TSTP Solution File: LCL239-10 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL239-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.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 07:52:06 EDT 2022
% Result : Unsatisfiable 0.76s 1.13s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : LCL239-10 : TPTP v8.1.0. Released v7.5.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Mon Jul 4 15:26:11 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.76/1.13 *** allocated 10000 integers for termspace/termends
% 0.76/1.13 *** allocated 10000 integers for clauses
% 0.76/1.13 *** allocated 10000 integers for justifications
% 0.76/1.13 Bliksem 1.12
% 0.76/1.13
% 0.76/1.13
% 0.76/1.13 Automatic Strategy Selection
% 0.76/1.13
% 0.76/1.13 Clauses:
% 0.76/1.13 [
% 0.76/1.13 [ =( ifeq( X, X, Y, Z ), Y ) ],
% 0.76/1.13 [ =( axiom( implies( or( X, X ), X ) ), true ) ],
% 0.76/1.13 [ =( axiom( implies( X, or( Y, X ) ) ), true ) ],
% 0.76/1.13 [ =( axiom( implies( or( X, Y ), or( Y, X ) ) ), true ) ],
% 0.76/1.13 [ =( axiom( implies( or( X, or( Y, Z ) ), or( Y, or( X, Z ) ) ) ), true
% 0.76/1.13 ) ],
% 0.76/1.13 [ =( axiom( implies( implies( X, Y ), implies( or( Z, X ), or( Z, Y ) )
% 0.76/1.13 ) ), true ) ],
% 0.76/1.13 [ =( implies( X, Y ), or( not( X ), Y ) ) ],
% 0.76/1.13 [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ],
% 0.76/1.13 [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem( X ), true,
% 0.76/1.13 theorem( Y ), true ), true ), true ) ],
% 0.76/1.13 [ =( and( X, Y ), not( or( not( X ), not( Y ) ) ) ) ],
% 0.76/1.13 [ ~( =( theorem( not( and( p, not( p ) ) ) ), true ) ) ]
% 0.76/1.13 ] .
% 0.76/1.13
% 0.76/1.13
% 0.76/1.13 percentage equality = 1.000000, percentage horn = 1.000000
% 0.76/1.13 This is a pure equality problem
% 0.76/1.13
% 0.76/1.13
% 0.76/1.13
% 0.76/1.13 Options Used:
% 0.76/1.13
% 0.76/1.13 useres = 1
% 0.76/1.13 useparamod = 1
% 0.76/1.13 useeqrefl = 1
% 0.76/1.13 useeqfact = 1
% 0.76/1.13 usefactor = 1
% 0.76/1.13 usesimpsplitting = 0
% 0.76/1.13 usesimpdemod = 5
% 0.76/1.13 usesimpres = 3
% 0.76/1.13
% 0.76/1.13 resimpinuse = 1000
% 0.76/1.13 resimpclauses = 20000
% 0.76/1.13 substype = eqrewr
% 0.76/1.13 backwardsubs = 1
% 0.76/1.13 selectoldest = 5
% 0.76/1.13
% 0.76/1.13 litorderings [0] = split
% 0.76/1.13 litorderings [1] = extend the termordering, first sorting on arguments
% 0.76/1.13
% 0.76/1.13 termordering = kbo
% 0.76/1.13
% 0.76/1.13 litapriori = 0
% 0.76/1.13 termapriori = 1
% 0.76/1.13 litaposteriori = 0
% 0.76/1.13 termaposteriori = 0
% 0.76/1.13 demodaposteriori = 0
% 0.76/1.13 ordereqreflfact = 0
% 0.76/1.13
% 0.76/1.13 litselect = negord
% 0.76/1.13
% 0.76/1.13 maxweight = 15
% 0.76/1.13 maxdepth = 30000
% 0.76/1.13 maxlength = 115
% 0.76/1.13 maxnrvars = 195
% 0.76/1.13 excuselevel = 1
% 0.76/1.13 increasemaxweight = 1
% 0.76/1.13
% 0.76/1.13 maxselected = 10000000
% 0.76/1.13 maxnrclauses = 10000000
% 0.76/1.13
% 0.76/1.13 showgenerated = 0
% 0.76/1.13 showkept = 0
% 0.76/1.13 showselected = 0
% 0.76/1.13 showdeleted = 0
% 0.76/1.13 showresimp = 1
% 0.76/1.13 showstatus = 2000
% 0.76/1.13
% 0.76/1.13 prologoutput = 1
% 0.76/1.13 nrgoals = 5000000
% 0.76/1.13 totalproof = 1
% 0.76/1.13
% 0.76/1.13 Symbols occurring in the translation:
% 0.76/1.13
% 0.76/1.13 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.76/1.13 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 0.76/1.13 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 0.76/1.13 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.76/1.13 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.76/1.13 ifeq [42, 4] (w:1, o:54, a:1, s:1, b:0),
% 0.76/1.13 or [43, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.76/1.13 implies [44, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.76/1.13 axiom [45, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.76/1.13 true [46, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.76/1.13 not [49, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.76/1.13 theorem [50, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.76/1.13 and [53, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.76/1.13 p [54, 0] (w:1, o:17, a:1, s:1, b:0).
% 0.76/1.13
% 0.76/1.13
% 0.76/1.13 Starting Search:
% 0.76/1.13
% 0.76/1.13
% 0.76/1.13 Bliksems!, er is een bewijs:
% 0.76/1.13 % SZS status Unsatisfiable
% 0.76/1.13 % SZS output start Refutation
% 0.76/1.13
% 0.76/1.13 clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.76/1.13 .
