TSTP Solution File: LCL535+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL535+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 : 600s
% DateTime : Sun Jul 17 12:52:58 EDT 2022
% Result : Theorem 4.85s 5.01s
% Output : CNFRefutation 4.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 57
% Syntax : Number of formulae : 283 ( 140 unt; 0 def)
% Number of atoms : 501 ( 152 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 408 ( 190 ~; 168 |; 20 &)
% ( 22 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 20 ( 17 usr; 17 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 18 con; 0-2 aty)
% Number of variables : 336 ( 8 sgn 80 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ) ).
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ) ).
fof(and_2,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ) ).
fof(and_3,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ) ).
fof(or_1,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ).
fof(hilbert_op_or,axiom,
op_or ).
fof(hilbert_op_implies_and,axiom,
op_implies_and ).
fof(hilbert_op_equiv,axiom,
op_equiv ).
fof(hilbert_modus_ponens,axiom,
modus_ponens ).
fof(hilbert_modus_tollens,axiom,
modus_tollens ).
fof(hilbert_implies_2,axiom,
implies_2 ).
fof(hilbert_and_2,axiom,
and_2 ).
fof(hilbert_and_3,axiom,
and_3 ).
fof(hilbert_or_1,axiom,
or_1 ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents ).
fof(necessitation,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ) ).
fof(axiom_M,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ) ).
fof(axiom_5,axiom,
( axiom_5
<=> ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ) ).
fof(axiom_m9,axiom,
( axiom_m9
<=> ! [X] : is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X))) ) ).
fof(op_possibly,axiom,
( op_possibly
=> ! [X] : possibly(X) = not(necessarily(not(X))) ) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ) ).
fof(km5_op_possibly,axiom,
op_possibly ).
fof(km5_necessitation,axiom,
necessitation ).
fof(km5_axiom_M,axiom,
axiom_M ).
fof(km5_axiom_5,axiom,
axiom_5 ).
fof(s1_0_op_possibly,axiom,
op_possibly ).
fof(s1_0_op_or,axiom,
op_or ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies ).
fof(s1_0_op_equiv,axiom,
op_equiv ).
fof(s1_0_m6s3m9b_axiom_m9,conjecture,
axiom_m9 ).
fof(subgoal_0,plain,
axiom_m9,
inference(strip,[],[s1_0_m6s3m9b_axiom_m9]) ).
fof(negate_0_0,plain,
~ axiom_m9,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ axiom_m9
<=> ? [X] : ~ is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X))) ),
inference(canonicalize,[],[axiom_m9]) ).
fof(normalize_0_1,plain,
! [X] :
( ( ~ axiom_m9
| is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X))) )
& ( ~ is_a_theorem(strict_implies(possibly(possibly(skolemFOFtoCNF_X_33)),possibly(skolemFOFtoCNF_X_33)))
| axiom_m9 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(strict_implies(possibly(possibly(skolemFOFtoCNF_X_33)),possibly(skolemFOFtoCNF_X_33)))
| axiom_m9 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ axiom_m9,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ necessitation
<=> ? [X] :
( ~ is_a_theorem(necessarily(X))
& is_a_theorem(X) ) ),
inference(canonicalize,[],[necessitation]) ).
fof(normalize_0_5,plain,
! [X] :
( ( ~ is_a_theorem(necessarily(skolemFOFtoCNF_X_15))
| necessitation )
& ( is_a_theorem(skolemFOFtoCNF_X_15)
| necessitation )
& ( ~ is_a_theorem(X)
| ~ necessitation
| is_a_theorem(necessarily(X)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X] :
( ~ is_a_theorem(X)
| ~ necessitation
| is_a_theorem(necessarily(X)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
necessitation,
inference(canonicalize,[],[km5_necessitation]) ).
fof(normalize_0_8,plain,
( ~ modus_tollens
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(canonicalize,[],[modus_tollens]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)))
| modus_tollens )
& ( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
modus_tollens,
inference(canonicalize,[],[hilbert_modus_tollens]) ).
fof(normalize_0_12,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
op_or,
inference(canonicalize,[],[s1_0_op_or]) ).
fof(normalize_0_15,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
op_implies_and,
inference(canonicalize,[],[hilbert_op_implies_and]) ).
fof(normalize_0_18,plain,
( ~ modus_ponens
<=> ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(X)
& is_a_theorem(implies(X,Y)) ) ),
inference(canonicalize,[],[modus_ponens]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ( ~ is_a_theorem(skolemFOFtoCNF_Y)
| modus_ponens )
& ( is_a_theorem(implies(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| modus_ponens )
& ( is_a_theorem(skolemFOFtoCNF_X)
| modus_ponens )
& ( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ) ),
inference(clausify,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
modus_ponens,
inference(canonicalize,[],[hilbert_modus_ponens]) ).
fof(normalize_0_22,plain,
( ~ or_1
<=> ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y))) ),
inference(canonicalize,[],[or_1]) ).
fof(normalize_0_23,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(skolemFOFtoCNF_X_9,or(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_9)))
| or_1 )
& ( ~ or_1
| is_a_theorem(implies(X,or(X,Y))) ) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [X,Y] :
( ~ or_1
| is_a_theorem(implies(X,or(X,Y))) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
or_1,
inference(canonicalize,[],[hilbert_or_1]) ).
fof(normalize_0_26,plain,
( ~ op_possibly
| ! [X] : possibly(X) = not(necessarily(not(X))) ),
inference(canonicalize,[],[op_possibly]) ).
fof(normalize_0_27,plain,
! [X] :
( ~ op_possibly
| possibly(X) = not(necessarily(not(X))) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
op_possibly,
inference(canonicalize,[],[s1_0_op_possibly]) ).
fof(normalize_0_29,plain,
( ~ substitution_of_equivalents
<=> ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_30,plain,
! [X,Y] :
( ( skolemFOFtoCNF_X_1 != skolemFOFtoCNF_Y_1
| substitution_of_equivalents )
& ( is_a_theorem(equiv(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| substitution_of_equivalents )
& ( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ) ),
inference(clausify,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [X,Y] :
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(conjunct,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
substitution_of_equivalents,
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_33,plain,
( ~ and_3
<=> ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[and_3]) ).
fof(normalize_0_34,plain,
! [X,Y] :
( ( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) )
& ( ~ is_a_theorem(implies(skolemFOFtoCNF_X_8,implies(skolemFOFtoCNF_Y_8,and(skolemFOFtoCNF_X_8,skolemFOFtoCNF_Y_8))))
| and_3 ) ),
inference(clausify,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [X,Y] :
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(conjunct,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
and_3,
inference(canonicalize,[],[hilbert_and_3]) ).
fof(normalize_0_37,plain,
( ~ implies_2
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[implies_2]) ).
fof(normalize_0_38,plain,
! [X,Y] :
( ( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )
& ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_4,implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)),implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)))
| implies_2 ) ),
inference(clausify,[],[normalize_0_37]) ).
