TSTP Solution File: LCL529+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL529+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n015.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 07:54:26 EDT 2022
% Result : Theorem 4.06s 4.46s
% Output : Refutation 4.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL529+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sat Jul 2 11:17:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.69/1.10 *** allocated 10000 integers for termspace/termends
% 0.69/1.10 *** allocated 10000 integers for clauses
% 0.69/1.10 *** allocated 10000 integers for justifications
% 0.69/1.10 Bliksem 1.12
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 Automatic Strategy Selection
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 Clauses:
% 0.69/1.10
% 0.69/1.10 { ! modus_ponens, ! alpha1( X ), is_a_theorem( X ) }.
% 0.69/1.10 { alpha1( skol1 ), modus_ponens }.
% 0.69/1.10 { ! is_a_theorem( skol1 ), modus_ponens }.
% 0.69/1.10 { ! alpha1( X ), is_a_theorem( skol2( Y ) ) }.
% 0.69/1.10 { ! alpha1( X ), is_a_theorem( implies( skol2( X ), X ) ) }.
% 0.69/1.10 { ! is_a_theorem( Y ), ! is_a_theorem( implies( Y, X ) ), alpha1( X ) }.
% 0.69/1.10 { ! substitution_of_equivalents, ! is_a_theorem( equiv( X, Y ) ), X = Y }.
% 0.69/1.10 { is_a_theorem( equiv( skol3, skol52 ) ), substitution_of_equivalents }.
% 0.69/1.10 { ! skol3 = skol52, substitution_of_equivalents }.
% 0.69/1.10 { ! modus_tollens, is_a_theorem( implies( implies( not( Y ), not( X ) ),
% 0.69/1.10 implies( X, Y ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( implies( not( skol53 ), not( skol4 ) ), implies
% 0.69/1.10 ( skol4, skol53 ) ) ), modus_tollens }.
% 0.69/1.10 { ! implies_1, is_a_theorem( implies( X, implies( Y, X ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( skol5, implies( skol54, skol5 ) ) ), implies_1 }
% 0.69/1.10 .
% 0.69/1.10 { ! implies_2, is_a_theorem( implies( implies( X, implies( X, Y ) ),
% 0.69/1.10 implies( X, Y ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( implies( skol6, implies( skol6, skol55 ) ),
% 0.69/1.10 implies( skol6, skol55 ) ) ), implies_2 }.
% 0.69/1.10 { ! implies_3, is_a_theorem( implies( implies( X, Y ), implies( implies( Y
% 0.69/1.10 , Z ), implies( X, Z ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( implies( skol7, skol56 ), implies( implies(
% 0.69/1.10 skol56, skol86 ), implies( skol7, skol86 ) ) ) ), implies_3 }.
% 0.69/1.10 { ! and_1, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( and( skol8, skol57 ), skol8 ) ), and_1 }.
% 0.69/1.10 { ! and_2, is_a_theorem( implies( and( X, Y ), Y ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( and( skol9, skol58 ), skol58 ) ), and_2 }.
% 0.69/1.10 { ! and_3, is_a_theorem( implies( X, implies( Y, and( X, Y ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( skol10, implies( skol59, and( skol10, skol59 ) )
% 0.69/1.10 ) ), and_3 }.
% 0.69/1.10 { ! or_1, is_a_theorem( implies( X, or( X, Y ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( skol11, or( skol11, skol60 ) ) ), or_1 }.
% 0.69/1.10 { ! or_2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( skol61, or( skol12, skol61 ) ) ), or_2 }.
% 0.69/1.10 { ! or_3, is_a_theorem( implies( implies( X, Z ), implies( implies( Y, Z )
% 0.69/1.10 , implies( or( X, Y ), Z ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( implies( skol13, skol87 ), implies( implies(
% 0.69/1.10 skol62, skol87 ), implies( or( skol13, skol62 ), skol87 ) ) ) ), or_3 }.
% 0.69/1.10 { ! equivalence_1, is_a_theorem( implies( equiv( X, Y ), implies( X, Y ) )
% 0.69/1.10 ) }.
% 0.69/1.10 { ! is_a_theorem( implies( equiv( skol14, skol63 ), implies( skol14, skol63
% 0.69/1.10 ) ) ), equivalence_1 }.
% 0.69/1.10 { ! equivalence_2, is_a_theorem( implies( equiv( X, Y ), implies( Y, X ) )
% 0.69/1.10 ) }.
% 0.69/1.10 { ! is_a_theorem( implies( equiv( skol15, skol64 ), implies( skol64, skol15
% 0.69/1.10 ) ) ), equivalence_2 }.
% 0.69/1.10 { ! equivalence_3, is_a_theorem( implies( implies( X, Y ), implies( implies
% 0.69/1.10 ( Y, X ), equiv( X, Y ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( implies( skol16, skol65 ), implies( implies(
% 0.69/1.10 skol65, skol16 ), equiv( skol16, skol65 ) ) ) ), equivalence_3 }.
% 0.69/1.10 { ! kn1, is_a_theorem( implies( X, and( X, X ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( skol17, and( skol17, skol17 ) ) ), kn1 }.
% 0.69/1.10 { ! kn2, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( and( skol18, skol66 ), skol18 ) ), kn2 }.
% 0.69/1.10 { ! kn3, is_a_theorem( implies( implies( X, Y ), implies( not( and( Y, Z )
% 0.69/1.10 ), not( and( Z, X ) ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( implies( skol19, skol67 ), implies( not( and(
% 0.69/1.10 skol67, skol88 ) ), not( and( skol88, skol19 ) ) ) ) ), kn3 }.
% 0.69/1.10 { ! cn1, is_a_theorem( implies( implies( X, Y ), implies( implies( Y, Z ),
% 0.69/1.10 implies( X, Z ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( implies( skol20, skol68 ), implies( implies(
% 0.69/1.10 skol68, skol89 ), implies( skol20, skol89 ) ) ) ), cn1 }.
% 0.69/1.10 { ! cn2, is_a_theorem( implies( X, implies( not( X ), Y ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( skol21, implies( not( skol21 ), skol69 ) ) ),
% 0.69/1.10 cn2 }.
% 0.69/1.10 { ! cn3, is_a_theorem( implies( implies( not( X ), X ), X ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( implies( not( skol22 ), skol22 ), skol22 ) ),
% 0.69/1.10 cn3 }.
% 0.69/1.10 { ! r1, is_a_theorem( implies( or( X, X ), X ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( or( skol23, skol23 ), skol23 ) ), r1 }.
% 0.69/1.10 { ! r2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( skol70, or( skol24, skol70 ) ) ), r2 }.
% 0.69/1.10 { ! r3, is_a_theorem( implies( or( X, Y ), or( Y, X ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( or( skol25, skol71 ), or( skol71, skol25 ) ) ),
% 0.69/1.10 r3 }.
% 0.69/1.10 { ! r4, is_a_theorem( implies( or( X, or( Y, Z ) ), or( Y, or( X, Z ) ) ) )
% 0.69/1.10 }.
% 0.69/1.10 { ! is_a_theorem( implies( or( skol26, or( skol72, skol90 ) ), or( skol72,
% 0.69/1.10 or( skol26, skol90 ) ) ) ), r4 }.
% 0.69/1.10 { ! r5, is_a_theorem( implies( implies( Y, Z ), implies( or( X, Y ), or( X
% 0.69/1.10 , Z ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( implies( skol73, skol91 ), implies( or( skol27,
% 0.69/1.10 skol73 ), or( skol27, skol91 ) ) ) ), r5 }.
% 0.69/1.10 { ! op_or, or( X, Y ) = not( and( not( X ), not( Y ) ) ) }.
% 0.69/1.10 { ! op_and, and( X, Y ) = not( or( not( X ), not( Y ) ) ) }.
% 0.69/1.10 { ! op_implies_and, implies( X, Y ) = not( and( X, not( Y ) ) ) }.
% 0.69/1.10 { ! op_implies_or, implies( X, Y ) = or( not( X ), Y ) }.
% 0.69/1.10 { ! op_equiv, equiv( X, Y ) = and( implies( X, Y ), implies( Y, X ) ) }.
% 0.69/1.10 { op_or }.
% 0.69/1.10 { op_implies_and }.
% 0.69/1.10 { op_equiv }.
% 0.69/1.10 { modus_ponens }.
% 0.69/1.10 { modus_tollens }.
% 0.69/1.10 { implies_1 }.
% 0.69/1.10 { implies_2 }.
% 0.69/1.10 { implies_3 }.
% 0.69/1.10 { and_1 }.
% 0.69/1.10 { and_2 }.
% 0.69/1.10 { and_3 }.
% 0.69/1.10 { or_1 }.
% 0.69/1.10 { or_2 }.
% 0.69/1.10 { or_3 }.
% 0.69/1.10 { equivalence_1 }.
% 0.69/1.10 { equivalence_2 }.
% 0.69/1.10 { equivalence_3 }.
% 0.69/1.10 { substitution_of_equivalents }.
% 0.69/1.10 { ! necessitation, ! is_a_theorem( X ), is_a_theorem( necessarily( X ) ) }
% 0.69/1.10 .
% 0.69/1.10 { is_a_theorem( skol28 ), necessitation }.
% 0.69/1.10 { ! is_a_theorem( necessarily( skol28 ) ), necessitation }.
% 0.69/1.10 { ! modus_ponens_strict_implies, ! alpha2( X ), is_a_theorem( X ) }.
% 0.69/1.10 { alpha2( skol29 ), modus_ponens_strict_implies }.
% 0.69/1.10 { ! is_a_theorem( skol29 ), modus_ponens_strict_implies }.
% 0.69/1.10 { ! alpha2( X ), is_a_theorem( skol30( Y ) ) }.
% 0.69/1.10 { ! alpha2( X ), is_a_theorem( strict_implies( skol30( X ), X ) ) }.
% 0.69/1.10 { ! is_a_theorem( Y ), ! is_a_theorem( strict_implies( Y, X ) ), alpha2( X
% 0.69/1.10 ) }.
% 0.69/1.10 { ! adjunction, ! alpha3( X, Y ), is_a_theorem( and( X, Y ) ) }.
% 0.69/1.10 { alpha3( skol31, skol74 ), adjunction }.
% 0.69/1.10 { ! is_a_theorem( and( skol31, skol74 ) ), adjunction }.
% 0.69/1.10 { ! alpha3( X, Y ), is_a_theorem( X ) }.
% 0.69/1.10 { ! alpha3( X, Y ), is_a_theorem( Y ) }.
% 0.69/1.10 { ! is_a_theorem( X ), ! is_a_theorem( Y ), alpha3( X, Y ) }.
% 0.69/1.10 { ! substitution_strict_equiv, ! is_a_theorem( strict_equiv( X, Y ) ), X =
% 0.69/1.10 Y }.
% 0.69/1.10 { is_a_theorem( strict_equiv( skol32, skol75 ) ), substitution_strict_equiv
% 0.69/1.10 }.
% 0.69/1.10 { ! skol32 = skol75, substitution_strict_equiv }.
% 0.69/1.10 { ! axiom_K, is_a_theorem( implies( necessarily( implies( X, Y ) ), implies
% 0.69/1.10 ( necessarily( X ), necessarily( Y ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( necessarily( implies( skol33, skol76 ) ),
% 0.69/1.10 implies( necessarily( skol33 ), necessarily( skol76 ) ) ) ), axiom_K }.
