TSTP Solution File: LCL203-10 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL203-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n004.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 07:51:41 EDT 2022
% Result : Unsatisfiable 0.96s 1.38s
% Output : Refutation 0.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL203-10 : TPTP v8.1.0. Released v7.3.0.
% 0.10/0.13 % Command : bliksem %s
% 0.13/0.32 % Computer : n004.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Sun Jul 3 23:41:08 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.96/1.38 *** allocated 10000 integers for termspace/termends
% 0.96/1.38 *** allocated 10000 integers for clauses
% 0.96/1.38 *** allocated 10000 integers for justifications
% 0.96/1.38 Bliksem 1.12
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 Automatic Strategy Selection
% 0.96/1.38
% 0.96/1.38 Clauses:
% 0.96/1.38 [
% 0.96/1.38 [ =( ifeq( X, X, Y, Z ), Y ) ],
% 0.96/1.38 [ =( axiom( implies( or( X, X ), X ) ), true ) ],
% 0.96/1.38 [ =( axiom( implies( X, or( Y, X ) ) ), true ) ],
% 0.96/1.38 [ =( axiom( implies( or( X, Y ), or( Y, X ) ) ), true ) ],
% 0.96/1.38 [ =( axiom( implies( or( X, or( Y, Z ) ), or( Y, or( X, Z ) ) ) ), true
% 0.96/1.38 ) ],
% 0.96/1.38 [ =( axiom( implies( implies( X, Y ), implies( or( Z, X ), or( Z, Y ) )
% 0.96/1.38 ) ), true ) ],
% 0.96/1.38 [ =( implies( X, Y ), or( not( X ), Y ) ) ],
% 0.96/1.38 [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ],
% 0.96/1.38 [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem( X ), true,
% 0.96/1.38 theorem( Y ), true ), true ), true ) ],
% 0.96/1.38 [ ~( =( theorem( implies( not( or( p, q ) ), or( not( p ), not( q ) ) )
% 0.96/1.38 ), true ) ) ]
% 0.96/1.38 ] .
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 percentage equality = 1.000000, percentage horn = 1.000000
% 0.96/1.38 This is a pure equality problem
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 Options Used:
% 0.96/1.38
% 0.96/1.38 useres = 1
% 0.96/1.38 useparamod = 1
% 0.96/1.38 useeqrefl = 1
% 0.96/1.38 useeqfact = 1
% 0.96/1.38 usefactor = 1
% 0.96/1.38 usesimpsplitting = 0
% 0.96/1.38 usesimpdemod = 5
% 0.96/1.38 usesimpres = 3
% 0.96/1.38
% 0.96/1.38 resimpinuse = 1000
% 0.96/1.38 resimpclauses = 20000
% 0.96/1.38 substype = eqrewr
% 0.96/1.38 backwardsubs = 1
% 0.96/1.38 selectoldest = 5
% 0.96/1.38
% 0.96/1.38 litorderings [0] = split
% 0.96/1.38 litorderings [1] = extend the termordering, first sorting on arguments
% 0.96/1.38
% 0.96/1.38 termordering = kbo
% 0.96/1.38
% 0.96/1.38 litapriori = 0
% 0.96/1.38 termapriori = 1
% 0.96/1.38 litaposteriori = 0
% 0.96/1.38 termaposteriori = 0
% 0.96/1.38 demodaposteriori = 0
% 0.96/1.38 ordereqreflfact = 0
% 0.96/1.38
% 0.96/1.38 litselect = negord
% 0.96/1.38
% 0.96/1.38 maxweight = 15
% 0.96/1.38 maxdepth = 30000
% 0.96/1.38 maxlength = 115
% 0.96/1.38 maxnrvars = 195
% 0.96/1.38 excuselevel = 1
% 0.96/1.38 increasemaxweight = 1
% 0.96/1.38
% 0.96/1.38 maxselected = 10000000
% 0.96/1.38 maxnrclauses = 10000000
% 0.96/1.38
% 0.96/1.38 showgenerated = 0
% 0.96/1.38 showkept = 0
% 0.96/1.38 showselected = 0
% 0.96/1.38 showdeleted = 0
% 0.96/1.38 showresimp = 1
% 0.96/1.38 showstatus = 2000
% 0.96/1.38
% 0.96/1.38 prologoutput = 1
% 0.96/1.38 nrgoals = 5000000
% 0.96/1.38 totalproof = 1
% 0.96/1.38
% 0.96/1.38 Symbols occurring in the translation:
% 0.96/1.38
% 0.96/1.38 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.96/1.38 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 0.96/1.38 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 0.96/1.38 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.38 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.38 ifeq [42, 4] (w:1, o:52, a:1, s:1, b:0),
% 0.96/1.38 or [43, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.96/1.38 implies [44, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.96/1.38 axiom [45, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.96/1.38 true [46, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.96/1.38 not [49, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.96/1.38 theorem [50, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.96/1.38 p [51, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.96/1.38 q [52, 0] (w:1, o:16, a:1, s:1, b:0).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 Starting Search:
% 0.96/1.38
% 0.96/1.38 Resimplifying inuse:
% 0.96/1.38 Done
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 Intermediate Status:
% 0.96/1.38 Generated: 50306
% 0.96/1.38 Kept: 2008
% 0.96/1.38 Inuse: 541
% 0.96/1.38 Deleted: 36
% 0.96/1.38 Deletedinuse: 5
% 0.96/1.38
% 0.96/1.38 Resimplifying inuse:
% 0.96/1.38 Done
% 0.96/1.38
% 0.96/1.38 Resimplifying inuse:
% 0.96/1.38 Done
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 Bliksems!, er is een bewijs:
% 0.96/1.38 % SZS status Unsatisfiable
% 0.96/1.38 % SZS output start Refutation
% 0.96/1.38
% 0.96/1.38 clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 1, [ =( axiom( implies( or( X, X ), X ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 2, [ =( axiom( implies( X, or( Y, X ) ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 3, [ =( axiom( implies( or( X, Y ), or( Y, X ) ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 5, [ =( axiom( implies( implies( X, Y ), implies( or( Z, X ), or( Z
% 0.96/1.38 , Y ) ) ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 7, [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 8, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem( X )
% 0.96/1.38 , true, theorem( Y ), true ), true ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 9, [ ~( =( theorem( implies( not( or( p, q ) ), implies( p, not( q
% 0.96/1.38 ) ) ) ), true ) ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 14, [ =( theorem( implies( or( X, Y ), or( Y, X ) ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 15, [ =( theorem( implies( or( X, X ), X ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 17, [ =( theorem( implies( X, or( Y, X ) ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 22, [ =( theorem( implies( implies( X, Y ), or( Y, not( X ) ) ) ),
% 0.96/1.38 true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 24, [ =( theorem( implies( implies( Y, not( X ) ), implies( X, not(
% 0.96/1.38 Y ) ) ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 25, [ =( theorem( implies( implies( X, Y ), implies( or( Z, X ), or(
% 0.96/1.38 Z, Y ) ) ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 29, [ =( ifeq( theorem( implies( X, Y ) ), true, theorem( or( Y,
% 0.96/1.38 not( X ) ) ), true ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 33, [ =( ifeq( theorem( implies( implies( or( X, X ), X ), Y ) ),
% 0.96/1.38 true, theorem( Y ), true ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 35, [ =( ifeq( theorem( implies( implies( X, or( Y, X ) ), Z ) ),
% 0.96/1.38 true, theorem( Z ), true ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 80, [ =( ifeq( theorem( implies( X, not( Y ) ) ), true, theorem(
% 0.96/1.38 implies( Y, not( X ) ) ), true ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 95, [ =( theorem( implies( implies( Y, Z ), implies( implies( X, Y
% 0.96/1.38 ), implies( X, Z ) ) ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 172, [ =( theorem( implies( or( Y, or( X, X ) ), or( Y, X ) ) ),
% 0.96/1.38 true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 187, [ =( theorem( implies( or( Z, X ), or( Z, or( Y, X ) ) ) ),
% 0.96/1.38 true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 200, [ =( theorem( implies( implies( X, Y ), implies( X, or( Z, Y )
% 0.96/1.38 ) ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 208, [ =( theorem( implies( implies( Z, Y ), implies( Z, implies( X
% 0.96/1.38 , Y ) ) ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 294, [ =( ifeq( theorem( implies( X, Y ) ), true, theorem( implies(
% 0.96/1.38 X, implies( Z, Y ) ) ), true ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 305, [ =( theorem( implies( implies( X, or( Y, Y ) ), implies( X, Y
% 0.96/1.38 ) ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 307, [ =( theorem( implies( X, X ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 314, [ =( theorem( or( X, not( X ) ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 324, [ =( theorem( implies( X, not( not( X ) ) ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 345, [ =( ifeq( theorem( implies( implies( X, not( not( X ) ) ), Y
% 0.96/1.38 ) ), true, theorem( Y ), true ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 3619, [ =( theorem( implies( implies( Y, X ), implies( Y, not( not(
% 0.96/1.38 X ) ) ) ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 3626, [ =( theorem( implies( X, not( not( or( Y, X ) ) ) ) ), true
% 0.96/1.38 ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 3703, [ =( theorem( implies( not( or( Y, X ) ), not( X ) ) ), true
% 0.96/1.38 ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 3711, [ =( theorem( implies( not( or( X, Y ) ), implies( Z, not( Y
% 0.96/1.38 ) ) ) ), true ) ] )
% 0.96/1.38 .