fof(normalize_0_39,plain,
! [X,Y] :
( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
implies_2,
inference(canonicalize,[],[hilbert_implies_2]) ).
fof(normalize_0_41,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_42,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_41]) ).
fof(normalize_0_43,plain,
op_equiv,
inference(canonicalize,[],[s1_0_op_equiv]) ).
fof(normalize_0_44,plain,
( ~ and_2
<=> ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[and_2]) ).
fof(normalize_0_45,plain,
! [X,Y] :
( ( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) )
& ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_X_7,skolemFOFtoCNF_Y_7),skolemFOFtoCNF_Y_7))
| and_2 ) ),
inference(clausify,[],[normalize_0_44]) ).
fof(normalize_0_46,plain,
! [X,Y] :
( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) ),
inference(conjunct,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
and_2,
inference(canonicalize,[],[hilbert_and_2]) ).
fof(normalize_0_48,plain,
( ~ axiom_5
<=> ? [X] : ~ is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_0_49,plain,
! [X] :
( ( ~ axiom_5
| is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) )
& ( ~ is_a_theorem(implies(possibly(skolemFOFtoCNF_X_23),necessarily(possibly(skolemFOFtoCNF_X_23))))
| axiom_5 ) ),
inference(clausify,[],[normalize_0_48]) ).
fof(normalize_0_50,plain,
! [X] :
( ~ axiom_5
| is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
inference(conjunct,[],[normalize_0_49]) ).
fof(normalize_0_51,plain,
axiom_5,
inference(canonicalize,[],[km5_axiom_5]) ).
fof(normalize_0_52,plain,
( ~ axiom_M
<=> ? [X] : ~ is_a_theorem(implies(necessarily(X),X)) ),
inference(canonicalize,[],[axiom_M]) ).
fof(normalize_0_53,plain,
! [X] :
( ( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) )
& ( ~ is_a_theorem(implies(necessarily(skolemFOFtoCNF_X_20),skolemFOFtoCNF_X_20))
| axiom_M ) ),
inference(clausify,[],[normalize_0_52]) ).
fof(normalize_0_54,plain,
! [X] :
( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) ),
inference(conjunct,[],[normalize_0_53]) ).
fof(normalize_0_55,plain,
axiom_M,
inference(canonicalize,[],[km5_axiom_M]) ).
fof(normalize_0_56,plain,
( ~ op_strict_implies
| ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(canonicalize,[],[op_strict_implies]) ).
fof(normalize_0_57,plain,
! [X,Y] :
( ~ op_strict_implies
| strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(clausify,[],[normalize_0_56]) ).
fof(normalize_0_58,plain,
op_strict_implies,
inference(canonicalize,[],[s1_0_op_strict_implies]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(strict_implies(possibly(possibly(skolemFOFtoCNF_X_33)),possibly(skolemFOFtoCNF_X_33)))
| axiom_m9 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ axiom_m9,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(strict_implies(possibly(possibly(skolemFOFtoCNF_X_33)),possibly(skolemFOFtoCNF_X_33))),
inference(resolve,[$cnf( axiom_m9 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(X)
| ~ necessitation
| is_a_theorem(necessarily(X)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
necessitation,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(X)
| is_a_theorem(necessarily(X)) ),
inference(resolve,[$cnf( necessitation )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(possibly(possibly(X_3783)),possibly(X_3783)))
| is_a_theorem(necessarily(implies(possibly(possibly(X_3783)),possibly(X_3783)))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(possibly(possibly(X_3783)),possibly(X_3783))))]]) ).
cnf(refute_0_7,plain,
( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
modus_tollens,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))),
inference(resolve,[$cnf( modus_tollens )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_11,plain,
op_or,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_14,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_15,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_17,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_18,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_20,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_20:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_22,plain,
( not(and(not(X),not(Y))) != implies(not(X),Y)
| or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) ),[1],$fot(implies(not(X),Y))]]) ).
cnf(refute_0_23,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_12,refute_0_23]) ).
cnf(refute_0_25,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_26,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
implies(not(Y),not(X)) = or(Y,not(X)),
inference(subst,[],[refute_0_26:[bind(X,$fot(Y)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_28,plain,
implies(implies(not(Y),not(X)),implies(X,Y)) = implies(implies(not(Y),not(X)),implies(X,Y)),
introduced(tautology,[refl,[$fot(implies(implies(not(Y),not(X)),implies(X,Y)))]]) ).
cnf(refute_0_29,plain,
( implies(implies(not(Y),not(X)),implies(X,Y)) != implies(implies(not(Y),not(X)),implies(X,Y))
| implies(not(Y),not(X)) != or(Y,not(X))
| implies(implies(not(Y),not(X)),implies(X,Y)) = implies(or(Y,not(X)),implies(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(Y),not(X)),implies(X,Y)),implies(implies(not(Y),not(X)),implies(X,Y))) ),[1,0],$fot(or(Y,not(X)))]]) ).
cnf(refute_0_30,plain,
( implies(not(Y),not(X)) != or(Y,not(X))
| implies(implies(not(Y),not(X)),implies(X,Y)) = implies(or(Y,not(X)),implies(X,Y)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),not(X)),implies(X,Y)),implies(implies(not(Y),not(X)),implies(X,Y))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
implies(implies(not(Y),not(X)),implies(X,Y)) = implies(or(Y,not(X)),implies(X,Y)),
inference(resolve,[$cnf( $equal(implies(not(Y),not(X)),or(Y,not(X))) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
( implies(implies(not(Y),not(X)),implies(X,Y)) != implies(or(Y,not(X)),implies(X,Y))
| ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| is_a_theorem(implies(or(Y,not(X)),implies(X,Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),[0],$fot(implies(or(Y,not(X)),implies(X,Y)))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| is_a_theorem(implies(or(Y,not(X)),implies(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),not(X)),implies(X,Y)),implies(or(Y,not(X)),implies(X,Y))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
is_a_theorem(implies(or(Y,not(X)),implies(X,Y))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )],[refute_0_9,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_36,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_36,refute_0_35]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(implies(or(Y,not(X)),implies(X,Y)))
| ~ is_a_theorem(or(Y,not(X)))
| is_a_theorem(implies(X,Y)) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(or(Y,not(X)))),bind(Y,$fot(implies(X,Y)))]]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(or(Y,not(X)))
| is_a_theorem(implies(X,Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(Y,not(X)),implies(X,Y))) )],[refute_0_34,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(or(possibly(X_3782),not(possibly(possibly(X_3782)))))
| is_a_theorem(implies(possibly(possibly(X_3782)),possibly(X_3782))) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(possibly(possibly(X_3782)))),bind(Y,$fot(possibly(X_3782)))]]) ).
