TSTP Solution File: LCL525+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL525+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n026.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 07:54:25 EDT 2022
% Result : Theorem 0.72s 1.25s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL525+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Mon Jul 4 21:15:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.68/1.08 *** allocated 10000 integers for termspace/termends
% 0.68/1.08 *** allocated 10000 integers for clauses
% 0.68/1.08 *** allocated 10000 integers for justifications
% 0.68/1.08 Bliksem 1.12
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 Automatic Strategy Selection
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 Clauses:
% 0.68/1.08
% 0.68/1.08 { ! modus_ponens, ! alpha1( X ), is_a_theorem( X ) }.
% 0.68/1.08 { alpha1( skol1 ), modus_ponens }.
% 0.68/1.08 { ! is_a_theorem( skol1 ), modus_ponens }.
% 0.68/1.08 { ! alpha1( X ), is_a_theorem( skol2( Y ) ) }.
% 0.68/1.08 { ! alpha1( X ), is_a_theorem( implies( skol2( X ), X ) ) }.
% 0.68/1.08 { ! is_a_theorem( Y ), ! is_a_theorem( implies( Y, X ) ), alpha1( X ) }.
% 0.68/1.08 { ! substitution_of_equivalents, ! is_a_theorem( equiv( X, Y ) ), X = Y }.
% 0.68/1.08 { is_a_theorem( equiv( skol3, skol52 ) ), substitution_of_equivalents }.
% 0.68/1.08 { ! skol3 = skol52, substitution_of_equivalents }.
% 0.68/1.08 { ! modus_tollens, is_a_theorem( implies( implies( not( Y ), not( X ) ),
% 0.68/1.08 implies( X, Y ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( implies( not( skol53 ), not( skol4 ) ), implies
% 0.68/1.08 ( skol4, skol53 ) ) ), modus_tollens }.
% 0.68/1.08 { ! implies_1, is_a_theorem( implies( X, implies( Y, X ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( skol5, implies( skol54, skol5 ) ) ), implies_1 }
% 0.68/1.08 .
% 0.68/1.08 { ! implies_2, is_a_theorem( implies( implies( X, implies( X, Y ) ),
% 0.68/1.08 implies( X, Y ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( implies( skol6, implies( skol6, skol55 ) ),
% 0.68/1.08 implies( skol6, skol55 ) ) ), implies_2 }.
% 0.68/1.08 { ! implies_3, is_a_theorem( implies( implies( X, Y ), implies( implies( Y
% 0.68/1.08 , Z ), implies( X, Z ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( implies( skol7, skol56 ), implies( implies(
% 0.68/1.08 skol56, skol86 ), implies( skol7, skol86 ) ) ) ), implies_3 }.
% 0.68/1.08 { ! and_1, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( and( skol8, skol57 ), skol8 ) ), and_1 }.
% 0.68/1.08 { ! and_2, is_a_theorem( implies( and( X, Y ), Y ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( and( skol9, skol58 ), skol58 ) ), and_2 }.
% 0.68/1.08 { ! and_3, is_a_theorem( implies( X, implies( Y, and( X, Y ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( skol10, implies( skol59, and( skol10, skol59 ) )
% 0.68/1.08 ) ), and_3 }.
% 0.68/1.08 { ! or_1, is_a_theorem( implies( X, or( X, Y ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( skol11, or( skol11, skol60 ) ) ), or_1 }.
% 0.68/1.08 { ! or_2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( skol61, or( skol12, skol61 ) ) ), or_2 }.
% 0.68/1.08 { ! or_3, is_a_theorem( implies( implies( X, Z ), implies( implies( Y, Z )
% 0.68/1.08 , implies( or( X, Y ), Z ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( implies( skol13, skol87 ), implies( implies(
% 0.68/1.08 skol62, skol87 ), implies( or( skol13, skol62 ), skol87 ) ) ) ), or_3 }.
% 0.68/1.08 { ! equivalence_1, is_a_theorem( implies( equiv( X, Y ), implies( X, Y ) )
% 0.68/1.08 ) }.
% 0.68/1.08 { ! is_a_theorem( implies( equiv( skol14, skol63 ), implies( skol14, skol63
% 0.68/1.08 ) ) ), equivalence_1 }.
% 0.68/1.08 { ! equivalence_2, is_a_theorem( implies( equiv( X, Y ), implies( Y, X ) )
% 0.68/1.08 ) }.
% 0.68/1.08 { ! is_a_theorem( implies( equiv( skol15, skol64 ), implies( skol64, skol15
% 0.68/1.08 ) ) ), equivalence_2 }.
% 0.68/1.08 { ! equivalence_3, is_a_theorem( implies( implies( X, Y ), implies( implies
% 0.68/1.08 ( Y, X ), equiv( X, Y ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( implies( skol16, skol65 ), implies( implies(
% 0.68/1.08 skol65, skol16 ), equiv( skol16, skol65 ) ) ) ), equivalence_3 }.
% 0.68/1.08 { ! kn1, is_a_theorem( implies( X, and( X, X ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( skol17, and( skol17, skol17 ) ) ), kn1 }.
% 0.68/1.08 { ! kn2, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( and( skol18, skol66 ), skol18 ) ), kn2 }.
% 0.68/1.08 { ! kn3, is_a_theorem( implies( implies( X, Y ), implies( not( and( Y, Z )
% 0.68/1.08 ), not( and( Z, X ) ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( implies( skol19, skol67 ), implies( not( and(
% 0.68/1.08 skol67, skol88 ) ), not( and( skol88, skol19 ) ) ) ) ), kn3 }.
% 0.68/1.08 { ! cn1, is_a_theorem( implies( implies( X, Y ), implies( implies( Y, Z ),
% 0.68/1.08 implies( X, Z ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( implies( skol20, skol68 ), implies( implies(
% 0.68/1.08 skol68, skol89 ), implies( skol20, skol89 ) ) ) ), cn1 }.
% 0.68/1.08 { ! cn2, is_a_theorem( implies( X, implies( not( X ), Y ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( skol21, implies( not( skol21 ), skol69 ) ) ),
% 0.68/1.08 cn2 }.
% 0.68/1.08 { ! cn3, is_a_theorem( implies( implies( not( X ), X ), X ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( implies( not( skol22 ), skol22 ), skol22 ) ),
% 0.68/1.08 cn3 }.
% 0.68/1.08 { ! r1, is_a_theorem( implies( or( X, X ), X ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( or( skol23, skol23 ), skol23 ) ), r1 }.
% 0.68/1.08 { ! r2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( skol70, or( skol24, skol70 ) ) ), r2 }.
% 0.68/1.08 { ! r3, is_a_theorem( implies( or( X, Y ), or( Y, X ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( or( skol25, skol71 ), or( skol71, skol25 ) ) ),
% 0.68/1.08 r3 }.
% 0.68/1.08 { ! r4, is_a_theorem( implies( or( X, or( Y, Z ) ), or( Y, or( X, Z ) ) ) )
% 0.68/1.08 }.
% 0.68/1.08 { ! is_a_theorem( implies( or( skol26, or( skol72, skol90 ) ), or( skol72,
% 0.68/1.08 or( skol26, skol90 ) ) ) ), r4 }.
% 0.68/1.08 { ! r5, is_a_theorem( implies( implies( Y, Z ), implies( or( X, Y ), or( X
% 0.68/1.08 , Z ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( implies( skol73, skol91 ), implies( or( skol27,
% 0.68/1.08 skol73 ), or( skol27, skol91 ) ) ) ), r5 }.
% 0.68/1.08 { ! op_or, or( X, Y ) = not( and( not( X ), not( Y ) ) ) }.
% 0.68/1.08 { ! op_and, and( X, Y ) = not( or( not( X ), not( Y ) ) ) }.
% 0.68/1.08 { ! op_implies_and, implies( X, Y ) = not( and( X, not( Y ) ) ) }.
% 0.68/1.08 { ! op_implies_or, implies( X, Y ) = or( not( X ), Y ) }.
% 0.68/1.08 { ! op_equiv, equiv( X, Y ) = and( implies( X, Y ), implies( Y, X ) ) }.
% 0.68/1.08 { op_or }.
% 0.68/1.08 { op_implies_and }.
% 0.68/1.08 { op_equiv }.
% 0.68/1.08 { modus_ponens }.
% 0.68/1.08 { modus_tollens }.
% 0.68/1.08 { implies_1 }.
% 0.68/1.08 { implies_2 }.
% 0.68/1.08 { implies_3 }.
% 0.68/1.08 { and_1 }.
% 0.68/1.08 { and_2 }.
% 0.68/1.08 { and_3 }.
% 0.68/1.08 { or_1 }.
% 0.68/1.08 { or_2 }.
% 0.68/1.08 { or_3 }.
% 0.68/1.08 { equivalence_1 }.
% 0.68/1.08 { equivalence_2 }.
% 0.68/1.08 { equivalence_3 }.
% 0.68/1.08 { substitution_of_equivalents }.
% 0.68/1.08 { ! necessitation, ! is_a_theorem( X ), is_a_theorem( necessarily( X ) ) }
% 0.68/1.08 .
% 0.68/1.08 { is_a_theorem( skol28 ), necessitation }.
% 0.68/1.08 { ! is_a_theorem( necessarily( skol28 ) ), necessitation }.
% 0.68/1.08 { ! modus_ponens_strict_implies, ! alpha2( X ), is_a_theorem( X ) }.
% 0.68/1.08 { alpha2( skol29 ), modus_ponens_strict_implies }.
% 0.68/1.08 { ! is_a_theorem( skol29 ), modus_ponens_strict_implies }.
% 0.68/1.08 { ! alpha2( X ), is_a_theorem( skol30( Y ) ) }.
% 0.68/1.08 { ! alpha2( X ), is_a_theorem( strict_implies( skol30( X ), X ) ) }.
% 0.68/1.08 { ! is_a_theorem( Y ), ! is_a_theorem( strict_implies( Y, X ) ), alpha2( X
% 0.68/1.08 ) }.
% 0.68/1.08 { ! adjunction, ! alpha3( X, Y ), is_a_theorem( and( X, Y ) ) }.
% 0.68/1.08 { alpha3( skol31, skol74 ), adjunction }.
% 0.68/1.08 { ! is_a_theorem( and( skol31, skol74 ) ), adjunction }.
% 0.68/1.08 { ! alpha3( X, Y ), is_a_theorem( X ) }.
% 0.68/1.08 { ! alpha3( X, Y ), is_a_theorem( Y ) }.
% 0.68/1.08 { ! is_a_theorem( X ), ! is_a_theorem( Y ), alpha3( X, Y ) }.
% 0.68/1.08 { ! substitution_strict_equiv, ! is_a_theorem( strict_equiv( X, Y ) ), X =
% 0.68/1.08 Y }.
% 0.68/1.08 { is_a_theorem( strict_equiv( skol32, skol75 ) ), substitution_strict_equiv
% 0.68/1.08 }.
% 0.68/1.08 { ! skol32 = skol75, substitution_strict_equiv }.
% 0.68/1.08 { ! axiom_K, is_a_theorem( implies( necessarily( implies( X, Y ) ), implies
% 0.68/1.08 ( necessarily( X ), necessarily( Y ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( necessarily( implies( skol33, skol76 ) ),
% 0.68/1.08 implies( necessarily( skol33 ), necessarily( skol76 ) ) ) ), axiom_K }.
% 0.68/1.08 { ! axiom_M, is_a_theorem( implies( necessarily( X ), X ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( necessarily( skol34 ), skol34 ) ), axiom_M }.
% 0.68/1.08 { ! axiom_4, is_a_theorem( implies( necessarily( X ), necessarily(
% 0.68/1.08 necessarily( X ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( necessarily( skol35 ), necessarily( necessarily
% 0.68/1.08 ( skol35 ) ) ) ), axiom_4 }.
% 0.68/1.08 { ! axiom_B, is_a_theorem( implies( X, necessarily( possibly( X ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( skol36, necessarily( possibly( skol36 ) ) ) ),
% 0.68/1.08 axiom_B }.
% 0.68/1.08 { ! axiom_5, is_a_theorem( implies( possibly( X ), necessarily( possibly( X
% 0.68/1.08 ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( possibly( skol37 ), necessarily( possibly(
% 0.68/1.08 skol37 ) ) ) ), axiom_5 }.
% 0.68/1.08 { ! axiom_s1, is_a_theorem( implies( and( necessarily( implies( X, Y ) ),
% 0.68/1.08 necessarily( implies( Y, Z ) ) ), necessarily( implies( X, Z ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( implies( and( necessarily( implies( skol38, skol77 ) ),
% 0.68/1.08 necessarily( implies( skol77, skol92 ) ) ), necessarily( implies( skol38
% 0.68/1.08 , skol92 ) ) ) ), axiom_s1 }.
% 0.68/1.08 { ! axiom_s2, is_a_theorem( strict_implies( possibly( and( X, Y ) ), and(
% 0.68/1.08 possibly( X ), possibly( Y ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( strict_implies( possibly( and( skol39, skol78 ) ), and(
% 0.68/1.08 possibly( skol39 ), possibly( skol78 ) ) ) ), axiom_s2 }.
