TSTP Solution File: LCL533+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL533+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 40.06s 40.23s
% Output : CNFRefutation 40.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 107
% Syntax : Number of formulae : 545 ( 265 unt; 0 def)
% Number of atoms : 970 ( 457 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 805 ( 380 ~; 363 |; 27 &)
% ( 26 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 22 ( 19 usr; 19 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 22 con; 0-2 aty)
% Number of variables : 710 ( 9 sgn 92 !; 22 ?)
% 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(or_2,axiom,
( or_2
<=> ! [X,Y] : is_a_theorem(implies(Y,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(hilbert_or_2,axiom,
or_2 ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents ).
fof(necessitation,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ) ).
fof(modus_ponens_strict_implies,axiom,
( modus_ponens_strict_implies
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(strict_implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
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_m6,axiom,
( axiom_m6
<=> ! [X] : is_a_theorem(strict_implies(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_m6,conjecture,
axiom_m6 ).
fof(subgoal_0,plain,
axiom_m6,
inference(strip,[],[s1_0_m6s3m9b_axiom_m6]) ).
fof(negate_0_0,plain,
~ axiom_m6,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ axiom_m6
<=> ? [X] : ~ is_a_theorem(strict_implies(X,possibly(X))) ),
inference(canonicalize,[],[axiom_m6]) ).
fof(normalize_0_1,plain,
! [X] :
( ( ~ axiom_m6
| is_a_theorem(strict_implies(X,possibly(X))) )
& ( ~ is_a_theorem(strict_implies(skolemFOFtoCNF_X_32,possibly(skolemFOFtoCNF_X_32)))
| axiom_m6 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(strict_implies(skolemFOFtoCNF_X_32,possibly(skolemFOFtoCNF_X_32)))
| axiom_m6 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ axiom_m6,
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,
( ~ axiom_M
<=> ? [X] : ~ is_a_theorem(implies(necessarily(X),X)) ),
inference(canonicalize,[],[axiom_M]) ).
fof(normalize_0_23,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_22]) ).
fof(normalize_0_24,plain,
! [X] :
( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
axiom_M,
inference(canonicalize,[],[km5_axiom_M]) ).
fof(normalize_0_26,plain,
( ~ op_strict_implies
| ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(canonicalize,[],[op_strict_implies]) ).
fof(normalize_0_27,plain,
! [X,Y] :
( ~ op_strict_implies
| strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
op_strict_implies,
inference(canonicalize,[],[s1_0_op_strict_implies]) ).
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,
( ~ or_2
<=> ? [X,Y] : ~ is_a_theorem(implies(Y,or(X,Y))) ),
inference(canonicalize,[],[or_2]) ).
fof(normalize_0_34,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(skolemFOFtoCNF_Y_10,or(skolemFOFtoCNF_X_10,skolemFOFtoCNF_Y_10)))
| or_2 )
& ( ~ or_2
| is_a_theorem(implies(Y,or(X,Y))) ) ),
inference(clausify,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [X,Y] :
( ~ or_2
| is_a_theorem(implies(Y,or(X,Y))) ),
inference(conjunct,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
or_2,
inference(canonicalize,[],[hilbert_or_2]) ).
fof(normalize_0_37,plain,
( ~ and_3
<=> ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[and_3]) ).
fof(normalize_0_38,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_37]) ).
fof(normalize_0_39,plain,
! [X,Y] :
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
and_3,
inference(canonicalize,[],[hilbert_and_3]) ).
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,
( ~ implies_2
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[implies_2]) ).
fof(normalize_0_45,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_44]) ).
fof(normalize_0_46,plain,
! [X,Y] :
( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(conjunct,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
implies_2,
inference(canonicalize,[],[hilbert_implies_2]) ).
fof(normalize_0_48,plain,
( ~ and_2
<=> ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[and_2]) ).
fof(normalize_0_49,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_48]) ).
fof(normalize_0_50,plain,
! [X,Y] :
( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) ),
inference(conjunct,[],[normalize_0_49]) ).
fof(normalize_0_51,plain,
and_2,
inference(canonicalize,[],[hilbert_and_2]) ).
fof(normalize_0_52,plain,
( ~ or_1
<=> ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y))) ),
inference(canonicalize,[],[or_1]) ).
fof(normalize_0_53,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_52]) ).
fof(normalize_0_54,plain,
! [X,Y] :
( ~ or_1
| is_a_theorem(implies(X,or(X,Y))) ),
inference(conjunct,[],[normalize_0_53]) ).
fof(normalize_0_55,plain,
or_1,
inference(canonicalize,[],[hilbert_or_1]) ).
fof(normalize_0_56,plain,
( ~ op_possibly
| ! [X] : possibly(X) = not(necessarily(not(X))) ),
inference(canonicalize,[],[op_possibly]) ).
fof(normalize_0_57,plain,
! [X] :
( ~ op_possibly
| possibly(X) = not(necessarily(not(X))) ),
inference(clausify,[],[normalize_0_56]) ).
fof(normalize_0_58,plain,
op_possibly,
inference(canonicalize,[],[s1_0_op_possibly]) ).
fof(normalize_0_59,plain,
( ~ axiom_5
<=> ? [X] : ~ is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_0_60,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_59]) ).
fof(normalize_0_61,plain,
! [X] :
( ~ axiom_5
| is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
inference(conjunct,[],[normalize_0_60]) ).
fof(normalize_0_62,plain,
axiom_5,
inference(canonicalize,[],[km5_axiom_5]) ).
fof(normalize_0_63,plain,
( ~ modus_ponens_strict_implies
<=> ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(X)
& is_a_theorem(strict_implies(X,Y)) ) ),
inference(canonicalize,[],[modus_ponens_strict_implies]) ).
fof(normalize_0_64,plain,
! [X,Y] :
( ( ~ is_a_theorem(skolemFOFtoCNF_Y_15)
| modus_ponens_strict_implies )
& ( is_a_theorem(skolemFOFtoCNF_X_16)
| modus_ponens_strict_implies )
& ( is_a_theorem(strict_implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| modus_ponens_strict_implies )
& ( ~ is_a_theorem(X)
| ~ is_a_theorem(strict_implies(X,Y))
| ~ modus_ponens_strict_implies
| is_a_theorem(Y) ) ),
inference(clausify,[],[normalize_0_63]) ).
fof(normalize_0_65,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(strict_implies(X,Y))
| ~ modus_ponens_strict_implies
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_64]) ).
fof(normalize_0_66,plain,
( ~ is_a_theorem(skolemFOFtoCNF_Y_15)
| modus_ponens_strict_implies ),
inference(conjunct,[],[normalize_0_64]) ).
fof(normalize_0_67,plain,
( is_a_theorem(skolemFOFtoCNF_X_16)
| modus_ponens_strict_implies ),
inference(conjunct,[],[normalize_0_64]) ).
fof(normalize_0_68,plain,
( is_a_theorem(strict_implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| modus_ponens_strict_implies ),
inference(conjunct,[],[normalize_0_64]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(strict_implies(skolemFOFtoCNF_X_32,possibly(skolemFOFtoCNF_X_32)))
| axiom_m6 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ axiom_m6,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(strict_implies(skolemFOFtoCNF_X_32,possibly(skolemFOFtoCNF_X_32))),
inference(resolve,[$cnf( axiom_m6 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(X)
| ~ necessitation
| is_a_theorem(necessarily(X)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
necessitation,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(X)
| is_a_theorem(necessarily(X)) ),
inference(resolve,[$cnf( necessitation )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(X_8720,possibly(X_8720)))
| is_a_theorem(necessarily(implies(X_8720,possibly(X_8720)))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(X_8720,possibly(X_8720))))]]) ).
cnf(refute_0_7,plain,
( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
modus_tollens,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))),
inference(resolve,[$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_8719),not(X_8719)))
| is_a_theorem(implies(X_8719,possibly(X_8719))) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_8719)),bind(Y,$fot(possibly(X_8719)))]]) ).
cnf(refute_0_41,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_42,plain,
axiom_M,
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(necessarily(X),X)),
inference(resolve,[$cnf( axiom_M )],[refute_0_42,refute_0_41]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(necessarily(X_350),X_350)),
inference(subst,[],[refute_0_43:[bind(X,$fot(X_350))]]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(implies(necessarily(X_350),X_350))
| ~ is_a_theorem(necessarily(X_350))
| is_a_theorem(X_350) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(necessarily(X_350))),bind(Y,$fot(X_350))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(necessarily(X_350))
| is_a_theorem(X_350) ),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(X_350),X_350)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(necessarily(or(possibly(X_8718),not(X_8718))))
| is_a_theorem(or(possibly(X_8718),not(X_8718))) ),
inference(subst,[],[refute_0_46:[bind(X_350,$fot(or(possibly(X_8718),not(X_8718))))]]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929)))))
| is_a_theorem(necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929)))))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))))]]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(not(and(necessarily(and(not(X_328),not(X_329))),or(X_328,X_329))))
| is_a_theorem(necessarily(not(and(necessarily(and(not(X_328),not(X_329))),or(X_328,X_329))))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(not(and(necessarily(and(not(X_328),not(X_329))),or(X_328,X_329)))))]]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(necessarily(and(X_314,not(X_315))),and(X_314,not(X_315)))),
inference(subst,[],[refute_0_43:[bind(X,$fot(and(X_314,not(X_315))))]]) ).
cnf(refute_0_51,plain,
implies(X,and(X_10,not(X_11))) = not(and(X,not(and(X_10,not(X_11))))),
inference(subst,[],[refute_0_15:[bind(Y,$fot(and(X_10,not(X_11))))]]) ).
cnf(refute_0_52,plain,
implies(X_10,X_11) = not(and(X_10,not(X_11))),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_53,plain,
( implies(X_10,X_11) != not(and(X_10,not(X_11)))
| not(and(X_10,not(X_11))) = implies(X_10,X_11) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X_10,X_11))),bind(Y0,$fot(not(and(X_10,not(X_11)))))]]) ).
cnf(refute_0_54,plain,
not(and(X_10,not(X_11))) = implies(X_10,X_11),
inference(resolve,[$cnf( $equal(implies(X_10,X_11),not(and(X_10,not(X_11)))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( implies(X,and(X_10,not(X_11))) != not(and(X,not(and(X_10,not(X_11)))))
| not(and(X_10,not(X_11))) != implies(X_10,X_11)
| implies(X,and(X_10,not(X_11))) = not(and(X,implies(X_10,X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,and(X_10,not(X_11))),not(and(X,not(and(X_10,not(X_11)))))) ),[1,0,1],$fot(implies(X_10,X_11))]]) ).
cnf(refute_0_56,plain,
( implies(X,and(X_10,not(X_11))) != not(and(X,not(and(X_10,not(X_11)))))
| implies(X,and(X_10,not(X_11))) = not(and(X,implies(X_10,X_11))) ),
inference(resolve,[$cnf( $equal(not(and(X_10,not(X_11))),implies(X_10,X_11)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
implies(X,and(X_10,not(X_11))) = not(and(X,implies(X_10,X_11))),
inference(resolve,[$cnf( $equal(implies(X,and(X_10,not(X_11))),not(and(X,not(and(X_10,not(X_11)))))) )],[refute_0_51,refute_0_56]) ).
cnf(refute_0_58,plain,
implies(necessarily(and(X_314,not(X_315))),and(X_314,not(X_315))) = not(and(necessarily(and(X_314,not(X_315))),implies(X_314,X_315))),
inference(subst,[],[refute_0_57:[bind(X,$fot(necessarily(and(X_314,not(X_315))))),bind(X_10,$fot(X_314)),bind(X_11,$fot(X_315))]]) ).
cnf(refute_0_59,plain,
( implies(necessarily(and(X_314,not(X_315))),and(X_314,not(X_315))) != not(and(necessarily(and(X_314,not(X_315))),implies(X_314,X_315)))
| ~ is_a_theorem(implies(necessarily(and(X_314,not(X_315))),and(X_314,not(X_315))))
| is_a_theorem(not(and(necessarily(and(X_314,not(X_315))),implies(X_314,X_315)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(necessarily(and(X_314,not(X_315))),and(X_314,not(X_315)))) ),[0],$fot(not(and(necessarily(and(X_314,not(X_315))),implies(X_314,X_315))))]]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(implies(necessarily(and(X_314,not(X_315))),and(X_314,not(X_315))))
| is_a_theorem(not(and(necessarily(and(X_314,not(X_315))),implies(X_314,X_315)))) ),
inference(resolve,[$cnf( $equal(implies(necessarily(and(X_314,not(X_315))),and(X_314,not(X_315))),not(and(necessarily(and(X_314,not(X_315))),implies(X_314,X_315)))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
is_a_theorem(not(and(necessarily(and(X_314,not(X_315))),implies(X_314,X_315)))),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(and(X_314,not(X_315))),and(X_314,not(X_315)))) )],[refute_0_50,refute_0_60]) ).
cnf(refute_0_62,plain,
is_a_theorem(not(and(necessarily(and(not(X),not(X_327))),implies(not(X),X_327)))),
inference(subst,[],[refute_0_61:[bind(X_314,$fot(not(X))),bind(X_315,$fot(X_327))]]) ).
cnf(refute_0_63,plain,
or(X,X_327) = implies(not(X),X_327),
inference(subst,[],[refute_0_24:[bind(Y,$fot(X_327))]]) ).
cnf(refute_0_64,plain,
( or(X,X_327) != implies(not(X),X_327)
| implies(not(X),X_327) = or(X,X_327) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(or(X,X_327))),bind(Y0,$fot(implies(not(X),X_327)))]]) ).