cnf(refute_0_41,plain,
( ~ or_1
| is_a_theorem(implies(X,or(X,Y))) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_42,plain,
or_1,
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(X,or(X,Y))),
inference(resolve,[$cnf( or_1 )],[refute_0_42,refute_0_41]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(necessarily(not(X_24)),or(necessarily(not(X_24)),Y))),
inference(subst,[],[refute_0_43:[bind(X,$fot(necessarily(not(X_24))))]]) ).
cnf(refute_0_45,plain,
or(necessarily(not(X)),X_11) = implies(not(necessarily(not(X))),X_11),
inference(subst,[],[refute_0_24:[bind(X,$fot(necessarily(not(X)))),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_46,plain,
( ~ op_possibly
| possibly(X) = not(necessarily(not(X))) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_47,plain,
op_possibly,
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_48,plain,
possibly(X) = not(necessarily(not(X))),
inference(resolve,[$cnf( op_possibly )],[refute_0_47,refute_0_46]) ).
cnf(refute_0_49,plain,
( possibly(X) != not(necessarily(not(X)))
| not(necessarily(not(X))) = possibly(X) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(possibly(X))),bind(Y0,$fot(not(necessarily(not(X)))))]]) ).
cnf(refute_0_50,plain,
not(necessarily(not(X))) = possibly(X),
inference(resolve,[$cnf( $equal(possibly(X),not(necessarily(not(X)))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( not(necessarily(not(X))) != possibly(X)
| or(necessarily(not(X)),X_11) != implies(not(necessarily(not(X))),X_11)
| or(necessarily(not(X)),X_11) = implies(possibly(X),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(or(necessarily(not(X)),X_11),implies(not(necessarily(not(X))),X_11)) ),[1,0],$fot(possibly(X))]]) ).
cnf(refute_0_52,plain,
( or(necessarily(not(X)),X_11) != implies(not(necessarily(not(X))),X_11)
| or(necessarily(not(X)),X_11) = implies(possibly(X),X_11) ),
inference(resolve,[$cnf( $equal(not(necessarily(not(X))),possibly(X)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
or(necessarily(not(X)),X_11) = implies(possibly(X),X_11),
inference(resolve,[$cnf( $equal(or(necessarily(not(X)),X_11),implies(not(necessarily(not(X))),X_11)) )],[refute_0_45,refute_0_52]) ).
cnf(refute_0_54,plain,
or(necessarily(not(X_24)),Y) = implies(possibly(X_24),Y),
inference(subst,[],[refute_0_53:[bind(X,$fot(X_24)),bind(X_11,$fot(Y))]]) ).
cnf(refute_0_55,plain,
( or(necessarily(not(X_24)),Y) != implies(possibly(X_24),Y)
| ~ is_a_theorem(implies(necessarily(not(X_24)),or(necessarily(not(X_24)),Y)))
| is_a_theorem(implies(necessarily(not(X_24)),implies(possibly(X_24),Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(necessarily(not(X_24)),or(necessarily(not(X_24)),Y))) ),[0,1],$fot(implies(possibly(X_24),Y))]]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(implies(necessarily(not(X_24)),or(necessarily(not(X_24)),Y)))
| is_a_theorem(implies(necessarily(not(X_24)),implies(possibly(X_24),Y))) ),
inference(resolve,[$cnf( $equal(or(necessarily(not(X_24)),Y),implies(possibly(X_24),Y)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(necessarily(not(X_24)),implies(possibly(X_24),Y))),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(not(X_24)),or(necessarily(not(X_24)),Y))) )],[refute_0_44,refute_0_56]) ).
cnf(refute_0_58,plain,
is_a_theorem(implies(necessarily(not(X_24)),implies(possibly(X_24),necessarily(not(X_132))))),
inference(subst,[],[refute_0_57:[bind(Y,$fot(necessarily(not(X_132))))]]) ).
cnf(refute_0_59,plain,
implies(X_7,necessarily(not(X))) = not(and(X_7,not(necessarily(not(X))))),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_7)),bind(Y,$fot(necessarily(not(X))))]]) ).
cnf(refute_0_60,plain,
( implies(X_7,necessarily(not(X))) != not(and(X_7,not(necessarily(not(X)))))
| not(necessarily(not(X))) != possibly(X)
| implies(X_7,necessarily(not(X))) = not(and(X_7,possibly(X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_7,necessarily(not(X))),not(and(X_7,not(necessarily(not(X)))))) ),[1,0,1],$fot(possibly(X))]]) ).
cnf(refute_0_61,plain,
( implies(X_7,necessarily(not(X))) != not(and(X_7,not(necessarily(not(X)))))
| implies(X_7,necessarily(not(X))) = not(and(X_7,possibly(X))) ),
inference(resolve,[$cnf( $equal(not(necessarily(not(X))),possibly(X)) )],[refute_0_50,refute_0_60]) ).
cnf(refute_0_62,plain,
implies(X_7,necessarily(not(X))) = not(and(X_7,possibly(X))),
inference(resolve,[$cnf( $equal(implies(X_7,necessarily(not(X))),not(and(X_7,not(necessarily(not(X)))))) )],[refute_0_59,refute_0_61]) ).
cnf(refute_0_63,plain,
implies(possibly(X_24),necessarily(not(X_132))) = not(and(possibly(X_24),possibly(X_132))),
inference(subst,[],[refute_0_62:[bind(X,$fot(X_132)),bind(X_7,$fot(possibly(X_24)))]]) ).
cnf(refute_0_64,plain,
( implies(possibly(X_24),necessarily(not(X_132))) != not(and(possibly(X_24),possibly(X_132)))
| ~ is_a_theorem(implies(necessarily(not(X_24)),implies(possibly(X_24),necessarily(not(X_132)))))
| is_a_theorem(implies(necessarily(not(X_24)),not(and(possibly(X_24),possibly(X_132))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(necessarily(not(X_24)),implies(possibly(X_24),necessarily(not(X_132))))) ),[0,1],$fot(not(and(possibly(X_24),possibly(X_132))))]]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(implies(necessarily(not(X_24)),implies(possibly(X_24),necessarily(not(X_132)))))
| is_a_theorem(implies(necessarily(not(X_24)),not(and(possibly(X_24),possibly(X_132))))) ),
inference(resolve,[$cnf( $equal(implies(possibly(X_24),necessarily(not(X_132))),not(and(possibly(X_24),possibly(X_132)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(necessarily(not(X_24)),not(and(possibly(X_24),possibly(X_132))))),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(not(X_24)),implies(possibly(X_24),necessarily(not(X_132))))) )],[refute_0_58,refute_0_65]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(necessarily(not(X_132)),not(and(possibly(X_132),possibly(X_132))))),
inference(subst,[],[refute_0_66:[bind(X_24,$fot(X_132))]]) ).
cnf(refute_0_68,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_69,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_70,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_69,refute_0_68]) ).