% 0.69/1.10 { ! axiom_M, is_a_theorem( implies( necessarily( X ), X ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( necessarily( skol34 ), skol34 ) ), axiom_M }.
% 0.69/1.10 { ! axiom_4, is_a_theorem( implies( necessarily( X ), necessarily(
% 0.69/1.10 necessarily( X ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( necessarily( skol35 ), necessarily( necessarily
% 0.69/1.10 ( skol35 ) ) ) ), axiom_4 }.
% 0.69/1.10 { ! axiom_B, is_a_theorem( implies( X, necessarily( possibly( X ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( skol36, necessarily( possibly( skol36 ) ) ) ),
% 0.69/1.10 axiom_B }.
% 0.69/1.10 { ! axiom_5, is_a_theorem( implies( possibly( X ), necessarily( possibly( X
% 0.69/1.10 ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( possibly( skol37 ), necessarily( possibly(
% 0.69/1.10 skol37 ) ) ) ), axiom_5 }.
% 0.69/1.10 { ! axiom_s1, is_a_theorem( implies( and( necessarily( implies( X, Y ) ),
% 0.69/1.10 necessarily( implies( Y, Z ) ) ), necessarily( implies( X, Z ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( implies( and( necessarily( implies( skol38, skol77 ) ),
% 0.69/1.10 necessarily( implies( skol77, skol92 ) ) ), necessarily( implies( skol38
% 0.69/1.10 , skol92 ) ) ) ), axiom_s1 }.
% 0.69/1.10 { ! axiom_s2, is_a_theorem( strict_implies( possibly( and( X, Y ) ), and(
% 0.69/1.10 possibly( X ), possibly( Y ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( strict_implies( possibly( and( skol39, skol78 ) ), and(
% 0.69/1.10 possibly( skol39 ), possibly( skol78 ) ) ) ), axiom_s2 }.
% 0.69/1.10 { ! axiom_s3, is_a_theorem( strict_implies( strict_implies( X, Y ),
% 0.69/1.10 strict_implies( not( possibly( Y ) ), not( possibly( X ) ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( strict_implies( strict_implies( skol40, skol79 ),
% 0.69/1.10 strict_implies( not( possibly( skol79 ) ), not( possibly( skol40 ) ) ) )
% 0.69/1.10 ), axiom_s3 }.
% 0.69/1.10 { ! axiom_s4, is_a_theorem( strict_implies( necessarily( X ), necessarily(
% 0.69/1.10 necessarily( X ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( strict_implies( necessarily( skol41 ), necessarily(
% 0.69/1.10 necessarily( skol41 ) ) ) ), axiom_s4 }.
% 0.69/1.10 { ! axiom_m1, is_a_theorem( strict_implies( and( X, Y ), and( Y, X ) ) ) }
% 0.69/1.10 .
% 0.69/1.10 { ! is_a_theorem( strict_implies( and( skol42, skol80 ), and( skol80,
% 0.69/1.10 skol42 ) ) ), axiom_m1 }.
% 0.69/1.10 { ! axiom_m2, is_a_theorem( strict_implies( and( X, Y ), X ) ) }.
% 0.69/1.10 { ! is_a_theorem( strict_implies( and( skol43, skol81 ), skol43 ) ),
% 0.69/1.10 axiom_m2 }.
% 0.69/1.10 { ! axiom_m3, is_a_theorem( strict_implies( and( and( X, Y ), Z ), and( X,
% 0.69/1.10 and( Y, Z ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( strict_implies( and( and( skol44, skol82 ), skol93 ), and
% 0.69/1.10 ( skol44, and( skol82, skol93 ) ) ) ), axiom_m3 }.
% 0.69/1.10 { ! axiom_m4, is_a_theorem( strict_implies( X, and( X, X ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( strict_implies( skol45, and( skol45, skol45 ) ) ),
% 0.69/1.10 axiom_m4 }.
% 0.69/1.10 { ! axiom_m5, is_a_theorem( strict_implies( and( strict_implies( X, Y ),
% 0.69/1.10 strict_implies( Y, Z ) ), strict_implies( X, Z ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( strict_implies( and( strict_implies( skol46, skol83 ),
% 0.69/1.10 strict_implies( skol83, skol94 ) ), strict_implies( skol46, skol94 ) ) )
% 0.69/1.10 , axiom_m5 }.
% 0.69/1.10 { ! axiom_m6, is_a_theorem( strict_implies( X, possibly( X ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( strict_implies( skol47, possibly( skol47 ) ) ), axiom_m6
% 0.69/1.10 }.
% 0.69/1.10 { ! axiom_m7, is_a_theorem( strict_implies( possibly( and( X, Y ) ), X ) )
% 0.69/1.10 }.
% 0.69/1.10 { ! is_a_theorem( strict_implies( possibly( and( skol48, skol84 ) ), skol48
% 0.69/1.10 ) ), axiom_m7 }.
% 0.69/1.10 { ! axiom_m8, is_a_theorem( strict_implies( strict_implies( X, Y ),
% 0.69/1.10 strict_implies( possibly( X ), possibly( Y ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( strict_implies( strict_implies( skol49, skol85 ),
% 0.69/1.10 strict_implies( possibly( skol49 ), possibly( skol85 ) ) ) ), axiom_m8 }
% 0.69/1.10 .
% 0.69/1.10 { ! axiom_m9, is_a_theorem( strict_implies( possibly( possibly( X ) ),
% 0.69/1.10 possibly( X ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( strict_implies( possibly( possibly( skol50 ) ), possibly
% 0.69/1.10 ( skol50 ) ) ), axiom_m9 }.
% 0.69/1.10 { ! axiom_m10, is_a_theorem( strict_implies( possibly( X ), necessarily(
% 0.69/1.10 possibly( X ) ) ) ) }.
% 0.69/1.10 { ! is_a_theorem( strict_implies( possibly( skol51 ), necessarily( possibly
% 0.69/1.10 ( skol51 ) ) ) ), axiom_m10 }.
% 0.69/1.10 { ! op_possibly, possibly( X ) = not( necessarily( not( X ) ) ) }.
% 0.69/1.10 { ! op_necessarily, necessarily( X ) = not( possibly( not( X ) ) ) }.
% 0.69/1.10 { ! op_strict_implies, strict_implies( X, Y ) = necessarily( implies( X, Y
% 0.69/1.10 ) ) }.
% 0.69/1.10 { ! op_strict_equiv, strict_equiv( X, Y ) = and( strict_implies( X, Y ),
% 0.69/1.10 strict_implies( Y, X ) ) }.
% 0.69/1.10 { op_possibly }.
% 0.69/1.10 { necessitation }.
% 0.69/1.10 { axiom_K }.
% 0.69/1.10 { axiom_M }.
% 0.69/1.10 { axiom_5 }.
% 0.69/1.10 { op_possibly }.
% 0.69/1.10 { op_or }.
% 0.69/1.10 { op_implies }.
% 0.69/1.10 { op_strict_implies }.
% 0.69/1.10 { op_equiv }.
% 0.69/1.10 { op_strict_equiv }.
% 0.69/1.10 { ! axiom_m2 }.
% 0.69/1.10
% 0.69/1.10 percentage equality = 0.046429, percentage horn = 0.959732
% 0.69/1.10 This is a problem with some equality
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 Options Used:
% 0.69/1.10
% 0.69/1.10 useres = 1
% 0.69/1.10 useparamod = 1
% 0.69/1.10 useeqrefl = 1
% 0.69/1.10 useeqfact = 1
% 0.69/1.10 usefactor = 1
% 0.69/1.10 usesimpsplitting = 0
% 0.69/1.10 usesimpdemod = 5
% 0.69/1.10 usesimpres = 3
% 0.69/1.10
% 0.69/1.10 resimpinuse = 1000
% 0.69/1.10 resimpclauses = 20000
% 0.69/1.10 substype = eqrewr
% 0.69/1.10 backwardsubs = 1
% 0.69/1.10 selectoldest = 5
% 0.69/1.10
% 0.69/1.10 litorderings [0] = split
% 0.69/1.10 litorderings [1] = extend the termordering, first sorting on arguments
% 0.69/1.10
% 0.69/1.10 termordering = kbo
% 0.69/1.10
% 0.69/1.10 litapriori = 0
% 0.69/1.10 termapriori = 1
% 0.69/1.10 litaposteriori = 0
% 0.69/1.10 termaposteriori = 0
% 0.69/1.10 demodaposteriori = 0
% 0.69/1.10 ordereqreflfact = 0
% 0.69/1.10
% 0.69/1.10 litselect = negord
% 0.69/1.10
% 0.69/1.10 maxweight = 15
% 0.69/1.10 maxdepth = 30000
% 0.69/1.10 maxlength = 115
% 0.69/1.10 maxnrvars = 195
% 0.69/1.10 excuselevel = 1
% 0.69/1.10 increasemaxweight = 1
% 0.69/1.10
% 0.69/1.10 maxselected = 10000000
% 0.69/1.10 maxnrclauses = 10000000
% 0.69/1.10
% 0.69/1.10 showgenerated = 0
% 0.69/1.10 showkept = 0
% 0.69/1.10 showselected = 0
% 0.69/1.10 showdeleted = 0
% 0.69/1.10 showresimp = 1
% 0.69/1.10 showstatus = 2000
% 0.69/1.10
% 0.69/1.10 prologoutput = 0
% 0.69/1.10 nrgoals = 5000000
% 0.69/1.10 totalproof = 1
% 0.69/1.10
% 0.69/1.10 Symbols occurring in the translation:
% 0.69/1.10
% 0.69/1.10 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.69/1.10 . [1, 2] (w:1, o:176, a:1, s:1, b:0),
% 0.69/1.10 ! [4, 1] (w:0, o:163, a:1, s:1, b:0),
% 0.69/1.10 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.10 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.10 modus_ponens [35, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.69/1.10 is_a_theorem [38, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.69/1.10 implies [39, 2] (w:1, o:200, a:1, s:1, b:0),
% 0.69/1.10 substitution_of_equivalents [40, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.69/1.10 equiv [41, 2] (w:1, o:201, a:1, s:1, b:0),
% 0.69/1.10 modus_tollens [42, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.69/1.10 not [43, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.69/1.10 implies_1 [44, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.69/1.10 implies_2 [45, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.69/1.10 implies_3 [46, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.69/1.10 and_1 [48, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.69/1.10 and [49, 2] (w:1, o:202, a:1, s:1, b:0),
% 0.69/1.10 and_2 [50, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.69/1.10 and_3 [51, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.69/1.10 or_1 [52, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.69/1.10 or [53, 2] (w:1, o:203, a:1, s:1, b:0),
