TSTP Solution File: LCL542+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL542+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n009.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 07:54:32 EDT 2022
% Result : Theorem 1.47s 1.88s
% Output : Refutation 1.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : LCL542+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.12 % Command : bliksem %s
% 0.11/0.31 % Computer : n009.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % DateTime : Sat Jul 2 16:36:52 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.39/1.07 *** allocated 10000 integers for termspace/termends
% 0.39/1.07 *** allocated 10000 integers for clauses
% 0.39/1.07 *** allocated 10000 integers for justifications
% 0.39/1.07 Bliksem 1.12
% 0.39/1.07
% 0.39/1.07
% 0.39/1.07 Automatic Strategy Selection
% 0.39/1.07
% 0.39/1.07
% 0.39/1.07 Clauses:
% 0.39/1.07
% 0.39/1.07 { ! modus_ponens, ! alpha1( X ), is_a_theorem( X ) }.
% 0.39/1.07 { alpha1( skol1 ), modus_ponens }.
% 0.39/1.07 { ! is_a_theorem( skol1 ), modus_ponens }.
% 0.39/1.07 { ! alpha1( X ), is_a_theorem( skol2( Y ) ) }.
% 0.39/1.07 { ! alpha1( X ), is_a_theorem( implies( skol2( X ), X ) ) }.
% 0.39/1.07 { ! is_a_theorem( Y ), ! is_a_theorem( implies( Y, X ) ), alpha1( X ) }.
% 0.39/1.07 { ! substitution_of_equivalents, ! is_a_theorem( equiv( X, Y ) ), X = Y }.
% 0.39/1.07 { is_a_theorem( equiv( skol3, skol52 ) ), substitution_of_equivalents }.
% 0.39/1.07 { ! skol3 = skol52, substitution_of_equivalents }.
% 0.39/1.07 { ! modus_tollens, is_a_theorem( implies( implies( not( Y ), not( X ) ),
% 0.39/1.07 implies( X, Y ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( implies( not( skol53 ), not( skol4 ) ), implies
% 0.39/1.07 ( skol4, skol53 ) ) ), modus_tollens }.
% 0.39/1.07 { ! implies_1, is_a_theorem( implies( X, implies( Y, X ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( skol5, implies( skol54, skol5 ) ) ), implies_1 }
% 0.39/1.07 .
% 0.39/1.07 { ! implies_2, is_a_theorem( implies( implies( X, implies( X, Y ) ),
% 0.39/1.07 implies( X, Y ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( implies( skol6, implies( skol6, skol55 ) ),
% 0.39/1.07 implies( skol6, skol55 ) ) ), implies_2 }.
% 0.39/1.07 { ! implies_3, is_a_theorem( implies( implies( X, Y ), implies( implies( Y
% 0.39/1.07 , Z ), implies( X, Z ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( implies( skol7, skol56 ), implies( implies(
% 0.39/1.07 skol56, skol86 ), implies( skol7, skol86 ) ) ) ), implies_3 }.
% 0.39/1.07 { ! and_1, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( and( skol8, skol57 ), skol8 ) ), and_1 }.
% 0.39/1.07 { ! and_2, is_a_theorem( implies( and( X, Y ), Y ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( and( skol9, skol58 ), skol58 ) ), and_2 }.
% 0.39/1.07 { ! and_3, is_a_theorem( implies( X, implies( Y, and( X, Y ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( skol10, implies( skol59, and( skol10, skol59 ) )
% 0.39/1.07 ) ), and_3 }.
% 0.39/1.07 { ! or_1, is_a_theorem( implies( X, or( X, Y ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( skol11, or( skol11, skol60 ) ) ), or_1 }.
% 0.39/1.07 { ! or_2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( skol61, or( skol12, skol61 ) ) ), or_2 }.
% 0.39/1.07 { ! or_3, is_a_theorem( implies( implies( X, Z ), implies( implies( Y, Z )
% 0.39/1.07 , implies( or( X, Y ), Z ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( implies( skol13, skol87 ), implies( implies(
% 0.39/1.07 skol62, skol87 ), implies( or( skol13, skol62 ), skol87 ) ) ) ), or_3 }.
% 0.39/1.07 { ! equivalence_1, is_a_theorem( implies( equiv( X, Y ), implies( X, Y ) )
% 0.39/1.07 ) }.
% 0.39/1.07 { ! is_a_theorem( implies( equiv( skol14, skol63 ), implies( skol14, skol63
% 0.39/1.07 ) ) ), equivalence_1 }.
% 0.39/1.07 { ! equivalence_2, is_a_theorem( implies( equiv( X, Y ), implies( Y, X ) )
% 0.39/1.07 ) }.
% 0.39/1.07 { ! is_a_theorem( implies( equiv( skol15, skol64 ), implies( skol64, skol15
% 0.39/1.07 ) ) ), equivalence_2 }.
% 0.39/1.07 { ! equivalence_3, is_a_theorem( implies( implies( X, Y ), implies( implies
% 0.39/1.07 ( Y, X ), equiv( X, Y ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( implies( skol16, skol65 ), implies( implies(
% 0.39/1.07 skol65, skol16 ), equiv( skol16, skol65 ) ) ) ), equivalence_3 }.
% 0.39/1.07 { ! kn1, is_a_theorem( implies( X, and( X, X ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( skol17, and( skol17, skol17 ) ) ), kn1 }.
% 0.39/1.07 { ! kn2, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( and( skol18, skol66 ), skol18 ) ), kn2 }.
% 0.39/1.07 { ! kn3, is_a_theorem( implies( implies( X, Y ), implies( not( and( Y, Z )
% 0.39/1.07 ), not( and( Z, X ) ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( implies( skol19, skol67 ), implies( not( and(
% 0.39/1.07 skol67, skol88 ) ), not( and( skol88, skol19 ) ) ) ) ), kn3 }.
% 0.39/1.07 { ! cn1, is_a_theorem( implies( implies( X, Y ), implies( implies( Y, Z ),
% 0.39/1.07 implies( X, Z ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( implies( skol20, skol68 ), implies( implies(
% 0.39/1.07 skol68, skol89 ), implies( skol20, skol89 ) ) ) ), cn1 }.
% 0.39/1.07 { ! cn2, is_a_theorem( implies( X, implies( not( X ), Y ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( skol21, implies( not( skol21 ), skol69 ) ) ),
% 0.39/1.07 cn2 }.
% 0.39/1.07 { ! cn3, is_a_theorem( implies( implies( not( X ), X ), X ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( implies( not( skol22 ), skol22 ), skol22 ) ),
% 0.39/1.07 cn3 }.
% 0.39/1.07 { ! r1, is_a_theorem( implies( or( X, X ), X ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( or( skol23, skol23 ), skol23 ) ), r1 }.
% 0.39/1.07 { ! r2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( skol70, or( skol24, skol70 ) ) ), r2 }.
% 0.39/1.07 { ! r3, is_a_theorem( implies( or( X, Y ), or( Y, X ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( or( skol25, skol71 ), or( skol71, skol25 ) ) ),
% 0.39/1.07 r3 }.
% 0.39/1.07 { ! r4, is_a_theorem( implies( or( X, or( Y, Z ) ), or( Y, or( X, Z ) ) ) )
% 0.39/1.07 }.
% 0.39/1.07 { ! is_a_theorem( implies( or( skol26, or( skol72, skol90 ) ), or( skol72,
% 0.39/1.07 or( skol26, skol90 ) ) ) ), r4 }.
% 0.39/1.07 { ! r5, is_a_theorem( implies( implies( Y, Z ), implies( or( X, Y ), or( X
% 0.39/1.07 , Z ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( implies( skol73, skol91 ), implies( or( skol27,
% 0.39/1.07 skol73 ), or( skol27, skol91 ) ) ) ), r5 }.
% 0.39/1.07 { ! op_or, or( X, Y ) = not( and( not( X ), not( Y ) ) ) }.
% 0.39/1.07 { ! op_and, and( X, Y ) = not( or( not( X ), not( Y ) ) ) }.
% 0.39/1.07 { ! op_implies_and, implies( X, Y ) = not( and( X, not( Y ) ) ) }.
% 0.39/1.07 { ! op_implies_or, implies( X, Y ) = or( not( X ), Y ) }.
% 0.39/1.07 { ! op_equiv, equiv( X, Y ) = and( implies( X, Y ), implies( Y, X ) ) }.
% 0.39/1.07 { op_or }.
% 0.39/1.07 { op_implies_and }.
% 0.39/1.07 { op_equiv }.
% 0.39/1.07 { modus_ponens }.
% 0.39/1.07 { modus_tollens }.
% 0.39/1.07 { implies_1 }.
% 0.39/1.07 { implies_2 }.
% 0.39/1.07 { implies_3 }.
% 0.39/1.07 { and_1 }.
% 0.39/1.07 { and_2 }.
% 0.39/1.07 { and_3 }.
% 0.39/1.07 { or_1 }.
% 0.39/1.07 { or_2 }.
% 0.39/1.07 { or_3 }.
% 0.39/1.07 { equivalence_1 }.
% 0.39/1.07 { equivalence_2 }.
% 0.39/1.07 { equivalence_3 }.
% 0.39/1.07 { substitution_of_equivalents }.
% 0.39/1.07 { ! necessitation, ! is_a_theorem( X ), is_a_theorem( necessarily( X ) ) }
% 0.39/1.07 .
% 0.39/1.07 { is_a_theorem( skol28 ), necessitation }.
% 0.39/1.07 { ! is_a_theorem( necessarily( skol28 ) ), necessitation }.
% 0.39/1.07 { ! modus_ponens_strict_implies, ! alpha2( X ), is_a_theorem( X ) }.
% 0.39/1.07 { alpha2( skol29 ), modus_ponens_strict_implies }.
% 0.39/1.07 { ! is_a_theorem( skol29 ), modus_ponens_strict_implies }.
% 0.39/1.07 { ! alpha2( X ), is_a_theorem( skol30( Y ) ) }.
% 0.39/1.07 { ! alpha2( X ), is_a_theorem( strict_implies( skol30( X ), X ) ) }.
% 0.39/1.07 { ! is_a_theorem( Y ), ! is_a_theorem( strict_implies( Y, X ) ), alpha2( X
% 0.39/1.07 ) }.
% 0.39/1.07 { ! adjunction, ! alpha3( X, Y ), is_a_theorem( and( X, Y ) ) }.
% 0.39/1.07 { alpha3( skol31, skol74 ), adjunction }.
% 0.39/1.07 { ! is_a_theorem( and( skol31, skol74 ) ), adjunction }.
% 0.39/1.07 { ! alpha3( X, Y ), is_a_theorem( X ) }.
% 0.39/1.07 { ! alpha3( X, Y ), is_a_theorem( Y ) }.
% 0.39/1.07 { ! is_a_theorem( X ), ! is_a_theorem( Y ), alpha3( X, Y ) }.
% 0.39/1.07 { ! substitution_strict_equiv, ! is_a_theorem( strict_equiv( X, Y ) ), X =
% 0.39/1.07 Y }.
% 0.39/1.07 { is_a_theorem( strict_equiv( skol32, skol75 ) ), substitution_strict_equiv
% 0.39/1.07 }.
% 0.39/1.07 { ! skol32 = skol75, substitution_strict_equiv }.
% 0.39/1.07 { ! axiom_K, is_a_theorem( implies( necessarily( implies( X, Y ) ), implies
% 0.39/1.07 ( necessarily( X ), necessarily( Y ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( necessarily( implies( skol33, skol76 ) ),
% 0.39/1.07 implies( necessarily( skol33 ), necessarily( skol76 ) ) ) ), axiom_K }.
% 0.39/1.07 { ! axiom_M, is_a_theorem( implies( necessarily( X ), X ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( necessarily( skol34 ), skol34 ) ), axiom_M }.
% 0.39/1.07 { ! axiom_4, is_a_theorem( implies( necessarily( X ), necessarily(
% 0.39/1.07 necessarily( X ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( necessarily( skol35 ), necessarily( necessarily
% 0.39/1.07 ( skol35 ) ) ) ), axiom_4 }.
% 0.39/1.07 { ! axiom_B, is_a_theorem( implies( X, necessarily( possibly( X ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( skol36, necessarily( possibly( skol36 ) ) ) ),
% 0.39/1.07 axiom_B }.
% 0.39/1.07 { ! axiom_5, is_a_theorem( implies( possibly( X ), necessarily( possibly( X
% 0.39/1.07 ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( possibly( skol37 ), necessarily( possibly(
% 0.39/1.07 skol37 ) ) ) ), axiom_5 }.
% 0.39/1.07 { ! axiom_s1, is_a_theorem( implies( and( necessarily( implies( X, Y ) ),
% 0.39/1.07 necessarily( implies( Y, Z ) ) ), necessarily( implies( X, Z ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( implies( and( necessarily( implies( skol38, skol77 ) ),
% 0.39/1.07 necessarily( implies( skol77, skol92 ) ) ), necessarily( implies( skol38
% 0.39/1.07 , skol92 ) ) ) ), axiom_s1 }.
% 0.39/1.07 { ! axiom_s2, is_a_theorem( strict_implies( possibly( and( X, Y ) ), and(
% 0.39/1.07 possibly( X ), possibly( Y ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( strict_implies( possibly( and( skol39, skol78 ) ), and(
% 0.39/1.07 possibly( skol39 ), possibly( skol78 ) ) ) ), axiom_s2 }.
% 0.39/1.07 { ! axiom_s3, is_a_theorem( strict_implies( strict_implies( X, Y ),
% 0.39/1.07 strict_implies( not( possibly( Y ) ), not( possibly( X ) ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( strict_implies( strict_implies( skol40, skol79 ),
% 0.39/1.07 strict_implies( not( possibly( skol79 ) ), not( possibly( skol40 ) ) ) )
% 0.39/1.07 ), axiom_s3 }.
% 0.39/1.07 { ! axiom_s4, is_a_theorem( strict_implies( necessarily( X ), necessarily(
% 0.39/1.07 necessarily( X ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( strict_implies( necessarily( skol41 ), necessarily(
% 0.39/1.07 necessarily( skol41 ) ) ) ), axiom_s4 }.
% 0.39/1.07 { ! axiom_m1, is_a_theorem( strict_implies( and( X, Y ), and( Y, X ) ) ) }
% 0.39/1.07 .
% 0.39/1.07 { ! is_a_theorem( strict_implies( and( skol42, skol80 ), and( skol80,
% 0.39/1.07 skol42 ) ) ), axiom_m1 }.
% 0.39/1.07 { ! axiom_m2, is_a_theorem( strict_implies( and( X, Y ), X ) ) }.
% 0.39/1.07 { ! is_a_theorem( strict_implies( and( skol43, skol81 ), skol43 ) ),
% 0.39/1.07 axiom_m2 }.
% 0.39/1.07 { ! axiom_m3, is_a_theorem( strict_implies( and( and( X, Y ), Z ), and( X,
% 0.39/1.07 and( Y, Z ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( strict_implies( and( and( skol44, skol82 ), skol93 ), and
% 0.39/1.07 ( skol44, and( skol82, skol93 ) ) ) ), axiom_m3 }.