cnf(refute_0_71,plain,
( ~ is_a_theorem(equiv(X_3620,and(X_3620,X_3620)))
| X_3620 = and(X_3620,X_3620) ),
inference(subst,[],[refute_0_70:[bind(X,$fot(X_3620)),bind(Y,$fot(and(X_3620,X_3620)))]]) ).
cnf(refute_0_72,plain,
( ~ is_a_theorem(implies(and(X_3619,X_3619),X_3619))
| ~ is_a_theorem(implies(implies(and(X_3619,X_3619),X_3619),equiv(X_3619,and(X_3619,X_3619))))
| is_a_theorem(equiv(X_3619,and(X_3619,X_3619))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(implies(and(X_3619,X_3619),X_3619))),bind(Y,$fot(equiv(X_3619,and(X_3619,X_3619))))]]) ).
cnf(refute_0_73,plain,
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_74,plain,
and_3,
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(X,implies(Y,and(X,Y)))),
inference(resolve,[$cnf( and_3 )],[refute_0_74,refute_0_73]) ).
cnf(refute_0_76,plain,
is_a_theorem(implies(X_384,implies(Y,and(X_384,Y)))),
inference(subst,[],[refute_0_75:[bind(X,$fot(X_384))]]) ).
cnf(refute_0_77,plain,
( ~ is_a_theorem(X_384)
| ~ is_a_theorem(implies(X_384,implies(Y,and(X_384,Y))))
| is_a_theorem(implies(Y,and(X_384,Y))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_384)),bind(Y,$fot(implies(Y,and(X_384,Y))))]]) ).
cnf(refute_0_78,plain,
( ~ is_a_theorem(X_384)
| is_a_theorem(implies(Y,and(X_384,Y))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_384,implies(Y,and(X_384,Y)))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( ~ is_a_theorem(implies(X_3324,and(X_3324,X_3324)))
| is_a_theorem(implies(Y,and(implies(X_3324,and(X_3324,X_3324)),Y))) ),
inference(subst,[],[refute_0_78:[bind(X_384,$fot(implies(X_3324,and(X_3324,X_3324))))]]) ).
cnf(refute_0_80,plain,
is_a_theorem(implies(X_3319,implies(X_3319,and(X_3319,X_3319)))),
inference(subst,[],[refute_0_75:[bind(X,$fot(X_3319)),bind(Y,$fot(X_3319))]]) ).
cnf(refute_0_81,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_82,plain,
implies_2,
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))),
inference(resolve,[$cnf( implies_2 )],[refute_0_82,refute_0_81]) ).
cnf(refute_0_84,plain,
( ~ is_a_theorem(implies(X,implies(X,Y)))
| ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| is_a_theorem(implies(X,Y)) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(implies(X,implies(X,Y)))),bind(Y,$fot(implies(X,Y)))]]) ).
cnf(refute_0_85,plain,
( ~ is_a_theorem(implies(X,implies(X,Y)))
| is_a_theorem(implies(X,Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( ~ is_a_theorem(implies(X_3319,implies(X_3319,and(X_3319,X_3319))))
| is_a_theorem(implies(X_3319,and(X_3319,X_3319))) ),
inference(subst,[],[refute_0_85:[bind(X,$fot(X_3319)),bind(Y,$fot(and(X_3319,X_3319)))]]) ).
cnf(refute_0_87,plain,
is_a_theorem(implies(X_3319,and(X_3319,X_3319))),
inference(resolve,[$cnf( is_a_theorem(implies(X_3319,implies(X_3319,and(X_3319,X_3319)))) )],[refute_0_80,refute_0_86]) ).
cnf(refute_0_88,plain,
is_a_theorem(implies(X_3324,and(X_3324,X_3324))),
inference(subst,[],[refute_0_87:[bind(X_3319,$fot(X_3324))]]) ).
cnf(refute_0_89,plain,
is_a_theorem(implies(Y,and(implies(X_3324,and(X_3324,X_3324)),Y))),
inference(resolve,[$cnf( is_a_theorem(implies(X_3324,and(X_3324,X_3324))) )],[refute_0_88,refute_0_79]) ).
cnf(refute_0_90,plain,
is_a_theorem(implies(implies(and(X_3443,X_3443),X_3443),and(implies(X_3443,and(X_3443,X_3443)),implies(and(X_3443,X_3443),X_3443)))),
inference(subst,[],[refute_0_89:[bind(Y,$fot(implies(and(X_3443,X_3443),X_3443))),bind(X_3324,$fot(X_3443))]]) ).
cnf(refute_0_91,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_92,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_43]) ).
cnf(refute_0_93,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_92,refute_0_91]) ).
cnf(refute_0_94,plain,
equiv(X_3443,and(X_3443,X_3443)) = and(implies(X_3443,and(X_3443,X_3443)),implies(and(X_3443,X_3443),X_3443)),
inference(subst,[],[refute_0_93:[bind(X,$fot(X_3443)),bind(Y,$fot(and(X_3443,X_3443)))]]) ).
cnf(refute_0_95,plain,
( equiv(X_3443,and(X_3443,X_3443)) != and(implies(X_3443,and(X_3443,X_3443)),implies(and(X_3443,X_3443),X_3443))
| and(implies(X_3443,and(X_3443,X_3443)),implies(and(X_3443,X_3443),X_3443)) = equiv(X_3443,and(X_3443,X_3443)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(equiv(X_3443,and(X_3443,X_3443)))),bind(Y0,$fot(and(implies(X_3443,and(X_3443,X_3443)),implies(and(X_3443,X_3443),X_3443))))]]) ).
cnf(refute_0_96,plain,
and(implies(X_3443,and(X_3443,X_3443)),implies(and(X_3443,X_3443),X_3443)) = equiv(X_3443,and(X_3443,X_3443)),
inference(resolve,[$cnf( $equal(equiv(X_3443,and(X_3443,X_3443)),and(implies(X_3443,and(X_3443,X_3443)),implies(and(X_3443,X_3443),X_3443))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
( and(implies(X_3443,and(X_3443,X_3443)),implies(and(X_3443,X_3443),X_3443)) != equiv(X_3443,and(X_3443,X_3443))
| ~ is_a_theorem(implies(implies(and(X_3443,X_3443),X_3443),and(implies(X_3443,and(X_3443,X_3443)),implies(and(X_3443,X_3443),X_3443))))
| is_a_theorem(implies(implies(and(X_3443,X_3443),X_3443),equiv(X_3443,and(X_3443,X_3443)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(and(X_3443,X_3443),X_3443),and(implies(X_3443,and(X_3443,X_3443)),implies(and(X_3443,X_3443),X_3443)))) ),[0,1],$fot(equiv(X_3443,and(X_3443,X_3443)))]]) ).