cnf(refute_0_65,plain,
implies(not(X),X_327) = or(X,X_327),
inference(resolve,[$cnf( $equal(or(X,X_327),implies(not(X),X_327)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( implies(not(X),X_327) != or(X,X_327)
| ~ is_a_theorem(not(and(necessarily(and(not(X),not(X_327))),implies(not(X),X_327))))
| is_a_theorem(not(and(necessarily(and(not(X),not(X_327))),or(X,X_327)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(necessarily(and(not(X),not(X_327))),implies(not(X),X_327)))) ),[0,0,1],$fot(or(X,X_327))]]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(not(and(necessarily(and(not(X),not(X_327))),implies(not(X),X_327))))
| is_a_theorem(not(and(necessarily(and(not(X),not(X_327))),or(X,X_327)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_327),or(X,X_327)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
is_a_theorem(not(and(necessarily(and(not(X),not(X_327))),or(X,X_327)))),
inference(resolve,[$cnf( is_a_theorem(not(and(necessarily(and(not(X),not(X_327))),implies(not(X),X_327)))) )],[refute_0_62,refute_0_67]) ).
cnf(refute_0_69,plain,
is_a_theorem(not(and(necessarily(and(not(X_328),not(X_329))),or(X_328,X_329)))),
inference(subst,[],[refute_0_68:[bind(X,$fot(X_328)),bind(X_327,$fot(X_329))]]) ).
cnf(refute_0_70,plain,
is_a_theorem(necessarily(not(and(necessarily(and(not(X_328),not(X_329))),or(X_328,X_329))))),
inference(resolve,[$cnf( is_a_theorem(not(and(necessarily(and(not(X_328),not(X_329))),or(X_328,X_329)))) )],[refute_0_69,refute_0_49]) ).
cnf(refute_0_71,plain,
is_a_theorem(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))),
inference(subst,[],[refute_0_70:[bind(X_328,$fot(X_928)),bind(X_329,$fot(X_929))]]) ).
cnf(refute_0_72,plain,
is_a_theorem(necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929)))))),
inference(resolve,[$cnf( is_a_theorem(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))) )],[refute_0_71,refute_0_48]) ).
cnf(refute_0_73,plain,
( ~ op_strict_implies
| strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_74,plain,
op_strict_implies,
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_75,plain,
strict_implies(X,Y) = necessarily(implies(X,Y)),
inference(resolve,[$cnf( op_strict_implies )],[refute_0_74,refute_0_73]) ).
cnf(refute_0_76,plain,
strict_implies(not(X_41),Y) = necessarily(implies(not(X_41),Y)),
inference(subst,[],[refute_0_75:[bind(X,$fot(not(X_41)))]]) ).
cnf(refute_0_77,plain,
or(X_41,Y) = implies(not(X_41),Y),
inference(subst,[],[refute_0_24:[bind(X,$fot(X_41))]]) ).
cnf(refute_0_78,plain,
( or(X_41,Y) != implies(not(X_41),Y)
| implies(not(X_41),Y) = or(X_41,Y) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(or(X_41,Y))),bind(Y0,$fot(implies(not(X_41),Y)))]]) ).
cnf(refute_0_79,plain,
implies(not(X_41),Y) = or(X_41,Y),
inference(resolve,[$cnf( $equal(or(X_41,Y),implies(not(X_41),Y)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
( implies(not(X_41),Y) != or(X_41,Y)
| strict_implies(not(X_41),Y) != necessarily(implies(not(X_41),Y))
| strict_implies(not(X_41),Y) = necessarily(or(X_41,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(strict_implies(not(X_41),Y),necessarily(implies(not(X_41),Y))) ),[1,0],$fot(or(X_41,Y))]]) ).
cnf(refute_0_81,plain,
( strict_implies(not(X_41),Y) != necessarily(implies(not(X_41),Y))
| strict_implies(not(X_41),Y) = necessarily(or(X_41,Y)) ),
inference(resolve,[$cnf( $equal(implies(not(X_41),Y),or(X_41,Y)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
strict_implies(not(X_41),Y) = necessarily(or(X_41,Y)),
inference(resolve,[$cnf( $equal(strict_implies(not(X_41),Y),necessarily(implies(not(X_41),Y))) )],[refute_0_76,refute_0_81]) ).
cnf(refute_0_83,plain,
strict_implies(not(possibly(X_4328)),Y) = necessarily(or(possibly(X_4328),Y)),
inference(subst,[],[refute_0_82:[bind(X_41,$fot(possibly(X_4328)))]]) ).
cnf(refute_0_84,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_85,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_86,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_85,refute_0_84]) ).
cnf(refute_0_87,plain,
( ~ is_a_theorem(equiv(X_4324,not(not(X_4324))))
| X_4324 = not(not(X_4324)) ),
inference(subst,[],[refute_0_86:[bind(X,$fot(X_4324)),bind(Y,$fot(not(not(X_4324))))]]) ).
cnf(refute_0_88,plain,
( ~ is_a_theorem(implies(or(not(X_4323),X_4323),equiv(X_4323,not(not(X_4323)))))
| ~ is_a_theorem(or(not(X_4323),X_4323))
| is_a_theorem(equiv(X_4323,not(not(X_4323)))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(or(not(X_4323),X_4323))),bind(Y,$fot(equiv(X_4323,not(not(X_4323)))))]]) ).
cnf(refute_0_89,plain,
( ~ or_2
| is_a_theorem(implies(Y,or(X,Y))) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_90,plain,
or_2,
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_91,plain,
is_a_theorem(implies(Y,or(X,Y))),
inference(resolve,[$cnf( or_2 )],[refute_0_90,refute_0_89]) ).
cnf(refute_0_92,plain,
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_93,plain,
and_3,
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_94,plain,
is_a_theorem(implies(X,implies(Y,and(X,Y)))),
inference(resolve,[$cnf( and_3 )],[refute_0_93,refute_0_92]) ).
cnf(refute_0_95,plain,
is_a_theorem(implies(X_349,implies(Y,and(X_349,Y)))),
inference(subst,[],[refute_0_94:[bind(X,$fot(X_349))]]) ).
cnf(refute_0_96,plain,
( ~ is_a_theorem(X_349)
| ~ is_a_theorem(implies(X_349,implies(Y,and(X_349,Y))))
| is_a_theorem(implies(Y,and(X_349,Y))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_349)),bind(Y,$fot(implies(Y,and(X_349,Y))))]]) ).
cnf(refute_0_97,plain,
( ~ is_a_theorem(X_349)
| is_a_theorem(implies(Y,and(X_349,Y))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_349,implies(Y,and(X_349,Y)))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
( ~ is_a_theorem(implies(Y,or(X,Y)))
| is_a_theorem(implies(X_527,and(implies(Y,or(X,Y)),X_527))) ),
inference(subst,[],[refute_0_97:[bind(Y,$fot(X_527)),bind(X_349,$fot(implies(Y,or(X,Y))))]]) ).
cnf(refute_0_99,plain,
is_a_theorem(implies(X_527,and(implies(Y,or(X,Y)),X_527))),
inference(resolve,[$cnf( is_a_theorem(implies(Y,or(X,Y))) )],[refute_0_91,refute_0_98]) ).
cnf(refute_0_100,plain,
is_a_theorem(implies(implies(or(X_2762,X_2763),X_2763),and(implies(X_2763,or(X_2762,X_2763)),implies(or(X_2762,X_2763),X_2763)))),
inference(subst,[],[refute_0_99:[bind(X,$fot(X_2762)),bind(Y,$fot(X_2763)),bind(X_527,$fot(implies(or(X_2762,X_2763),X_2763)))]]) ).
cnf(refute_0_101,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_102,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_43]) ).
cnf(refute_0_103,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_102,refute_0_101]) ).
cnf(refute_0_104,plain,
equiv(X_2763,or(X_2762,X_2763)) = and(implies(X_2763,or(X_2762,X_2763)),implies(or(X_2762,X_2763),X_2763)),
inference(subst,[],[refute_0_103:[bind(X,$fot(X_2763)),bind(Y,$fot(or(X_2762,X_2763)))]]) ).
cnf(refute_0_105,plain,
( equiv(X_2763,or(X_2762,X_2763)) != and(implies(X_2763,or(X_2762,X_2763)),implies(or(X_2762,X_2763),X_2763))
| and(implies(X_2763,or(X_2762,X_2763)),implies(or(X_2762,X_2763),X_2763)) = equiv(X_2763,or(X_2762,X_2763)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(equiv(X_2763,or(X_2762,X_2763)))),bind(Y0,$fot(and(implies(X_2763,or(X_2762,X_2763)),implies(or(X_2762,X_2763),X_2763))))]]) ).
cnf(refute_0_106,plain,
and(implies(X_2763,or(X_2762,X_2763)),implies(or(X_2762,X_2763),X_2763)) = equiv(X_2763,or(X_2762,X_2763)),
inference(resolve,[$cnf( $equal(equiv(X_2763,or(X_2762,X_2763)),and(implies(X_2763,or(X_2762,X_2763)),implies(or(X_2762,X_2763),X_2763))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
( and(implies(X_2763,or(X_2762,X_2763)),implies(or(X_2762,X_2763),X_2763)) != equiv(X_2763,or(X_2762,X_2763))
| ~ is_a_theorem(implies(implies(or(X_2762,X_2763),X_2763),and(implies(X_2763,or(X_2762,X_2763)),implies(or(X_2762,X_2763),X_2763))))
| is_a_theorem(implies(implies(or(X_2762,X_2763),X_2763),equiv(X_2763,or(X_2762,X_2763)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(or(X_2762,X_2763),X_2763),and(implies(X_2763,or(X_2762,X_2763)),implies(or(X_2762,X_2763),X_2763)))) ),[0,1],$fot(equiv(X_2763,or(X_2762,X_2763)))]]) ).
cnf(refute_0_108,plain,
( ~ is_a_theorem(implies(implies(or(X_2762,X_2763),X_2763),and(implies(X_2763,or(X_2762,X_2763)),implies(or(X_2762,X_2763),X_2763))))
| is_a_theorem(implies(implies(or(X_2762,X_2763),X_2763),equiv(X_2763,or(X_2762,X_2763)))) ),
inference(resolve,[$cnf( $equal(and(implies(X_2763,or(X_2762,X_2763)),implies(or(X_2762,X_2763),X_2763)),equiv(X_2763,or(X_2762,X_2763))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
is_a_theorem(implies(implies(or(X_2762,X_2763),X_2763),equiv(X_2763,or(X_2762,X_2763)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_2762,X_2763),X_2763),and(implies(X_2763,or(X_2762,X_2763)),implies(or(X_2762,X_2763),X_2763)))) )],[refute_0_100,refute_0_108]) ).
cnf(refute_0_110,plain,
is_a_theorem(implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,or(X_4322,X_4322)))),
inference(subst,[],[refute_0_109:[bind(X_2762,$fot(X_4322)),bind(X_2763,$fot(X_4322))]]) ).
cnf(refute_0_111,plain,
implies(not(Y),Y) = not(and(not(Y),not(Y))),
inference(subst,[],[refute_0_15:[bind(X,$fot(not(Y)))]]) ).
cnf(refute_0_112,plain,
( ~ is_a_theorem(equiv(X_2163,and(X_2163,X_2163)))
| X_2163 = and(X_2163,X_2163) ),
inference(subst,[],[refute_0_86:[bind(X,$fot(X_2163)),bind(Y,$fot(and(X_2163,X_2163)))]]) ).
cnf(refute_0_113,plain,
( ~ is_a_theorem(implies(and(X_2162,X_2162),X_2162))
| ~ is_a_theorem(implies(implies(and(X_2162,X_2162),X_2162),equiv(X_2162,and(X_2162,X_2162))))
| is_a_theorem(equiv(X_2162,and(X_2162,X_2162))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(implies(and(X_2162,X_2162),X_2162))),bind(Y,$fot(equiv(X_2162,and(X_2162,X_2162))))]]) ).
cnf(refute_0_114,plain,
( ~ is_a_theorem(implies(X_1054,and(X_1054,X_1054)))
| is_a_theorem(implies(Y,and(implies(X_1054,and(X_1054,X_1054)),Y))) ),
inference(subst,[],[refute_0_97:[bind(X_349,$fot(implies(X_1054,and(X_1054,X_1054))))]]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(X_1050,implies(X_1050,and(X_1050,X_1050)))),
inference(subst,[],[refute_0_94:[bind(X,$fot(X_1050)),bind(Y,$fot(X_1050))]]) ).
cnf(refute_0_116,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_117,plain,
implies_2,
inference(canonicalize,[],[normalize_0_47]) ).
cnf(refute_0_118,plain,
is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))),
inference(resolve,[$cnf( implies_2 )],[refute_0_117,refute_0_116]) ).
cnf(refute_0_119,plain,
( ~ is_a_theorem(implies(X,implies(X,Y)))
| ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| is_a_theorem(implies(X,Y)) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(implies(X,implies(X,Y)))),bind(Y,$fot(implies(X,Y)))]]) ).
cnf(refute_0_120,plain,
( ~ is_a_theorem(implies(X,implies(X,Y)))
| is_a_theorem(implies(X,Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( ~ is_a_theorem(implies(X_1050,implies(X_1050,and(X_1050,X_1050))))
| is_a_theorem(implies(X_1050,and(X_1050,X_1050))) ),
inference(subst,[],[refute_0_120:[bind(X,$fot(X_1050)),bind(Y,$fot(and(X_1050,X_1050)))]]) ).
cnf(refute_0_122,plain,
is_a_theorem(implies(X_1050,and(X_1050,X_1050))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1050,implies(X_1050,and(X_1050,X_1050)))) )],[refute_0_115,refute_0_121]) ).
