TSTP Solution File: LCL538+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL538+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 07:54:30 EDT 2022
% Result : Theorem 0.95s 1.35s
% Output : Refutation 0.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL538+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.31 % Computer : n026.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % DateTime : Mon Jul 4 21:00:22 EDT 2022
% 0.12/0.31 % CPUTime :
% 0.40/1.08 *** allocated 10000 integers for termspace/termends
% 0.40/1.08 *** allocated 10000 integers for clauses
% 0.40/1.08 *** allocated 10000 integers for justifications
% 0.40/1.08 Bliksem 1.12
% 0.40/1.08
% 0.40/1.08
% 0.40/1.08 Automatic Strategy Selection
% 0.40/1.08
% 0.40/1.08
% 0.40/1.08 Clauses:
% 0.40/1.08
% 0.40/1.08 { ! modus_ponens, ! alpha1( X ), is_a_theorem( X ) }.
% 0.40/1.08 { alpha1( skol1 ), modus_ponens }.
% 0.40/1.08 { ! is_a_theorem( skol1 ), modus_ponens }.
% 0.40/1.08 { ! alpha1( X ), is_a_theorem( skol2( Y ) ) }.
% 0.40/1.08 { ! alpha1( X ), is_a_theorem( implies( skol2( X ), X ) ) }.
% 0.40/1.08 { ! is_a_theorem( Y ), ! is_a_theorem( implies( Y, X ) ), alpha1( X ) }.
% 0.40/1.08 { ! substitution_of_equivalents, ! is_a_theorem( equiv( X, Y ) ), X = Y }.
% 0.40/1.08 { is_a_theorem( equiv( skol3, skol52 ) ), substitution_of_equivalents }.
% 0.40/1.08 { ! skol3 = skol52, substitution_of_equivalents }.
% 0.40/1.08 { ! modus_tollens, is_a_theorem( implies( implies( not( Y ), not( X ) ),
% 0.40/1.08 implies( X, Y ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( implies( not( skol53 ), not( skol4 ) ), implies
% 0.40/1.08 ( skol4, skol53 ) ) ), modus_tollens }.
% 0.40/1.08 { ! implies_1, is_a_theorem( implies( X, implies( Y, X ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( skol5, implies( skol54, skol5 ) ) ), implies_1 }
% 0.40/1.08 .
% 0.40/1.08 { ! implies_2, is_a_theorem( implies( implies( X, implies( X, Y ) ),
% 0.40/1.08 implies( X, Y ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( implies( skol6, implies( skol6, skol55 ) ),
% 0.40/1.08 implies( skol6, skol55 ) ) ), implies_2 }.
% 0.40/1.08 { ! implies_3, is_a_theorem( implies( implies( X, Y ), implies( implies( Y
% 0.40/1.08 , Z ), implies( X, Z ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( implies( skol7, skol56 ), implies( implies(
% 0.40/1.08 skol56, skol86 ), implies( skol7, skol86 ) ) ) ), implies_3 }.
% 0.40/1.08 { ! and_1, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( and( skol8, skol57 ), skol8 ) ), and_1 }.
% 0.40/1.08 { ! and_2, is_a_theorem( implies( and( X, Y ), Y ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( and( skol9, skol58 ), skol58 ) ), and_2 }.
% 0.40/1.08 { ! and_3, is_a_theorem( implies( X, implies( Y, and( X, Y ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( skol10, implies( skol59, and( skol10, skol59 ) )
% 0.40/1.08 ) ), and_3 }.
% 0.40/1.08 { ! or_1, is_a_theorem( implies( X, or( X, Y ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( skol11, or( skol11, skol60 ) ) ), or_1 }.
% 0.40/1.08 { ! or_2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( skol61, or( skol12, skol61 ) ) ), or_2 }.
% 0.40/1.08 { ! or_3, is_a_theorem( implies( implies( X, Z ), implies( implies( Y, Z )
% 0.40/1.08 , implies( or( X, Y ), Z ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( implies( skol13, skol87 ), implies( implies(
% 0.40/1.08 skol62, skol87 ), implies( or( skol13, skol62 ), skol87 ) ) ) ), or_3 }.
% 0.40/1.08 { ! equivalence_1, is_a_theorem( implies( equiv( X, Y ), implies( X, Y ) )
% 0.40/1.08 ) }.
% 0.40/1.08 { ! is_a_theorem( implies( equiv( skol14, skol63 ), implies( skol14, skol63
% 0.40/1.08 ) ) ), equivalence_1 }.
% 0.40/1.08 { ! equivalence_2, is_a_theorem( implies( equiv( X, Y ), implies( Y, X ) )
% 0.40/1.08 ) }.
% 0.40/1.08 { ! is_a_theorem( implies( equiv( skol15, skol64 ), implies( skol64, skol15
% 0.40/1.08 ) ) ), equivalence_2 }.
% 0.40/1.08 { ! equivalence_3, is_a_theorem( implies( implies( X, Y ), implies( implies
% 0.40/1.08 ( Y, X ), equiv( X, Y ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( implies( skol16, skol65 ), implies( implies(
% 0.40/1.08 skol65, skol16 ), equiv( skol16, skol65 ) ) ) ), equivalence_3 }.
% 0.40/1.08 { ! kn1, is_a_theorem( implies( X, and( X, X ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( skol17, and( skol17, skol17 ) ) ), kn1 }.
% 0.40/1.08 { ! kn2, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( and( skol18, skol66 ), skol18 ) ), kn2 }.
% 0.40/1.08 { ! kn3, is_a_theorem( implies( implies( X, Y ), implies( not( and( Y, Z )
% 0.40/1.08 ), not( and( Z, X ) ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( implies( skol19, skol67 ), implies( not( and(
% 0.40/1.08 skol67, skol88 ) ), not( and( skol88, skol19 ) ) ) ) ), kn3 }.
% 0.40/1.08 { ! cn1, is_a_theorem( implies( implies( X, Y ), implies( implies( Y, Z ),
% 0.40/1.08 implies( X, Z ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( implies( skol20, skol68 ), implies( implies(
% 0.40/1.08 skol68, skol89 ), implies( skol20, skol89 ) ) ) ), cn1 }.
% 0.40/1.08 { ! cn2, is_a_theorem( implies( X, implies( not( X ), Y ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( skol21, implies( not( skol21 ), skol69 ) ) ),
% 0.40/1.08 cn2 }.
% 0.40/1.08 { ! cn3, is_a_theorem( implies( implies( not( X ), X ), X ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( implies( not( skol22 ), skol22 ), skol22 ) ),
% 0.40/1.08 cn3 }.
% 0.40/1.08 { ! r1, is_a_theorem( implies( or( X, X ), X ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( or( skol23, skol23 ), skol23 ) ), r1 }.
% 0.40/1.08 { ! r2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( skol70, or( skol24, skol70 ) ) ), r2 }.
% 0.40/1.08 { ! r3, is_a_theorem( implies( or( X, Y ), or( Y, X ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( or( skol25, skol71 ), or( skol71, skol25 ) ) ),
% 0.40/1.08 r3 }.
% 0.40/1.08 { ! r4, is_a_theorem( implies( or( X, or( Y, Z ) ), or( Y, or( X, Z ) ) ) )
% 0.40/1.08 }.
% 0.40/1.08 { ! is_a_theorem( implies( or( skol26, or( skol72, skol90 ) ), or( skol72,
% 0.40/1.08 or( skol26, skol90 ) ) ) ), r4 }.
% 0.40/1.08 { ! r5, is_a_theorem( implies( implies( Y, Z ), implies( or( X, Y ), or( X
% 0.40/1.08 , Z ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( implies( skol73, skol91 ), implies( or( skol27,
% 0.40/1.08 skol73 ), or( skol27, skol91 ) ) ) ), r5 }.
% 0.40/1.08 { ! op_or, or( X, Y ) = not( and( not( X ), not( Y ) ) ) }.
% 0.40/1.08 { ! op_and, and( X, Y ) = not( or( not( X ), not( Y ) ) ) }.
% 0.40/1.08 { ! op_implies_and, implies( X, Y ) = not( and( X, not( Y ) ) ) }.
% 0.40/1.08 { ! op_implies_or, implies( X, Y ) = or( not( X ), Y ) }.
% 0.40/1.08 { ! op_equiv, equiv( X, Y ) = and( implies( X, Y ), implies( Y, X ) ) }.
% 0.40/1.08 { op_or }.
% 0.40/1.08 { op_implies_and }.
% 0.40/1.08 { op_equiv }.
% 0.40/1.08 { modus_ponens }.
% 0.40/1.08 { modus_tollens }.
% 0.40/1.08 { implies_1 }.
% 0.40/1.08 { implies_2 }.
% 0.40/1.08 { implies_3 }.
% 0.40/1.08 { and_1 }.
% 0.40/1.08 { and_2 }.
% 0.40/1.08 { and_3 }.
% 0.40/1.08 { or_1 }.
% 0.40/1.08 { or_2 }.
% 0.40/1.08 { or_3 }.
% 0.40/1.08 { equivalence_1 }.
% 0.40/1.08 { equivalence_2 }.
% 0.40/1.08 { equivalence_3 }.
% 0.40/1.08 { substitution_of_equivalents }.
% 0.40/1.08 { ! necessitation, ! is_a_theorem( X ), is_a_theorem( necessarily( X ) ) }
% 0.40/1.08 .
% 0.40/1.08 { is_a_theorem( skol28 ), necessitation }.
% 0.40/1.08 { ! is_a_theorem( necessarily( skol28 ) ), necessitation }.
% 0.40/1.08 { ! modus_ponens_strict_implies, ! alpha2( X ), is_a_theorem( X ) }.
% 0.40/1.08 { alpha2( skol29 ), modus_ponens_strict_implies }.
% 0.40/1.08 { ! is_a_theorem( skol29 ), modus_ponens_strict_implies }.
% 0.40/1.08 { ! alpha2( X ), is_a_theorem( skol30( Y ) ) }.
% 0.40/1.08 { ! alpha2( X ), is_a_theorem( strict_implies( skol30( X ), X ) ) }.
% 0.40/1.08 { ! is_a_theorem( Y ), ! is_a_theorem( strict_implies( Y, X ) ), alpha2( X
% 0.40/1.08 ) }.
% 0.40/1.08 { ! adjunction, ! alpha3( X, Y ), is_a_theorem( and( X, Y ) ) }.
% 0.40/1.08 { alpha3( skol31, skol74 ), adjunction }.
% 0.40/1.08 { ! is_a_theorem( and( skol31, skol74 ) ), adjunction }.
% 0.40/1.08 { ! alpha3( X, Y ), is_a_theorem( X ) }.
% 0.40/1.08 { ! alpha3( X, Y ), is_a_theorem( Y ) }.
% 0.40/1.08 { ! is_a_theorem( X ), ! is_a_theorem( Y ), alpha3( X, Y ) }.
% 0.40/1.08 { ! substitution_strict_equiv, ! is_a_theorem( strict_equiv( X, Y ) ), X =
% 0.40/1.08 Y }.
% 0.40/1.08 { is_a_theorem( strict_equiv( skol32, skol75 ) ), substitution_strict_equiv
% 0.40/1.08 }.
% 0.40/1.08 { ! skol32 = skol75, substitution_strict_equiv }.
% 0.40/1.08 { ! axiom_K, is_a_theorem( implies( necessarily( implies( X, Y ) ), implies
% 0.40/1.08 ( necessarily( X ), necessarily( Y ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( necessarily( implies( skol33, skol76 ) ),
% 0.40/1.08 implies( necessarily( skol33 ), necessarily( skol76 ) ) ) ), axiom_K }.
% 0.40/1.08 { ! axiom_M, is_a_theorem( implies( necessarily( X ), X ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( necessarily( skol34 ), skol34 ) ), axiom_M }.
% 0.40/1.08 { ! axiom_4, is_a_theorem( implies( necessarily( X ), necessarily(
% 0.40/1.08 necessarily( X ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( necessarily( skol35 ), necessarily( necessarily
% 0.40/1.08 ( skol35 ) ) ) ), axiom_4 }.
% 0.40/1.08 { ! axiom_B, is_a_theorem( implies( X, necessarily( possibly( X ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( skol36, necessarily( possibly( skol36 ) ) ) ),
% 0.40/1.08 axiom_B }.
% 0.40/1.08 { ! axiom_5, is_a_theorem( implies( possibly( X ), necessarily( possibly( X
% 0.40/1.08 ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( possibly( skol37 ), necessarily( possibly(
% 0.40/1.08 skol37 ) ) ) ), axiom_5 }.
% 0.40/1.08 { ! axiom_s1, is_a_theorem( implies( and( necessarily( implies( X, Y ) ),
% 0.40/1.08 necessarily( implies( Y, Z ) ) ), necessarily( implies( X, Z ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( implies( and( necessarily( implies( skol38, skol77 ) ),
% 0.40/1.08 necessarily( implies( skol77, skol92 ) ) ), necessarily( implies( skol38
% 0.40/1.08 , skol92 ) ) ) ), axiom_s1 }.
% 0.40/1.08 { ! axiom_s2, is_a_theorem( strict_implies( possibly( and( X, Y ) ), and(
% 0.40/1.08 possibly( X ), possibly( Y ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( strict_implies( possibly( and( skol39, skol78 ) ), and(
% 0.40/1.08 possibly( skol39 ), possibly( skol78 ) ) ) ), axiom_s2 }.
% 0.40/1.08 { ! axiom_s3, is_a_theorem( strict_implies( strict_implies( X, Y ),
% 0.40/1.08 strict_implies( not( possibly( Y ) ), not( possibly( X ) ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( strict_implies( strict_implies( skol40, skol79 ),
% 0.40/1.08 strict_implies( not( possibly( skol79 ) ), not( possibly( skol40 ) ) ) )
% 0.40/1.08 ), axiom_s3 }.
% 0.40/1.08 { ! axiom_s4, is_a_theorem( strict_implies( necessarily( X ), necessarily(
% 0.40/1.08 necessarily( X ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( strict_implies( necessarily( skol41 ), necessarily(
% 0.40/1.08 necessarily( skol41 ) ) ) ), axiom_s4 }.