% 0.69/1.10 or_2 [54, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.69/1.10 or_3 [55, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.69/1.10 equivalence_1 [56, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.69/1.10 equivalence_2 [57, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.69/1.10 equivalence_3 [58, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.69/1.10 kn1 [59, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.69/1.10 kn2 [61, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.69/1.10 kn3 [63, 0] (w:1, o:35, a:1, s:1, b:0),
% 0.69/1.10 cn1 [65, 0] (w:1, o:37, a:1, s:1, b:0),
% 0.69/1.10 cn2 [66, 0] (w:1, o:38, a:1, s:1, b:0),
% 0.69/1.10 cn3 [67, 0] (w:1, o:39, a:1, s:1, b:0),
% 0.69/1.10 r1 [68, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.69/1.10 r2 [69, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.69/1.10 r3 [70, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.69/1.10 r4 [71, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.69/1.10 r5 [72, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.69/1.10 op_or [73, 0] (w:1, o:41, a:1, s:1, b:0),
% 0.69/1.10 op_and [74, 0] (w:1, o:42, a:1, s:1, b:0),
% 0.69/1.10 op_implies_and [75, 0] (w:1, o:43, a:1, s:1, b:0),
% 0.69/1.10 op_implies_or [76, 0] (w:1, o:44, a:1, s:1, b:0),
% 0.69/1.10 op_equiv [77, 0] (w:1, o:45, a:1, s:1, b:0),
% 0.69/1.10 necessitation [78, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.69/1.10 necessarily [79, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.69/1.10 modus_ponens_strict_implies [80, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.69/1.10 strict_implies [81, 2] (w:1, o:204, a:1, s:1, b:0),
% 0.69/1.10 adjunction [82, 0] (w:1, o:46, a:1, s:1, b:0),
% 0.69/1.10 substitution_strict_equiv [83, 0] (w:1, o:47, a:1, s:1, b:0),
% 0.69/1.10 strict_equiv [84, 2] (w:1, o:205, a:1, s:1, b:0),
% 0.69/1.10 axiom_K [85, 0] (w:1, o:48, a:1, s:1, b:0),
% 0.69/1.10 axiom_M [86, 0] (w:1, o:49, a:1, s:1, b:0),
% 0.69/1.10 axiom_4 [87, 0] (w:1, o:50, a:1, s:1, b:0),
% 0.69/1.10 axiom_B [88, 0] (w:1, o:51, a:1, s:1, b:0),
% 0.69/1.10 possibly [89, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.69/1.10 axiom_5 [90, 0] (w:1, o:52, a:1, s:1, b:0),
% 0.69/1.10 axiom_s1 [91, 0] (w:1, o:53, a:1, s:1, b:0),
% 0.69/1.10 axiom_s2 [92, 0] (w:1, o:54, a:1, s:1, b:0),
% 0.69/1.10 axiom_s3 [93, 0] (w:1, o:55, a:1, s:1, b:0),
% 0.69/1.10 axiom_s4 [94, 0] (w:1, o:56, a:1, s:1, b:0),
% 0.69/1.10 axiom_m1 [95, 0] (w:1, o:57, a:1, s:1, b:0),
% 0.69/1.10 axiom_m2 [96, 0] (w:1, o:59, a:1, s:1, b:0),
% 0.69/1.10 axiom_m3 [97, 0] (w:1, o:60, a:1, s:1, b:0),
% 0.69/1.10 axiom_m4 [98, 0] (w:1, o:61, a:1, s:1, b:0),
% 0.69/1.10 axiom_m5 [99, 0] (w:1, o:62, a:1, s:1, b:0),
% 0.69/1.10 axiom_m6 [100, 0] (w:1, o:63, a:1, s:1, b:0),
% 0.69/1.10 axiom_m7 [101, 0] (w:1, o:64, a:1, s:1, b:0),
% 0.69/1.10 axiom_m8 [102, 0] (w:1, o:65, a:1, s:1, b:0),
% 0.69/1.10 axiom_m9 [103, 0] (w:1, o:66, a:1, s:1, b:0),
% 0.69/1.10 axiom_m10 [104, 0] (w:1, o:58, a:1, s:1, b:0),
% 0.69/1.10 op_possibly [105, 0] (w:1, o:67, a:1, s:1, b:0),
% 0.69/1.10 op_necessarily [106, 0] (w:1, o:40, a:1, s:1, b:0),
% 0.69/1.10 op_strict_implies [107, 0] (w:1, o:68, a:1, s:1, b:0),
% 0.69/1.10 op_strict_equiv [108, 0] (w:1, o:69, a:1, s:1, b:0),
% 0.69/1.10 op_implies [109, 0] (w:1, o:70, a:1, s:1, b:0),
% 0.69/1.10 alpha1 [110, 1] (w:1, o:172, a:1, s:1, b:1),
% 0.69/1.10 alpha2 [111, 1] (w:1, o:173, a:1, s:1, b:1),
% 0.69/1.10 alpha3 [112, 2] (w:1, o:206, a:1, s:1, b:1),
% 0.69/1.10 skol1 [113, 0] (w:1, o:71, a:1, s:1, b:1),
% 0.69/1.10 skol2 [114, 1] (w:1, o:174, a:1, s:1, b:1),
% 2.45/2.86 skol3 [115, 0] (w:1, o:82, a:1, s:1, b:1),
% 2.45/2.86 skol4 [116, 0] (w:1, o:92, a:1, s:1, b:1),
% 2.45/2.86 skol5 [117, 0] (w:1, o:103, a:1, s:1, b:1),
% 2.45/2.86 skol6 [118, 0] (w:1, o:114, a:1, s:1, b:1),
% 2.45/2.86 skol7 [119, 0] (w:1, o:125, a:1, s:1, b:1),
% 2.45/2.86 skol8 [120, 0] (w:1, o:136, a:1, s:1, b:1),
% 2.45/2.86 skol9 [121, 0] (w:1, o:147, a:1, s:1, b:1),
% 2.45/2.86 skol10 [122, 0] (w:1, o:148, a:1, s:1, b:1),
% 2.45/2.86 skol11 [123, 0] (w:1, o:149, a:1, s:1, b:1),
% 2.45/2.86 skol12 [124, 0] (w:1, o:150, a:1, s:1, b:1),
% 2.45/2.86 skol13 [125, 0] (w:1, o:151, a:1, s:1, b:1),
% 2.45/2.86 skol14 [126, 0] (w:1, o:152, a:1, s:1, b:1),
% 2.45/2.86 skol15 [127, 0] (w:1, o:153, a:1, s:1, b:1),
% 2.45/2.86 skol16 [128, 0] (w:1, o:154, a:1, s:1, b:1),
% 2.45/2.86 skol17 [129, 0] (w:1, o:155, a:1, s:1, b:1),
% 2.45/2.86 skol18 [130, 0] (w:1, o:156, a:1, s:1, b:1),
% 2.45/2.86 skol19 [131, 0] (w:1, o:157, a:1, s:1, b:1),
% 2.45/2.86 skol20 [132, 0] (w:1, o:72, a:1, s:1, b:1),
% 2.45/2.86 skol21 [133, 0] (w:1, o:73, a:1, s:1, b:1),
% 2.45/2.86 skol22 [134, 0] (w:1, o:74, a:1, s:1, b:1),
% 2.45/2.86 skol23 [135, 0] (w:1, o:75, a:1, s:1, b:1),
% 2.45/2.86 skol24 [136, 0] (w:1, o:76, a:1, s:1, b:1),
% 2.45/2.86 skol25 [137, 0] (w:1, o:77, a:1, s:1, b:1),
% 2.45/2.86 skol26 [138, 0] (w:1, o:78, a:1, s:1, b:1),
% 2.45/2.86 skol27 [139, 0] (w:1, o:79, a:1, s:1, b:1),
% 2.45/2.86 skol28 [140, 0] (w:1, o:80, a:1, s:1, b:1),
% 2.45/2.86 skol29 [141, 0] (w:1, o:81, a:1, s:1, b:1),
% 2.45/2.86 skol30 [142, 1] (w:1, o:175, a:1, s:1, b:1),
% 2.45/2.86 skol31 [143, 0] (w:1, o:83, a:1, s:1, b:1),
% 2.45/2.86 skol32 [144, 0] (w:1, o:84, a:1, s:1, b:1),
% 2.45/2.86 skol33 [145, 0] (w:1, o:85, a:1, s:1, b:1),
% 2.45/2.86 skol34 [146, 0] (w:1, o:86, a:1, s:1, b:1),
% 2.45/2.86 skol35 [147, 0] (w:1, o:87, a:1, s:1, b:1),
% 2.45/2.86 skol36 [148, 0] (w:1, o:88, a:1, s:1, b:1),
% 2.45/2.86 skol37 [149, 0] (w:1, o:89, a:1, s:1, b:1),
% 2.45/2.86 skol38 [150, 0] (w:1, o:90, a:1, s:1, b:1),
% 2.45/2.86 skol39 [151, 0] (w:1, o:91, a:1, s:1, b:1),
% 2.45/2.86 skol40 [152, 0] (w:1, o:93, a:1, s:1, b:1),
% 2.45/2.86 skol41 [153, 0] (w:1, o:94, a:1, s:1, b:1),
% 2.45/2.86 skol42 [154, 0] (w:1, o:95, a:1, s:1, b:1),
% 2.45/2.86 skol43 [155, 0] (w:1, o:96, a:1, s:1, b:1),
% 2.45/2.86 skol44 [156, 0] (w:1, o:97, a:1, s:1, b:1),
% 2.45/2.86 skol45 [157, 0] (w:1, o:98, a:1, s:1, b:1),
% 2.45/2.86 skol46 [158, 0] (w:1, o:99, a:1, s:1, b:1),
% 2.45/2.86 skol47 [159, 0] (w:1, o:100, a:1, s:1, b:1),
% 2.45/2.86 skol48 [160, 0] (w:1, o:101, a:1, s:1, b:1),
% 2.45/2.86 skol49 [161, 0] (w:1, o:102, a:1, s:1, b:1),
% 2.45/2.86 skol50 [162, 0] (w:1, o:104, a:1, s:1, b:1),
% 2.45/2.86 skol51 [163, 0] (w:1, o:105, a:1, s:1, b:1),
% 2.45/2.86 skol52 [164, 0] (w:1, o:106, a:1, s:1, b:1),
% 2.45/2.86 skol53 [165, 0] (w:1, o:107, a:1, s:1, b:1),
% 2.45/2.86 skol54 [166, 0] (w:1, o:108, a:1, s:1, b:1),
% 2.45/2.86 skol55 [167, 0] (w:1, o:109, a:1, s:1, b:1),
% 2.45/2.86 skol56 [168, 0] (w:1, o:110, a:1, s:1, b:1),
% 2.45/2.86 skol57 [169, 0] (w:1, o:111, a:1, s:1, b:1),
% 2.45/2.86 skol58 [170, 0] (w:1, o:112, a:1, s:1, b:1),
% 2.45/2.86 skol59 [171, 0] (w:1, o:113, a:1, s:1, b:1),
% 2.45/2.86 skol60 [172, 0] (w:1, o:115, a:1, s:1, b:1),
% 2.45/2.86 skol61 [173, 0] (w:1, o:116, a:1, s:1, b:1),
% 2.45/2.86 skol62 [174, 0] (w:1, o:117, a:1, s:1, b:1),
% 2.45/2.86 skol63 [175, 0] (w:1, o:118, a:1, s:1, b:1),
% 2.45/2.86 skol64 [176, 0] (w:1, o:119, a:1, s:1, b:1),
% 2.45/2.86 skol65 [177, 0] (w:1, o:120, a:1, s:1, b:1),
% 2.45/2.86 skol66 [178, 0] (w:1, o:121, a:1, s:1, b:1),
% 2.45/2.86 skol67 [179, 0] (w:1, o:122, a:1, s:1, b:1),
% 2.45/2.86 skol68 [180, 0] (w:1, o:123, a:1, s:1, b:1),
% 2.45/2.86 skol69 [181, 0] (w:1, o:124, a:1, s:1, b:1),
% 2.45/2.86 skol70 [182, 0] (w:1, o:126, a:1, s:1, b:1),
% 2.45/2.86 skol71 [183, 0] (w:1, o:127, a:1, s:1, b:1),
% 2.45/2.86 skol72 [184, 0] (w:1, o:128, a:1, s:1, b:1),
% 2.45/2.86 skol73 [185, 0] (w:1, o:129, a:1, s:1, b:1),
% 2.45/2.86 skol74 [186, 0] (w:1, o:130, a:1, s:1, b:1),
% 2.45/2.86 skol75 [187, 0] (w:1, o:131, a:1, s:1, b:1),
% 2.45/2.86 skol76 [188, 0] (w:1, o:132, a:1, s:1, b:1),
% 2.45/2.86 skol77 [189, 0] (w:1, o:133, a:1, s:1, b:1),
% 2.45/2.86 skol78 [190, 0] (w:1, o:134, a:1, s:1, b:1),
% 2.45/2.86 skol79 [191, 0] (w:1, o:135, a:1, s:1, b:1),
% 2.45/2.86 skol80 [192, 0] (w:1, o:137, a:1, s:1, b:1),
% 2.45/2.86 skol81 [193, 0] (w:1, o:138, a:1, s:1, b:1),
% 4.06/4.45 skol82 [194, 0] (w:1, o:139, a:1, s:1, b:1),
% 4.06/4.45 skol83 [195, 0] (w:1, o:140, a:1, s:1, b:1),
% 4.06/4.45 skol84 [196, 0] (w:1, o:141, a:1, s:1, b:1),
% 4.06/4.45 skol85 [197, 0] (w:1, o:142, a:1, s:1, b:1),
% 4.06/4.45 skol86 [198, 0] (w:1, o:143, a:1, s:1, b:1),
% 4.06/4.45 skol87 [199, 0] (w:1, o:144, a:1, s:1, b:1),
% 4.06/4.45 skol88 [200, 0] (w:1, o:145, a:1, s:1, b:1),
% 4.06/4.45 skol89 [201, 0] (w:1, o:146, a:1, s:1, b:1),
% 4.06/4.45 skol90 [202, 0] (w:1, o:158, a:1, s:1, b:1),
% 4.06/4.45 skol91 [203, 0] (w:1, o:159, a:1, s:1, b:1),
% 4.06/4.45 skol92 [204, 0] (w:1, o:160, a:1, s:1, b:1),
% 4.06/4.45 skol93 [205, 0] (w:1, o:161, a:1, s:1, b:1),
% 4.06/4.45 skol94 [206, 0] (w:1, o:162, a:1, s:1, b:1).