cnf(refute_0_123,plain,
is_a_theorem(implies(X_1054,and(X_1054,X_1054))),
inference(subst,[],[refute_0_122:[bind(X_1050,$fot(X_1054))]]) ).
cnf(refute_0_124,plain,
is_a_theorem(implies(Y,and(implies(X_1054,and(X_1054,X_1054)),Y))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1054,and(X_1054,X_1054))) )],[refute_0_123,refute_0_114]) ).
cnf(refute_0_125,plain,
is_a_theorem(implies(implies(and(X_2159,X_2159),X_2159),and(implies(X_2159,and(X_2159,X_2159)),implies(and(X_2159,X_2159),X_2159)))),
inference(subst,[],[refute_0_124:[bind(Y,$fot(implies(and(X_2159,X_2159),X_2159))),bind(X_1054,$fot(X_2159))]]) ).
cnf(refute_0_126,plain,
equiv(X_2159,and(X_2159,X_2159)) = and(implies(X_2159,and(X_2159,X_2159)),implies(and(X_2159,X_2159),X_2159)),
inference(subst,[],[refute_0_103:[bind(X,$fot(X_2159)),bind(Y,$fot(and(X_2159,X_2159)))]]) ).
cnf(refute_0_127,plain,
( equiv(X_2159,and(X_2159,X_2159)) != and(implies(X_2159,and(X_2159,X_2159)),implies(and(X_2159,X_2159),X_2159))
| and(implies(X_2159,and(X_2159,X_2159)),implies(and(X_2159,X_2159),X_2159)) = equiv(X_2159,and(X_2159,X_2159)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(equiv(X_2159,and(X_2159,X_2159)))),bind(Y0,$fot(and(implies(X_2159,and(X_2159,X_2159)),implies(and(X_2159,X_2159),X_2159))))]]) ).
cnf(refute_0_128,plain,
and(implies(X_2159,and(X_2159,X_2159)),implies(and(X_2159,X_2159),X_2159)) = equiv(X_2159,and(X_2159,X_2159)),
inference(resolve,[$cnf( $equal(equiv(X_2159,and(X_2159,X_2159)),and(implies(X_2159,and(X_2159,X_2159)),implies(and(X_2159,X_2159),X_2159))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
( and(implies(X_2159,and(X_2159,X_2159)),implies(and(X_2159,X_2159),X_2159)) != equiv(X_2159,and(X_2159,X_2159))
| ~ is_a_theorem(implies(implies(and(X_2159,X_2159),X_2159),and(implies(X_2159,and(X_2159,X_2159)),implies(and(X_2159,X_2159),X_2159))))
| is_a_theorem(implies(implies(and(X_2159,X_2159),X_2159),equiv(X_2159,and(X_2159,X_2159)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(and(X_2159,X_2159),X_2159),and(implies(X_2159,and(X_2159,X_2159)),implies(and(X_2159,X_2159),X_2159)))) ),[0,1],$fot(equiv(X_2159,and(X_2159,X_2159)))]]) ).
cnf(refute_0_130,plain,
( ~ is_a_theorem(implies(implies(and(X_2159,X_2159),X_2159),and(implies(X_2159,and(X_2159,X_2159)),implies(and(X_2159,X_2159),X_2159))))
| is_a_theorem(implies(implies(and(X_2159,X_2159),X_2159),equiv(X_2159,and(X_2159,X_2159)))) ),
inference(resolve,[$cnf( $equal(and(implies(X_2159,and(X_2159,X_2159)),implies(and(X_2159,X_2159),X_2159)),equiv(X_2159,and(X_2159,X_2159))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
is_a_theorem(implies(implies(and(X_2159,X_2159),X_2159),equiv(X_2159,and(X_2159,X_2159)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_2159,X_2159),X_2159),and(implies(X_2159,and(X_2159,X_2159)),implies(and(X_2159,X_2159),X_2159)))) )],[refute_0_125,refute_0_130]) ).
cnf(refute_0_132,plain,
is_a_theorem(implies(implies(and(X_2162,X_2162),X_2162),equiv(X_2162,and(X_2162,X_2162)))),
inference(subst,[],[refute_0_131:[bind(X_2159,$fot(X_2162))]]) ).
cnf(refute_0_133,plain,
( ~ is_a_theorem(implies(and(X_2162,X_2162),X_2162))
| is_a_theorem(equiv(X_2162,and(X_2162,X_2162))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_2162,X_2162),X_2162),equiv(X_2162,and(X_2162,X_2162)))) )],[refute_0_132,refute_0_113]) ).
cnf(refute_0_134,plain,
( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[normalize_0_50]) ).
cnf(refute_0_135,plain,
and_2,
inference(canonicalize,[],[normalize_0_51]) ).
cnf(refute_0_136,plain,
is_a_theorem(implies(and(X,Y),Y)),
inference(resolve,[$cnf( and_2 )],[refute_0_135,refute_0_134]) ).
cnf(refute_0_137,plain,
is_a_theorem(implies(and(X_2162,X_2162),X_2162)),
inference(subst,[],[refute_0_136:[bind(X,$fot(X_2162)),bind(Y,$fot(X_2162))]]) ).
cnf(refute_0_138,plain,
is_a_theorem(equiv(X_2162,and(X_2162,X_2162))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_2162,X_2162),X_2162)) )],[refute_0_137,refute_0_133]) ).
cnf(refute_0_139,plain,
is_a_theorem(equiv(X_2163,and(X_2163,X_2163))),
inference(subst,[],[refute_0_138:[bind(X_2162,$fot(X_2163))]]) ).
cnf(refute_0_140,plain,
X_2163 = and(X_2163,X_2163),
inference(resolve,[$cnf( is_a_theorem(equiv(X_2163,and(X_2163,X_2163))) )],[refute_0_139,refute_0_112]) ).
cnf(refute_0_141,plain,
not(Y) = and(not(Y),not(Y)),
inference(subst,[],[refute_0_140:[bind(X_2163,$fot(not(Y)))]]) ).
cnf(refute_0_142,plain,
( not(Y) != and(not(Y),not(Y))
| and(not(Y),not(Y)) = not(Y) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(not(Y))),bind(Y0,$fot(and(not(Y),not(Y))))]]) ).
cnf(refute_0_143,plain,
and(not(Y),not(Y)) = not(Y),
inference(resolve,[$cnf( $equal(not(Y),and(not(Y),not(Y))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
( and(not(Y),not(Y)) != not(Y)
| implies(not(Y),Y) != not(and(not(Y),not(Y)))
| implies(not(Y),Y) = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(Y),Y),not(and(not(Y),not(Y)))) ),[1,0],$fot(not(Y))]]) ).
cnf(refute_0_145,plain,
( implies(not(Y),Y) != not(and(not(Y),not(Y)))
| implies(not(Y),Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(and(not(Y),not(Y)),not(Y)) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
implies(not(Y),Y) = not(not(Y)),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),not(and(not(Y),not(Y)))) )],[refute_0_111,refute_0_145]) ).
cnf(refute_0_147,plain,
implies(not(Y),Y) = or(Y,Y),
inference(subst,[],[refute_0_26:[bind(X,$fot(Y))]]) ).
cnf(refute_0_148,plain,
( implies(not(Y),Y) != not(not(Y))
| implies(not(Y),Y) != or(Y,Y)
| or(Y,Y) = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(Y),Y),not(not(Y))) ),[0],$fot(or(Y,Y))]]) ).
cnf(refute_0_149,plain,
( implies(not(Y),Y) != not(not(Y))
| or(Y,Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),or(Y,Y)) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
or(Y,Y) = not(not(Y)),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),not(not(Y))) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
or(X_4322,X_4322) = not(not(X_4322)),
inference(subst,[],[refute_0_150:[bind(Y,$fot(X_4322))]]) ).
cnf(refute_0_152,plain,
( or(X_4322,X_4322) != not(not(X_4322))
| ~ is_a_theorem(implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,or(X_4322,X_4322))))
| is_a_theorem(implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,or(X_4322,X_4322)))) ),[0,1,1],$fot(not(not(X_4322)))]]) ).
cnf(refute_0_153,plain,
( ~ is_a_theorem(implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,or(X_4322,X_4322))))
| is_a_theorem(implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322))))) ),
inference(resolve,[$cnf( $equal(or(X_4322,X_4322),not(not(X_4322))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
is_a_theorem(implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,or(X_4322,X_4322)))) )],[refute_0_110,refute_0_153]) ).
cnf(refute_0_155,plain,
implies(not(not(X_4322)),X_4322) = or(not(X_4322),X_4322),
inference(subst,[],[refute_0_26:[bind(X,$fot(not(X_4322))),bind(Y,$fot(X_4322))]]) ).
cnf(refute_0_156,plain,
implies(or(X_4322,X_4322),X_4322) = implies(or(X_4322,X_4322),X_4322),
introduced(tautology,[refl,[$fot(implies(or(X_4322,X_4322),X_4322))]]) ).
cnf(refute_0_157,plain,
( implies(or(X_4322,X_4322),X_4322) != implies(or(X_4322,X_4322),X_4322)
| or(X_4322,X_4322) != not(not(X_4322))
| implies(or(X_4322,X_4322),X_4322) = implies(not(not(X_4322)),X_4322) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_4322,X_4322),X_4322),implies(or(X_4322,X_4322),X_4322)) ),[1,0],$fot(not(not(X_4322)))]]) ).
cnf(refute_0_158,plain,
( or(X_4322,X_4322) != not(not(X_4322))
| implies(or(X_4322,X_4322),X_4322) = implies(not(not(X_4322)),X_4322) ),
inference(resolve,[$cnf( $equal(implies(or(X_4322,X_4322),X_4322),implies(or(X_4322,X_4322),X_4322)) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
implies(or(X_4322,X_4322),X_4322) = implies(not(not(X_4322)),X_4322),
inference(resolve,[$cnf( $equal(or(X_4322,X_4322),not(not(X_4322))) )],[refute_0_151,refute_0_158]) ).
cnf(refute_0_160,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_161,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_18,refute_0_160]) ).
cnf(refute_0_162,plain,
( implies(not(not(X_4322)),X_4322) != or(not(X_4322),X_4322)
| implies(or(X_4322,X_4322),X_4322) != implies(not(not(X_4322)),X_4322)
| implies(or(X_4322,X_4322),X_4322) = or(not(X_4322),X_4322) ),
inference(subst,[],[refute_0_161:[bind(X0,$fot(implies(or(X_4322,X_4322),X_4322))),bind(Y0,$fot(implies(not(not(X_4322)),X_4322))),bind(Z,$fot(or(not(X_4322),X_4322)))]]) ).
cnf(refute_0_163,plain,
( implies(not(not(X_4322)),X_4322) != or(not(X_4322),X_4322)
| implies(or(X_4322,X_4322),X_4322) = or(not(X_4322),X_4322) ),
inference(resolve,[$cnf( $equal(implies(or(X_4322,X_4322),X_4322),implies(not(not(X_4322)),X_4322)) )],[refute_0_159,refute_0_162]) ).
cnf(refute_0_164,plain,
implies(or(X_4322,X_4322),X_4322) = or(not(X_4322),X_4322),
inference(resolve,[$cnf( $equal(implies(not(not(X_4322)),X_4322),or(not(X_4322),X_4322)) )],[refute_0_155,refute_0_163]) ).
cnf(refute_0_165,plain,
implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322)))) = implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322)))),
introduced(tautology,[refl,[$fot(implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322)))))]]) ).
cnf(refute_0_166,plain,
( implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322)))) != implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322))))
| implies(or(X_4322,X_4322),X_4322) != or(not(X_4322),X_4322)
| implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322)))) = implies(or(not(X_4322),X_4322),equiv(X_4322,not(not(X_4322)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322)))),implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322))))) ),[1,0],$fot(or(not(X_4322),X_4322))]]) ).
cnf(refute_0_167,plain,
( implies(or(X_4322,X_4322),X_4322) != or(not(X_4322),X_4322)
| implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322)))) = implies(or(not(X_4322),X_4322),equiv(X_4322,not(not(X_4322)))) ),
inference(resolve,[$cnf( $equal(implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322)))),implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322))))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322)))) = implies(or(not(X_4322),X_4322),equiv(X_4322,not(not(X_4322)))),
inference(resolve,[$cnf( $equal(implies(or(X_4322,X_4322),X_4322),or(not(X_4322),X_4322)) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
( implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322)))) != implies(or(not(X_4322),X_4322),equiv(X_4322,not(not(X_4322))))
| ~ is_a_theorem(implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322)))))
| is_a_theorem(implies(or(not(X_4322),X_4322),equiv(X_4322,not(not(X_4322))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322))))) ),[0],$fot(implies(or(not(X_4322),X_4322),equiv(X_4322,not(not(X_4322)))))]]) ).
cnf(refute_0_170,plain,
( ~ is_a_theorem(implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322)))))
| is_a_theorem(implies(or(not(X_4322),X_4322),equiv(X_4322,not(not(X_4322))))) ),
inference(resolve,[$cnf( $equal(implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322)))),implies(or(not(X_4322),X_4322),equiv(X_4322,not(not(X_4322))))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
is_a_theorem(implies(or(not(X_4322),X_4322),equiv(X_4322,not(not(X_4322))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_4322,X_4322),X_4322),equiv(X_4322,not(not(X_4322))))) )],[refute_0_154,refute_0_170]) ).
cnf(refute_0_172,plain,
is_a_theorem(implies(or(not(X_4323),X_4323),equiv(X_4323,not(not(X_4323))))),
inference(subst,[],[refute_0_171:[bind(X_4322,$fot(X_4323))]]) ).