% 0.40/1.08 { ! axiom_m1, is_a_theorem( strict_implies( and( X, Y ), and( Y, X ) ) ) }
% 0.40/1.08 .
% 0.40/1.08 { ! is_a_theorem( strict_implies( and( skol42, skol80 ), and( skol80,
% 0.40/1.08 skol42 ) ) ), axiom_m1 }.
% 0.40/1.08 { ! axiom_m2, is_a_theorem( strict_implies( and( X, Y ), X ) ) }.
% 0.40/1.08 { ! is_a_theorem( strict_implies( and( skol43, skol81 ), skol43 ) ),
% 0.40/1.08 axiom_m2 }.
% 0.40/1.08 { ! axiom_m3, is_a_theorem( strict_implies( and( and( X, Y ), Z ), and( X,
% 0.40/1.08 and( Y, Z ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( strict_implies( and( and( skol44, skol82 ), skol93 ), and
% 0.40/1.08 ( skol44, and( skol82, skol93 ) ) ) ), axiom_m3 }.
% 0.40/1.08 { ! axiom_m4, is_a_theorem( strict_implies( X, and( X, X ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( strict_implies( skol45, and( skol45, skol45 ) ) ),
% 0.40/1.08 axiom_m4 }.
% 0.40/1.08 { ! axiom_m5, is_a_theorem( strict_implies( and( strict_implies( X, Y ),
% 0.40/1.08 strict_implies( Y, Z ) ), strict_implies( X, Z ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( strict_implies( and( strict_implies( skol46, skol83 ),
% 0.40/1.08 strict_implies( skol83, skol94 ) ), strict_implies( skol46, skol94 ) ) )
% 0.40/1.08 , axiom_m5 }.
% 0.40/1.08 { ! axiom_m6, is_a_theorem( strict_implies( X, possibly( X ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( strict_implies( skol47, possibly( skol47 ) ) ), axiom_m6
% 0.40/1.08 }.
% 0.40/1.08 { ! axiom_m7, is_a_theorem( strict_implies( possibly( and( X, Y ) ), X ) )
% 0.40/1.08 }.
% 0.40/1.08 { ! is_a_theorem( strict_implies( possibly( and( skol48, skol84 ) ), skol48
% 0.40/1.08 ) ), axiom_m7 }.
% 0.40/1.08 { ! axiom_m8, is_a_theorem( strict_implies( strict_implies( X, Y ),
% 0.40/1.08 strict_implies( possibly( X ), possibly( Y ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( strict_implies( strict_implies( skol49, skol85 ),
% 0.40/1.08 strict_implies( possibly( skol49 ), possibly( skol85 ) ) ) ), axiom_m8 }
% 0.40/1.08 .
% 0.40/1.08 { ! axiom_m9, is_a_theorem( strict_implies( possibly( possibly( X ) ),
% 0.40/1.08 possibly( X ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( strict_implies( possibly( possibly( skol50 ) ), possibly
% 0.40/1.08 ( skol50 ) ) ), axiom_m9 }.
% 0.40/1.08 { ! axiom_m10, is_a_theorem( strict_implies( possibly( X ), necessarily(
% 0.40/1.08 possibly( X ) ) ) ) }.
% 0.40/1.08 { ! is_a_theorem( strict_implies( possibly( skol51 ), necessarily( possibly
% 0.40/1.08 ( skol51 ) ) ) ), axiom_m10 }.
% 0.40/1.08 { ! op_possibly, possibly( X ) = not( necessarily( not( X ) ) ) }.
% 0.40/1.08 { ! op_necessarily, necessarily( X ) = not( possibly( not( X ) ) ) }.
% 0.40/1.08 { ! op_strict_implies, strict_implies( X, Y ) = necessarily( implies( X, Y
% 0.40/1.08 ) ) }.
% 0.40/1.08 { ! op_strict_equiv, strict_equiv( X, Y ) = and( strict_implies( X, Y ),
% 0.40/1.08 strict_implies( Y, X ) ) }.
% 0.40/1.08 { op_possibly }.
% 0.40/1.08 { necessitation }.
% 0.40/1.08 { axiom_K }.
% 0.40/1.08 { axiom_M }.
% 0.40/1.08 { axiom_4 }.
% 0.40/1.08 { axiom_B }.
% 0.40/1.08 { op_possibly }.
% 0.40/1.08 { op_or }.
% 0.40/1.08 { op_implies }.
% 0.40/1.08 { op_strict_implies }.
% 0.40/1.08 { op_equiv }.
% 0.40/1.08 { op_strict_equiv }.
% 0.40/1.08 { ! modus_ponens_strict_implies }.
% 0.40/1.08
% 0.40/1.08 percentage equality = 0.046263, percentage horn = 0.960000
% 0.40/1.08 This is a problem with some equality
% 0.40/1.08
% 0.40/1.08
% 0.40/1.08
% 0.40/1.08 Options Used:
% 0.40/1.08
% 0.40/1.08 useres = 1
% 0.40/1.08 useparamod = 1
% 0.40/1.08 useeqrefl = 1
% 0.40/1.08 useeqfact = 1
% 0.40/1.08 usefactor = 1
% 0.40/1.08 usesimpsplitting = 0
% 0.40/1.08 usesimpdemod = 5
% 0.40/1.08 usesimpres = 3
% 0.40/1.08
% 0.40/1.08 resimpinuse = 1000
% 0.40/1.08 resimpclauses = 20000
% 0.40/1.08 substype = eqrewr
% 0.40/1.08 backwardsubs = 1
% 0.40/1.08 selectoldest = 5
% 0.40/1.08
% 0.40/1.08 litorderings [0] = split
% 0.40/1.08 litorderings [1] = extend the termordering, first sorting on arguments
% 0.40/1.08
% 0.40/1.08 termordering = kbo
% 0.40/1.08
% 0.40/1.08 litapriori = 0
% 0.40/1.08 termapriori = 1
% 0.40/1.08 litaposteriori = 0
% 0.40/1.08 termaposteriori = 0
% 0.40/1.08 demodaposteriori = 0
% 0.40/1.08 ordereqreflfact = 0
% 0.40/1.08
% 0.40/1.08 litselect = negord
% 0.40/1.08
% 0.40/1.08 maxweight = 15
% 0.40/1.08 maxdepth = 30000
% 0.40/1.08 maxlength = 115
% 0.40/1.08 maxnrvars = 195
% 0.40/1.08 excuselevel = 1
% 0.40/1.08 increasemaxweight = 1
% 0.40/1.08
% 0.40/1.08 maxselected = 10000000
% 0.40/1.08 maxnrclauses = 10000000
% 0.40/1.08
% 0.40/1.08 showgenerated = 0
% 0.40/1.08 showkept = 0
% 0.40/1.08 showselected = 0
% 0.40/1.08 showdeleted = 0
% 0.40/1.08 showresimp = 1
% 0.40/1.08 showstatus = 2000
% 0.40/1.08
% 0.40/1.08 prologoutput = 0
% 0.40/1.08 nrgoals = 5000000
% 0.40/1.08 totalproof = 1
% 0.40/1.08
% 0.40/1.08 Symbols occurring in the translation:
% 0.40/1.08
% 0.40/1.08 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.40/1.08 . [1, 2] (w:1, o:176, a:1, s:1, b:0),
% 0.40/1.08 ! [4, 1] (w:0, o:163, a:1, s:1, b:0),
% 0.40/1.08 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.40/1.08 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.40/1.08 modus_ponens [35, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.40/1.08 is_a_theorem [38, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.40/1.08 implies [39, 2] (w:1, o:200, a:1, s:1, b:0),
% 0.40/1.08 substitution_of_equivalents [40, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.40/1.08 equiv [41, 2] (w:1, o:201, a:1, s:1, b:0),
% 0.40/1.08 modus_tollens [42, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.40/1.08 not [43, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.40/1.08 implies_1 [44, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.40/1.08 implies_2 [45, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.40/1.08 implies_3 [46, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.40/1.08 and_1 [48, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.40/1.08 and [49, 2] (w:1, o:202, a:1, s:1, b:0),
% 0.40/1.08 and_2 [50, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.40/1.08 and_3 [51, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.40/1.08 or_1 [52, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.40/1.08 or [53, 2] (w:1, o:203, a:1, s:1, b:0),
% 0.40/1.08 or_2 [54, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.40/1.08 or_3 [55, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.40/1.08 equivalence_1 [56, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.40/1.08 equivalence_2 [57, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.40/1.08 equivalence_3 [58, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.40/1.08 kn1 [59, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.40/1.08 kn2 [61, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.40/1.08 kn3 [63, 0] (w:1, o:35, a:1, s:1, b:0),
% 0.40/1.08 cn1 [65, 0] (w:1, o:37, a:1, s:1, b:0),
% 0.40/1.08 cn2 [66, 0] (w:1, o:38, a:1, s:1, b:0),
% 0.40/1.08 cn3 [67, 0] (w:1, o:39, a:1, s:1, b:0),
% 0.40/1.08 r1 [68, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.40/1.08 r2 [69, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.40/1.08 r3 [70, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.40/1.08 r4 [71, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.40/1.08 r5 [72, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.40/1.08 op_or [73, 0] (w:1, o:41, a:1, s:1, b:0),
% 0.40/1.08 op_and [74, 0] (w:1, o:42, a:1, s:1, b:0),
% 0.40/1.08 op_implies_and [75, 0] (w:1, o:43, a:1, s:1, b:0),
% 0.40/1.08 op_implies_or [76, 0] (w:1, o:44, a:1, s:1, b:0),
% 0.40/1.08 op_equiv [77, 0] (w:1, o:45, a:1, s:1, b:0),
% 0.40/1.08 necessitation [78, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.40/1.08 necessarily [79, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.40/1.08 modus_ponens_strict_implies [80, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.40/1.08 strict_implies [81, 2] (w:1, o:204, a:1, s:1, b:0),
% 0.40/1.08 adjunction [82, 0] (w:1, o:46, a:1, s:1, b:0),
% 0.40/1.08 substitution_strict_equiv [83, 0] (w:1, o:47, a:1, s:1, b:0),
% 0.40/1.08 strict_equiv [84, 2] (w:1, o:205, a:1, s:1, b:0),
% 0.40/1.08 axiom_K [85, 0] (w:1, o:48, a:1, s:1, b:0),
% 0.40/1.08 axiom_M [86, 0] (w:1, o:49, a:1, s:1, b:0),
% 0.40/1.08 axiom_4 [87, 0] (w:1, o:50, a:1, s:1, b:0),
% 0.40/1.08 axiom_B [88, 0] (w:1, o:51, a:1, s:1, b:0),
% 0.40/1.08 possibly [89, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.40/1.08 axiom_5 [90, 0] (w:1, o:52, a:1, s:1, b:0),
% 0.40/1.08 axiom_s1 [91, 0] (w:1, o:53, a:1, s:1, b:0),
% 0.40/1.08 axiom_s2 [92, 0] (w:1, o:54, a:1, s:1, b:0),
% 0.40/1.08 axiom_s3 [93, 0] (w:1, o:55, a:1, s:1, b:0),
% 0.40/1.08 axiom_s4 [94, 0] (w:1, o:56, a:1, s:1, b:0),
% 0.40/1.08 axiom_m1 [95, 0] (w:1, o:57, a:1, s:1, b:0),
% 0.40/1.08 axiom_m2 [96, 0] (w:1, o:59, a:1, s:1, b:0),
% 0.40/1.08 axiom_m3 [97, 0] (w:1, o:60, a:1, s:1, b:0),
% 0.40/1.08 axiom_m4 [98, 0] (w:1, o:61, a:1, s:1, b:0),
% 0.40/1.08 axiom_m5 [99, 0] (w:1, o:62, a:1, s:1, b:0),
% 0.40/1.08 axiom_m6 [100, 0] (w:1, o:63, a:1, s:1, b:0),
% 0.40/1.08 axiom_m7 [101, 0] (w:1, o:64, a:1, s:1, b:0),
% 0.40/1.08 axiom_m8 [102, 0] (w:1, o:65, a:1, s:1, b:0),
% 0.40/1.08 axiom_m9 [103, 0] (w:1, o:66, a:1, s:1, b:0),
% 0.40/1.08 axiom_m10 [104, 0] (w:1, o:58, a:1, s:1, b:0),
% 0.40/1.08 op_possibly [105, 0] (w:1, o:67, a:1, s:1, b:0),