% 4.06/4.45
% 4.06/4.45
% 4.06/4.45 Starting Search:
% 4.06/4.45
% 4.06/4.45 *** allocated 15000 integers for clauses
% 4.06/4.45 *** allocated 22500 integers for clauses
% 4.06/4.45 *** allocated 33750 integers for clauses
% 4.06/4.45 *** allocated 50625 integers for clauses
% 4.06/4.45 *** allocated 15000 integers for termspace/termends
% 4.06/4.45 *** allocated 75937 integers for clauses
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45 *** allocated 22500 integers for termspace/termends
% 4.06/4.45 *** allocated 113905 integers for clauses
% 4.06/4.45
% 4.06/4.45 Intermediate Status:
% 4.06/4.45 Generated: 4146
% 4.06/4.45 Kept: 2016
% 4.06/4.45 Inuse: 279
% 4.06/4.45 Deleted: 53
% 4.06/4.45 Deletedinuse: 6
% 4.06/4.45
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45 *** allocated 33750 integers for termspace/termends
% 4.06/4.45 *** allocated 170857 integers for clauses
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45 *** allocated 50625 integers for termspace/termends
% 4.06/4.45 *** allocated 256285 integers for clauses
% 4.06/4.45
% 4.06/4.45 Intermediate Status:
% 4.06/4.45 Generated: 7858
% 4.06/4.45 Kept: 4049
% 4.06/4.45 Inuse: 390
% 4.06/4.45 Deleted: 62
% 4.06/4.45 Deletedinuse: 7
% 4.06/4.45
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45 *** allocated 75937 integers for termspace/termends
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45 *** allocated 384427 integers for clauses
% 4.06/4.45
% 4.06/4.45 Intermediate Status:
% 4.06/4.45 Generated: 13034
% 4.06/4.45 Kept: 6424
% 4.06/4.45 Inuse: 500
% 4.06/4.45 Deleted: 73
% 4.06/4.45 Deletedinuse: 7
% 4.06/4.45
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45 *** allocated 113905 integers for termspace/termends
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45 *** allocated 576640 integers for clauses
% 4.06/4.45
% 4.06/4.45 Intermediate Status:
% 4.06/4.45 Generated: 17022
% 4.06/4.45 Kept: 8431
% 4.06/4.45 Inuse: 557
% 4.06/4.45 Deleted: 81
% 4.06/4.45 Deletedinuse: 13
% 4.06/4.45
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45 *** allocated 170857 integers for termspace/termends
% 4.06/4.45
% 4.06/4.45 Intermediate Status:
% 4.06/4.45 Generated: 20579
% 4.06/4.45 Kept: 10439
% 4.06/4.45 Inuse: 605
% 4.06/4.45 Deleted: 89
% 4.06/4.45 Deletedinuse: 13
% 4.06/4.45
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45
% 4.06/4.45 Intermediate Status:
% 4.06/4.45 Generated: 24299
% 4.06/4.45 Kept: 12449
% 4.06/4.45 Inuse: 654
% 4.06/4.45 Deleted: 89
% 4.06/4.45 Deletedinuse: 13
% 4.06/4.45
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45 *** allocated 864960 integers for clauses
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45
% 4.06/4.45 Intermediate Status:
% 4.06/4.45 Generated: 27507
% 4.06/4.45 Kept: 14496
% 4.06/4.45 Inuse: 687
% 4.06/4.45 Deleted: 89
% 4.06/4.45 Deletedinuse: 13
% 4.06/4.45
% 4.06/4.45 *** allocated 256285 integers for termspace/termends
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45
% 4.06/4.45 Intermediate Status:
% 4.06/4.45 Generated: 31973
% 4.06/4.45 Kept: 16609
% 4.06/4.45 Inuse: 744
% 4.06/4.45 Deleted: 90
% 4.06/4.45 Deletedinuse: 13
% 4.06/4.45
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.45 Done
% 4.06/4.45
% 4.06/4.45
% 4.06/4.45 Intermediate Status:
% 4.06/4.45 Generated: 35989
% 4.06/4.45 Kept: 18654
% 4.06/4.45 Inuse: 784
% 4.06/4.45 Deleted: 95
% 4.06/4.45 Deletedinuse: 13
% 4.06/4.45
% 4.06/4.45 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46 Resimplifying clauses:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46 *** allocated 1297440 integers for clauses
% 4.06/4.46
% 4.06/4.46 Intermediate Status:
% 4.06/4.46 Generated: 41032
% 4.06/4.46 Kept: 20660
% 4.06/4.46 Inuse: 841
% 4.06/4.46 Deleted: 1063
% 4.06/4.46 Deletedinuse: 59
% 4.06/4.46
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46 *** allocated 384427 integers for termspace/termends
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46
% 4.06/4.46 Intermediate Status:
% 4.06/4.46 Generated: 44673
% 4.06/4.46 Kept: 22720
% 4.06/4.46 Inuse: 891
% 4.06/4.46 Deleted: 1066
% 4.06/4.46 Deletedinuse: 60
% 4.06/4.46
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46
% 4.06/4.46 Intermediate Status:
% 4.06/4.46 Generated: 48051
% 4.06/4.46 Kept: 24881
% 4.06/4.46 Inuse: 917
% 4.06/4.46 Deleted: 1066
% 4.06/4.46 Deletedinuse: 60
% 4.06/4.46
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46
% 4.06/4.46 Intermediate Status:
% 4.06/4.46 Generated: 52402
% 4.06/4.46 Kept: 26930
% 4.06/4.46 Inuse: 970
% 4.06/4.46 Deleted: 1066
% 4.06/4.46 Deletedinuse: 60
% 4.06/4.46
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46
% 4.06/4.46 Intermediate Status:
% 4.06/4.46 Generated: 58076
% 4.06/4.46 Kept: 28930
% 4.06/4.46 Inuse: 1040
% 4.06/4.46 Deleted: 1066
% 4.06/4.46 Deletedinuse: 60
% 4.06/4.46
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46
% 4.06/4.46 Intermediate Status:
% 4.06/4.46 Generated: 62203
% 4.06/4.46 Kept: 30995
% 4.06/4.46 Inuse: 1069
% 4.06/4.46 Deleted: 1072
% 4.06/4.46 Deletedinuse: 60
% 4.06/4.46
% 4.06/4.46 *** allocated 1946160 integers for clauses
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46 *** allocated 576640 integers for termspace/termends
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46
% 4.06/4.46 Intermediate Status:
% 4.06/4.46 Generated: 66993
% 4.06/4.46 Kept: 33177
% 4.06/4.46 Inuse: 1101
% 4.06/4.46 Deleted: 1072
% 4.06/4.46 Deletedinuse: 60
% 4.06/4.46
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46
% 4.06/4.46 Intermediate Status:
% 4.06/4.46 Generated: 70351
% 4.06/4.46 Kept: 35367
% 4.06/4.46 Inuse: 1129
% 4.06/4.46 Deleted: 1072
% 4.06/4.46 Deletedinuse: 60
% 4.06/4.46
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46
% 4.06/4.46 Intermediate Status:
% 4.06/4.46 Generated: 76182
% 4.06/4.46 Kept: 37391
% 4.06/4.46 Inuse: 1158
% 4.06/4.46 Deleted: 1073
% 4.06/4.46 Deletedinuse: 61
% 4.06/4.46
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46
% 4.06/4.46 Intermediate Status:
% 4.06/4.46 Generated: 80583
% 4.06/4.46 Kept: 39395
% 4.06/4.46 Inuse: 1190
% 4.06/4.46 Deleted: 1073
% 4.06/4.46 Deletedinuse: 61
% 4.06/4.46
% 4.06/4.46 Resimplifying inuse:
% 4.06/4.46 Done
% 4.06/4.46
% 4.06/4.46 Resimplifying clauses:
% 4.06/4.46
% 4.06/4.46 Bliksems!, er is een bewijs:
% 4.06/4.46 % SZS status Theorem
% 4.06/4.46 % SZS output start Refutation
% 4.06/4.46
% 4.06/4.46 (17) {G0,W7,D4,L2,V2,M2} I { ! and_1, is_a_theorem( implies( and( X, Y ), X
% 4.06/4.46 ) ) }.
% 4.06/4.46 (70) {G0,W1,D1,L1,V0,M1} I { and_1 }.
% 4.06/4.46 (80) {G0,W6,D3,L3,V1,M3} I { ! necessitation, ! is_a_theorem( X ),
% 4.06/4.46 is_a_theorem( necessarily( X ) ) }.
% 4.06/4.46 (119) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( strict_implies( and( skol43,
% 4.06/4.46 skol81 ), skol43 ) ), axiom_m2 }.