% 0.76/1.13 clause( 1, [ =( axiom( implies( or( X, X ), X ) ), true ) ] )
% 0.76/1.13 .
% 0.76/1.13 clause( 2, [ =( axiom( implies( X, or( Y, X ) ) ), true ) ] )
% 0.76/1.13 .
% 0.76/1.13 clause( 3, [ =( axiom( implies( or( X, Y ), or( Y, X ) ) ), true ) ] )
% 0.76/1.13 .
% 0.76/1.13 clause( 5, [ =( axiom( implies( implies( X, Y ), implies( or( Z, X ), or( Z
% 0.76/1.13 , Y ) ) ) ), true ) ] )
% 0.76/1.13 .
% 0.76/1.13 clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.76/1.13 .
% 0.76/1.13 clause( 7, [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ] )
% 0.76/1.13 .
% 0.76/1.13 clause( 8, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem( X )
% 0.76/1.13 , true, theorem( Y ), true ), true ), true ) ] )
% 0.76/1.13 .
% 0.76/1.13 clause( 9, [ =( not( implies( X, not( Y ) ) ), and( X, Y ) ) ] )
% 0.76/1.13 .
% 0.76/1.13 clause( 10, [ ~( =( theorem( not( and( p, not( p ) ) ) ), true ) ) ] )
% 0.76/1.13 .
% 0.76/1.13 clause( 15, [ =( theorem( implies( or( X, Y ), or( Y, X ) ) ), true ) ] )
% 0.76/1.13 .
% 0.76/1.13 clause( 16, [ =( theorem( implies( or( X, X ), X ) ), true ) ] )
% 0.76/1.13 .
% 0.76/1.13 clause( 18, [ =( theorem( implies( X, or( Y, X ) ) ), true ) ] )
% 0.76/1.13 .
% 0.76/1.13 clause( 25, [ =( theorem( implies( implies( X, Y ), or( Y, not( X ) ) ) ),
% 0.76/1.13 true ) ] )
% 0.76/1.13 .
% 0.76/1.13 clause( 28, [ =( theorem( implies( implies( X, Y ), implies( or( Z, X ), or(
% 0.76/1.13 Z, Y ) ) ) ), true ) ] )
% 0.76/1.13 .
% 0.76/1.13 clause( 33, [ =( ifeq( theorem( implies( X, Y ) ), true, theorem( or( Y,
% 0.76/1.13 not( X ) ) ), true ), true ) ] )
% 0.76/1.13 .
% 0.76/1.14 clause( 36, [ =( ifeq( theorem( implies( implies( or( X, X ), X ), Y ) ),
% 0.76/1.14 true, theorem( Y ), true ), true ) ] )
% 0.76/1.14 .
% 0.76/1.14 clause( 38, [ =( ifeq( theorem( implies( implies( X, or( Y, X ) ), Z ) ),
% 0.76/1.14 true, theorem( Z ), true ), true ) ] )
% 0.76/1.14 .
% 0.76/1.14 clause( 198, [ =( theorem( implies( or( Y, or( X, X ) ), or( Y, X ) ) ),
% 0.76/1.14 true ) ] )
% 0.76/1.14 .
% 0.76/1.14 clause( 398, [ =( theorem( implies( implies( X, or( Y, Y ) ), implies( X, Y
% 0.76/1.14 ) ) ), true ) ] )
% 0.76/1.14 .
% 0.76/1.14 clause( 400, [ =( theorem( implies( X, X ) ), true ) ] )
% 0.76/1.14 .
% 0.76/1.14 clause( 408, [ =( theorem( or( X, not( X ) ) ), true ) ] )
% 0.76/1.14 .
% 0.76/1.14 clause( 421, [ =( theorem( implies( X, not( not( X ) ) ) ), true ) ] )
% 0.76/1.14 .
% 0.76/1.14 clause( 451, [ =( ifeq( theorem( X ), true, theorem( not( not( X ) ) ),
% 0.76/1.14 true ), true ) ] )
% 0.76/1.14 .
% 0.76/1.14 clause( 579, [ =( theorem( not( and( X, not( X ) ) ) ), true ) ] )
% 0.76/1.14 .
% 0.76/1.14 clause( 665, [] )
% 0.76/1.14 .
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 % SZS output end Refutation
% 0.76/1.14 found a proof!