% 0.96/1.38 clause( 3753, [] )
% 0.96/1.38 .
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 % SZS output end Refutation
% 0.96/1.38 found a proof!
% 0.96/1.38
% 0.96/1.38 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.96/1.38
% 0.96/1.38 initialclauses(
% 0.96/1.38 [ clause( 3755, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , clause( 3756, [ =( axiom( implies( or( X, X ), X ) ), true ) ] )
% 0.96/1.38 , clause( 3757, [ =( axiom( implies( X, or( Y, X ) ) ), true ) ] )
% 0.96/1.38 , clause( 3758, [ =( axiom( implies( or( X, Y ), or( Y, X ) ) ), true ) ]
% 0.96/1.38 )
% 0.96/1.38 , clause( 3759, [ =( axiom( implies( or( X, or( Y, Z ) ), or( Y, or( X, Z )
% 0.96/1.38 ) ) ), true ) ] )
% 0.96/1.38 , clause( 3760, [ =( axiom( implies( implies( X, Y ), implies( or( Z, X ),
% 0.96/1.38 or( Z, Y ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 3761, [ =( implies( X, Y ), or( not( X ), Y ) ) ] )
% 0.96/1.38 , clause( 3762, [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ]
% 0.96/1.38 )
% 0.96/1.38 , clause( 3763, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem(
% 0.96/1.38 X ), true, theorem( Y ), true ), true ), true ) ] )
% 0.96/1.38 , clause( 3764, [ ~( =( theorem( implies( not( or( p, q ) ), or( not( p ),
% 0.96/1.38 not( q ) ) ) ), true ) ) ] )
% 0.96/1.38 ] ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , clause( 3755, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.96/1.38 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 1, [ =( axiom( implies( or( X, X ), X ) ), true ) ] )
% 0.96/1.38 , clause( 3756, [ =( axiom( implies( or( X, X ), X ) ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 2, [ =( axiom( implies( X, or( Y, X ) ) ), true ) ] )
% 0.96/1.38 , clause( 3757, [ =( axiom( implies( X, or( Y, X ) ) ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 3, [ =( axiom( implies( or( X, Y ), or( Y, X ) ) ), true ) ] )
% 0.96/1.38 , clause( 3758, [ =( axiom( implies( or( X, Y ), or( Y, X ) ) ), true ) ]
% 0.96/1.38 )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 5, [ =( axiom( implies( implies( X, Y ), implies( or( Z, X ), or( Z
% 0.96/1.38 , Y ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 3760, [ =( axiom( implies( implies( X, Y ), implies( or( Z, X ),
% 0.96/1.38 or( Z, Y ) ) ) ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.96/1.38 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3787, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.96/1.38 , clause( 3761, [ =( implies( X, Y ), or( not( X ), Y ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.96/1.38 , clause( 3787, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 7, [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ] )
% 0.96/1.38 , clause( 3762, [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ]
% 0.96/1.38 )
% 0.96/1.38 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 8, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem( X )
% 0.96/1.38 , true, theorem( Y ), true ), true ), true ) ] )
% 0.96/1.38 , clause( 3763, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem(
% 0.96/1.38 X ), true, theorem( Y ), true ), true ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3827, [ ~( =( theorem( implies( not( or( p, q ) ), implies( p, not(
% 0.96/1.38 q ) ) ) ), true ) ) ] )
% 0.96/1.38 , clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.96/1.38 , 0, clause( 3764, [ ~( =( theorem( implies( not( or( p, q ) ), or( not( p
% 0.96/1.38 ), not( q ) ) ) ), true ) ) ] )
% 0.96/1.38 , 0, 8, substitution( 0, [ :=( X, p ), :=( Y, not( q ) )] ), substitution(
% 0.96/1.38 1, [] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 9, [ ~( =( theorem( implies( not( or( p, q ) ), implies( p, not( q
% 0.96/1.38 ) ) ) ), true ) ) ] )
% 0.96/1.38 , clause( 3827, [ ~( =( theorem( implies( not( or( p, q ) ), implies( p,
% 0.96/1.38 not( q ) ) ) ), true ) ) ] )
% 0.96/1.38 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3830, [ =( true, ifeq( axiom( X ), true, theorem( X ), true ) ) ]
% 0.96/1.38 )
% 0.96/1.38 , clause( 7, [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3832, [ =( true, ifeq( true, true, theorem( implies( or( X, Y ), or(
% 0.96/1.38 Y, X ) ) ), true ) ) ] )
% 0.96/1.38 , clause( 3, [ =( axiom( implies( or( X, Y ), or( Y, X ) ) ), true ) ] )
% 0.96/1.38 , 0, clause( 3830, [ =( true, ifeq( axiom( X ), true, theorem( X ), true )
% 0.96/1.38 ) ] )
% 0.96/1.38 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.96/1.38 :=( X, implies( or( X, Y ), or( Y, X ) ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3833, [ =( true, theorem( implies( or( X, Y ), or( Y, X ) ) ) ) ]
% 0.96/1.38 )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3832, [ =( true, ifeq( true, true, theorem( implies( or( X, Y
% 0.96/1.38 ), or( Y, X ) ) ), true ) ) ] )
% 0.96/1.38 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( or( X, Y
% 0.96/1.38 ), or( Y, X ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ),
% 0.96/1.38 :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3834, [ =( theorem( implies( or( X, Y ), or( Y, X ) ) ), true ) ]
% 0.96/1.38 )
% 0.96/1.38 , clause( 3833, [ =( true, theorem( implies( or( X, Y ), or( Y, X ) ) ) ) ]
% 0.96/1.38 )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 14, [ =( theorem( implies( or( X, Y ), or( Y, X ) ) ), true ) ] )
% 0.96/1.38 , clause( 3834, [ =( theorem( implies( or( X, Y ), or( Y, X ) ) ), true ) ]
% 0.96/1.38 )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3836, [ =( true, ifeq( axiom( X ), true, theorem( X ), true ) ) ]
% 0.96/1.38 )
% 0.96/1.38 , clause( 7, [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3838, [ =( true, ifeq( true, true, theorem( implies( or( X, X ), X
% 0.96/1.38 ) ), true ) ) ] )
% 0.96/1.38 , clause( 1, [ =( axiom( implies( or( X, X ), X ) ), true ) ] )
% 0.96/1.38 , 0, clause( 3836, [ =( true, ifeq( axiom( X ), true, theorem( X ), true )
% 0.96/1.38 ) ] )
% 0.96/1.38 , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, implies(
% 0.96/1.38 or( X, X ), X ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3839, [ =( true, theorem( implies( or( X, X ), X ) ) ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3838, [ =( true, ifeq( true, true, theorem( implies( or( X, X
% 0.96/1.38 ), X ) ), true ) ) ] )
% 0.96/1.38 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( or( X, X
% 0.96/1.38 ), X ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3840, [ =( theorem( implies( or( X, X ), X ) ), true ) ] )
% 0.96/1.38 , clause( 3839, [ =( true, theorem( implies( or( X, X ), X ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 15, [ =( theorem( implies( or( X, X ), X ) ), true ) ] )
% 0.96/1.38 , clause( 3840, [ =( theorem( implies( or( X, X ), X ) ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3842, [ =( true, ifeq( axiom( X ), true, theorem( X ), true ) ) ]
% 0.96/1.38 )
% 0.96/1.38 , clause( 7, [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3844, [ =( true, ifeq( true, true, theorem( implies( X, or( Y, X )