% 0.40/1.08 op_necessarily [106, 0] (w:1, o:40, a:1, s:1, b:0),
% 0.40/1.08 op_strict_implies [107, 0] (w:1, o:68, a:1, s:1, b:0),
% 0.40/1.08 op_strict_equiv [108, 0] (w:1, o:69, a:1, s:1, b:0),
% 0.40/1.08 op_implies [109, 0] (w:1, o:70, a:1, s:1, b:0),
% 0.40/1.08 alpha1 [110, 1] (w:1, o:172, a:1, s:1, b:1),
% 0.40/1.08 alpha2 [111, 1] (w:1, o:173, a:1, s:1, b:1),
% 0.40/1.08 alpha3 [112, 2] (w:1, o:206, a:1, s:1, b:1),
% 0.40/1.08 skol1 [113, 0] (w:1, o:71, a:1, s:1, b:1),
% 0.95/1.35 skol2 [114, 1] (w:1, o:174, a:1, s:1, b:1),
% 0.95/1.35 skol3 [115, 0] (w:1, o:82, a:1, s:1, b:1),
% 0.95/1.35 skol4 [116, 0] (w:1, o:92, a:1, s:1, b:1),
% 0.95/1.35 skol5 [117, 0] (w:1, o:103, a:1, s:1, b:1),
% 0.95/1.35 skol6 [118, 0] (w:1, o:114, a:1, s:1, b:1),
% 0.95/1.35 skol7 [119, 0] (w:1, o:125, a:1, s:1, b:1),
% 0.95/1.35 skol8 [120, 0] (w:1, o:136, a:1, s:1, b:1),
% 0.95/1.35 skol9 [121, 0] (w:1, o:147, a:1, s:1, b:1),
% 0.95/1.35 skol10 [122, 0] (w:1, o:148, a:1, s:1, b:1),
% 0.95/1.35 skol11 [123, 0] (w:1, o:149, a:1, s:1, b:1),
% 0.95/1.35 skol12 [124, 0] (w:1, o:150, a:1, s:1, b:1),
% 0.95/1.35 skol13 [125, 0] (w:1, o:151, a:1, s:1, b:1),
% 0.95/1.35 skol14 [126, 0] (w:1, o:152, a:1, s:1, b:1),
% 0.95/1.35 skol15 [127, 0] (w:1, o:153, a:1, s:1, b:1),
% 0.95/1.35 skol16 [128, 0] (w:1, o:154, a:1, s:1, b:1),
% 0.95/1.35 skol17 [129, 0] (w:1, o:155, a:1, s:1, b:1),
% 0.95/1.35 skol18 [130, 0] (w:1, o:156, a:1, s:1, b:1),
% 0.95/1.35 skol19 [131, 0] (w:1, o:157, a:1, s:1, b:1),
% 0.95/1.35 skol20 [132, 0] (w:1, o:72, a:1, s:1, b:1),
% 0.95/1.35 skol21 [133, 0] (w:1, o:73, a:1, s:1, b:1),
% 0.95/1.35 skol22 [134, 0] (w:1, o:74, a:1, s:1, b:1),
% 0.95/1.35 skol23 [135, 0] (w:1, o:75, a:1, s:1, b:1),
% 0.95/1.35 skol24 [136, 0] (w:1, o:76, a:1, s:1, b:1),
% 0.95/1.35 skol25 [137, 0] (w:1, o:77, a:1, s:1, b:1),
% 0.95/1.35 skol26 [138, 0] (w:1, o:78, a:1, s:1, b:1),
% 0.95/1.35 skol27 [139, 0] (w:1, o:79, a:1, s:1, b:1),
% 0.95/1.35 skol28 [140, 0] (w:1, o:80, a:1, s:1, b:1),
% 0.95/1.35 skol29 [141, 0] (w:1, o:81, a:1, s:1, b:1),
% 0.95/1.35 skol30 [142, 1] (w:1, o:175, a:1, s:1, b:1),
% 0.95/1.35 skol31 [143, 0] (w:1, o:83, a:1, s:1, b:1),
% 0.95/1.35 skol32 [144, 0] (w:1, o:84, a:1, s:1, b:1),
% 0.95/1.35 skol33 [145, 0] (w:1, o:85, a:1, s:1, b:1),
% 0.95/1.35 skol34 [146, 0] (w:1, o:86, a:1, s:1, b:1),
% 0.95/1.35 skol35 [147, 0] (w:1, o:87, a:1, s:1, b:1),
% 0.95/1.35 skol36 [148, 0] (w:1, o:88, a:1, s:1, b:1),
% 0.95/1.35 skol37 [149, 0] (w:1, o:89, a:1, s:1, b:1),
% 0.95/1.35 skol38 [150, 0] (w:1, o:90, a:1, s:1, b:1),
% 0.95/1.35 skol39 [151, 0] (w:1, o:91, a:1, s:1, b:1),
% 0.95/1.35 skol40 [152, 0] (w:1, o:93, a:1, s:1, b:1),
% 0.95/1.35 skol41 [153, 0] (w:1, o:94, a:1, s:1, b:1),
% 0.95/1.35 skol42 [154, 0] (w:1, o:95, a:1, s:1, b:1),
% 0.95/1.35 skol43 [155, 0] (w:1, o:96, a:1, s:1, b:1),
% 0.95/1.35 skol44 [156, 0] (w:1, o:97, a:1, s:1, b:1),
% 0.95/1.35 skol45 [157, 0] (w:1, o:98, a:1, s:1, b:1),
% 0.95/1.35 skol46 [158, 0] (w:1, o:99, a:1, s:1, b:1),
% 0.95/1.35 skol47 [159, 0] (w:1, o:100, a:1, s:1, b:1),
% 0.95/1.35 skol48 [160, 0] (w:1, o:101, a:1, s:1, b:1),
% 0.95/1.35 skol49 [161, 0] (w:1, o:102, a:1, s:1, b:1),
% 0.95/1.35 skol50 [162, 0] (w:1, o:104, a:1, s:1, b:1),
% 0.95/1.35 skol51 [163, 0] (w:1, o:105, a:1, s:1, b:1),
% 0.95/1.35 skol52 [164, 0] (w:1, o:106, a:1, s:1, b:1),
% 0.95/1.35 skol53 [165, 0] (w:1, o:107, a:1, s:1, b:1),
% 0.95/1.35 skol54 [166, 0] (w:1, o:108, a:1, s:1, b:1),
% 0.95/1.35 skol55 [167, 0] (w:1, o:109, a:1, s:1, b:1),
% 0.95/1.35 skol56 [168, 0] (w:1, o:110, a:1, s:1, b:1),
% 0.95/1.35 skol57 [169, 0] (w:1, o:111, a:1, s:1, b:1),
% 0.95/1.35 skol58 [170, 0] (w:1, o:112, a:1, s:1, b:1),
% 0.95/1.35 skol59 [171, 0] (w:1, o:113, a:1, s:1, b:1),
% 0.95/1.35 skol60 [172, 0] (w:1, o:115, a:1, s:1, b:1),
% 0.95/1.35 skol61 [173, 0] (w:1, o:116, a:1, s:1, b:1),
% 0.95/1.35 skol62 [174, 0] (w:1, o:117, a:1, s:1, b:1),
% 0.95/1.35 skol63 [175, 0] (w:1, o:118, a:1, s:1, b:1),
% 0.95/1.35 skol64 [176, 0] (w:1, o:119, a:1, s:1, b:1),
% 0.95/1.35 skol65 [177, 0] (w:1, o:120, a:1, s:1, b:1),
% 0.95/1.35 skol66 [178, 0] (w:1, o:121, a:1, s:1, b:1),
% 0.95/1.35 skol67 [179, 0] (w:1, o:122, a:1, s:1, b:1),
% 0.95/1.35 skol68 [180, 0] (w:1, o:123, a:1, s:1, b:1),
% 0.95/1.35 skol69 [181, 0] (w:1, o:124, a:1, s:1, b:1),
% 0.95/1.35 skol70 [182, 0] (w:1, o:126, a:1, s:1, b:1),
% 0.95/1.35 skol71 [183, 0] (w:1, o:127, a:1, s:1, b:1),
% 0.95/1.35 skol72 [184, 0] (w:1, o:128, a:1, s:1, b:1),
% 0.95/1.35 skol73 [185, 0] (w:1, o:129, a:1, s:1, b:1),
% 0.95/1.35 skol74 [186, 0] (w:1, o:130, a:1, s:1, b:1),
% 0.95/1.35 skol75 [187, 0] (w:1, o:131, a:1, s:1, b:1),
% 0.95/1.35 skol76 [188, 0] (w:1, o:132, a:1, s:1, b:1),
% 0.95/1.35 skol77 [189, 0] (w:1, o:133, a:1, s:1, b:1),
% 0.95/1.35 skol78 [190, 0] (w:1, o:134, a:1, s:1, b:1),
% 0.95/1.35 skol79 [191, 0] (w:1, o:135, a:1, s:1, b:1),
% 0.95/1.35 skol80 [192, 0] (w:1, o:137, a:1, s:1, b:1),
% 0.95/1.35 skol81 [193, 0] (w:1, o:138, a:1, s:1, b:1),
% 0.95/1.35 skol82 [194, 0] (w:1, o:139, a:1, s:1, b:1),
% 0.95/1.35 skol83 [195, 0] (w:1, o:140, a:1, s:1, b:1),
% 0.95/1.35 skol84 [196, 0] (w:1, o:141, a:1, s:1, b:1),
% 0.95/1.35 skol85 [197, 0] (w:1, o:142, a:1, s:1, b:1),
% 0.95/1.35 skol86 [198, 0] (w:1, o:143, a:1, s:1, b:1),
% 0.95/1.35 skol87 [199, 0] (w:1, o:144, a:1, s:1, b:1),
% 0.95/1.35 skol88 [200, 0] (w:1, o:145, a:1, s:1, b:1),
% 0.95/1.35 skol89 [201, 0] (w:1, o:146, a:1, s:1, b:1),
% 0.95/1.35 skol90 [202, 0] (w:1, o:158, a:1, s:1, b:1),
% 0.95/1.35 skol91 [203, 0] (w:1, o:159, a:1, s:1, b:1),
% 0.95/1.35 skol92 [204, 0] (w:1, o:160, a:1, s:1, b:1),
% 0.95/1.35 skol93 [205, 0] (w:1, o:161, a:1, s:1, b:1),
% 0.95/1.35 skol94 [206, 0] (w:1, o:162, a:1, s:1, b:1).
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35 Starting Search:
% 0.95/1.35
% 0.95/1.35 *** allocated 15000 integers for clauses
% 0.95/1.35 *** allocated 22500 integers for clauses
% 0.95/1.35 *** allocated 33750 integers for clauses
% 0.95/1.35 *** allocated 50625 integers for clauses
% 0.95/1.35 *** allocated 75937 integers for clauses
% 0.95/1.35 *** allocated 15000 integers for termspace/termends
% 0.95/1.35 Resimplifying inuse:
% 0.95/1.35 Done
% 0.95/1.35
% 0.95/1.35 *** allocated 113905 integers for clauses
% 0.95/1.35 *** allocated 22500 integers for termspace/termends
% 0.95/1.35 *** allocated 33750 integers for termspace/termends
% 0.95/1.35 *** allocated 170857 integers for clauses
% 0.95/1.35
% 0.95/1.35 Intermediate Status:
% 0.95/1.35 Generated: 4341
% 0.95/1.35 Kept: 2432
% 0.95/1.35 Inuse: 288
% 0.95/1.35 Deleted: 56
% 0.95/1.35 Deletedinuse: 8
% 0.95/1.35
% 0.95/1.35 Resimplifying inuse:
% 0.95/1.35 Done
% 0.95/1.35
% 0.95/1.35 *** allocated 50625 integers for termspace/termends
% 0.95/1.35 *** allocated 256285 integers for clauses
% 0.95/1.35 Resimplifying inuse:
% 0.95/1.35 Done
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35 Intermediate Status:
% 0.95/1.35 Generated: 8945
% 0.95/1.35 Kept: 4456
% 0.95/1.35 Inuse: 432
% 0.95/1.35 Deleted: 69
% 0.95/1.35 Deletedinuse: 9
% 0.95/1.35
% 0.95/1.35 Resimplifying inuse:
% 0.95/1.35 Done
% 0.95/1.35
% 0.95/1.35 *** allocated 75937 integers for termspace/termends
% 0.95/1.35 *** allocated 384427 integers for clauses
% 0.95/1.35 Resimplifying inuse:
% 0.95/1.35 Done
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35 Intermediate Status:
% 0.95/1.35 Generated: 13044
% 0.95/1.35 Kept: 6610
% 0.95/1.35 Inuse: 504
% 0.95/1.35 Deleted: 80
% 0.95/1.35 Deletedinuse: 13
% 0.95/1.35
% 0.95/1.35 Resimplifying inuse:
% 0.95/1.35 Done
% 0.95/1.35
% 0.95/1.35 *** allocated 113905 integers for termspace/termends
% 0.95/1.35 Resimplifying inuse:
% 0.95/1.35 Done
% 0.95/1.35
% 0.95/1.35 *** allocated 576640 integers for clauses
% 0.95/1.35
% 0.95/1.35 Intermediate Status:
% 0.95/1.35 Generated: 16206
% 0.95/1.35 Kept: 8662
% 0.95/1.35 Inuse: 549
% 0.95/1.35 Deleted: 80
% 0.95/1.35 Deletedinuse: 13
% 0.95/1.35
% 0.95/1.35 Resimplifying inuse:
% 0.95/1.35 Done
% 0.95/1.35
% 0.95/1.35 Resimplifying inuse:
% 0.95/1.35 Done
% 0.95/1.35
% 0.95/1.35 *** allocated 170857 integers for termspace/termends
% 0.95/1.35
% 0.95/1.35 Intermediate Status:
% 0.95/1.35 Generated: 19379
% 0.95/1.35 Kept: 10675
% 0.95/1.35 Inuse: 607
% 0.95/1.35 Deleted: 84
% 0.95/1.35 Deletedinuse: 13
% 0.95/1.35
% 0.95/1.35 Resimplifying inuse:
% 0.95/1.35
% 0.95/1.35 Bliksems!, er is een bewijs:
% 0.95/1.35 % SZS status Theorem
% 0.95/1.35 % SZS output start Refutation
% 0.95/1.35
% 0.95/1.35 (0) {G0,W5,D2,L3,V1,M3} I { ! modus_ponens, ! alpha1( X ), is_a_theorem( X
% 0.95/1.35 ) }.
% 0.95/1.35 (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem( implies( Y
% 0.95/1.35 , X ) ), alpha1( X ) }.
% 0.95/1.35 (11) {G0,W7,D4,L2,V2,M2} I { ! implies_1, is_a_theorem( implies( X, implies
% 0.95/1.35 ( Y, X ) ) ) }.
% 0.95/1.35 (65) {G0,W1,D1,L1,V0,M1} I { modus_ponens }.
% 0.95/1.35 (67) {G0,W1,D1,L1,V0,M1} I { implies_1 }.
% 0.95/1.35 (84) {G0,W3,D2,L2,V0,M2} I { alpha2( skol29 ), modus_ponens_strict_implies
% 0.95/1.35 }.
% 0.95/1.35 (85) {G0,W3,D2,L2,V0,M2} I { ! is_a_theorem( skol29 ),
% 0.95/1.35 modus_ponens_strict_implies }.
% 0.95/1.35 (86) {G0,W5,D3,L2,V2,M2} I { ! alpha2( X ), is_a_theorem( skol30( Y ) ) }.
% 0.95/1.35 (87) {G0,W7,D4,L2,V1,M2} I { ! alpha2( X ), is_a_theorem( strict_implies(
% 0.95/1.35 skol30( X ), X ) ) }.
% 0.95/1.35 (92) {G0,W5,D2,L2,V2,M2} I { ! alpha3( X, Y ), is_a_theorem( X ) }.