% 0.76/1.14
% 0.76/1.14 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.76/1.14
% 0.76/1.14 initialclauses(
% 0.76/1.14 [ clause( 667, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.76/1.14 , clause( 668, [ =( axiom( implies( or( X, X ), X ) ), true ) ] )
% 0.76/1.14 , clause( 669, [ =( axiom( implies( X, or( Y, X ) ) ), true ) ] )
% 0.76/1.14 , clause( 670, [ =( axiom( implies( or( X, Y ), or( Y, X ) ) ), true ) ] )
% 0.76/1.14 , clause( 671, [ =( axiom( implies( or( X, or( Y, Z ) ), or( Y, or( X, Z )
% 0.76/1.14 ) ) ), true ) ] )
% 0.76/1.14 , clause( 672, [ =( axiom( implies( implies( X, Y ), implies( or( Z, X ),
% 0.76/1.14 or( Z, Y ) ) ) ), true ) ] )
% 0.76/1.14 , clause( 673, [ =( implies( X, Y ), or( not( X ), Y ) ) ] )
% 0.76/1.14 , clause( 674, [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ]
% 0.76/1.14 )
% 0.76/1.14 , clause( 675, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem(
% 0.76/1.14 X ), true, theorem( Y ), true ), true ), true ) ] )
% 0.76/1.14 , clause( 676, [ =( and( X, Y ), not( or( not( X ), not( Y ) ) ) ) ] )
% 0.76/1.14 , clause( 677, [ ~( =( theorem( not( and( p, not( p ) ) ) ), true ) ) ] )
% 0.76/1.14 ] ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.76/1.14 , clause( 667, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.76/1.14 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 1, [ =( axiom( implies( or( X, X ), X ) ), true ) ] )
% 0.76/1.14 , clause( 668, [ =( axiom( implies( or( X, X ), X ) ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 2, [ =( axiom( implies( X, or( Y, X ) ) ), true ) ] )
% 0.76/1.14 , clause( 669, [ =( axiom( implies( X, or( Y, X ) ) ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.14 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 3, [ =( axiom( implies( or( X, Y ), or( Y, X ) ) ), true ) ] )
% 0.76/1.14 , clause( 670, [ =( axiom( implies( or( X, Y ), or( Y, X ) ) ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.14 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 5, [ =( axiom( implies( implies( X, Y ), implies( or( Z, X ), or( Z
% 0.76/1.14 , Y ) ) ) ), true ) ] )
% 0.76/1.14 , clause( 672, [ =( axiom( implies( implies( X, Y ), implies( or( Z, X ),
% 0.76/1.14 or( Z, Y ) ) ) ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.76/1.14 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 700, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.76/1.14 , clause( 673, [ =( implies( X, Y ), or( not( X ), Y ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.76/1.14 , clause( 700, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.14 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 7, [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ] )
% 0.76/1.14 , clause( 674, [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ]
% 0.76/1.14 )
% 0.76/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 8, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem( X )
% 0.76/1.14 , true, theorem( Y ), true ), true ), true ) ] )
% 0.76/1.14 , clause( 675, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem(
% 0.76/1.14 X ), true, theorem( Y ), true ), true ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.14 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 740, [ =( and( X, Y ), not( implies( X, not( Y ) ) ) ) ] )
% 0.76/1.14 , clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.76/1.14 , 0, clause( 676, [ =( and( X, Y ), not( or( not( X ), not( Y ) ) ) ) ] )
% 0.76/1.14 , 0, 5, substitution( 0, [ :=( X, X ), :=( Y, not( Y ) )] ), substitution(
% 0.76/1.14 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 741, [ =( not( implies( X, not( Y ) ) ), and( X, Y ) ) ] )
% 0.76/1.14 , clause( 740, [ =( and( X, Y ), not( implies( X, not( Y ) ) ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 9, [ =( not( implies( X, not( Y ) ) ), and( X, Y ) ) ] )
% 0.76/1.14 , clause( 741, [ =( not( implies( X, not( Y ) ) ), and( X, Y ) ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.14 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 10, [ ~( =( theorem( not( and( p, not( p ) ) ) ), true ) ) ] )
% 0.76/1.14 , clause( 677, [ ~( =( theorem( not( and( p, not( p ) ) ) ), true ) ) ] )
% 0.76/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 754, [ =( true, ifeq( axiom( X ), true, theorem( X ), true ) ) ] )
% 0.76/1.14 , clause( 7, [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 756, [ =( true, ifeq( true, true, theorem( implies( or( X, Y ), or(
% 0.76/1.14 Y, X ) ) ), true ) ) ] )
% 0.76/1.14 , clause( 3, [ =( axiom( implies( or( X, Y ), or( Y, X ) ) ), true ) ] )
% 0.76/1.14 , 0, clause( 754, [ =( true, ifeq( axiom( X ), true, theorem( X ), true ) )
% 0.76/1.14 ] )
% 0.76/1.14 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.76/1.14 :=( X, implies( or( X, Y ), or( Y, X ) ) )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 757, [ =( true, theorem( implies( or( X, Y ), or( Y, X ) ) ) ) ] )
% 0.76/1.14 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.76/1.14 , 0, clause( 756, [ =( true, ifeq( true, true, theorem( implies( or( X, Y )
% 0.76/1.14 , or( Y, X ) ) ), true ) ) ] )
% 0.76/1.14 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( or( X, Y