% 0.68/1.08 { ! axiom_s3, is_a_theorem( strict_implies( strict_implies( X, Y ),
% 0.68/1.08 strict_implies( not( possibly( Y ) ), not( possibly( X ) ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( strict_implies( strict_implies( skol40, skol79 ),
% 0.68/1.08 strict_implies( not( possibly( skol79 ) ), not( possibly( skol40 ) ) ) )
% 0.68/1.08 ), axiom_s3 }.
% 0.68/1.08 { ! axiom_s4, is_a_theorem( strict_implies( necessarily( X ), necessarily(
% 0.68/1.08 necessarily( X ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( strict_implies( necessarily( skol41 ), necessarily(
% 0.68/1.08 necessarily( skol41 ) ) ) ), axiom_s4 }.
% 0.68/1.08 { ! axiom_m1, is_a_theorem( strict_implies( and( X, Y ), and( Y, X ) ) ) }
% 0.68/1.08 .
% 0.68/1.08 { ! is_a_theorem( strict_implies( and( skol42, skol80 ), and( skol80,
% 0.68/1.08 skol42 ) ) ), axiom_m1 }.
% 0.68/1.08 { ! axiom_m2, is_a_theorem( strict_implies( and( X, Y ), X ) ) }.
% 0.68/1.08 { ! is_a_theorem( strict_implies( and( skol43, skol81 ), skol43 ) ),
% 0.68/1.08 axiom_m2 }.
% 0.68/1.08 { ! axiom_m3, is_a_theorem( strict_implies( and( and( X, Y ), Z ), and( X,
% 0.68/1.08 and( Y, Z ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( strict_implies( and( and( skol44, skol82 ), skol93 ), and
% 0.68/1.08 ( skol44, and( skol82, skol93 ) ) ) ), axiom_m3 }.
% 0.68/1.08 { ! axiom_m4, is_a_theorem( strict_implies( X, and( X, X ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( strict_implies( skol45, and( skol45, skol45 ) ) ),
% 0.68/1.08 axiom_m4 }.
% 0.68/1.08 { ! axiom_m5, is_a_theorem( strict_implies( and( strict_implies( X, Y ),
% 0.68/1.08 strict_implies( Y, Z ) ), strict_implies( X, Z ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( strict_implies( and( strict_implies( skol46, skol83 ),
% 0.68/1.08 strict_implies( skol83, skol94 ) ), strict_implies( skol46, skol94 ) ) )
% 0.68/1.08 , axiom_m5 }.
% 0.68/1.08 { ! axiom_m6, is_a_theorem( strict_implies( X, possibly( X ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( strict_implies( skol47, possibly( skol47 ) ) ), axiom_m6
% 0.68/1.08 }.
% 0.68/1.08 { ! axiom_m7, is_a_theorem( strict_implies( possibly( and( X, Y ) ), X ) )
% 0.68/1.08 }.
% 0.68/1.08 { ! is_a_theorem( strict_implies( possibly( and( skol48, skol84 ) ), skol48
% 0.68/1.08 ) ), axiom_m7 }.
% 0.68/1.08 { ! axiom_m8, is_a_theorem( strict_implies( strict_implies( X, Y ),
% 0.68/1.08 strict_implies( possibly( X ), possibly( Y ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( strict_implies( strict_implies( skol49, skol85 ),
% 0.68/1.08 strict_implies( possibly( skol49 ), possibly( skol85 ) ) ) ), axiom_m8 }
% 0.68/1.08 .
% 0.68/1.08 { ! axiom_m9, is_a_theorem( strict_implies( possibly( possibly( X ) ),
% 0.68/1.08 possibly( X ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( strict_implies( possibly( possibly( skol50 ) ), possibly
% 0.68/1.08 ( skol50 ) ) ), axiom_m9 }.
% 0.68/1.08 { ! axiom_m10, is_a_theorem( strict_implies( possibly( X ), necessarily(
% 0.68/1.08 possibly( X ) ) ) ) }.
% 0.68/1.08 { ! is_a_theorem( strict_implies( possibly( skol51 ), necessarily( possibly
% 0.68/1.08 ( skol51 ) ) ) ), axiom_m10 }.
% 0.68/1.08 { ! op_possibly, possibly( X ) = not( necessarily( not( X ) ) ) }.
% 0.68/1.08 { ! op_necessarily, necessarily( X ) = not( possibly( not( X ) ) ) }.
% 0.68/1.08 { ! op_strict_implies, strict_implies( X, Y ) = necessarily( implies( X, Y
% 0.68/1.08 ) ) }.
% 0.68/1.08 { ! op_strict_equiv, strict_equiv( X, Y ) = and( strict_implies( X, Y ),
% 0.68/1.08 strict_implies( Y, X ) ) }.
% 0.68/1.08 { op_possibly }.
% 0.68/1.08 { necessitation }.
% 0.68/1.08 { axiom_K }.
% 0.68/1.08 { axiom_M }.
% 0.68/1.08 { axiom_5 }.
% 0.68/1.08 { op_possibly }.
% 0.68/1.08 { op_or }.
% 0.68/1.08 { op_implies }.
% 0.68/1.08 { op_strict_implies }.
% 0.68/1.08 { op_equiv }.
% 0.68/1.08 { op_strict_equiv }.
% 0.68/1.08 { ! modus_ponens_strict_implies }.
% 0.68/1.08
% 0.68/1.08 percentage equality = 0.046429, percentage horn = 0.959732
% 0.68/1.08 This is a problem with some equality
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 Options Used:
% 0.68/1.08
% 0.68/1.08 useres = 1
% 0.68/1.08 useparamod = 1
% 0.68/1.08 useeqrefl = 1
% 0.68/1.08 useeqfact = 1
% 0.68/1.08 usefactor = 1
% 0.68/1.08 usesimpsplitting = 0
% 0.68/1.08 usesimpdemod = 5
% 0.68/1.08 usesimpres = 3
% 0.68/1.08
% 0.68/1.08 resimpinuse = 1000
% 0.68/1.08 resimpclauses = 20000
% 0.68/1.08 substype = eqrewr
% 0.68/1.08 backwardsubs = 1
% 0.68/1.08 selectoldest = 5
% 0.68/1.08
% 0.68/1.08 litorderings [0] = split
% 0.68/1.08 litorderings [1] = extend the termordering, first sorting on arguments
% 0.68/1.08
% 0.68/1.08 termordering = kbo
% 0.68/1.08
% 0.68/1.08 litapriori = 0
% 0.68/1.08 termapriori = 1
% 0.68/1.08 litaposteriori = 0
% 0.68/1.08 termaposteriori = 0
% 0.68/1.08 demodaposteriori = 0
% 0.68/1.08 ordereqreflfact = 0
% 0.68/1.08
% 0.68/1.08 litselect = negord
% 0.68/1.08
% 0.68/1.08 maxweight = 15
% 0.68/1.08 maxdepth = 30000
% 0.68/1.08 maxlength = 115
% 0.68/1.08 maxnrvars = 195
% 0.68/1.08 excuselevel = 1
% 0.68/1.08 increasemaxweight = 1
% 0.68/1.08
% 0.68/1.08 maxselected = 10000000
% 0.68/1.08 maxnrclauses = 10000000
% 0.68/1.08
% 0.68/1.08 showgenerated = 0
% 0.68/1.08 showkept = 0
% 0.68/1.08 showselected = 0
% 0.68/1.08 showdeleted = 0
% 0.68/1.08 showresimp = 1
% 0.68/1.08 showstatus = 2000
% 0.68/1.08
% 0.68/1.08 prologoutput = 0
% 0.68/1.08 nrgoals = 5000000
% 0.68/1.08 totalproof = 1
% 0.68/1.08
% 0.68/1.08 Symbols occurring in the translation:
% 0.68/1.08
% 0.68/1.08 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.68/1.08 . [1, 2] (w:1, o:176, a:1, s:1, b:0),
% 0.68/1.08 ! [4, 1] (w:0, o:163, a:1, s:1, b:0),
% 0.68/1.08 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.68/1.08 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.68/1.08 modus_ponens [35, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.68/1.08 is_a_theorem [38, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.68/1.08 implies [39, 2] (w:1, o:200, a:1, s:1, b:0),
% 0.68/1.08 substitution_of_equivalents [40, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.68/1.08 equiv [41, 2] (w:1, o:201, a:1, s:1, b:0),
% 0.68/1.08 modus_tollens [42, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.68/1.08 not [43, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.68/1.08 implies_1 [44, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.68/1.08 implies_2 [45, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.68/1.08 implies_3 [46, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.68/1.08 and_1 [48, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.68/1.08 and [49, 2] (w:1, o:202, a:1, s:1, b:0),
% 0.68/1.08 and_2 [50, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.68/1.08 and_3 [51, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.68/1.08 or_1 [52, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.68/1.08 or [53, 2] (w:1, o:203, a:1, s:1, b:0),
% 0.68/1.08 or_2 [54, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.68/1.08 or_3 [55, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.68/1.08 equivalence_1 [56, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.68/1.08 equivalence_2 [57, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.68/1.08 equivalence_3 [58, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.68/1.08 kn1 [59, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.68/1.08 kn2 [61, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.68/1.08 kn3 [63, 0] (w:1, o:35, a:1, s:1, b:0),
% 0.68/1.08 cn1 [65, 0] (w:1, o:37, a:1, s:1, b:0),
% 0.68/1.08 cn2 [66, 0] (w:1, o:38, a:1, s:1, b:0),
% 0.68/1.08 cn3 [67, 0] (w:1, o:39, a:1, s:1, b:0),
% 0.68/1.08 r1 [68, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.68/1.08 r2 [69, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.68/1.08 r3 [70, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.68/1.08 r4 [71, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.68/1.08 r5 [72, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.68/1.08 op_or [73, 0] (w:1, o:41, a:1, s:1, b:0),
% 0.68/1.08 op_and [74, 0] (w:1, o:42, a:1, s:1, b:0),
% 0.68/1.08 op_implies_and [75, 0] (w:1, o:43, a:1, s:1, b:0),
% 0.68/1.08 op_implies_or [76, 0] (w:1, o:44, a:1, s:1, b:0),
% 0.68/1.08 op_equiv [77, 0] (w:1, o:45, a:1, s:1, b:0),
% 0.68/1.08 necessitation [78, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.68/1.08 necessarily [79, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.68/1.08 modus_ponens_strict_implies [80, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.68/1.08 strict_implies [81, 2] (w:1, o:204, a:1, s:1, b:0),
% 0.68/1.08 adjunction [82, 0] (w:1, o:46, a:1, s:1, b:0),
% 0.68/1.08 substitution_strict_equiv [83, 0] (w:1, o:47, a:1, s:1, b:0),
% 0.68/1.08 strict_equiv [84, 2] (w:1, o:205, a:1, s:1, b:0),
% 0.68/1.08 axiom_K [85, 0] (w:1, o:48, a:1, s:1, b:0),
% 0.68/1.08 axiom_M [86, 0] (w:1, o:49, a:1, s:1, b:0),
% 0.68/1.08 axiom_4 [87, 0] (w:1, o:50, a:1, s:1, b:0),
% 0.68/1.08 axiom_B [88, 0] (w:1, o:51, a:1, s:1, b:0),