% 0.96/1.38 ) ), true ) ) ] )
% 0.96/1.38 , clause( 2, [ =( axiom( implies( X, or( Y, X ) ) ), true ) ] )
% 0.96/1.38 , 0, clause( 3842, [ =( true, ifeq( axiom( X ), true, theorem( X ), true )
% 0.96/1.38 ) ] )
% 0.96/1.38 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.96/1.38 :=( X, implies( X, or( Y, X ) ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3845, [ =( true, theorem( implies( X, or( Y, X ) ) ) ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3844, [ =( true, ifeq( true, true, theorem( implies( X, or( Y
% 0.96/1.38 , X ) ) ), true ) ) ] )
% 0.96/1.38 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( X, or( Y
% 0.96/1.38 , X ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 0.96/1.38 ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3846, [ =( theorem( implies( X, or( Y, X ) ) ), true ) ] )
% 0.96/1.38 , clause( 3845, [ =( true, theorem( implies( X, or( Y, X ) ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 17, [ =( theorem( implies( X, or( Y, X ) ) ), true ) ] )
% 0.96/1.38 , clause( 3846, [ =( theorem( implies( X, or( Y, X ) ) ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3848, [ =( true, theorem( implies( or( X, Y ), or( Y, X ) ) ) ) ]
% 0.96/1.38 )
% 0.96/1.38 , clause( 14, [ =( theorem( implies( or( X, Y ), or( Y, X ) ) ), true ) ]
% 0.96/1.38 )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3849, [ =( true, theorem( implies( implies( X, Y ), or( Y, not( X )
% 0.96/1.38 ) ) ) ) ] )
% 0.96/1.38 , clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.96/1.38 , 0, clause( 3848, [ =( true, theorem( implies( or( X, Y ), or( Y, X ) ) )
% 0.96/1.38 ) ] )
% 0.96/1.38 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.96/1.38 :=( X, not( X ) ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3851, [ =( theorem( implies( implies( X, Y ), or( Y, not( X ) ) ) )
% 0.96/1.38 , true ) ] )
% 0.96/1.38 , clause( 3849, [ =( true, theorem( implies( implies( X, Y ), or( Y, not( X
% 0.96/1.38 ) ) ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 22, [ =( theorem( implies( implies( X, Y ), or( Y, not( X ) ) ) ),
% 0.96/1.38 true ) ] )
% 0.96/1.38 , clause( 3851, [ =( theorem( implies( implies( X, Y ), or( Y, not( X ) ) )
% 0.96/1.38 ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3854, [ =( true, theorem( implies( implies( X, Y ), or( Y, not( X )
% 0.96/1.38 ) ) ) ) ] )
% 0.96/1.38 , clause( 22, [ =( theorem( implies( implies( X, Y ), or( Y, not( X ) ) ) )
% 0.96/1.38 , true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3855, [ =( true, theorem( implies( implies( X, not( Y ) ), implies(
% 0.96/1.38 Y, not( X ) ) ) ) ) ] )
% 0.96/1.38 , clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.96/1.38 , 0, clause( 3854, [ =( true, theorem( implies( implies( X, Y ), or( Y, not(
% 0.96/1.38 X ) ) ) ) ) ] )
% 0.96/1.38 , 0, 8, substitution( 0, [ :=( X, Y ), :=( Y, not( X ) )] ), substitution(
% 0.96/1.38 1, [ :=( X, X ), :=( Y, not( Y ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3856, [ =( theorem( implies( implies( X, not( Y ) ), implies( Y,
% 0.96/1.38 not( X ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 3855, [ =( true, theorem( implies( implies( X, not( Y ) ),
% 0.96/1.38 implies( Y, not( X ) ) ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 24, [ =( theorem( implies( implies( Y, not( X ) ), implies( X, not(
% 0.96/1.38 Y ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 3856, [ =( theorem( implies( implies( X, not( Y ) ), implies( Y,
% 0.96/1.38 not( X ) ) ) ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3858, [ =( true, ifeq( axiom( X ), true, theorem( X ), true ) ) ]
% 0.96/1.38 )
% 0.96/1.38 , clause( 7, [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3860, [ =( true, ifeq( true, true, theorem( implies( implies( X, Y
% 0.96/1.38 ), implies( or( Z, X ), or( Z, Y ) ) ) ), true ) ) ] )
% 0.96/1.38 , clause( 5, [ =( axiom( implies( implies( X, Y ), implies( or( Z, X ), or(
% 0.96/1.38 Z, Y ) ) ) ), true ) ] )
% 0.96/1.38 , 0, clause( 3858, [ =( true, ifeq( axiom( X ), true, theorem( X ), true )
% 0.96/1.38 ) ] )
% 0.96/1.38 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.96/1.38 substitution( 1, [ :=( X, implies( implies( X, Y ), implies( or( Z, X ),
% 0.96/1.38 or( Z, Y ) ) ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3861, [ =( true, theorem( implies( implies( X, Y ), implies( or( Z
% 0.96/1.38 , X ), or( Z, Y ) ) ) ) ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3860, [ =( true, ifeq( true, true, theorem( implies( implies(
% 0.96/1.38 X, Y ), implies( or( Z, X ), or( Z, Y ) ) ) ), true ) ) ] )
% 0.96/1.38 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( implies(
% 0.96/1.38 X, Y ), implies( or( Z, X ), or( Z, Y ) ) ) ) ), :=( Z, true )] ),
% 0.96/1.38 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3862, [ =( theorem( implies( implies( X, Y ), implies( or( Z, X ),
% 0.96/1.38 or( Z, Y ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 3861, [ =( true, theorem( implies( implies( X, Y ), implies( or(
% 0.96/1.38 Z, X ), or( Z, Y ) ) ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 25, [ =( theorem( implies( implies( X, Y ), implies( or( Z, X ), or(
% 0.96/1.38 Z, Y ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 3862, [ =( theorem( implies( implies( X, Y ), implies( or( Z, X )
% 0.96/1.38 , or( Z, Y ) ) ) ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.96/1.38 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3864, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.96/1.38 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.96/1.38 , clause( 8, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem( X
% 0.96/1.38 ), true, theorem( Y ), true ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3866, [ =( true, ifeq( true, true, ifeq( theorem( implies( X, Y ) )
% 0.96/1.38 , true, theorem( or( Y, not( X ) ) ), true ), true ) ) ] )
% 0.96/1.38 , clause( 22, [ =( theorem( implies( implies( X, Y ), or( Y, not( X ) ) ) )
% 0.96/1.38 , true ) ] )
% 0.96/1.38 , 0, clause( 3864, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.96/1.38 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.96/1.38 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.96/1.38 :=( X, implies( X, Y ) ), :=( Y, or( Y, not( X ) ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3871, [ =( true, ifeq( theorem( implies( X, Y ) ), true, theorem(
% 0.96/1.38 or( Y, not( X ) ) ), true ) ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3866, [ =( true, ifeq( true, true, ifeq( theorem( implies( X,
% 0.96/1.38 Y ) ), true, theorem( or( Y, not( X ) ) ), true ), true ) ) ] )
% 0.96/1.38 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( theorem( implies( X
% 0.96/1.38 , Y ) ), true, theorem( or( Y, not( X ) ) ), true ) ), :=( Z, true )] ),
% 0.96/1.38 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3872, [ =( ifeq( theorem( implies( X, Y ) ), true, theorem( or( Y,
% 0.96/1.38 not( X ) ) ), true ), true ) ] )