% 0.76/1.14 ), or( Y, X ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ),
% 0.76/1.14 :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 758, [ =( theorem( implies( or( X, Y ), or( Y, X ) ) ), true ) ] )
% 0.76/1.14 , clause( 757, [ =( true, theorem( implies( or( X, Y ), or( Y, X ) ) ) ) ]
% 0.76/1.14 )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 15, [ =( theorem( implies( or( X, Y ), or( Y, X ) ) ), true ) ] )
% 0.76/1.14 , clause( 758, [ =( theorem( implies( or( X, Y ), or( Y, X ) ) ), true ) ]
% 0.76/1.14 )
% 0.76/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.14 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 760, [ =( true, ifeq( axiom( X ), true, theorem( X ), true ) ) ] )
% 0.76/1.14 , clause( 7, [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 762, [ =( true, ifeq( true, true, theorem( implies( or( X, X ), X )
% 0.76/1.14 ), true ) ) ] )
% 0.76/1.14 , clause( 1, [ =( axiom( implies( or( X, X ), X ) ), true ) ] )
% 0.76/1.14 , 0, clause( 760, [ =( true, ifeq( axiom( X ), true, theorem( X ), true ) )
% 0.76/1.14 ] )
% 0.76/1.14 , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, implies(
% 0.76/1.14 or( X, X ), X ) )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 763, [ =( true, theorem( implies( or( X, X ), X ) ) ) ] )
% 0.76/1.14 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.76/1.14 , 0, clause( 762, [ =( true, ifeq( true, true, theorem( implies( or( X, X )
% 0.76/1.14 , X ) ), true ) ) ] )
% 0.76/1.14 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( or( X, X
% 0.76/1.14 ), X ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 764, [ =( theorem( implies( or( X, X ), X ) ), true ) ] )
% 0.76/1.14 , clause( 763, [ =( true, theorem( implies( or( X, X ), X ) ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 16, [ =( theorem( implies( or( X, X ), X ) ), true ) ] )
% 0.76/1.14 , clause( 764, [ =( theorem( implies( or( X, X ), X ) ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 766, [ =( true, ifeq( axiom( X ), true, theorem( X ), true ) ) ] )
% 0.76/1.14 , clause( 7, [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 768, [ =( true, ifeq( true, true, theorem( implies( X, or( Y, X ) )
% 0.76/1.14 ), true ) ) ] )
% 0.76/1.14 , clause( 2, [ =( axiom( implies( X, or( Y, X ) ) ), true ) ] )
% 0.76/1.14 , 0, clause( 766, [ =( true, ifeq( axiom( X ), true, theorem( X ), true ) )
% 0.76/1.14 ] )
% 0.76/1.14 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.76/1.14 :=( X, implies( X, or( Y, X ) ) )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 769, [ =( true, theorem( implies( X, or( Y, X ) ) ) ) ] )
% 0.76/1.14 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.76/1.14 , 0, clause( 768, [ =( true, ifeq( true, true, theorem( implies( X, or( Y,
% 0.76/1.14 X ) ) ), true ) ) ] )
% 0.76/1.14 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( X, or( Y
% 0.76/1.14 , X ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 0.76/1.14 ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 770, [ =( theorem( implies( X, or( Y, X ) ) ), true ) ] )
% 0.76/1.14 , clause( 769, [ =( true, theorem( implies( X, or( Y, X ) ) ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 18, [ =( theorem( implies( X, or( Y, X ) ) ), true ) ] )
% 0.76/1.14 , clause( 770, [ =( theorem( implies( X, or( Y, X ) ) ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.14 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 772, [ =( true, theorem( implies( or( X, Y ), or( Y, X ) ) ) ) ] )
% 0.76/1.14 , clause( 15, [ =( theorem( implies( or( X, Y ), or( Y, X ) ) ), true ) ]
% 0.76/1.14 )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 773, [ =( true, theorem( implies( implies( X, Y ), or( Y, not( X )
% 0.76/1.14 ) ) ) ) ] )
% 0.76/1.14 , clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.76/1.14 , 0, clause( 772, [ =( true, theorem( implies( or( X, Y ), or( Y, X ) ) ) )
% 0.76/1.14 ] )
% 0.76/1.14 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.76/1.14 :=( X, not( X ) ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 775, [ =( theorem( implies( implies( X, Y ), or( Y, not( X ) ) ) )
% 0.76/1.14 , true ) ] )
% 0.76/1.14 , clause( 773, [ =( true, theorem( implies( implies( X, Y ), or( Y, not( X
% 0.76/1.14 ) ) ) ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 25, [ =( theorem( implies( implies( X, Y ), or( Y, not( X ) ) ) ),
% 0.76/1.14 true ) ] )
% 0.76/1.14 , clause( 775, [ =( theorem( implies( implies( X, Y ), or( Y, not( X ) ) )
% 0.76/1.14 ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.14 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 778, [ =( true, ifeq( axiom( X ), true, theorem( X ), true ) ) ] )
% 0.76/1.14 , clause( 7, [ =( ifeq( axiom( X ), true, theorem( X ), true ), true ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 780, [ =( true, ifeq( true, true, theorem( implies( implies( X, Y )
% 0.76/1.14 , implies( or( Z, X ), or( Z, Y ) ) ) ), true ) ) ] )
% 0.76/1.14 , clause( 5, [ =( axiom( implies( implies( X, Y ), implies( or( Z, X ), or(
% 0.76/1.14 Z, Y ) ) ) ), true ) ] )
% 0.76/1.14 , 0, clause( 778, [ =( true, ifeq( axiom( X ), true, theorem( X ), true ) )
% 0.76/1.14 ] )