% 0.39/1.07 { ! axiom_m4, is_a_theorem( strict_implies( X, and( X, X ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( strict_implies( skol45, and( skol45, skol45 ) ) ),
% 0.39/1.07 axiom_m4 }.
% 0.39/1.07 { ! axiom_m5, is_a_theorem( strict_implies( and( strict_implies( X, Y ),
% 0.39/1.07 strict_implies( Y, Z ) ), strict_implies( X, Z ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( strict_implies( and( strict_implies( skol46, skol83 ),
% 0.39/1.07 strict_implies( skol83, skol94 ) ), strict_implies( skol46, skol94 ) ) )
% 0.39/1.07 , axiom_m5 }.
% 0.39/1.07 { ! axiom_m6, is_a_theorem( strict_implies( X, possibly( X ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( strict_implies( skol47, possibly( skol47 ) ) ), axiom_m6
% 0.39/1.07 }.
% 0.39/1.07 { ! axiom_m7, is_a_theorem( strict_implies( possibly( and( X, Y ) ), X ) )
% 0.39/1.07 }.
% 0.39/1.07 { ! is_a_theorem( strict_implies( possibly( and( skol48, skol84 ) ), skol48
% 0.39/1.07 ) ), axiom_m7 }.
% 0.39/1.07 { ! axiom_m8, is_a_theorem( strict_implies( strict_implies( X, Y ),
% 0.39/1.07 strict_implies( possibly( X ), possibly( Y ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( strict_implies( strict_implies( skol49, skol85 ),
% 0.39/1.07 strict_implies( possibly( skol49 ), possibly( skol85 ) ) ) ), axiom_m8 }
% 0.39/1.07 .
% 0.39/1.07 { ! axiom_m9, is_a_theorem( strict_implies( possibly( possibly( X ) ),
% 0.39/1.07 possibly( X ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( strict_implies( possibly( possibly( skol50 ) ), possibly
% 0.39/1.07 ( skol50 ) ) ), axiom_m9 }.
% 0.39/1.07 { ! axiom_m10, is_a_theorem( strict_implies( possibly( X ), necessarily(
% 0.39/1.07 possibly( X ) ) ) ) }.
% 0.39/1.07 { ! is_a_theorem( strict_implies( possibly( skol51 ), necessarily( possibly
% 0.39/1.07 ( skol51 ) ) ) ), axiom_m10 }.
% 0.39/1.07 { ! op_possibly, possibly( X ) = not( necessarily( not( X ) ) ) }.
% 0.39/1.07 { ! op_necessarily, necessarily( X ) = not( possibly( not( X ) ) ) }.
% 0.39/1.07 { ! op_strict_implies, strict_implies( X, Y ) = necessarily( implies( X, Y
% 0.39/1.07 ) ) }.
% 0.39/1.07 { ! op_strict_equiv, strict_equiv( X, Y ) = and( strict_implies( X, Y ),
% 0.39/1.07 strict_implies( Y, X ) ) }.
% 0.39/1.07 { op_possibly }.
% 0.39/1.07 { necessitation }.
% 0.39/1.07 { axiom_K }.
% 0.39/1.07 { axiom_M }.
% 0.39/1.07 { axiom_4 }.
% 0.39/1.07 { axiom_B }.
% 0.39/1.07 { op_possibly }.
% 0.39/1.07 { op_or }.
% 0.39/1.07 { op_implies }.
% 0.39/1.07 { op_strict_implies }.
% 0.39/1.07 { op_equiv }.
% 0.39/1.07 { op_strict_equiv }.
% 0.39/1.07 { ! axiom_m2 }.
% 0.39/1.07
% 0.39/1.07 percentage equality = 0.046263, percentage horn = 0.960000
% 0.39/1.07 This is a problem with some equality
% 0.39/1.07
% 0.39/1.07
% 0.39/1.07
% 0.39/1.07 Options Used:
% 0.39/1.07
% 0.39/1.07 useres = 1
% 0.39/1.07 useparamod = 1
% 0.39/1.07 useeqrefl = 1
% 0.39/1.07 useeqfact = 1
% 0.39/1.07 usefactor = 1
% 0.39/1.07 usesimpsplitting = 0
% 0.39/1.07 usesimpdemod = 5
% 0.39/1.07 usesimpres = 3
% 0.39/1.07
% 0.39/1.07 resimpinuse = 1000
% 0.39/1.07 resimpclauses = 20000
% 0.39/1.07 substype = eqrewr
% 0.39/1.07 backwardsubs = 1
% 0.39/1.07 selectoldest = 5
% 0.39/1.07
% 0.39/1.07 litorderings [0] = split
% 0.39/1.07 litorderings [1] = extend the termordering, first sorting on arguments
% 0.39/1.07
% 0.39/1.07 termordering = kbo
% 0.39/1.07
% 0.39/1.07 litapriori = 0
% 0.39/1.07 termapriori = 1
% 0.39/1.07 litaposteriori = 0
% 0.39/1.07 termaposteriori = 0
% 0.39/1.07 demodaposteriori = 0
% 0.39/1.07 ordereqreflfact = 0
% 0.39/1.07
% 0.39/1.07 litselect = negord
% 0.39/1.07
% 0.39/1.07 maxweight = 15
% 0.39/1.07 maxdepth = 30000
% 0.39/1.07 maxlength = 115
% 0.39/1.07 maxnrvars = 195
% 0.39/1.07 excuselevel = 1
% 0.39/1.07 increasemaxweight = 1
% 0.39/1.07
% 0.39/1.07 maxselected = 10000000
% 0.39/1.07 maxnrclauses = 10000000
% 0.39/1.07
% 0.39/1.07 showgenerated = 0
% 0.39/1.07 showkept = 0
% 0.39/1.07 showselected = 0
% 0.39/1.07 showdeleted = 0
% 0.39/1.07 showresimp = 1
% 0.39/1.07 showstatus = 2000
% 0.39/1.07
% 0.39/1.07 prologoutput = 0
% 0.39/1.07 nrgoals = 5000000
% 0.39/1.07 totalproof = 1
% 0.39/1.07
% 0.39/1.07 Symbols occurring in the translation:
% 0.39/1.07
% 0.39/1.07 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.39/1.07 . [1, 2] (w:1, o:176, a:1, s:1, b:0),
% 0.39/1.07 ! [4, 1] (w:0, o:163, a:1, s:1, b:0),
% 0.39/1.07 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.39/1.07 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.39/1.07 modus_ponens [35, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.39/1.07 is_a_theorem [38, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.39/1.07 implies [39, 2] (w:1, o:200, a:1, s:1, b:0),
% 0.39/1.07 substitution_of_equivalents [40, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.39/1.07 equiv [41, 2] (w:1, o:201, a:1, s:1, b:0),
% 0.39/1.07 modus_tollens [42, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.39/1.07 not [43, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.39/1.07 implies_1 [44, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.39/1.07 implies_2 [45, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.39/1.07 implies_3 [46, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.39/1.07 and_1 [48, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.39/1.07 and [49, 2] (w:1, o:202, a:1, s:1, b:0),
% 0.39/1.07 and_2 [50, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.39/1.07 and_3 [51, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.39/1.07 or_1 [52, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.39/1.07 or [53, 2] (w:1, o:203, a:1, s:1, b:0),
% 0.39/1.07 or_2 [54, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.39/1.07 or_3 [55, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.39/1.07 equivalence_1 [56, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.39/1.07 equivalence_2 [57, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.39/1.07 equivalence_3 [58, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.39/1.07 kn1 [59, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.39/1.07 kn2 [61, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.39/1.07 kn3 [63, 0] (w:1, o:35, a:1, s:1, b:0),
% 0.39/1.07 cn1 [65, 0] (w:1, o:37, a:1, s:1, b:0),
% 0.39/1.07 cn2 [66, 0] (w:1, o:38, a:1, s:1, b:0),
% 0.39/1.07 cn3 [67, 0] (w:1, o:39, a:1, s:1, b:0),
% 0.39/1.07 r1 [68, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.39/1.07 r2 [69, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.39/1.07 r3 [70, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.39/1.07 r4 [71, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.39/1.07 r5 [72, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.39/1.07 op_or [73, 0] (w:1, o:41, a:1, s:1, b:0),
% 0.39/1.07 op_and [74, 0] (w:1, o:42, a:1, s:1, b:0),
% 0.39/1.07 op_implies_and [75, 0] (w:1, o:43, a:1, s:1, b:0),
% 0.39/1.07 op_implies_or [76, 0] (w:1, o:44, a:1, s:1, b:0),
% 0.39/1.07 op_equiv [77, 0] (w:1, o:45, a:1, s:1, b:0),
% 0.39/1.07 necessitation [78, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.39/1.07 necessarily [79, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.39/1.07 modus_ponens_strict_implies [80, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.39/1.07 strict_implies [81, 2] (w:1, o:204, a:1, s:1, b:0),
% 0.39/1.07 adjunction [82, 0] (w:1, o:46, a:1, s:1, b:0),
% 0.39/1.07 substitution_strict_equiv [83, 0] (w:1, o:47, a:1, s:1, b:0),
% 0.39/1.07 strict_equiv [84, 2] (w:1, o:205, a:1, s:1, b:0),
% 0.39/1.07 axiom_K [85, 0] (w:1, o:48, a:1, s:1, b:0),
% 0.39/1.07 axiom_M [86, 0] (w:1, o:49, a:1, s:1, b:0),
% 0.39/1.07 axiom_4 [87, 0] (w:1, o:50, a:1, s:1, b:0),
% 0.39/1.07 axiom_B [88, 0] (w:1, o:51, a:1, s:1, b:0),
% 0.39/1.07 possibly [89, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.39/1.07 axiom_5 [90, 0] (w:1, o:52, a:1, s:1, b:0),
% 0.39/1.07 axiom_s1 [91, 0] (w:1, o:53, a:1, s:1, b:0),
% 0.39/1.07 axiom_s2 [92, 0] (w:1, o:54, a:1, s:1, b:0),
% 0.39/1.07 axiom_s3 [93, 0] (w:1, o:55, a:1, s:1, b:0),
% 0.39/1.07 axiom_s4 [94, 0] (w:1, o:56, a:1, s:1, b:0),
% 0.39/1.07 axiom_m1 [95, 0] (w:1, o:57, a:1, s:1, b:0),
% 0.39/1.07 axiom_m2 [96, 0] (w:1, o:59, a:1, s:1, b:0),
% 0.39/1.07 axiom_m3 [97, 0] (w:1, o:60, a:1, s:1, b:0),
% 0.39/1.07 axiom_m4 [98, 0] (w:1, o:61, a:1, s:1, b:0),
% 0.39/1.07 axiom_m5 [99, 0] (w:1, o:62, a:1, s:1, b:0),
% 0.39/1.07 axiom_m6 [100, 0] (w:1, o:63, a:1, s:1, b:0),
% 0.39/1.07 axiom_m7 [101, 0] (w:1, o:64, a:1, s:1, b:0),
% 0.39/1.07 axiom_m8 [102, 0] (w:1, o:65, a:1, s:1, b:0),
% 0.39/1.07 axiom_m9 [103, 0] (w:1, o:66, a:1, s:1, b:0),
% 0.39/1.07 axiom_m10 [104, 0] (w:1, o:58, a:1, s:1, b:0),
% 0.39/1.07 op_possibly [105, 0] (w:1, o:67, a:1, s:1, b:0),
% 0.39/1.07 op_necessarily [106, 0] (w:1, o:40, a:1, s:1, b:0),
% 0.39/1.07 op_strict_implies [107, 0] (w:1, o:68, a:1, s:1, b:0),
% 0.39/1.07 op_strict_equiv [108, 0] (w:1, o:69, a:1, s:1, b:0),
% 0.39/1.07 op_implies [109, 0] (w:1, o:70, a:1, s:1, b:0),
% 0.39/1.07 alpha1 [110, 1] (w:1, o:172, a:1, s:1, b:1),
% 0.39/1.07 alpha2 [111, 1] (w:1, o:173, a:1, s:1, b:1),
% 0.39/1.07 alpha3 [112, 2] (w:1, o:206, a:1, s:1, b:1),
% 0.39/1.07 skol1 [113, 0] (w:1, o:71, a:1, s:1, b:1),
% 0.39/1.07 skol2 [114, 1] (w:1, o:174, a:1, s:1, b:1),
% 1.47/1.87 skol3 [115, 0] (w:1, o:82, a:1, s:1, b:1),
% 1.47/1.87 skol4 [116, 0] (w:1, o:92, a:1, s:1, b:1),
% 1.47/1.87 skol5 [117, 0] (w:1, o:103, a:1, s:1, b:1),
% 1.47/1.87 skol6 [118, 0] (w:1, o:114, a:1, s:1, b:1),
% 1.47/1.87 skol7 [119, 0] (w:1, o:125, a:1, s:1, b:1),
% 1.47/1.87 skol8 [120, 0] (w:1, o:136, a:1, s:1, b:1),
% 1.47/1.87 skol9 [121, 0] (w:1, o:147, a:1, s:1, b:1),
% 1.47/1.87 skol10 [122, 0] (w:1, o:148, a:1, s:1, b:1),
% 1.47/1.87 skol11 [123, 0] (w:1, o:149, a:1, s:1, b:1),
% 1.47/1.87 skol12 [124, 0] (w:1, o:150, a:1, s:1, b:1),
% 1.47/1.87 skol13 [125, 0] (w:1, o:151, a:1, s:1, b:1),
% 1.47/1.87 skol14 [126, 0] (w:1, o:152, a:1, s:1, b:1),
% 1.47/1.87 skol15 [127, 0] (w:1, o:153, a:1, s:1, b:1),
% 1.47/1.87 skol16 [128, 0] (w:1, o:154, a:1, s:1, b:1),
% 1.47/1.87 skol17 [129, 0] (w:1, o:155, a:1, s:1, b:1),
% 1.47/1.87 skol18 [130, 0] (w:1, o:156, a:1, s:1, b:1),
% 1.47/1.87 skol19 [131, 0] (w:1, o:157, a:1, s:1, b:1),