% 0.96/1.38 , clause( 3871, [ =( true, ifeq( theorem( implies( X, Y ) ), true, theorem(
% 0.96/1.38 or( Y, not( X ) ) ), true ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 29, [ =( ifeq( theorem( implies( X, Y ) ), true, theorem( or( Y,
% 0.96/1.38 not( X ) ) ), true ), true ) ] )
% 0.96/1.38 , clause( 3872, [ =( ifeq( theorem( implies( X, Y ) ), true, theorem( or( Y
% 0.96/1.38 , not( X ) ) ), true ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3874, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.96/1.38 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.96/1.38 , clause( 8, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem( X
% 0.96/1.38 ), true, theorem( Y ), true ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3877, [ =( true, ifeq( theorem( implies( implies( or( X, X ), X ),
% 0.96/1.38 Y ) ), true, ifeq( true, true, theorem( Y ), true ), true ) ) ] )
% 0.96/1.38 , clause( 15, [ =( theorem( implies( or( X, X ), X ) ), true ) ] )
% 0.96/1.38 , 0, clause( 3874, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.96/1.38 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.96/1.38 , 0, 13, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 0.96/1.38 implies( or( X, X ), X ) ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3879, [ =( true, ifeq( theorem( implies( implies( or( X, X ), X ),
% 0.96/1.38 Y ) ), true, theorem( Y ), true ) ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3877, [ =( true, ifeq( theorem( implies( implies( or( X, X ),
% 0.96/1.38 X ), Y ) ), true, ifeq( true, true, theorem( Y ), true ), true ) ) ] )
% 0.96/1.38 , 0, 12, substitution( 0, [ :=( X, true ), :=( Y, theorem( Y ) ), :=( Z,
% 0.96/1.38 true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3880, [ =( ifeq( theorem( implies( implies( or( X, X ), X ), Y ) )
% 0.96/1.38 , true, theorem( Y ), true ), true ) ] )
% 0.96/1.38 , clause( 3879, [ =( true, ifeq( theorem( implies( implies( or( X, X ), X )
% 0.96/1.38 , Y ) ), true, theorem( Y ), true ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 33, [ =( ifeq( theorem( implies( implies( or( X, X ), X ), Y ) ),
% 0.96/1.38 true, theorem( Y ), true ), true ) ] )
% 0.96/1.38 , clause( 3880, [ =( ifeq( theorem( implies( implies( or( X, X ), X ), Y )
% 0.96/1.38 ), true, theorem( Y ), true ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3882, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.96/1.38 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.96/1.38 , clause( 8, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem( X
% 0.96/1.38 ), true, theorem( Y ), true ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3885, [ =( true, ifeq( theorem( implies( implies( X, or( Y, X ) ),
% 0.96/1.38 Z ) ), true, ifeq( true, true, theorem( Z ), true ), true ) ) ] )
% 0.96/1.38 , clause( 17, [ =( theorem( implies( X, or( Y, X ) ) ), true ) ] )
% 0.96/1.38 , 0, clause( 3882, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.96/1.38 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.96/1.38 , 0, 13, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.96/1.38 :=( X, implies( X, or( Y, X ) ) ), :=( Y, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3887, [ =( true, ifeq( theorem( implies( implies( X, or( Y, X ) ),
% 0.96/1.38 Z ) ), true, theorem( Z ), true ) ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3885, [ =( true, ifeq( theorem( implies( implies( X, or( Y, X
% 0.96/1.38 ) ), Z ) ), true, ifeq( true, true, theorem( Z ), true ), true ) ) ] )
% 0.96/1.38 , 0, 12, substitution( 0, [ :=( X, true ), :=( Y, theorem( Z ) ), :=( Z,
% 0.96/1.38 true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3888, [ =( ifeq( theorem( implies( implies( X, or( Y, X ) ), Z ) )
% 0.96/1.38 , true, theorem( Z ), true ), true ) ] )
% 0.96/1.38 , clause( 3887, [ =( true, ifeq( theorem( implies( implies( X, or( Y, X ) )
% 0.96/1.38 , Z ) ), true, theorem( Z ), true ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 35, [ =( ifeq( theorem( implies( implies( X, or( Y, X ) ), Z ) ),
% 0.96/1.38 true, theorem( Z ), true ), true ) ] )
% 0.96/1.38 , clause( 3888, [ =( ifeq( theorem( implies( implies( X, or( Y, X ) ), Z )
% 0.96/1.38 ), true, theorem( Z ), true ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.96/1.38 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3890, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.96/1.38 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.96/1.38 , clause( 8, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem( X
% 0.96/1.38 ), true, theorem( Y ), true ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3892, [ =( true, ifeq( true, true, ifeq( theorem( implies( X, not(
% 0.96/1.38 Y ) ) ), true, theorem( implies( Y, not( X ) ) ), true ), true ) ) ] )
% 0.96/1.38 , clause( 24, [ =( theorem( implies( implies( Y, not( X ) ), implies( X,
% 0.96/1.38 not( Y ) ) ) ), true ) ] )
% 0.96/1.38 , 0, clause( 3890, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.96/1.38 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.96/1.38 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 0.96/1.38 :=( X, implies( X, not( Y ) ) ), :=( Y, implies( Y, not( X ) ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3897, [ =( true, ifeq( theorem( implies( X, not( Y ) ) ), true,
% 0.96/1.38 theorem( implies( Y, not( X ) ) ), true ) ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3892, [ =( true, ifeq( true, true, ifeq( theorem( implies( X,
% 0.96/1.38 not( Y ) ) ), true, theorem( implies( Y, not( X ) ) ), true ), true ) ) ]
% 0.96/1.38 )
% 0.96/1.38 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( theorem( implies( X
% 0.96/1.38 , not( Y ) ) ), true, theorem( implies( Y, not( X ) ) ), true ) ), :=( Z
% 0.96/1.38 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3898, [ =( ifeq( theorem( implies( X, not( Y ) ) ), true, theorem(
% 0.96/1.38 implies( Y, not( X ) ) ), true ), true ) ] )
% 0.96/1.38 , clause( 3897, [ =( true, ifeq( theorem( implies( X, not( Y ) ) ), true,
% 0.96/1.38 theorem( implies( Y, not( X ) ) ), true ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 80, [ =( ifeq( theorem( implies( X, not( Y ) ) ), true, theorem(
% 0.96/1.38 implies( Y, not( X ) ) ), true ), true ) ] )
% 0.96/1.38 , clause( 3898, [ =( ifeq( theorem( implies( X, not( Y ) ) ), true, theorem(
% 0.96/1.38 implies( Y, not( X ) ) ), true ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3900, [ =( true, theorem( implies( implies( X, Y ), implies( or( Z
% 0.96/1.38 , X ), or( Z, Y ) ) ) ) ) ] )
% 0.96/1.38 , clause( 25, [ =( theorem( implies( implies( X, Y ), implies( or( Z, X ),
% 0.96/1.38 or( Z, Y ) ) ) ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3903, [ =( true, theorem( implies( implies( X, Y ), implies( or(
% 0.96/1.38 not( Z ), X ), implies( Z, Y ) ) ) ) ) ] )
% 0.96/1.38 , clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.96/1.38 , 0, clause( 3900, [ =( true, theorem( implies( implies( X, Y ), implies(