cnf(refute_0_173,plain,
( ~ is_a_theorem(or(not(X_4323),X_4323))
| is_a_theorem(equiv(X_4323,not(not(X_4323)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X_4323),X_4323),equiv(X_4323,not(not(X_4323))))) )],[refute_0_172,refute_0_88]) ).
cnf(refute_0_174,plain,
is_a_theorem(implies(or(Y,not(not(X_41))),implies(not(X_41),Y))),
inference(subst,[],[refute_0_34:[bind(X,$fot(not(X_41)))]]) ).
cnf(refute_0_175,plain,
( implies(not(X_41),Y) != or(X_41,Y)
| ~ is_a_theorem(implies(or(Y,not(not(X_41))),implies(not(X_41),Y)))
| is_a_theorem(implies(or(Y,not(not(X_41))),or(X_41,Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(Y,not(not(X_41))),implies(not(X_41),Y))) ),[0,1],$fot(or(X_41,Y))]]) ).
cnf(refute_0_176,plain,
( ~ is_a_theorem(implies(or(Y,not(not(X_41))),implies(not(X_41),Y)))
| is_a_theorem(implies(or(Y,not(not(X_41))),or(X_41,Y))) ),
inference(resolve,[$cnf( $equal(implies(not(X_41),Y),or(X_41,Y)) )],[refute_0_79,refute_0_175]) ).
cnf(refute_0_177,plain,
is_a_theorem(implies(or(Y,not(not(X_41))),or(X_41,Y))),
inference(resolve,[$cnf( is_a_theorem(implies(or(Y,not(not(X_41))),implies(not(X_41),Y))) )],[refute_0_174,refute_0_176]) ).
cnf(refute_0_178,plain,
( ~ is_a_theorem(implies(or(Y,not(not(X_41))),or(X_41,Y)))
| ~ is_a_theorem(or(Y,not(not(X_41))))
| is_a_theorem(or(X_41,Y)) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(or(Y,not(not(X_41))))),bind(Y,$fot(or(X_41,Y)))]]) ).
cnf(refute_0_179,plain,
( ~ is_a_theorem(or(Y,not(not(X_41))))
| is_a_theorem(or(X_41,Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(Y,not(not(X_41))),or(X_41,Y))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
( ~ is_a_theorem(or(X_2178,not(not(not(X_2178)))))
| is_a_theorem(or(not(X_2178),X_2178)) ),
inference(subst,[],[refute_0_179:[bind(Y,$fot(X_2178)),bind(X_41,$fot(not(X_2178)))]]) ).
cnf(refute_0_181,plain,
( ~ or_1
| is_a_theorem(implies(X,or(X,Y))) ),
inference(canonicalize,[],[normalize_0_54]) ).
cnf(refute_0_182,plain,
or_1,
inference(canonicalize,[],[normalize_0_55]) ).
cnf(refute_0_183,plain,
is_a_theorem(implies(X,or(X,Y))),
inference(resolve,[$cnf( or_1 )],[refute_0_182,refute_0_181]) ).
cnf(refute_0_184,plain,
is_a_theorem(implies(not(X_41),or(not(X_41),Y))),
inference(subst,[],[refute_0_183:[bind(X,$fot(not(X_41)))]]) ).
cnf(refute_0_185,plain,
or(X_41,or(not(X_41),Y)) = implies(not(X_41),or(not(X_41),Y)),
inference(subst,[],[refute_0_24:[bind(X,$fot(X_41)),bind(Y,$fot(or(not(X_41),Y)))]]) ).
cnf(refute_0_186,plain,
( or(X_41,or(not(X_41),Y)) != implies(not(X_41),or(not(X_41),Y))
| implies(not(X_41),or(not(X_41),Y)) = or(X_41,or(not(X_41),Y)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(or(X_41,or(not(X_41),Y)))),bind(Y0,$fot(implies(not(X_41),or(not(X_41),Y))))]]) ).
cnf(refute_0_187,plain,
implies(not(X_41),or(not(X_41),Y)) = or(X_41,or(not(X_41),Y)),
inference(resolve,[$cnf( $equal(or(X_41,or(not(X_41),Y)),implies(not(X_41),or(not(X_41),Y))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
( implies(not(X_41),or(not(X_41),Y)) != or(X_41,or(not(X_41),Y))
| ~ is_a_theorem(implies(not(X_41),or(not(X_41),Y)))
| is_a_theorem(or(X_41,or(not(X_41),Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X_41),or(not(X_41),Y))) ),[0],$fot(or(X_41,or(not(X_41),Y)))]]) ).
cnf(refute_0_189,plain,
( ~ is_a_theorem(implies(not(X_41),or(not(X_41),Y)))
| is_a_theorem(or(X_41,or(not(X_41),Y))) ),
inference(resolve,[$cnf( $equal(implies(not(X_41),or(not(X_41),Y)),or(X_41,or(not(X_41),Y))) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
is_a_theorem(or(X_41,or(not(X_41),Y))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_41),or(not(X_41),Y))) )],[refute_0_184,refute_0_189]) ).
cnf(refute_0_191,plain,
is_a_theorem(or(X_41,or(not(X_41),not(X_41)))),
inference(subst,[],[refute_0_190:[bind(Y,$fot(not(X_41)))]]) ).
cnf(refute_0_192,plain,
or(not(X_41),not(X_41)) = not(not(not(X_41))),
inference(subst,[],[refute_0_150:[bind(Y,$fot(not(X_41)))]]) ).
cnf(refute_0_193,plain,
( or(not(X_41),not(X_41)) != not(not(not(X_41)))
| ~ is_a_theorem(or(X_41,or(not(X_41),not(X_41))))
| is_a_theorem(or(X_41,not(not(not(X_41))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_41,or(not(X_41),not(X_41)))) ),[0,1],$fot(not(not(not(X_41))))]]) ).
cnf(refute_0_194,plain,
( ~ is_a_theorem(or(X_41,or(not(X_41),not(X_41))))
| is_a_theorem(or(X_41,not(not(not(X_41))))) ),
inference(resolve,[$cnf( $equal(or(not(X_41),not(X_41)),not(not(not(X_41)))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
is_a_theorem(or(X_41,not(not(not(X_41))))),
inference(resolve,[$cnf( is_a_theorem(or(X_41,or(not(X_41),not(X_41)))) )],[refute_0_191,refute_0_194]) ).
cnf(refute_0_196,plain,
is_a_theorem(or(X_2178,not(not(not(X_2178))))),
inference(subst,[],[refute_0_195:[bind(X_41,$fot(X_2178))]]) ).
cnf(refute_0_197,plain,
is_a_theorem(or(not(X_2178),X_2178)),
inference(resolve,[$cnf( is_a_theorem(or(X_2178,not(not(not(X_2178))))) )],[refute_0_196,refute_0_180]) ).
cnf(refute_0_198,plain,
is_a_theorem(or(not(X_4323),X_4323)),
inference(subst,[],[refute_0_197:[bind(X_2178,$fot(X_4323))]]) ).
cnf(refute_0_199,plain,
is_a_theorem(equiv(X_4323,not(not(X_4323)))),
inference(resolve,[$cnf( is_a_theorem(or(not(X_4323),X_4323)) )],[refute_0_198,refute_0_173]) ).
cnf(refute_0_200,plain,
is_a_theorem(equiv(X_4324,not(not(X_4324)))),
inference(subst,[],[refute_0_199:[bind(X_4323,$fot(X_4324))]]) ).
cnf(refute_0_201,plain,
X_4324 = not(not(X_4324)),
inference(resolve,[$cnf( is_a_theorem(equiv(X_4324,not(not(X_4324)))) )],[refute_0_200,refute_0_87]) ).
cnf(refute_0_202,plain,
necessarily(not(X)) = not(not(necessarily(not(X)))),
inference(subst,[],[refute_0_201:[bind(X_4324,$fot(necessarily(not(X))))]]) ).
cnf(refute_0_203,plain,
( ~ op_possibly
| possibly(X) = not(necessarily(not(X))) ),
inference(canonicalize,[],[normalize_0_57]) ).
cnf(refute_0_204,plain,
op_possibly,
inference(canonicalize,[],[normalize_0_58]) ).
cnf(refute_0_205,plain,
possibly(X) = not(necessarily(not(X))),
inference(resolve,[$cnf( op_possibly )],[refute_0_204,refute_0_203]) ).
cnf(refute_0_206,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_207,plain,
not(necessarily(not(X))) = possibly(X),
inference(resolve,[$cnf( $equal(possibly(X),not(necessarily(not(X)))) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
( necessarily(not(X)) != not(not(necessarily(not(X))))
| not(necessarily(not(X))) != possibly(X)
| necessarily(not(X)) = not(possibly(X)) ),
introduced(tautology,[equality,[$cnf( $equal(necessarily(not(X)),not(not(necessarily(not(X))))) ),[1,0],$fot(possibly(X))]]) ).
cnf(refute_0_209,plain,
( necessarily(not(X)) != not(not(necessarily(not(X))))
| necessarily(not(X)) = not(possibly(X)) ),
inference(resolve,[$cnf( $equal(not(necessarily(not(X))),possibly(X)) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
necessarily(not(X)) = not(possibly(X)),
inference(resolve,[$cnf( $equal(necessarily(not(X)),not(not(necessarily(not(X))))) )],[refute_0_202,refute_0_209]) ).
cnf(refute_0_211,plain,
necessarily(not(X_4328)) = not(possibly(X_4328)),
inference(subst,[],[refute_0_210:[bind(X,$fot(X_4328))]]) ).
cnf(refute_0_212,plain,
( necessarily(not(X_4328)) != not(possibly(X_4328))
| not(possibly(X_4328)) = necessarily(not(X_4328)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(necessarily(not(X_4328)))),bind(Y0,$fot(not(possibly(X_4328))))]]) ).
cnf(refute_0_213,plain,
not(possibly(X_4328)) = necessarily(not(X_4328)),
inference(resolve,[$cnf( $equal(necessarily(not(X_4328)),not(possibly(X_4328))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
( not(possibly(X_4328)) != necessarily(not(X_4328))
| strict_implies(not(possibly(X_4328)),Y) != necessarily(or(possibly(X_4328),Y))
| strict_implies(necessarily(not(X_4328)),Y) = necessarily(or(possibly(X_4328),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(strict_implies(not(possibly(X_4328)),Y),necessarily(or(possibly(X_4328),Y))) ),[0,0],$fot(necessarily(not(X_4328)))]]) ).
cnf(refute_0_215,plain,
( strict_implies(not(possibly(X_4328)),Y) != necessarily(or(possibly(X_4328),Y))
| strict_implies(necessarily(not(X_4328)),Y) = necessarily(or(possibly(X_4328),Y)) ),
inference(resolve,[$cnf( $equal(not(possibly(X_4328)),necessarily(not(X_4328))) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
strict_implies(necessarily(not(X_4328)),Y) = necessarily(or(possibly(X_4328),Y)),
inference(resolve,[$cnf( $equal(strict_implies(not(possibly(X_4328)),Y),necessarily(or(possibly(X_4328),Y))) )],[refute_0_83,refute_0_215]) ).
cnf(refute_0_217,plain,
strict_implies(necessarily(not(or(X_928,X_929))),not(or(X_928,X_929))) = necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929)))),
inference(subst,[],[refute_0_216:[bind(Y,$fot(not(or(X_928,X_929)))),bind(X_4328,$fot(or(X_928,X_929)))]]) ).
cnf(refute_0_218,plain,
implies(not(X_928),X_929) = or(X_928,X_929),
inference(subst,[],[refute_0_26:[bind(X,$fot(X_928)),bind(Y,$fot(X_929))]]) ).
cnf(refute_0_219,plain,
not(implies(not(X_928),X_929)) = not(implies(not(X_928),X_929)),
introduced(tautology,[refl,[$fot(not(implies(not(X_928),X_929)))]]) ).
cnf(refute_0_220,plain,
( implies(not(X_928),X_929) != or(X_928,X_929)
| not(implies(not(X_928),X_929)) != not(implies(not(X_928),X_929))
| not(implies(not(X_928),X_929)) = not(or(X_928,X_929)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(X_928),X_929)),not(implies(not(X_928),X_929))) ),[1,0],$fot(or(X_928,X_929))]]) ).
cnf(refute_0_221,plain,
( implies(not(X_928),X_929) != or(X_928,X_929)
| not(implies(not(X_928),X_929)) = not(or(X_928,X_929)) ),
inference(resolve,[$cnf( $equal(not(implies(not(X_928),X_929)),not(implies(not(X_928),X_929))) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
not(implies(not(X_928),X_929)) = not(or(X_928,X_929)),
inference(resolve,[$cnf( $equal(implies(not(X_928),X_929),or(X_928,X_929)) )],[refute_0_218,refute_0_221]) ).
cnf(refute_0_223,plain,
and(X,not(Y)) = not(not(and(X,not(Y)))),
inference(subst,[],[refute_0_201:[bind(X_4324,$fot(and(X,not(Y))))]]) ).
cnf(refute_0_224,plain,
( and(X,not(Y)) != not(not(and(X,not(Y))))
| not(and(X,not(Y))) != implies(X,Y)
| and(X,not(Y)) = not(implies(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,not(Y)),not(not(and(X,not(Y))))) ),[1,0],$fot(implies(X,Y))]]) ).
cnf(refute_0_225,plain,
( and(X,not(Y)) != not(not(and(X,not(Y))))
| and(X,not(Y)) = not(implies(X,Y)) ),
inference(resolve,[$cnf( $equal(not(and(X,not(Y))),implies(X,Y)) )],[refute_0_20,refute_0_224]) ).
cnf(refute_0_226,plain,
and(X,not(Y)) = not(implies(X,Y)),
inference(resolve,[$cnf( $equal(and(X,not(Y)),not(not(and(X,not(Y))))) )],[refute_0_223,refute_0_225]) ).