cnf(refute_0_98,plain,
( ~ is_a_theorem(implies(implies(and(X_3443,X_3443),X_3443),and(implies(X_3443,and(X_3443,X_3443)),implies(and(X_3443,X_3443),X_3443))))
| is_a_theorem(implies(implies(and(X_3443,X_3443),X_3443),equiv(X_3443,and(X_3443,X_3443)))) ),
inference(resolve,[$cnf( $equal(and(implies(X_3443,and(X_3443,X_3443)),implies(and(X_3443,X_3443),X_3443)),equiv(X_3443,and(X_3443,X_3443))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
is_a_theorem(implies(implies(and(X_3443,X_3443),X_3443),equiv(X_3443,and(X_3443,X_3443)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_3443,X_3443),X_3443),and(implies(X_3443,and(X_3443,X_3443)),implies(and(X_3443,X_3443),X_3443)))) )],[refute_0_90,refute_0_98]) ).
cnf(refute_0_100,plain,
is_a_theorem(implies(implies(and(X_3619,X_3619),X_3619),equiv(X_3619,and(X_3619,X_3619)))),
inference(subst,[],[refute_0_99:[bind(X_3443,$fot(X_3619))]]) ).
cnf(refute_0_101,plain,
( ~ is_a_theorem(implies(and(X_3619,X_3619),X_3619))
| is_a_theorem(equiv(X_3619,and(X_3619,X_3619))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_3619,X_3619),X_3619),equiv(X_3619,and(X_3619,X_3619)))) )],[refute_0_100,refute_0_72]) ).
cnf(refute_0_102,plain,
( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_103,plain,
and_2,
inference(canonicalize,[],[normalize_0_47]) ).
cnf(refute_0_104,plain,
is_a_theorem(implies(and(X,Y),Y)),
inference(resolve,[$cnf( and_2 )],[refute_0_103,refute_0_102]) ).
cnf(refute_0_105,plain,
is_a_theorem(implies(and(X_3619,X_3619),X_3619)),
inference(subst,[],[refute_0_104:[bind(X,$fot(X_3619)),bind(Y,$fot(X_3619))]]) ).
cnf(refute_0_106,plain,
is_a_theorem(equiv(X_3619,and(X_3619,X_3619))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_3619,X_3619),X_3619)) )],[refute_0_105,refute_0_101]) ).
cnf(refute_0_107,plain,
is_a_theorem(equiv(X_3620,and(X_3620,X_3620))),
inference(subst,[],[refute_0_106:[bind(X_3619,$fot(X_3620))]]) ).
cnf(refute_0_108,plain,
X_3620 = and(X_3620,X_3620),
inference(resolve,[$cnf( is_a_theorem(equiv(X_3620,and(X_3620,X_3620))) )],[refute_0_107,refute_0_71]) ).
cnf(refute_0_109,plain,
possibly(X_132) = and(possibly(X_132),possibly(X_132)),
inference(subst,[],[refute_0_108:[bind(X_3620,$fot(possibly(X_132)))]]) ).
cnf(refute_0_110,plain,
( possibly(X_132) != and(possibly(X_132),possibly(X_132))
| and(possibly(X_132),possibly(X_132)) = possibly(X_132) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(possibly(X_132))),bind(Y0,$fot(and(possibly(X_132),possibly(X_132))))]]) ).
cnf(refute_0_111,plain,
and(possibly(X_132),possibly(X_132)) = possibly(X_132),
inference(resolve,[$cnf( $equal(possibly(X_132),and(possibly(X_132),possibly(X_132))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( and(possibly(X_132),possibly(X_132)) != possibly(X_132)
| ~ is_a_theorem(implies(necessarily(not(X_132)),not(and(possibly(X_132),possibly(X_132)))))
| is_a_theorem(implies(necessarily(not(X_132)),not(possibly(X_132)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(necessarily(not(X_132)),not(and(possibly(X_132),possibly(X_132))))) ),[0,1,0],$fot(possibly(X_132))]]) ).
cnf(refute_0_113,plain,
( ~ is_a_theorem(implies(necessarily(not(X_132)),not(and(possibly(X_132),possibly(X_132)))))
| is_a_theorem(implies(necessarily(not(X_132)),not(possibly(X_132)))) ),
inference(resolve,[$cnf( $equal(and(possibly(X_132),possibly(X_132)),possibly(X_132)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
is_a_theorem(implies(necessarily(not(X_132)),not(possibly(X_132)))),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(not(X_132)),not(and(possibly(X_132),possibly(X_132))))) )],[refute_0_67,refute_0_113]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(necessarily(not(possibly(X_1))),not(possibly(possibly(X_1))))),
inference(subst,[],[refute_0_114:[bind(X_132,$fot(possibly(X_1)))]]) ).
cnf(refute_0_116,plain,
( ~ is_a_theorem(equiv(possibly(X_1620),necessarily(possibly(X_1620))))
| possibly(X_1620) = necessarily(possibly(X_1620)) ),
inference(subst,[],[refute_0_70:[bind(X,$fot(possibly(X_1620))),bind(Y,$fot(necessarily(possibly(X_1620))))]]) ).
cnf(refute_0_117,plain,
( ~ is_a_theorem(implies(implies(necessarily(possibly(X_1619)),possibly(X_1619)),equiv(possibly(X_1619),necessarily(possibly(X_1619)))))
| ~ is_a_theorem(implies(necessarily(possibly(X_1619)),possibly(X_1619)))
| is_a_theorem(equiv(possibly(X_1619),necessarily(possibly(X_1619)))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(implies(necessarily(possibly(X_1619)),possibly(X_1619)))),bind(Y,$fot(equiv(possibly(X_1619),necessarily(possibly(X_1619)))))]]) ).
cnf(refute_0_118,plain,
( ~ axiom_5
| is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
inference(canonicalize,[],[normalize_0_50]) ).
cnf(refute_0_119,plain,
axiom_5,
inference(canonicalize,[],[normalize_0_51]) ).
cnf(refute_0_120,plain,
is_a_theorem(implies(possibly(X),necessarily(possibly(X)))),
inference(resolve,[$cnf( axiom_5 )],[refute_0_119,refute_0_118]) ).
cnf(refute_0_121,plain,
( ~ is_a_theorem(implies(possibly(X),necessarily(possibly(X))))
| is_a_theorem(implies(X_1086,and(implies(possibly(X),necessarily(possibly(X))),X_1086))) ),
inference(subst,[],[refute_0_78:[bind(Y,$fot(X_1086)),bind(X_384,$fot(implies(possibly(X),necessarily(possibly(X)))))]]) ).
cnf(refute_0_122,plain,
is_a_theorem(implies(X_1086,and(implies(possibly(X),necessarily(possibly(X))),X_1086))),
inference(resolve,[$cnf( is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
is_a_theorem(implies(implies(necessarily(possibly(X_1088)),possibly(X_1088)),and(implies(possibly(X_1088),necessarily(possibly(X_1088))),implies(necessarily(possibly(X_1088)),possibly(X_1088))))),
inference(subst,[],[refute_0_122:[bind(X,$fot(X_1088)),bind(X_1086,$fot(implies(necessarily(possibly(X_1088)),possibly(X_1088))))]]) ).