% 4.06/4.46 (138) {G0,W9,D4,L2,V2,M2} I { ! op_strict_implies, necessarily( implies( X
% 4.06/4.46 , Y ) ) ==> strict_implies( X, Y ) }.
% 4.06/4.46 (141) {G0,W1,D1,L1,V0,M1} I { necessitation }.
% 4.06/4.46 (146) {G0,W1,D1,L1,V0,M1} I { op_strict_implies }.
% 4.06/4.46 (148) {G0,W1,D1,L1,V0,M1} I { ! axiom_m2 }.
% 4.06/4.46 (219) {G1,W5,D3,L2,V1,M2} S(80);r(141) { ! is_a_theorem( X ), is_a_theorem
% 4.06/4.46 ( necessarily( X ) ) }.
% 4.06/4.46 (256) {G1,W6,D4,L1,V2,M1} S(17);r(70) { is_a_theorem( implies( and( X, Y )
% 4.06/4.46 , X ) ) }.
% 4.06/4.46 (270) {G2,W7,D5,L1,V2,M1} R(256,219) { is_a_theorem( necessarily( implies(
% 4.06/4.46 and( X, Y ), X ) ) ) }.
% 4.06/4.46 (3944) {G1,W6,D4,L1,V0,M1} S(119);r(148) { ! is_a_theorem( strict_implies(
% 4.06/4.46 and( skol43, skol81 ), skol43 ) ) }.
% 4.06/4.46 (5486) {G1,W8,D4,L1,V2,M1} S(138);r(146) { necessarily( implies( X, Y ) )
% 4.06/4.46 ==> strict_implies( X, Y ) }.
% 4.06/4.46 (20170) {G3,W6,D4,L1,V2,M1} S(270);d(5486) { is_a_theorem( strict_implies(
% 4.06/4.46 and( X, Y ), X ) ) }.
% 4.06/4.46 (40419) {G4,W0,D0,L0,V0,M0} S(3944);r(20170) { }.
% 4.06/4.46
% 4.06/4.46
% 4.06/4.46 % SZS output end Refutation
% 4.06/4.46 found a proof!
% 4.06/4.46
% 4.06/4.46
% 4.06/4.46 Unprocessed initial clauses:
% 4.06/4.46
% 4.06/4.46 (40421) {G0,W5,D2,L3,V1,M3} { ! modus_ponens, ! alpha1( X ), is_a_theorem
% 4.06/4.46 ( X ) }.
% 4.06/4.46 (40422) {G0,W3,D2,L2,V0,M2} { alpha1( skol1 ), modus_ponens }.
% 4.06/4.46 (40423) {G0,W3,D2,L2,V0,M2} { ! is_a_theorem( skol1 ), modus_ponens }.
% 4.06/4.46 (40424) {G0,W5,D3,L2,V2,M2} { ! alpha1( X ), is_a_theorem( skol2( Y ) )
% 4.06/4.46 }.
% 4.06/4.46 (40425) {G0,W7,D4,L2,V1,M2} { ! alpha1( X ), is_a_theorem( implies( skol2
% 4.06/4.46 ( X ), X ) ) }.
% 4.06/4.46 (40426) {G0,W8,D3,L3,V2,M3} { ! is_a_theorem( Y ), ! is_a_theorem( implies
% 4.06/4.46 ( Y, X ) ), alpha1( X ) }.
% 4.06/4.46 (40427) {G0,W8,D3,L3,V2,M3} { ! substitution_of_equivalents, !
% 4.06/4.46 is_a_theorem( equiv( X, Y ) ), X = Y }.
% 4.06/4.46 (40428) {G0,W5,D3,L2,V0,M2} { is_a_theorem( equiv( skol3, skol52 ) ),
% 4.06/4.46 substitution_of_equivalents }.
% 4.06/4.46 (40429) {G0,W4,D2,L2,V0,M2} { ! skol3 = skol52,
% 4.06/4.46 substitution_of_equivalents }.
% 4.06/4.46 (40430) {G0,W11,D5,L2,V2,M2} { ! modus_tollens, is_a_theorem( implies(
% 4.06/4.46 implies( not( Y ), not( X ) ), implies( X, Y ) ) ) }.
% 4.06/4.46 (40431) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( not(
% 4.06/4.46 skol53 ), not( skol4 ) ), implies( skol4, skol53 ) ) ), modus_tollens }.
% 4.06/4.46 (40432) {G0,W7,D4,L2,V2,M2} { ! implies_1, is_a_theorem( implies( X,
% 4.06/4.46 implies( Y, X ) ) ) }.
% 4.06/4.46 (40433) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol5, implies(
% 4.06/4.46 skol54, skol5 ) ) ), implies_1 }.
% 4.06/4.46 (40434) {G0,W11,D5,L2,V2,M2} { ! implies_2, is_a_theorem( implies( implies
% 4.06/4.46 ( X, implies( X, Y ) ), implies( X, Y ) ) ) }.
% 4.06/4.46 (40435) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol6,
% 4.06/4.46 implies( skol6, skol55 ) ), implies( skol6, skol55 ) ) ), implies_2 }.
% 4.06/4.46 (40436) {G0,W13,D5,L2,V3,M2} { ! implies_3, is_a_theorem( implies( implies
% 4.06/4.46 ( X, Y ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 4.06/4.46 (40437) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol7,
% 4.06/4.46 skol56 ), implies( implies( skol56, skol86 ), implies( skol7, skol86 ) )
% 4.06/4.46 ) ), implies_3 }.
% 4.06/4.46 (40438) {G0,W7,D4,L2,V2,M2} { ! and_1, is_a_theorem( implies( and( X, Y )
% 4.06/4.46 , X ) ) }.
% 4.06/4.46 (40439) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol8, skol57
% 4.06/4.46 ), skol8 ) ), and_1 }.
% 4.06/4.46 (40440) {G0,W7,D4,L2,V2,M2} { ! and_2, is_a_theorem( implies( and( X, Y )
% 4.06/4.46 , Y ) ) }.
% 4.06/4.46 (40441) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol9, skol58
% 4.06/4.46 ), skol58 ) ), and_2 }.
% 4.06/4.46 (40442) {G0,W9,D5,L2,V2,M2} { ! and_3, is_a_theorem( implies( X, implies(
% 4.06/4.46 Y, and( X, Y ) ) ) ) }.
% 4.06/4.46 (40443) {G0,W9,D5,L2,V0,M2} { ! is_a_theorem( implies( skol10, implies(
% 4.06/4.46 skol59, and( skol10, skol59 ) ) ) ), and_3 }.
% 4.06/4.46 (40444) {G0,W7,D4,L2,V2,M2} { ! or_1, is_a_theorem( implies( X, or( X, Y )
% 4.06/4.46 ) ) }.
% 4.06/4.46 (40445) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol11, or( skol11
% 4.06/4.46 , skol60 ) ) ), or_1 }.
% 4.06/4.46 (40446) {G0,W7,D4,L2,V2,M2} { ! or_2, is_a_theorem( implies( Y, or( X, Y )
% 4.06/4.46 ) ) }.
% 4.06/4.46 (40447) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol61, or( skol12
% 4.06/4.46 , skol61 ) ) ), or_2 }.
% 4.06/4.46 (40448) {G0,W15,D6,L2,V3,M2} { ! or_3, is_a_theorem( implies( implies( X,
% 4.06/4.46 Z ), implies( implies( Y, Z ), implies( or( X, Y ), Z ) ) ) ) }.
% 4.06/4.46 (40449) {G0,W15,D6,L2,V0,M2} { ! is_a_theorem( implies( implies( skol13,
% 4.06/4.46 skol87 ), implies( implies( skol62, skol87 ), implies( or( skol13, skol62
% 4.06/4.46 ), skol87 ) ) ) ), or_3 }.
% 4.06/4.46 (40450) {G0,W9,D4,L2,V2,M2} { ! equivalence_1, is_a_theorem( implies(
% 4.06/4.46 equiv( X, Y ), implies( X, Y ) ) ) }.
% 4.06/4.46 (40451) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( equiv( skol14,
% 4.06/4.46 skol63 ), implies( skol14, skol63 ) ) ), equivalence_1 }.
% 4.06/4.46 (40452) {G0,W9,D4,L2,V2,M2} { ! equivalence_2, is_a_theorem( implies(
% 4.06/4.46 equiv( X, Y ), implies( Y, X ) ) ) }.
% 4.06/4.46 (40453) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( equiv( skol15,
% 4.06/4.46 skol64 ), implies( skol64, skol15 ) ) ), equivalence_2 }.
% 4.06/4.46 (40454) {G0,W13,D5,L2,V2,M2} { ! equivalence_3, is_a_theorem( implies(
% 4.06/4.46 implies( X, Y ), implies( implies( Y, X ), equiv( X, Y ) ) ) ) }.
% 4.06/4.46 (40455) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol16,
% 4.06/4.46 skol65 ), implies( implies( skol65, skol16 ), equiv( skol16, skol65 ) ) )
% 4.06/4.46 ), equivalence_3 }.
% 4.06/4.46 (40456) {G0,W7,D4,L2,V1,M2} { ! kn1, is_a_theorem( implies( X, and( X, X )
% 4.06/4.46 ) ) }.
% 4.06/4.46 (40457) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol17, and( skol17
% 4.06/4.46 , skol17 ) ) ), kn1 }.
% 4.06/4.46 (40458) {G0,W7,D4,L2,V2,M2} { ! kn2, is_a_theorem( implies( and( X, Y ), X
% 4.06/4.46 ) ) }.
% 4.06/4.46 (40459) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol18, skol66
% 4.06/4.46 ), skol18 ) ), kn2 }.
% 4.06/4.46 (40460) {G0,W15,D6,L2,V3,M2} { ! kn3, is_a_theorem( implies( implies( X, Y
% 4.06/4.46 ), implies( not( and( Y, Z ) ), not( and( Z, X ) ) ) ) ) }.
% 4.06/4.46 (40461) {G0,W15,D6,L2,V0,M2} { ! is_a_theorem( implies( implies( skol19,
% 4.06/4.46 skol67 ), implies( not( and( skol67, skol88 ) ), not( and( skol88, skol19
% 4.06/4.46 ) ) ) ) ), kn3 }.
% 4.06/4.46 (40462) {G0,W13,D5,L2,V3,M2} { ! cn1, is_a_theorem( implies( implies( X, Y
% 4.06/4.46 ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 4.06/4.46 (40463) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol20,
% 4.06/4.46 skol68 ), implies( implies( skol68, skol89 ), implies( skol20, skol89 ) )
% 4.06/4.46 ) ), cn1 }.
% 4.06/4.46 (40464) {G0,W8,D5,L2,V2,M2} { ! cn2, is_a_theorem( implies( X, implies(
% 4.06/4.46 not( X ), Y ) ) ) }.
% 4.06/4.46 (40465) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( skol21, implies(
% 4.06/4.46 not( skol21 ), skol69 ) ) ), cn2 }.
% 4.06/4.46 (40466) {G0,W8,D5,L2,V1,M2} { ! cn3, is_a_theorem( implies( implies( not(
% 4.06/4.46 X ), X ), X ) ) }.
% 4.06/4.46 (40467) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( not(
% 4.06/4.46 skol22 ), skol22 ), skol22 ) ), cn3 }.