cnf(refute_0_227,plain,
and(not(X_928),not(X_929)) = not(implies(not(X_928),X_929)),
inference(subst,[],[refute_0_226:[bind(X,$fot(not(X_928))),bind(Y,$fot(X_929))]]) ).
cnf(refute_0_228,plain,
( and(not(X_928),not(X_929)) != not(implies(not(X_928),X_929))
| not(implies(not(X_928),X_929)) != not(or(X_928,X_929))
| and(not(X_928),not(X_929)) = not(or(X_928,X_929)) ),
inference(subst,[],[refute_0_161:[bind(X0,$fot(and(not(X_928),not(X_929)))),bind(Y0,$fot(not(implies(not(X_928),X_929)))),bind(Z,$fot(not(or(X_928,X_929))))]]) ).
cnf(refute_0_229,plain,
( not(implies(not(X_928),X_929)) != not(or(X_928,X_929))
| and(not(X_928),not(X_929)) = not(or(X_928,X_929)) ),
inference(resolve,[$cnf( $equal(and(not(X_928),not(X_929)),not(implies(not(X_928),X_929))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
and(not(X_928),not(X_929)) = not(or(X_928,X_929)),
inference(resolve,[$cnf( $equal(not(implies(not(X_928),X_929)),not(or(X_928,X_929))) )],[refute_0_222,refute_0_229]) ).
cnf(refute_0_231,plain,
necessarily(and(not(X_928),not(X_929))) = necessarily(and(not(X_928),not(X_929))),
introduced(tautology,[refl,[$fot(necessarily(and(not(X_928),not(X_929))))]]) ).
cnf(refute_0_232,plain,
( and(not(X_928),not(X_929)) != not(or(X_928,X_929))
| necessarily(and(not(X_928),not(X_929))) != necessarily(and(not(X_928),not(X_929)))
| necessarily(and(not(X_928),not(X_929))) = necessarily(not(or(X_928,X_929))) ),
introduced(tautology,[equality,[$cnf( $equal(necessarily(and(not(X_928),not(X_929))),necessarily(and(not(X_928),not(X_929)))) ),[1,0],$fot(not(or(X_928,X_929)))]]) ).
cnf(refute_0_233,plain,
( and(not(X_928),not(X_929)) != not(or(X_928,X_929))
| necessarily(and(not(X_928),not(X_929))) = necessarily(not(or(X_928,X_929))) ),
inference(resolve,[$cnf( $equal(necessarily(and(not(X_928),not(X_929))),necessarily(and(not(X_928),not(X_929)))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
necessarily(and(not(X_928),not(X_929))) = necessarily(not(or(X_928,X_929))),
inference(resolve,[$cnf( $equal(and(not(X_928),not(X_929)),not(or(X_928,X_929))) )],[refute_0_230,refute_0_233]) ).
cnf(refute_0_235,plain,
strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))) = strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))),
introduced(tautology,[refl,[$fot(strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))))]]) ).
cnf(refute_0_236,plain,
( necessarily(and(not(X_928),not(X_929))) != necessarily(not(or(X_928,X_929)))
| strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))) != strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929)))
| strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))) = strict_implies(necessarily(not(or(X_928,X_929))),not(or(X_928,X_929))) ),
introduced(tautology,[equality,[$cnf( $equal(strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))),strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929)))) ),[1,0],$fot(necessarily(not(or(X_928,X_929))))]]) ).
cnf(refute_0_237,plain,
( necessarily(and(not(X_928),not(X_929))) != necessarily(not(or(X_928,X_929)))
| strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))) = strict_implies(necessarily(not(or(X_928,X_929))),not(or(X_928,X_929))) ),
inference(resolve,[$cnf( $equal(strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))),strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929)))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))) = strict_implies(necessarily(not(or(X_928,X_929))),not(or(X_928,X_929))),
inference(resolve,[$cnf( $equal(necessarily(and(not(X_928),not(X_929))),necessarily(not(or(X_928,X_929)))) )],[refute_0_234,refute_0_237]) ).
cnf(refute_0_239,plain,
( strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))) != strict_implies(necessarily(not(or(X_928,X_929))),not(or(X_928,X_929)))
| strict_implies(necessarily(not(or(X_928,X_929))),not(or(X_928,X_929))) != necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929))))
| strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))) = necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929)))) ),
inference(subst,[],[refute_0_161:[bind(X0,$fot(strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))))),bind(Y0,$fot(strict_implies(necessarily(not(or(X_928,X_929))),not(or(X_928,X_929))))),bind(Z,$fot(necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929))))))]]) ).
cnf(refute_0_240,plain,
( strict_implies(necessarily(not(or(X_928,X_929))),not(or(X_928,X_929))) != necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929))))
| strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))) = necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929)))) ),
inference(resolve,[$cnf( $equal(strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))),strict_implies(necessarily(not(or(X_928,X_929))),not(or(X_928,X_929)))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))) = necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929)))),
inference(resolve,[$cnf( $equal(strict_implies(necessarily(not(or(X_928,X_929))),not(or(X_928,X_929))),necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929))))) )],[refute_0_217,refute_0_240]) ).
cnf(refute_0_242,plain,
strict_implies(X,not(X_5685)) = necessarily(implies(X,not(X_5685))),
inference(subst,[],[refute_0_75:[bind(Y,$fot(not(X_5685)))]]) ).
cnf(refute_0_243,plain,
implies(X,not(X_4325)) = not(and(X,not(not(X_4325)))),
inference(subst,[],[refute_0_15:[bind(Y,$fot(not(X_4325)))]]) ).
cnf(refute_0_244,plain,
X_4325 = not(not(X_4325)),
inference(subst,[],[refute_0_201:[bind(X_4324,$fot(X_4325))]]) ).
cnf(refute_0_245,plain,
( X_4325 != not(not(X_4325))
| not(not(X_4325)) = X_4325 ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(X_4325)),bind(Y0,$fot(not(not(X_4325))))]]) ).
cnf(refute_0_246,plain,
not(not(X_4325)) = X_4325,
inference(resolve,[$cnf( $equal(X_4325,not(not(X_4325))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
( implies(X,not(X_4325)) != not(and(X,not(not(X_4325))))
| not(not(X_4325)) != X_4325
| implies(X,not(X_4325)) = not(and(X,X_4325)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,not(X_4325)),not(and(X,not(not(X_4325))))) ),[1,0,1],$fot(X_4325)]]) ).
cnf(refute_0_248,plain,
( implies(X,not(X_4325)) != not(and(X,not(not(X_4325))))
| implies(X,not(X_4325)) = not(and(X,X_4325)) ),
inference(resolve,[$cnf( $equal(not(not(X_4325)),X_4325) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
implies(X,not(X_4325)) = not(and(X,X_4325)),
inference(resolve,[$cnf( $equal(implies(X,not(X_4325)),not(and(X,not(not(X_4325))))) )],[refute_0_243,refute_0_248]) ).
cnf(refute_0_250,plain,
implies(X,not(X_5685)) = not(and(X,X_5685)),
inference(subst,[],[refute_0_249:[bind(X_4325,$fot(X_5685))]]) ).
cnf(refute_0_251,plain,
( implies(X,not(X_5685)) != not(and(X,X_5685))
| strict_implies(X,not(X_5685)) != necessarily(implies(X,not(X_5685)))
| strict_implies(X,not(X_5685)) = necessarily(not(and(X,X_5685))) ),
introduced(tautology,[equality,[$cnf( $equal(strict_implies(X,not(X_5685)),necessarily(implies(X,not(X_5685)))) ),[1,0],$fot(not(and(X,X_5685)))]]) ).
cnf(refute_0_252,plain,
( strict_implies(X,not(X_5685)) != necessarily(implies(X,not(X_5685)))
| strict_implies(X,not(X_5685)) = necessarily(not(and(X,X_5685))) ),
inference(resolve,[$cnf( $equal(implies(X,not(X_5685)),not(and(X,X_5685))) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
strict_implies(X,not(X_5685)) = necessarily(not(and(X,X_5685))),
inference(resolve,[$cnf( $equal(strict_implies(X,not(X_5685)),necessarily(implies(X,not(X_5685)))) )],[refute_0_242,refute_0_252]) ).
cnf(refute_0_254,plain,
( strict_implies(X,not(X_5685)) != necessarily(not(and(X,X_5685)))
| necessarily(not(and(X,X_5685))) = strict_implies(X,not(X_5685)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(strict_implies(X,not(X_5685)))),bind(Y0,$fot(necessarily(not(and(X,X_5685)))))]]) ).
cnf(refute_0_255,plain,
necessarily(not(and(X,X_5685))) = strict_implies(X,not(X_5685)),
inference(resolve,[$cnf( $equal(strict_implies(X,not(X_5685)),necessarily(not(and(X,X_5685)))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929)))) = strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))),
inference(subst,[],[refute_0_255:[bind(X,$fot(necessarily(and(not(X_928),not(X_929))))),bind(X_5685,$fot(or(X_928,X_929)))]]) ).
cnf(refute_0_257,plain,
strict_implies(X,necessarily(not(X_137))) = necessarily(implies(X,necessarily(not(X_137)))),
inference(subst,[],[refute_0_75:[bind(Y,$fot(necessarily(not(X_137))))]]) ).
cnf(refute_0_258,plain,
implies(X_10,necessarily(not(X))) = not(and(X_10,not(necessarily(not(X))))),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_10)),bind(Y,$fot(necessarily(not(X))))]]) ).
cnf(refute_0_259,plain,
( implies(X_10,necessarily(not(X))) != not(and(X_10,not(necessarily(not(X)))))
| not(necessarily(not(X))) != possibly(X)
| implies(X_10,necessarily(not(X))) = not(and(X_10,possibly(X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_10,necessarily(not(X))),not(and(X_10,not(necessarily(not(X)))))) ),[1,0,1],$fot(possibly(X))]]) ).
cnf(refute_0_260,plain,
( implies(X_10,necessarily(not(X))) != not(and(X_10,not(necessarily(not(X)))))
| implies(X_10,necessarily(not(X))) = not(and(X_10,possibly(X))) ),
inference(resolve,[$cnf( $equal(not(necessarily(not(X))),possibly(X)) )],[refute_0_207,refute_0_259]) ).
cnf(refute_0_261,plain,
implies(X_10,necessarily(not(X))) = not(and(X_10,possibly(X))),
inference(resolve,[$cnf( $equal(implies(X_10,necessarily(not(X))),not(and(X_10,not(necessarily(not(X)))))) )],[refute_0_258,refute_0_260]) ).
cnf(refute_0_262,plain,
implies(X,necessarily(not(X_137))) = not(and(X,possibly(X_137))),
inference(subst,[],[refute_0_261:[bind(X,$fot(X_137)),bind(X_10,$fot(X))]]) ).
cnf(refute_0_263,plain,
( implies(X,necessarily(not(X_137))) != not(and(X,possibly(X_137)))
| strict_implies(X,necessarily(not(X_137))) != necessarily(implies(X,necessarily(not(X_137))))
| strict_implies(X,necessarily(not(X_137))) = necessarily(not(and(X,possibly(X_137)))) ),
introduced(tautology,[equality,[$cnf( $equal(strict_implies(X,necessarily(not(X_137))),necessarily(implies(X,necessarily(not(X_137))))) ),[1,0],$fot(not(and(X,possibly(X_137))))]]) ).
cnf(refute_0_264,plain,
( strict_implies(X,necessarily(not(X_137))) != necessarily(implies(X,necessarily(not(X_137))))
| strict_implies(X,necessarily(not(X_137))) = necessarily(not(and(X,possibly(X_137)))) ),
inference(resolve,[$cnf( $equal(implies(X,necessarily(not(X_137))),not(and(X,possibly(X_137)))) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
strict_implies(X,necessarily(not(X_137))) = necessarily(not(and(X,possibly(X_137)))),
inference(resolve,[$cnf( $equal(strict_implies(X,necessarily(not(X_137))),necessarily(implies(X,necessarily(not(X_137))))) )],[refute_0_257,refute_0_264]) ).
cnf(refute_0_266,plain,
strict_implies(possibly(X_137),necessarily(not(X_137))) = necessarily(not(and(possibly(X_137),possibly(X_137)))),
inference(subst,[],[refute_0_265:[bind(X,$fot(possibly(X_137)))]]) ).
cnf(refute_0_267,plain,
possibly(X_137) = and(possibly(X_137),possibly(X_137)),
inference(subst,[],[refute_0_140:[bind(X_2163,$fot(possibly(X_137)))]]) ).
cnf(refute_0_268,plain,
( possibly(X_137) != and(possibly(X_137),possibly(X_137))
| and(possibly(X_137),possibly(X_137)) = possibly(X_137) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(possibly(X_137))),bind(Y0,$fot(and(possibly(X_137),possibly(X_137))))]]) ).
cnf(refute_0_269,plain,
and(possibly(X_137),possibly(X_137)) = possibly(X_137),
inference(resolve,[$cnf( $equal(possibly(X_137),and(possibly(X_137),possibly(X_137))) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
( and(possibly(X_137),possibly(X_137)) != possibly(X_137)
| strict_implies(possibly(X_137),necessarily(not(X_137))) != necessarily(not(and(possibly(X_137),possibly(X_137))))
| strict_implies(possibly(X_137),necessarily(not(X_137))) = necessarily(not(possibly(X_137))) ),
introduced(tautology,[equality,[$cnf( $equal(strict_implies(possibly(X_137),necessarily(not(X_137))),necessarily(not(and(possibly(X_137),possibly(X_137))))) ),[1,0,0],$fot(possibly(X_137))]]) ).