% 0.96/1.38 or( Z, X ), or( Z, Y ) ) ) ) ) ] )
% 0.96/1.38 , 0, 12, substitution( 0, [ :=( X, Z ), :=( Y, Y )] ), substitution( 1, [
% 0.96/1.38 :=( X, X ), :=( Y, Y ), :=( Z, not( Z ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3905, [ =( true, theorem( implies( implies( X, Y ), implies(
% 0.96/1.38 implies( Z, X ), implies( Z, Y ) ) ) ) ) ] )
% 0.96/1.38 , clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.96/1.38 , 0, clause( 3903, [ =( true, theorem( implies( implies( X, Y ), implies(
% 0.96/1.38 or( not( Z ), X ), implies( Z, Y ) ) ) ) ) ] )
% 0.96/1.38 , 0, 8, substitution( 0, [ :=( X, Z ), :=( Y, X )] ), substitution( 1, [
% 0.96/1.38 :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3906, [ =( theorem( implies( implies( X, Y ), implies( implies( Z,
% 0.96/1.38 X ), implies( Z, Y ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 3905, [ =( true, theorem( implies( implies( X, Y ), implies(
% 0.96/1.38 implies( Z, X ), implies( Z, Y ) ) ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 95, [ =( theorem( implies( implies( Y, Z ), implies( implies( X, Y
% 0.96/1.38 ), implies( X, Z ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 3906, [ =( theorem( implies( implies( X, Y ), implies( implies( Z
% 0.96/1.38 , X ), implies( Z, Y ) ) ) ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 0.96/1.38 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3908, [ =( true, ifeq( theorem( implies( implies( or( X, X ), X ),
% 0.96/1.38 Y ) ), true, theorem( Y ), true ) ) ] )
% 0.96/1.38 , clause( 33, [ =( ifeq( theorem( implies( implies( or( X, X ), X ), Y ) )
% 0.96/1.38 , true, theorem( Y ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3910, [ =( true, ifeq( true, true, theorem( implies( or( Y, or( X,
% 0.96/1.38 X ) ), or( Y, X ) ) ), true ) ) ] )
% 0.96/1.38 , clause( 25, [ =( theorem( implies( implies( X, Y ), implies( or( Z, X ),
% 0.96/1.38 or( Z, Y ) ) ) ), true ) ] )
% 0.96/1.38 , 0, clause( 3908, [ =( true, ifeq( theorem( implies( implies( or( X, X ),
% 0.96/1.38 X ), Y ) ), true, theorem( Y ), true ) ) ] )
% 0.96/1.38 , 0, 3, substitution( 0, [ :=( X, or( X, X ) ), :=( Y, X ), :=( Z, Y )] ),
% 0.96/1.38 substitution( 1, [ :=( X, X ), :=( Y, implies( or( Y, or( X, X ) ), or( Y
% 0.96/1.38 , X ) ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3912, [ =( true, theorem( implies( or( X, or( Y, Y ) ), or( X, Y )
% 0.96/1.38 ) ) ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3910, [ =( true, ifeq( true, true, theorem( implies( or( Y, or(
% 0.96/1.38 X, X ) ), or( Y, X ) ) ), true ) ) ] )
% 0.96/1.38 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( or( X,
% 0.96/1.38 or( Y, Y ) ), or( X, Y ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=(
% 0.96/1.38 X, Y ), :=( Y, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3913, [ =( theorem( implies( or( X, or( Y, Y ) ), or( X, Y ) ) ),
% 0.96/1.38 true ) ] )
% 0.96/1.38 , clause( 3912, [ =( true, theorem( implies( or( X, or( Y, Y ) ), or( X, Y
% 0.96/1.38 ) ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 172, [ =( theorem( implies( or( Y, or( X, X ) ), or( Y, X ) ) ),
% 0.96/1.38 true ) ] )
% 0.96/1.38 , clause( 3913, [ =( theorem( implies( or( X, or( Y, Y ) ), or( X, Y ) ) )
% 0.96/1.38 , true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3915, [ =( true, ifeq( theorem( implies( implies( X, or( Y, X ) ),
% 0.96/1.38 Z ) ), true, theorem( Z ), true ) ) ] )
% 0.96/1.38 , clause( 35, [ =( ifeq( theorem( implies( implies( X, or( Y, X ) ), Z ) )
% 0.96/1.38 , true, theorem( Z ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3917, [ =( true, ifeq( true, true, theorem( implies( or( Z, X ), or(
% 0.96/1.38 Z, or( Y, X ) ) ) ), true ) ) ] )
% 0.96/1.38 , clause( 25, [ =( theorem( implies( implies( X, Y ), implies( or( Z, X ),
% 0.96/1.38 or( Z, Y ) ) ) ), true ) ] )
% 0.96/1.38 , 0, clause( 3915, [ =( true, ifeq( theorem( implies( implies( X, or( Y, X
% 0.96/1.38 ) ), Z ) ), true, theorem( Z ), true ) ) ] )
% 0.96/1.38 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, or( Y, X ) ), :=( Z, Z )] ),
% 0.96/1.38 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( or( Z, X ), or(
% 0.96/1.38 Z, or( Y, X ) ) ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3919, [ =( true, theorem( implies( or( X, Y ), or( X, or( Z, Y ) )
% 0.96/1.38 ) ) ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3917, [ =( true, ifeq( true, true, theorem( implies( or( Z, X
% 0.96/1.38 ), or( Z, or( Y, X ) ) ) ), true ) ) ] )
% 0.96/1.38 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( or( X, Y
% 0.96/1.38 ), or( X, or( Z, Y ) ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X
% 0.96/1.38 , Y ), :=( Y, Z ), :=( Z, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3920, [ =( theorem( implies( or( X, Y ), or( X, or( Z, Y ) ) ) ),
% 0.96/1.38 true ) ] )
% 0.96/1.38 , clause( 3919, [ =( true, theorem( implies( or( X, Y ), or( X, or( Z, Y )
% 0.96/1.38 ) ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 187, [ =( theorem( implies( or( Z, X ), or( Z, or( Y, X ) ) ) ),
% 0.96/1.38 true ) ] )
% 0.96/1.38 , clause( 3920, [ =( theorem( implies( or( X, Y ), or( X, or( Z, Y ) ) ) )
% 0.96/1.38 , true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 0.96/1.38 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3922, [ =( true, theorem( implies( or( X, Y ), or( X, or( Z, Y ) )
% 0.96/1.38 ) ) ) ] )
% 0.96/1.38 , clause( 187, [ =( theorem( implies( or( Z, X ), or( Z, or( Y, X ) ) ) ),
% 0.96/1.38 true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3925, [ =( true, theorem( implies( or( not( X ), Y ), implies( X,
% 0.96/1.38 or( Z, Y ) ) ) ) ) ] )
% 0.96/1.38 , clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.96/1.38 , 0, clause( 3922, [ =( true, theorem( implies( or( X, Y ), or( X, or( Z, Y
% 0.96/1.38 ) ) ) ) ) ] )
% 0.96/1.38 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, or( Z, Y ) )] ),
% 0.96/1.38 substitution( 1, [ :=( X, not( X ) ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3928, [ =( true, theorem( implies( implies( X, Y ), implies( X, or(
% 0.96/1.38 Z, Y ) ) ) ) ) ] )
% 0.96/1.38 , clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.96/1.38 , 0, clause( 3925, [ =( true, theorem( implies( or( not( X ), Y ), implies(
% 0.96/1.38 X, or( Z, Y ) ) ) ) ) ] )
% 0.96/1.38 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.96/1.38 :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3929, [ =( theorem( implies( implies( X, Y ), implies( X, or( Z, Y
% 0.96/1.38 ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 3928, [ =( true, theorem( implies( implies( X, Y ), implies( X,
% 0.96/1.38 or( Z, Y ) ) ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 200, [ =( theorem( implies( implies( X, Y ), implies( X, or( Z, Y )
% 0.96/1.38 ) ) ), true ) ] )
% 0.96/1.38 , clause( 3929, [ =( theorem( implies( implies( X, Y ), implies( X, or( Z,
