ] )
% 0.73/1.52 , 0, clause( 8, [ ~( =( 'big_V'( not( x ), not( y ) ), not( 'big_hat'( x, y
% 0.73/1.52 ) ) ) ) ] )
% 0.73/1.52 , 0, 2, substitution( 0, [ :=( X, x ), :=( Y, y )] ), substitution( 1, [] )
% 0.73/1.52 ).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 eqrefl(
% 0.73/1.52 clause( 4321, [] )
% 0.73/1.52 , clause( 4320, [ ~( =( not( 'big_hat'( x, y ) ), not( 'big_hat'( x, y ) )
% 0.73/1.52 ) ) ] )
% 0.73/1.52 , 0, substitution( 0, [] )).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 subsumption(
% 0.73/1.52 clause( 4040, [] )
% 0.73/1.52 , clause( 4321, [] )
% 0.73/1.52 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 end.
% 0.73/1.52
% 0.73/1.52 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.73/1.52
% 0.73/1.52 Memory use:
% 0.73/1.52
% 0.73/1.52 space for terms: 57452
% 0.73/1.52 space for clauses: 200306
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 clauses generated: 36159
% 0.73/1.52 clauses kept: 4041
% 0.73/1.52 clauses selected: 210
% 0.73/1.52 clauses deleted: 89
% 0.73/1.52 clauses inuse deleted: 42
% 0.73/1.52
% 0.73/1.52 subsentry: 303007
% 0.73/1.52 literals s-matched: 134876
% 0.73/1.52 literals matched: 126773
% 0.73/1.52 full subsumption: 67149
% 0.73/1.52
% 0.73/1.52 checksum: -1870545159
% 0.73/1.52
% 0.73/1.52
% 0.73/1.52 Bliksem ended
%------------------------------------------------------------------------------