% 4.06/4.46 (40468) {G0,W7,D4,L2,V1,M2} { ! r1, is_a_theorem( implies( or( X, X ), X )
% 4.06/4.46 ) }.
% 4.06/4.46 (40469) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( or( skol23, skol23
% 4.06/4.46 ), skol23 ) ), r1 }.
% 4.06/4.46 (40470) {G0,W7,D4,L2,V2,M2} { ! r2, is_a_theorem( implies( Y, or( X, Y ) )
% 4.06/4.46 ) }.
% 4.06/4.46 (40471) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol70, or( skol24
% 4.06/4.46 , skol70 ) ) ), r2 }.
% 4.06/4.46 (40472) {G0,W9,D4,L2,V2,M2} { ! r3, is_a_theorem( implies( or( X, Y ), or
% 4.06/4.46 ( Y, X ) ) ) }.
% 4.06/4.46 (40473) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( or( skol25, skol71
% 4.06/4.46 ), or( skol71, skol25 ) ) ), r3 }.
% 4.06/4.46 (40474) {G0,W13,D5,L2,V3,M2} { ! r4, is_a_theorem( implies( or( X, or( Y,
% 4.06/4.46 Z ) ), or( Y, or( X, Z ) ) ) ) }.
% 4.06/4.46 (40475) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( or( skol26, or(
% 4.06/4.46 skol72, skol90 ) ), or( skol72, or( skol26, skol90 ) ) ) ), r4 }.
% 4.06/4.46 (40476) {G0,W13,D5,L2,V3,M2} { ! r5, is_a_theorem( implies( implies( Y, Z
% 4.06/4.46 ), implies( or( X, Y ), or( X, Z ) ) ) ) }.
% 4.06/4.46 (40477) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol73,
% 4.06/4.46 skol91 ), implies( or( skol27, skol73 ), or( skol27, skol91 ) ) ) ), r5
% 4.06/4.46 }.
% 4.06/4.46 (40478) {G0,W11,D5,L2,V2,M2} { ! op_or, or( X, Y ) = not( and( not( X ),
% 4.06/4.46 not( Y ) ) ) }.
% 4.06/4.46 (40479) {G0,W11,D5,L2,V2,M2} { ! op_and, and( X, Y ) = not( or( not( X ),
% 4.06/4.46 not( Y ) ) ) }.
% 4.06/4.46 (40480) {G0,W10,D5,L2,V2,M2} { ! op_implies_and, implies( X, Y ) = not(
% 4.06/4.46 and( X, not( Y ) ) ) }.
% 4.06/4.46 (40481) {G0,W9,D4,L2,V2,M2} { ! op_implies_or, implies( X, Y ) = or( not(
% 4.06/4.46 X ), Y ) }.
% 4.06/4.46 (40482) {G0,W12,D4,L2,V2,M2} { ! op_equiv, equiv( X, Y ) = and( implies( X
% 4.06/4.46 , Y ), implies( Y, X ) ) }.
% 4.06/4.46 (40483) {G0,W1,D1,L1,V0,M1} { op_or }.
% 4.06/4.46 (40484) {G0,W1,D1,L1,V0,M1} { op_implies_and }.
% 4.06/4.46 (40485) {G0,W1,D1,L1,V0,M1} { op_equiv }.
% 4.06/4.46 (40486) {G0,W1,D1,L1,V0,M1} { modus_ponens }.
% 4.06/4.46 (40487) {G0,W1,D1,L1,V0,M1} { modus_tollens }.
% 4.06/4.46 (40488) {G0,W1,D1,L1,V0,M1} { implies_1 }.
% 4.06/4.46 (40489) {G0,W1,D1,L1,V0,M1} { implies_2 }.
% 4.06/4.46 (40490) {G0,W1,D1,L1,V0,M1} { implies_3 }.
% 4.06/4.46 (40491) {G0,W1,D1,L1,V0,M1} { and_1 }.
% 4.06/4.46 (40492) {G0,W1,D1,L1,V0,M1} { and_2 }.
% 4.06/4.46 (40493) {G0,W1,D1,L1,V0,M1} { and_3 }.
% 4.06/4.46 (40494) {G0,W1,D1,L1,V0,M1} { or_1 }.
% 4.06/4.46 (40495) {G0,W1,D1,L1,V0,M1} { or_2 }.
% 4.06/4.46 (40496) {G0,W1,D1,L1,V0,M1} { or_3 }.
% 4.06/4.46 (40497) {G0,W1,D1,L1,V0,M1} { equivalence_1 }.
% 4.06/4.46 (40498) {G0,W1,D1,L1,V0,M1} { equivalence_2 }.
% 4.06/4.46 (40499) {G0,W1,D1,L1,V0,M1} { equivalence_3 }.
% 4.06/4.46 (40500) {G0,W1,D1,L1,V0,M1} { substitution_of_equivalents }.
% 4.06/4.46 (40501) {G0,W6,D3,L3,V1,M3} { ! necessitation, ! is_a_theorem( X ),
% 4.06/4.46 is_a_theorem( necessarily( X ) ) }.
% 4.06/4.46 (40502) {G0,W3,D2,L2,V0,M2} { is_a_theorem( skol28 ), necessitation }.
% 4.06/4.46 (40503) {G0,W4,D3,L2,V0,M2} { ! is_a_theorem( necessarily( skol28 ) ),
% 4.06/4.46 necessitation }.
% 4.06/4.46 (40504) {G0,W5,D2,L3,V1,M3} { ! modus_ponens_strict_implies, ! alpha2( X )
% 4.06/4.46 , is_a_theorem( X ) }.
% 4.06/4.46 (40505) {G0,W3,D2,L2,V0,M2} { alpha2( skol29 ),
% 4.06/4.46 modus_ponens_strict_implies }.
% 4.06/4.46 (40506) {G0,W3,D2,L2,V0,M2} { ! is_a_theorem( skol29 ),
% 4.06/4.46 modus_ponens_strict_implies }.
% 4.06/4.46 (40507) {G0,W5,D3,L2,V2,M2} { ! alpha2( X ), is_a_theorem( skol30( Y ) )
% 4.06/4.46 }.
% 4.06/4.46 (40508) {G0,W7,D4,L2,V1,M2} { ! alpha2( X ), is_a_theorem( strict_implies
% 4.06/4.46 ( skol30( X ), X ) ) }.
% 4.06/4.46 (40509) {G0,W8,D3,L3,V2,M3} { ! is_a_theorem( Y ), ! is_a_theorem(
% 4.06/4.46 strict_implies( Y, X ) ), alpha2( X ) }.
% 4.06/4.46 (40510) {G0,W8,D3,L3,V2,M3} { ! adjunction, ! alpha3( X, Y ), is_a_theorem
% 4.06/4.46 ( and( X, Y ) ) }.
% 4.06/4.46 (40511) {G0,W4,D2,L2,V0,M2} { alpha3( skol31, skol74 ), adjunction }.
% 4.06/4.46 (40512) {G0,W5,D3,L2,V0,M2} { ! is_a_theorem( and( skol31, skol74 ) ),
% 4.06/4.46 adjunction }.
% 4.06/4.46 (40513) {G0,W5,D2,L2,V2,M2} { ! alpha3( X, Y ), is_a_theorem( X ) }.
% 4.06/4.46 (40514) {G0,W5,D2,L2,V2,M2} { ! alpha3( X, Y ), is_a_theorem( Y ) }.
% 4.06/4.46 (40515) {G0,W7,D2,L3,V2,M3} { ! is_a_theorem( X ), ! is_a_theorem( Y ),
% 4.06/4.46 alpha3( X, Y ) }.
% 4.06/4.46 (40516) {G0,W8,D3,L3,V2,M3} { ! substitution_strict_equiv, ! is_a_theorem
% 4.06/4.46 ( strict_equiv( X, Y ) ), X = Y }.
% 4.06/4.46 (40517) {G0,W5,D3,L2,V0,M2} { is_a_theorem( strict_equiv( skol32, skol75 )
% 4.06/4.46 ), substitution_strict_equiv }.
% 4.06/4.46 (40518) {G0,W4,D2,L2,V0,M2} { ! skol32 = skol75, substitution_strict_equiv
% 4.06/4.46 }.
% 4.06/4.46 (40519) {G0,W12,D5,L2,V2,M2} { ! axiom_K, is_a_theorem( implies(
% 4.06/4.46 necessarily( implies( X, Y ) ), implies( necessarily( X ), necessarily( Y
% 4.06/4.46 ) ) ) ) }.
% 4.06/4.46 (40520) {G0,W12,D5,L2,V0,M2} { ! is_a_theorem( implies( necessarily(
% 4.06/4.46 implies( skol33, skol76 ) ), implies( necessarily( skol33 ), necessarily
% 4.06/4.46 ( skol76 ) ) ) ), axiom_K }.
% 4.06/4.46 (40521) {G0,W6,D4,L2,V1,M2} { ! axiom_M, is_a_theorem( implies(
% 4.06/4.46 necessarily( X ), X ) ) }.
% 4.06/4.46 (40522) {G0,W6,D4,L2,V0,M2} { ! is_a_theorem( implies( necessarily( skol34
% 4.06/4.46 ), skol34 ) ), axiom_M }.
% 4.06/4.46 (40523) {G0,W8,D5,L2,V1,M2} { ! axiom_4, is_a_theorem( implies(
% 4.06/4.46 necessarily( X ), necessarily( necessarily( X ) ) ) ) }.
% 4.06/4.46 (40524) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( necessarily( skol35
% 4.06/4.46 ), necessarily( necessarily( skol35 ) ) ) ), axiom_4 }.
% 4.06/4.46 (40525) {G0,W7,D5,L2,V1,M2} { ! axiom_B, is_a_theorem( implies( X,
% 4.06/4.46 necessarily( possibly( X ) ) ) ) }.
% 4.06/4.46 (40526) {G0,W7,D5,L2,V0,M2} { ! is_a_theorem( implies( skol36, necessarily
% 4.06/4.46 ( possibly( skol36 ) ) ) ), axiom_B }.
% 4.06/4.46 (40527) {G0,W8,D5,L2,V1,M2} { ! axiom_5, is_a_theorem( implies( possibly(
% 4.06/4.46 X ), necessarily( possibly( X ) ) ) ) }.
% 4.06/4.46 (40528) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( possibly( skol37 )
% 4.06/4.46 , necessarily( possibly( skol37 ) ) ) ), axiom_5 }.
% 4.06/4.46 (40529) {G0,W16,D6,L2,V3,M2} { ! axiom_s1, is_a_theorem( implies( and(
% 4.06/4.46 necessarily( implies( X, Y ) ), necessarily( implies( Y, Z ) ) ),
% 4.06/4.46 necessarily( implies( X, Z ) ) ) ) }.
% 4.06/4.46 (40530) {G0,W16,D6,L2,V0,M2} { ! is_a_theorem( implies( and( necessarily(
% 4.06/4.46 implies( skol38, skol77 ) ), necessarily( implies( skol77, skol92 ) ) ),
% 4.06/4.46 necessarily( implies( skol38, skol92 ) ) ) ), axiom_s1 }.
% 4.06/4.46 (40531) {G0,W12,D5,L2,V2,M2} { ! axiom_s2, is_a_theorem( strict_implies(
% 4.06/4.46 possibly( and( X, Y ) ), and( possibly( X ), possibly( Y ) ) ) ) }.