cnf(refute_0_271,plain,
( strict_implies(possibly(X_137),necessarily(not(X_137))) != necessarily(not(and(possibly(X_137),possibly(X_137))))
| strict_implies(possibly(X_137),necessarily(not(X_137))) = necessarily(not(possibly(X_137))) ),
inference(resolve,[$cnf( $equal(and(possibly(X_137),possibly(X_137)),possibly(X_137)) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
strict_implies(possibly(X_137),necessarily(not(X_137))) = necessarily(not(possibly(X_137))),
inference(resolve,[$cnf( $equal(strict_implies(possibly(X_137),necessarily(not(X_137))),necessarily(not(and(possibly(X_137),possibly(X_137))))) )],[refute_0_266,refute_0_271]) ).
cnf(refute_0_273,plain,
( ~ is_a_theorem(equiv(necessarily(possibly(X_1527)),possibly(X_1527)))
| necessarily(possibly(X_1527)) = possibly(X_1527) ),
inference(subst,[],[refute_0_86:[bind(X,$fot(necessarily(possibly(X_1527)))),bind(Y,$fot(possibly(X_1527)))]]) ).
cnf(refute_0_274,plain,
( ~ axiom_5
| is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
inference(canonicalize,[],[normalize_0_61]) ).
cnf(refute_0_275,plain,
axiom_5,
inference(canonicalize,[],[normalize_0_62]) ).
cnf(refute_0_276,plain,
is_a_theorem(implies(possibly(X),necessarily(possibly(X)))),
inference(resolve,[$cnf( axiom_5 )],[refute_0_275,refute_0_274]) ).
cnf(refute_0_277,plain,
( ~ is_a_theorem(implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647)))
| is_a_theorem(necessarily(implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647)))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647))))]]) ).
cnf(refute_0_278,plain,
( ~ is_a_theorem(implies(necessarily(X),X))
| is_a_theorem(implies(X_527,and(implies(necessarily(X),X),X_527))) ),
inference(subst,[],[refute_0_97:[bind(Y,$fot(X_527)),bind(X_349,$fot(implies(necessarily(X),X)))]]) ).
cnf(refute_0_279,plain,
is_a_theorem(implies(X_527,and(implies(necessarily(X),X),X_527))),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(X),X)) )],[refute_0_43,refute_0_278]) ).
cnf(refute_0_280,plain,
is_a_theorem(implies(implies(X_529,necessarily(X_529)),and(implies(necessarily(X_529),X_529),implies(X_529,necessarily(X_529))))),
inference(subst,[],[refute_0_279:[bind(X,$fot(X_529)),bind(X_527,$fot(implies(X_529,necessarily(X_529))))]]) ).
cnf(refute_0_281,plain,
equiv(necessarily(X_529),X_529) = and(implies(necessarily(X_529),X_529),implies(X_529,necessarily(X_529))),
inference(subst,[],[refute_0_103:[bind(X,$fot(necessarily(X_529))),bind(Y,$fot(X_529))]]) ).
cnf(refute_0_282,plain,
( equiv(necessarily(X_529),X_529) != and(implies(necessarily(X_529),X_529),implies(X_529,necessarily(X_529)))
| and(implies(necessarily(X_529),X_529),implies(X_529,necessarily(X_529))) = equiv(necessarily(X_529),X_529) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(equiv(necessarily(X_529),X_529))),bind(Y0,$fot(and(implies(necessarily(X_529),X_529),implies(X_529,necessarily(X_529)))))]]) ).
cnf(refute_0_283,plain,
and(implies(necessarily(X_529),X_529),implies(X_529,necessarily(X_529))) = equiv(necessarily(X_529),X_529),
inference(resolve,[$cnf( $equal(equiv(necessarily(X_529),X_529),and(implies(necessarily(X_529),X_529),implies(X_529,necessarily(X_529)))) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
( and(implies(necessarily(X_529),X_529),implies(X_529,necessarily(X_529))) != equiv(necessarily(X_529),X_529)
| ~ is_a_theorem(implies(implies(X_529,necessarily(X_529)),and(implies(necessarily(X_529),X_529),implies(X_529,necessarily(X_529)))))
| is_a_theorem(implies(implies(X_529,necessarily(X_529)),equiv(necessarily(X_529),X_529))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_529,necessarily(X_529)),and(implies(necessarily(X_529),X_529),implies(X_529,necessarily(X_529))))) ),[0,1],$fot(equiv(necessarily(X_529),X_529))]]) ).
cnf(refute_0_285,plain,
( ~ is_a_theorem(implies(implies(X_529,necessarily(X_529)),and(implies(necessarily(X_529),X_529),implies(X_529,necessarily(X_529)))))
| is_a_theorem(implies(implies(X_529,necessarily(X_529)),equiv(necessarily(X_529),X_529))) ),
inference(resolve,[$cnf( $equal(and(implies(necessarily(X_529),X_529),implies(X_529,necessarily(X_529))),equiv(necessarily(X_529),X_529)) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
is_a_theorem(implies(implies(X_529,necessarily(X_529)),equiv(necessarily(X_529),X_529))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_529,necessarily(X_529)),and(implies(necessarily(X_529),X_529),implies(X_529,necessarily(X_529))))) )],[refute_0_280,refute_0_285]) ).
cnf(refute_0_287,plain,
is_a_theorem(implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647))),
inference(subst,[],[refute_0_286:[bind(X_529,$fot(X_647))]]) ).
cnf(refute_0_288,plain,
is_a_theorem(necessarily(implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647))) )],[refute_0_287,refute_0_277]) ).
cnf(refute_0_289,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_290,plain,
necessarily(implies(X,Y)) = strict_implies(X,Y),
inference(resolve,[$cnf( $equal(strict_implies(X,Y),necessarily(implies(X,Y))) )],[refute_0_75,refute_0_289]) ).
cnf(refute_0_291,plain,
necessarily(implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647))) = strict_implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647)),
inference(subst,[],[refute_0_290:[bind(X,$fot(implies(X_647,necessarily(X_647)))),bind(Y,$fot(equiv(necessarily(X_647),X_647)))]]) ).
cnf(refute_0_292,plain,
( necessarily(implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647))) != strict_implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647))
| ~ is_a_theorem(necessarily(implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647))))
| is_a_theorem(strict_implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(necessarily(implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647)))) ),[0],$fot(strict_implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647)))]]) ).
cnf(refute_0_293,plain,
( ~ is_a_theorem(necessarily(implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647))))
| is_a_theorem(strict_implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647))) ),
inference(resolve,[$cnf( $equal(necessarily(implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647))),strict_implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647))) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
is_a_theorem(strict_implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647))),
inference(resolve,[$cnf( is_a_theorem(necessarily(implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647)))) )],[refute_0_288,refute_0_293]) ).
cnf(refute_0_295,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(strict_implies(X,Y))
| ~ modus_ponens_strict_implies
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_65]) ).
cnf(refute_0_296,plain,
( ~ is_a_theorem(skolemFOFtoCNF_Y_15)
| modus_ponens_strict_implies ),
inference(canonicalize,[],[normalize_0_66]) ).
cnf(refute_0_297,plain,
( is_a_theorem(skolemFOFtoCNF_X_16)
| modus_ponens_strict_implies ),
inference(canonicalize,[],[normalize_0_67]) ).
cnf(refute_0_298,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| ~ is_a_theorem(skolemFOFtoCNF_X_16)
| is_a_theorem(skolemFOFtoCNF_Y_15) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(skolemFOFtoCNF_X_16)),bind(Y,$fot(skolemFOFtoCNF_Y_15))]]) ).
cnf(refute_0_299,plain,
( is_a_theorem(strict_implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| modus_ponens_strict_implies ),
inference(canonicalize,[],[normalize_0_68]) ).
cnf(refute_0_300,plain,
is_a_theorem(implies(necessarily(implies(X_3,X_4)),implies(X_3,X_4))),
inference(subst,[],[refute_0_43:[bind(X,$fot(implies(X_3,X_4)))]]) ).
cnf(refute_0_301,plain,
strict_implies(X_3,X_4) = necessarily(implies(X_3,X_4)),
inference(subst,[],[refute_0_75:[bind(X,$fot(X_3)),bind(Y,$fot(X_4))]]) ).
cnf(refute_0_302,plain,
( strict_implies(X_3,X_4) != necessarily(implies(X_3,X_4))
| necessarily(implies(X_3,X_4)) = strict_implies(X_3,X_4) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(strict_implies(X_3,X_4))),bind(Y0,$fot(necessarily(implies(X_3,X_4))))]]) ).
cnf(refute_0_303,plain,
necessarily(implies(X_3,X_4)) = strict_implies(X_3,X_4),
inference(resolve,[$cnf( $equal(strict_implies(X_3,X_4),necessarily(implies(X_3,X_4))) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
( necessarily(implies(X_3,X_4)) != strict_implies(X_3,X_4)
| ~ is_a_theorem(implies(necessarily(implies(X_3,X_4)),implies(X_3,X_4)))
| is_a_theorem(implies(strict_implies(X_3,X_4),implies(X_3,X_4))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(necessarily(implies(X_3,X_4)),implies(X_3,X_4))) ),[0,0],$fot(strict_implies(X_3,X_4))]]) ).
cnf(refute_0_305,plain,
( ~ is_a_theorem(implies(necessarily(implies(X_3,X_4)),implies(X_3,X_4)))
| is_a_theorem(implies(strict_implies(X_3,X_4),implies(X_3,X_4))) ),
inference(resolve,[$cnf( $equal(necessarily(implies(X_3,X_4)),strict_implies(X_3,X_4)) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
is_a_theorem(implies(strict_implies(X_3,X_4),implies(X_3,X_4))),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(implies(X_3,X_4)),implies(X_3,X_4))) )],[refute_0_300,refute_0_305]) ).
cnf(refute_0_307,plain,
( ~ is_a_theorem(implies(strict_implies(X_3,X_4),implies(X_3,X_4)))
| ~ is_a_theorem(strict_implies(X_3,X_4))
| is_a_theorem(implies(X_3,X_4)) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(strict_implies(X_3,X_4))),bind(Y,$fot(implies(X_3,X_4)))]]) ).
cnf(refute_0_308,plain,
( ~ is_a_theorem(strict_implies(X_3,X_4))
| is_a_theorem(implies(X_3,X_4)) ),
inference(resolve,[$cnf( is_a_theorem(implies(strict_implies(X_3,X_4),implies(X_3,X_4))) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
( ~ is_a_theorem(strict_implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| is_a_theorem(implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15)) ),
inference(subst,[],[refute_0_308:[bind(X_3,$fot(skolemFOFtoCNF_X_16)),bind(X_4,$fot(skolemFOFtoCNF_Y_15))]]) ).
cnf(refute_0_310,plain,
( is_a_theorem(implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| modus_ponens_strict_implies ),
inference(resolve,[$cnf( is_a_theorem(strict_implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15)) )],[refute_0_299,refute_0_309]) ).
cnf(refute_0_311,plain,
( ~ is_a_theorem(skolemFOFtoCNF_X_16)
| is_a_theorem(skolemFOFtoCNF_Y_15)
| modus_ponens_strict_implies ),
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15)) )],[refute_0_310,refute_0_298]) ).
cnf(refute_0_312,plain,
( is_a_theorem(skolemFOFtoCNF_Y_15)
| modus_ponens_strict_implies ),
inference(resolve,[$cnf( is_a_theorem(skolemFOFtoCNF_X_16) )],[refute_0_297,refute_0_311]) ).
cnf(refute_0_313,plain,
modus_ponens_strict_implies,
inference(resolve,[$cnf( is_a_theorem(skolemFOFtoCNF_Y_15) )],[refute_0_312,refute_0_296]) ).
cnf(refute_0_314,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(strict_implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens_strict_implies )],[refute_0_313,refute_0_295]) ).
cnf(refute_0_315,plain,
( ~ is_a_theorem(implies(X_647,necessarily(X_647)))
| ~ is_a_theorem(strict_implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647)))
| is_a_theorem(equiv(necessarily(X_647),X_647)) ),
inference(subst,[],[refute_0_314:[bind(X,$fot(implies(X_647,necessarily(X_647)))),bind(Y,$fot(equiv(necessarily(X_647),X_647)))]]) ).
cnf(refute_0_316,plain,
( ~ is_a_theorem(implies(X_647,necessarily(X_647)))
| is_a_theorem(equiv(necessarily(X_647),X_647)) ),
inference(resolve,[$cnf( is_a_theorem(strict_implies(implies(X_647,necessarily(X_647)),equiv(necessarily(X_647),X_647))) )],[refute_0_294,refute_0_315]) ).
cnf(refute_0_317,plain,
( ~ is_a_theorem(implies(possibly(X),necessarily(possibly(X))))
| is_a_theorem(equiv(necessarily(possibly(X)),possibly(X))) ),
inference(subst,[],[refute_0_316:[bind(X_647,$fot(possibly(X)))]]) ).
cnf(refute_0_318,plain,
is_a_theorem(equiv(necessarily(possibly(X)),possibly(X))),
inference(resolve,[$cnf( is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) )],[refute_0_276,refute_0_317]) ).
cnf(refute_0_319,plain,
is_a_theorem(equiv(necessarily(possibly(X_1527)),possibly(X_1527))),
inference(subst,[],[refute_0_318:[bind(X,$fot(X_1527))]]) ).
cnf(refute_0_320,plain,
necessarily(possibly(X_1527)) = possibly(X_1527),
inference(resolve,[$cnf( is_a_theorem(equiv(necessarily(possibly(X_1527)),possibly(X_1527))) )],[refute_0_319,refute_0_273]) ).