% 0.96/1.38 Y ) ) ) ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.96/1.38 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3931, [ =( true, theorem( implies( implies( X, Y ), implies( X, or(
% 0.96/1.38 Z, Y ) ) ) ) ) ] )
% 0.96/1.38 , clause( 200, [ =( theorem( implies( implies( X, Y ), implies( X, or( Z, Y
% 0.96/1.38 ) ) ) ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3932, [ =( true, theorem( implies( implies( X, Y ), implies( X,
% 0.96/1.38 implies( Z, Y ) ) ) ) ) ] )
% 0.96/1.38 , clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.96/1.38 , 0, clause( 3931, [ =( true, theorem( implies( implies( X, Y ), implies( X
% 0.96/1.38 , or( Z, Y ) ) ) ) ) ] )
% 0.96/1.38 , 0, 9, substitution( 0, [ :=( X, Z ), :=( Y, Y )] ), substitution( 1, [
% 0.96/1.38 :=( X, X ), :=( Y, Y ), :=( Z, not( Z ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3933, [ =( theorem( implies( implies( X, Y ), implies( X, implies(
% 0.96/1.38 Z, Y ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 3932, [ =( true, theorem( implies( implies( X, Y ), implies( X,
% 0.96/1.38 implies( Z, Y ) ) ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 208, [ =( theorem( implies( implies( Z, Y ), implies( Z, implies( X
% 0.96/1.38 , Y ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 3933, [ =( theorem( implies( implies( X, Y ), implies( X, implies(
% 0.96/1.38 Z, Y ) ) ) ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 0.96/1.38 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3935, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.96/1.38 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.96/1.38 , clause( 8, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem( X
% 0.96/1.38 ), true, theorem( Y ), true ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3937, [ =( true, ifeq( true, true, ifeq( theorem( implies( X, Y ) )
% 0.96/1.38 , true, theorem( implies( X, implies( Z, Y ) ) ), true ), true ) ) ] )
% 0.96/1.38 , clause( 208, [ =( theorem( implies( implies( Z, Y ), implies( Z, implies(
% 0.96/1.38 X, Y ) ) ) ), true ) ] )
% 0.96/1.38 , 0, clause( 3935, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.96/1.38 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.96/1.38 , 0, 3, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 0.96/1.38 substitution( 1, [ :=( X, implies( X, Y ) ), :=( Y, implies( X, implies(
% 0.96/1.38 Z, Y ) ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3942, [ =( true, ifeq( theorem( implies( X, Y ) ), true, theorem(
% 0.96/1.38 implies( X, implies( Z, Y ) ) ), true ) ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3937, [ =( true, ifeq( true, true, ifeq( theorem( implies( X,
% 0.96/1.38 Y ) ), true, theorem( implies( X, implies( Z, Y ) ) ), true ), true ) ) ]
% 0.96/1.38 )
% 0.96/1.38 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( theorem( implies( X
% 0.96/1.38 , Y ) ), true, theorem( implies( X, implies( Z, Y ) ) ), true ) ), :=( Z
% 0.96/1.38 , true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )
% 0.96/1.38 ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3943, [ =( ifeq( theorem( implies( X, Y ) ), true, theorem( implies(
% 0.96/1.38 X, implies( Z, Y ) ) ), true ), true ) ] )
% 0.96/1.38 , clause( 3942, [ =( true, ifeq( theorem( implies( X, Y ) ), true, theorem(
% 0.96/1.38 implies( X, implies( Z, Y ) ) ), true ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 294, [ =( ifeq( theorem( implies( X, Y ) ), true, theorem( implies(
% 0.96/1.38 X, implies( Z, Y ) ) ), true ), true ) ] )
% 0.96/1.38 , clause( 3943, [ =( ifeq( theorem( implies( X, Y ) ), true, theorem(
% 0.96/1.38 implies( X, implies( Z, Y ) ) ), true ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.96/1.38 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3945, [ =( true, theorem( implies( or( X, or( Y, Y ) ), or( X, Y )
% 0.96/1.38 ) ) ) ] )
% 0.96/1.38 , clause( 172, [ =( theorem( implies( or( Y, or( X, X ) ), or( Y, X ) ) ),
% 0.96/1.38 true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3949, [ =( true, theorem( implies( or( not( X ), or( Y, Y ) ),
% 0.96/1.38 implies( X, Y ) ) ) ) ] )
% 0.96/1.38 , clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.96/1.38 , 0, clause( 3945, [ =( true, theorem( implies( or( X, or( Y, Y ) ), or( X
% 0.96/1.38 , Y ) ) ) ) ] )
% 0.96/1.38 , 0, 10, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.96/1.38 :=( X, not( X ) ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3951, [ =( true, theorem( implies( implies( X, or( Y, Y ) ),
% 0.96/1.38 implies( X, Y ) ) ) ) ] )
% 0.96/1.38 , clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.96/1.38 , 0, clause( 3949, [ =( true, theorem( implies( or( not( X ), or( Y, Y ) )
% 0.96/1.38 , implies( X, Y ) ) ) ) ] )
% 0.96/1.38 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, or( Y, Y ) )] ),
% 0.96/1.38 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3952, [ =( theorem( implies( implies( X, or( Y, Y ) ), implies( X,
% 0.96/1.38 Y ) ) ), true ) ] )
% 0.96/1.38 , clause( 3951, [ =( true, theorem( implies( implies( X, or( Y, Y ) ),
% 0.96/1.38 implies( X, Y ) ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 305, [ =( theorem( implies( implies( X, or( Y, Y ) ), implies( X, Y
% 0.96/1.38 ) ) ), true ) ] )
% 0.96/1.38 , clause( 3952, [ =( theorem( implies( implies( X, or( Y, Y ) ), implies( X
% 0.96/1.38 , Y ) ) ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3954, [ =( true, ifeq( theorem( implies( implies( X, or( Y, X ) ),
% 0.96/1.38 Z ) ), true, theorem( Z ), true ) ) ] )
% 0.96/1.38 , clause( 35, [ =( ifeq( theorem( implies( implies( X, or( Y, X ) ), Z ) )
% 0.96/1.38 , true, theorem( Z ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3956, [ =( true, ifeq( true, true, theorem( implies( X, X ) ), true
% 0.96/1.38 ) ) ] )
% 0.96/1.38 , clause( 305, [ =( theorem( implies( implies( X, or( Y, Y ) ), implies( X
% 0.96/1.38 , Y ) ) ), true ) ] )
% 0.96/1.38 , 0, clause( 3954, [ =( true, ifeq( theorem( implies( implies( X, or( Y, X
% 0.96/1.38 ) ), Z ) ), true, theorem( Z ), true ) ) ] )
% 0.96/1.38 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, X )] ), substitution( 1, [
% 0.96/1.38 :=( X, X ), :=( Y, X ), :=( Z, implies( X, X ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3958, [ =( true, theorem( implies( X, X ) ) ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3956, [ =( true, ifeq( true, true, theorem( implies( X, X ) )
% 0.96/1.38 , true ) ) ] )
% 0.96/1.38 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( X, X ) )
% 0.96/1.38 ), :=( Z, true )] ), substitution( 1, [ :=( X, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3959, [ =( theorem( implies( X, X ) ), true ) ] )
% 0.96/1.38 , clause( 3958, [ =( true, theorem( implies( X, X ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 307, [ =( theorem( implies( X, X ) ), true ) ] )
% 0.96/1.38 , clause( 3959, [ =( theorem( implies( X, X ) ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3961, [ =( true, ifeq( theorem( implies( X, Y ) ), true, theorem(
% 0.96/1.38 or( Y, not( X ) ) ), true ) ) ] )