% 4.06/4.46 (40532) {G0,W12,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( possibly(
% 4.06/4.46 and( skol39, skol78 ) ), and( possibly( skol39 ), possibly( skol78 ) ) )
% 4.06/4.46 ), axiom_s2 }.
% 4.06/4.46 (40533) {G0,W13,D6,L2,V2,M2} { ! axiom_s3, is_a_theorem( strict_implies(
% 4.06/4.46 strict_implies( X, Y ), strict_implies( not( possibly( Y ) ), not(
% 4.06/4.46 possibly( X ) ) ) ) ) }.
% 4.06/4.46 (40534) {G0,W13,D6,L2,V0,M2} { ! is_a_theorem( strict_implies(
% 4.06/4.46 strict_implies( skol40, skol79 ), strict_implies( not( possibly( skol79 )
% 4.06/4.46 ), not( possibly( skol40 ) ) ) ) ), axiom_s3 }.
% 4.06/4.46 (40535) {G0,W8,D5,L2,V1,M2} { ! axiom_s4, is_a_theorem( strict_implies(
% 4.06/4.46 necessarily( X ), necessarily( necessarily( X ) ) ) ) }.
% 4.06/4.46 (40536) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( necessarily
% 4.06/4.46 ( skol41 ), necessarily( necessarily( skol41 ) ) ) ), axiom_s4 }.
% 4.06/4.46 (40537) {G0,W9,D4,L2,V2,M2} { ! axiom_m1, is_a_theorem( strict_implies(
% 4.06/4.46 and( X, Y ), and( Y, X ) ) ) }.
% 4.06/4.46 (40538) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( and( skol42
% 4.06/4.46 , skol80 ), and( skol80, skol42 ) ) ), axiom_m1 }.
% 4.06/4.46 (40539) {G0,W7,D4,L2,V2,M2} { ! axiom_m2, is_a_theorem( strict_implies(
% 4.06/4.46 and( X, Y ), X ) ) }.
% 4.06/4.46 (40540) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( and( skol43
% 4.06/4.46 , skol81 ), skol43 ) ), axiom_m2 }.
% 4.06/4.46 (40541) {G0,W13,D5,L2,V3,M2} { ! axiom_m3, is_a_theorem( strict_implies(
% 4.06/4.46 and( and( X, Y ), Z ), and( X, and( Y, Z ) ) ) ) }.
% 4.06/4.46 (40542) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( and( and(
% 4.06/4.46 skol44, skol82 ), skol93 ), and( skol44, and( skol82, skol93 ) ) ) ),
% 4.06/4.46 axiom_m3 }.
% 4.06/4.46 (40543) {G0,W7,D4,L2,V1,M2} { ! axiom_m4, is_a_theorem( strict_implies( X
% 4.06/4.46 , and( X, X ) ) ) }.
% 4.06/4.46 (40544) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( skol45, and
% 4.06/4.46 ( skol45, skol45 ) ) ), axiom_m4 }.
% 4.06/4.46 (40545) {G0,W13,D5,L2,V3,M2} { ! axiom_m5, is_a_theorem( strict_implies(
% 4.06/4.46 and( strict_implies( X, Y ), strict_implies( Y, Z ) ), strict_implies( X
% 4.06/4.46 , Z ) ) ) }.
% 4.06/4.46 (40546) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( and(
% 4.06/4.46 strict_implies( skol46, skol83 ), strict_implies( skol83, skol94 ) ),
% 4.06/4.46 strict_implies( skol46, skol94 ) ) ), axiom_m5 }.
% 4.06/4.46 (40547) {G0,W6,D4,L2,V1,M2} { ! axiom_m6, is_a_theorem( strict_implies( X
% 4.06/4.46 , possibly( X ) ) ) }.
% 4.06/4.46 (40548) {G0,W6,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( skol47,
% 4.06/4.46 possibly( skol47 ) ) ), axiom_m6 }.
% 4.06/4.46 (40549) {G0,W8,D5,L2,V2,M2} { ! axiom_m7, is_a_theorem( strict_implies(
% 4.06/4.46 possibly( and( X, Y ) ), X ) ) }.
% 4.06/4.46 (40550) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( possibly(
% 4.06/4.46 and( skol48, skol84 ) ), skol48 ) ), axiom_m7 }.
% 4.06/4.46 (40551) {G0,W11,D5,L2,V2,M2} { ! axiom_m8, is_a_theorem( strict_implies(
% 4.06/4.46 strict_implies( X, Y ), strict_implies( possibly( X ), possibly( Y ) ) )
% 4.06/4.46 ) }.
% 4.06/4.46 (40552) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( strict_implies(
% 4.06/4.46 strict_implies( skol49, skol85 ), strict_implies( possibly( skol49 ),
% 4.06/4.46 possibly( skol85 ) ) ) ), axiom_m8 }.
% 4.06/4.46 (40553) {G0,W8,D5,L2,V1,M2} { ! axiom_m9, is_a_theorem( strict_implies(
% 4.06/4.46 possibly( possibly( X ) ), possibly( X ) ) ) }.
% 4.06/4.46 (40554) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( possibly(
% 4.06/4.46 possibly( skol50 ) ), possibly( skol50 ) ) ), axiom_m9 }.
% 4.06/4.46 (40555) {G0,W8,D5,L2,V1,M2} { ! axiom_m10, is_a_theorem( strict_implies(
% 4.06/4.46 possibly( X ), necessarily( possibly( X ) ) ) ) }.
% 4.06/4.46 (40556) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( possibly(
% 4.06/4.46 skol51 ), necessarily( possibly( skol51 ) ) ) ), axiom_m10 }.
% 4.06/4.46 (40557) {G0,W8,D5,L2,V1,M2} { ! op_possibly, possibly( X ) = not(
% 4.06/4.46 necessarily( not( X ) ) ) }.
% 4.06/4.46 (40558) {G0,W8,D5,L2,V1,M2} { ! op_necessarily, necessarily( X ) = not(
% 4.06/4.46 possibly( not( X ) ) ) }.
% 4.06/4.46 (40559) {G0,W9,D4,L2,V2,M2} { ! op_strict_implies, strict_implies( X, Y )
% 4.06/4.46 = necessarily( implies( X, Y ) ) }.
% 4.06/4.46 (40560) {G0,W12,D4,L2,V2,M2} { ! op_strict_equiv, strict_equiv( X, Y ) =
% 4.06/4.46 and( strict_implies( X, Y ), strict_implies( Y, X ) ) }.
% 4.06/4.46 (40561) {G0,W1,D1,L1,V0,M1} { op_possibly }.
% 4.06/4.46 (40562) {G0,W1,D1,L1,V0,M1} { necessitation }.
% 4.06/4.46 (40563) {G0,W1,D1,L1,V0,M1} { axiom_K }.
% 4.06/4.46 (40564) {G0,W1,D1,L1,V0,M1} { axiom_M }.
% 4.06/4.46 (40565) {G0,W1,D1,L1,V0,M1} { axiom_5 }.
% 4.06/4.46 (40566) {G0,W1,D1,L1,V0,M1} { op_possibly }.
% 4.06/4.46 (40567) {G0,W1,D1,L1,V0,M1} { op_or }.
% 4.06/4.46 (40568) {G0,W1,D1,L1,V0,M1} { op_implies }.
% 4.06/4.46 (40569) {G0,W1,D1,L1,V0,M1} { op_strict_implies }.
% 4.06/4.46 (40570) {G0,W1,D1,L1,V0,M1} { op_equiv }.
% 4.06/4.46 (40571) {G0,W1,D1,L1,V0,M1} { op_strict_equiv }.
% 4.06/4.46 (40572) {G0,W1,D1,L1,V0,M1} { ! axiom_m2 }.
% 4.06/4.46
% 4.06/4.46
% 4.06/4.46 Total Proof:
% 4.06/4.46
% 4.06/4.46 subsumption: (17) {G0,W7,D4,L2,V2,M2} I { ! and_1, is_a_theorem( implies(
% 4.06/4.46 and( X, Y ), X ) ) }.
% 4.06/4.46 parent0: (40438) {G0,W7,D4,L2,V2,M2} { ! and_1, is_a_theorem( implies( and
% 4.06/4.46 ( X, Y ), X ) ) }.
% 4.06/4.46 substitution0:
% 4.06/4.46 X := X
% 4.06/4.46 Y := Y
% 4.06/4.46 end
% 4.06/4.46 permutation0:
% 4.06/4.46 0 ==> 0
% 4.06/4.46 1 ==> 1
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 subsumption: (70) {G0,W1,D1,L1,V0,M1} I { and_1 }.
% 4.06/4.46 parent0: (40491) {G0,W1,D1,L1,V0,M1} { and_1 }.
% 4.06/4.46 substitution0:
% 4.06/4.46 end
% 4.06/4.46 permutation0:
% 4.06/4.46 0 ==> 0
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 subsumption: (80) {G0,W6,D3,L3,V1,M3} I { ! necessitation, ! is_a_theorem(
% 4.06/4.46 X ), is_a_theorem( necessarily( X ) ) }.
% 4.06/4.46 parent0: (40501) {G0,W6,D3,L3,V1,M3} { ! necessitation, ! is_a_theorem( X
% 4.06/4.46 ), is_a_theorem( necessarily( X ) ) }.
% 4.06/4.46 substitution0:
% 4.06/4.46 X := X
% 4.06/4.46 end
% 4.06/4.46 permutation0:
% 4.06/4.46 0 ==> 0
% 4.06/4.46 1 ==> 1
% 4.06/4.46 2 ==> 2
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 subsumption: (119) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( strict_implies(
% 4.06/4.46 and( skol43, skol81 ), skol43 ) ), axiom_m2 }.
% 4.06/4.46 parent0: (40540) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( and
% 4.06/4.46 ( skol43, skol81 ), skol43 ) ), axiom_m2 }.
% 4.06/4.46 substitution0:
% 4.06/4.46 end
% 4.06/4.46 permutation0:
% 4.06/4.46 0 ==> 0
% 4.06/4.46 1 ==> 1
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 eqswap: (40611) {G0,W9,D4,L2,V2,M2} { necessarily( implies( X, Y ) ) =
% 4.06/4.46 strict_implies( X, Y ), ! op_strict_implies }.
% 4.06/4.46 parent0[1]: (40559) {G0,W9,D4,L2,V2,M2} { ! op_strict_implies,
% 4.06/4.46 strict_implies( X, Y ) = necessarily( implies( X, Y ) ) }.
% 4.06/4.46 substitution0:
% 4.06/4.46 X := X
% 4.06/4.46 Y := Y
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 subsumption: (138) {G0,W9,D4,L2,V2,M2} I { ! op_strict_implies, necessarily
% 4.06/4.46 ( implies( X, Y ) ) ==> strict_implies( X, Y ) }.
% 4.06/4.46 parent0: (40611) {G0,W9,D4,L2,V2,M2} { necessarily( implies( X, Y ) ) =
% 4.06/4.46 strict_implies( X, Y ), ! op_strict_implies }.
% 4.06/4.46 substitution0:
% 4.06/4.46 X := X
% 4.06/4.46 Y := Y
% 4.06/4.46 end
% 4.06/4.46 permutation0:
% 4.06/4.46 0 ==> 1
% 4.06/4.46 1 ==> 0
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 subsumption: (141) {G0,W1,D1,L1,V0,M1} I { necessitation }.