% 0.76/1.14 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.76/1.14 substitution( 1, [ :=( X, implies( implies( X, Y ), implies( or( Z, X ),
% 0.76/1.14 or( Z, Y ) ) ) )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 781, [ =( true, theorem( implies( implies( X, Y ), implies( or( Z,
% 0.76/1.14 X ), or( Z, Y ) ) ) ) ) ] )
% 0.76/1.14 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.76/1.14 , 0, clause( 780, [ =( true, ifeq( true, true, theorem( implies( implies( X
% 0.76/1.14 , Y ), implies( or( Z, X ), or( Z, Y ) ) ) ), true ) ) ] )
% 0.76/1.14 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( implies(
% 0.76/1.14 X, Y ), implies( or( Z, X ), or( Z, Y ) ) ) ) ), :=( Z, true )] ),
% 0.76/1.14 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 782, [ =( theorem( implies( implies( X, Y ), implies( or( Z, X ),
% 0.76/1.14 or( Z, Y ) ) ) ), true ) ] )
% 0.76/1.14 , clause( 781, [ =( true, theorem( implies( implies( X, Y ), implies( or( Z
% 0.76/1.14 , X ), or( Z, Y ) ) ) ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 28, [ =( theorem( implies( implies( X, Y ), implies( or( Z, X ), or(
% 0.76/1.14 Z, Y ) ) ) ), true ) ] )
% 0.76/1.14 , clause( 782, [ =( theorem( implies( implies( X, Y ), implies( or( Z, X )
% 0.76/1.14 , or( Z, Y ) ) ) ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.76/1.14 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 784, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.76/1.14 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.76/1.14 , clause( 8, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem( X
% 0.76/1.14 ), true, theorem( Y ), true ), true ), true ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 786, [ =( true, ifeq( true, true, ifeq( theorem( implies( X, Y ) )
% 0.76/1.14 , true, theorem( or( Y, not( X ) ) ), true ), true ) ) ] )
% 0.76/1.14 , clause( 25, [ =( theorem( implies( implies( X, Y ), or( Y, not( X ) ) ) )
% 0.76/1.14 , true ) ] )
% 0.76/1.14 , 0, clause( 784, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.76/1.14 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.76/1.14 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.76/1.14 :=( X, implies( X, Y ) ), :=( Y, or( Y, not( X ) ) )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 791, [ =( true, ifeq( theorem( implies( X, Y ) ), true, theorem( or(
% 0.76/1.14 Y, not( X ) ) ), true ) ) ] )
% 0.76/1.14 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.76/1.14 , 0, clause( 786, [ =( true, ifeq( true, true, ifeq( theorem( implies( X, Y
% 0.76/1.14 ) ), true, theorem( or( Y, not( X ) ) ), true ), true ) ) ] )
% 0.76/1.14 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( theorem( implies( X
% 0.76/1.14 , Y ) ), true, theorem( or( Y, not( X ) ) ), true ) ), :=( Z, true )] ),
% 0.76/1.14 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 792, [ =( ifeq( theorem( implies( X, Y ) ), true, theorem( or( Y,
% 0.76/1.14 not( X ) ) ), true ), true ) ] )
% 0.76/1.14 , clause( 791, [ =( true, ifeq( theorem( implies( X, Y ) ), true, theorem(
% 0.76/1.14 or( Y, not( X ) ) ), true ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 33, [ =( ifeq( theorem( implies( X, Y ) ), true, theorem( or( Y,
% 0.76/1.14 not( X ) ) ), true ), true ) ] )
% 0.76/1.14 , clause( 792, [ =( ifeq( theorem( implies( X, Y ) ), true, theorem( or( Y
% 0.76/1.14 , not( X ) ) ), true ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.14 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 794, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.76/1.14 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.76/1.14 , clause( 8, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem( X
% 0.76/1.14 ), true, theorem( Y ), true ), true ), true ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 797, [ =( true, ifeq( theorem( implies( implies( or( X, X ), X ), Y
% 0.76/1.14 ) ), true, ifeq( true, true, theorem( Y ), true ), true ) ) ] )
% 0.76/1.14 , clause( 16, [ =( theorem( implies( or( X, X ), X ) ), true ) ] )
% 0.76/1.14 , 0, clause( 794, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.76/1.14 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.76/1.14 , 0, 13, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 0.76/1.14 implies( or( X, X ), X ) ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 799, [ =( true, ifeq( theorem( implies( implies( or( X, X ), X ), Y
% 0.76/1.14 ) ), true, theorem( Y ), true ) ) ] )
% 0.76/1.14 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.76/1.14 , 0, clause( 797, [ =( true, ifeq( theorem( implies( implies( or( X, X ), X
% 0.76/1.14 ), Y ) ), true, ifeq( true, true, theorem( Y ), true ), true ) ) ] )
% 0.76/1.14 , 0, 12, substitution( 0, [ :=( X, true ), :=( Y, theorem( Y ) ), :=( Z,
% 0.76/1.14 true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 800, [ =( ifeq( theorem( implies( implies( or( X, X ), X ), Y ) ),
% 0.76/1.14 true, theorem( Y ), true ), true ) ] )
% 0.76/1.14 , clause( 799, [ =( true, ifeq( theorem( implies( implies( or( X, X ), X )
% 0.76/1.14 , Y ) ), true, theorem( Y ), true ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 36, [ =( ifeq( theorem( implies( implies( or( X, X ), X ), Y ) ),
% 0.76/1.14 true, theorem( Y ), true ), true ) ] )