% 1.47/1.87 skol20 [132, 0] (w:1, o:72, a:1, s:1, b:1),
% 1.47/1.87 skol21 [133, 0] (w:1, o:73, a:1, s:1, b:1),
% 1.47/1.87 skol22 [134, 0] (w:1, o:74, a:1, s:1, b:1),
% 1.47/1.87 skol23 [135, 0] (w:1, o:75, a:1, s:1, b:1),
% 1.47/1.87 skol24 [136, 0] (w:1, o:76, a:1, s:1, b:1),
% 1.47/1.87 skol25 [137, 0] (w:1, o:77, a:1, s:1, b:1),
% 1.47/1.87 skol26 [138, 0] (w:1, o:78, a:1, s:1, b:1),
% 1.47/1.87 skol27 [139, 0] (w:1, o:79, a:1, s:1, b:1),
% 1.47/1.87 skol28 [140, 0] (w:1, o:80, a:1, s:1, b:1),
% 1.47/1.87 skol29 [141, 0] (w:1, o:81, a:1, s:1, b:1),
% 1.47/1.87 skol30 [142, 1] (w:1, o:175, a:1, s:1, b:1),
% 1.47/1.87 skol31 [143, 0] (w:1, o:83, a:1, s:1, b:1),
% 1.47/1.87 skol32 [144, 0] (w:1, o:84, a:1, s:1, b:1),
% 1.47/1.87 skol33 [145, 0] (w:1, o:85, a:1, s:1, b:1),
% 1.47/1.87 skol34 [146, 0] (w:1, o:86, a:1, s:1, b:1),
% 1.47/1.87 skol35 [147, 0] (w:1, o:87, a:1, s:1, b:1),
% 1.47/1.87 skol36 [148, 0] (w:1, o:88, a:1, s:1, b:1),
% 1.47/1.87 skol37 [149, 0] (w:1, o:89, a:1, s:1, b:1),
% 1.47/1.87 skol38 [150, 0] (w:1, o:90, a:1, s:1, b:1),
% 1.47/1.87 skol39 [151, 0] (w:1, o:91, a:1, s:1, b:1),
% 1.47/1.87 skol40 [152, 0] (w:1, o:93, a:1, s:1, b:1),
% 1.47/1.87 skol41 [153, 0] (w:1, o:94, a:1, s:1, b:1),
% 1.47/1.87 skol42 [154, 0] (w:1, o:95, a:1, s:1, b:1),
% 1.47/1.87 skol43 [155, 0] (w:1, o:96, a:1, s:1, b:1),
% 1.47/1.87 skol44 [156, 0] (w:1, o:97, a:1, s:1, b:1),
% 1.47/1.87 skol45 [157, 0] (w:1, o:98, a:1, s:1, b:1),
% 1.47/1.87 skol46 [158, 0] (w:1, o:99, a:1, s:1, b:1),
% 1.47/1.87 skol47 [159, 0] (w:1, o:100, a:1, s:1, b:1),
% 1.47/1.87 skol48 [160, 0] (w:1, o:101, a:1, s:1, b:1),
% 1.47/1.87 skol49 [161, 0] (w:1, o:102, a:1, s:1, b:1),
% 1.47/1.87 skol50 [162, 0] (w:1, o:104, a:1, s:1, b:1),
% 1.47/1.87 skol51 [163, 0] (w:1, o:105, a:1, s:1, b:1),
% 1.47/1.87 skol52 [164, 0] (w:1, o:106, a:1, s:1, b:1),
% 1.47/1.87 skol53 [165, 0] (w:1, o:107, a:1, s:1, b:1),
% 1.47/1.87 skol54 [166, 0] (w:1, o:108, a:1, s:1, b:1),
% 1.47/1.87 skol55 [167, 0] (w:1, o:109, a:1, s:1, b:1),
% 1.47/1.87 skol56 [168, 0] (w:1, o:110, a:1, s:1, b:1),
% 1.47/1.87 skol57 [169, 0] (w:1, o:111, a:1, s:1, b:1),
% 1.47/1.87 skol58 [170, 0] (w:1, o:112, a:1, s:1, b:1),
% 1.47/1.87 skol59 [171, 0] (w:1, o:113, a:1, s:1, b:1),
% 1.47/1.87 skol60 [172, 0] (w:1, o:115, a:1, s:1, b:1),
% 1.47/1.87 skol61 [173, 0] (w:1, o:116, a:1, s:1, b:1),
% 1.47/1.87 skol62 [174, 0] (w:1, o:117, a:1, s:1, b:1),
% 1.47/1.87 skol63 [175, 0] (w:1, o:118, a:1, s:1, b:1),
% 1.47/1.87 skol64 [176, 0] (w:1, o:119, a:1, s:1, b:1),
% 1.47/1.87 skol65 [177, 0] (w:1, o:120, a:1, s:1, b:1),
% 1.47/1.87 skol66 [178, 0] (w:1, o:121, a:1, s:1, b:1),
% 1.47/1.87 skol67 [179, 0] (w:1, o:122, a:1, s:1, b:1),
% 1.47/1.87 skol68 [180, 0] (w:1, o:123, a:1, s:1, b:1),
% 1.47/1.87 skol69 [181, 0] (w:1, o:124, a:1, s:1, b:1),
% 1.47/1.87 skol70 [182, 0] (w:1, o:126, a:1, s:1, b:1),
% 1.47/1.87 skol71 [183, 0] (w:1, o:127, a:1, s:1, b:1),
% 1.47/1.87 skol72 [184, 0] (w:1, o:128, a:1, s:1, b:1),
% 1.47/1.87 skol73 [185, 0] (w:1, o:129, a:1, s:1, b:1),
% 1.47/1.87 skol74 [186, 0] (w:1, o:130, a:1, s:1, b:1),
% 1.47/1.87 skol75 [187, 0] (w:1, o:131, a:1, s:1, b:1),
% 1.47/1.87 skol76 [188, 0] (w:1, o:132, a:1, s:1, b:1),
% 1.47/1.87 skol77 [189, 0] (w:1, o:133, a:1, s:1, b:1),
% 1.47/1.87 skol78 [190, 0] (w:1, o:134, a:1, s:1, b:1),
% 1.47/1.87 skol79 [191, 0] (w:1, o:135, a:1, s:1, b:1),
% 1.47/1.87 skol80 [192, 0] (w:1, o:137, a:1, s:1, b:1),
% 1.47/1.87 skol81 [193, 0] (w:1, o:138, a:1, s:1, b:1),
% 1.47/1.87 skol82 [194, 0] (w:1, o:139, a:1, s:1, b:1),
% 1.47/1.87 skol83 [195, 0] (w:1, o:140, a:1, s:1, b:1),
% 1.47/1.87 skol84 [196, 0] (w:1, o:141, a:1, s:1, b:1),
% 1.47/1.87 skol85 [197, 0] (w:1, o:142, a:1, s:1, b:1),
% 1.47/1.87 skol86 [198, 0] (w:1, o:143, a:1, s:1, b:1),
% 1.47/1.87 skol87 [199, 0] (w:1, o:144, a:1, s:1, b:1),
% 1.47/1.87 skol88 [200, 0] (w:1, o:145, a:1, s:1, b:1),
% 1.47/1.87 skol89 [201, 0] (w:1, o:146, a:1, s:1, b:1),
% 1.47/1.87 skol90 [202, 0] (w:1, o:158, a:1, s:1, b:1),
% 1.47/1.87 skol91 [203, 0] (w:1, o:159, a:1, s:1, b:1),
% 1.47/1.87 skol92 [204, 0] (w:1, o:160, a:1, s:1, b:1),
% 1.47/1.87 skol93 [205, 0] (w:1, o:161, a:1, s:1, b:1),
% 1.47/1.87 skol94 [206, 0] (w:1, o:162, a:1, s:1, b:1).
% 1.47/1.87
% 1.47/1.87
% 1.47/1.87 Starting Search:
% 1.47/1.87
% 1.47/1.87 *** allocated 15000 integers for clauses
% 1.47/1.87 *** allocated 22500 integers for clauses
% 1.47/1.87 *** allocated 33750 integers for clauses
% 1.47/1.87 *** allocated 50625 integers for clauses
% 1.47/1.87 *** allocated 15000 integers for termspace/termends
% 1.47/1.87 *** allocated 75937 integers for clauses
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87 *** allocated 22500 integers for termspace/termends
% 1.47/1.87 *** allocated 113905 integers for clauses
% 1.47/1.87
% 1.47/1.87 Intermediate Status:
% 1.47/1.87 Generated: 4131
% 1.47/1.87 Kept: 2003
% 1.47/1.87 Inuse: 279
% 1.47/1.87 Deleted: 53
% 1.47/1.87 Deletedinuse: 6
% 1.47/1.87
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87 *** allocated 33750 integers for termspace/termends
% 1.47/1.87 *** allocated 170857 integers for clauses
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87 *** allocated 50625 integers for termspace/termends
% 1.47/1.87 *** allocated 256285 integers for clauses
% 1.47/1.87
% 1.47/1.87 Intermediate Status:
% 1.47/1.87 Generated: 8038
% 1.47/1.87 Kept: 4004
% 1.47/1.87 Inuse: 381
% 1.47/1.87 Deleted: 63
% 1.47/1.87 Deletedinuse: 7
% 1.47/1.87
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87 *** allocated 75937 integers for termspace/termends
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87 *** allocated 384427 integers for clauses
% 1.47/1.87
% 1.47/1.87 Intermediate Status:
% 1.47/1.87 Generated: 12505
% 1.47/1.87 Kept: 6014
% 1.47/1.87 Inuse: 492
% 1.47/1.87 Deleted: 75
% 1.47/1.87 Deletedinuse: 8
% 1.47/1.87
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87 *** allocated 113905 integers for termspace/termends
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87 *** allocated 576640 integers for clauses
% 1.47/1.87
% 1.47/1.87 Intermediate Status:
% 1.47/1.87 Generated: 16132
% 1.47/1.87 Kept: 8066
% 1.47/1.87 Inuse: 531
% 1.47/1.87 Deleted: 82
% 1.47/1.87 Deletedinuse: 12
% 1.47/1.87
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87 *** allocated 170857 integers for termspace/termends
% 1.47/1.87
% 1.47/1.87 Intermediate Status:
% 1.47/1.87 Generated: 19012
% 1.47/1.87 Kept: 10076
% 1.47/1.87 Inuse: 569
% 1.47/1.87 Deleted: 84
% 1.47/1.87 Deletedinuse: 12
% 1.47/1.87
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87
% 1.47/1.87 Intermediate Status:
% 1.47/1.87 Generated: 22215
% 1.47/1.87 Kept: 12076
% 1.47/1.87 Inuse: 606
% 1.47/1.87 Deleted: 84
% 1.47/1.87 Deletedinuse: 12
% 1.47/1.87
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87 *** allocated 864960 integers for clauses
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87
% 1.47/1.87 Intermediate Status:
% 1.47/1.87 Generated: 26912
% 1.47/1.87 Kept: 14116
% 1.47/1.87 Inuse: 670
% 1.47/1.87 Deleted: 84
% 1.47/1.87 Deletedinuse: 12
% 1.47/1.87
% 1.47/1.87 *** allocated 256285 integers for termspace/termends
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87
% 1.47/1.87 Intermediate Status:
% 1.47/1.87 Generated: 30546
% 1.47/1.87 Kept: 16116
% 1.47/1.87 Inuse: 720
% 1.47/1.87 Deleted: 277
% 1.47/1.87 Deletedinuse: 202
% 1.47/1.87
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87 Resimplifying inuse:
% 1.47/1.87 Done
% 1.47/1.87
% 1.47/1.87
% 1.47/1.87 Intermediate Status:
% 1.47/1.87 Generated: 34171
% 1.47/1.87 Kept: 18122
% 1.47/1.87 Inuse: 794
% 1.47/1.87 Deleted: 284
% 1.47/1.87 Deletedinuse: 204
% 1.47/1.88
% 1.47/1.88 Resimplifying inuse:
% 1.47/1.88 Done
% 1.47/1.88
% 1.47/1.88 Resimplifying clauses:
% 1.47/1.88
% 1.47/1.88 Bliksems!, er is een bewijs:
% 1.47/1.88 % SZS status Theorem
% 1.47/1.88 % SZS output start Refutation
% 1.47/1.88
% 1.47/1.88 (0) {G0,W5,D2,L3,V1,M3} I { ! modus_ponens, ! alpha1( X ), is_a_theorem( X
% 1.47/1.88 ) }.
% 1.47/1.88 (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem( implies( Y
% 1.47/1.88 , X ) ), alpha1( X ) }.
% 1.47/1.88 (11) {G0,W7,D4,L2,V2,M2} I { ! implies_1, is_a_theorem( implies( X, implies
% 1.47/1.88 ( Y, X ) ) ) }.
% 1.47/1.88 (17) {G0,W7,D4,L2,V2,M2} I { ! and_1, is_a_theorem( implies( and( X, Y ), X
% 1.47/1.88 ) ) }.
% 1.47/1.88 (65) {G0,W1,D1,L1,V0,M1} I { modus_ponens }.
% 1.47/1.88 (67) {G0,W1,D1,L1,V0,M1} I { implies_1 }.
% 1.47/1.88 (70) {G0,W1,D1,L1,V0,M1} I { and_1 }.
% 1.47/1.88 (80) {G0,W6,D3,L3,V1,M3} I { ! necessitation, ! is_a_theorem( X ),
% 1.47/1.88 is_a_theorem( necessarily( X ) ) }.
% 1.47/1.88 (83) {G0,W5,D2,L3,V1,M3} I { ! modus_ponens_strict_implies, ! alpha2( X ),
% 1.47/1.88 is_a_theorem( X ) }.
% 1.47/1.88 (84) {G0,W3,D2,L2,V0,M2} I { alpha2( skol29 ), modus_ponens_strict_implies
% 1.47/1.88 }.
% 1.47/1.88 (85) {G0,W3,D2,L2,V0,M2} I { ! is_a_theorem( skol29 ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 (86) {G0,W5,D3,L2,V2,M2} I { ! alpha2( X ), is_a_theorem( skol30( Y ) ) }.
% 1.47/1.88 (87) {G0,W7,D4,L2,V1,M2} I { ! alpha2( X ), is_a_theorem( strict_implies(
% 1.47/1.88 skol30( X ), X ) ) }.
% 1.47/1.88 (88) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem(
% 1.47/1.88 strict_implies( Y, X ) ), alpha2( X ) }.
% 1.47/1.88 (100) {G0,W6,D4,L2,V1,M2} I { ! axiom_M, is_a_theorem( implies( necessarily
% 1.47/1.88 ( X ), X ) ) }.
% 1.47/1.88 (119) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( strict_implies( and( skol43,
% 1.47/1.88 skol81 ), skol43 ) ), axiom_m2 }.
% 1.47/1.88 (138) {G0,W9,D4,L2,V2,M2} I { ! op_strict_implies, necessarily( implies( X
% 1.47/1.88 , Y ) ) ==> strict_implies( X, Y ) }.
% 1.47/1.88 (141) {G0,W1,D1,L1,V0,M1} I { necessitation }.
% 1.47/1.88 (143) {G0,W1,D1,L1,V0,M1} I { axiom_M }.
% 1.47/1.88 (147) {G0,W1,D1,L1,V0,M1} I { op_strict_implies }.
% 1.47/1.88 (149) {G0,W1,D1,L1,V0,M1} I { ! axiom_m2 }.
% 1.47/1.88 (151) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ), is_a_theorem( X ) }.
% 1.47/1.88 (157) {G2,W3,D2,L2,V0,M2} R(151,85) { ! alpha1( skol29 ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 (161) {G3,W7,D3,L3,V1,M3} R(157,5) { modus_ponens_strict_implies, !