cnf(refute_0_321,plain,
necessarily(possibly(necessarily(not(X_1529)))) = possibly(necessarily(not(X_1529))),
inference(subst,[],[refute_0_320:[bind(X_1527,$fot(necessarily(not(X_1529))))]]) ).
cnf(refute_0_322,plain,
possibly(necessarily(not(X_0))) = not(necessarily(not(necessarily(not(X_0))))),
inference(subst,[],[refute_0_205:[bind(X,$fot(necessarily(not(X_0))))]]) ).
cnf(refute_0_323,plain,
possibly(X_0) = not(necessarily(not(X_0))),
inference(subst,[],[refute_0_205:[bind(X,$fot(X_0))]]) ).
cnf(refute_0_324,plain,
( possibly(X_0) != not(necessarily(not(X_0)))
| not(necessarily(not(X_0))) = possibly(X_0) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(possibly(X_0))),bind(Y0,$fot(not(necessarily(not(X_0)))))]]) ).
cnf(refute_0_325,plain,
not(necessarily(not(X_0))) = possibly(X_0),
inference(resolve,[$cnf( $equal(possibly(X_0),not(necessarily(not(X_0)))) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
( not(necessarily(not(X_0))) != possibly(X_0)
| possibly(necessarily(not(X_0))) != not(necessarily(not(necessarily(not(X_0)))))
| possibly(necessarily(not(X_0))) = not(necessarily(possibly(X_0))) ),
introduced(tautology,[equality,[$cnf( $equal(possibly(necessarily(not(X_0))),not(necessarily(not(necessarily(not(X_0)))))) ),[1,0,0],$fot(possibly(X_0))]]) ).
cnf(refute_0_327,plain,
( possibly(necessarily(not(X_0))) != not(necessarily(not(necessarily(not(X_0)))))
| possibly(necessarily(not(X_0))) = not(necessarily(possibly(X_0))) ),
inference(resolve,[$cnf( $equal(not(necessarily(not(X_0))),possibly(X_0)) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
possibly(necessarily(not(X_0))) = not(necessarily(possibly(X_0))),
inference(resolve,[$cnf( $equal(possibly(necessarily(not(X_0))),not(necessarily(not(necessarily(not(X_0)))))) )],[refute_0_322,refute_0_327]) ).
cnf(refute_0_329,plain,
necessarily(possibly(X_0)) = possibly(X_0),
inference(subst,[],[refute_0_320:[bind(X_1527,$fot(X_0))]]) ).
cnf(refute_0_330,plain,
not(necessarily(possibly(X_0))) = not(necessarily(possibly(X_0))),
introduced(tautology,[refl,[$fot(not(necessarily(possibly(X_0))))]]) ).
cnf(refute_0_331,plain,
( necessarily(possibly(X_0)) != possibly(X_0)
| not(necessarily(possibly(X_0))) != not(necessarily(possibly(X_0)))
| not(necessarily(possibly(X_0))) = not(possibly(X_0)) ),
introduced(tautology,[equality,[$cnf( $equal(not(necessarily(possibly(X_0))),not(necessarily(possibly(X_0)))) ),[1,0],$fot(possibly(X_0))]]) ).
cnf(refute_0_332,plain,
( necessarily(possibly(X_0)) != possibly(X_0)
| not(necessarily(possibly(X_0))) = not(possibly(X_0)) ),
inference(resolve,[$cnf( $equal(not(necessarily(possibly(X_0))),not(necessarily(possibly(X_0)))) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
not(necessarily(possibly(X_0))) = not(possibly(X_0)),
inference(resolve,[$cnf( $equal(necessarily(possibly(X_0)),possibly(X_0)) )],[refute_0_329,refute_0_332]) ).
cnf(refute_0_334,plain,
( not(necessarily(possibly(X_0))) != not(possibly(X_0))
| possibly(necessarily(not(X_0))) != not(necessarily(possibly(X_0)))
| possibly(necessarily(not(X_0))) = not(possibly(X_0)) ),
introduced(tautology,[equality,[$cnf( $equal(possibly(necessarily(not(X_0))),not(necessarily(possibly(X_0)))) ),[1],$fot(not(possibly(X_0)))]]) ).
cnf(refute_0_335,plain,
( possibly(necessarily(not(X_0))) != not(necessarily(possibly(X_0)))
| possibly(necessarily(not(X_0))) = not(possibly(X_0)) ),
inference(resolve,[$cnf( $equal(not(necessarily(possibly(X_0))),not(possibly(X_0))) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
possibly(necessarily(not(X_0))) = not(possibly(X_0)),
inference(resolve,[$cnf( $equal(possibly(necessarily(not(X_0))),not(necessarily(possibly(X_0)))) )],[refute_0_328,refute_0_335]) ).
cnf(refute_0_337,plain,
possibly(necessarily(not(X_1529))) = not(possibly(X_1529)),
inference(subst,[],[refute_0_336:[bind(X_0,$fot(X_1529))]]) ).
cnf(refute_0_338,plain,
( necessarily(possibly(necessarily(not(X_1529)))) != possibly(necessarily(not(X_1529)))
| possibly(necessarily(not(X_1529))) != not(possibly(X_1529))
| necessarily(not(possibly(X_1529))) = possibly(necessarily(not(X_1529))) ),
introduced(tautology,[equality,[$cnf( $equal(necessarily(possibly(necessarily(not(X_1529)))),possibly(necessarily(not(X_1529)))) ),[0,0],$fot(not(possibly(X_1529)))]]) ).
cnf(refute_0_339,plain,
( necessarily(possibly(necessarily(not(X_1529)))) != possibly(necessarily(not(X_1529)))
| necessarily(not(possibly(X_1529))) = possibly(necessarily(not(X_1529))) ),
inference(resolve,[$cnf( $equal(possibly(necessarily(not(X_1529))),not(possibly(X_1529))) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
necessarily(not(possibly(X_1529))) = possibly(necessarily(not(X_1529))),
inference(resolve,[$cnf( $equal(necessarily(possibly(necessarily(not(X_1529)))),possibly(necessarily(not(X_1529)))) )],[refute_0_321,refute_0_339]) ).
cnf(refute_0_341,plain,
( necessarily(not(possibly(X_1529))) != possibly(necessarily(not(X_1529)))
| possibly(necessarily(not(X_1529))) != not(possibly(X_1529))
| necessarily(not(possibly(X_1529))) = not(possibly(X_1529)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(necessarily(not(possibly(X_1529))),not(possibly(X_1529))) ),[0],$fot(possibly(necessarily(not(X_1529))))]]) ).
cnf(refute_0_342,plain,
( necessarily(not(possibly(X_1529))) != possibly(necessarily(not(X_1529)))
| necessarily(not(possibly(X_1529))) = not(possibly(X_1529)) ),
inference(resolve,[$cnf( $equal(possibly(necessarily(not(X_1529))),not(possibly(X_1529))) )],[refute_0_337,refute_0_341]) ).
cnf(refute_0_343,plain,
necessarily(not(possibly(X_1529))) = not(possibly(X_1529)),
inference(resolve,[$cnf( $equal(necessarily(not(possibly(X_1529))),possibly(necessarily(not(X_1529)))) )],[refute_0_340,refute_0_342]) ).
cnf(refute_0_344,plain,
necessarily(not(possibly(X_137))) = not(possibly(X_137)),
inference(subst,[],[refute_0_343:[bind(X_1529,$fot(X_137))]]) ).
cnf(refute_0_345,plain,
( necessarily(not(possibly(X_137))) != not(possibly(X_137))
| strict_implies(possibly(X_137),necessarily(not(X_137))) != necessarily(not(possibly(X_137)))
| strict_implies(possibly(X_137),necessarily(not(X_137))) = not(possibly(X_137)) ),
introduced(tautology,[equality,[$cnf( $equal(strict_implies(possibly(X_137),necessarily(not(X_137))),necessarily(not(possibly(X_137)))) ),[1],$fot(not(possibly(X_137)))]]) ).
cnf(refute_0_346,plain,
( strict_implies(possibly(X_137),necessarily(not(X_137))) != necessarily(not(possibly(X_137)))
| strict_implies(possibly(X_137),necessarily(not(X_137))) = not(possibly(X_137)) ),
inference(resolve,[$cnf( $equal(necessarily(not(possibly(X_137))),not(possibly(X_137))) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
strict_implies(possibly(X_137),necessarily(not(X_137))) = not(possibly(X_137)),
inference(resolve,[$cnf( $equal(strict_implies(possibly(X_137),necessarily(not(X_137))),necessarily(not(possibly(X_137)))) )],[refute_0_272,refute_0_346]) ).
cnf(refute_0_348,plain,
strict_implies(possibly(not(X_4325)),necessarily(not(not(X_4325)))) = not(possibly(not(X_4325))),
inference(subst,[],[refute_0_347:[bind(X_137,$fot(not(X_4325)))]]) ).
cnf(refute_0_349,plain,
( not(not(X_4325)) != X_4325
| strict_implies(possibly(not(X_4325)),necessarily(not(not(X_4325)))) != not(possibly(not(X_4325)))
| strict_implies(possibly(not(X_4325)),necessarily(X_4325)) = not(possibly(not(X_4325))) ),
introduced(tautology,[equality,[$cnf( $equal(strict_implies(possibly(not(X_4325)),necessarily(not(not(X_4325)))),not(possibly(not(X_4325)))) ),[0,1,0],$fot(X_4325)]]) ).
cnf(refute_0_350,plain,
( strict_implies(possibly(not(X_4325)),necessarily(not(not(X_4325)))) != not(possibly(not(X_4325)))
| strict_implies(possibly(not(X_4325)),necessarily(X_4325)) = not(possibly(not(X_4325))) ),
inference(resolve,[$cnf( $equal(not(not(X_4325)),X_4325) )],[refute_0_246,refute_0_349]) ).
cnf(refute_0_351,plain,
strict_implies(possibly(not(X_4325)),necessarily(X_4325)) = not(possibly(not(X_4325))),
inference(resolve,[$cnf( $equal(strict_implies(possibly(not(X_4325)),necessarily(not(not(X_4325)))),not(possibly(not(X_4325)))) )],[refute_0_348,refute_0_350]) ).
cnf(refute_0_352,plain,
( X_4324 != not(not(X_4324))
| not(not(X_4324)) = X_4324 ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(X_4324)),bind(Y0,$fot(not(not(X_4324))))]]) ).
cnf(refute_0_353,plain,
not(not(X_4324)) = X_4324,
inference(resolve,[$cnf( $equal(X_4324,not(not(X_4324))) )],[refute_0_201,refute_0_352]) ).
cnf(refute_0_354,plain,
not(not(Y)) = Y,
inference(subst,[],[refute_0_353:[bind(X_4324,$fot(Y))]]) ).
cnf(refute_0_355,plain,
( not(not(Y)) != Y
| or(Y,Y) != not(not(Y))
| or(Y,Y) = Y ),
introduced(tautology,[equality,[$cnf( $equal(or(Y,Y),not(not(Y))) ),[1],$fot(Y)]]) ).
cnf(refute_0_356,plain,
( or(Y,Y) != not(not(Y))
| or(Y,Y) = Y ),
inference(resolve,[$cnf( $equal(not(not(Y)),Y) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
or(Y,Y) = Y,
inference(resolve,[$cnf( $equal(or(Y,Y),not(not(Y))) )],[refute_0_150,refute_0_356]) ).
cnf(refute_0_358,plain,
or(necessarily(X_4325),necessarily(X_4325)) = necessarily(X_4325),
inference(subst,[],[refute_0_357:[bind(Y,$fot(necessarily(X_4325)))]]) ).
cnf(refute_0_359,plain,
necessarily(or(necessarily(X_4325),necessarily(X_4325))) = necessarily(or(necessarily(X_4325),necessarily(X_4325))),
introduced(tautology,[refl,[$fot(necessarily(or(necessarily(X_4325),necessarily(X_4325))))]]) ).
cnf(refute_0_360,plain,
( necessarily(or(necessarily(X_4325),necessarily(X_4325))) != necessarily(or(necessarily(X_4325),necessarily(X_4325)))
| or(necessarily(X_4325),necessarily(X_4325)) != necessarily(X_4325)
| necessarily(or(necessarily(X_4325),necessarily(X_4325))) = necessarily(necessarily(X_4325)) ),
introduced(tautology,[equality,[$cnf( $equal(necessarily(or(necessarily(X_4325),necessarily(X_4325))),necessarily(or(necessarily(X_4325),necessarily(X_4325)))) ),[1,0],$fot(necessarily(X_4325))]]) ).
cnf(refute_0_361,plain,
( or(necessarily(X_4325),necessarily(X_4325)) != necessarily(X_4325)
| necessarily(or(necessarily(X_4325),necessarily(X_4325))) = necessarily(necessarily(X_4325)) ),
inference(resolve,[$cnf( $equal(necessarily(or(necessarily(X_4325),necessarily(X_4325))),necessarily(or(necessarily(X_4325),necessarily(X_4325)))) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
necessarily(or(necessarily(X_4325),necessarily(X_4325))) = necessarily(necessarily(X_4325)),
inference(resolve,[$cnf( $equal(or(necessarily(X_4325),necessarily(X_4325)),necessarily(X_4325)) )],[refute_0_358,refute_0_361]) ).
cnf(refute_0_363,plain,
strict_implies(not(necessarily(X_4325)),necessarily(X_4325)) = necessarily(or(necessarily(X_4325),necessarily(X_4325))),
inference(subst,[],[refute_0_82:[bind(Y,$fot(necessarily(X_4325))),bind(X_41,$fot(necessarily(X_4325)))]]) ).