% 0.76/1.14 , clause( 800, [ =( ifeq( theorem( implies( implies( or( X, X ), X ), Y ) )
% 0.76/1.14 , true, theorem( Y ), true ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.14 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 802, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.76/1.14 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.76/1.14 , clause( 8, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem( X
% 0.76/1.14 ), true, theorem( Y ), true ), true ), true ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 805, [ =( true, ifeq( theorem( implies( implies( X, or( Y, X ) ), Z
% 0.76/1.14 ) ), true, ifeq( true, true, theorem( Z ), true ), true ) ) ] )
% 0.76/1.14 , clause( 18, [ =( theorem( implies( X, or( Y, X ) ) ), true ) ] )
% 0.76/1.14 , 0, clause( 802, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.76/1.14 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.76/1.14 , 0, 13, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.76/1.14 :=( X, implies( X, or( Y, X ) ) ), :=( Y, Z )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 807, [ =( true, ifeq( theorem( implies( implies( X, or( Y, X ) ), Z
% 0.76/1.14 ) ), true, theorem( Z ), true ) ) ] )
% 0.76/1.14 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.76/1.14 , 0, clause( 805, [ =( true, ifeq( theorem( implies( implies( X, or( Y, X )
% 0.76/1.14 ), Z ) ), true, ifeq( true, true, theorem( Z ), true ), true ) ) ] )
% 0.76/1.14 , 0, 12, substitution( 0, [ :=( X, true ), :=( Y, theorem( Z ) ), :=( Z,
% 0.76/1.14 true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 808, [ =( ifeq( theorem( implies( implies( X, or( Y, X ) ), Z ) ),
% 0.76/1.14 true, theorem( Z ), true ), true ) ] )
% 0.76/1.14 , clause( 807, [ =( true, ifeq( theorem( implies( implies( X, or( Y, X ) )
% 0.76/1.14 , Z ) ), true, theorem( Z ), true ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 38, [ =( ifeq( theorem( implies( implies( X, or( Y, X ) ), Z ) ),
% 0.76/1.14 true, theorem( Z ), true ), true ) ] )
% 0.76/1.14 , clause( 808, [ =( ifeq( theorem( implies( implies( X, or( Y, X ) ), Z ) )
% 0.76/1.14 , true, theorem( Z ), true ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.76/1.14 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 810, [ =( true, ifeq( theorem( implies( implies( or( X, X ), X ), Y
% 0.76/1.14 ) ), true, theorem( Y ), true ) ) ] )
% 0.76/1.14 , clause( 36, [ =( ifeq( theorem( implies( implies( or( X, X ), X ), Y ) )
% 0.76/1.14 , true, theorem( Y ), true ), true ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 812, [ =( true, ifeq( true, true, theorem( implies( or( Y, or( X, X
% 0.76/1.14 ) ), or( Y, X ) ) ), true ) ) ] )
% 0.76/1.14 , clause( 28, [ =( theorem( implies( implies( X, Y ), implies( or( Z, X ),
% 0.76/1.14 or( Z, Y ) ) ) ), true ) ] )
% 0.76/1.14 , 0, clause( 810, [ =( true, ifeq( theorem( implies( implies( or( X, X ), X
% 0.76/1.14 ), Y ) ), true, theorem( Y ), true ) ) ] )
% 0.76/1.14 , 0, 3, substitution( 0, [ :=( X, or( X, X ) ), :=( Y, X ), :=( Z, Y )] ),
% 0.76/1.14 substitution( 1, [ :=( X, X ), :=( Y, implies( or( Y, or( X, X ) ), or( Y
% 0.76/1.14 , X ) ) )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 814, [ =( true, theorem( implies( or( X, or( Y, Y ) ), or( X, Y ) )
% 0.76/1.14 ) ) ] )
% 0.76/1.14 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.76/1.14 , 0, clause( 812, [ =( true, ifeq( true, true, theorem( implies( or( Y, or(
% 0.76/1.14 X, X ) ), or( Y, X ) ) ), true ) ) ] )
% 0.76/1.14 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( or( X,
% 0.76/1.14 or( Y, Y ) ), or( X, Y ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=(
% 0.76/1.14 X, Y ), :=( Y, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 815, [ =( theorem( implies( or( X, or( Y, Y ) ), or( X, Y ) ) ),
% 0.76/1.14 true ) ] )
% 0.76/1.14 , clause( 814, [ =( true, theorem( implies( or( X, or( Y, Y ) ), or( X, Y )
% 0.76/1.14 ) ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 198, [ =( theorem( implies( or( Y, or( X, X ) ), or( Y, X ) ) ),
% 0.76/1.14 true ) ] )
% 0.76/1.14 , clause( 815, [ =( theorem( implies( or( X, or( Y, Y ) ), or( X, Y ) ) ),
% 0.76/1.14 true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.14 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 817, [ =( true, theorem( implies( or( X, or( Y, Y ) ), or( X, Y ) )
% 0.76/1.14 ) ) ] )
% 0.76/1.14 , clause( 198, [ =( theorem( implies( or( Y, or( X, X ) ), or( Y, X ) ) ),
% 0.76/1.14 true ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 821, [ =( true, theorem( implies( or( not( X ), or( Y, Y ) ),
% 0.76/1.14 implies( X, Y ) ) ) ) ] )
% 0.76/1.14 , clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.76/1.14 , 0, clause( 817, [ =( true, theorem( implies( or( X, or( Y, Y ) ), or( X,
% 0.76/1.14 Y ) ) ) ) ] )
% 0.76/1.14 , 0, 10, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.76/1.14 :=( X, not( X ) ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 823, [ =( true, theorem( implies( implies( X, or( Y, Y ) ), implies(
% 0.76/1.14 X, Y ) ) ) ) ] )
% 0.76/1.14 , clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.76/1.14 , 0, clause( 821, [ =( true, theorem( implies( or( not( X ), or( Y, Y ) ),