% 0.96/1.38 , clause( 29, [ =( ifeq( theorem( implies( X, Y ) ), true, theorem( or( Y,
% 0.96/1.38 not( X ) ) ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3963, [ =( true, ifeq( true, true, theorem( or( X, not( X ) ) ),
% 0.96/1.38 true ) ) ] )
% 0.96/1.38 , clause( 307, [ =( theorem( implies( X, X ) ), true ) ] )
% 0.96/1.38 , 0, clause( 3961, [ =( true, ifeq( theorem( implies( X, Y ) ), true,
% 0.96/1.38 theorem( or( Y, not( X ) ) ), true ) ) ] )
% 0.96/1.38 , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.96/1.38 :=( Y, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3964, [ =( true, theorem( or( X, not( X ) ) ) ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3963, [ =( true, ifeq( true, true, theorem( or( X, not( X ) )
% 0.96/1.38 ), true ) ) ] )
% 0.96/1.38 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( or( X, not( X ) )
% 0.96/1.38 ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3965, [ =( theorem( or( X, not( X ) ) ), true ) ] )
% 0.96/1.38 , clause( 3964, [ =( true, theorem( or( X, not( X ) ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 314, [ =( theorem( or( X, not( X ) ) ), true ) ] )
% 0.96/1.38 , clause( 3965, [ =( theorem( or( X, not( X ) ) ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3967, [ =( true, theorem( or( X, not( X ) ) ) ) ] )
% 0.96/1.38 , clause( 314, [ =( theorem( or( X, not( X ) ) ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3968, [ =( true, theorem( implies( X, not( not( X ) ) ) ) ) ] )
% 0.96/1.38 , clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.96/1.38 , 0, clause( 3967, [ =( true, theorem( or( X, not( X ) ) ) ) ] )
% 0.96/1.38 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, not( not( X ) ) )] ),
% 0.96/1.38 substitution( 1, [ :=( X, not( X ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3969, [ =( theorem( implies( X, not( not( X ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 3968, [ =( true, theorem( implies( X, not( not( X ) ) ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 324, [ =( theorem( implies( X, not( not( X ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 3969, [ =( theorem( implies( X, not( not( X ) ) ) ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3971, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.96/1.38 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.96/1.38 , clause( 8, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem( X
% 0.96/1.38 ), true, theorem( Y ), true ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3974, [ =( true, ifeq( theorem( implies( implies( X, not( not( X )
% 0.96/1.38 ) ), Y ) ), true, ifeq( true, true, theorem( Y ), true ), true ) ) ] )
% 0.96/1.38 , clause( 324, [ =( theorem( implies( X, not( not( X ) ) ) ), true ) ] )
% 0.96/1.38 , 0, clause( 3971, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.96/1.38 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.96/1.38 , 0, 13, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 0.96/1.38 implies( X, not( not( X ) ) ) ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3976, [ =( true, ifeq( theorem( implies( implies( X, not( not( X )
% 0.96/1.38 ) ), Y ) ), true, theorem( Y ), true ) ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3974, [ =( true, ifeq( theorem( implies( implies( X, not( not(
% 0.96/1.38 X ) ) ), Y ) ), true, ifeq( true, true, theorem( Y ), true ), true ) ) ]
% 0.96/1.38 )
% 0.96/1.38 , 0, 12, substitution( 0, [ :=( X, true ), :=( Y, theorem( Y ) ), :=( Z,
% 0.96/1.38 true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3977, [ =( ifeq( theorem( implies( implies( X, not( not( X ) ) ), Y
% 0.96/1.38 ) ), true, theorem( Y ), true ), true ) ] )
% 0.96/1.38 , clause( 3976, [ =( true, ifeq( theorem( implies( implies( X, not( not( X
% 0.96/1.38 ) ) ), Y ) ), true, theorem( Y ), true ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 345, [ =( ifeq( theorem( implies( implies( X, not( not( X ) ) ), Y
% 0.96/1.38 ) ), true, theorem( Y ), true ), true ) ] )
% 0.96/1.38 , clause( 3977, [ =( ifeq( theorem( implies( implies( X, not( not( X ) ) )
% 0.96/1.38 , Y ) ), true, theorem( Y ), true ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3979, [ =( true, ifeq( theorem( implies( implies( X, not( not( X )
% 0.96/1.38 ) ), Y ) ), true, theorem( Y ), true ) ) ] )
% 0.96/1.38 , clause( 345, [ =( ifeq( theorem( implies( implies( X, not( not( X ) ) ),
% 0.96/1.38 Y ) ), true, theorem( Y ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3981, [ =( true, ifeq( true, true, theorem( implies( implies( Y, X
% 0.96/1.38 ), implies( Y, not( not( X ) ) ) ) ), true ) ) ] )
% 0.96/1.38 , clause( 95, [ =( theorem( implies( implies( Y, Z ), implies( implies( X,
% 0.96/1.38 Y ), implies( X, Z ) ) ) ), true ) ] )
% 0.96/1.38 , 0, clause( 3979, [ =( true, ifeq( theorem( implies( implies( X, not( not(
% 0.96/1.38 X ) ) ), Y ) ), true, theorem( Y ), true ) ) ] )
% 0.96/1.38 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, not( not( X ) ) )] )
% 0.96/1.38 , substitution( 1, [ :=( X, X ), :=( Y, implies( implies( Y, X ), implies(
% 0.96/1.38 Y, not( not( X ) ) ) ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3983, [ =( true, theorem( implies( implies( X, Y ), implies( X, not(
% 0.96/1.38 not( Y ) ) ) ) ) ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3981, [ =( true, ifeq( true, true, theorem( implies( implies(
% 0.96/1.38 Y, X ), implies( Y, not( not( X ) ) ) ) ), true ) ) ] )
% 0.96/1.38 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( implies(
% 0.96/1.38 X, Y ), implies( X, not( not( Y ) ) ) ) ) ), :=( Z, true )] ),
% 0.96/1.38 substitution( 1, [ :=( X, Y ), :=( Y, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3984, [ =( theorem( implies( implies( X, Y ), implies( X, not( not(
% 0.96/1.38 Y ) ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 3983, [ =( true, theorem( implies( implies( X, Y ), implies( X,
% 0.96/1.38 not( not( Y ) ) ) ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 3619, [ =( theorem( implies( implies( Y, X ), implies( Y, not( not(
% 0.96/1.38 X ) ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 3984, [ =( theorem( implies( implies( X, Y ), implies( X, not(
% 0.96/1.38 not( Y ) ) ) ) ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3986, [ =( true, ifeq( theorem( implies( implies( X, or( Y, X ) ),
% 0.96/1.38 Z ) ), true, theorem( Z ), true ) ) ] )
% 0.96/1.38 , clause( 35, [ =( ifeq( theorem( implies( implies( X, or( Y, X ) ), Z ) )
% 0.96/1.38 , true, theorem( Z ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3988, [ =( true, ifeq( true, true, theorem( implies( X, not( not(
% 0.96/1.38 or( Y, X ) ) ) ) ), true ) ) ] )
% 0.96/1.38 , clause( 3619, [ =( theorem( implies( implies( Y, X ), implies( Y, not(
% 0.96/1.38 not( X ) ) ) ) ), true ) ] )
% 0.96/1.38 , 0, clause( 3986, [ =( true, ifeq( theorem( implies( implies( X, or( Y, X
% 0.96/1.38 ) ), Z ) ), true, theorem( Z ), true ) ) ] )
% 0.96/1.38 , 0, 3, substitution( 0, [ :=( X, or( Y, X ) ), :=( Y, X )] ),