% 0.95/1.35 (93) {G0,W5,D2,L2,V2,M2} I { ! alpha3( X, Y ), is_a_theorem( Y ) }.
% 0.95/1.35 (94) {G0,W7,D2,L3,V2,M3} I { ! is_a_theorem( X ), ! is_a_theorem( Y ),
% 0.95/1.35 alpha3( X, Y ) }.
% 0.95/1.35 (100) {G0,W6,D4,L2,V1,M2} I { ! axiom_M, is_a_theorem( implies( necessarily
% 0.95/1.35 ( X ), X ) ) }.
% 0.95/1.35 (138) {G0,W9,D4,L2,V2,M2} I { ! op_strict_implies, necessarily( implies( X
% 0.95/1.35 , Y ) ) ==> strict_implies( X, Y ) }.
% 0.95/1.35 (143) {G0,W1,D1,L1,V0,M1} I { axiom_M }.
% 0.95/1.35 (147) {G0,W1,D1,L1,V0,M1} I { op_strict_implies }.
% 0.95/1.35 (149) {G0,W1,D1,L1,V0,M1} I { ! modus_ponens_strict_implies }.
% 0.95/1.35 (151) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ), is_a_theorem( X ) }.
% 0.95/1.35 (156) {G1,W2,D2,L1,V0,M1} S(85);r(149) { ! is_a_theorem( skol29 ) }.
% 0.95/1.35 (158) {G1,W2,D2,L1,V0,M1} S(84);r(149) { alpha2( skol29 ) }.
% 0.95/1.35 (159) {G2,W2,D2,L1,V0,M1} R(151,156) { ! alpha1( skol29 ) }.
% 0.95/1.35 (163) {G3,W6,D3,L2,V1,M2} R(159,5) { ! is_a_theorem( X ), ! is_a_theorem(
% 0.95/1.35 implies( X, skol29 ) ) }.
% 0.95/1.35 (183) {G1,W6,D4,L1,V2,M1} S(11);r(67) { is_a_theorem( implies( X, implies(
% 0.95/1.35 Y, X ) ) ) }.
% 0.95/1.35 (185) {G2,W3,D3,L1,V1,M1} R(86,158) { is_a_theorem( skol30( X ) ) }.
% 0.95/1.35 (199) {G4,W7,D3,L2,V2,M2} R(163,92) { ! is_a_theorem( implies( X, skol29 )
% 0.95/1.35 ), ! alpha3( X, Y ) }.
% 0.95/1.35 (761) {G2,W6,D3,L2,V2,M2} R(183,5) { ! is_a_theorem( X ), alpha1( implies(
% 0.95/1.35 Y, X ) ) }.
% 0.95/1.35 (812) {G3,W6,D3,L2,V2,M2} R(761,151) { ! is_a_theorem( X ), is_a_theorem(
% 0.95/1.35 implies( Y, X ) ) }.
% 0.95/1.35 (947) {G4,W6,D2,L3,V2,M3} R(812,5) { ! is_a_theorem( X ), ! is_a_theorem( Y
% 0.95/1.35 ), alpha1( X ) }.
% 0.95/1.35 (948) {G5,W4,D2,L2,V1,M2} F(947) { ! is_a_theorem( X ), alpha1( X ) }.
% 0.95/1.35 (970) {G6,W5,D2,L2,V2,M2} R(948,93) { alpha1( X ), ! alpha3( Y, X ) }.
% 0.95/1.35 (1409) {G2,W5,D4,L1,V0,M1} R(87,158) { is_a_theorem( strict_implies( skol30
% 0.95/1.35 ( skol29 ), skol29 ) ) }.
% 0.95/1.35 (1412) {G6,W5,D4,L1,V0,M1} R(1409,948) { alpha1( strict_implies( skol30(
% 0.95/1.35 skol29 ), skol29 ) ) }.
% 0.95/1.35 (1850) {G3,W6,D3,L2,V2,M2} R(94,185) { ! is_a_theorem( X ), alpha3( skol30
% 0.95/1.35 ( Y ), X ) }.
% 0.95/1.35 (2550) {G1,W5,D4,L1,V1,M1} S(100);r(143) { is_a_theorem( implies(
% 0.95/1.35 necessarily( X ), X ) ) }.
% 0.95/1.35 (2580) {G2,W5,D3,L2,V1,M2} R(2550,5) { ! is_a_theorem( necessarily( X ) ),
% 0.95/1.35 alpha1( X ) }.
% 0.95/1.35 (2653) {G3,W5,D3,L2,V1,M2} R(2580,151) { alpha1( X ), ! alpha1( necessarily
% 0.95/1.35 ( X ) ) }.
% 0.95/1.35 (2832) {G4,W5,D3,L2,V1,M2} R(2653,151) { ! alpha1( necessarily( X ) ),
% 0.95/1.35 is_a_theorem( X ) }.
% 0.95/1.35 (2848) {G7,W6,D3,L2,V2,M2} R(2832,970) { is_a_theorem( X ), ! alpha3( Y,
% 0.95/1.35 necessarily( X ) ) }.
% 0.95/1.35 (4529) {G4,W6,D3,L2,V2,M2} R(1850,151) { alpha3( skol30( X ), Y ), ! alpha1
% 0.95/1.35 ( Y ) }.
% 0.95/1.35 (5026) {G1,W8,D4,L1,V2,M1} S(138);r(147) { necessarily( implies( X, Y ) )
% 0.95/1.35 ==> strict_implies( X, Y ) }.
% 0.95/1.35 (10713) {G8,W8,D3,L2,V3,M2} R(199,2848);d(5026) { ! alpha3( X, Y ), !
% 0.95/1.35 alpha3( Z, strict_implies( X, skol29 ) ) }.
% 0.95/1.35 (10730) {G9,W5,D3,L1,V1,M1} F(10713) { ! alpha3( X, strict_implies( X,
% 0.95/1.35 skol29 ) ) }.
% 0.95/1.35 (10731) {G10,W5,D4,L1,V1,M1} R(10730,4529) { ! alpha1( strict_implies(
% 0.95/1.35 skol30( X ), skol29 ) ) }.
% 0.95/1.35 (10799) {G11,W0,D0,L0,V0,M0} S(1412);r(10731) { }.
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35 % SZS output end Refutation
% 0.95/1.35 found a proof!
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35 Unprocessed initial clauses:
% 0.95/1.35
% 0.95/1.35 (10801) {G0,W5,D2,L3,V1,M3} { ! modus_ponens, ! alpha1( X ), is_a_theorem
% 0.95/1.35 ( X ) }.
% 0.95/1.35 (10802) {G0,W3,D2,L2,V0,M2} { alpha1( skol1 ), modus_ponens }.
% 0.95/1.35 (10803) {G0,W3,D2,L2,V0,M2} { ! is_a_theorem( skol1 ), modus_ponens }.
% 0.95/1.35 (10804) {G0,W5,D3,L2,V2,M2} { ! alpha1( X ), is_a_theorem( skol2( Y ) )
% 0.95/1.35 }.
% 0.95/1.35 (10805) {G0,W7,D4,L2,V1,M2} { ! alpha1( X ), is_a_theorem( implies( skol2
% 0.95/1.35 ( X ), X ) ) }.
% 0.95/1.35 (10806) {G0,W8,D3,L3,V2,M3} { ! is_a_theorem( Y ), ! is_a_theorem( implies
% 0.95/1.35 ( Y, X ) ), alpha1( X ) }.
% 0.95/1.35 (10807) {G0,W8,D3,L3,V2,M3} { ! substitution_of_equivalents, !
% 0.95/1.35 is_a_theorem( equiv( X, Y ) ), X = Y }.
% 0.95/1.35 (10808) {G0,W5,D3,L2,V0,M2} { is_a_theorem( equiv( skol3, skol52 ) ),
% 0.95/1.35 substitution_of_equivalents }.
% 0.95/1.35 (10809) {G0,W4,D2,L2,V0,M2} { ! skol3 = skol52,
% 0.95/1.35 substitution_of_equivalents }.
% 0.95/1.35 (10810) {G0,W11,D5,L2,V2,M2} { ! modus_tollens, is_a_theorem( implies(
% 0.95/1.35 implies( not( Y ), not( X ) ), implies( X, Y ) ) ) }.
% 0.95/1.35 (10811) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( not(
% 0.95/1.35 skol53 ), not( skol4 ) ), implies( skol4, skol53 ) ) ), modus_tollens }.
% 0.95/1.35 (10812) {G0,W7,D4,L2,V2,M2} { ! implies_1, is_a_theorem( implies( X,
% 0.95/1.35 implies( Y, X ) ) ) }.
% 0.95/1.35 (10813) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol5, implies(
% 0.95/1.35 skol54, skol5 ) ) ), implies_1 }.
% 0.95/1.35 (10814) {G0,W11,D5,L2,V2,M2} { ! implies_2, is_a_theorem( implies( implies
% 0.95/1.35 ( X, implies( X, Y ) ), implies( X, Y ) ) ) }.
% 0.95/1.35 (10815) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol6,
% 0.95/1.35 implies( skol6, skol55 ) ), implies( skol6, skol55 ) ) ), implies_2 }.
% 0.95/1.35 (10816) {G0,W13,D5,L2,V3,M2} { ! implies_3, is_a_theorem( implies( implies
% 0.95/1.35 ( X, Y ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 0.95/1.35 (10817) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol7,
% 0.95/1.35 skol56 ), implies( implies( skol56, skol86 ), implies( skol7, skol86 ) )
% 0.95/1.35 ) ), implies_3 }.
% 0.95/1.35 (10818) {G0,W7,D4,L2,V2,M2} { ! and_1, is_a_theorem( implies( and( X, Y )
% 0.95/1.35 , X ) ) }.
% 0.95/1.35 (10819) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol8, skol57
% 0.95/1.35 ), skol8 ) ), and_1 }.
% 0.95/1.35 (10820) {G0,W7,D4,L2,V2,M2} { ! and_2, is_a_theorem( implies( and( X, Y )
% 0.95/1.35 , Y ) ) }.
% 0.95/1.35 (10821) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol9, skol58
% 0.95/1.35 ), skol58 ) ), and_2 }.
% 0.95/1.35 (10822) {G0,W9,D5,L2,V2,M2} { ! and_3, is_a_theorem( implies( X, implies(
% 0.95/1.35 Y, and( X, Y ) ) ) ) }.
% 0.95/1.35 (10823) {G0,W9,D5,L2,V0,M2} { ! is_a_theorem( implies( skol10, implies(
% 0.95/1.35 skol59, and( skol10, skol59 ) ) ) ), and_3 }.
% 0.95/1.35 (10824) {G0,W7,D4,L2,V2,M2} { ! or_1, is_a_theorem( implies( X, or( X, Y )
% 0.95/1.35 ) ) }.
% 0.95/1.35 (10825) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol11, or( skol11
% 0.95/1.35 , skol60 ) ) ), or_1 }.
% 0.95/1.35 (10826) {G0,W7,D4,L2,V2,M2} { ! or_2, is_a_theorem( implies( Y, or( X, Y )
% 0.95/1.35 ) ) }.
% 0.95/1.35 (10827) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol61, or( skol12
% 0.95/1.35 , skol61 ) ) ), or_2 }.
% 0.95/1.35 (10828) {G0,W15,D6,L2,V3,M2} { ! or_3, is_a_theorem( implies( implies( X,
% 0.95/1.35 Z ), implies( implies( Y, Z ), implies( or( X, Y ), Z ) ) ) ) }.
% 0.95/1.35 (10829) {G0,W15,D6,L2,V0,M2} { ! is_a_theorem( implies( implies( skol13,
% 0.95/1.35 skol87 ), implies( implies( skol62, skol87 ), implies( or( skol13, skol62
% 0.95/1.35 ), skol87 ) ) ) ), or_3 }.
% 0.95/1.35 (10830) {G0,W9,D4,L2,V2,M2} { ! equivalence_1, is_a_theorem( implies(
% 0.95/1.35 equiv( X, Y ), implies( X, Y ) ) ) }.
% 0.95/1.35 (10831) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( equiv( skol14,
% 0.95/1.35 skol63 ), implies( skol14, skol63 ) ) ), equivalence_1 }.
% 0.95/1.35 (10832) {G0,W9,D4,L2,V2,M2} { ! equivalence_2, is_a_theorem( implies(
% 0.95/1.35 equiv( X, Y ), implies( Y, X ) ) ) }.
% 0.95/1.35 (10833) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( equiv( skol15,
% 0.95/1.35 skol64 ), implies( skol64, skol15 ) ) ), equivalence_2 }.
% 0.95/1.35 (10834) {G0,W13,D5,L2,V2,M2} { ! equivalence_3, is_a_theorem( implies(
% 0.95/1.35 implies( X, Y ), implies( implies( Y, X ), equiv( X, Y ) ) ) ) }.
% 0.95/1.35 (10835) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol16,
% 0.95/1.35 skol65 ), implies( implies( skol65, skol16 ), equiv( skol16, skol65 ) ) )
% 0.95/1.35 ), equivalence_3 }.
% 0.95/1.35 (10836) {G0,W7,D4,L2,V1,M2} { ! kn1, is_a_theorem( implies( X, and( X, X )
% 0.95/1.35 ) ) }.
% 0.95/1.35 (10837) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol17, and( skol17
% 0.95/1.35 , skol17 ) ) ), kn1 }.
% 0.95/1.35 (10838) {G0,W7,D4,L2,V2,M2} { ! kn2, is_a_theorem( implies( and( X, Y ), X
% 0.95/1.35 ) ) }.
% 0.95/1.35 (10839) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol18, skol66
% 0.95/1.35 ), skol18 ) ), kn2 }.
% 0.95/1.35 (10840) {G0,W15,D6,L2,V3,M2} { ! kn3, is_a_theorem( implies( implies( X, Y
% 0.95/1.35 ), implies( not( and( Y, Z ) ), not( and( Z, X ) ) ) ) ) }.
% 0.95/1.35 (10841) {G0,W15,D6,L2,V0,M2} { ! is_a_theorem( implies( implies( skol19,
% 0.95/1.35 skol67 ), implies( not( and( skol67, skol88 ) ), not( and( skol88, skol19
% 0.95/1.35 ) ) ) ) ), kn3 }.