% 0.68/1.08 possibly [89, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.68/1.08 axiom_5 [90, 0] (w:1, o:52, a:1, s:1, b:0),
% 0.68/1.08 axiom_s1 [91, 0] (w:1, o:53, a:1, s:1, b:0),
% 0.68/1.08 axiom_s2 [92, 0] (w:1, o:54, a:1, s:1, b:0),
% 0.68/1.08 axiom_s3 [93, 0] (w:1, o:55, a:1, s:1, b:0),
% 0.68/1.08 axiom_s4 [94, 0] (w:1, o:56, a:1, s:1, b:0),
% 0.68/1.08 axiom_m1 [95, 0] (w:1, o:57, a:1, s:1, b:0),
% 0.68/1.08 axiom_m2 [96, 0] (w:1, o:59, a:1, s:1, b:0),
% 0.68/1.08 axiom_m3 [97, 0] (w:1, o:60, a:1, s:1, b:0),
% 0.68/1.08 axiom_m4 [98, 0] (w:1, o:61, a:1, s:1, b:0),
% 0.68/1.08 axiom_m5 [99, 0] (w:1, o:62, a:1, s:1, b:0),
% 0.68/1.08 axiom_m6 [100, 0] (w:1, o:63, a:1, s:1, b:0),
% 0.68/1.08 axiom_m7 [101, 0] (w:1, o:64, a:1, s:1, b:0),
% 0.68/1.08 axiom_m8 [102, 0] (w:1, o:65, a:1, s:1, b:0),
% 0.68/1.08 axiom_m9 [103, 0] (w:1, o:66, a:1, s:1, b:0),
% 0.68/1.08 axiom_m10 [104, 0] (w:1, o:58, a:1, s:1, b:0),
% 0.68/1.08 op_possibly [105, 0] (w:1, o:67, a:1, s:1, b:0),
% 0.68/1.08 op_necessarily [106, 0] (w:1, o:40, a:1, s:1, b:0),
% 0.68/1.08 op_strict_implies [107, 0] (w:1, o:68, a:1, s:1, b:0),
% 0.68/1.08 op_strict_equiv [108, 0] (w:1, o:69, a:1, s:1, b:0),
% 0.68/1.08 op_implies [109, 0] (w:1, o:70, a:1, s:1, b:0),
% 0.68/1.08 alpha1 [110, 1] (w:1, o:172, a:1, s:1, b:1),
% 0.68/1.08 alpha2 [111, 1] (w:1, o:173, a:1, s:1, b:1),
% 0.68/1.08 alpha3 [112, 2] (w:1, o:206, a:1, s:1, b:1),
% 0.68/1.08 skol1 [113, 0] (w:1, o:71, a:1, s:1, b:1),
% 0.72/1.25 skol2 [114, 1] (w:1, o:174, a:1, s:1, b:1),
% 0.72/1.25 skol3 [115, 0] (w:1, o:82, a:1, s:1, b:1),
% 0.72/1.25 skol4 [116, 0] (w:1, o:92, a:1, s:1, b:1),
% 0.72/1.25 skol5 [117, 0] (w:1, o:103, a:1, s:1, b:1),
% 0.72/1.25 skol6 [118, 0] (w:1, o:114, a:1, s:1, b:1),
% 0.72/1.25 skol7 [119, 0] (w:1, o:125, a:1, s:1, b:1),
% 0.72/1.25 skol8 [120, 0] (w:1, o:136, a:1, s:1, b:1),
% 0.72/1.25 skol9 [121, 0] (w:1, o:147, a:1, s:1, b:1),
% 0.72/1.25 skol10 [122, 0] (w:1, o:148, a:1, s:1, b:1),
% 0.72/1.25 skol11 [123, 0] (w:1, o:149, a:1, s:1, b:1),
% 0.72/1.25 skol12 [124, 0] (w:1, o:150, a:1, s:1, b:1),
% 0.72/1.25 skol13 [125, 0] (w:1, o:151, a:1, s:1, b:1),
% 0.72/1.25 skol14 [126, 0] (w:1, o:152, a:1, s:1, b:1),
% 0.72/1.25 skol15 [127, 0] (w:1, o:153, a:1, s:1, b:1),
% 0.72/1.25 skol16 [128, 0] (w:1, o:154, a:1, s:1, b:1),
% 0.72/1.25 skol17 [129, 0] (w:1, o:155, a:1, s:1, b:1),
% 0.72/1.25 skol18 [130, 0] (w:1, o:156, a:1, s:1, b:1),
% 0.72/1.25 skol19 [131, 0] (w:1, o:157, a:1, s:1, b:1),
% 0.72/1.25 skol20 [132, 0] (w:1, o:72, a:1, s:1, b:1),
% 0.72/1.25 skol21 [133, 0] (w:1, o:73, a:1, s:1, b:1),
% 0.72/1.25 skol22 [134, 0] (w:1, o:74, a:1, s:1, b:1),
% 0.72/1.25 skol23 [135, 0] (w:1, o:75, a:1, s:1, b:1),
% 0.72/1.25 skol24 [136, 0] (w:1, o:76, a:1, s:1, b:1),
% 0.72/1.25 skol25 [137, 0] (w:1, o:77, a:1, s:1, b:1),
% 0.72/1.25 skol26 [138, 0] (w:1, o:78, a:1, s:1, b:1),
% 0.72/1.25 skol27 [139, 0] (w:1, o:79, a:1, s:1, b:1),
% 0.72/1.25 skol28 [140, 0] (w:1, o:80, a:1, s:1, b:1),
% 0.72/1.25 skol29 [141, 0] (w:1, o:81, a:1, s:1, b:1),
% 0.72/1.25 skol30 [142, 1] (w:1, o:175, a:1, s:1, b:1),
% 0.72/1.25 skol31 [143, 0] (w:1, o:83, a:1, s:1, b:1),
% 0.72/1.25 skol32 [144, 0] (w:1, o:84, a:1, s:1, b:1),
% 0.72/1.25 skol33 [145, 0] (w:1, o:85, a:1, s:1, b:1),
% 0.72/1.25 skol34 [146, 0] (w:1, o:86, a:1, s:1, b:1),
% 0.72/1.25 skol35 [147, 0] (w:1, o:87, a:1, s:1, b:1),
% 0.72/1.25 skol36 [148, 0] (w:1, o:88, a:1, s:1, b:1),
% 0.72/1.25 skol37 [149, 0] (w:1, o:89, a:1, s:1, b:1),
% 0.72/1.25 skol38 [150, 0] (w:1, o:90, a:1, s:1, b:1),
% 0.72/1.25 skol39 [151, 0] (w:1, o:91, a:1, s:1, b:1),
% 0.72/1.25 skol40 [152, 0] (w:1, o:93, a:1, s:1, b:1),
% 0.72/1.25 skol41 [153, 0] (w:1, o:94, a:1, s:1, b:1),
% 0.72/1.25 skol42 [154, 0] (w:1, o:95, a:1, s:1, b:1),
% 0.72/1.25 skol43 [155, 0] (w:1, o:96, a:1, s:1, b:1),
% 0.72/1.25 skol44 [156, 0] (w:1, o:97, a:1, s:1, b:1),
% 0.72/1.25 skol45 [157, 0] (w:1, o:98, a:1, s:1, b:1),
% 0.72/1.25 skol46 [158, 0] (w:1, o:99, a:1, s:1, b:1),
% 0.72/1.25 skol47 [159, 0] (w:1, o:100, a:1, s:1, b:1),
% 0.72/1.25 skol48 [160, 0] (w:1, o:101, a:1, s:1, b:1),
% 0.72/1.25 skol49 [161, 0] (w:1, o:102, a:1, s:1, b:1),
% 0.72/1.25 skol50 [162, 0] (w:1, o:104, a:1, s:1, b:1),
% 0.72/1.25 skol51 [163, 0] (w:1, o:105, a:1, s:1, b:1),
% 0.72/1.25 skol52 [164, 0] (w:1, o:106, a:1, s:1, b:1),
% 0.72/1.25 skol53 [165, 0] (w:1, o:107, a:1, s:1, b:1),
% 0.72/1.25 skol54 [166, 0] (w:1, o:108, a:1, s:1, b:1),
% 0.72/1.25 skol55 [167, 0] (w:1, o:109, a:1, s:1, b:1),
% 0.72/1.25 skol56 [168, 0] (w:1, o:110, a:1, s:1, b:1),
% 0.72/1.25 skol57 [169, 0] (w:1, o:111, a:1, s:1, b:1),
% 0.72/1.25 skol58 [170, 0] (w:1, o:112, a:1, s:1, b:1),
% 0.72/1.25 skol59 [171, 0] (w:1, o:113, a:1, s:1, b:1),
% 0.72/1.25 skol60 [172, 0] (w:1, o:115, a:1, s:1, b:1),
% 0.72/1.25 skol61 [173, 0] (w:1, o:116, a:1, s:1, b:1),
% 0.72/1.25 skol62 [174, 0] (w:1, o:117, a:1, s:1, b:1),
% 0.72/1.25 skol63 [175, 0] (w:1, o:118, a:1, s:1, b:1),
% 0.72/1.25 skol64 [176, 0] (w:1, o:119, a:1, s:1, b:1),
% 0.72/1.25 skol65 [177, 0] (w:1, o:120, a:1, s:1, b:1),
% 0.72/1.25 skol66 [178, 0] (w:1, o:121, a:1, s:1, b:1),
% 0.72/1.25 skol67 [179, 0] (w:1, o:122, a:1, s:1, b:1),
% 0.72/1.25 skol68 [180, 0] (w:1, o:123, a:1, s:1, b:1),
% 0.72/1.25 skol69 [181, 0] (w:1, o:124, a:1, s:1, b:1),
% 0.72/1.25 skol70 [182, 0] (w:1, o:126, a:1, s:1, b:1),
% 0.72/1.25 skol71 [183, 0] (w:1, o:127, a:1, s:1, b:1),
% 0.72/1.25 skol72 [184, 0] (w:1, o:128, a:1, s:1, b:1),
% 0.72/1.25 skol73 [185, 0] (w:1, o:129, a:1, s:1, b:1),
% 0.72/1.25 skol74 [186, 0] (w:1, o:130, a:1, s:1, b:1),
% 0.72/1.25 skol75 [187, 0] (w:1, o:131, a:1, s:1, b:1),
% 0.72/1.25 skol76 [188, 0] (w:1, o:132, a:1, s:1, b:1),
% 0.72/1.25 skol77 [189, 0] (w:1, o:133, a:1, s:1, b:1),
% 0.72/1.25 skol78 [190, 0] (w:1, o:134, a:1, s:1, b:1),
% 0.72/1.25 skol79 [191, 0] (w:1, o:135, a:1, s:1, b:1),
% 0.72/1.25 skol80 [192, 0] (w:1, o:137, a:1, s:1, b:1),
% 0.72/1.25 skol81 [193, 0] (w:1, o:138, a:1, s:1, b:1),
% 0.72/1.25 skol82 [194, 0] (w:1, o:139, a:1, s:1, b:1),
% 0.72/1.25 skol83 [195, 0] (w:1, o:140, a:1, s:1, b:1),
% 0.72/1.25 skol84 [196, 0] (w:1, o:141, a:1, s:1, b:1),
% 0.72/1.25 skol85 [197, 0] (w:1, o:142, a:1, s:1, b:1),
% 0.72/1.25 skol86 [198, 0] (w:1, o:143, a:1, s:1, b:1),
% 0.72/1.25 skol87 [199, 0] (w:1, o:144, a:1, s:1, b:1),
% 0.72/1.25 skol88 [200, 0] (w:1, o:145, a:1, s:1, b:1),
% 0.72/1.25 skol89 [201, 0] (w:1, o:146, a:1, s:1, b:1),
% 0.72/1.25 skol90 [202, 0] (w:1, o:158, a:1, s:1, b:1),
% 0.72/1.25 skol91 [203, 0] (w:1, o:159, a:1, s:1, b:1),
% 0.72/1.25 skol92 [204, 0] (w:1, o:160, a:1, s:1, b:1),
% 0.72/1.25 skol93 [205, 0] (w:1, o:161, a:1, s:1, b:1),
% 0.72/1.25 skol94 [206, 0] (w:1, o:162, a:1, s:1, b:1).
% 0.72/1.25
% 0.72/1.25
% 0.72/1.25 Starting Search:
% 0.72/1.25
% 0.72/1.25 *** allocated 15000 integers for clauses
% 0.72/1.25 *** allocated 22500 integers for clauses
% 0.72/1.25 *** allocated 33750 integers for clauses
% 0.72/1.25 *** allocated 50625 integers for clauses
% 0.72/1.25 *** allocated 75937 integers for clauses
% 0.72/1.25 *** allocated 15000 integers for termspace/termends
% 0.72/1.25 Resimplifying inuse:
% 0.72/1.25 Done
% 0.72/1.25
% 0.72/1.25 *** allocated 113905 integers for clauses
% 0.72/1.25 *** allocated 22500 integers for termspace/termends
% 0.72/1.25 *** allocated 33750 integers for termspace/termends
% 0.72/1.25 *** allocated 170857 integers for clauses
% 0.72/1.25
% 0.72/1.25 Intermediate Status:
% 0.72/1.25 Generated: 4280
% 0.72/1.25 Kept: 2427
% 0.72/1.25 Inuse: 283
% 0.72/1.25 Deleted: 56
% 0.72/1.25 Deletedinuse: 8
% 0.72/1.25
% 0.72/1.25 Resimplifying inuse:
% 0.72/1.25 Done
% 0.72/1.25
% 0.72/1.25 *** allocated 50625 integers for termspace/termends
% 0.72/1.25 *** allocated 256285 integers for clauses
% 0.72/1.25 Resimplifying inuse:
% 0.72/1.25 Done
% 0.72/1.25
% 0.72/1.25
% 0.72/1.25 Intermediate Status:
% 0.72/1.25 Generated: 8612
% 0.72/1.25 Kept: 4493
% 0.72/1.25 Inuse: 442
% 0.72/1.25 Deleted: 67
% 0.72/1.25 Deletedinuse: 9
% 0.72/1.25
% 0.72/1.25 Resimplifying inuse:
% 0.72/1.25 Done
% 0.72/1.25
% 0.72/1.25 *** allocated 75937 integers for termspace/termends
% 0.72/1.25 *** allocated 384427 integers for clauses
% 0.72/1.25 Resimplifying inuse:
% 0.72/1.25 Done
% 0.72/1.25
% 0.72/1.25
% 0.72/1.25 Intermediate Status:
% 0.72/1.25 Generated: 13038
% 0.72/1.25 Kept: 6662
% 0.72/1.25 Inuse: 516
% 0.72/1.25 Deleted: 80
% 0.72/1.25 Deletedinuse: 15
% 0.72/1.25
% 0.72/1.25 *** allocated 113905 integers for termspace/termends
% 0.72/1.25 Resimplifying inuse:
% 0.72/1.25 Done
% 0.72/1.25
% 0.72/1.25 *** allocated 576640 integers for clauses
% 0.72/1.25 Resimplifying inuse:
% 0.72/1.25 Done
% 0.72/1.25
% 0.72/1.25
% 0.72/1.25 Bliksems!, er is een bewijs:
% 0.72/1.25 % SZS status Theorem
% 0.72/1.25 % SZS output start Refutation
% 0.72/1.25
% 0.72/1.25 (0) {G0,W5,D2,L3,V1,M3} I { ! modus_ponens, ! alpha1( X ), is_a_theorem( X
% 0.72/1.25 ) }.
% 0.72/1.25 (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem( implies( Y
% 0.72/1.25 , X ) ), alpha1( X ) }.