cnf(refute_0_124,plain,
equiv(possibly(X_1088),necessarily(possibly(X_1088))) = and(implies(possibly(X_1088),necessarily(possibly(X_1088))),implies(necessarily(possibly(X_1088)),possibly(X_1088))),
inference(subst,[],[refute_0_93:[bind(X,$fot(possibly(X_1088))),bind(Y,$fot(necessarily(possibly(X_1088))))]]) ).
cnf(refute_0_125,plain,
( equiv(possibly(X_1088),necessarily(possibly(X_1088))) != and(implies(possibly(X_1088),necessarily(possibly(X_1088))),implies(necessarily(possibly(X_1088)),possibly(X_1088)))
| and(implies(possibly(X_1088),necessarily(possibly(X_1088))),implies(necessarily(possibly(X_1088)),possibly(X_1088))) = equiv(possibly(X_1088),necessarily(possibly(X_1088))) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(equiv(possibly(X_1088),necessarily(possibly(X_1088))))),bind(Y0,$fot(and(implies(possibly(X_1088),necessarily(possibly(X_1088))),implies(necessarily(possibly(X_1088)),possibly(X_1088)))))]]) ).
cnf(refute_0_126,plain,
and(implies(possibly(X_1088),necessarily(possibly(X_1088))),implies(necessarily(possibly(X_1088)),possibly(X_1088))) = equiv(possibly(X_1088),necessarily(possibly(X_1088))),
inference(resolve,[$cnf( $equal(equiv(possibly(X_1088),necessarily(possibly(X_1088))),and(implies(possibly(X_1088),necessarily(possibly(X_1088))),implies(necessarily(possibly(X_1088)),possibly(X_1088)))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
( and(implies(possibly(X_1088),necessarily(possibly(X_1088))),implies(necessarily(possibly(X_1088)),possibly(X_1088))) != equiv(possibly(X_1088),necessarily(possibly(X_1088)))
| ~ is_a_theorem(implies(implies(necessarily(possibly(X_1088)),possibly(X_1088)),and(implies(possibly(X_1088),necessarily(possibly(X_1088))),implies(necessarily(possibly(X_1088)),possibly(X_1088)))))
| is_a_theorem(implies(implies(necessarily(possibly(X_1088)),possibly(X_1088)),equiv(possibly(X_1088),necessarily(possibly(X_1088))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(necessarily(possibly(X_1088)),possibly(X_1088)),and(implies(possibly(X_1088),necessarily(possibly(X_1088))),implies(necessarily(possibly(X_1088)),possibly(X_1088))))) ),[0,1],$fot(equiv(possibly(X_1088),necessarily(possibly(X_1088))))]]) ).
cnf(refute_0_128,plain,
( ~ is_a_theorem(implies(implies(necessarily(possibly(X_1088)),possibly(X_1088)),and(implies(possibly(X_1088),necessarily(possibly(X_1088))),implies(necessarily(possibly(X_1088)),possibly(X_1088)))))
| is_a_theorem(implies(implies(necessarily(possibly(X_1088)),possibly(X_1088)),equiv(possibly(X_1088),necessarily(possibly(X_1088))))) ),
inference(resolve,[$cnf( $equal(and(implies(possibly(X_1088),necessarily(possibly(X_1088))),implies(necessarily(possibly(X_1088)),possibly(X_1088))),equiv(possibly(X_1088),necessarily(possibly(X_1088)))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(implies(necessarily(possibly(X_1088)),possibly(X_1088)),equiv(possibly(X_1088),necessarily(possibly(X_1088))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(necessarily(possibly(X_1088)),possibly(X_1088)),and(implies(possibly(X_1088),necessarily(possibly(X_1088))),implies(necessarily(possibly(X_1088)),possibly(X_1088))))) )],[refute_0_123,refute_0_128]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(implies(necessarily(possibly(X_1619)),possibly(X_1619)),equiv(possibly(X_1619),necessarily(possibly(X_1619))))),
inference(subst,[],[refute_0_129:[bind(X_1088,$fot(X_1619))]]) ).
cnf(refute_0_131,plain,
( ~ is_a_theorem(implies(necessarily(possibly(X_1619)),possibly(X_1619)))
| is_a_theorem(equiv(possibly(X_1619),necessarily(possibly(X_1619)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(necessarily(possibly(X_1619)),possibly(X_1619)),equiv(possibly(X_1619),necessarily(possibly(X_1619))))) )],[refute_0_130,refute_0_117]) ).
cnf(refute_0_132,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) ),
inference(canonicalize,[],[normalize_0_54]) ).
cnf(refute_0_133,plain,
axiom_M,
inference(canonicalize,[],[normalize_0_55]) ).
cnf(refute_0_134,plain,
is_a_theorem(implies(necessarily(X),X)),
inference(resolve,[$cnf( axiom_M )],[refute_0_133,refute_0_132]) ).
cnf(refute_0_135,plain,
is_a_theorem(implies(necessarily(possibly(X_1619)),possibly(X_1619))),
inference(subst,[],[refute_0_134:[bind(X,$fot(possibly(X_1619)))]]) ).
cnf(refute_0_136,plain,
is_a_theorem(equiv(possibly(X_1619),necessarily(possibly(X_1619)))),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(possibly(X_1619)),possibly(X_1619))) )],[refute_0_135,refute_0_131]) ).
cnf(refute_0_137,plain,
is_a_theorem(equiv(possibly(X_1620),necessarily(possibly(X_1620)))),
inference(subst,[],[refute_0_136:[bind(X_1619,$fot(X_1620))]]) ).
cnf(refute_0_138,plain,
possibly(X_1620) = necessarily(possibly(X_1620)),
inference(resolve,[$cnf( is_a_theorem(equiv(possibly(X_1620),necessarily(possibly(X_1620)))) )],[refute_0_137,refute_0_116]) ).
cnf(refute_0_139,plain,
possibly(necessarily(not(X_1))) = necessarily(possibly(necessarily(not(X_1)))),
inference(subst,[],[refute_0_138:[bind(X_1620,$fot(necessarily(not(X_1))))]]) ).
cnf(refute_0_140,plain,
possibly(necessarily(not(X_1))) = not(necessarily(not(necessarily(not(X_1))))),
inference(subst,[],[refute_0_48:[bind(X,$fot(necessarily(not(X_1))))]]) ).
cnf(refute_0_141,plain,
possibly(X_1) = not(necessarily(not(X_1))),
inference(subst,[],[refute_0_48:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_142,plain,
( possibly(X_1) != not(necessarily(not(X_1)))
| not(necessarily(not(X_1))) = possibly(X_1) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(possibly(X_1))),bind(Y0,$fot(not(necessarily(not(X_1)))))]]) ).