% 0.95/1.35 (10842) {G0,W13,D5,L2,V3,M2} { ! cn1, is_a_theorem( implies( implies( X, Y
% 0.95/1.35 ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 0.95/1.35 (10843) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol20,
% 0.95/1.35 skol68 ), implies( implies( skol68, skol89 ), implies( skol20, skol89 ) )
% 0.95/1.35 ) ), cn1 }.
% 0.95/1.35 (10844) {G0,W8,D5,L2,V2,M2} { ! cn2, is_a_theorem( implies( X, implies(
% 0.95/1.35 not( X ), Y ) ) ) }.
% 0.95/1.35 (10845) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( skol21, implies(
% 0.95/1.35 not( skol21 ), skol69 ) ) ), cn2 }.
% 0.95/1.35 (10846) {G0,W8,D5,L2,V1,M2} { ! cn3, is_a_theorem( implies( implies( not(
% 0.95/1.35 X ), X ), X ) ) }.
% 0.95/1.35 (10847) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( not(
% 0.95/1.35 skol22 ), skol22 ), skol22 ) ), cn3 }.
% 0.95/1.35 (10848) {G0,W7,D4,L2,V1,M2} { ! r1, is_a_theorem( implies( or( X, X ), X )
% 0.95/1.35 ) }.
% 0.95/1.35 (10849) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( or( skol23, skol23
% 0.95/1.35 ), skol23 ) ), r1 }.
% 0.95/1.35 (10850) {G0,W7,D4,L2,V2,M2} { ! r2, is_a_theorem( implies( Y, or( X, Y ) )
% 0.95/1.35 ) }.
% 0.95/1.35 (10851) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol70, or( skol24
% 0.95/1.35 , skol70 ) ) ), r2 }.
% 0.95/1.35 (10852) {G0,W9,D4,L2,V2,M2} { ! r3, is_a_theorem( implies( or( X, Y ), or
% 0.95/1.35 ( Y, X ) ) ) }.
% 0.95/1.35 (10853) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( or( skol25, skol71
% 0.95/1.35 ), or( skol71, skol25 ) ) ), r3 }.
% 0.95/1.35 (10854) {G0,W13,D5,L2,V3,M2} { ! r4, is_a_theorem( implies( or( X, or( Y,
% 0.95/1.35 Z ) ), or( Y, or( X, Z ) ) ) ) }.
% 0.95/1.35 (10855) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( or( skol26, or(
% 0.95/1.35 skol72, skol90 ) ), or( skol72, or( skol26, skol90 ) ) ) ), r4 }.
% 0.95/1.35 (10856) {G0,W13,D5,L2,V3,M2} { ! r5, is_a_theorem( implies( implies( Y, Z
% 0.95/1.35 ), implies( or( X, Y ), or( X, Z ) ) ) ) }.
% 0.95/1.35 (10857) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol73,
% 0.95/1.35 skol91 ), implies( or( skol27, skol73 ), or( skol27, skol91 ) ) ) ), r5
% 0.95/1.35 }.
% 0.95/1.35 (10858) {G0,W11,D5,L2,V2,M2} { ! op_or, or( X, Y ) = not( and( not( X ),
% 0.95/1.35 not( Y ) ) ) }.
% 0.95/1.35 (10859) {G0,W11,D5,L2,V2,M2} { ! op_and, and( X, Y ) = not( or( not( X ),
% 0.95/1.35 not( Y ) ) ) }.
% 0.95/1.35 (10860) {G0,W10,D5,L2,V2,M2} { ! op_implies_and, implies( X, Y ) = not(
% 0.95/1.35 and( X, not( Y ) ) ) }.
% 0.95/1.35 (10861) {G0,W9,D4,L2,V2,M2} { ! op_implies_or, implies( X, Y ) = or( not(
% 0.95/1.35 X ), Y ) }.
% 0.95/1.35 (10862) {G0,W12,D4,L2,V2,M2} { ! op_equiv, equiv( X, Y ) = and( implies( X
% 0.95/1.35 , Y ), implies( Y, X ) ) }.
% 0.95/1.35 (10863) {G0,W1,D1,L1,V0,M1} { op_or }.
% 0.95/1.35 (10864) {G0,W1,D1,L1,V0,M1} { op_implies_and }.
% 0.95/1.35 (10865) {G0,W1,D1,L1,V0,M1} { op_equiv }.
% 0.95/1.35 (10866) {G0,W1,D1,L1,V0,M1} { modus_ponens }.
% 0.95/1.35 (10867) {G0,W1,D1,L1,V0,M1} { modus_tollens }.
% 0.95/1.35 (10868) {G0,W1,D1,L1,V0,M1} { implies_1 }.
% 0.95/1.35 (10869) {G0,W1,D1,L1,V0,M1} { implies_2 }.
% 0.95/1.35 (10870) {G0,W1,D1,L1,V0,M1} { implies_3 }.
% 0.95/1.35 (10871) {G0,W1,D1,L1,V0,M1} { and_1 }.
% 0.95/1.35 (10872) {G0,W1,D1,L1,V0,M1} { and_2 }.
% 0.95/1.35 (10873) {G0,W1,D1,L1,V0,M1} { and_3 }.
% 0.95/1.35 (10874) {G0,W1,D1,L1,V0,M1} { or_1 }.
% 0.95/1.35 (10875) {G0,W1,D1,L1,V0,M1} { or_2 }.
% 0.95/1.35 (10876) {G0,W1,D1,L1,V0,M1} { or_3 }.
% 0.95/1.35 (10877) {G0,W1,D1,L1,V0,M1} { equivalence_1 }.
% 0.95/1.35 (10878) {G0,W1,D1,L1,V0,M1} { equivalence_2 }.
% 0.95/1.35 (10879) {G0,W1,D1,L1,V0,M1} { equivalence_3 }.
% 0.95/1.35 (10880) {G0,W1,D1,L1,V0,M1} { substitution_of_equivalents }.
% 0.95/1.35 (10881) {G0,W6,D3,L3,V1,M3} { ! necessitation, ! is_a_theorem( X ),
% 0.95/1.35 is_a_theorem( necessarily( X ) ) }.
% 0.95/1.35 (10882) {G0,W3,D2,L2,V0,M2} { is_a_theorem( skol28 ), necessitation }.
% 0.95/1.35 (10883) {G0,W4,D3,L2,V0,M2} { ! is_a_theorem( necessarily( skol28 ) ),
% 0.95/1.35 necessitation }.
% 0.95/1.35 (10884) {G0,W5,D2,L3,V1,M3} { ! modus_ponens_strict_implies, ! alpha2( X )
% 0.95/1.35 , is_a_theorem( X ) }.
% 0.95/1.35 (10885) {G0,W3,D2,L2,V0,M2} { alpha2( skol29 ),
% 0.95/1.35 modus_ponens_strict_implies }.
% 0.95/1.35 (10886) {G0,W3,D2,L2,V0,M2} { ! is_a_theorem( skol29 ),
% 0.95/1.35 modus_ponens_strict_implies }.
% 0.95/1.35 (10887) {G0,W5,D3,L2,V2,M2} { ! alpha2( X ), is_a_theorem( skol30( Y ) )
% 0.95/1.35 }.
% 0.95/1.35 (10888) {G0,W7,D4,L2,V1,M2} { ! alpha2( X ), is_a_theorem( strict_implies
% 0.95/1.35 ( skol30( X ), X ) ) }.
% 0.95/1.35 (10889) {G0,W8,D3,L3,V2,M3} { ! is_a_theorem( Y ), ! is_a_theorem(
% 0.95/1.35 strict_implies( Y, X ) ), alpha2( X ) }.
% 0.95/1.35 (10890) {G0,W8,D3,L3,V2,M3} { ! adjunction, ! alpha3( X, Y ), is_a_theorem
% 0.95/1.35 ( and( X, Y ) ) }.
% 0.95/1.35 (10891) {G0,W4,D2,L2,V0,M2} { alpha3( skol31, skol74 ), adjunction }.
% 0.95/1.35 (10892) {G0,W5,D3,L2,V0,M2} { ! is_a_theorem( and( skol31, skol74 ) ),
% 0.95/1.35 adjunction }.
% 0.95/1.35 (10893) {G0,W5,D2,L2,V2,M2} { ! alpha3( X, Y ), is_a_theorem( X ) }.
% 0.95/1.35 (10894) {G0,W5,D2,L2,V2,M2} { ! alpha3( X, Y ), is_a_theorem( Y ) }.
% 0.95/1.35 (10895) {G0,W7,D2,L3,V2,M3} { ! is_a_theorem( X ), ! is_a_theorem( Y ),
% 0.95/1.35 alpha3( X, Y ) }.
% 0.95/1.35 (10896) {G0,W8,D3,L3,V2,M3} { ! substitution_strict_equiv, ! is_a_theorem
% 0.95/1.35 ( strict_equiv( X, Y ) ), X = Y }.
% 0.95/1.35 (10897) {G0,W5,D3,L2,V0,M2} { is_a_theorem( strict_equiv( skol32, skol75 )
% 0.95/1.35 ), substitution_strict_equiv }.
% 0.95/1.35 (10898) {G0,W4,D2,L2,V0,M2} { ! skol32 = skol75, substitution_strict_equiv
% 0.95/1.35 }.
% 0.95/1.35 (10899) {G0,W12,D5,L2,V2,M2} { ! axiom_K, is_a_theorem( implies(
% 0.95/1.35 necessarily( implies( X, Y ) ), implies( necessarily( X ), necessarily( Y
% 0.95/1.35 ) ) ) ) }.
% 0.95/1.35 (10900) {G0,W12,D5,L2,V0,M2} { ! is_a_theorem( implies( necessarily(
% 0.95/1.35 implies( skol33, skol76 ) ), implies( necessarily( skol33 ), necessarily
% 0.95/1.35 ( skol76 ) ) ) ), axiom_K }.
% 0.95/1.35 (10901) {G0,W6,D4,L2,V1,M2} { ! axiom_M, is_a_theorem( implies(
% 0.95/1.35 necessarily( X ), X ) ) }.
% 0.95/1.35 (10902) {G0,W6,D4,L2,V0,M2} { ! is_a_theorem( implies( necessarily( skol34
% 0.95/1.35 ), skol34 ) ), axiom_M }.
% 0.95/1.35 (10903) {G0,W8,D5,L2,V1,M2} { ! axiom_4, is_a_theorem( implies(
% 0.95/1.35 necessarily( X ), necessarily( necessarily( X ) ) ) ) }.
% 0.95/1.35 (10904) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( necessarily( skol35
% 0.95/1.35 ), necessarily( necessarily( skol35 ) ) ) ), axiom_4 }.
% 0.95/1.35 (10905) {G0,W7,D5,L2,V1,M2} { ! axiom_B, is_a_theorem( implies( X,
% 0.95/1.35 necessarily( possibly( X ) ) ) ) }.
% 0.95/1.35 (10906) {G0,W7,D5,L2,V0,M2} { ! is_a_theorem( implies( skol36, necessarily
% 0.95/1.35 ( possibly( skol36 ) ) ) ), axiom_B }.
% 0.95/1.35 (10907) {G0,W8,D5,L2,V1,M2} { ! axiom_5, is_a_theorem( implies( possibly(
% 0.95/1.35 X ), necessarily( possibly( X ) ) ) ) }.
% 0.95/1.35 (10908) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( possibly( skol37 )
% 0.95/1.35 , necessarily( possibly( skol37 ) ) ) ), axiom_5 }.
% 0.95/1.35 (10909) {G0,W16,D6,L2,V3,M2} { ! axiom_s1, is_a_theorem( implies( and(
% 0.95/1.35 necessarily( implies( X, Y ) ), necessarily( implies( Y, Z ) ) ),
% 0.95/1.35 necessarily( implies( X, Z ) ) ) ) }.
% 0.95/1.35 (10910) {G0,W16,D6,L2,V0,M2} { ! is_a_theorem( implies( and( necessarily(
% 0.95/1.35 implies( skol38, skol77 ) ), necessarily( implies( skol77, skol92 ) ) ),
% 0.95/1.35 necessarily( implies( skol38, skol92 ) ) ) ), axiom_s1 }.
% 0.95/1.35 (10911) {G0,W12,D5,L2,V2,M2} { ! axiom_s2, is_a_theorem( strict_implies(
% 0.95/1.35 possibly( and( X, Y ) ), and( possibly( X ), possibly( Y ) ) ) ) }.
% 0.95/1.35 (10912) {G0,W12,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( possibly(
% 0.95/1.35 and( skol39, skol78 ) ), and( possibly( skol39 ), possibly( skol78 ) ) )
% 0.95/1.35 ), axiom_s2 }.
% 0.95/1.35 (10913) {G0,W13,D6,L2,V2,M2} { ! axiom_s3, is_a_theorem( strict_implies(
% 0.95/1.35 strict_implies( X, Y ), strict_implies( not( possibly( Y ) ), not(
% 0.95/1.35 possibly( X ) ) ) ) ) }.
% 0.95/1.35 (10914) {G0,W13,D6,L2,V0,M2} { ! is_a_theorem( strict_implies(
% 0.95/1.35 strict_implies( skol40, skol79 ), strict_implies( not( possibly( skol79 )
% 0.95/1.35 ), not( possibly( skol40 ) ) ) ) ), axiom_s3 }.
% 0.95/1.35 (10915) {G0,W8,D5,L2,V1,M2} { ! axiom_s4, is_a_theorem( strict_implies(
% 0.95/1.35 necessarily( X ), necessarily( necessarily( X ) ) ) ) }.
% 0.95/1.35 (10916) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( necessarily
% 0.95/1.35 ( skol41 ), necessarily( necessarily( skol41 ) ) ) ), axiom_s4 }.
% 0.95/1.35 (10917) {G0,W9,D4,L2,V2,M2} { ! axiom_m1, is_a_theorem( strict_implies(
% 0.95/1.35 and( X, Y ), and( Y, X ) ) ) }.
% 0.95/1.35 (10918) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( and( skol42
% 0.95/1.35 , skol80 ), and( skol80, skol42 ) ) ), axiom_m1 }.