% 0.96/1.38 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, implies( X, not( not(
% 0.96/1.38 or( Y, X ) ) ) ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3990, [ =( true, theorem( implies( X, not( not( or( Y, X ) ) ) ) )
% 0.96/1.38 ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3988, [ =( true, ifeq( true, true, theorem( implies( X, not(
% 0.96/1.38 not( or( Y, X ) ) ) ) ), true ) ) ] )
% 0.96/1.38 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( X, not(
% 0.96/1.38 not( or( Y, X ) ) ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X
% 0.96/1.38 ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3991, [ =( theorem( implies( X, not( not( or( Y, X ) ) ) ) ), true
% 0.96/1.38 ) ] )
% 0.96/1.38 , clause( 3990, [ =( true, theorem( implies( X, not( not( or( Y, X ) ) ) )
% 0.96/1.38 ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 3626, [ =( theorem( implies( X, not( not( or( Y, X ) ) ) ) ), true
% 0.96/1.38 ) ] )
% 0.96/1.38 , clause( 3991, [ =( theorem( implies( X, not( not( or( Y, X ) ) ) ) ),
% 0.96/1.38 true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3993, [ =( true, ifeq( theorem( implies( X, not( Y ) ) ), true,
% 0.96/1.38 theorem( implies( Y, not( X ) ) ), true ) ) ] )
% 0.96/1.38 , clause( 80, [ =( ifeq( theorem( implies( X, not( Y ) ) ), true, theorem(
% 0.96/1.38 implies( Y, not( X ) ) ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3995, [ =( true, ifeq( true, true, theorem( implies( not( or( Y, X
% 0.96/1.38 ) ), not( X ) ) ), true ) ) ] )
% 0.96/1.38 , clause( 3626, [ =( theorem( implies( X, not( not( or( Y, X ) ) ) ) ),
% 0.96/1.38 true ) ] )
% 0.96/1.38 , 0, clause( 3993, [ =( true, ifeq( theorem( implies( X, not( Y ) ) ), true
% 0.96/1.38 , theorem( implies( Y, not( X ) ) ), true ) ) ] )
% 0.96/1.38 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.96/1.38 :=( X, X ), :=( Y, not( or( Y, X ) ) )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 3997, [ =( true, theorem( implies( not( or( X, Y ) ), not( Y ) ) )
% 0.96/1.38 ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 3995, [ =( true, ifeq( true, true, theorem( implies( not( or(
% 0.96/1.38 Y, X ) ), not( X ) ) ), true ) ) ] )
% 0.96/1.38 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( not( or(
% 0.96/1.38 X, Y ) ), not( Y ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y )
% 0.96/1.38 , :=( Y, X )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 3998, [ =( theorem( implies( not( or( X, Y ) ), not( Y ) ) ), true
% 0.96/1.38 ) ] )
% 0.96/1.38 , clause( 3997, [ =( true, theorem( implies( not( or( X, Y ) ), not( Y ) )
% 0.96/1.38 ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 3703, [ =( theorem( implies( not( or( Y, X ) ), not( X ) ) ), true
% 0.96/1.38 ) ] )
% 0.96/1.38 , clause( 3998, [ =( theorem( implies( not( or( X, Y ) ), not( Y ) ) ),
% 0.96/1.38 true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.96/1.38 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 4000, [ =( true, ifeq( theorem( implies( X, Y ) ), true, theorem(
% 0.96/1.38 implies( X, implies( Z, Y ) ) ), true ) ) ] )
% 0.96/1.38 , clause( 294, [ =( ifeq( theorem( implies( X, Y ) ), true, theorem(
% 0.96/1.38 implies( X, implies( Z, Y ) ) ), true ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 4002, [ =( true, ifeq( true, true, theorem( implies( not( or( X, Y
% 0.96/1.38 ) ), implies( Z, not( Y ) ) ) ), true ) ) ] )
% 0.96/1.38 , clause( 3703, [ =( theorem( implies( not( or( Y, X ) ), not( X ) ) ),
% 0.96/1.38 true ) ] )
% 0.96/1.38 , 0, clause( 4000, [ =( true, ifeq( theorem( implies( X, Y ) ), true,
% 0.96/1.38 theorem( implies( X, implies( Z, Y ) ) ), true ) ) ] )
% 0.96/1.38 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 0.96/1.38 :=( X, not( or( X, Y ) ) ), :=( Y, not( Y ) ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 paramod(
% 0.96/1.38 clause( 4003, [ =( true, theorem( implies( not( or( X, Y ) ), implies( Z,
% 0.96/1.38 not( Y ) ) ) ) ) ] )
% 0.96/1.38 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.96/1.38 , 0, clause( 4002, [ =( true, ifeq( true, true, theorem( implies( not( or(
% 0.96/1.38 X, Y ) ), implies( Z, not( Y ) ) ) ), true ) ) ] )
% 0.96/1.38 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( not( or(
% 0.96/1.38 X, Y ) ), implies( Z, not( Y ) ) ) ) ), :=( Z, true )] ), substitution( 1
% 0.96/1.38 , [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 4004, [ =( theorem( implies( not( or( X, Y ) ), implies( Z, not( Y
% 0.96/1.38 ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 4003, [ =( true, theorem( implies( not( or( X, Y ) ), implies( Z
% 0.96/1.38 , not( Y ) ) ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 3711, [ =( theorem( implies( not( or( X, Y ) ), implies( Z, not( Y
% 0.96/1.38 ) ) ) ), true ) ] )
% 0.96/1.38 , clause( 4004, [ =( theorem( implies( not( or( X, Y ) ), implies( Z, not(
% 0.96/1.38 Y ) ) ) ), true ) ] )
% 0.96/1.38 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.96/1.38 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 4005, [ =( true, theorem( implies( not( or( X, Y ) ), implies( Z,
% 0.96/1.38 not( Y ) ) ) ) ) ] )
% 0.96/1.38 , clause( 3711, [ =( theorem( implies( not( or( X, Y ) ), implies( Z, not(
% 0.96/1.38 Y ) ) ) ), true ) ] )
% 0.96/1.38 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 eqswap(
% 0.96/1.38 clause( 4006, [ ~( =( true, theorem( implies( not( or( p, q ) ), implies( p
% 0.96/1.38 , not( q ) ) ) ) ) ) ] )
% 0.96/1.38 , clause( 9, [ ~( =( theorem( implies( not( or( p, q ) ), implies( p, not(
% 0.96/1.38 q ) ) ) ), true ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 resolution(
% 0.96/1.38 clause( 4007, [] )
% 0.96/1.38 , clause( 4006, [ ~( =( true, theorem( implies( not( or( p, q ) ), implies(
% 0.96/1.38 p, not( q ) ) ) ) ) ) ] )
% 0.96/1.38 , 0, clause( 4005, [ =( true, theorem( implies( not( or( X, Y ) ), implies(
% 0.96/1.38 Z, not( Y ) ) ) ) ) ] )
% 0.96/1.38 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, p ), :=( Y, q ), :=(
% 0.96/1.38 Z, p )] )).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 subsumption(
% 0.96/1.38 clause( 3753, [] )
% 0.96/1.38 , clause( 4007, [] )
% 0.96/1.38 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 end.
% 0.96/1.38
% 0.96/1.38 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.96/1.38
% 0.96/1.38 Memory use:
% 0.96/1.38
% 0.96/1.38 space for terms: 52412
% 0.96/1.38 space for clauses: 383389
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 clauses generated: 111629
% 0.96/1.38 clauses kept: 3754
% 0.96/1.38 clauses selected: 832
% 0.96/1.38 clauses deleted: 46
% 0.96/1.38 clauses inuse deleted: 10
% 0.96/1.38
% 0.96/1.38 subsentry: 708
% 0.96/1.38 literals s-matched: 294
% 0.96/1.38 literals matched: 294
% 0.96/1.38 full subsumption: 0
% 0.96/1.38
% 0.96/1.38 checksum: -1144459407
% 0.96/1.38
% 0.96/1.38
% 0.96/1.38 Bliksem ended
%------------------------------------------------------------------------------