% 1.47/1.88 is_a_theorem( X ), ! is_a_theorem( implies( X, skol29 ) ) }.
% 1.47/1.88 (180) {G1,W6,D4,L1,V2,M1} S(11);r(67) { is_a_theorem( implies( X, implies(
% 1.47/1.88 Y, X ) ) ) }.
% 1.47/1.88 (191) {G1,W4,D3,L2,V1,M2} R(86,84) { is_a_theorem( skol30( X ) ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 (220) {G1,W5,D3,L2,V1,M2} S(80);r(141) { ! is_a_theorem( X ), is_a_theorem
% 1.47/1.88 ( necessarily( X ) ) }.
% 1.47/1.88 (234) {G2,W5,D3,L2,V1,M2} R(220,151) { is_a_theorem( necessarily( X ) ), !
% 1.47/1.88 alpha1( X ) }.
% 1.47/1.88 (247) {G3,W9,D3,L3,V2,M3} R(234,5) { is_a_theorem( necessarily( X ) ), !
% 1.47/1.88 is_a_theorem( Y ), ! is_a_theorem( implies( Y, X ) ) }.
% 1.47/1.88 (254) {G1,W6,D4,L1,V2,M1} S(17);r(70) { is_a_theorem( implies( and( X, Y )
% 1.47/1.88 , X ) ) }.
% 1.47/1.88 (663) {G2,W6,D3,L2,V2,M2} R(180,5) { ! is_a_theorem( X ), alpha1( implies(
% 1.47/1.88 Y, X ) ) }.
% 1.47/1.88 (714) {G3,W6,D3,L2,V2,M2} R(663,151) { ! is_a_theorem( X ), is_a_theorem(
% 1.47/1.88 implies( Y, X ) ) }.
% 1.47/1.88 (814) {G4,W6,D2,L3,V2,M3} R(714,5) { ! is_a_theorem( X ), ! is_a_theorem( Y
% 1.47/1.88 ), alpha1( X ) }.
% 1.47/1.88 (815) {G5,W4,D2,L2,V1,M2} F(814) { ! is_a_theorem( X ), alpha1( X ) }.
% 1.47/1.88 (822) {G6,W6,D4,L1,V2,M1} R(815,254) { alpha1( implies( and( X, Y ), X ) )
% 1.47/1.88 }.
% 1.47/1.88 (839) {G6,W5,D2,L3,V1,M3} R(815,83) { alpha1( X ), !
% 1.47/1.88 modus_ponens_strict_implies, ! alpha2( X ) }.
% 1.47/1.88 (2662) {G1,W5,D4,L1,V1,M1} S(100);r(143) { is_a_theorem( implies(
% 1.47/1.88 necessarily( X ), X ) ) }.
% 1.47/1.88 (2691) {G2,W5,D3,L2,V1,M2} R(2662,5) { ! is_a_theorem( necessarily( X ) ),
% 1.47/1.88 alpha1( X ) }.
% 1.47/1.88 (2747) {G3,W5,D3,L2,V1,M2} R(2691,151) { ! is_a_theorem( necessarily( X ) )
% 1.47/1.88 , is_a_theorem( X ) }.
% 1.47/1.88 (4041) {G1,W6,D4,L1,V0,M1} S(119);r(149) { ! is_a_theorem( strict_implies(
% 1.47/1.88 and( skol43, skol81 ), skol43 ) ) }.
% 1.47/1.88 (5677) {G1,W8,D4,L1,V2,M1} S(138);r(147) { necessarily( implies( X, Y ) )
% 1.47/1.88 ==> strict_implies( X, Y ) }.
% 1.47/1.88 (7311) {G4,W6,D4,L2,V1,M2} R(161,191);f { modus_ponens_strict_implies, !
% 1.47/1.88 is_a_theorem( implies( skol30( X ), skol29 ) ) }.
% 1.47/1.88 (14401) {G2,W6,D4,L1,V0,M1} R(4041,151) { ! alpha1( strict_implies( and(
% 1.47/1.88 skol43, skol81 ), skol43 ) ) }.
% 1.47/1.88 (15551) {G5,W6,D4,L2,V1,M2} R(7311,2747);d(5677) {
% 1.47/1.88 modus_ponens_strict_implies, ! is_a_theorem( strict_implies( skol30( X )
% 1.47/1.88 , skol29 ) ) }.
% 1.47/1.88 (15618) {G6,W1,D1,L1,V0,M1} R(15551,87);r(84) { modus_ponens_strict_implies
% 1.47/1.88 }.
% 1.47/1.88 (15675) {G7,W4,D2,L2,V1,M2} R(15618,839) { alpha1( X ), ! alpha2( X ) }.
% 1.47/1.88 (15688) {G8,W6,D4,L1,V0,M1} R(15675,14401) { ! alpha2( strict_implies( and
% 1.47/1.88 ( skol43, skol81 ), skol43 ) ) }.
% 1.47/1.88 (17581) {G4,W6,D3,L2,V2,M2} R(247,180);d(5677) { ! is_a_theorem( Y ),
% 1.47/1.88 is_a_theorem( strict_implies( X, Y ) ) }.
% 1.47/1.88 (17750) {G5,W6,D2,L3,V2,M3} R(17581,88) { ! is_a_theorem( X ), !
% 1.47/1.88 is_a_theorem( Y ), alpha2( X ) }.
% 1.47/1.88 (17815) {G6,W4,D2,L2,V1,M2} F(17750) { ! is_a_theorem( X ), alpha2( X ) }.
% 1.47/1.88 (18096) {G7,W5,D3,L2,V1,M2} R(17815,234) { alpha2( necessarily( X ) ), !
% 1.47/1.88 alpha1( X ) }.
% 1.47/1.88 (19852) {G8,W6,D4,L1,V2,M1} R(18096,822);d(5677) { alpha2( strict_implies(
% 1.47/1.88 and( X, Y ), X ) ) }.
% 1.47/1.88 (20001) {G9,W0,D0,L0,V0,M0} S(15688);r(19852) { }.
% 1.47/1.88
% 1.47/1.88
% 1.47/1.88 % SZS output end Refutation
% 1.47/1.88 found a proof!
% 1.47/1.88
% 1.47/1.88
% 1.47/1.88 Unprocessed initial clauses:
% 1.47/1.88
% 1.47/1.88 (20003) {G0,W5,D2,L3,V1,M3} { ! modus_ponens, ! alpha1( X ), is_a_theorem
% 1.47/1.88 ( X ) }.
% 1.47/1.88 (20004) {G0,W3,D2,L2,V0,M2} { alpha1( skol1 ), modus_ponens }.
% 1.47/1.88 (20005) {G0,W3,D2,L2,V0,M2} { ! is_a_theorem( skol1 ), modus_ponens }.
% 1.47/1.88 (20006) {G0,W5,D3,L2,V2,M2} { ! alpha1( X ), is_a_theorem( skol2( Y ) )
% 1.47/1.88 }.
% 1.47/1.88 (20007) {G0,W7,D4,L2,V1,M2} { ! alpha1( X ), is_a_theorem( implies( skol2
% 1.47/1.88 ( X ), X ) ) }.
% 1.47/1.88 (20008) {G0,W8,D3,L3,V2,M3} { ! is_a_theorem( Y ), ! is_a_theorem( implies
% 1.47/1.88 ( Y, X ) ), alpha1( X ) }.
% 1.47/1.88 (20009) {G0,W8,D3,L3,V2,M3} { ! substitution_of_equivalents, !
% 1.47/1.88 is_a_theorem( equiv( X, Y ) ), X = Y }.
% 1.47/1.88 (20010) {G0,W5,D3,L2,V0,M2} { is_a_theorem( equiv( skol3, skol52 ) ),
% 1.47/1.88 substitution_of_equivalents }.
% 1.47/1.88 (20011) {G0,W4,D2,L2,V0,M2} { ! skol3 = skol52,
% 1.47/1.88 substitution_of_equivalents }.
% 1.47/1.88 (20012) {G0,W11,D5,L2,V2,M2} { ! modus_tollens, is_a_theorem( implies(
% 1.47/1.88 implies( not( Y ), not( X ) ), implies( X, Y ) ) ) }.
% 1.47/1.88 (20013) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( not(
% 1.47/1.88 skol53 ), not( skol4 ) ), implies( skol4, skol53 ) ) ), modus_tollens }.
% 1.47/1.88 (20014) {G0,W7,D4,L2,V2,M2} { ! implies_1, is_a_theorem( implies( X,
% 1.47/1.88 implies( Y, X ) ) ) }.
% 1.47/1.88 (20015) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol5, implies(
% 1.47/1.88 skol54, skol5 ) ) ), implies_1 }.
% 1.47/1.88 (20016) {G0,W11,D5,L2,V2,M2} { ! implies_2, is_a_theorem( implies( implies
% 1.47/1.88 ( X, implies( X, Y ) ), implies( X, Y ) ) ) }.
% 1.47/1.88 (20017) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol6,
% 1.47/1.88 implies( skol6, skol55 ) ), implies( skol6, skol55 ) ) ), implies_2 }.
% 1.47/1.88 (20018) {G0,W13,D5,L2,V3,M2} { ! implies_3, is_a_theorem( implies( implies
% 1.47/1.88 ( X, Y ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 1.47/1.88 (20019) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol7,
% 1.47/1.88 skol56 ), implies( implies( skol56, skol86 ), implies( skol7, skol86 ) )
% 1.47/1.88 ) ), implies_3 }.
% 1.47/1.88 (20020) {G0,W7,D4,L2,V2,M2} { ! and_1, is_a_theorem( implies( and( X, Y )
% 1.47/1.88 , X ) ) }.
% 1.47/1.88 (20021) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol8, skol57
% 1.47/1.88 ), skol8 ) ), and_1 }.
% 1.47/1.88 (20022) {G0,W7,D4,L2,V2,M2} { ! and_2, is_a_theorem( implies( and( X, Y )
% 1.47/1.88 , Y ) ) }.
% 1.47/1.88 (20023) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol9, skol58
% 1.47/1.88 ), skol58 ) ), and_2 }.
% 1.47/1.88 (20024) {G0,W9,D5,L2,V2,M2} { ! and_3, is_a_theorem( implies( X, implies(
% 1.47/1.88 Y, and( X, Y ) ) ) ) }.
% 1.47/1.88 (20025) {G0,W9,D5,L2,V0,M2} { ! is_a_theorem( implies( skol10, implies(
% 1.47/1.88 skol59, and( skol10, skol59 ) ) ) ), and_3 }.
% 1.47/1.88 (20026) {G0,W7,D4,L2,V2,M2} { ! or_1, is_a_theorem( implies( X, or( X, Y )
% 1.47/1.88 ) ) }.
% 1.47/1.88 (20027) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol11, or( skol11
% 1.47/1.88 , skol60 ) ) ), or_1 }.
% 1.47/1.88 (20028) {G0,W7,D4,L2,V2,M2} { ! or_2, is_a_theorem( implies( Y, or( X, Y )
% 1.47/1.88 ) ) }.
% 1.47/1.88 (20029) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol61, or( skol12
% 1.47/1.88 , skol61 ) ) ), or_2 }.
% 1.47/1.88 (20030) {G0,W15,D6,L2,V3,M2} { ! or_3, is_a_theorem( implies( implies( X,
% 1.47/1.88 Z ), implies( implies( Y, Z ), implies( or( X, Y ), Z ) ) ) ) }.
% 1.47/1.88 (20031) {G0,W15,D6,L2,V0,M2} { ! is_a_theorem( implies( implies( skol13,
% 1.47/1.88 skol87 ), implies( implies( skol62, skol87 ), implies( or( skol13, skol62
% 1.47/1.88 ), skol87 ) ) ) ), or_3 }.
% 1.47/1.88 (20032) {G0,W9,D4,L2,V2,M2} { ! equivalence_1, is_a_theorem( implies(
% 1.47/1.88 equiv( X, Y ), implies( X, Y ) ) ) }.
% 1.47/1.88 (20033) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( equiv( skol14,
% 1.47/1.88 skol63 ), implies( skol14, skol63 ) ) ), equivalence_1 }.
% 1.47/1.88 (20034) {G0,W9,D4,L2,V2,M2} { ! equivalence_2, is_a_theorem( implies(
% 1.47/1.88 equiv( X, Y ), implies( Y, X ) ) ) }.
% 1.47/1.88 (20035) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( equiv( skol15,
% 1.47/1.88 skol64 ), implies( skol64, skol15 ) ) ), equivalence_2 }.
% 1.47/1.88 (20036) {G0,W13,D5,L2,V2,M2} { ! equivalence_3, is_a_theorem( implies(
% 1.47/1.88 implies( X, Y ), implies( implies( Y, X ), equiv( X, Y ) ) ) ) }.
% 1.47/1.88 (20037) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol16,
% 1.47/1.88 skol65 ), implies( implies( skol65, skol16 ), equiv( skol16, skol65 ) ) )
% 1.47/1.88 ), equivalence_3 }.
% 1.47/1.88 (20038) {G0,W7,D4,L2,V1,M2} { ! kn1, is_a_theorem( implies( X, and( X, X )
% 1.47/1.88 ) ) }.
% 1.47/1.88 (20039) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol17, and( skol17
% 1.47/1.88 , skol17 ) ) ), kn1 }.
% 1.47/1.88 (20040) {G0,W7,D4,L2,V2,M2} { ! kn2, is_a_theorem( implies( and( X, Y ), X
% 1.47/1.88 ) ) }.
% 1.47/1.88 (20041) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol18, skol66
% 1.47/1.88 ), skol18 ) ), kn2 }.
% 1.47/1.88 (20042) {G0,W15,D6,L2,V3,M2} { ! kn3, is_a_theorem( implies( implies( X, Y
% 1.47/1.88 ), implies( not( and( Y, Z ) ), not( and( Z, X ) ) ) ) ) }.
% 1.47/1.88 (20043) {G0,W15,D6,L2,V0,M2} { ! is_a_theorem( implies( implies( skol19,
% 1.47/1.88 skol67 ), implies( not( and( skol67, skol88 ) ), not( and( skol88, skol19
% 1.47/1.88 ) ) ) ) ), kn3 }.
% 1.47/1.88 (20044) {G0,W13,D5,L2,V3,M2} { ! cn1, is_a_theorem( implies( implies( X, Y
% 1.47/1.88 ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 1.47/1.88 (20045) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol20,
% 1.47/1.88 skol68 ), implies( implies( skol68, skol89 ), implies( skol20, skol89 ) )
% 1.47/1.88 ) ), cn1 }.
% 1.47/1.88 (20046) {G0,W8,D5,L2,V2,M2} { ! cn2, is_a_theorem( implies( X, implies(
% 1.47/1.88 not( X ), Y ) ) ) }.
% 1.47/1.88 (20047) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( skol21, implies(
% 1.47/1.88 not( skol21 ), skol69 ) ) ), cn2 }.