% 0.72/1.25 (11) {G0,W7,D4,L2,V2,M2} I { ! implies_1, is_a_theorem( implies( X, implies
% 0.72/1.25 ( Y, X ) ) ) }.
% 0.72/1.25 (65) {G0,W1,D1,L1,V0,M1} I { modus_ponens }.
% 0.72/1.25 (67) {G0,W1,D1,L1,V0,M1} I { implies_1 }.
% 0.72/1.25 (84) {G0,W3,D2,L2,V0,M2} I { alpha2( skol29 ), modus_ponens_strict_implies
% 0.72/1.25 }.
% 0.72/1.25 (85) {G0,W3,D2,L2,V0,M2} I { ! is_a_theorem( skol29 ),
% 0.72/1.25 modus_ponens_strict_implies }.
% 0.72/1.25 (86) {G0,W5,D3,L2,V2,M2} I { ! alpha2( X ), is_a_theorem( skol30( Y ) ) }.
% 0.72/1.25 (87) {G0,W7,D4,L2,V1,M2} I { ! alpha2( X ), is_a_theorem( strict_implies(
% 0.72/1.25 skol30( X ), X ) ) }.
% 0.72/1.25 (93) {G0,W5,D2,L2,V2,M2} I { ! alpha3( X, Y ), is_a_theorem( Y ) }.
% 0.72/1.25 (94) {G0,W7,D2,L3,V2,M3} I { ! is_a_theorem( X ), ! is_a_theorem( Y ),
% 0.72/1.25 alpha3( X, Y ) }.
% 0.72/1.25 (100) {G0,W6,D4,L2,V1,M2} I { ! axiom_M, is_a_theorem( implies( necessarily
% 0.72/1.25 ( X ), X ) ) }.
% 0.72/1.25 (138) {G0,W9,D4,L2,V2,M2} I { ! op_strict_implies, necessarily( implies( X
% 0.72/1.25 , Y ) ) ==> strict_implies( X, Y ) }.
% 0.72/1.25 (143) {G0,W1,D1,L1,V0,M1} I { axiom_M }.
% 0.72/1.25 (146) {G0,W1,D1,L1,V0,M1} I { op_strict_implies }.
% 0.72/1.25 (148) {G0,W1,D1,L1,V0,M1} I { ! modus_ponens_strict_implies }.
% 0.72/1.25 (149) {G1,W5,D2,L2,V1,M2} F(94) { ! is_a_theorem( X ), alpha3( X, X ) }.
% 0.72/1.25 (150) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ), is_a_theorem( X ) }.
% 0.72/1.25 (155) {G1,W2,D2,L1,V0,M1} S(85);r(148) { ! is_a_theorem( skol29 ) }.
% 0.72/1.25 (157) {G1,W2,D2,L1,V0,M1} S(84);r(148) { alpha2( skol29 ) }.
% 0.72/1.25 (158) {G2,W2,D2,L1,V0,M1} R(150,155) { ! alpha1( skol29 ) }.
% 0.72/1.25 (162) {G3,W6,D3,L2,V1,M2} R(158,5) { ! is_a_theorem( X ), ! is_a_theorem(
% 0.72/1.25 implies( X, skol29 ) ) }.
% 0.72/1.25 (178) {G2,W5,D2,L2,V1,M2} R(149,150) { alpha3( X, X ), ! alpha1( X ) }.
% 0.72/1.25 (181) {G1,W6,D4,L1,V2,M1} S(11);r(67) { is_a_theorem( implies( X, implies(
% 0.72/1.25 Y, X ) ) ) }.
% 0.72/1.25 (184) {G2,W3,D3,L1,V1,M1} R(86,157) { is_a_theorem( skol30( X ) ) }.
% 0.72/1.25 (196) {G4,W5,D4,L1,V1,M1} R(162,184) { ! is_a_theorem( implies( skol30( X )
% 0.72/1.25 , skol29 ) ) }.
% 0.72/1.25 (217) {G5,W6,D4,L1,V2,M1} R(196,93) { ! alpha3( X, implies( skol30( Y ),
% 0.72/1.25 skol29 ) ) }.
% 0.72/1.25 (760) {G2,W6,D3,L2,V2,M2} R(181,5) { ! is_a_theorem( X ), alpha1( implies(
% 0.72/1.25 Y, X ) ) }.
% 0.72/1.25 (811) {G3,W6,D3,L2,V2,M2} R(760,150) { ! is_a_theorem( X ), is_a_theorem(
% 0.72/1.25 implies( Y, X ) ) }.
% 0.72/1.25 (947) {G4,W6,D2,L3,V2,M3} R(811,5) { ! is_a_theorem( X ), ! is_a_theorem( Y
% 0.72/1.25 ), alpha1( X ) }.
% 0.72/1.25 (948) {G5,W4,D2,L2,V1,M2} F(947) { ! is_a_theorem( X ), alpha1( X ) }.
% 0.72/1.25 (1400) {G2,W5,D4,L1,V0,M1} R(87,157) { is_a_theorem( strict_implies( skol30
% 0.72/1.25 ( skol29 ), skol29 ) ) }.
% 0.72/1.25 (1403) {G6,W5,D4,L1,V0,M1} R(1400,948) { alpha1( strict_implies( skol30(
% 0.72/1.25 skol29 ), skol29 ) ) }.
% 0.72/1.25 (2545) {G1,W5,D4,L1,V1,M1} S(100);r(143) { is_a_theorem( implies(
% 0.72/1.25 necessarily( X ), X ) ) }.
% 0.72/1.25 (2575) {G2,W5,D3,L2,V1,M2} R(2545,5) { ! is_a_theorem( necessarily( X ) ),
% 0.72/1.25 alpha1( X ) }.
% 0.72/1.25 (2647) {G3,W5,D3,L2,V1,M2} R(2575,150) { alpha1( X ), ! alpha1( necessarily
% 0.72/1.25 ( X ) ) }.
% 0.72/1.25 (2883) {G4,W6,D3,L2,V1,M2} R(2647,178) { ! alpha1( necessarily( X ) ),
% 0.72/1.25 alpha3( X, X ) }.
% 0.72/1.25 (5037) {G1,W8,D4,L1,V2,M1} S(138);r(146) { necessarily( implies( X, Y ) )
% 0.72/1.25 ==> strict_implies( X, Y ) }.
% 0.72/1.25 (8423) {G6,W5,D4,L1,V1,M1} R(2883,217);d(5037) { ! alpha1( strict_implies(
% 0.72/1.25 skol30( X ), skol29 ) ) }.
% 0.72/1.25 (8536) {G7,W0,D0,L0,V0,M0} R(8423,1403) { }.
% 0.72/1.25
% 0.72/1.25
% 0.72/1.25 % SZS output end Refutation
% 0.72/1.25 found a proof!
% 0.72/1.25
% 0.72/1.25
% 0.72/1.25 Unprocessed initial clauses:
% 0.72/1.25
% 0.72/1.25 (8538) {G0,W5,D2,L3,V1,M3} { ! modus_ponens, ! alpha1( X ), is_a_theorem(
% 0.72/1.25 X ) }.
% 0.72/1.25 (8539) {G0,W3,D2,L2,V0,M2} { alpha1( skol1 ), modus_ponens }.
% 0.72/1.25 (8540) {G0,W3,D2,L2,V0,M2} { ! is_a_theorem( skol1 ), modus_ponens }.
% 0.72/1.25 (8541) {G0,W5,D3,L2,V2,M2} { ! alpha1( X ), is_a_theorem( skol2( Y ) ) }.
% 0.72/1.25 (8542) {G0,W7,D4,L2,V1,M2} { ! alpha1( X ), is_a_theorem( implies( skol2(
% 0.72/1.25 X ), X ) ) }.
% 0.72/1.25 (8543) {G0,W8,D3,L3,V2,M3} { ! is_a_theorem( Y ), ! is_a_theorem( implies
% 0.72/1.25 ( Y, X ) ), alpha1( X ) }.
% 0.72/1.25 (8544) {G0,W8,D3,L3,V2,M3} { ! substitution_of_equivalents, ! is_a_theorem
% 0.72/1.25 ( equiv( X, Y ) ), X = Y }.
% 0.72/1.25 (8545) {G0,W5,D3,L2,V0,M2} { is_a_theorem( equiv( skol3, skol52 ) ),
% 0.72/1.25 substitution_of_equivalents }.
% 0.72/1.25 (8546) {G0,W4,D2,L2,V0,M2} { ! skol3 = skol52, substitution_of_equivalents
% 0.72/1.25 }.
% 0.72/1.25 (8547) {G0,W11,D5,L2,V2,M2} { ! modus_tollens, is_a_theorem( implies(
% 0.72/1.25 implies( not( Y ), not( X ) ), implies( X, Y ) ) ) }.
% 0.72/1.25 (8548) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( not(
% 0.72/1.25 skol53 ), not( skol4 ) ), implies( skol4, skol53 ) ) ), modus_tollens }.
% 0.72/1.25 (8549) {G0,W7,D4,L2,V2,M2} { ! implies_1, is_a_theorem( implies( X,
% 0.72/1.25 implies( Y, X ) ) ) }.
% 0.72/1.25 (8550) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol5, implies(
% 0.72/1.25 skol54, skol5 ) ) ), implies_1 }.
% 0.72/1.25 (8551) {G0,W11,D5,L2,V2,M2} { ! implies_2, is_a_theorem( implies( implies
% 0.72/1.25 ( X, implies( X, Y ) ), implies( X, Y ) ) ) }.
% 0.72/1.25 (8552) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol6,
% 0.72/1.25 implies( skol6, skol55 ) ), implies( skol6, skol55 ) ) ), implies_2 }.
% 0.72/1.25 (8553) {G0,W13,D5,L2,V3,M2} { ! implies_3, is_a_theorem( implies( implies
% 0.72/1.25 ( X, Y ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 0.72/1.25 (8554) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol7,
% 0.72/1.25 skol56 ), implies( implies( skol56, skol86 ), implies( skol7, skol86 ) )
% 0.72/1.25 ) ), implies_3 }.
% 0.72/1.25 (8555) {G0,W7,D4,L2,V2,M2} { ! and_1, is_a_theorem( implies( and( X, Y ),
% 0.72/1.25 X ) ) }.
% 0.72/1.25 (8556) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol8, skol57 )
% 0.72/1.25 , skol8 ) ), and_1 }.
% 0.72/1.25 (8557) {G0,W7,D4,L2,V2,M2} { ! and_2, is_a_theorem( implies( and( X, Y ),
% 0.72/1.25 Y ) ) }.
% 0.72/1.25 (8558) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol9, skol58 )
% 0.72/1.25 , skol58 ) ), and_2 }.
% 0.72/1.25 (8559) {G0,W9,D5,L2,V2,M2} { ! and_3, is_a_theorem( implies( X, implies( Y
% 0.72/1.25 , and( X, Y ) ) ) ) }.
% 0.72/1.25 (8560) {G0,W9,D5,L2,V0,M2} { ! is_a_theorem( implies( skol10, implies(
% 0.72/1.25 skol59, and( skol10, skol59 ) ) ) ), and_3 }.
% 0.72/1.25 (8561) {G0,W7,D4,L2,V2,M2} { ! or_1, is_a_theorem( implies( X, or( X, Y )
% 0.72/1.25 ) ) }.
% 0.72/1.25 (8562) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol11, or( skol11,
% 0.72/1.25 skol60 ) ) ), or_1 }.
% 0.72/1.25 (8563) {G0,W7,D4,L2,V2,M2} { ! or_2, is_a_theorem( implies( Y, or( X, Y )
% 0.72/1.25 ) ) }.
% 0.72/1.25 (8564) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol61, or( skol12,
% 0.72/1.25 skol61 ) ) ), or_2 }.
% 0.72/1.25 (8565) {G0,W15,D6,L2,V3,M2} { ! or_3, is_a_theorem( implies( implies( X, Z
% 0.72/1.25 ), implies( implies( Y, Z ), implies( or( X, Y ), Z ) ) ) ) }.
% 0.72/1.25 (8566) {G0,W15,D6,L2,V0,M2} { ! is_a_theorem( implies( implies( skol13,
% 0.72/1.25 skol87 ), implies( implies( skol62, skol87 ), implies( or( skol13, skol62
% 0.72/1.25 ), skol87 ) ) ) ), or_3 }.
% 0.72/1.25 (8567) {G0,W9,D4,L2,V2,M2} { ! equivalence_1, is_a_theorem( implies( equiv
% 0.72/1.25 ( X, Y ), implies( X, Y ) ) ) }.
% 0.72/1.25 (8568) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( equiv( skol14,
% 0.72/1.25 skol63 ), implies( skol14, skol63 ) ) ), equivalence_1 }.
% 0.72/1.25 (8569) {G0,W9,D4,L2,V2,M2} { ! equivalence_2, is_a_theorem( implies( equiv
% 0.72/1.25 ( X, Y ), implies( Y, X ) ) ) }.
% 0.72/1.25 (8570) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( equiv( skol15,
% 0.72/1.25 skol64 ), implies( skol64, skol15 ) ) ), equivalence_2 }.
% 0.72/1.25 (8571) {G0,W13,D5,L2,V2,M2} { ! equivalence_3, is_a_theorem( implies(
% 0.72/1.25 implies( X, Y ), implies( implies( Y, X ), equiv( X, Y ) ) ) ) }.