% 0.95/1.35 (10919) {G0,W7,D4,L2,V2,M2} { ! axiom_m2, is_a_theorem( strict_implies(
% 0.95/1.35 and( X, Y ), X ) ) }.
% 0.95/1.35 (10920) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( and( skol43
% 0.95/1.35 , skol81 ), skol43 ) ), axiom_m2 }.
% 0.95/1.35 (10921) {G0,W13,D5,L2,V3,M2} { ! axiom_m3, is_a_theorem( strict_implies(
% 0.95/1.35 and( and( X, Y ), Z ), and( X, and( Y, Z ) ) ) ) }.
% 0.95/1.35 (10922) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( and( and(
% 0.95/1.35 skol44, skol82 ), skol93 ), and( skol44, and( skol82, skol93 ) ) ) ),
% 0.95/1.35 axiom_m3 }.
% 0.95/1.35 (10923) {G0,W7,D4,L2,V1,M2} { ! axiom_m4, is_a_theorem( strict_implies( X
% 0.95/1.35 , and( X, X ) ) ) }.
% 0.95/1.35 (10924) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( skol45, and
% 0.95/1.35 ( skol45, skol45 ) ) ), axiom_m4 }.
% 0.95/1.35 (10925) {G0,W13,D5,L2,V3,M2} { ! axiom_m5, is_a_theorem( strict_implies(
% 0.95/1.35 and( strict_implies( X, Y ), strict_implies( Y, Z ) ), strict_implies( X
% 0.95/1.35 , Z ) ) ) }.
% 0.95/1.35 (10926) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( and(
% 0.95/1.35 strict_implies( skol46, skol83 ), strict_implies( skol83, skol94 ) ),
% 0.95/1.35 strict_implies( skol46, skol94 ) ) ), axiom_m5 }.
% 0.95/1.35 (10927) {G0,W6,D4,L2,V1,M2} { ! axiom_m6, is_a_theorem( strict_implies( X
% 0.95/1.35 , possibly( X ) ) ) }.
% 0.95/1.35 (10928) {G0,W6,D4,L2,V0,M2} { ! is_a_theorem( strict_implies( skol47,
% 0.95/1.35 possibly( skol47 ) ) ), axiom_m6 }.
% 0.95/1.35 (10929) {G0,W8,D5,L2,V2,M2} { ! axiom_m7, is_a_theorem( strict_implies(
% 0.95/1.35 possibly( and( X, Y ) ), X ) ) }.
% 0.95/1.35 (10930) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( possibly(
% 0.95/1.35 and( skol48, skol84 ) ), skol48 ) ), axiom_m7 }.
% 0.95/1.35 (10931) {G0,W11,D5,L2,V2,M2} { ! axiom_m8, is_a_theorem( strict_implies(
% 0.95/1.35 strict_implies( X, Y ), strict_implies( possibly( X ), possibly( Y ) ) )
% 0.95/1.35 ) }.
% 0.95/1.35 (10932) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( strict_implies(
% 0.95/1.35 strict_implies( skol49, skol85 ), strict_implies( possibly( skol49 ),
% 0.95/1.35 possibly( skol85 ) ) ) ), axiom_m8 }.
% 0.95/1.35 (10933) {G0,W8,D5,L2,V1,M2} { ! axiom_m9, is_a_theorem( strict_implies(
% 0.95/1.35 possibly( possibly( X ) ), possibly( X ) ) ) }.
% 0.95/1.35 (10934) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( possibly(
% 0.95/1.35 possibly( skol50 ) ), possibly( skol50 ) ) ), axiom_m9 }.
% 0.95/1.35 (10935) {G0,W8,D5,L2,V1,M2} { ! axiom_m10, is_a_theorem( strict_implies(
% 0.95/1.35 possibly( X ), necessarily( possibly( X ) ) ) ) }.
% 0.95/1.35 (10936) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( strict_implies( possibly(
% 0.95/1.35 skol51 ), necessarily( possibly( skol51 ) ) ) ), axiom_m10 }.
% 0.95/1.35 (10937) {G0,W8,D5,L2,V1,M2} { ! op_possibly, possibly( X ) = not(
% 0.95/1.35 necessarily( not( X ) ) ) }.
% 0.95/1.35 (10938) {G0,W8,D5,L2,V1,M2} { ! op_necessarily, necessarily( X ) = not(
% 0.95/1.35 possibly( not( X ) ) ) }.
% 0.95/1.35 (10939) {G0,W9,D4,L2,V2,M2} { ! op_strict_implies, strict_implies( X, Y )
% 0.95/1.35 = necessarily( implies( X, Y ) ) }.
% 0.95/1.35 (10940) {G0,W12,D4,L2,V2,M2} { ! op_strict_equiv, strict_equiv( X, Y ) =
% 0.95/1.35 and( strict_implies( X, Y ), strict_implies( Y, X ) ) }.
% 0.95/1.35 (10941) {G0,W1,D1,L1,V0,M1} { op_possibly }.
% 0.95/1.35 (10942) {G0,W1,D1,L1,V0,M1} { necessitation }.
% 0.95/1.35 (10943) {G0,W1,D1,L1,V0,M1} { axiom_K }.
% 0.95/1.35 (10944) {G0,W1,D1,L1,V0,M1} { axiom_M }.
% 0.95/1.35 (10945) {G0,W1,D1,L1,V0,M1} { axiom_4 }.
% 0.95/1.35 (10946) {G0,W1,D1,L1,V0,M1} { axiom_B }.
% 0.95/1.35 (10947) {G0,W1,D1,L1,V0,M1} { op_possibly }.
% 0.95/1.35 (10948) {G0,W1,D1,L1,V0,M1} { op_or }.
% 0.95/1.35 (10949) {G0,W1,D1,L1,V0,M1} { op_implies }.
% 0.95/1.35 (10950) {G0,W1,D1,L1,V0,M1} { op_strict_implies }.
% 0.95/1.35 (10951) {G0,W1,D1,L1,V0,M1} { op_equiv }.
% 0.95/1.35 (10952) {G0,W1,D1,L1,V0,M1} { op_strict_equiv }.
% 0.95/1.35 (10953) {G0,W1,D1,L1,V0,M1} { ! modus_ponens_strict_implies }.
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35 Total Proof:
% 0.95/1.35
% 0.95/1.35 subsumption: (0) {G0,W5,D2,L3,V1,M3} I { ! modus_ponens, ! alpha1( X ),
% 0.95/1.35 is_a_theorem( X ) }.
% 0.95/1.35 parent0: (10801) {G0,W5,D2,L3,V1,M3} { ! modus_ponens, ! alpha1( X ),
% 0.95/1.35 is_a_theorem( X ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 2 ==> 2
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), !
% 0.95/1.35 is_a_theorem( implies( Y, X ) ), alpha1( X ) }.
% 0.95/1.35 parent0: (10806) {G0,W8,D3,L3,V2,M3} { ! is_a_theorem( Y ), ! is_a_theorem
% 0.95/1.35 ( implies( Y, X ) ), alpha1( X ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 2 ==> 2
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (11) {G0,W7,D4,L2,V2,M2} I { ! implies_1, is_a_theorem(
% 0.95/1.35 implies( X, implies( Y, X ) ) ) }.
% 0.95/1.35 parent0: (10812) {G0,W7,D4,L2,V2,M2} { ! implies_1, is_a_theorem( implies
% 0.95/1.35 ( X, implies( Y, X ) ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (65) {G0,W1,D1,L1,V0,M1} I { modus_ponens }.
% 0.95/1.35 parent0: (10866) {G0,W1,D1,L1,V0,M1} { modus_ponens }.
% 0.95/1.35 substitution0:
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (67) {G0,W1,D1,L1,V0,M1} I { implies_1 }.
% 0.95/1.35 parent0: (10868) {G0,W1,D1,L1,V0,M1} { implies_1 }.
% 0.95/1.35 substitution0:
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (84) {G0,W3,D2,L2,V0,M2} I { alpha2( skol29 ),
% 0.95/1.35 modus_ponens_strict_implies }.
% 0.95/1.35 parent0: (10885) {G0,W3,D2,L2,V0,M2} { alpha2( skol29 ),
% 0.95/1.35 modus_ponens_strict_implies }.
% 0.95/1.35 substitution0:
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (85) {G0,W3,D2,L2,V0,M2} I { ! is_a_theorem( skol29 ),
% 0.95/1.35 modus_ponens_strict_implies }.
% 0.95/1.35 parent0: (10886) {G0,W3,D2,L2,V0,M2} { ! is_a_theorem( skol29 ),
% 0.95/1.35 modus_ponens_strict_implies }.
% 0.95/1.35 substitution0:
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (86) {G0,W5,D3,L2,V2,M2} I { ! alpha2( X ), is_a_theorem(
% 0.95/1.35 skol30( Y ) ) }.
% 0.95/1.35 parent0: (10887) {G0,W5,D3,L2,V2,M2} { ! alpha2( X ), is_a_theorem( skol30
% 0.95/1.35 ( Y ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (87) {G0,W7,D4,L2,V1,M2} I { ! alpha2( X ), is_a_theorem(
% 0.95/1.35 strict_implies( skol30( X ), X ) ) }.
% 0.95/1.35 parent0: (10888) {G0,W7,D4,L2,V1,M2} { ! alpha2( X ), is_a_theorem(
% 0.95/1.35 strict_implies( skol30( X ), X ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (92) {G0,W5,D2,L2,V2,M2} I { ! alpha3( X, Y ), is_a_theorem( X
% 0.95/1.35 ) }.
% 0.95/1.35 parent0: (10893) {G0,W5,D2,L2,V2,M2} { ! alpha3( X, Y ), is_a_theorem( X )
% 0.95/1.35 }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (93) {G0,W5,D2,L2,V2,M2} I { ! alpha3( X, Y ), is_a_theorem( Y
% 0.95/1.35 ) }.
% 0.95/1.35 parent0: (10894) {G0,W5,D2,L2,V2,M2} { ! alpha3( X, Y ), is_a_theorem( Y )
% 0.95/1.35 }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (94) {G0,W7,D2,L3,V2,M3} I { ! is_a_theorem( X ), !
% 0.95/1.35 is_a_theorem( Y ), alpha3( X, Y ) }.
% 0.95/1.35 parent0: (10895) {G0,W7,D2,L3,V2,M3} { ! is_a_theorem( X ), ! is_a_theorem
% 0.95/1.35 ( Y ), alpha3( X, Y ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 2 ==> 2
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (100) {G0,W6,D4,L2,V1,M2} I { ! axiom_M, is_a_theorem( implies
% 0.95/1.35 ( necessarily( X ), X ) ) }.
% 0.95/1.35 parent0: (10901) {G0,W6,D4,L2,V1,M2} { ! axiom_M, is_a_theorem( implies(
% 0.95/1.35 necessarily( X ), X ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 eqswap: (11042) {G0,W9,D4,L2,V2,M2} { necessarily( implies( X, Y ) ) =
% 0.95/1.35 strict_implies( X, Y ), ! op_strict_implies }.
% 0.95/1.35 parent0[1]: (10939) {G0,W9,D4,L2,V2,M2} { ! op_strict_implies,
% 0.95/1.35 strict_implies( X, Y ) = necessarily( implies( X, Y ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (138) {G0,W9,D4,L2,V2,M2} I { ! op_strict_implies, necessarily
% 0.95/1.35 ( implies( X, Y ) ) ==> strict_implies( X, Y ) }.
% 0.95/1.35 parent0: (11042) {G0,W9,D4,L2,V2,M2} { necessarily( implies( X, Y ) ) =
% 0.95/1.35 strict_implies( X, Y ), ! op_strict_implies }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 1
% 0.95/1.35 1 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (143) {G0,W1,D1,L1,V0,M1} I { axiom_M }.
% 0.95/1.35 parent0: (10944) {G0,W1,D1,L1,V0,M1} { axiom_M }.
% 0.95/1.35 substitution0:
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (147) {G0,W1,D1,L1,V0,M1} I { op_strict_implies }.
% 0.95/1.35 parent0: (10950) {G0,W1,D1,L1,V0,M1} { op_strict_implies }.
% 0.95/1.35 substitution0:
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (149) {G0,W1,D1,L1,V0,M1} I { ! modus_ponens_strict_implies
% 0.95/1.35 }.
% 0.95/1.35 parent0: (10953) {G0,W1,D1,L1,V0,M1} { ! modus_ponens_strict_implies }.
% 0.95/1.35 substitution0:
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11085) {G1,W4,D2,L2,V1,M2} { ! alpha1( X ), is_a_theorem( X )
% 0.95/1.35 }.
% 0.95/1.35 parent0[0]: (0) {G0,W5,D2,L3,V1,M3} I { ! modus_ponens, ! alpha1( X ),
% 0.95/1.35 is_a_theorem( X ) }.
% 0.95/1.35 parent1[0]: (65) {G0,W1,D1,L1,V0,M1} I { modus_ponens }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (151) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 0.95/1.35 is_a_theorem( X ) }.
% 0.95/1.35 parent0: (11085) {G1,W4,D2,L2,V1,M2} { ! alpha1( X ), is_a_theorem( X )
% 0.95/1.35 }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11086) {G1,W2,D2,L1,V0,M1} { ! is_a_theorem( skol29 ) }.
% 0.95/1.35 parent0[0]: (149) {G0,W1,D1,L1,V0,M1} I { ! modus_ponens_strict_implies }.
% 0.95/1.35 parent1[1]: (85) {G0,W3,D2,L2,V0,M2} I { ! is_a_theorem( skol29 ),
% 0.95/1.35 modus_ponens_strict_implies }.
% 0.95/1.35 substitution0:
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (156) {G1,W2,D2,L1,V0,M1} S(85);r(149) { ! is_a_theorem(
% 0.95/1.35 skol29 ) }.
% 0.95/1.35 parent0: (11086) {G1,W2,D2,L1,V0,M1} { ! is_a_theorem( skol29 ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11087) {G1,W2,D2,L1,V0,M1} { alpha2( skol29 ) }.
% 0.95/1.35 parent0[0]: (149) {G0,W1,D1,L1,V0,M1} I { ! modus_ponens_strict_implies }.