% 0.76/1.14 implies( X, Y ) ) ) ) ] )
% 0.76/1.14 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, or( Y, Y ) )] ),
% 0.76/1.14 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 824, [ =( theorem( implies( implies( X, or( Y, Y ) ), implies( X, Y
% 0.76/1.14 ) ) ), true ) ] )
% 0.76/1.14 , clause( 823, [ =( true, theorem( implies( implies( X, or( Y, Y ) ),
% 0.76/1.14 implies( X, Y ) ) ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 398, [ =( theorem( implies( implies( X, or( Y, Y ) ), implies( X, Y
% 0.76/1.14 ) ) ), true ) ] )
% 0.76/1.14 , clause( 824, [ =( theorem( implies( implies( X, or( Y, Y ) ), implies( X
% 0.76/1.14 , Y ) ) ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.14 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 826, [ =( true, ifeq( theorem( implies( implies( X, or( Y, X ) ), Z
% 0.76/1.14 ) ), true, theorem( Z ), true ) ) ] )
% 0.76/1.14 , clause( 38, [ =( ifeq( theorem( implies( implies( X, or( Y, X ) ), Z ) )
% 0.76/1.14 , true, theorem( Z ), true ), true ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 828, [ =( true, ifeq( true, true, theorem( implies( X, X ) ), true
% 0.76/1.14 ) ) ] )
% 0.76/1.14 , clause( 398, [ =( theorem( implies( implies( X, or( Y, Y ) ), implies( X
% 0.76/1.14 , Y ) ) ), true ) ] )
% 0.76/1.14 , 0, clause( 826, [ =( true, ifeq( theorem( implies( implies( X, or( Y, X )
% 0.76/1.14 ), Z ) ), true, theorem( Z ), true ) ) ] )
% 0.76/1.14 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, X )] ), substitution( 1, [
% 0.76/1.14 :=( X, X ), :=( Y, X ), :=( Z, implies( X, X ) )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 830, [ =( true, theorem( implies( X, X ) ) ) ] )
% 0.76/1.14 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.76/1.14 , 0, clause( 828, [ =( true, ifeq( true, true, theorem( implies( X, X ) ),
% 0.76/1.14 true ) ) ] )
% 0.76/1.14 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( implies( X, X ) )
% 0.76/1.14 ), :=( Z, true )] ), substitution( 1, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 831, [ =( theorem( implies( X, X ) ), true ) ] )
% 0.76/1.14 , clause( 830, [ =( true, theorem( implies( X, X ) ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 400, [ =( theorem( implies( X, X ) ), true ) ] )
% 0.76/1.14 , clause( 831, [ =( theorem( implies( X, X ) ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 833, [ =( true, ifeq( theorem( implies( X, Y ) ), true, theorem( or(
% 0.76/1.14 Y, not( X ) ) ), true ) ) ] )
% 0.76/1.14 , clause( 33, [ =( ifeq( theorem( implies( X, Y ) ), true, theorem( or( Y,
% 0.76/1.14 not( X ) ) ), true ), true ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 835, [ =( true, ifeq( true, true, theorem( or( X, not( X ) ) ),
% 0.76/1.14 true ) ) ] )
% 0.76/1.14 , clause( 400, [ =( theorem( implies( X, X ) ), true ) ] )
% 0.76/1.14 , 0, clause( 833, [ =( true, ifeq( theorem( implies( X, Y ) ), true,
% 0.76/1.14 theorem( or( Y, not( X ) ) ), true ) ) ] )
% 0.76/1.14 , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.76/1.14 :=( Y, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 836, [ =( true, theorem( or( X, not( X ) ) ) ) ] )
% 0.76/1.14 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.76/1.14 , 0, clause( 835, [ =( true, ifeq( true, true, theorem( or( X, not( X ) ) )
% 0.76/1.14 , true ) ) ] )
% 0.76/1.14 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( or( X, not( X ) )
% 0.76/1.14 ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 837, [ =( theorem( or( X, not( X ) ) ), true ) ] )
% 0.76/1.14 , clause( 836, [ =( true, theorem( or( X, not( X ) ) ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 408, [ =( theorem( or( X, not( X ) ) ), true ) ] )
% 0.76/1.14 , clause( 837, [ =( theorem( or( X, not( X ) ) ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 839, [ =( true, theorem( or( X, not( X ) ) ) ) ] )
% 0.76/1.14 , clause( 408, [ =( theorem( or( X, not( X ) ) ), true ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 840, [ =( true, theorem( implies( X, not( not( X ) ) ) ) ) ] )
% 0.76/1.14 , clause( 6, [ =( or( not( X ), Y ), implies( X, Y ) ) ] )
% 0.76/1.14 , 0, clause( 839, [ =( true, theorem( or( X, not( X ) ) ) ) ] )
% 0.76/1.14 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, not( not( X ) ) )] ),
% 0.76/1.14 substitution( 1, [ :=( X, not( X ) )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 841, [ =( theorem( implies( X, not( not( X ) ) ) ), true ) ] )
% 0.76/1.14 , clause( 840, [ =( true, theorem( implies( X, not( not( X ) ) ) ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 421, [ =( theorem( implies( X, not( not( X ) ) ) ), true ) ] )
% 0.76/1.14 , clause( 841, [ =( theorem( implies( X, not( not( X ) ) ) ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 843, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.76/1.14 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.76/1.14 , clause( 8, [ =( ifeq( theorem( implies( X, Y ) ), true, ifeq( theorem( X
% 0.76/1.14 ), true, theorem( Y ), true ), true ), true ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 845, [ =( true, ifeq( true, true, ifeq( theorem( X ), true, theorem(
% 0.76/1.14 not( not( X ) ) ), true ), true ) ) ] )