% 0.72/1.25 (8572) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol16,
% 0.72/1.25 skol65 ), implies( implies( skol65, skol16 ), equiv( skol16, skol65 ) ) )
% 0.72/1.25 ), equivalence_3 }.
% 0.72/1.25 (8573) {G0,W7,D4,L2,V1,M2} { ! kn1, is_a_theorem( implies( X, and( X, X )
% 0.72/1.25 ) ) }.
% 0.72/1.25 (8574) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol17, and( skol17
% 0.72/1.25 , skol17 ) ) ), kn1 }.
% 0.72/1.25 (8575) {G0,W7,D4,L2,V2,M2} { ! kn2, is_a_theorem( implies( and( X, Y ), X
% 0.72/1.25 ) ) }.
% 0.72/1.25 (8576) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol18, skol66
% 0.72/1.25 ), skol18 ) ), kn2 }.
% 0.72/1.25 (8577) {G0,W15,D6,L2,V3,M2} { ! kn3, is_a_theorem( implies( implies( X, Y
% 0.72/1.25 ), implies( not( and( Y, Z ) ), not( and( Z, X ) ) ) ) ) }.
% 0.72/1.25 (8578) {G0,W15,D6,L2,V0,M2} { ! is_a_theorem( implies( implies( skol19,
% 0.72/1.25 skol67 ), implies( not( and( skol67, skol88 ) ), not( and( skol88, skol19
% 0.72/1.25 ) ) ) ) ), kn3 }.
% 0.72/1.25 (8579) {G0,W13,D5,L2,V3,M2} { ! cn1, is_a_theorem( implies( implies( X, Y
% 0.72/1.25 ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 0.72/1.25 (8580) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol20,
% 0.72/1.25 skol68 ), implies( implies( skol68, skol89 ), implies( skol20, skol89 ) )
% 0.72/1.25 ) ), cn1 }.
% 0.72/1.25 (8581) {G0,W8,D5,L2,V2,M2} { ! cn2, is_a_theorem( implies( X, implies( not
% 0.72/1.25 ( X ), Y ) ) ) }.
% 0.72/1.25 (8582) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( skol21, implies( not
% 0.72/1.25 ( skol21 ), skol69 ) ) ), cn2 }.
% 0.72/1.25 (8583) {G0,W8,D5,L2,V1,M2} { ! cn3, is_a_theorem( implies( implies( not( X
% 0.72/1.25 ), X ), X ) ) }.
% 0.72/1.25 (8584) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( not( skol22
% 0.72/1.25 ), skol22 ), skol22 ) ), cn3 }.
% 0.72/1.25 (8585) {G0,W7,D4,L2,V1,M2} { ! r1, is_a_theorem( implies( or( X, X ), X )
% 0.72/1.25 ) }.
% 0.72/1.25 (8586) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( or( skol23, skol23 )
% 0.72/1.25 , skol23 ) ), r1 }.
% 0.72/1.25 (8587) {G0,W7,D4,L2,V2,M2} { ! r2, is_a_theorem( implies( Y, or( X, Y ) )
% 0.72/1.25 ) }.
% 0.72/1.25 (8588) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol70, or( skol24,
% 0.72/1.25 skol70 ) ) ), r2 }.
% 0.72/1.25 (8589) {G0,W9,D4,L2,V2,M2} { ! r3, is_a_theorem( implies( or( X, Y ), or(
% 0.72/1.25 Y, X ) ) ) }.
% 0.72/1.25 (8590) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( or( skol25, skol71 )
% 0.72/1.25 , or( skol71, skol25 ) ) ), r3 }.
% 0.72/1.25 (8591) {G0,W13,D5,L2,V3,M2} { ! r4, is_a_theorem( implies( or( X, or( Y, Z
% 0.72/1.25 ) ), or( Y, or( X, Z ) ) ) ) }.
% 0.72/1.25 (8592) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( or( skol26, or(
% 0.72/1.25 skol72, skol90 ) ), or( skol72, or( skol26, skol90 ) ) ) ), r4 }.
% 0.72/1.25 (8593) {G0,W13,D5,L2,V3,M2} { ! r5, is_a_theorem( implies( implies( Y, Z )
% 0.72/1.25 , implies( or( X, Y ), or( X, Z ) ) ) ) }.
% 0.72/1.25 (8594) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol73,
% 0.72/1.25 skol91 ), implies( or( skol27, skol73 ), or( skol27, skol91 ) ) ) ), r5
% 0.72/1.25 }.
% 0.72/1.25 (8595) {G0,W11,D5,L2,V2,M2} { ! op_or, or( X, Y ) = not( and( not( X ),
% 0.72/1.25 not( Y ) ) ) }.
% 0.72/1.25 (8596) {G0,W11,D5,L2,V2,M2} { ! op_and, and( X, Y ) = not( or( not( X ),
% 0.72/1.25 not( Y ) ) ) }.
% 0.72/1.25 (8597) {G0,W10,D5,L2,V2,M2} { ! op_implies_and, implies( X, Y ) = not( and
% 0.72/1.25 ( X, not( Y ) ) ) }.
% 0.72/1.25 (8598) {G0,W9,D4,L2,V2,M2} { ! op_implies_or, implies( X, Y ) = or( not( X
% 0.72/1.25 ), Y ) }.
% 0.72/1.25 (8599) {G0,W12,D4,L2,V2,M2} { ! op_equiv, equiv( X, Y ) = and( implies( X
% 0.72/1.25 , Y ), implies( Y, X ) ) }.
% 0.72/1.25 (8600) {G0,W1,D1,L1,V0,M1} { op_or }.
% 0.72/1.25 (8601) {G0,W1,D1,L1,V0,M1} { op_implies_and }.
% 0.72/1.25 (8602) {G0,W1,D1,L1,V0,M1} { op_equiv }.
% 0.72/1.25 (8603) {G0,W1,D1,L1,V0,M1} { modus_ponens }.
% 0.72/1.25 (8604) {G0,W1,D1,L1,V0,M1} { modus_tollens }.
% 0.72/1.25 (8605) {G0,W1,D1,L1,V0,M1} { implies_1 }.
% 0.72/1.25 (8606) {G0,W1,D1,L1,V0,M1} { implies_2 }.
% 0.72/1.25 (8607) {G0,W1,D1,L1,V0,M1} { implies_3 }.
% 0.72/1.25 (8608) {G0,W1,D1,L1,V0,M1} { and_1 }.
% 0.72/1.25 (8609) {G0,W1,D1,L1,V0,M1} { and_2 }.
% 0.72/1.25 (8610) {G0,W1,D1,L1,V0,M1} { and_3 }.
% 0.72/1.25 (8611) {G0,W1,D1,L1,V0,M1} { or_1 }.
% 0.72/1.25 (8612) {G0,W1,D1,L1,V0,M1} { or_2 }.
% 0.72/1.25 (8613) {G0,W1,D1,L1,V0,M1} { or_3 }.
% 0.72/1.25 (8614) {G0,W1,D1,L1,V0,M1} { equivalence_1 }.
% 0.72/1.25 (8615) {G0,W1,D1,L1,V0,M1} { equivalence_2 }.
% 0.72/1.25 (8616) {G0,W1,D1,L1,V0,M1} { equivalence_3 }.
% 0.72/1.25 (8617) {G0,W1,D1,L1,V0,M1} { substitution_of_equivalents }.
% 0.72/1.25 (8618) {G0,W6,D3,L3,V1,M3} { ! necessitation, ! is_a_theorem( X ),
% 0.72/1.25 is_a_theorem( necessarily( X ) ) }.
% 0.72/1.25 (8619) {G0,W3,D2,L2,V0,M2} { is_a_theorem( skol28 ), necessitation }.
% 0.72/1.25 (8620) {G0,W4,D3,L2,V0,M2} { ! is_a_theorem( necessarily( skol28 ) ),
% 0.72/1.25 necessitation }.
% 0.72/1.25 (8621) {G0,W5,D2,L3,V1,M3} { ! modus_ponens_strict_implies, ! alpha2( X )
% 0.72/1.25 , is_a_theorem( X ) }.
% 0.72/1.25 (8622) {G0,W3,D2,L2,V0,M2} { alpha2( skol29 ), modus_ponens_strict_implies
% 0.72/1.25 }.
% 0.72/1.25 (8623) {G0,W3,D2,L2,V0,M2} { ! is_a_theorem( skol29 ),
% 0.72/1.25 modus_ponens_strict_implies }.
% 0.72/1.25 (8624) {G0,W5,D3,L2,V2,M2} { ! alpha2( X ), is_a_theorem( skol30( Y ) )
% 0.72/1.25 }.
% 0.72/1.25 (8625) {G0,W7,D4,L2,V1,M2} { ! alpha2( X ), is_a_theorem( strict_implies(
% 0.72/1.25 skol30( X ), X ) ) }.
% 0.72/1.25 (8626) {G0,W8,D3,L3,V2,M3} { ! is_a_theorem( Y ), ! is_a_theorem(
% 0.72/1.25 strict_implies( Y, X ) ), alpha2( X ) }.
% 0.72/1.25 (8627) {G0,W8,D3,L3,V2,M3} { ! adjunction, ! alpha3( X, Y ), is_a_theorem
% 0.72/1.25 ( and( X, Y ) ) }.
% 0.72/1.25 (8628) {G0,W4,D2,L2,V0,M2} { alpha3( skol31, skol74 ), adjunction }.
% 0.72/1.25 (8629) {G0,W5,D3,L2,V0,M2} { ! is_a_theorem( and( skol31, skol74 ) ),
% 0.72/1.25 adjunction }.
% 0.72/1.25 (8630) {G0,W5,D2,L2,V2,M2} { ! alpha3( X, Y ), is_a_theorem( X ) }.
% 0.72/1.25 (8631) {G0,W5,D2,L2,V2,M2} { ! alpha3( X, Y ), is_a_theorem( Y ) }.
% 0.72/1.25 (8632) {G0,W7,D2,L3,V2,M3} { ! is_a_theorem( X ), ! is_a_theorem( Y ),
% 0.72/1.25 alpha3( X, Y ) }.
% 0.72/1.25 (8633) {G0,W8,D3,L3,V2,M3} { ! substitution_strict_equiv, ! is_a_theorem(
% 0.72/1.25 strict_equiv( X, Y ) ), X = Y }.
% 0.72/1.25 (8634) {G0,W5,D3,L2,V0,M2} { is_a_theorem( strict_equiv( skol32, skol75 )
% 0.72/1.25 ), substitution_strict_equiv }.
% 0.72/1.25 (8635) {G0,W4,D2,L2,V0,M2} { ! skol32 = skol75, substitution_strict_equiv
% 0.72/1.25 }.
% 0.72/1.25 (8636) {G0,W12,D5,L2,V2,M2} { ! axiom_K, is_a_theorem( implies(
% 0.72/1.25 necessarily( implies( X, Y ) ), implies( necessarily( X ), necessarily( Y
% 0.72/1.25 ) ) ) ) }.
% 0.72/1.25 (8637) {G0,W12,D5,L2,V0,M2} { ! is_a_theorem( implies( necessarily(
% 0.72/1.25 implies( skol33, skol76 ) ), implies( necessarily( skol33 ), necessarily
% 0.72/1.25 ( skol76 ) ) ) ), axiom_K }.
% 0.72/1.25 (8638) {G0,W6,D4,L2,V1,M2} { ! axiom_M, is_a_theorem( implies( necessarily
% 0.72/1.25 ( X ), X ) ) }.
% 0.72/1.25 (8639) {G0,W6,D4,L2,V0,M2} { ! is_a_theorem( implies( necessarily( skol34
% 0.72/1.25 ), skol34 ) ), axiom_M }.
% 0.72/1.25 (8640) {G0,W8,D5,L2,V1,M2} { ! axiom_4, is_a_theorem( implies( necessarily
% 0.72/1.25 ( X ), necessarily( necessarily( X ) ) ) ) }.
% 0.72/1.25 (8641) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( necessarily( skol35
% 0.72/1.25 ), necessarily( necessarily( skol35 ) ) ) ), axiom_4 }.
% 0.72/1.25 (8642) {G0,W7,D5,L2,V1,M2} { ! axiom_B, is_a_theorem( implies( X,
% 0.72/1.25 necessarily( possibly( X ) ) ) ) }.
% 0.72/1.25 (8643) {G0,W7,D5,L2,V0,M2} { ! is_a_theorem( implies( skol36, necessarily
% 0.72/1.25 ( possibly( skol36 ) ) ) ), axiom_B }.
% 0.72/1.25 (8644) {G0,W8,D5,L2,V1,M2} { ! axiom_5, is_a_theorem( implies( possibly( X
% 0.72/1.25 ), necessarily( possibly( X ) ) ) ) }.
% 0.72/1.25 (8645) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( possibly( skol37 ),
% 0.72/1.25 necessarily( possibly( skol37 ) ) ) ), axiom_5 }.
% 0.72/1.25 (8646) {G0,W16,D6,L2,V3,M2} { ! axiom_s1, is_a_theorem( implies( and(
% 0.72/1.25 necessarily( implies( X, Y ) ), necessarily( implies( Y, Z ) ) ),
% 0.72/1.25 necessarily( implies( X, Z ) ) ) ) }.