% 0.95/1.35 parent1[1]: (84) {G0,W3,D2,L2,V0,M2} I { alpha2( skol29 ),
% 0.95/1.35 modus_ponens_strict_implies }.
% 0.95/1.35 substitution0:
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (158) {G1,W2,D2,L1,V0,M1} S(84);r(149) { alpha2( skol29 ) }.
% 0.95/1.35 parent0: (11087) {G1,W2,D2,L1,V0,M1} { alpha2( skol29 ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11088) {G2,W2,D2,L1,V0,M1} { ! alpha1( skol29 ) }.
% 0.95/1.35 parent0[0]: (156) {G1,W2,D2,L1,V0,M1} S(85);r(149) { ! is_a_theorem( skol29
% 0.95/1.35 ) }.
% 0.95/1.35 parent1[1]: (151) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 0.95/1.35 is_a_theorem( X ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 X := skol29
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (159) {G2,W2,D2,L1,V0,M1} R(151,156) { ! alpha1( skol29 ) }.
% 0.95/1.35 parent0: (11088) {G2,W2,D2,L1,V0,M1} { ! alpha1( skol29 ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11089) {G1,W6,D3,L2,V1,M2} { ! is_a_theorem( X ), !
% 0.95/1.35 is_a_theorem( implies( X, skol29 ) ) }.
% 0.95/1.35 parent0[0]: (159) {G2,W2,D2,L1,V0,M1} R(151,156) { ! alpha1( skol29 ) }.
% 0.95/1.35 parent1[2]: (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem
% 0.95/1.35 ( implies( Y, X ) ), alpha1( X ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 X := skol29
% 0.95/1.35 Y := X
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (163) {G3,W6,D3,L2,V1,M2} R(159,5) { ! is_a_theorem( X ), !
% 0.95/1.35 is_a_theorem( implies( X, skol29 ) ) }.
% 0.95/1.35 parent0: (11089) {G1,W6,D3,L2,V1,M2} { ! is_a_theorem( X ), ! is_a_theorem
% 0.95/1.35 ( implies( X, skol29 ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11090) {G1,W6,D4,L1,V2,M1} { is_a_theorem( implies( X,
% 0.95/1.35 implies( Y, X ) ) ) }.
% 0.95/1.35 parent0[0]: (11) {G0,W7,D4,L2,V2,M2} I { ! implies_1, is_a_theorem( implies
% 0.95/1.35 ( X, implies( Y, X ) ) ) }.
% 0.95/1.35 parent1[0]: (67) {G0,W1,D1,L1,V0,M1} I { implies_1 }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (183) {G1,W6,D4,L1,V2,M1} S(11);r(67) { is_a_theorem( implies
% 0.95/1.35 ( X, implies( Y, X ) ) ) }.
% 0.95/1.35 parent0: (11090) {G1,W6,D4,L1,V2,M1} { is_a_theorem( implies( X, implies(
% 0.95/1.35 Y, X ) ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11091) {G1,W3,D3,L1,V1,M1} { is_a_theorem( skol30( X ) ) }.
% 0.95/1.35 parent0[0]: (86) {G0,W5,D3,L2,V2,M2} I { ! alpha2( X ), is_a_theorem(
% 0.95/1.35 skol30( Y ) ) }.
% 0.95/1.35 parent1[0]: (158) {G1,W2,D2,L1,V0,M1} S(84);r(149) { alpha2( skol29 ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := skol29
% 0.95/1.35 Y := X
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (185) {G2,W3,D3,L1,V1,M1} R(86,158) { is_a_theorem( skol30( X
% 0.95/1.35 ) ) }.
% 0.95/1.35 parent0: (11091) {G1,W3,D3,L1,V1,M1} { is_a_theorem( skol30( X ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11092) {G1,W7,D3,L2,V2,M2} { ! is_a_theorem( implies( X,
% 0.95/1.35 skol29 ) ), ! alpha3( X, Y ) }.
% 0.95/1.35 parent0[0]: (163) {G3,W6,D3,L2,V1,M2} R(159,5) { ! is_a_theorem( X ), !
% 0.95/1.35 is_a_theorem( implies( X, skol29 ) ) }.
% 0.95/1.35 parent1[1]: (92) {G0,W5,D2,L2,V2,M2} I { ! alpha3( X, Y ), is_a_theorem( X
% 0.95/1.35 ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 X := X
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (199) {G4,W7,D3,L2,V2,M2} R(163,92) { ! is_a_theorem( implies
% 0.95/1.35 ( X, skol29 ) ), ! alpha3( X, Y ) }.
% 0.95/1.35 parent0: (11092) {G1,W7,D3,L2,V2,M2} { ! is_a_theorem( implies( X, skol29
% 0.95/1.35 ) ), ! alpha3( X, Y ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11095) {G1,W6,D3,L2,V2,M2} { ! is_a_theorem( X ), alpha1(
% 0.95/1.35 implies( Y, X ) ) }.
% 0.95/1.35 parent0[1]: (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem
% 0.95/1.35 ( implies( Y, X ) ), alpha1( X ) }.
% 0.95/1.35 parent1[0]: (183) {G1,W6,D4,L1,V2,M1} S(11);r(67) { is_a_theorem( implies(
% 0.95/1.35 X, implies( Y, X ) ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := implies( Y, X )
% 0.95/1.35 Y := X
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 X := X
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (761) {G2,W6,D3,L2,V2,M2} R(183,5) { ! is_a_theorem( X ),
% 0.95/1.35 alpha1( implies( Y, X ) ) }.
% 0.95/1.35 parent0: (11095) {G1,W6,D3,L2,V2,M2} { ! is_a_theorem( X ), alpha1(
% 0.95/1.35 implies( Y, X ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11097) {G2,W6,D3,L2,V2,M2} { is_a_theorem( implies( X, Y ) )
% 0.95/1.35 , ! is_a_theorem( Y ) }.
% 0.95/1.35 parent0[0]: (151) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 0.95/1.35 is_a_theorem( X ) }.
% 0.95/1.35 parent1[1]: (761) {G2,W6,D3,L2,V2,M2} R(183,5) { ! is_a_theorem( X ),
% 0.95/1.35 alpha1( implies( Y, X ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := implies( X, Y )
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 X := Y
% 0.95/1.35 Y := X
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (812) {G3,W6,D3,L2,V2,M2} R(761,151) { ! is_a_theorem( X ),
% 0.95/1.35 is_a_theorem( implies( Y, X ) ) }.
% 0.95/1.35 parent0: (11097) {G2,W6,D3,L2,V2,M2} { is_a_theorem( implies( X, Y ) ), !
% 0.95/1.35 is_a_theorem( Y ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := Y
% 0.95/1.35 Y := X
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 1
% 0.95/1.35 1 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11099) {G1,W6,D2,L3,V2,M3} { ! is_a_theorem( X ), alpha1( Y )
% 0.95/1.35 , ! is_a_theorem( Y ) }.
% 0.95/1.35 parent0[1]: (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem
% 0.95/1.35 ( implies( Y, X ) ), alpha1( X ) }.
% 0.95/1.35 parent1[1]: (812) {G3,W6,D3,L2,V2,M2} R(761,151) { ! is_a_theorem( X ),
% 0.95/1.35 is_a_theorem( implies( Y, X ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := Y
% 0.95/1.35 Y := X
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 X := Y
% 0.95/1.35 Y := X
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (947) {G4,W6,D2,L3,V2,M3} R(812,5) { ! is_a_theorem( X ), !
% 0.95/1.35 is_a_theorem( Y ), alpha1( X ) }.
% 0.95/1.35 parent0: (11099) {G1,W6,D2,L3,V2,M3} { ! is_a_theorem( X ), alpha1( Y ), !
% 0.95/1.35 is_a_theorem( Y ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := X
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 2
% 0.95/1.35 2 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 factor: (11101) {G4,W4,D2,L2,V1,M2} { ! is_a_theorem( X ), alpha1( X ) }.
% 0.95/1.35 parent0[0, 1]: (947) {G4,W6,D2,L3,V2,M3} R(812,5) { ! is_a_theorem( X ), !
% 0.95/1.35 is_a_theorem( Y ), alpha1( X ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := X
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (948) {G5,W4,D2,L2,V1,M2} F(947) { ! is_a_theorem( X ), alpha1
% 0.95/1.35 ( X ) }.
% 0.95/1.35 parent0: (11101) {G4,W4,D2,L2,V1,M2} { ! is_a_theorem( X ), alpha1( X )
% 0.95/1.35 }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11102) {G1,W5,D2,L2,V2,M2} { alpha1( X ), ! alpha3( Y, X )
% 0.95/1.35 }.
% 0.95/1.35 parent0[0]: (948) {G5,W4,D2,L2,V1,M2} F(947) { ! is_a_theorem( X ), alpha1
% 0.95/1.35 ( X ) }.
% 0.95/1.35 parent1[1]: (93) {G0,W5,D2,L2,V2,M2} I { ! alpha3( X, Y ), is_a_theorem( Y
% 0.95/1.35 ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 X := Y
% 0.95/1.35 Y := X
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (970) {G6,W5,D2,L2,V2,M2} R(948,93) { alpha1( X ), ! alpha3( Y
% 0.95/1.35 , X ) }.
% 0.95/1.35 parent0: (11102) {G1,W5,D2,L2,V2,M2} { alpha1( X ), ! alpha3( Y, X ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11103) {G1,W5,D4,L1,V0,M1} { is_a_theorem( strict_implies(
% 0.95/1.35 skol30( skol29 ), skol29 ) ) }.
% 0.95/1.35 parent0[0]: (87) {G0,W7,D4,L2,V1,M2} I { ! alpha2( X ), is_a_theorem(
% 0.95/1.35 strict_implies( skol30( X ), X ) ) }.
% 0.95/1.35 parent1[0]: (158) {G1,W2,D2,L1,V0,M1} S(84);r(149) { alpha2( skol29 ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := skol29
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (1409) {G2,W5,D4,L1,V0,M1} R(87,158) { is_a_theorem(
% 0.95/1.35 strict_implies( skol30( skol29 ), skol29 ) ) }.
% 0.95/1.35 parent0: (11103) {G1,W5,D4,L1,V0,M1} { is_a_theorem( strict_implies(
% 0.95/1.35 skol30( skol29 ), skol29 ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11104) {G3,W5,D4,L1,V0,M1} { alpha1( strict_implies( skol30(
% 0.95/1.35 skol29 ), skol29 ) ) }.
% 0.95/1.35 parent0[0]: (948) {G5,W4,D2,L2,V1,M2} F(947) { ! is_a_theorem( X ), alpha1
% 0.95/1.35 ( X ) }.
% 0.95/1.35 parent1[0]: (1409) {G2,W5,D4,L1,V0,M1} R(87,158) { is_a_theorem(
% 0.95/1.35 strict_implies( skol30( skol29 ), skol29 ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := strict_implies( skol30( skol29 ), skol29 )
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (1412) {G6,W5,D4,L1,V0,M1} R(1409,948) { alpha1(
% 0.95/1.35 strict_implies( skol30( skol29 ), skol29 ) ) }.
% 0.95/1.35 parent0: (11104) {G3,W5,D4,L1,V0,M1} { alpha1( strict_implies( skol30(
% 0.95/1.35 skol29 ), skol29 ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11105) {G1,W6,D3,L2,V2,M2} { ! is_a_theorem( Y ), alpha3(
% 0.95/1.35 skol30( X ), Y ) }.
% 0.95/1.35 parent0[0]: (94) {G0,W7,D2,L3,V2,M3} I { ! is_a_theorem( X ), !
% 0.95/1.35 is_a_theorem( Y ), alpha3( X, Y ) }.
% 0.95/1.35 parent1[0]: (185) {G2,W3,D3,L1,V1,M1} R(86,158) { is_a_theorem( skol30( X )
% 0.95/1.35 ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := skol30( X )
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (1850) {G3,W6,D3,L2,V2,M2} R(94,185) { ! is_a_theorem( X ),
% 0.95/1.35 alpha3( skol30( Y ), X ) }.
% 0.95/1.35 parent0: (11105) {G1,W6,D3,L2,V2,M2} { ! is_a_theorem( Y ), alpha3( skol30
% 0.95/1.35 ( X ), Y ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := Y
% 0.95/1.35 Y := X
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11107) {G1,W5,D4,L1,V1,M1} { is_a_theorem( implies(
% 0.95/1.35 necessarily( X ), X ) ) }.
% 0.95/1.35 parent0[0]: (100) {G0,W6,D4,L2,V1,M2} I { ! axiom_M, is_a_theorem( implies
% 0.95/1.35 ( necessarily( X ), X ) ) }.
% 0.95/1.35 parent1[0]: (143) {G0,W1,D1,L1,V0,M1} I { axiom_M }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (2550) {G1,W5,D4,L1,V1,M1} S(100);r(143) { is_a_theorem(
% 0.95/1.35 implies( necessarily( X ), X ) ) }.
% 0.95/1.35 parent0: (11107) {G1,W5,D4,L1,V1,M1} { is_a_theorem( implies( necessarily
% 0.95/1.35 ( X ), X ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11109) {G1,W5,D3,L2,V1,M2} { ! is_a_theorem( necessarily( X )
% 0.95/1.35 ), alpha1( X ) }.
% 0.95/1.35 parent0[1]: (5) {G0,W8,D3,L3,V2,M3} I { ! is_a_theorem( Y ), ! is_a_theorem
% 0.95/1.35 ( implies( Y, X ) ), alpha1( X ) }.
% 0.95/1.35 parent1[0]: (2550) {G1,W5,D4,L1,V1,M1} S(100);r(143) { is_a_theorem(
% 0.95/1.35 implies( necessarily( X ), X ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := necessarily( X )
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (2580) {G2,W5,D3,L2,V1,M2} R(2550,5) { ! is_a_theorem(
% 0.95/1.35 necessarily( X ) ), alpha1( X ) }.
% 0.95/1.35 parent0: (11109) {G1,W5,D3,L2,V1,M2} { ! is_a_theorem( necessarily( X ) )
% 0.95/1.35 , alpha1( X ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11110) {G2,W5,D3,L2,V1,M2} { alpha1( X ), ! alpha1(
% 0.95/1.35 necessarily( X ) ) }.