% 0.76/1.14 , clause( 421, [ =( theorem( implies( X, not( not( X ) ) ) ), true ) ] )
% 0.76/1.14 , 0, clause( 843, [ =( true, ifeq( theorem( implies( X, Y ) ), true, ifeq(
% 0.76/1.14 theorem( X ), true, theorem( Y ), true ), true ) ) ] )
% 0.76/1.14 , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.76/1.14 :=( Y, not( not( X ) ) )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 850, [ =( true, ifeq( theorem( X ), true, theorem( not( not( X ) )
% 0.76/1.14 ), true ) ) ] )
% 0.76/1.14 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.76/1.14 , 0, clause( 845, [ =( true, ifeq( true, true, ifeq( theorem( X ), true,
% 0.76/1.14 theorem( not( not( X ) ) ), true ), true ) ) ] )
% 0.76/1.14 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( theorem( X ), true,
% 0.76/1.14 theorem( not( not( X ) ) ), true ) ), :=( Z, true )] ), substitution( 1
% 0.76/1.14 , [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 851, [ =( ifeq( theorem( X ), true, theorem( not( not( X ) ) ),
% 0.76/1.14 true ), true ) ] )
% 0.76/1.14 , clause( 850, [ =( true, ifeq( theorem( X ), true, theorem( not( not( X )
% 0.76/1.14 ) ), true ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 451, [ =( ifeq( theorem( X ), true, theorem( not( not( X ) ) ),
% 0.76/1.14 true ), true ) ] )
% 0.76/1.14 , clause( 851, [ =( ifeq( theorem( X ), true, theorem( not( not( X ) ) ),
% 0.76/1.14 true ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 853, [ =( true, ifeq( theorem( X ), true, theorem( not( not( X ) )
% 0.76/1.14 ), true ) ) ] )
% 0.76/1.14 , clause( 451, [ =( ifeq( theorem( X ), true, theorem( not( not( X ) ) ),
% 0.76/1.14 true ), true ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 856, [ =( true, ifeq( true, true, theorem( not( not( implies( X,
% 0.76/1.14 not( not( X ) ) ) ) ) ), true ) ) ] )
% 0.76/1.14 , clause( 421, [ =( theorem( implies( X, not( not( X ) ) ) ), true ) ] )
% 0.76/1.14 , 0, clause( 853, [ =( true, ifeq( theorem( X ), true, theorem( not( not( X
% 0.76/1.14 ) ) ), true ) ) ] )
% 0.76/1.14 , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, implies(
% 0.76/1.14 X, not( not( X ) ) ) )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 857, [ =( true, theorem( not( not( implies( X, not( not( X ) ) ) )
% 0.76/1.14 ) ) ) ] )
% 0.76/1.14 , clause( 0, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 0.76/1.14 , 0, clause( 856, [ =( true, ifeq( true, true, theorem( not( not( implies(
% 0.76/1.14 X, not( not( X ) ) ) ) ) ), true ) ) ] )
% 0.76/1.14 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, theorem( not( not( implies(
% 0.76/1.14 X, not( not( X ) ) ) ) ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X
% 0.76/1.14 , X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 paramod(
% 0.76/1.14 clause( 858, [ =( true, theorem( not( and( X, not( X ) ) ) ) ) ] )
% 0.76/1.14 , clause( 9, [ =( not( implies( X, not( Y ) ) ), and( X, Y ) ) ] )
% 0.76/1.14 , 0, clause( 857, [ =( true, theorem( not( not( implies( X, not( not( X ) )
% 0.76/1.14 ) ) ) ) ) ] )
% 0.76/1.14 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, not( X ) )] ), substitution(
% 0.76/1.14 1, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 859, [ =( theorem( not( and( X, not( X ) ) ) ), true ) ] )
% 0.76/1.14 , clause( 858, [ =( true, theorem( not( and( X, not( X ) ) ) ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 579, [ =( theorem( not( and( X, not( X ) ) ) ), true ) ] )
% 0.76/1.14 , clause( 859, [ =( theorem( not( and( X, not( X ) ) ) ), true ) ] )
% 0.76/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 860, [ =( true, theorem( not( and( X, not( X ) ) ) ) ) ] )
% 0.76/1.14 , clause( 579, [ =( theorem( not( and( X, not( X ) ) ) ), true ) ] )
% 0.76/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 eqswap(
% 0.76/1.14 clause( 861, [ ~( =( true, theorem( not( and( p, not( p ) ) ) ) ) ) ] )
% 0.76/1.14 , clause( 10, [ ~( =( theorem( not( and( p, not( p ) ) ) ), true ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 resolution(
% 0.76/1.14 clause( 862, [] )
% 0.76/1.14 , clause( 861, [ ~( =( true, theorem( not( and( p, not( p ) ) ) ) ) ) ] )
% 0.76/1.14 , 0, clause( 860, [ =( true, theorem( not( and( X, not( X ) ) ) ) ) ] )
% 0.76/1.14 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, p )] )).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 subsumption(
% 0.76/1.14 clause( 665, [] )
% 0.76/1.14 , clause( 862, [] )
% 0.76/1.14 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 end.
% 0.76/1.14
% 0.76/1.14 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.76/1.14
% 0.76/1.14 Memory use:
% 0.76/1.14
% 0.76/1.14 space for terms: 8753
% 0.76/1.14 space for clauses: 73722
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 clauses generated: 4920
% 0.76/1.14 clauses kept: 666
% 0.76/1.14 clauses selected: 169
% 0.76/1.14 clauses deleted: 9
% 0.76/1.14 clauses inuse deleted: 0
% 0.76/1.14
% 0.76/1.14 subsentry: 597
% 0.76/1.14 literals s-matched: 247
% 0.76/1.14 literals matched: 247
% 0.76/1.14 full subsumption: 0
% 0.76/1.14
% 0.76/1.14 checksum: 2060776093
% 0.76/1.14
% 0.76/1.14
% 0.76/1.14 Bliksem ended
%------------------------------------------------------------------------------