% 0.72/1.25 (8647) {G0,W16,D6,L2,V0,M2} { ! is_a_theorem( implies( and( necessarily(
% 0.72/1.25 implies( skol38, skol77 ) ), necessarily( implies( skol77, skol92 ) ) ),
% 0.72/1.25 necessarily( implies( skol38, skol92 ) ) ) ), axiom_s1 }.
% 0.72/1.25 (8648) {G0,W12,D5,L2,V2,M2} { ! axiom_s2, is_a_theorem( strict_implies(
% 0.72/1.25 possibly( and( X, Y ) ), and( possibly( X ), possibly( Y ) ) ) ) }.
% 0.72/1.25 (8649) {G0,W12,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( possibly(
% 0.72/1.25 and( skol39, skol78 ) ), and( possibly( skol39 ), possibly( skol78 ) ) )
% 0.72/1.25 ), axiom_s2 }.
% 0.72/1.25 (8650) {G0,W13,D6,L2,V2,M2} { ! axiom_s3, is_a_theorem( strict_implies(
% 0.72/1.25 strict_implies( X, Y ), strict_implies( not( possibly( Y ) ), not(
% 0.72/1.25 possibly( X ) ) ) ) ) }.
% 0.72/1.25 (8651) {G0,W13,D6,L2,V0,M2} { ! is_a_theorem( strict_implies(
% 0.72/1.25 strict_implies( skol40, skol79 ), strict_implies( not( possibly( skol79 )
% 0.72/1.25 ), not( possibly( skol40 ) ) ) ) ), axiom_s3 }.
% 0.72/1.25 (8652) {G0,W8,D5,L2,V1,M2} { ! axiom_s4, is_a_theorem( strict_implies(
% 0.72/1.25 necessarily( X ), necessarily( necessarily( X ) ) ) ) }.
% 0.72/1.25 (8653) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( necessarily(
% 0.72/1.25 skol41 ), necessarily( necessarily( skol41 ) ) ) ), axiom_s4 }.
% 0.72/1.25 (8654) {G0,W9,D4,L2,V2,M2} { ! axiom_m1, is_a_theorem( strict_implies( and
% 0.72/1.25 ( X, Y ), and( Y, X ) ) ) }.
% 0.72/1.25 (8655) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( and( skol42,
% 0.72/1.25 skol80 ), and( skol80, skol42 ) ) ), axiom_m1 }.
% 0.72/1.25 (8656) {G0,W7,D4,L2,V2,M2} { ! axiom_m2, is_a_theorem( strict_implies( and
% 0.72/1.25 ( X, Y ), X ) ) }.
% 0.72/1.25 (8657) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( and( skol43,
% 0.72/1.25 skol81 ), skol43 ) ), axiom_m2 }.
% 0.72/1.25 (8658) {G0,W13,D5,L2,V3,M2} { ! axiom_m3, is_a_theorem( strict_implies(
% 0.72/1.25 and( and( X, Y ), Z ), and( X, and( Y, Z ) ) ) ) }.
% 0.72/1.25 (8659) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( and( and(
% 0.72/1.25 skol44, skol82 ), skol93 ), and( skol44, and( skol82, skol93 ) ) ) ),
% 0.72/1.25 axiom_m3 }.
% 0.72/1.25 (8660) {G0,W7,D4,L2,V1,M2} { ! axiom_m4, is_a_theorem( strict_implies( X,
% 0.72/1.25 and( X, X ) ) ) }.
% 0.72/1.25 (8661) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( skol45, and(
% 0.72/1.25 skol45, skol45 ) ) ), axiom_m4 }.
% 0.72/1.25 (8662) {G0,W13,D5,L2,V3,M2} { ! axiom_m5, is_a_theorem( strict_implies(
% 0.72/1.25 and( strict_implies( X, Y ), strict_implies( Y, Z ) ), strict_implies( X
% 0.72/1.25 , Z ) ) ) }.
% 0.72/1.25 (8663) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( and(
% 0.72/1.25 strict_implies( skol46, skol83 ), strict_implies( skol83, skol94 ) ),
% 0.72/1.25 strict_implies( skol46, skol94 ) ) ), axiom_m5 }.
% 0.72/1.25 (8664) {G0,W6,D4,L2,V1,M2} { ! axiom_m6, is_a_theorem( strict_implies( X,
% 0.72/1.25 possibly( X ) ) ) }.
% 0.72/1.25 (8665) {G0,W6,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( skol47,
% 0.72/1.25 possibly( skol47 ) ) ), axiom_m6 }.
% 0.72/1.25 (8666) {G0,W8,D5,L2,V2,M2} { ! axiom_m7, is_a_theorem( strict_implies(
% 0.72/1.25 possibly( and( X, Y ) ), X ) ) }.
% 0.72/1.25 (8667) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( possibly( and
% 0.72/1.25 ( skol48, skol84 ) ), skol48 ) ), axiom_m7 }.
% 0.72/1.25 (8668) {G0,W11,D5,L2,V2,M2} { ! axiom_m8, is_a_theorem( strict_implies(
% 0.72/1.25 strict_implies( X, Y ), strict_implies( possibly( X ), possibly( Y ) ) )
% 0.72/1.25 ) }.
% 0.72/1.25 (8669) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( strict_implies(
% 0.72/1.25 strict_implies( skol49, skol85 ), strict_implies( possibly( skol49 ),
% 0.72/1.25 possibly( skol85 ) ) ) ), axiom_m8 }.
% 0.72/1.25 (8670) {G0,W8,D5,L2,V1,M2} { ! axiom_m9, is_a_theorem( strict_implies(
% 0.72/1.25 possibly( possibly( X ) ), possibly( X ) ) ) }.
% 0.72/1.25 (8671) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( possibly(
% 0.72/1.25 possibly( skol50 ) ), possibly( skol50 ) ) ), axiom_m9 }.
% 0.72/1.25 (8672) {G0,W8,D5,L2,V1,M2} { ! axiom_m10, is_a_theorem( strict_implies(
% 0.72/1.25 possibly( X ), necessarily( possibly( X ) ) ) ) }.
% 0.72/1.25 (8673) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( possibly(
% 0.72/1.25 skol51 ), necessarily( possibly( skol51 ) ) ) ), axiom_m10 }.
% 0.72/1.25 (8674) {G0,W8,D5,L2,V1,M2} { ! op_possibly, possibly( X ) = not(
% 0.72/1.25 necessarily( not( X ) ) ) }.
% 0.72/1.25 (8675) {G0,W8,D5,L2,V1,M2} { ! op_necessarily, necessarily( X ) = not(
% 0.72/1.25 possibly( not( X ) ) ) }.
% 0.72/1.25 (8676) {G0,W9,D4,L2,V2,M2} { ! op_strict_implies, strict_implies( X, Y ) =
% 0.72/1.25 necessarily( implies( X, Y ) ) }.
% 0.72/1.25 (8677) {G0,W12,D4,L2,V2,M2} { ! op_strict_equiv, strict_equiv( X, Y ) =
% 0.72/1.25 and( strict_implies( X, Y ), strict_implies( Y, X ) ) }.
% 0.72/1.25 (8678) {G0,W1,D1,L1,V0,M1} { op_possibly }.
% 0.72/1.25 (8679) {G0,W1,D1,L1,V0,M1} { necessitation }.
% 0.72/1.25 (8680) {G0,W1,D1,L1,V0,M1} { axiom_K }.
% 0.72/1.25 (8681) {G0,W1,D1,L1,V0,M1} { axiom_M }.
% 0.72/1.25 (8682) {G0,W1,D1,L1,V0,M1} { axiom_5 }.
% 0.72/1.25 (8683) {G0,W1,D1,L1,V0,M1} { op_possibly }.
% 0.72/1.25 (8684) {G0,W1,D1,L1,V0,M1} { op_or }.
% 0.72/1.25 (8685) {G0,W1,D1,L1,V0,M1} { op_implies }.
% 0.72/1.25 (8686) {G0,W1,D1,L1,V0,M1} { op_strict_implies }.
% 0.72/1.25 (8687) {G0,W1,D1,L1,V0,M1} { op_equiv }.
% 0.72/1.25 (8688) {G0,W1,D1,L1,V0,M1} { op_strict_equiv }.
% 0.72/1.25 (8689) {G0,W1,D1,L1,V0,M1} { ! modus_ponens_strict_implies }.
% 0.72/1.25
% 0.72/1.25
% 0.72/1.25 Total Proof:
% 0.72/1.25
% 0.72/1.25 subsumption: (0) {G0,W5,D2,L3,V1,M3} I { ! modus_ponens, ! alpha1( X ),
% 0.72/1.25 is_a_theorem( X ) }.
% 0.72/1.25 parent0: (8538) {G0,W5,D2,L3,V1,M3} { ! modus_ponens, ! alpha1( X ),
% 0.72/1.25 is_a_theorem( X ) }.
% 0.72/1.25 substitution0:
% 0.72/1.25 X := X
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 0
% 0.72/1.25 1 ==> 1
% 0.72/1.25 2 ==> 2
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 subsumption: (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), !
% 0.72/1.25 is_a_theorem( implies( Y, X ) ), alpha1( X ) }.
% 0.72/1.25 parent0: (8543) {G0,W8,D3,L3,V2,M3} { ! is_a_theorem( Y ), ! is_a_theorem
% 0.72/1.25 ( implies( Y, X ) ), alpha1( X ) }.
% 0.72/1.25 substitution0:
% 0.72/1.25 X := X
% 0.72/1.25 Y := Y
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 0
% 0.72/1.25 1 ==> 1
% 0.72/1.25 2 ==> 2
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 subsumption: (11) {G0,W7,D4,L2,V2,M2} I { ! implies_1, is_a_theorem(
% 0.72/1.25 implies( X, implies( Y, X ) ) ) }.
% 0.72/1.25 parent0: (8549) {G0,W7,D4,L2,V2,M2} { ! implies_1, is_a_theorem( implies(
% 0.72/1.25 X, implies( Y, X ) ) ) }.
% 0.72/1.25 substitution0:
% 0.72/1.25 X := X
% 0.72/1.25 Y := Y
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 0
% 0.72/1.25 1 ==> 1
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 subsumption: (65) {G0,W1,D1,L1,V0,M1} I { modus_ponens }.
% 0.72/1.25 parent0: (8603) {G0,W1,D1,L1,V0,M1} { modus_ponens }.
% 0.72/1.25 substitution0:
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 0
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 subsumption: (67) {G0,W1,D1,L1,V0,M1} I { implies_1 }.
% 0.72/1.25 parent0: (8605) {G0,W1,D1,L1,V0,M1} { implies_1 }.
% 0.72/1.25 substitution0:
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 0
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 subsumption: (84) {G0,W3,D2,L2,V0,M2} I { alpha2( skol29 ),
% 0.72/1.25 modus_ponens_strict_implies }.
% 0.72/1.25 parent0: (8622) {G0,W3,D2,L2,V0,M2} { alpha2( skol29 ),
% 0.72/1.25 modus_ponens_strict_implies }.
% 0.72/1.25 substitution0:
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 0
% 0.72/1.25 1 ==> 1
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 subsumption: (85) {G0,W3,D2,L2,V0,M2} I { ! is_a_theorem( skol29 ),
% 0.72/1.25 modus_ponens_strict_implies }.
% 0.72/1.25 parent0: (8623) {G0,W3,D2,L2,V0,M2} { ! is_a_theorem( skol29 ),
% 0.72/1.25 modus_ponens_strict_implies }.
% 0.72/1.25 substitution0:
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 0
% 0.72/1.25 1 ==> 1
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 subsumption: (86) {G0,W5,D3,L2,V2,M2} I { ! alpha2( X ), is_a_theorem(
% 0.72/1.25 skol30( Y ) ) }.
% 0.72/1.25 parent0: (8624) {G0,W5,D3,L2,V2,M2} { ! alpha2( X ), is_a_theorem( skol30
% 0.72/1.25 ( Y ) ) }.
% 0.72/1.25 substitution0:
% 0.72/1.25 X := X
% 0.72/1.25 Y := Y
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 0
% 0.72/1.25 1 ==> 1
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 subsumption: (87) {G0,W7,D4,L2,V1,M2} I { ! alpha2( X ), is_a_theorem(
% 0.72/1.25 strict_implies( skol30( X ), X ) ) }.
% 0.72/1.25 parent0: (8625) {G0,W7,D4,L2,V1,M2} { ! alpha2( X ), is_a_theorem(
% 0.72/1.25 strict_implies( skol30( X ), X ) ) }.
% 0.72/1.25 substitution0:
% 0.72/1.25 X := X
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 0
% 0.72/1.25 1 ==> 1
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 subsumption: (93) {G0,W5,D2,L2,V2,M2} I { ! alpha3( X, Y ), is_a_theorem( Y
% 0.72/1.25 ) }.
% 0.72/1.25 parent0: (8631) {G0,W5,D2,L2,V2,M2} { ! alpha3( X, Y ), is_a_theorem( Y )
% 0.72/1.25 }.
% 0.72/1.25 substitution0:
% 0.72/1.25 X := X
% 0.72/1.25 Y := Y
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 0
% 0.72/1.25 1 ==> 1
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 subsumption: (94) {G0,W7,D2,L3,V2,M3} I { ! is_a_theorem( X ), !