cnf(refute_0_143,plain,
not(necessarily(not(X_1))) = possibly(X_1),
inference(resolve,[$cnf( $equal(possibly(X_1),not(necessarily(not(X_1)))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
( not(necessarily(not(X_1))) != possibly(X_1)
| possibly(necessarily(not(X_1))) != not(necessarily(not(necessarily(not(X_1)))))
| possibly(necessarily(not(X_1))) = not(necessarily(possibly(X_1))) ),
introduced(tautology,[equality,[$cnf( $equal(possibly(necessarily(not(X_1))),not(necessarily(not(necessarily(not(X_1)))))) ),[1,0,0],$fot(possibly(X_1))]]) ).
cnf(refute_0_145,plain,
( possibly(necessarily(not(X_1))) != not(necessarily(not(necessarily(not(X_1)))))
| possibly(necessarily(not(X_1))) = not(necessarily(possibly(X_1))) ),
inference(resolve,[$cnf( $equal(not(necessarily(not(X_1))),possibly(X_1)) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
possibly(necessarily(not(X_1))) = not(necessarily(possibly(X_1))),
inference(resolve,[$cnf( $equal(possibly(necessarily(not(X_1))),not(necessarily(not(necessarily(not(X_1)))))) )],[refute_0_140,refute_0_145]) ).
cnf(refute_0_147,plain,
( possibly(X_1620) != necessarily(possibly(X_1620))
| necessarily(possibly(X_1620)) = possibly(X_1620) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(possibly(X_1620))),bind(Y0,$fot(necessarily(possibly(X_1620))))]]) ).
cnf(refute_0_148,plain,
necessarily(possibly(X_1620)) = possibly(X_1620),
inference(resolve,[$cnf( $equal(possibly(X_1620),necessarily(possibly(X_1620))) )],[refute_0_138,refute_0_147]) ).
cnf(refute_0_149,plain,
necessarily(possibly(X_1)) = possibly(X_1),
inference(subst,[],[refute_0_148:[bind(X_1620,$fot(X_1))]]) ).
cnf(refute_0_150,plain,
not(necessarily(possibly(X_1))) = not(necessarily(possibly(X_1))),
introduced(tautology,[refl,[$fot(not(necessarily(possibly(X_1))))]]) ).
cnf(refute_0_151,plain,
( necessarily(possibly(X_1)) != possibly(X_1)
| not(necessarily(possibly(X_1))) != not(necessarily(possibly(X_1)))
| not(necessarily(possibly(X_1))) = not(possibly(X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(not(necessarily(possibly(X_1))),not(necessarily(possibly(X_1)))) ),[1,0],$fot(possibly(X_1))]]) ).
cnf(refute_0_152,plain,
( necessarily(possibly(X_1)) != possibly(X_1)
| not(necessarily(possibly(X_1))) = not(possibly(X_1)) ),
inference(resolve,[$cnf( $equal(not(necessarily(possibly(X_1))),not(necessarily(possibly(X_1)))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
not(necessarily(possibly(X_1))) = not(possibly(X_1)),
inference(resolve,[$cnf( $equal(necessarily(possibly(X_1)),possibly(X_1)) )],[refute_0_149,refute_0_152]) ).
cnf(refute_0_154,plain,
( not(necessarily(possibly(X_1))) != not(possibly(X_1))
| possibly(necessarily(not(X_1))) != not(necessarily(possibly(X_1)))
| possibly(necessarily(not(X_1))) = not(possibly(X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(possibly(necessarily(not(X_1))),not(necessarily(possibly(X_1)))) ),[1],$fot(not(possibly(X_1)))]]) ).
cnf(refute_0_155,plain,
( possibly(necessarily(not(X_1))) != not(necessarily(possibly(X_1)))
| possibly(necessarily(not(X_1))) = not(possibly(X_1)) ),
inference(resolve,[$cnf( $equal(not(necessarily(possibly(X_1))),not(possibly(X_1))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
possibly(necessarily(not(X_1))) = not(possibly(X_1)),
inference(resolve,[$cnf( $equal(possibly(necessarily(not(X_1))),not(necessarily(possibly(X_1)))) )],[refute_0_146,refute_0_155]) ).
cnf(refute_0_157,plain,
( possibly(necessarily(not(X_1))) != necessarily(possibly(necessarily(not(X_1))))
| possibly(necessarily(not(X_1))) != not(possibly(X_1))
| possibly(necessarily(not(X_1))) = necessarily(not(possibly(X_1))) ),
introduced(tautology,[equality,[$cnf( $equal(possibly(necessarily(not(X_1))),necessarily(possibly(necessarily(not(X_1))))) ),[1,0],$fot(not(possibly(X_1)))]]) ).
cnf(refute_0_158,plain,
( possibly(necessarily(not(X_1))) != necessarily(possibly(necessarily(not(X_1))))
| possibly(necessarily(not(X_1))) = necessarily(not(possibly(X_1))) ),
inference(resolve,[$cnf( $equal(possibly(necessarily(not(X_1))),not(possibly(X_1))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
possibly(necessarily(not(X_1))) = necessarily(not(possibly(X_1))),
inference(resolve,[$cnf( $equal(possibly(necessarily(not(X_1))),necessarily(possibly(necessarily(not(X_1))))) )],[refute_0_139,refute_0_158]) ).
cnf(refute_0_160,plain,
( possibly(necessarily(not(X_1))) != necessarily(not(possibly(X_1)))
| possibly(necessarily(not(X_1))) != not(possibly(X_1))
| not(possibly(X_1)) = necessarily(not(possibly(X_1))) ),
introduced(tautology,[equality,[$cnf( $equal(possibly(necessarily(not(X_1))),necessarily(not(possibly(X_1)))) ),[0],$fot(not(possibly(X_1)))]]) ).
cnf(refute_0_161,plain,
( possibly(necessarily(not(X_1))) != necessarily(not(possibly(X_1)))
| not(possibly(X_1)) = necessarily(not(possibly(X_1))) ),
inference(resolve,[$cnf( $equal(possibly(necessarily(not(X_1))),not(possibly(X_1))) )],[refute_0_156,refute_0_160]) ).
cnf(refute_0_162,plain,
not(possibly(X_1)) = necessarily(not(possibly(X_1))),
inference(resolve,[$cnf( $equal(possibly(necessarily(not(X_1))),necessarily(not(possibly(X_1)))) )],[refute_0_159,refute_0_161]) ).
cnf(refute_0_163,plain,
( not(possibly(X_1)) != necessarily(not(possibly(X_1)))
| necessarily(not(possibly(X_1))) = not(possibly(X_1)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(not(possibly(X_1)))),bind(Y0,$fot(necessarily(not(possibly(X_1)))))]]) ).