% 0.95/1.35 parent0[0]: (2580) {G2,W5,D3,L2,V1,M2} R(2550,5) { ! is_a_theorem(
% 0.95/1.35 necessarily( X ) ), alpha1( X ) }.
% 0.95/1.35 parent1[1]: (151) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 0.95/1.35 is_a_theorem( X ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 X := necessarily( X )
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (2653) {G3,W5,D3,L2,V1,M2} R(2580,151) { alpha1( X ), ! alpha1
% 0.95/1.35 ( necessarily( X ) ) }.
% 0.95/1.35 parent0: (11110) {G2,W5,D3,L2,V1,M2} { alpha1( X ), ! alpha1( necessarily
% 0.95/1.35 ( X ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11111) {G2,W5,D3,L2,V1,M2} { is_a_theorem( X ), ! alpha1(
% 0.95/1.35 necessarily( X ) ) }.
% 0.95/1.35 parent0[0]: (151) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 0.95/1.35 is_a_theorem( X ) }.
% 0.95/1.35 parent1[0]: (2653) {G3,W5,D3,L2,V1,M2} R(2580,151) { alpha1( X ), ! alpha1
% 0.95/1.35 ( necessarily( X ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (2832) {G4,W5,D3,L2,V1,M2} R(2653,151) { ! alpha1( necessarily
% 0.95/1.35 ( X ) ), is_a_theorem( X ) }.
% 0.95/1.35 parent0: (11111) {G2,W5,D3,L2,V1,M2} { is_a_theorem( X ), ! alpha1(
% 0.95/1.35 necessarily( X ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 1
% 0.95/1.35 1 ==> 0
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11112) {G5,W6,D3,L2,V2,M2} { is_a_theorem( X ), ! alpha3( Y,
% 0.95/1.35 necessarily( X ) ) }.
% 0.95/1.35 parent0[0]: (2832) {G4,W5,D3,L2,V1,M2} R(2653,151) { ! alpha1( necessarily
% 0.95/1.35 ( X ) ), is_a_theorem( X ) }.
% 0.95/1.35 parent1[0]: (970) {G6,W5,D2,L2,V2,M2} R(948,93) { alpha1( X ), ! alpha3( Y
% 0.95/1.35 , X ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 end
% 0.95/1.35 substitution1:
% 0.95/1.35 X := necessarily( X )
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 subsumption: (2848) {G7,W6,D3,L2,V2,M2} R(2832,970) { is_a_theorem( X ), !
% 0.95/1.35 alpha3( Y, necessarily( X ) ) }.
% 0.95/1.35 parent0: (11112) {G5,W6,D3,L2,V2,M2} { is_a_theorem( X ), ! alpha3( Y,
% 0.95/1.35 necessarily( X ) ) }.
% 0.95/1.35 substitution0:
% 0.95/1.35 X := X
% 0.95/1.35 Y := Y
% 0.95/1.35 end
% 0.95/1.35 permutation0:
% 0.95/1.35 0 ==> 0
% 0.95/1.35 1 ==> 1
% 0.95/1.35 end
% 0.95/1.35
% 0.95/1.35 resolution: (11113) {G2,W6,D3,L2,V2,M2} { alpha3( skol30( Y ), X ), !
% 0.95/1.36 alpha1( X ) }.
% 0.95/1.36 parent0[0]: (1850) {G3,W6,D3,L2,V2,M2} R(94,185) { ! is_a_theorem( X ),
% 0.95/1.36 alpha3( skol30( Y ), X ) }.
% 0.95/1.36 parent1[1]: (151) {G1,W4,D2,L2,V1,M2} S(0);r(65) { ! alpha1( X ),
% 0.95/1.36 is_a_theorem( X ) }.
% 0.95/1.36 substitution0:
% 0.95/1.36 X := X
% 0.95/1.36 Y := Y
% 0.95/1.36 end
% 0.95/1.36 substitution1:
% 0.95/1.36 X := X
% 0.95/1.36 end
% 0.95/1.36
% 0.95/1.36 subsumption: (4529) {G4,W6,D3,L2,V2,M2} R(1850,151) { alpha3( skol30( X ),
% 0.95/1.36 Y ), ! alpha1( Y ) }.
% 0.95/1.36 parent0: (11113) {G2,W6,D3,L2,V2,M2} { alpha3( skol30( Y ), X ), ! alpha1
% 0.95/1.36 ( X ) }.
% 0.95/1.36 substitution0:
% 0.95/1.36 X := Y
% 0.95/1.36 Y := X
% 0.95/1.36 end
% 0.95/1.36 permutation0:
% 0.95/1.36 0 ==> 0
% 0.95/1.36 1 ==> 1
% 0.95/1.36 end
% 0.95/1.36
% 0.95/1.36 resolution: (11115) {G1,W8,D4,L1,V2,M1} { necessarily( implies( X, Y ) )
% 0.95/1.36 ==> strict_implies( X, Y ) }.
% 0.95/1.36 parent0[0]: (138) {G0,W9,D4,L2,V2,M2} I { ! op_strict_implies, necessarily
% 0.95/1.36 ( implies( X, Y ) ) ==> strict_implies( X, Y ) }.
% 0.95/1.36 parent1[0]: (147) {G0,W1,D1,L1,V0,M1} I { op_strict_implies }.
% 0.95/1.36 substitution0:
% 0.95/1.36 X := X
% 0.95/1.36 Y := Y
% 0.95/1.36 end
% 0.95/1.36 substitution1:
% 0.95/1.36 end
% 0.95/1.36
% 0.95/1.36 subsumption: (5026) {G1,W8,D4,L1,V2,M1} S(138);r(147) { necessarily(
% 0.95/1.36 implies( X, Y ) ) ==> strict_implies( X, Y ) }.
% 0.95/1.36 parent0: (11115) {G1,W8,D4,L1,V2,M1} { necessarily( implies( X, Y ) ) ==>
% 0.95/1.36 strict_implies( X, Y ) }.
% 0.95/1.36 substitution0:
% 0.95/1.36 X := X
% 0.95/1.36 Y := Y
% 0.95/1.36 end
% 0.95/1.36 permutation0:
% 0.95/1.36 0 ==> 0
% 0.95/1.36 end
% 0.95/1.36
% 0.95/1.36 resolution: (11118) {G5,W9,D4,L2,V3,M2} { ! alpha3( X, Y ), ! alpha3( Z,
% 0.95/1.36 necessarily( implies( X, skol29 ) ) ) }.
% 0.95/1.36 parent0[0]: (199) {G4,W7,D3,L2,V2,M2} R(163,92) { ! is_a_theorem( implies(
% 0.95/1.36 X, skol29 ) ), ! alpha3( X, Y ) }.
% 0.95/1.36 parent1[0]: (2848) {G7,W6,D3,L2,V2,M2} R(2832,970) { is_a_theorem( X ), !
% 0.95/1.36 alpha3( Y, necessarily( X ) ) }.
% 0.95/1.36 substitution0:
% 0.95/1.36 X := X
% 0.95/1.36 Y := Y
% 0.95/1.36 end
% 0.95/1.36 substitution1:
% 0.95/1.36 X := implies( X, skol29 )
% 0.95/1.36 Y := Z
% 0.95/1.36 end
% 0.95/1.36
% 0.95/1.36 paramod: (11121) {G2,W8,D3,L2,V3,M2} { ! alpha3( X, strict_implies( Y,
% 0.95/1.36 skol29 ) ), ! alpha3( Y, Z ) }.
% 0.95/1.36 parent0[0]: (5026) {G1,W8,D4,L1,V2,M1} S(138);r(147) { necessarily( implies
% 0.95/1.36 ( X, Y ) ) ==> strict_implies( X, Y ) }.
% 0.95/1.36 parent1[1; 3]: (11118) {G5,W9,D4,L2,V3,M2} { ! alpha3( X, Y ), ! alpha3( Z
% 0.95/1.36 , necessarily( implies( X, skol29 ) ) ) }.
% 0.95/1.36 substitution0:
% 0.95/1.36 X := Y
% 0.95/1.36 Y := skol29
% 0.95/1.36 end
% 0.95/1.36 substitution1:
% 0.95/1.36 X := Y
% 0.95/1.36 Y := Z
% 0.95/1.36 Z := X
% 0.95/1.36 end
% 0.95/1.36
% 0.95/1.36 subsumption: (10713) {G8,W8,D3,L2,V3,M2} R(199,2848);d(5026) { ! alpha3( X
% 0.95/1.36 , Y ), ! alpha3( Z, strict_implies( X, skol29 ) ) }.
% 0.95/1.36 parent0: (11121) {G2,W8,D3,L2,V3,M2} { ! alpha3( X, strict_implies( Y,
% 0.95/1.36 skol29 ) ), ! alpha3( Y, Z ) }.
% 0.95/1.36 substitution0:
% 0.95/1.36 X := Z
% 0.95/1.36 Y := X
% 0.95/1.36 Z := Y
% 0.95/1.36 end
% 0.95/1.36 permutation0:
% 0.95/1.36 0 ==> 1
% 0.95/1.36 1 ==> 0
% 0.95/1.36 end
% 0.95/1.36
% 0.95/1.36 factor: (11123) {G8,W5,D3,L1,V1,M1} { ! alpha3( X, strict_implies( X,
% 0.95/1.36 skol29 ) ) }.
% 0.95/1.36 parent0[0, 1]: (10713) {G8,W8,D3,L2,V3,M2} R(199,2848);d(5026) { ! alpha3(
% 0.95/1.36 X, Y ), ! alpha3( Z, strict_implies( X, skol29 ) ) }.
% 0.95/1.36 substitution0:
% 0.95/1.36 X := X
% 0.95/1.36 Y := strict_implies( X, skol29 )
% 0.95/1.36 Z := X
% 0.95/1.36 end
% 0.95/1.36
% 0.95/1.36 subsumption: (10730) {G9,W5,D3,L1,V1,M1} F(10713) { ! alpha3( X,
% 0.95/1.36 strict_implies( X, skol29 ) ) }.
% 0.95/1.36 parent0: (11123) {G8,W5,D3,L1,V1,M1} { ! alpha3( X, strict_implies( X,
% 0.95/1.36 skol29 ) ) }.
% 0.95/1.36 substitution0:
% 0.95/1.36 X := X
% 0.95/1.36 end
% 0.95/1.36 permutation0:
% 0.95/1.36 0 ==> 0
% 0.95/1.36 end
% 0.95/1.36
% 0.95/1.36 resolution: (11124) {G5,W5,D4,L1,V1,M1} { ! alpha1( strict_implies( skol30
% 0.95/1.36 ( X ), skol29 ) ) }.
% 0.95/1.36 parent0[0]: (10730) {G9,W5,D3,L1,V1,M1} F(10713) { ! alpha3( X,
% 0.95/1.36 strict_implies( X, skol29 ) ) }.
% 0.95/1.36 parent1[0]: (4529) {G4,W6,D3,L2,V2,M2} R(1850,151) { alpha3( skol30( X ), Y
% 0.95/1.36 ), ! alpha1( Y ) }.
% 0.95/1.36 substitution0:
% 0.95/1.36 X := skol30( X )
% 0.95/1.36 end
% 0.95/1.36 substitution1:
% 0.95/1.36 X := X
% 0.95/1.36 Y := strict_implies( skol30( X ), skol29 )
% 0.95/1.36 end
% 0.95/1.36
% 0.95/1.36 subsumption: (10731) {G10,W5,D4,L1,V1,M1} R(10730,4529) { ! alpha1(
% 0.95/1.36 strict_implies( skol30( X ), skol29 ) ) }.
% 0.95/1.36 parent0: (11124) {G5,W5,D4,L1,V1,M1} { ! alpha1( strict_implies( skol30( X
% 0.95/1.36 ), skol29 ) ) }.
% 0.95/1.36 substitution0:
% 0.95/1.36 X := X
% 0.95/1.36 end
% 0.95/1.36 permutation0:
% 0.95/1.36 0 ==> 0
% 0.95/1.36 end
% 0.95/1.36
% 0.95/1.36 resolution: (11125) {G7,W0,D0,L0,V0,M0} { }.
% 0.95/1.36 parent0[0]: (10731) {G10,W5,D4,L1,V1,M1} R(10730,4529) { ! alpha1(
% 0.95/1.36 strict_implies( skol30( X ), skol29 ) ) }.
% 0.95/1.36 parent1[0]: (1412) {G6,W5,D4,L1,V0,M1} R(1409,948) { alpha1( strict_implies
% 0.95/1.36 ( skol30( skol29 ), skol29 ) ) }.
% 0.95/1.36 substitution0:
% 0.95/1.36 X := skol29
% 0.95/1.36 end
% 0.95/1.36 substitution1:
% 0.95/1.36 end
% 0.95/1.36
% 0.95/1.36 subsumption: (10799) {G11,W0,D0,L0,V0,M0} S(1412);r(10731) { }.
% 0.95/1.36 parent0: (11125) {G7,W0,D0,L0,V0,M0} { }.
% 0.95/1.36 substitution0:
% 0.95/1.36 end
% 0.95/1.36 permutation0:
% 0.95/1.36 end
% 0.95/1.36
% 0.95/1.36 Proof check complete!
% 0.95/1.36
% 0.95/1.36 Memory use:
% 0.95/1.36
% 0.95/1.36 space for terms: 121685
% 0.95/1.36 space for clauses: 519864
% 0.95/1.36
% 0.95/1.36
% 0.95/1.36 clauses generated: 19720
% 0.95/1.36 clauses kept: 10800
% 0.95/1.36 clauses selected: 614
% 0.95/1.36 clauses deleted: 85
% 0.95/1.36 clauses inuse deleted: 14
% 0.95/1.36
% 0.95/1.36 subsentry: 44484
% 0.95/1.36 literals s-matched: 33066
% 0.95/1.36 literals matched: 29371
% 0.95/1.36 full subsumption: 2469
% 0.95/1.36
% 0.95/1.36 checksum: -1277388346
% 0.95/1.36
% 0.95/1.36
% 0.95/1.36 Bliksem ended
%------------------------------------------------------------------------------