% 0.72/1.25 is_a_theorem( Y ), alpha3( X, Y ) }.
% 0.72/1.25 parent0: (8632) {G0,W7,D2,L3,V2,M3} { ! is_a_theorem( X ), ! is_a_theorem
% 0.72/1.25 ( Y ), alpha3( X, Y ) }.
% 0.72/1.25 substitution0:
% 0.72/1.25 X := X
% 0.72/1.25 Y := Y
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 0
% 0.72/1.25 1 ==> 1
% 0.72/1.25 2 ==> 2
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 subsumption: (100) {G0,W6,D4,L2,V1,M2} I { ! axiom_M, is_a_theorem( implies
% 0.72/1.25 ( necessarily( X ), X ) ) }.
% 0.72/1.25 parent0: (8638) {G0,W6,D4,L2,V1,M2} { ! axiom_M, is_a_theorem( implies(
% 0.72/1.25 necessarily( X ), X ) ) }.
% 0.72/1.25 substitution0:
% 0.72/1.25 X := X
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 0
% 0.72/1.25 1 ==> 1
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 eqswap: (8771) {G0,W9,D4,L2,V2,M2} { necessarily( implies( X, Y ) ) =
% 0.72/1.25 strict_implies( X, Y ), ! op_strict_implies }.
% 0.72/1.25 parent0[1]: (8676) {G0,W9,D4,L2,V2,M2} { ! op_strict_implies,
% 0.72/1.25 strict_implies( X, Y ) = necessarily( implies( X, Y ) ) }.
% 0.72/1.25 substitution0:
% 0.72/1.25 X := X
% 0.72/1.25 Y := Y
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 subsumption: (138) {G0,W9,D4,L2,V2,M2} I { ! op_strict_implies, necessarily
% 0.72/1.25 ( implies( X, Y ) ) ==> strict_implies( X, Y ) }.
% 0.72/1.25 parent0: (8771) {G0,W9,D4,L2,V2,M2} { necessarily( implies( X, Y ) ) =
% 0.72/1.25 strict_implies( X, Y ), ! op_strict_implies }.
% 0.72/1.25 substitution0:
% 0.72/1.25 X := X
% 0.72/1.25 Y := Y
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 1
% 0.72/1.25 1 ==> 0
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 subsumption: (143) {G0,W1,D1,L1,V0,M1} I { axiom_M }.
% 0.72/1.25 parent0: (8681) {G0,W1,D1,L1,V0,M1} { axiom_M }.
% 0.72/1.25 substitution0:
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 0
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 subsumption: (146) {G0,W1,D1,L1,V0,M1} I { op_strict_implies }.
% 0.72/1.25 parent0: (8686) {G0,W1,D1,L1,V0,M1} { op_strict_implies }.
% 0.72/1.25 substitution0:
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 0
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 subsumption: (148) {G0,W1,D1,L1,V0,M1} I { ! modus_ponens_strict_implies
% 0.72/1.25 }.
% 0.72/1.25 parent0: (8689) {G0,W1,D1,L1,V0,M1} { ! modus_ponens_strict_implies }.
% 0.72/1.25 substitution0:
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 0
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 factor: (8814) {G0,W5,D2,L2,V1,M2} { ! is_a_theorem( X ), alpha3( X, X )
% 0.72/1.25 }.
% 0.72/1.25 parent0[0, 1]: (94) {G0,W7,D2,L3,V2,M3} I { ! is_a_theorem( X ), !
% 0.72/1.25 is_a_theorem( Y ), alpha3( X, Y ) }.
% 0.72/1.25 substitution0:
% 0.72/1.25 X := X
% 0.72/1.25 Y := X
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 subsumption: (149) {G1,W5,D2,L2,V1,M2} F(94) { ! is_a_theorem( X ), alpha3
% 0.72/1.25 ( X, X ) }.
% 0.72/1.25 parent0: (8814) {G0,W5,D2,L2,V1,M2} { ! is_a_theorem( X ), alpha3( X, X )
% 0.72/1.25 }.
% 0.72/1.25 substitution0:
% 0.72/1.25 X := X
% 0.72/1.25 end
% 0.72/1.25 permutation0:
% 0.72/1.25 0 ==> 0
% 0.72/1.25 1 ==> 1
% 0.72/1.25 end
% 0.72/1.25
% 0.72/1.25 resolution: (8815) {G1,W4,D2,L2,V1,M2} { ! alpha1( X ), is_a_theorem( X )
% 0.72/1.26 }.
% 0.72/1.26 parent0[0]: (0) {G0,W5,D2,L3,V1,M3} I { ! modus_ponens, ! alpha1( X ),
% 0.72/1.26 is_a_theorem( X ) }.
% 0.72/1.26 parent1[0]: (65) {G0,W1,D1,L1,V0,M1} I { modus_ponens }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (150) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 0.72/1.26 is_a_theorem( X ) }.
% 0.72/1.26 parent0: (8815) {G1,W4,D2,L2,V1,M2} { ! alpha1( X ), is_a_theorem( X ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 1 ==> 1
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8816) {G1,W2,D2,L1,V0,M1} { ! is_a_theorem( skol29 ) }.
% 0.72/1.26 parent0[0]: (148) {G0,W1,D1,L1,V0,M1} I { ! modus_ponens_strict_implies }.
% 0.72/1.26 parent1[1]: (85) {G0,W3,D2,L2,V0,M2} I { ! is_a_theorem( skol29 ),
% 0.72/1.26 modus_ponens_strict_implies }.
% 0.72/1.26 substitution0:
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (155) {G1,W2,D2,L1,V0,M1} S(85);r(148) { ! is_a_theorem(
% 0.72/1.26 skol29 ) }.
% 0.72/1.26 parent0: (8816) {G1,W2,D2,L1,V0,M1} { ! is_a_theorem( skol29 ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8817) {G1,W2,D2,L1,V0,M1} { alpha2( skol29 ) }.
% 0.72/1.26 parent0[0]: (148) {G0,W1,D1,L1,V0,M1} I { ! modus_ponens_strict_implies }.
% 0.72/1.26 parent1[1]: (84) {G0,W3,D2,L2,V0,M2} I { alpha2( skol29 ),
% 0.72/1.26 modus_ponens_strict_implies }.
% 0.72/1.26 substitution0:
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (157) {G1,W2,D2,L1,V0,M1} S(84);r(148) { alpha2( skol29 ) }.
% 0.72/1.26 parent0: (8817) {G1,W2,D2,L1,V0,M1} { alpha2( skol29 ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8818) {G2,W2,D2,L1,V0,M1} { ! alpha1( skol29 ) }.
% 0.72/1.26 parent0[0]: (155) {G1,W2,D2,L1,V0,M1} S(85);r(148) { ! is_a_theorem( skol29
% 0.72/1.26 ) }.
% 0.72/1.26 parent1[1]: (150) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 0.72/1.26 is_a_theorem( X ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 X := skol29
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (158) {G2,W2,D2,L1,V0,M1} R(150,155) { ! alpha1( skol29 ) }.
% 0.72/1.26 parent0: (8818) {G2,W2,D2,L1,V0,M1} { ! alpha1( skol29 ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8819) {G1,W6,D3,L2,V1,M2} { ! is_a_theorem( X ), !
% 0.72/1.26 is_a_theorem( implies( X, skol29 ) ) }.
% 0.72/1.26 parent0[0]: (158) {G2,W2,D2,L1,V0,M1} R(150,155) { ! alpha1( skol29 ) }.
% 0.72/1.26 parent1[2]: (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem
% 0.72/1.26 ( implies( Y, X ) ), alpha1( X ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 X := skol29
% 0.72/1.26 Y := X
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (162) {G3,W6,D3,L2,V1,M2} R(158,5) { ! is_a_theorem( X ), !
% 0.72/1.26 is_a_theorem( implies( X, skol29 ) ) }.
% 0.72/1.26 parent0: (8819) {G1,W6,D3,L2,V1,M2} { ! is_a_theorem( X ), ! is_a_theorem
% 0.72/1.26 ( implies( X, skol29 ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 1 ==> 1
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8820) {G2,W5,D2,L2,V1,M2} { alpha3( X, X ), ! alpha1( X ) }.
% 0.72/1.26 parent0[0]: (149) {G1,W5,D2,L2,V1,M2} F(94) { ! is_a_theorem( X ), alpha3(
% 0.72/1.26 X, X ) }.
% 0.72/1.26 parent1[1]: (150) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 0.72/1.26 is_a_theorem( X ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (178) {G2,W5,D2,L2,V1,M2} R(149,150) { alpha3( X, X ), !
% 0.72/1.26 alpha1( X ) }.
% 0.72/1.26 parent0: (8820) {G2,W5,D2,L2,V1,M2} { alpha3( X, X ), ! alpha1( X ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 1 ==> 1
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8821) {G1,W6,D4,L1,V2,M1} { is_a_theorem( implies( X, implies
% 0.72/1.26 ( Y, X ) ) ) }.
% 0.72/1.26 parent0[0]: (11) {G0,W7,D4,L2,V2,M2} I { ! implies_1, is_a_theorem( implies
% 0.72/1.26 ( X, implies( Y, X ) ) ) }.
% 0.72/1.26 parent1[0]: (67) {G0,W1,D1,L1,V0,M1} I { implies_1 }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 Y := Y
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (181) {G1,W6,D4,L1,V2,M1} S(11);r(67) { is_a_theorem( implies
% 0.72/1.26 ( X, implies( Y, X ) ) ) }.
% 0.72/1.26 parent0: (8821) {G1,W6,D4,L1,V2,M1} { is_a_theorem( implies( X, implies( Y
% 0.72/1.26 , X ) ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 Y := Y
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8822) {G1,W3,D3,L1,V1,M1} { is_a_theorem( skol30( X ) ) }.
% 0.72/1.26 parent0[0]: (86) {G0,W5,D3,L2,V2,M2} I { ! alpha2( X ), is_a_theorem(
% 0.72/1.26 skol30( Y ) ) }.
% 0.72/1.26 parent1[0]: (157) {G1,W2,D2,L1,V0,M1} S(84);r(148) { alpha2( skol29 ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := skol29
% 0.72/1.26 Y := X
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (184) {G2,W3,D3,L1,V1,M1} R(86,157) { is_a_theorem( skol30( X
% 0.72/1.26 ) ) }.
% 0.72/1.26 parent0: (8822) {G1,W3,D3,L1,V1,M1} { is_a_theorem( skol30( X ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8823) {G3,W5,D4,L1,V1,M1} { ! is_a_theorem( implies( skol30(
% 0.72/1.26 X ), skol29 ) ) }.
% 0.72/1.26 parent0[0]: (162) {G3,W6,D3,L2,V1,M2} R(158,5) { ! is_a_theorem( X ), !
% 0.72/1.26 is_a_theorem( implies( X, skol29 ) ) }.
% 0.72/1.26 parent1[0]: (184) {G2,W3,D3,L1,V1,M1} R(86,157) { is_a_theorem( skol30( X )
% 0.72/1.26 ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := skol30( X )
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (196) {G4,W5,D4,L1,V1,M1} R(162,184) { ! is_a_theorem( implies
% 0.72/1.26 ( skol30( X ), skol29 ) ) }.
% 0.72/1.26 parent0: (8823) {G3,W5,D4,L1,V1,M1} { ! is_a_theorem( implies( skol30( X )
% 0.72/1.26 , skol29 ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8824) {G1,W6,D4,L1,V2,M1} { ! alpha3( Y, implies( skol30( X )
% 0.72/1.26 , skol29 ) ) }.
% 0.72/1.26 parent0[0]: (196) {G4,W5,D4,L1,V1,M1} R(162,184) { ! is_a_theorem( implies
% 0.72/1.26 ( skol30( X ), skol29 ) ) }.
% 0.72/1.26 parent1[1]: (93) {G0,W5,D2,L2,V2,M2} I { ! alpha3( X, Y ), is_a_theorem( Y
% 0.72/1.26 ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 X := Y
% 0.72/1.26 Y := implies( skol30( X ), skol29 )
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (217) {G5,W6,D4,L1,V2,M1} R(196,93) { ! alpha3( X, implies(
% 0.72/1.26 skol30( Y ), skol29 ) ) }.
% 0.72/1.26 parent0: (8824) {G1,W6,D4,L1,V2,M1} { ! alpha3( Y, implies( skol30( X ),
% 0.72/1.26 skol29 ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := Y
% 0.72/1.26 Y := X
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8826) {G1,W6,D3,L2,V2,M2} { ! is_a_theorem( X ), alpha1(
% 0.72/1.26 implies( Y, X ) ) }.
% 0.72/1.26 parent0[1]: (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem
% 0.72/1.26 ( implies( Y, X ) ), alpha1( X ) }.
% 0.72/1.26 parent1[0]: (181) {G1,W6,D4,L1,V2,M1} S(11);r(67) { is_a_theorem( implies(
% 0.72/1.26 X, implies( Y, X ) ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := implies( Y, X )
% 0.72/1.26 Y := X
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 X := X
% 0.72/1.26 Y := Y
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (760) {G2,W6,D3,L2,V2,M2} R(181,5) { ! is_a_theorem( X ),
% 0.72/1.26 alpha1( implies( Y, X ) ) }.