cnf(refute_0_164,plain,
necessarily(not(possibly(X_1))) = not(possibly(X_1)),
inference(resolve,[$cnf( $equal(not(possibly(X_1)),necessarily(not(possibly(X_1)))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
( necessarily(not(possibly(X_1))) != not(possibly(X_1))
| ~ is_a_theorem(implies(necessarily(not(possibly(X_1))),not(possibly(possibly(X_1)))))
| is_a_theorem(implies(not(possibly(X_1)),not(possibly(possibly(X_1))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(necessarily(not(possibly(X_1))),not(possibly(possibly(X_1))))) ),[0,0],$fot(not(possibly(X_1)))]]) ).
cnf(refute_0_166,plain,
( ~ is_a_theorem(implies(necessarily(not(possibly(X_1))),not(possibly(possibly(X_1)))))
| is_a_theorem(implies(not(possibly(X_1)),not(possibly(possibly(X_1))))) ),
inference(resolve,[$cnf( $equal(necessarily(not(possibly(X_1))),not(possibly(X_1))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
is_a_theorem(implies(not(possibly(X_1)),not(possibly(possibly(X_1))))),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(not(possibly(X_1))),not(possibly(possibly(X_1))))) )],[refute_0_115,refute_0_166]) ).
cnf(refute_0_168,plain,
implies(not(possibly(X_1)),not(possibly(possibly(X_1)))) = or(possibly(X_1),not(possibly(possibly(X_1)))),
inference(subst,[],[refute_0_26:[bind(X,$fot(possibly(X_1))),bind(Y,$fot(not(possibly(possibly(X_1)))))]]) ).
cnf(refute_0_169,plain,
( implies(not(possibly(X_1)),not(possibly(possibly(X_1)))) != or(possibly(X_1),not(possibly(possibly(X_1))))
| ~ is_a_theorem(implies(not(possibly(X_1)),not(possibly(possibly(X_1)))))
| is_a_theorem(or(possibly(X_1),not(possibly(possibly(X_1))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(possibly(X_1)),not(possibly(possibly(X_1))))) ),[0],$fot(or(possibly(X_1),not(possibly(possibly(X_1)))))]]) ).
cnf(refute_0_170,plain,
( ~ is_a_theorem(implies(not(possibly(X_1)),not(possibly(possibly(X_1)))))
| is_a_theorem(or(possibly(X_1),not(possibly(possibly(X_1))))) ),
inference(resolve,[$cnf( $equal(implies(not(possibly(X_1)),not(possibly(possibly(X_1)))),or(possibly(X_1),not(possibly(possibly(X_1))))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
is_a_theorem(or(possibly(X_1),not(possibly(possibly(X_1))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(possibly(X_1)),not(possibly(possibly(X_1))))) )],[refute_0_167,refute_0_170]) ).
cnf(refute_0_172,plain,
is_a_theorem(or(possibly(X_3782),not(possibly(possibly(X_3782))))),
inference(subst,[],[refute_0_171:[bind(X_1,$fot(X_3782))]]) ).
cnf(refute_0_173,plain,
is_a_theorem(implies(possibly(possibly(X_3782)),possibly(X_3782))),
inference(resolve,[$cnf( is_a_theorem(or(possibly(X_3782),not(possibly(possibly(X_3782))))) )],[refute_0_172,refute_0_40]) ).
cnf(refute_0_174,plain,
is_a_theorem(implies(possibly(possibly(X_3783)),possibly(X_3783))),
inference(subst,[],[refute_0_173:[bind(X_3782,$fot(X_3783))]]) ).
cnf(refute_0_175,plain,
is_a_theorem(necessarily(implies(possibly(possibly(X_3783)),possibly(X_3783)))),
inference(resolve,[$cnf( is_a_theorem(implies(possibly(possibly(X_3783)),possibly(X_3783))) )],[refute_0_174,refute_0_6]) ).
cnf(refute_0_176,plain,
( ~ op_strict_implies
| strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(canonicalize,[],[normalize_0_57]) ).
cnf(refute_0_177,plain,
op_strict_implies,
inference(canonicalize,[],[normalize_0_58]) ).
cnf(refute_0_178,plain,
strict_implies(X,Y) = necessarily(implies(X,Y)),
inference(resolve,[$cnf( op_strict_implies )],[refute_0_177,refute_0_176]) ).
cnf(refute_0_179,plain,
( strict_implies(X,Y) != necessarily(implies(X,Y))
| necessarily(implies(X,Y)) = strict_implies(X,Y) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(strict_implies(X,Y))),bind(Y0,$fot(necessarily(implies(X,Y))))]]) ).
cnf(refute_0_180,plain,
necessarily(implies(X,Y)) = strict_implies(X,Y),
inference(resolve,[$cnf( $equal(strict_implies(X,Y),necessarily(implies(X,Y))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
necessarily(implies(possibly(possibly(X_3783)),possibly(X_3783))) = strict_implies(possibly(possibly(X_3783)),possibly(X_3783)),
inference(subst,[],[refute_0_180:[bind(X,$fot(possibly(possibly(X_3783)))),bind(Y,$fot(possibly(X_3783)))]]) ).
cnf(refute_0_182,plain,
( necessarily(implies(possibly(possibly(X_3783)),possibly(X_3783))) != strict_implies(possibly(possibly(X_3783)),possibly(X_3783))
| ~ is_a_theorem(necessarily(implies(possibly(possibly(X_3783)),possibly(X_3783))))
| is_a_theorem(strict_implies(possibly(possibly(X_3783)),possibly(X_3783))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(necessarily(implies(possibly(possibly(X_3783)),possibly(X_3783)))) ),[0],$fot(strict_implies(possibly(possibly(X_3783)),possibly(X_3783)))]]) ).
cnf(refute_0_183,plain,
( ~ is_a_theorem(necessarily(implies(possibly(possibly(X_3783)),possibly(X_3783))))
| is_a_theorem(strict_implies(possibly(possibly(X_3783)),possibly(X_3783))) ),
inference(resolve,[$cnf( $equal(necessarily(implies(possibly(possibly(X_3783)),possibly(X_3783))),strict_implies(possibly(possibly(X_3783)),possibly(X_3783))) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
is_a_theorem(strict_implies(possibly(possibly(X_3783)),possibly(X_3783))),
inference(resolve,[$cnf( is_a_theorem(necessarily(implies(possibly(possibly(X_3783)),possibly(X_3783)))) )],[refute_0_175,refute_0_183]) ).
cnf(refute_0_185,plain,
is_a_theorem(strict_implies(possibly(possibly(skolemFOFtoCNF_X_33)),possibly(skolemFOFtoCNF_X_33))),
inference(subst,[],[refute_0_184:[bind(X_3783,$fot(skolemFOFtoCNF_X_33))]]) ).
cnf(refute_0_186,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(strict_implies(possibly(possibly(skolemFOFtoCNF_X_33)),possibly(skolemFOFtoCNF_X_33))) )],[refute_0_185,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL535+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 13:21:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.85/5.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.85/5.01
% 4.85/5.01 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.85/5.03
%------------------------------------------------------------------------------