% 1.47/1.88 (20048) {G0,W8,D5,L2,V1,M2} { ! cn3, is_a_theorem( implies( implies( not(
% 1.47/1.88 X ), X ), X ) ) }.
% 1.47/1.88 (20049) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( not(
% 1.47/1.88 skol22 ), skol22 ), skol22 ) ), cn3 }.
% 1.47/1.88 (20050) {G0,W7,D4,L2,V1,M2} { ! r1, is_a_theorem( implies( or( X, X ), X )
% 1.47/1.88 ) }.
% 1.47/1.88 (20051) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( or( skol23, skol23
% 1.47/1.88 ), skol23 ) ), r1 }.
% 1.47/1.88 (20052) {G0,W7,D4,L2,V2,M2} { ! r2, is_a_theorem( implies( Y, or( X, Y ) )
% 1.47/1.88 ) }.
% 1.47/1.88 (20053) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol70, or( skol24
% 1.47/1.88 , skol70 ) ) ), r2 }.
% 1.47/1.88 (20054) {G0,W9,D4,L2,V2,M2} { ! r3, is_a_theorem( implies( or( X, Y ), or
% 1.47/1.88 ( Y, X ) ) ) }.
% 1.47/1.88 (20055) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( or( skol25, skol71
% 1.47/1.88 ), or( skol71, skol25 ) ) ), r3 }.
% 1.47/1.88 (20056) {G0,W13,D5,L2,V3,M2} { ! r4, is_a_theorem( implies( or( X, or( Y,
% 1.47/1.88 Z ) ), or( Y, or( X, Z ) ) ) ) }.
% 1.47/1.88 (20057) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( or( skol26, or(
% 1.47/1.88 skol72, skol90 ) ), or( skol72, or( skol26, skol90 ) ) ) ), r4 }.
% 1.47/1.88 (20058) {G0,W13,D5,L2,V3,M2} { ! r5, is_a_theorem( implies( implies( Y, Z
% 1.47/1.88 ), implies( or( X, Y ), or( X, Z ) ) ) ) }.
% 1.47/1.88 (20059) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol73,
% 1.47/1.88 skol91 ), implies( or( skol27, skol73 ), or( skol27, skol91 ) ) ) ), r5
% 1.47/1.88 }.
% 1.47/1.88 (20060) {G0,W11,D5,L2,V2,M2} { ! op_or, or( X, Y ) = not( and( not( X ),
% 1.47/1.88 not( Y ) ) ) }.
% 1.47/1.88 (20061) {G0,W11,D5,L2,V2,M2} { ! op_and, and( X, Y ) = not( or( not( X ),
% 1.47/1.88 not( Y ) ) ) }.
% 1.47/1.88 (20062) {G0,W10,D5,L2,V2,M2} { ! op_implies_and, implies( X, Y ) = not(
% 1.47/1.88 and( X, not( Y ) ) ) }.
% 1.47/1.88 (20063) {G0,W9,D4,L2,V2,M2} { ! op_implies_or, implies( X, Y ) = or( not(
% 1.47/1.88 X ), Y ) }.
% 1.47/1.88 (20064) {G0,W12,D4,L2,V2,M2} { ! op_equiv, equiv( X, Y ) = and( implies( X
% 1.47/1.88 , Y ), implies( Y, X ) ) }.
% 1.47/1.88 (20065) {G0,W1,D1,L1,V0,M1} { op_or }.
% 1.47/1.88 (20066) {G0,W1,D1,L1,V0,M1} { op_implies_and }.
% 1.47/1.88 (20067) {G0,W1,D1,L1,V0,M1} { op_equiv }.
% 1.47/1.88 (20068) {G0,W1,D1,L1,V0,M1} { modus_ponens }.
% 1.47/1.88 (20069) {G0,W1,D1,L1,V0,M1} { modus_tollens }.
% 1.47/1.88 (20070) {G0,W1,D1,L1,V0,M1} { implies_1 }.
% 1.47/1.88 (20071) {G0,W1,D1,L1,V0,M1} { implies_2 }.
% 1.47/1.88 (20072) {G0,W1,D1,L1,V0,M1} { implies_3 }.
% 1.47/1.88 (20073) {G0,W1,D1,L1,V0,M1} { and_1 }.
% 1.47/1.88 (20074) {G0,W1,D1,L1,V0,M1} { and_2 }.
% 1.47/1.88 (20075) {G0,W1,D1,L1,V0,M1} { and_3 }.
% 1.47/1.88 (20076) {G0,W1,D1,L1,V0,M1} { or_1 }.
% 1.47/1.88 (20077) {G0,W1,D1,L1,V0,M1} { or_2 }.
% 1.47/1.88 (20078) {G0,W1,D1,L1,V0,M1} { or_3 }.
% 1.47/1.88 (20079) {G0,W1,D1,L1,V0,M1} { equivalence_1 }.
% 1.47/1.88 (20080) {G0,W1,D1,L1,V0,M1} { equivalence_2 }.
% 1.47/1.88 (20081) {G0,W1,D1,L1,V0,M1} { equivalence_3 }.
% 1.47/1.88 (20082) {G0,W1,D1,L1,V0,M1} { substitution_of_equivalents }.
% 1.47/1.88 (20083) {G0,W6,D3,L3,V1,M3} { ! necessitation, ! is_a_theorem( X ),
% 1.47/1.88 is_a_theorem( necessarily( X ) ) }.
% 1.47/1.88 (20084) {G0,W3,D2,L2,V0,M2} { is_a_theorem( skol28 ), necessitation }.
% 1.47/1.88 (20085) {G0,W4,D3,L2,V0,M2} { ! is_a_theorem( necessarily( skol28 ) ),
% 1.47/1.88 necessitation }.
% 1.47/1.88 (20086) {G0,W5,D2,L3,V1,M3} { ! modus_ponens_strict_implies, ! alpha2( X )
% 1.47/1.88 , is_a_theorem( X ) }.
% 1.47/1.88 (20087) {G0,W3,D2,L2,V0,M2} { alpha2( skol29 ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 (20088) {G0,W3,D2,L2,V0,M2} { ! is_a_theorem( skol29 ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 (20089) {G0,W5,D3,L2,V2,M2} { ! alpha2( X ), is_a_theorem( skol30( Y ) )
% 1.47/1.88 }.
% 1.47/1.88 (20090) {G0,W7,D4,L2,V1,M2} { ! alpha2( X ), is_a_theorem( strict_implies
% 1.47/1.88 ( skol30( X ), X ) ) }.
% 1.47/1.88 (20091) {G0,W8,D3,L3,V2,M3} { ! is_a_theorem( Y ), ! is_a_theorem(
% 1.47/1.88 strict_implies( Y, X ) ), alpha2( X ) }.
% 1.47/1.88 (20092) {G0,W8,D3,L3,V2,M3} { ! adjunction, ! alpha3( X, Y ), is_a_theorem
% 1.47/1.88 ( and( X, Y ) ) }.
% 1.47/1.88 (20093) {G0,W4,D2,L2,V0,M2} { alpha3( skol31, skol74 ), adjunction }.
% 1.47/1.88 (20094) {G0,W5,D3,L2,V0,M2} { ! is_a_theorem( and( skol31, skol74 ) ),
% 1.47/1.88 adjunction }.
% 1.47/1.88 (20095) {G0,W5,D2,L2,V2,M2} { ! alpha3( X, Y ), is_a_theorem( X ) }.
% 1.47/1.88 (20096) {G0,W5,D2,L2,V2,M2} { ! alpha3( X, Y ), is_a_theorem( Y ) }.
% 1.47/1.88 (20097) {G0,W7,D2,L3,V2,M3} { ! is_a_theorem( X ), ! is_a_theorem( Y ),
% 1.47/1.88 alpha3( X, Y ) }.
% 1.47/1.88 (20098) {G0,W8,D3,L3,V2,M3} { ! substitution_strict_equiv, ! is_a_theorem
% 1.47/1.88 ( strict_equiv( X, Y ) ), X = Y }.
% 1.47/1.88 (20099) {G0,W5,D3,L2,V0,M2} { is_a_theorem( strict_equiv( skol32, skol75 )
% 1.47/1.88 ), substitution_strict_equiv }.
% 1.47/1.88 (20100) {G0,W4,D2,L2,V0,M2} { ! skol32 = skol75, substitution_strict_equiv
% 1.47/1.88 }.
% 1.47/1.88 (20101) {G0,W12,D5,L2,V2,M2} { ! axiom_K, is_a_theorem( implies(
% 1.47/1.88 necessarily( implies( X, Y ) ), implies( necessarily( X ), necessarily( Y
% 1.47/1.88 ) ) ) ) }.
% 1.47/1.88 (20102) {G0,W12,D5,L2,V0,M2} { ! is_a_theorem( implies( necessarily(
% 1.47/1.88 implies( skol33, skol76 ) ), implies( necessarily( skol33 ), necessarily
% 1.47/1.88 ( skol76 ) ) ) ), axiom_K }.
% 1.47/1.88 (20103) {G0,W6,D4,L2,V1,M2} { ! axiom_M, is_a_theorem( implies(
% 1.47/1.88 necessarily( X ), X ) ) }.
% 1.47/1.88 (20104) {G0,W6,D4,L2,V0,M2} { ! is_a_theorem( implies( necessarily( skol34
% 1.47/1.88 ), skol34 ) ), axiom_M }.
% 1.47/1.88 (20105) {G0,W8,D5,L2,V1,M2} { ! axiom_4, is_a_theorem( implies(
% 1.47/1.88 necessarily( X ), necessarily( necessarily( X ) ) ) ) }.
% 1.47/1.88 (20106) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( necessarily( skol35
% 1.47/1.88 ), necessarily( necessarily( skol35 ) ) ) ), axiom_4 }.
% 1.47/1.88 (20107) {G0,W7,D5,L2,V1,M2} { ! axiom_B, is_a_theorem( implies( X,
% 1.47/1.88 necessarily( possibly( X ) ) ) ) }.
% 1.47/1.88 (20108) {G0,W7,D5,L2,V0,M2} { ! is_a_theorem( implies( skol36, necessarily
% 1.47/1.88 ( possibly( skol36 ) ) ) ), axiom_B }.
% 1.47/1.88 (20109) {G0,W8,D5,L2,V1,M2} { ! axiom_5, is_a_theorem( implies( possibly(
% 1.47/1.88 X ), necessarily( possibly( X ) ) ) ) }.
% 1.47/1.88 (20110) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( possibly( skol37 )
% 1.47/1.88 , necessarily( possibly( skol37 ) ) ) ), axiom_5 }.
% 1.47/1.88 (20111) {G0,W16,D6,L2,V3,M2} { ! axiom_s1, is_a_theorem( implies( and(
% 1.47/1.88 necessarily( implies( X, Y ) ), necessarily( implies( Y, Z ) ) ),
% 1.47/1.88 necessarily( implies( X, Z ) ) ) ) }.
% 1.47/1.88 (20112) {G0,W16,D6,L2,V0,M2} { ! is_a_theorem( implies( and( necessarily(
% 1.47/1.88 implies( skol38, skol77 ) ), necessarily( implies( skol77, skol92 ) ) ),
% 1.47/1.88 necessarily( implies( skol38, skol92 ) ) ) ), axiom_s1 }.
% 1.47/1.88 (20113) {G0,W12,D5,L2,V2,M2} { ! axiom_s2, is_a_theorem( strict_implies(
% 1.47/1.88 possibly( and( X, Y ) ), and( possibly( X ), possibly( Y ) ) ) ) }.
% 1.47/1.88 (20114) {G0,W12,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( possibly(
% 1.47/1.88 and( skol39, skol78 ) ), and( possibly( skol39 ), possibly( skol78 ) ) )
% 1.47/1.88 ), axiom_s2 }.
% 1.47/1.88 (20115) {G0,W13,D6,L2,V2,M2} { ! axiom_s3, is_a_theorem( strict_implies(
% 1.47/1.88 strict_implies( X, Y ), strict_implies( not( possibly( Y ) ), not(
% 1.47/1.88 possibly( X ) ) ) ) ) }.
% 1.47/1.88 (20116) {G0,W13,D6,L2,V0,M2} { ! is_a_theorem( strict_implies(
% 1.47/1.88 strict_implies( skol40, skol79 ), strict_implies( not( possibly( skol79 )
% 1.47/1.88 ), not( possibly( skol40 ) ) ) ) ), axiom_s3 }.
% 1.47/1.88 (20117) {G0,W8,D5,L2,V1,M2} { ! axiom_s4, is_a_theorem( strict_implies(
% 1.47/1.88 necessarily( X ), necessarily( necessarily( X ) ) ) ) }.
% 1.47/1.88 (20118) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( necessarily
% 1.47/1.88 ( skol41 ), necessarily( necessarily( skol41 ) ) ) ), axiom_s4 }.
% 1.47/1.88 (20119) {G0,W9,D4,L2,V2,M2} { ! axiom_m1, is_a_theorem( strict_implies(
% 1.47/1.88 and( X, Y ), and( Y, X ) ) ) }.
% 1.47/1.88 (20120) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( and( skol42
% 1.47/1.88 , skol80 ), and( skol80, skol42 ) ) ), axiom_m1 }.
% 1.47/1.88 (20121) {G0,W7,D4,L2,V2,M2} { ! axiom_m2, is_a_theorem( strict_implies(
% 1.47/1.88 and( X, Y ), X ) ) }.
% 1.47/1.88 (20122) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( and( skol43
% 1.47/1.88 , skol81 ), skol43 ) ), axiom_m2 }.
% 1.47/1.88 (20123) {G0,W13,D5,L2,V3,M2} { ! axiom_m3, is_a_theorem( strict_implies(
% 1.47/1.88 and( and( X, Y ), Z ), and( X, and( Y, Z ) ) ) ) }.
% 1.47/1.88 (20124) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( and( and(
% 1.47/1.88 skol44, skol82 ), skol93 ), and( skol44, and( skol82, skol93 ) ) ) ),
% 1.47/1.88 axiom_m3 }.
% 1.47/1.88 (20125) {G0,W7,D4,L2,V1,M2} { ! axiom_m4, is_a_theorem( strict_implies( X
% 1.47/1.88 , and( X, X ) ) ) }.
% 1.47/1.88 (20126) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( skol45, and
% 1.47/1.88 ( skol45, skol45 ) ) ), axiom_m4 }.
% 1.47/1.88 (20127) {G0,W13,D5,L2,V3,M2} { ! axiom_m5, is_a_theorem( strict_implies(
% 1.47/1.88 and( strict_implies( X, Y ), strict_implies( Y, Z ) ), strict_implies( X
% 1.47/1.88 , Z ) ) ) }.
% 1.47/1.88 (20128) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( and(
% 1.47/1.88 strict_implies( skol46, skol83 ), strict_implies( skol83, skol94 ) ),
% 1.47/1.88 strict_implies( skol46, skol94 ) ) ), axiom_m5 }.