% 0.72/1.26 parent0: (8826) {G1,W6,D3,L2,V2,M2} { ! is_a_theorem( X ), alpha1( implies
% 0.72/1.26 ( Y, X ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 Y := Y
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 1 ==> 1
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8828) {G2,W6,D3,L2,V2,M2} { is_a_theorem( implies( X, Y ) ),
% 0.72/1.26 ! is_a_theorem( Y ) }.
% 0.72/1.26 parent0[0]: (150) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 0.72/1.26 is_a_theorem( X ) }.
% 0.72/1.26 parent1[1]: (760) {G2,W6,D3,L2,V2,M2} R(181,5) { ! is_a_theorem( X ),
% 0.72/1.26 alpha1( implies( Y, X ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := implies( X, Y )
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 X := Y
% 0.72/1.26 Y := X
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (811) {G3,W6,D3,L2,V2,M2} R(760,150) { ! is_a_theorem( X ),
% 0.72/1.26 is_a_theorem( implies( Y, X ) ) }.
% 0.72/1.26 parent0: (8828) {G2,W6,D3,L2,V2,M2} { is_a_theorem( implies( X, Y ) ), !
% 0.72/1.26 is_a_theorem( Y ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := Y
% 0.72/1.26 Y := X
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 1
% 0.72/1.26 1 ==> 0
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8830) {G1,W6,D2,L3,V2,M3} { ! is_a_theorem( X ), alpha1( Y )
% 0.72/1.26 , ! is_a_theorem( Y ) }.
% 0.72/1.26 parent0[1]: (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem
% 0.72/1.26 ( implies( Y, X ) ), alpha1( X ) }.
% 0.72/1.26 parent1[1]: (811) {G3,W6,D3,L2,V2,M2} R(760,150) { ! is_a_theorem( X ),
% 0.72/1.26 is_a_theorem( implies( Y, X ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := Y
% 0.72/1.26 Y := X
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 X := Y
% 0.72/1.26 Y := X
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (947) {G4,W6,D2,L3,V2,M3} R(811,5) { ! is_a_theorem( X ), !
% 0.72/1.26 is_a_theorem( Y ), alpha1( X ) }.
% 0.72/1.26 parent0: (8830) {G1,W6,D2,L3,V2,M3} { ! is_a_theorem( X ), alpha1( Y ), !
% 0.72/1.26 is_a_theorem( Y ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 Y := X
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 1 ==> 2
% 0.72/1.26 2 ==> 0
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 factor: (8832) {G4,W4,D2,L2,V1,M2} { ! is_a_theorem( X ), alpha1( X ) }.
% 0.72/1.26 parent0[0, 1]: (947) {G4,W6,D2,L3,V2,M3} R(811,5) { ! is_a_theorem( X ), !
% 0.72/1.26 is_a_theorem( Y ), alpha1( X ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 Y := X
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (948) {G5,W4,D2,L2,V1,M2} F(947) { ! is_a_theorem( X ), alpha1
% 0.72/1.26 ( X ) }.
% 0.72/1.26 parent0: (8832) {G4,W4,D2,L2,V1,M2} { ! is_a_theorem( X ), alpha1( X ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 1 ==> 1
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8833) {G1,W5,D4,L1,V0,M1} { is_a_theorem( strict_implies(
% 0.72/1.26 skol30( skol29 ), skol29 ) ) }.
% 0.72/1.26 parent0[0]: (87) {G0,W7,D4,L2,V1,M2} I { ! alpha2( X ), is_a_theorem(
% 0.72/1.26 strict_implies( skol30( X ), X ) ) }.
% 0.72/1.26 parent1[0]: (157) {G1,W2,D2,L1,V0,M1} S(84);r(148) { alpha2( skol29 ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := skol29
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (1400) {G2,W5,D4,L1,V0,M1} R(87,157) { is_a_theorem(
% 0.72/1.26 strict_implies( skol30( skol29 ), skol29 ) ) }.
% 0.72/1.26 parent0: (8833) {G1,W5,D4,L1,V0,M1} { is_a_theorem( strict_implies( skol30
% 0.72/1.26 ( skol29 ), skol29 ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8834) {G3,W5,D4,L1,V0,M1} { alpha1( strict_implies( skol30(
% 0.72/1.26 skol29 ), skol29 ) ) }.
% 0.72/1.26 parent0[0]: (948) {G5,W4,D2,L2,V1,M2} F(947) { ! is_a_theorem( X ), alpha1
% 0.72/1.26 ( X ) }.
% 0.72/1.26 parent1[0]: (1400) {G2,W5,D4,L1,V0,M1} R(87,157) { is_a_theorem(
% 0.72/1.26 strict_implies( skol30( skol29 ), skol29 ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := strict_implies( skol30( skol29 ), skol29 )
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (1403) {G6,W5,D4,L1,V0,M1} R(1400,948) { alpha1(
% 0.72/1.26 strict_implies( skol30( skol29 ), skol29 ) ) }.
% 0.72/1.26 parent0: (8834) {G3,W5,D4,L1,V0,M1} { alpha1( strict_implies( skol30(
% 0.72/1.26 skol29 ), skol29 ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8835) {G1,W5,D4,L1,V1,M1} { is_a_theorem( implies(
% 0.72/1.26 necessarily( X ), X ) ) }.
% 0.72/1.26 parent0[0]: (100) {G0,W6,D4,L2,V1,M2} I { ! axiom_M, is_a_theorem( implies
% 0.72/1.26 ( necessarily( X ), X ) ) }.
% 0.72/1.26 parent1[0]: (143) {G0,W1,D1,L1,V0,M1} I { axiom_M }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (2545) {G1,W5,D4,L1,V1,M1} S(100);r(143) { is_a_theorem(
% 0.72/1.26 implies( necessarily( X ), X ) ) }.
% 0.72/1.26 parent0: (8835) {G1,W5,D4,L1,V1,M1} { is_a_theorem( implies( necessarily(
% 0.72/1.26 X ), X ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8837) {G1,W5,D3,L2,V1,M2} { ! is_a_theorem( necessarily( X )
% 0.72/1.26 ), alpha1( X ) }.
% 0.72/1.26 parent0[1]: (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem
% 0.72/1.26 ( implies( Y, X ) ), alpha1( X ) }.
% 0.72/1.26 parent1[0]: (2545) {G1,W5,D4,L1,V1,M1} S(100);r(143) { is_a_theorem(
% 0.72/1.26 implies( necessarily( X ), X ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 Y := necessarily( X )
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (2575) {G2,W5,D3,L2,V1,M2} R(2545,5) { ! is_a_theorem(
% 0.72/1.26 necessarily( X ) ), alpha1( X ) }.
% 0.72/1.26 parent0: (8837) {G1,W5,D3,L2,V1,M2} { ! is_a_theorem( necessarily( X ) ),
% 0.72/1.26 alpha1( X ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 1 ==> 1
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8838) {G2,W5,D3,L2,V1,M2} { alpha1( X ), ! alpha1(
% 0.72/1.26 necessarily( X ) ) }.
% 0.72/1.26 parent0[0]: (2575) {G2,W5,D3,L2,V1,M2} R(2545,5) { ! is_a_theorem(
% 0.72/1.26 necessarily( X ) ), alpha1( X ) }.
% 0.72/1.26 parent1[1]: (150) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 0.72/1.26 is_a_theorem( X ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 X := necessarily( X )
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (2647) {G3,W5,D3,L2,V1,M2} R(2575,150) { alpha1( X ), ! alpha1
% 0.72/1.26 ( necessarily( X ) ) }.
% 0.72/1.26 parent0: (8838) {G2,W5,D3,L2,V1,M2} { alpha1( X ), ! alpha1( necessarily(
% 0.72/1.26 X ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 1 ==> 1
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8839) {G3,W6,D3,L2,V1,M2} { alpha3( X, X ), ! alpha1(
% 0.72/1.26 necessarily( X ) ) }.
% 0.72/1.26 parent0[1]: (178) {G2,W5,D2,L2,V1,M2} R(149,150) { alpha3( X, X ), ! alpha1
% 0.72/1.26 ( X ) }.
% 0.72/1.26 parent1[0]: (2647) {G3,W5,D3,L2,V1,M2} R(2575,150) { alpha1( X ), ! alpha1
% 0.72/1.26 ( necessarily( X ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (2883) {G4,W6,D3,L2,V1,M2} R(2647,178) { ! alpha1( necessarily
% 0.72/1.26 ( X ) ), alpha3( X, X ) }.
% 0.72/1.26 parent0: (8839) {G3,W6,D3,L2,V1,M2} { alpha3( X, X ), ! alpha1(
% 0.72/1.26 necessarily( X ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 1
% 0.72/1.26 1 ==> 0
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8841) {G1,W8,D4,L1,V2,M1} { necessarily( implies( X, Y ) )
% 0.72/1.26 ==> strict_implies( X, Y ) }.
% 0.72/1.26 parent0[0]: (138) {G0,W9,D4,L2,V2,M2} I { ! op_strict_implies, necessarily
% 0.72/1.26 ( implies( X, Y ) ) ==> strict_implies( X, Y ) }.
% 0.72/1.26 parent1[0]: (146) {G0,W1,D1,L1,V0,M1} I { op_strict_implies }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 Y := Y
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (5037) {G1,W8,D4,L1,V2,M1} S(138);r(146) { necessarily(
% 0.72/1.26 implies( X, Y ) ) ==> strict_implies( X, Y ) }.
% 0.72/1.26 parent0: (8841) {G1,W8,D4,L1,V2,M1} { necessarily( implies( X, Y ) ) ==>
% 0.72/1.26 strict_implies( X, Y ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 Y := Y
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8844) {G5,W6,D5,L1,V1,M1} { ! alpha1( necessarily( implies(
% 0.72/1.26 skol30( X ), skol29 ) ) ) }.
% 0.72/1.26 parent0[0]: (217) {G5,W6,D4,L1,V2,M1} R(196,93) { ! alpha3( X, implies(
% 0.72/1.26 skol30( Y ), skol29 ) ) }.
% 0.72/1.26 parent1[1]: (2883) {G4,W6,D3,L2,V1,M2} R(2647,178) { ! alpha1( necessarily
% 0.72/1.26 ( X ) ), alpha3( X, X ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := implies( skol30( X ), skol29 )
% 0.72/1.26 Y := X
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 X := implies( skol30( X ), skol29 )
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 paramod: (8845) {G2,W5,D4,L1,V1,M1} { ! alpha1( strict_implies( skol30( X
% 0.72/1.26 ), skol29 ) ) }.
% 0.72/1.26 parent0[0]: (5037) {G1,W8,D4,L1,V2,M1} S(138);r(146) { necessarily( implies
% 0.72/1.26 ( X, Y ) ) ==> strict_implies( X, Y ) }.
% 0.72/1.26 parent1[0; 2]: (8844) {G5,W6,D5,L1,V1,M1} { ! alpha1( necessarily( implies
% 0.72/1.26 ( skol30( X ), skol29 ) ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := skol30( X )
% 0.72/1.26 Y := skol29
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (8423) {G6,W5,D4,L1,V1,M1} R(2883,217);d(5037) { ! alpha1(
% 0.72/1.26 strict_implies( skol30( X ), skol29 ) ) }.
% 0.72/1.26 parent0: (8845) {G2,W5,D4,L1,V1,M1} { ! alpha1( strict_implies( skol30( X
% 0.72/1.26 ), skol29 ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := X
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 0 ==> 0
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 resolution: (8846) {G7,W0,D0,L0,V0,M0} { }.
% 0.72/1.26 parent0[0]: (8423) {G6,W5,D4,L1,V1,M1} R(2883,217);d(5037) { ! alpha1(
% 0.72/1.26 strict_implies( skol30( X ), skol29 ) ) }.
% 0.72/1.26 parent1[0]: (1403) {G6,W5,D4,L1,V0,M1} R(1400,948) { alpha1( strict_implies
% 0.72/1.26 ( skol30( skol29 ), skol29 ) ) }.
% 0.72/1.26 substitution0:
% 0.72/1.26 X := skol29
% 0.72/1.26 end
% 0.72/1.26 substitution1:
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 subsumption: (8536) {G7,W0,D0,L0,V0,M0} R(8423,1403) { }.
% 0.72/1.26 parent0: (8846) {G7,W0,D0,L0,V0,M0} { }.
% 0.72/1.26 substitution0:
% 0.72/1.26 end
% 0.72/1.26 permutation0:
% 0.72/1.26 end
% 0.72/1.26
% 0.72/1.26 Proof check complete!
% 0.72/1.26
% 0.72/1.26 Memory use:
% 0.72/1.26
% 0.72/1.26 space for terms: 95568
% 0.72/1.26 space for clauses: 428006
% 0.72/1.26
% 0.72/1.26
% 0.72/1.26 clauses generated: 16231
% 0.72/1.26 clauses kept: 8537
% 0.72/1.26 clauses selected: 570
% 0.72/1.26 clauses deleted: 83
% 0.72/1.26 clauses inuse deleted: 15
% 0.72/1.26
% 0.72/1.26 subsentry: 31592
% 0.72/1.26 literals s-matched: 24493
% 0.72/1.26 literals matched: 22315
% 0.72/1.26 full subsumption: 1963
% 0.72/1.26
% 0.72/1.26 checksum: -1135774306
% 0.72/1.26
% 0.72/1.26
% 0.72/1.26 Bliksem ended
%------------------------------------------------------------------------------