% 4.06/4.46 parent0: (40562) {G0,W1,D1,L1,V0,M1} { necessitation }.
% 4.06/4.46 substitution0:
% 4.06/4.46 end
% 4.06/4.46 permutation0:
% 4.06/4.46 0 ==> 0
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 subsumption: (146) {G0,W1,D1,L1,V0,M1} I { op_strict_implies }.
% 4.06/4.46 parent0: (40569) {G0,W1,D1,L1,V0,M1} { op_strict_implies }.
% 4.06/4.46 substitution0:
% 4.06/4.46 end
% 4.06/4.46 permutation0:
% 4.06/4.46 0 ==> 0
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 subsumption: (148) {G0,W1,D1,L1,V0,M1} I { ! axiom_m2 }.
% 4.06/4.46 parent0: (40572) {G0,W1,D1,L1,V0,M1} { ! axiom_m2 }.
% 4.06/4.46 substitution0:
% 4.06/4.46 end
% 4.06/4.46 permutation0:
% 4.06/4.46 0 ==> 0
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 resolution: (40654) {G1,W5,D3,L2,V1,M2} { ! is_a_theorem( X ),
% 4.06/4.46 is_a_theorem( necessarily( X ) ) }.
% 4.06/4.46 parent0[0]: (80) {G0,W6,D3,L3,V1,M3} I { ! necessitation, ! is_a_theorem( X
% 4.06/4.46 ), is_a_theorem( necessarily( X ) ) }.
% 4.06/4.46 parent1[0]: (141) {G0,W1,D1,L1,V0,M1} I { necessitation }.
% 4.06/4.46 substitution0:
% 4.06/4.46 X := X
% 4.06/4.46 end
% 4.06/4.46 substitution1:
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 subsumption: (219) {G1,W5,D3,L2,V1,M2} S(80);r(141) { ! is_a_theorem( X ),
% 4.06/4.46 is_a_theorem( necessarily( X ) ) }.
% 4.06/4.46 parent0: (40654) {G1,W5,D3,L2,V1,M2} { ! is_a_theorem( X ), is_a_theorem(
% 4.06/4.46 necessarily( X ) ) }.
% 4.06/4.46 substitution0:
% 4.06/4.46 X := X
% 4.06/4.46 end
% 4.06/4.46 permutation0:
% 4.06/4.46 0 ==> 0
% 4.06/4.46 1 ==> 1
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 resolution: (40655) {G1,W6,D4,L1,V2,M1} { is_a_theorem( implies( and( X, Y
% 4.06/4.46 ), X ) ) }.
% 4.06/4.46 parent0[0]: (17) {G0,W7,D4,L2,V2,M2} I { ! and_1, is_a_theorem( implies(
% 4.06/4.46 and( X, Y ), X ) ) }.
% 4.06/4.46 parent1[0]: (70) {G0,W1,D1,L1,V0,M1} I { and_1 }.
% 4.06/4.46 substitution0:
% 4.06/4.46 X := X
% 4.06/4.46 Y := Y
% 4.06/4.46 end
% 4.06/4.46 substitution1:
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 subsumption: (256) {G1,W6,D4,L1,V2,M1} S(17);r(70) { is_a_theorem( implies
% 4.06/4.46 ( and( X, Y ), X ) ) }.
% 4.06/4.46 parent0: (40655) {G1,W6,D4,L1,V2,M1} { is_a_theorem( implies( and( X, Y )
% 4.06/4.46 , X ) ) }.
% 4.06/4.46 substitution0:
% 4.06/4.46 X := X
% 4.06/4.46 Y := Y
% 4.06/4.46 end
% 4.06/4.46 permutation0:
% 4.06/4.46 0 ==> 0
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 resolution: (40656) {G2,W7,D5,L1,V2,M1} { is_a_theorem( necessarily(
% 4.06/4.46 implies( and( X, Y ), X ) ) ) }.
% 4.06/4.46 parent0[0]: (219) {G1,W5,D3,L2,V1,M2} S(80);r(141) { ! is_a_theorem( X ),
% 4.06/4.46 is_a_theorem( necessarily( X ) ) }.
% 4.06/4.46 parent1[0]: (256) {G1,W6,D4,L1,V2,M1} S(17);r(70) { is_a_theorem( implies(
% 4.06/4.46 and( X, Y ), X ) ) }.
% 4.06/4.46 substitution0:
% 4.06/4.46 X := implies( and( X, Y ), X )
% 4.06/4.46 end
% 4.06/4.46 substitution1:
% 4.06/4.46 X := X
% 4.06/4.46 Y := Y
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 subsumption: (270) {G2,W7,D5,L1,V2,M1} R(256,219) { is_a_theorem(
% 4.06/4.46 necessarily( implies( and( X, Y ), X ) ) ) }.
% 4.06/4.46 parent0: (40656) {G2,W7,D5,L1,V2,M1} { is_a_theorem( necessarily( implies
% 4.06/4.46 ( and( X, Y ), X ) ) ) }.
% 4.06/4.46 substitution0:
% 4.06/4.46 X := X
% 4.06/4.46 Y := Y
% 4.06/4.46 end
% 4.06/4.46 permutation0:
% 4.06/4.46 0 ==> 0
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 resolution: (40657) {G1,W6,D4,L1,V0,M1} { ! is_a_theorem( strict_implies(
% 4.06/4.46 and( skol43, skol81 ), skol43 ) ) }.
% 4.06/4.46 parent0[0]: (148) {G0,W1,D1,L1,V0,M1} I { ! axiom_m2 }.
% 4.06/4.46 parent1[1]: (119) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( strict_implies(
% 4.06/4.46 and( skol43, skol81 ), skol43 ) ), axiom_m2 }.
% 4.06/4.46 substitution0:
% 4.06/4.46 end
% 4.06/4.46 substitution1:
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 subsumption: (3944) {G1,W6,D4,L1,V0,M1} S(119);r(148) { ! is_a_theorem(
% 4.06/4.46 strict_implies( and( skol43, skol81 ), skol43 ) ) }.
% 4.06/4.46 parent0: (40657) {G1,W6,D4,L1,V0,M1} { ! is_a_theorem( strict_implies( and
% 4.06/4.46 ( skol43, skol81 ), skol43 ) ) }.
% 4.06/4.46 substitution0:
% 4.06/4.46 end
% 4.06/4.46 permutation0:
% 4.06/4.46 0 ==> 0
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 resolution: (40659) {G1,W8,D4,L1,V2,M1} { necessarily( implies( X, Y ) )
% 4.06/4.46 ==> strict_implies( X, Y ) }.
% 4.06/4.46 parent0[0]: (138) {G0,W9,D4,L2,V2,M2} I { ! op_strict_implies, necessarily
% 4.06/4.46 ( implies( X, Y ) ) ==> strict_implies( X, Y ) }.
% 4.06/4.46 parent1[0]: (146) {G0,W1,D1,L1,V0,M1} I { op_strict_implies }.
% 4.06/4.46 substitution0:
% 4.06/4.46 X := X
% 4.06/4.46 Y := Y
% 4.06/4.46 end
% 4.06/4.46 substitution1:
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 subsumption: (5486) {G1,W8,D4,L1,V2,M1} S(138);r(146) { necessarily(
% 4.06/4.46 implies( X, Y ) ) ==> strict_implies( X, Y ) }.
% 4.06/4.46 parent0: (40659) {G1,W8,D4,L1,V2,M1} { necessarily( implies( X, Y ) ) ==>
% 4.06/4.46 strict_implies( X, Y ) }.
% 4.06/4.46 substitution0:
% 4.06/4.46 X := X
% 4.06/4.46 Y := Y
% 4.06/4.46 end
% 4.06/4.46 permutation0:
% 4.06/4.46 0 ==> 0
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 paramod: (40662) {G2,W6,D4,L1,V2,M1} { is_a_theorem( strict_implies( and(
% 4.06/4.46 X, Y ), X ) ) }.
% 4.06/4.46 parent0[0]: (5486) {G1,W8,D4,L1,V2,M1} S(138);r(146) { necessarily( implies
% 4.06/4.46 ( X, Y ) ) ==> strict_implies( X, Y ) }.
% 4.06/4.46 parent1[0; 1]: (270) {G2,W7,D5,L1,V2,M1} R(256,219) { is_a_theorem(
% 4.06/4.46 necessarily( implies( and( X, Y ), X ) ) ) }.
% 4.06/4.46 substitution0:
% 4.06/4.46 X := and( X, Y )
% 4.06/4.46 Y := X
% 4.06/4.46 end
% 4.06/4.46 substitution1:
% 4.06/4.46 X := X
% 4.06/4.46 Y := Y
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 subsumption: (20170) {G3,W6,D4,L1,V2,M1} S(270);d(5486) { is_a_theorem(
% 4.06/4.46 strict_implies( and( X, Y ), X ) ) }.
% 4.06/4.46 parent0: (40662) {G2,W6,D4,L1,V2,M1} { is_a_theorem( strict_implies( and(
% 4.06/4.46 X, Y ), X ) ) }.
% 4.06/4.46 substitution0:
% 4.06/4.46 X := X
% 4.06/4.46 Y := Y
% 4.06/4.46 end
% 4.06/4.46 permutation0:
% 4.06/4.46 0 ==> 0
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 resolution: (40663) {G2,W0,D0,L0,V0,M0} { }.
% 4.06/4.46 parent0[0]: (3944) {G1,W6,D4,L1,V0,M1} S(119);r(148) { ! is_a_theorem(
% 4.06/4.46 strict_implies( and( skol43, skol81 ), skol43 ) ) }.
% 4.06/4.46 parent1[0]: (20170) {G3,W6,D4,L1,V2,M1} S(270);d(5486) { is_a_theorem(
% 4.06/4.46 strict_implies( and( X, Y ), X ) ) }.
% 4.06/4.46 substitution0:
% 4.06/4.46 end
% 4.06/4.46 substitution1:
% 4.06/4.46 X := skol43
% 4.06/4.46 Y := skol81
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 subsumption: (40419) {G4,W0,D0,L0,V0,M0} S(3944);r(20170) { }.
% 4.06/4.46 parent0: (40663) {G2,W0,D0,L0,V0,M0} { }.
% 4.06/4.46 substitution0:
% 4.06/4.46 end
% 4.06/4.46 permutation0:
% 4.06/4.46 end
% 4.06/4.46
% 4.06/4.46 Proof check complete!
% 4.06/4.46
% 4.06/4.46 Memory use:
% 4.06/4.46
% 4.06/4.46 space for terms: 477470
% 4.06/4.46 space for clauses: 1641679
% 4.06/4.46
% 4.06/4.46
% 4.06/4.46 clauses generated: 81855
% 4.06/4.46 clauses kept: 40420
% 4.06/4.46 clauses selected: 1194
% 4.06/4.46 clauses deleted: 1621
% 4.06/4.46 clauses inuse deleted: 61
% 4.06/4.46
% 4.06/4.46 subsentry: 531284
% 4.06/4.46 literals s-matched: 398951
% 4.06/4.46 literals matched: 364811
% 4.06/4.46 full subsumption: 48037
% 4.06/4.46
% 4.06/4.46 checksum: -1110356190
% 4.06/4.46
% 4.06/4.46
% 4.06/4.46 Bliksem ended
%------------------------------------------------------------------------------