% 1.47/1.88 (20129) {G0,W6,D4,L2,V1,M2} { ! axiom_m6, is_a_theorem( strict_implies( X
% 1.47/1.88 , possibly( X ) ) ) }.
% 1.47/1.88 (20130) {G0,W6,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( skol47,
% 1.47/1.88 possibly( skol47 ) ) ), axiom_m6 }.
% 1.47/1.88 (20131) {G0,W8,D5,L2,V2,M2} { ! axiom_m7, is_a_theorem( strict_implies(
% 1.47/1.88 possibly( and( X, Y ) ), X ) ) }.
% 1.47/1.88 (20132) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( possibly(
% 1.47/1.88 and( skol48, skol84 ) ), skol48 ) ), axiom_m7 }.
% 1.47/1.88 (20133) {G0,W11,D5,L2,V2,M2} { ! axiom_m8, is_a_theorem( strict_implies(
% 1.47/1.88 strict_implies( X, Y ), strict_implies( possibly( X ), possibly( Y ) ) )
% 1.47/1.88 ) }.
% 1.47/1.88 (20134) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( strict_implies(
% 1.47/1.88 strict_implies( skol49, skol85 ), strict_implies( possibly( skol49 ),
% 1.47/1.88 possibly( skol85 ) ) ) ), axiom_m8 }.
% 1.47/1.88 (20135) {G0,W8,D5,L2,V1,M2} { ! axiom_m9, is_a_theorem( strict_implies(
% 1.47/1.88 possibly( possibly( X ) ), possibly( X ) ) ) }.
% 1.47/1.88 (20136) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( possibly(
% 1.47/1.88 possibly( skol50 ) ), possibly( skol50 ) ) ), axiom_m9 }.
% 1.47/1.88 (20137) {G0,W8,D5,L2,V1,M2} { ! axiom_m10, is_a_theorem( strict_implies(
% 1.47/1.88 possibly( X ), necessarily( possibly( X ) ) ) ) }.
% 1.47/1.88 (20138) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( possibly(
% 1.47/1.88 skol51 ), necessarily( possibly( skol51 ) ) ) ), axiom_m10 }.
% 1.47/1.88 (20139) {G0,W8,D5,L2,V1,M2} { ! op_possibly, possibly( X ) = not(
% 1.47/1.88 necessarily( not( X ) ) ) }.
% 1.47/1.88 (20140) {G0,W8,D5,L2,V1,M2} { ! op_necessarily, necessarily( X ) = not(
% 1.47/1.88 possibly( not( X ) ) ) }.
% 1.47/1.88 (20141) {G0,W9,D4,L2,V2,M2} { ! op_strict_implies, strict_implies( X, Y )
% 1.47/1.88 = necessarily( implies( X, Y ) ) }.
% 1.47/1.88 (20142) {G0,W12,D4,L2,V2,M2} { ! op_strict_equiv, strict_equiv( X, Y ) =
% 1.47/1.88 and( strict_implies( X, Y ), strict_implies( Y, X ) ) }.
% 1.47/1.88 (20143) {G0,W1,D1,L1,V0,M1} { op_possibly }.
% 1.47/1.88 (20144) {G0,W1,D1,L1,V0,M1} { necessitation }.
% 1.47/1.88 (20145) {G0,W1,D1,L1,V0,M1} { axiom_K }.
% 1.47/1.88 (20146) {G0,W1,D1,L1,V0,M1} { axiom_M }.
% 1.47/1.88 (20147) {G0,W1,D1,L1,V0,M1} { axiom_4 }.
% 1.47/1.88 (20148) {G0,W1,D1,L1,V0,M1} { axiom_B }.
% 1.47/1.88 (20149) {G0,W1,D1,L1,V0,M1} { op_possibly }.
% 1.47/1.88 (20150) {G0,W1,D1,L1,V0,M1} { op_or }.
% 1.47/1.88 (20151) {G0,W1,D1,L1,V0,M1} { op_implies }.
% 1.47/1.88 (20152) {G0,W1,D1,L1,V0,M1} { op_strict_implies }.
% 1.47/1.88 (20153) {G0,W1,D1,L1,V0,M1} { op_equiv }.
% 1.47/1.88 (20154) {G0,W1,D1,L1,V0,M1} { op_strict_equiv }.
% 1.47/1.88 (20155) {G0,W1,D1,L1,V0,M1} { ! axiom_m2 }.
% 1.47/1.88
% 1.47/1.88
% 1.47/1.88 Total Proof:
% 1.47/1.88
% 1.47/1.88 subsumption: (0) {G0,W5,D2,L3,V1,M3} I { ! modus_ponens, ! alpha1( X ),
% 1.47/1.88 is_a_theorem( X ) }.
% 1.47/1.88 parent0: (20003) {G0,W5,D2,L3,V1,M3} { ! modus_ponens, ! alpha1( X ),
% 1.47/1.88 is_a_theorem( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 2 ==> 2
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), !
% 1.47/1.88 is_a_theorem( implies( Y, X ) ), alpha1( X ) }.
% 1.47/1.88 parent0: (20008) {G0,W8,D3,L3,V2,M3} { ! is_a_theorem( Y ), ! is_a_theorem
% 1.47/1.88 ( implies( Y, X ) ), alpha1( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 2 ==> 2
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (11) {G0,W7,D4,L2,V2,M2} I { ! implies_1, is_a_theorem(
% 1.47/1.88 implies( X, implies( Y, X ) ) ) }.
% 1.47/1.88 parent0: (20014) {G0,W7,D4,L2,V2,M2} { ! implies_1, is_a_theorem( implies
% 1.47/1.88 ( X, implies( Y, X ) ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (17) {G0,W7,D4,L2,V2,M2} I { ! and_1, is_a_theorem( implies(
% 1.47/1.88 and( X, Y ), X ) ) }.
% 1.47/1.88 parent0: (20020) {G0,W7,D4,L2,V2,M2} { ! and_1, is_a_theorem( implies( and
% 1.47/1.88 ( X, Y ), X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (65) {G0,W1,D1,L1,V0,M1} I { modus_ponens }.
% 1.47/1.88 parent0: (20068) {G0,W1,D1,L1,V0,M1} { modus_ponens }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (67) {G0,W1,D1,L1,V0,M1} I { implies_1 }.
% 1.47/1.88 parent0: (20070) {G0,W1,D1,L1,V0,M1} { implies_1 }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (70) {G0,W1,D1,L1,V0,M1} I { and_1 }.
% 1.47/1.88 parent0: (20073) {G0,W1,D1,L1,V0,M1} { and_1 }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (80) {G0,W6,D3,L3,V1,M3} I { ! necessitation, ! is_a_theorem(
% 1.47/1.88 X ), is_a_theorem( necessarily( X ) ) }.
% 1.47/1.88 parent0: (20083) {G0,W6,D3,L3,V1,M3} { ! necessitation, ! is_a_theorem( X
% 1.47/1.88 ), is_a_theorem( necessarily( X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 2 ==> 2
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (83) {G0,W5,D2,L3,V1,M3} I { ! modus_ponens_strict_implies, !
% 1.47/1.88 alpha2( X ), is_a_theorem( X ) }.
% 1.47/1.88 parent0: (20086) {G0,W5,D2,L3,V1,M3} { ! modus_ponens_strict_implies, !
% 1.47/1.88 alpha2( X ), is_a_theorem( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 2 ==> 2
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (84) {G0,W3,D2,L2,V0,M2} I { alpha2( skol29 ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 parent0: (20087) {G0,W3,D2,L2,V0,M2} { alpha2( skol29 ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (85) {G0,W3,D2,L2,V0,M2} I { ! is_a_theorem( skol29 ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 parent0: (20088) {G0,W3,D2,L2,V0,M2} { ! is_a_theorem( skol29 ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (86) {G0,W5,D3,L2,V2,M2} I { ! alpha2( X ), is_a_theorem(
% 1.47/1.88 skol30( Y ) ) }.
% 1.47/1.88 parent0: (20089) {G0,W5,D3,L2,V2,M2} { ! alpha2( X ), is_a_theorem( skol30
% 1.47/1.88 ( Y ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (87) {G0,W7,D4,L2,V1,M2} I { ! alpha2( X ), is_a_theorem(
% 1.47/1.88 strict_implies( skol30( X ), X ) ) }.
% 1.47/1.88 parent0: (20090) {G0,W7,D4,L2,V1,M2} { ! alpha2( X ), is_a_theorem(
% 1.47/1.88 strict_implies( skol30( X ), X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (88) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), !
% 1.47/1.88 is_a_theorem( strict_implies( Y, X ) ), alpha2( X ) }.
% 1.47/1.88 parent0: (20091) {G0,W8,D3,L3,V2,M3} { ! is_a_theorem( Y ), ! is_a_theorem
% 1.47/1.88 ( strict_implies( Y, X ) ), alpha2( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 2 ==> 2
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (100) {G0,W6,D4,L2,V1,M2} I { ! axiom_M, is_a_theorem( implies
% 1.47/1.88 ( necessarily( X ), X ) ) }.
% 1.47/1.88 parent0: (20103) {G0,W6,D4,L2,V1,M2} { ! axiom_M, is_a_theorem( implies(
% 1.47/1.88 necessarily( X ), X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (119) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( strict_implies(
% 1.47/1.88 and( skol43, skol81 ), skol43 ) ), axiom_m2 }.
% 1.47/1.88 parent0: (20122) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( and
% 1.47/1.88 ( skol43, skol81 ), skol43 ) ), axiom_m2 }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 eqswap: (20262) {G0,W9,D4,L2,V2,M2} { necessarily( implies( X, Y ) ) =
% 1.47/1.88 strict_implies( X, Y ), ! op_strict_implies }.
% 1.47/1.88 parent0[1]: (20141) {G0,W9,D4,L2,V2,M2} { ! op_strict_implies,
% 1.47/1.88 strict_implies( X, Y ) = necessarily( implies( X, Y ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (138) {G0,W9,D4,L2,V2,M2} I { ! op_strict_implies, necessarily
% 1.47/1.88 ( implies( X, Y ) ) ==> strict_implies( X, Y ) }.
% 1.47/1.88 parent0: (20262) {G0,W9,D4,L2,V2,M2} { necessarily( implies( X, Y ) ) =
% 1.47/1.88 strict_implies( X, Y ), ! op_strict_implies }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 1
% 1.47/1.88 1 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (141) {G0,W1,D1,L1,V0,M1} I { necessitation }.
% 1.47/1.88 parent0: (20144) {G0,W1,D1,L1,V0,M1} { necessitation }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (143) {G0,W1,D1,L1,V0,M1} I { axiom_M }.
% 1.47/1.88 parent0: (20146) {G0,W1,D1,L1,V0,M1} { axiom_M }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (147) {G0,W1,D1,L1,V0,M1} I { op_strict_implies }.
% 1.47/1.88 parent0: (20152) {G0,W1,D1,L1,V0,M1} { op_strict_implies }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (149) {G0,W1,D1,L1,V0,M1} I { ! axiom_m2 }.
% 1.47/1.88 parent0: (20155) {G0,W1,D1,L1,V0,M1} { ! axiom_m2 }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20319) {G1,W4,D2,L2,V1,M2} { ! alpha1( X ), is_a_theorem( X )
% 1.47/1.88 }.
% 1.47/1.88 parent0[0]: (0) {G0,W5,D2,L3,V1,M3} I { ! modus_ponens, ! alpha1( X ),
% 1.47/1.88 is_a_theorem( X ) }.
% 1.47/1.88 parent1[0]: (65) {G0,W1,D1,L1,V0,M1} I { modus_ponens }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (151) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 1.47/1.88 is_a_theorem( X ) }.
% 1.47/1.88 parent0: (20319) {G1,W4,D2,L2,V1,M2} { ! alpha1( X ), is_a_theorem( X )
% 1.47/1.88 }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20320) {G1,W3,D2,L2,V0,M2} { modus_ponens_strict_implies, !
% 1.47/1.88 alpha1( skol29 ) }.
% 1.47/1.88 parent0[0]: (85) {G0,W3,D2,L2,V0,M2} I { ! is_a_theorem( skol29 ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 parent1[1]: (151) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 1.47/1.88 is_a_theorem( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := skol29
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (157) {G2,W3,D2,L2,V0,M2} R(151,85) { ! alpha1( skol29 ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 parent0: (20320) {G1,W3,D2,L2,V0,M2} { modus_ponens_strict_implies, !
% 1.47/1.88 alpha1( skol29 ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 1
% 1.47/1.88 1 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20321) {G1,W7,D3,L3,V1,M3} { modus_ponens_strict_implies, !
% 1.47/1.88 is_a_theorem( X ), ! is_a_theorem( implies( X, skol29 ) ) }.
% 1.47/1.88 parent0[0]: (157) {G2,W3,D2,L2,V0,M2} R(151,85) { ! alpha1( skol29 ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 parent1[2]: (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem
% 1.47/1.88 ( implies( Y, X ) ), alpha1( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := skol29
% 1.47/1.88 Y := X
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (161) {G3,W7,D3,L3,V1,M3} R(157,5) {
% 1.47/1.88 modus_ponens_strict_implies, ! is_a_theorem( X ), ! is_a_theorem( implies
% 1.47/1.88 ( X, skol29 ) ) }.
% 1.47/1.88 parent0: (20321) {G1,W7,D3,L3,V1,M3} { modus_ponens_strict_implies, !
% 1.47/1.88 is_a_theorem( X ), ! is_a_theorem( implies( X, skol29 ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 2 ==> 2
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20322) {G1,W6,D4,L1,V2,M1} { is_a_theorem( implies( X,
% 1.47/1.88 implies( Y, X ) ) ) }.
% 1.47/1.88 parent0[0]: (11) {G0,W7,D4,L2,V2,M2} I { ! implies_1, is_a_theorem( implies
% 1.47/1.88 ( X, implies( Y, X ) ) ) }.
% 1.47/1.88 parent1[0]: (67) {G0,W1,D1,L1,V0,M1} I { implies_1 }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (180) {G1,W6,D4,L1,V2,M1} S(11);r(67) { is_a_theorem( implies
% 1.47/1.88 ( X, implies( Y, X ) ) ) }.
% 1.47/1.88 parent0: (20322) {G1,W6,D4,L1,V2,M1} { is_a_theorem( implies( X, implies(
% 1.47/1.88 Y, X ) ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20323) {G1,W4,D3,L2,V1,M2} { is_a_theorem( skol30( X ) ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 parent0[0]: (86) {G0,W5,D3,L2,V2,M2} I { ! alpha2( X ), is_a_theorem(
% 1.47/1.88 skol30( Y ) ) }.
% 1.47/1.88 parent1[0]: (84) {G0,W3,D2,L2,V0,M2} I { alpha2( skol29 ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := skol29
% 1.47/1.88 Y := X
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (191) {G1,W4,D3,L2,V1,M2} R(86,84) { is_a_theorem( skol30( X )
% 1.47/1.88 ), modus_ponens_strict_implies }.
% 1.47/1.88 parent0: (20323) {G1,W4,D3,L2,V1,M2} { is_a_theorem( skol30( X ) ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20324) {G1,W5,D3,L2,V1,M2} { ! is_a_theorem( X ),
% 1.47/1.88 is_a_theorem( necessarily( X ) ) }.
% 1.47/1.88 parent0[0]: (80) {G0,W6,D3,L3,V1,M3} I { ! necessitation, ! is_a_theorem( X
% 1.47/1.88 ), is_a_theorem( necessarily( X ) ) }.
% 1.47/1.88 parent1[0]: (141) {G0,W1,D1,L1,V0,M1} I { necessitation }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (220) {G1,W5,D3,L2,V1,M2} S(80);r(141) { ! is_a_theorem( X ),
% 1.47/1.88 is_a_theorem( necessarily( X ) ) }.
% 1.47/1.88 parent0: (20324) {G1,W5,D3,L2,V1,M2} { ! is_a_theorem( X ), is_a_theorem(
% 1.47/1.88 necessarily( X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20325) {G2,W5,D3,L2,V1,M2} { is_a_theorem( necessarily( X ) )
% 1.47/1.88 , ! alpha1( X ) }.
% 1.47/1.88 parent0[0]: (220) {G1,W5,D3,L2,V1,M2} S(80);r(141) { ! is_a_theorem( X ),
% 1.47/1.88 is_a_theorem( necessarily( X ) ) }.
% 1.47/1.88 parent1[1]: (151) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 1.47/1.88 is_a_theorem( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (234) {G2,W5,D3,L2,V1,M2} R(220,151) { is_a_theorem(
% 1.47/1.88 necessarily( X ) ), ! alpha1( X ) }.
% 1.47/1.88 parent0: (20325) {G2,W5,D3,L2,V1,M2} { is_a_theorem( necessarily( X ) ), !
% 1.47/1.88 alpha1( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20326) {G1,W9,D3,L3,V2,M3} { is_a_theorem( necessarily( X ) )
% 1.47/1.88 , ! is_a_theorem( Y ), ! is_a_theorem( implies( Y, X ) ) }.
% 1.47/1.88 parent0[1]: (234) {G2,W5,D3,L2,V1,M2} R(220,151) { is_a_theorem(
% 1.47/1.88 necessarily( X ) ), ! alpha1( X ) }.
% 1.47/1.88 parent1[2]: (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem
% 1.47/1.88 ( implies( Y, X ) ), alpha1( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (247) {G3,W9,D3,L3,V2,M3} R(234,5) { is_a_theorem( necessarily
% 1.47/1.88 ( X ) ), ! is_a_theorem( Y ), ! is_a_theorem( implies( Y, X ) ) }.
% 1.47/1.88 parent0: (20326) {G1,W9,D3,L3,V2,M3} { is_a_theorem( necessarily( X ) ), !
% 1.47/1.88 is_a_theorem( Y ), ! is_a_theorem( implies( Y, X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 2 ==> 2
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20327) {G1,W6,D4,L1,V2,M1} { is_a_theorem( implies( and( X, Y
% 1.47/1.88 ), X ) ) }.
% 1.47/1.88 parent0[0]: (17) {G0,W7,D4,L2,V2,M2} I { ! and_1, is_a_theorem( implies(
% 1.47/1.88 and( X, Y ), X ) ) }.
% 1.47/1.88 parent1[0]: (70) {G0,W1,D1,L1,V0,M1} I { and_1 }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (254) {G1,W6,D4,L1,V2,M1} S(17);r(70) { is_a_theorem( implies
% 1.47/1.88 ( and( X, Y ), X ) ) }.
% 1.47/1.88 parent0: (20327) {G1,W6,D4,L1,V2,M1} { is_a_theorem( implies( and( X, Y )
% 1.47/1.88 , X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20329) {G1,W6,D3,L2,V2,M2} { ! is_a_theorem( X ), alpha1(
% 1.47/1.88 implies( Y, X ) ) }.
% 1.47/1.88 parent0[1]: (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem
% 1.47/1.88 ( implies( Y, X ) ), alpha1( X ) }.
% 1.47/1.88 parent1[0]: (180) {G1,W6,D4,L1,V2,M1} S(11);r(67) { is_a_theorem( implies(
% 1.47/1.88 X, implies( Y, X ) ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := implies( Y, X )
% 1.47/1.88 Y := X
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (663) {G2,W6,D3,L2,V2,M2} R(180,5) { ! is_a_theorem( X ),
% 1.47/1.88 alpha1( implies( Y, X ) ) }.
% 1.47/1.88 parent0: (20329) {G1,W6,D3,L2,V2,M2} { ! is_a_theorem( X ), alpha1(
% 1.47/1.88 implies( Y, X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20331) {G2,W6,D3,L2,V2,M2} { is_a_theorem( implies( X, Y ) )
% 1.47/1.88 , ! is_a_theorem( Y ) }.
% 1.47/1.88 parent0[0]: (151) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 1.47/1.88 is_a_theorem( X ) }.
% 1.47/1.88 parent1[1]: (663) {G2,W6,D3,L2,V2,M2} R(180,5) { ! is_a_theorem( X ),
% 1.47/1.88 alpha1( implies( Y, X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := implies( X, Y )
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := Y
% 1.47/1.88 Y := X
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (714) {G3,W6,D3,L2,V2,M2} R(663,151) { ! is_a_theorem( X ),
% 1.47/1.88 is_a_theorem( implies( Y, X ) ) }.
% 1.47/1.88 parent0: (20331) {G2,W6,D3,L2,V2,M2} { is_a_theorem( implies( X, Y ) ), !
% 1.47/1.88 is_a_theorem( Y ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := Y
% 1.47/1.88 Y := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 1
% 1.47/1.88 1 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20333) {G1,W6,D2,L3,V2,M3} { ! is_a_theorem( X ), alpha1( Y )
% 1.47/1.88 , ! is_a_theorem( Y ) }.
% 1.47/1.88 parent0[1]: (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem
% 1.47/1.88 ( implies( Y, X ) ), alpha1( X ) }.
% 1.47/1.88 parent1[1]: (714) {G3,W6,D3,L2,V2,M2} R(663,151) { ! is_a_theorem( X ),
% 1.47/1.88 is_a_theorem( implies( Y, X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := Y
% 1.47/1.88 Y := X
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := Y
% 1.47/1.88 Y := X
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (814) {G4,W6,D2,L3,V2,M3} R(714,5) { ! is_a_theorem( X ), !
% 1.47/1.88 is_a_theorem( Y ), alpha1( X ) }.
% 1.47/1.88 parent0: (20333) {G1,W6,D2,L3,V2,M3} { ! is_a_theorem( X ), alpha1( Y ), !
% 1.47/1.88 is_a_theorem( Y ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 2
% 1.47/1.88 2 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 factor: (20335) {G4,W4,D2,L2,V1,M2} { ! is_a_theorem( X ), alpha1( X ) }.
% 1.47/1.88 parent0[0, 1]: (814) {G4,W6,D2,L3,V2,M3} R(714,5) { ! is_a_theorem( X ), !
% 1.47/1.88 is_a_theorem( Y ), alpha1( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := X
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (815) {G5,W4,D2,L2,V1,M2} F(814) { ! is_a_theorem( X ), alpha1
% 1.47/1.88 ( X ) }.
% 1.47/1.88 parent0: (20335) {G4,W4,D2,L2,V1,M2} { ! is_a_theorem( X ), alpha1( X )
% 1.47/1.88 }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20336) {G2,W6,D4,L1,V2,M1} { alpha1( implies( and( X, Y ), X
% 1.47/1.88 ) ) }.
% 1.47/1.88 parent0[0]: (815) {G5,W4,D2,L2,V1,M2} F(814) { ! is_a_theorem( X ), alpha1
% 1.47/1.88 ( X ) }.
% 1.47/1.88 parent1[0]: (254) {G1,W6,D4,L1,V2,M1} S(17);r(70) { is_a_theorem( implies(
% 1.47/1.88 and( X, Y ), X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := implies( and( X, Y ), X )
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (822) {G6,W6,D4,L1,V2,M1} R(815,254) { alpha1( implies( and( X
% 1.47/1.88 , Y ), X ) ) }.
% 1.47/1.88 parent0: (20336) {G2,W6,D4,L1,V2,M1} { alpha1( implies( and( X, Y ), X ) )
% 1.47/1.88 }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20337) {G1,W5,D2,L3,V1,M3} { alpha1( X ), !
% 1.47/1.88 modus_ponens_strict_implies, ! alpha2( X ) }.
% 1.47/1.88 parent0[0]: (815) {G5,W4,D2,L2,V1,M2} F(814) { ! is_a_theorem( X ), alpha1
% 1.47/1.88 ( X ) }.
% 1.47/1.88 parent1[2]: (83) {G0,W5,D2,L3,V1,M3} I { ! modus_ponens_strict_implies, !
% 1.47/1.88 alpha2( X ), is_a_theorem( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (839) {G6,W5,D2,L3,V1,M3} R(815,83) { alpha1( X ), !
% 1.47/1.88 modus_ponens_strict_implies, ! alpha2( X ) }.
% 1.47/1.88 parent0: (20337) {G1,W5,D2,L3,V1,M3} { alpha1( X ), !
% 1.47/1.88 modus_ponens_strict_implies, ! alpha2( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 2 ==> 2
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20338) {G1,W5,D4,L1,V1,M1} { is_a_theorem( implies(
% 1.47/1.88 necessarily( X ), X ) ) }.
% 1.47/1.88 parent0[0]: (100) {G0,W6,D4,L2,V1,M2} I { ! axiom_M, is_a_theorem( implies
% 1.47/1.88 ( necessarily( X ), X ) ) }.
% 1.47/1.88 parent1[0]: (143) {G0,W1,D1,L1,V0,M1} I { axiom_M }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (2662) {G1,W5,D4,L1,V1,M1} S(100);r(143) { is_a_theorem(
% 1.47/1.88 implies( necessarily( X ), X ) ) }.
% 1.47/1.88 parent0: (20338) {G1,W5,D4,L1,V1,M1} { is_a_theorem( implies( necessarily
% 1.47/1.88 ( X ), X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20340) {G1,W5,D3,L2,V1,M2} { ! is_a_theorem( necessarily( X )
% 1.47/1.88 ), alpha1( X ) }.
% 1.47/1.88 parent0[1]: (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem
% 1.47/1.88 ( implies( Y, X ) ), alpha1( X ) }.
% 1.47/1.88 parent1[0]: (2662) {G1,W5,D4,L1,V1,M1} S(100);r(143) { is_a_theorem(
% 1.47/1.88 implies( necessarily( X ), X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := necessarily( X )
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (2691) {G2,W5,D3,L2,V1,M2} R(2662,5) { ! is_a_theorem(
% 1.47/1.88 necessarily( X ) ), alpha1( X ) }.
% 1.47/1.88 parent0: (20340) {G1,W5,D3,L2,V1,M2} { ! is_a_theorem( necessarily( X ) )
% 1.47/1.88 , alpha1( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20342) {G2,W5,D3,L2,V1,M2} { is_a_theorem( X ), !
% 1.47/1.88 is_a_theorem( necessarily( X ) ) }.
% 1.47/1.88 parent0[0]: (151) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 1.47/1.88 is_a_theorem( X ) }.
% 1.47/1.88 parent1[1]: (2691) {G2,W5,D3,L2,V1,M2} R(2662,5) { ! is_a_theorem(
% 1.47/1.88 necessarily( X ) ), alpha1( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (2747) {G3,W5,D3,L2,V1,M2} R(2691,151) { ! is_a_theorem(
% 1.47/1.88 necessarily( X ) ), is_a_theorem( X ) }.
% 1.47/1.88 parent0: (20342) {G2,W5,D3,L2,V1,M2} { is_a_theorem( X ), ! is_a_theorem(
% 1.47/1.88 necessarily( X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 1
% 1.47/1.88 1 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20343) {G1,W6,D4,L1,V0,M1} { ! is_a_theorem( strict_implies(
% 1.47/1.88 and( skol43, skol81 ), skol43 ) ) }.
% 1.47/1.88 parent0[0]: (149) {G0,W1,D1,L1,V0,M1} I { ! axiom_m2 }.
% 1.47/1.88 parent1[1]: (119) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( strict_implies(
% 1.47/1.88 and( skol43, skol81 ), skol43 ) ), axiom_m2 }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (4041) {G1,W6,D4,L1,V0,M1} S(119);r(149) { ! is_a_theorem(
% 1.47/1.88 strict_implies( and( skol43, skol81 ), skol43 ) ) }.
% 1.47/1.88 parent0: (20343) {G1,W6,D4,L1,V0,M1} { ! is_a_theorem( strict_implies( and
% 1.47/1.88 ( skol43, skol81 ), skol43 ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20345) {G1,W8,D4,L1,V2,M1} { necessarily( implies( X, Y ) )
% 1.47/1.88 ==> strict_implies( X, Y ) }.
% 1.47/1.88 parent0[0]: (138) {G0,W9,D4,L2,V2,M2} I { ! op_strict_implies, necessarily
% 1.47/1.88 ( implies( X, Y ) ) ==> strict_implies( X, Y ) }.
% 1.47/1.88 parent1[0]: (147) {G0,W1,D1,L1,V0,M1} I { op_strict_implies }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (5677) {G1,W8,D4,L1,V2,M1} S(138);r(147) { necessarily(
% 1.47/1.88 implies( X, Y ) ) ==> strict_implies( X, Y ) }.
% 1.47/1.88 parent0: (20345) {G1,W8,D4,L1,V2,M1} { necessarily( implies( X, Y ) ) ==>
% 1.47/1.88 strict_implies( X, Y ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20347) {G2,W7,D4,L3,V1,M3} { modus_ponens_strict_implies, !
% 1.47/1.88 is_a_theorem( implies( skol30( X ), skol29 ) ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 parent0[1]: (161) {G3,W7,D3,L3,V1,M3} R(157,5) {
% 1.47/1.88 modus_ponens_strict_implies, ! is_a_theorem( X ), ! is_a_theorem( implies
% 1.47/1.88 ( X, skol29 ) ) }.
% 1.47/1.88 parent1[0]: (191) {G1,W4,D3,L2,V1,M2} R(86,84) { is_a_theorem( skol30( X )
% 1.47/1.88 ), modus_ponens_strict_implies }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := skol30( X )
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 factor: (20348) {G2,W6,D4,L2,V1,M2} { modus_ponens_strict_implies, !
% 1.47/1.88 is_a_theorem( implies( skol30( X ), skol29 ) ) }.
% 1.47/1.88 parent0[0, 2]: (20347) {G2,W7,D4,L3,V1,M3} { modus_ponens_strict_implies,
% 1.47/1.88 ! is_a_theorem( implies( skol30( X ), skol29 ) ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (7311) {G4,W6,D4,L2,V1,M2} R(161,191);f {
% 1.47/1.88 modus_ponens_strict_implies, ! is_a_theorem( implies( skol30( X ), skol29
% 1.47/1.88 ) ) }.
% 1.47/1.88 parent0: (20348) {G2,W6,D4,L2,V1,M2} { modus_ponens_strict_implies, !
% 1.47/1.88 is_a_theorem( implies( skol30( X ), skol29 ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20349) {G2,W6,D4,L1,V0,M1} { ! alpha1( strict_implies( and(
% 1.47/1.88 skol43, skol81 ), skol43 ) ) }.
% 1.47/1.88 parent0[0]: (4041) {G1,W6,D4,L1,V0,M1} S(119);r(149) { ! is_a_theorem(
% 1.47/1.88 strict_implies( and( skol43, skol81 ), skol43 ) ) }.
% 1.47/1.88 parent1[1]: (151) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 1.47/1.88 is_a_theorem( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := strict_implies( and( skol43, skol81 ), skol43 )
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (14401) {G2,W6,D4,L1,V0,M1} R(4041,151) { ! alpha1(
% 1.47/1.88 strict_implies( and( skol43, skol81 ), skol43 ) ) }.
% 1.47/1.88 parent0: (20349) {G2,W6,D4,L1,V0,M1} { ! alpha1( strict_implies( and(
% 1.47/1.88 skol43, skol81 ), skol43 ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20351) {G4,W7,D5,L2,V1,M2} { modus_ponens_strict_implies, !
% 1.47/1.88 is_a_theorem( necessarily( implies( skol30( X ), skol29 ) ) ) }.
% 1.47/1.88 parent0[1]: (7311) {G4,W6,D4,L2,V1,M2} R(161,191);f {
% 1.47/1.88 modus_ponens_strict_implies, ! is_a_theorem( implies( skol30( X ), skol29
% 1.47/1.88 ) ) }.
% 1.47/1.88 parent1[1]: (2747) {G3,W5,D3,L2,V1,M2} R(2691,151) { ! is_a_theorem(
% 1.47/1.88 necessarily( X ) ), is_a_theorem( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := implies( skol30( X ), skol29 )
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 paramod: (20352) {G2,W6,D4,L2,V1,M2} { ! is_a_theorem( strict_implies(
% 1.47/1.88 skol30( X ), skol29 ) ), modus_ponens_strict_implies }.
% 1.47/1.88 parent0[0]: (5677) {G1,W8,D4,L1,V2,M1} S(138);r(147) { necessarily( implies
% 1.47/1.88 ( X, Y ) ) ==> strict_implies( X, Y ) }.
% 1.47/1.88 parent1[1; 2]: (20351) {G4,W7,D5,L2,V1,M2} { modus_ponens_strict_implies,
% 1.47/1.88 ! is_a_theorem( necessarily( implies( skol30( X ), skol29 ) ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := skol30( X )
% 1.47/1.88 Y := skol29
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (15551) {G5,W6,D4,L2,V1,M2} R(7311,2747);d(5677) {
% 1.47/1.88 modus_ponens_strict_implies, ! is_a_theorem( strict_implies( skol30( X )
% 1.47/1.88 , skol29 ) ) }.
% 1.47/1.88 parent0: (20352) {G2,W6,D4,L2,V1,M2} { ! is_a_theorem( strict_implies(
% 1.47/1.88 skol30( X ), skol29 ) ), modus_ponens_strict_implies }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 1
% 1.47/1.88 1 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20353) {G1,W3,D2,L2,V0,M2} { modus_ponens_strict_implies, !
% 1.47/1.88 alpha2( skol29 ) }.
% 1.47/1.88 parent0[1]: (15551) {G5,W6,D4,L2,V1,M2} R(7311,2747);d(5677) {
% 1.47/1.88 modus_ponens_strict_implies, ! is_a_theorem( strict_implies( skol30( X )
% 1.47/1.88 , skol29 ) ) }.
% 1.47/1.88 parent1[1]: (87) {G0,W7,D4,L2,V1,M2} I { ! alpha2( X ), is_a_theorem(
% 1.47/1.88 strict_implies( skol30( X ), X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := skol29
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := skol29
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20354) {G1,W2,D1,L2,V0,M2} { modus_ponens_strict_implies,
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 parent0[1]: (20353) {G1,W3,D2,L2,V0,M2} { modus_ponens_strict_implies, !
% 1.47/1.88 alpha2( skol29 ) }.
% 1.47/1.88 parent1[0]: (84) {G0,W3,D2,L2,V0,M2} I { alpha2( skol29 ),
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 factor: (20355) {G1,W1,D1,L1,V0,M1} { modus_ponens_strict_implies }.
% 1.47/1.88 parent0[0, 1]: (20354) {G1,W2,D1,L2,V0,M2} { modus_ponens_strict_implies,
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (15618) {G6,W1,D1,L1,V0,M1} R(15551,87);r(84) {
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 parent0: (20355) {G1,W1,D1,L1,V0,M1} { modus_ponens_strict_implies }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20356) {G7,W4,D2,L2,V1,M2} { alpha1( X ), ! alpha2( X ) }.
% 1.47/1.88 parent0[1]: (839) {G6,W5,D2,L3,V1,M3} R(815,83) { alpha1( X ), !
% 1.47/1.88 modus_ponens_strict_implies, ! alpha2( X ) }.
% 1.47/1.88 parent1[0]: (15618) {G6,W1,D1,L1,V0,M1} R(15551,87);r(84) {
% 1.47/1.88 modus_ponens_strict_implies }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (15675) {G7,W4,D2,L2,V1,M2} R(15618,839) { alpha1( X ), !
% 1.47/1.88 alpha2( X ) }.
% 1.47/1.88 parent0: (20356) {G7,W4,D2,L2,V1,M2} { alpha1( X ), ! alpha2( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20357) {G3,W6,D4,L1,V0,M1} { ! alpha2( strict_implies( and(
% 1.47/1.88 skol43, skol81 ), skol43 ) ) }.
% 1.47/1.88 parent0[0]: (14401) {G2,W6,D4,L1,V0,M1} R(4041,151) { ! alpha1(
% 1.47/1.88 strict_implies( and( skol43, skol81 ), skol43 ) ) }.
% 1.47/1.88 parent1[0]: (15675) {G7,W4,D2,L2,V1,M2} R(15618,839) { alpha1( X ), !
% 1.47/1.88 alpha2( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := strict_implies( and( skol43, skol81 ), skol43 )
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (15688) {G8,W6,D4,L1,V0,M1} R(15675,14401) { ! alpha2(
% 1.47/1.88 strict_implies( and( skol43, skol81 ), skol43 ) ) }.
% 1.47/1.88 parent0: (20357) {G3,W6,D4,L1,V0,M1} { ! alpha2( strict_implies( and(
% 1.47/1.88 skol43, skol81 ), skol43 ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20360) {G2,W7,D4,L2,V2,M2} { is_a_theorem( necessarily(
% 1.47/1.88 implies( X, Y ) ) ), ! is_a_theorem( Y ) }.
% 1.47/1.88 parent0[2]: (247) {G3,W9,D3,L3,V2,M3} R(234,5) { is_a_theorem( necessarily
% 1.47/1.88 ( X ) ), ! is_a_theorem( Y ), ! is_a_theorem( implies( Y, X ) ) }.
% 1.47/1.88 parent1[0]: (180) {G1,W6,D4,L1,V2,M1} S(11);r(67) { is_a_theorem( implies(
% 1.47/1.88 X, implies( Y, X ) ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := implies( X, Y )
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := Y
% 1.47/1.88 Y := X
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 paramod: (20361) {G2,W6,D3,L2,V2,M2} { is_a_theorem( strict_implies( X, Y
% 1.47/1.88 ) ), ! is_a_theorem( Y ) }.
% 1.47/1.88 parent0[0]: (5677) {G1,W8,D4,L1,V2,M1} S(138);r(147) { necessarily( implies
% 1.47/1.88 ( X, Y ) ) ==> strict_implies( X, Y ) }.
% 1.47/1.88 parent1[0; 1]: (20360) {G2,W7,D4,L2,V2,M2} { is_a_theorem( necessarily(
% 1.47/1.88 implies( X, Y ) ) ), ! is_a_theorem( Y ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (17581) {G4,W6,D3,L2,V2,M2} R(247,180);d(5677) { !
% 1.47/1.88 is_a_theorem( Y ), is_a_theorem( strict_implies( X, Y ) ) }.
% 1.47/1.88 parent0: (20361) {G2,W6,D3,L2,V2,M2} { is_a_theorem( strict_implies( X, Y
% 1.47/1.88 ) ), ! is_a_theorem( Y ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 1
% 1.47/1.88 1 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20363) {G1,W6,D2,L3,V2,M3} { ! is_a_theorem( X ), alpha2( Y )
% 1.47/1.88 , ! is_a_theorem( Y ) }.
% 1.47/1.88 parent0[1]: (88) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), !
% 1.47/1.88 is_a_theorem( strict_implies( Y, X ) ), alpha2( X ) }.
% 1.47/1.88 parent1[1]: (17581) {G4,W6,D3,L2,V2,M2} R(247,180);d(5677) { ! is_a_theorem
% 1.47/1.88 ( Y ), is_a_theorem( strict_implies( X, Y ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := Y
% 1.47/1.88 Y := X
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (17750) {G5,W6,D2,L3,V2,M3} R(17581,88) { ! is_a_theorem( X )
% 1.47/1.88 , ! is_a_theorem( Y ), alpha2( X ) }.
% 1.47/1.88 parent0: (20363) {G1,W6,D2,L3,V2,M3} { ! is_a_theorem( X ), alpha2( Y ), !
% 1.47/1.88 is_a_theorem( Y ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 2
% 1.47/1.88 2 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 factor: (20365) {G5,W4,D2,L2,V1,M2} { ! is_a_theorem( X ), alpha2( X ) }.
% 1.47/1.88 parent0[0, 1]: (17750) {G5,W6,D2,L3,V2,M3} R(17581,88) { ! is_a_theorem( X
% 1.47/1.88 ), ! is_a_theorem( Y ), alpha2( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := X
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (17815) {G6,W4,D2,L2,V1,M2} F(17750) { ! is_a_theorem( X ),
% 1.47/1.88 alpha2( X ) }.
% 1.47/1.88 parent0: (20365) {G5,W4,D2,L2,V1,M2} { ! is_a_theorem( X ), alpha2( X )
% 1.47/1.88 }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20366) {G3,W5,D3,L2,V1,M2} { alpha2( necessarily( X ) ), !
% 1.47/1.88 alpha1( X ) }.
% 1.47/1.88 parent0[0]: (17815) {G6,W4,D2,L2,V1,M2} F(17750) { ! is_a_theorem( X ),
% 1.47/1.88 alpha2( X ) }.
% 1.47/1.88 parent1[0]: (234) {G2,W5,D3,L2,V1,M2} R(220,151) { is_a_theorem(
% 1.47/1.88 necessarily( X ) ), ! alpha1( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := necessarily( X )
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (18096) {G7,W5,D3,L2,V1,M2} R(17815,234) { alpha2( necessarily
% 1.47/1.88 ( X ) ), ! alpha1( X ) }.
% 1.47/1.88 parent0: (20366) {G3,W5,D3,L2,V1,M2} { alpha2( necessarily( X ) ), !
% 1.47/1.88 alpha1( X ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 1 ==> 1
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20368) {G7,W7,D5,L1,V2,M1} { alpha2( necessarily( implies(
% 1.47/1.88 and( X, Y ), X ) ) ) }.
% 1.47/1.88 parent0[1]: (18096) {G7,W5,D3,L2,V1,M2} R(17815,234) { alpha2( necessarily
% 1.47/1.88 ( X ) ), ! alpha1( X ) }.
% 1.47/1.88 parent1[0]: (822) {G6,W6,D4,L1,V2,M1} R(815,254) { alpha1( implies( and( X
% 1.47/1.88 , Y ), X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := implies( and( X, Y ), X )
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 paramod: (20369) {G2,W6,D4,L1,V2,M1} { alpha2( strict_implies( and( X, Y )
% 1.47/1.88 , X ) ) }.
% 1.47/1.88 parent0[0]: (5677) {G1,W8,D4,L1,V2,M1} S(138);r(147) { necessarily( implies
% 1.47/1.88 ( X, Y ) ) ==> strict_implies( X, Y ) }.
% 1.47/1.88 parent1[0; 1]: (20368) {G7,W7,D5,L1,V2,M1} { alpha2( necessarily( implies
% 1.47/1.88 ( and( X, Y ), X ) ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := and( X, Y )
% 1.47/1.88 Y := X
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (19852) {G8,W6,D4,L1,V2,M1} R(18096,822);d(5677) { alpha2(
% 1.47/1.88 strict_implies( and( X, Y ), X ) ) }.
% 1.47/1.88 parent0: (20369) {G2,W6,D4,L1,V2,M1} { alpha2( strict_implies( and( X, Y )
% 1.47/1.88 , X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 X := X
% 1.47/1.88 Y := Y
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 0 ==> 0
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 resolution: (20370) {G9,W0,D0,L0,V0,M0} { }.
% 1.47/1.88 parent0[0]: (15688) {G8,W6,D4,L1,V0,M1} R(15675,14401) { ! alpha2(
% 1.47/1.88 strict_implies( and( skol43, skol81 ), skol43 ) ) }.
% 1.47/1.88 parent1[0]: (19852) {G8,W6,D4,L1,V2,M1} R(18096,822);d(5677) { alpha2(
% 1.47/1.88 strict_implies( and( X, Y ), X ) ) }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 substitution1:
% 1.47/1.88 X := skol43
% 1.47/1.88 Y := skol81
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 subsumption: (20001) {G9,W0,D0,L0,V0,M0} S(15688);r(19852) { }.
% 1.47/1.88 parent0: (20370) {G9,W0,D0,L0,V0,M0} { }.
% 1.47/1.88 substitution0:
% 1.47/1.88 end
% 1.47/1.88 permutation0:
% 1.47/1.88 end
% 1.47/1.88
% 1.47/1.88 Proof check complete!
% 1.47/1.88
% 1.47/1.88 Memory use:
% 1.47/1.88
% 1.47/1.88 space for terms: 230919
% 1.47/1.88 space for clauses: 852206
% 1.47/1.88
% 1.47/1.88
% 1.47/1.88 clauses generated: 39115
% 1.47/1.88 clauses kept: 20002
% 1.47/1.88 clauses selected: 888
% 1.47/1.88 clauses deleted: 377
% 1.47/1.88 clauses inuse deleted: 228
% 1.47/1.88
% 1.47/1.88 subsentry: 127445
% 1.47/1.88 literals s-matched: 99608
% 1.47/1.88 literals matched: 91031
% 1.47/1.88 full subsumption: 11182
% 1.47/1.88
% 1.47/1.88 checksum: -2129115877
% 1.47/1.88
% 1.47/1.88
% 1.47/1.88 Bliksem ended
%------------------------------------------------------------------------------