cnf(refute_0_364,plain,
( necessarily(or(necessarily(X_4325),necessarily(X_4325))) != necessarily(necessarily(X_4325))
| strict_implies(not(necessarily(X_4325)),necessarily(X_4325)) != necessarily(or(necessarily(X_4325),necessarily(X_4325)))
| strict_implies(not(necessarily(X_4325)),necessarily(X_4325)) = necessarily(necessarily(X_4325)) ),
inference(subst,[],[refute_0_161:[bind(X0,$fot(strict_implies(not(necessarily(X_4325)),necessarily(X_4325)))),bind(Y0,$fot(necessarily(or(necessarily(X_4325),necessarily(X_4325))))),bind(Z,$fot(necessarily(necessarily(X_4325))))]]) ).
cnf(refute_0_365,plain,
( necessarily(or(necessarily(X_4325),necessarily(X_4325))) != necessarily(necessarily(X_4325))
| strict_implies(not(necessarily(X_4325)),necessarily(X_4325)) = necessarily(necessarily(X_4325)) ),
inference(resolve,[$cnf( $equal(strict_implies(not(necessarily(X_4325)),necessarily(X_4325)),necessarily(or(necessarily(X_4325),necessarily(X_4325)))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
strict_implies(not(necessarily(X_4325)),necessarily(X_4325)) = necessarily(necessarily(X_4325)),
inference(resolve,[$cnf( $equal(necessarily(or(necessarily(X_4325),necessarily(X_4325))),necessarily(necessarily(X_4325))) )],[refute_0_362,refute_0_365]) ).
cnf(refute_0_367,plain,
possibly(not(X_4325)) = not(necessarily(not(not(X_4325)))),
inference(subst,[],[refute_0_205:[bind(X,$fot(not(X_4325)))]]) ).
cnf(refute_0_368,plain,
( not(not(X_4325)) != X_4325
| possibly(not(X_4325)) != not(necessarily(not(not(X_4325))))
| possibly(not(X_4325)) = not(necessarily(X_4325)) ),
introduced(tautology,[equality,[$cnf( $equal(possibly(not(X_4325)),not(necessarily(not(not(X_4325))))) ),[1,0,0],$fot(X_4325)]]) ).
cnf(refute_0_369,plain,
( possibly(not(X_4325)) != not(necessarily(not(not(X_4325))))
| possibly(not(X_4325)) = not(necessarily(X_4325)) ),
inference(resolve,[$cnf( $equal(not(not(X_4325)),X_4325) )],[refute_0_246,refute_0_368]) ).
cnf(refute_0_370,plain,
possibly(not(X_4325)) = not(necessarily(X_4325)),
inference(resolve,[$cnf( $equal(possibly(not(X_4325)),not(necessarily(not(not(X_4325))))) )],[refute_0_367,refute_0_369]) ).
cnf(refute_0_371,plain,
strict_implies(possibly(not(X_4325)),necessarily(X_4325)) = strict_implies(possibly(not(X_4325)),necessarily(X_4325)),
introduced(tautology,[refl,[$fot(strict_implies(possibly(not(X_4325)),necessarily(X_4325)))]]) ).
cnf(refute_0_372,plain,
( possibly(not(X_4325)) != not(necessarily(X_4325))
| strict_implies(possibly(not(X_4325)),necessarily(X_4325)) != strict_implies(possibly(not(X_4325)),necessarily(X_4325))
| strict_implies(possibly(not(X_4325)),necessarily(X_4325)) = strict_implies(not(necessarily(X_4325)),necessarily(X_4325)) ),
introduced(tautology,[equality,[$cnf( $equal(strict_implies(possibly(not(X_4325)),necessarily(X_4325)),strict_implies(possibly(not(X_4325)),necessarily(X_4325))) ),[1,0],$fot(not(necessarily(X_4325)))]]) ).
cnf(refute_0_373,plain,
( possibly(not(X_4325)) != not(necessarily(X_4325))
| strict_implies(possibly(not(X_4325)),necessarily(X_4325)) = strict_implies(not(necessarily(X_4325)),necessarily(X_4325)) ),
inference(resolve,[$cnf( $equal(strict_implies(possibly(not(X_4325)),necessarily(X_4325)),strict_implies(possibly(not(X_4325)),necessarily(X_4325))) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
strict_implies(possibly(not(X_4325)),necessarily(X_4325)) = strict_implies(not(necessarily(X_4325)),necessarily(X_4325)),
inference(resolve,[$cnf( $equal(possibly(not(X_4325)),not(necessarily(X_4325))) )],[refute_0_370,refute_0_373]) ).
cnf(refute_0_375,plain,
( strict_implies(not(necessarily(X_4325)),necessarily(X_4325)) != necessarily(necessarily(X_4325))
| strict_implies(possibly(not(X_4325)),necessarily(X_4325)) != strict_implies(not(necessarily(X_4325)),necessarily(X_4325))
| strict_implies(possibly(not(X_4325)),necessarily(X_4325)) = necessarily(necessarily(X_4325)) ),
inference(subst,[],[refute_0_161:[bind(X0,$fot(strict_implies(possibly(not(X_4325)),necessarily(X_4325)))),bind(Y0,$fot(strict_implies(not(necessarily(X_4325)),necessarily(X_4325)))),bind(Z,$fot(necessarily(necessarily(X_4325))))]]) ).
cnf(refute_0_376,plain,
( strict_implies(not(necessarily(X_4325)),necessarily(X_4325)) != necessarily(necessarily(X_4325))
| strict_implies(possibly(not(X_4325)),necessarily(X_4325)) = necessarily(necessarily(X_4325)) ),
inference(resolve,[$cnf( $equal(strict_implies(possibly(not(X_4325)),necessarily(X_4325)),strict_implies(not(necessarily(X_4325)),necessarily(X_4325))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
strict_implies(possibly(not(X_4325)),necessarily(X_4325)) = necessarily(necessarily(X_4325)),
inference(resolve,[$cnf( $equal(strict_implies(not(necessarily(X_4325)),necessarily(X_4325)),necessarily(necessarily(X_4325))) )],[refute_0_366,refute_0_376]) ).
cnf(refute_0_378,plain,
( strict_implies(possibly(not(X_4325)),necessarily(X_4325)) != necessarily(necessarily(X_4325))
| strict_implies(possibly(not(X_4325)),necessarily(X_4325)) != not(possibly(not(X_4325)))
| necessarily(necessarily(X_4325)) = not(possibly(not(X_4325))) ),
introduced(tautology,[equality,[$cnf( $equal(strict_implies(possibly(not(X_4325)),necessarily(X_4325)),not(possibly(not(X_4325)))) ),[0],$fot(necessarily(necessarily(X_4325)))]]) ).
cnf(refute_0_379,plain,
( strict_implies(possibly(not(X_4325)),necessarily(X_4325)) != not(possibly(not(X_4325)))
| necessarily(necessarily(X_4325)) = not(possibly(not(X_4325))) ),
inference(resolve,[$cnf( $equal(strict_implies(possibly(not(X_4325)),necessarily(X_4325)),necessarily(necessarily(X_4325))) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
necessarily(not(not(X_4325))) = necessarily(not(not(X_4325))),
introduced(tautology,[refl,[$fot(necessarily(not(not(X_4325))))]]) ).
cnf(refute_0_381,plain,
( necessarily(not(not(X_4325))) != necessarily(not(not(X_4325)))
| not(not(X_4325)) != X_4325
| necessarily(not(not(X_4325))) = necessarily(X_4325) ),
introduced(tautology,[equality,[$cnf( $equal(necessarily(not(not(X_4325))),necessarily(not(not(X_4325)))) ),[1,0],$fot(X_4325)]]) ).
cnf(refute_0_382,plain,
( not(not(X_4325)) != X_4325
| necessarily(not(not(X_4325))) = necessarily(X_4325) ),
inference(resolve,[$cnf( $equal(necessarily(not(not(X_4325))),necessarily(not(not(X_4325)))) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
necessarily(not(not(X_4325))) = necessarily(X_4325),
inference(resolve,[$cnf( $equal(not(not(X_4325)),X_4325) )],[refute_0_246,refute_0_382]) ).
cnf(refute_0_384,plain,
( necessarily(not(X)) != not(possibly(X))
| not(possibly(X)) = necessarily(not(X)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(necessarily(not(X)))),bind(Y0,$fot(not(possibly(X))))]]) ).
cnf(refute_0_385,plain,
not(possibly(X)) = necessarily(not(X)),
inference(resolve,[$cnf( $equal(necessarily(not(X)),not(possibly(X))) )],[refute_0_210,refute_0_384]) ).
cnf(refute_0_386,plain,
not(possibly(not(X_4325))) = necessarily(not(not(X_4325))),
inference(subst,[],[refute_0_385:[bind(X,$fot(not(X_4325)))]]) ).
cnf(refute_0_387,plain,
( necessarily(not(not(X_4325))) != necessarily(X_4325)
| not(possibly(not(X_4325))) != necessarily(not(not(X_4325)))
| not(possibly(not(X_4325))) = necessarily(X_4325) ),
inference(subst,[],[refute_0_161:[bind(X0,$fot(not(possibly(not(X_4325))))),bind(Y0,$fot(necessarily(not(not(X_4325))))),bind(Z,$fot(necessarily(X_4325)))]]) ).
cnf(refute_0_388,plain,
( necessarily(not(not(X_4325))) != necessarily(X_4325)
| not(possibly(not(X_4325))) = necessarily(X_4325) ),
inference(resolve,[$cnf( $equal(not(possibly(not(X_4325))),necessarily(not(not(X_4325)))) )],[refute_0_386,refute_0_387]) ).
cnf(refute_0_389,plain,
not(possibly(not(X_4325))) = necessarily(X_4325),
inference(resolve,[$cnf( $equal(necessarily(not(not(X_4325))),necessarily(X_4325)) )],[refute_0_383,refute_0_388]) ).
cnf(refute_0_390,plain,
( necessarily(necessarily(X_4325)) != not(possibly(not(X_4325)))
| not(possibly(not(X_4325))) != necessarily(X_4325)
| necessarily(necessarily(X_4325)) = necessarily(X_4325) ),
introduced(tautology,[equality,[$cnf( ~ $equal(necessarily(necessarily(X_4325)),necessarily(X_4325)) ),[0],$fot(not(possibly(not(X_4325))))]]) ).
cnf(refute_0_391,plain,
( necessarily(necessarily(X_4325)) != not(possibly(not(X_4325)))
| necessarily(necessarily(X_4325)) = necessarily(X_4325) ),
inference(resolve,[$cnf( $equal(not(possibly(not(X_4325))),necessarily(X_4325)) )],[refute_0_389,refute_0_390]) ).
cnf(refute_0_392,plain,
( strict_implies(possibly(not(X_4325)),necessarily(X_4325)) != not(possibly(not(X_4325)))
| necessarily(necessarily(X_4325)) = necessarily(X_4325) ),
inference(resolve,[$cnf( $equal(necessarily(necessarily(X_4325)),not(possibly(not(X_4325)))) )],[refute_0_379,refute_0_391]) ).
cnf(refute_0_393,plain,
necessarily(necessarily(X_4325)) = necessarily(X_4325),
inference(resolve,[$cnf( $equal(strict_implies(possibly(not(X_4325)),necessarily(X_4325)),not(possibly(not(X_4325)))) )],[refute_0_351,refute_0_392]) ).
cnf(refute_0_394,plain,
necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))) = necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929)))),
inference(subst,[],[refute_0_393:[bind(X_4325,$fot(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929)))))]]) ).
cnf(refute_0_395,plain,
( necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))) != necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))
| necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929)))) != strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929)))
| necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))) = strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))) ),
inference(subst,[],[refute_0_161:[bind(X0,$fot(necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))))),bind(Y0,$fot(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929)))))),bind(Z,$fot(strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929)))))]]) ).
cnf(refute_0_396,plain,
( necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929)))) != strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929)))
| necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))) = strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))) ),
inference(resolve,[$cnf( $equal(necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))),necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))) )],[refute_0_394,refute_0_395]) ).
cnf(refute_0_397,plain,
necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))) = strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))),
inference(resolve,[$cnf( $equal(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929)))),strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929)))) )],[refute_0_256,refute_0_396]) ).
cnf(refute_0_398,plain,
( necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))) != strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929)))
| strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))) != necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929))))
| necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))) = necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929)))) ),
inference(subst,[],[refute_0_161:[bind(X0,$fot(necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))))),bind(Y0,$fot(strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))))),bind(Z,$fot(necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929))))))]]) ).
cnf(refute_0_399,plain,
( strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))) != necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929))))
| necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))) = necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929)))) ),
inference(resolve,[$cnf( $equal(necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))),strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929)))) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))) = necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929)))),
inference(resolve,[$cnf( $equal(strict_implies(necessarily(and(not(X_928),not(X_929))),not(or(X_928,X_929))),necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929))))) )],[refute_0_241,refute_0_399]) ).
cnf(refute_0_401,plain,
( necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))) != necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929))))
| ~ is_a_theorem(necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))))
| is_a_theorem(necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929)))))) ),[0],$fot(necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929)))))]]) ).
cnf(refute_0_402,plain,
( ~ is_a_theorem(necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))))
| is_a_theorem(necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929))))) ),
inference(resolve,[$cnf( $equal(necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929))))),necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929))))) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
is_a_theorem(necessarily(or(possibly(or(X_928,X_929)),not(or(X_928,X_929))))),
inference(resolve,[$cnf( is_a_theorem(necessarily(necessarily(not(and(necessarily(and(not(X_928),not(X_929))),or(X_928,X_929)))))) )],[refute_0_72,refute_0_402]) ).
cnf(refute_0_404,plain,
is_a_theorem(necessarily(or(possibly(or(X_8717,X_8717)),not(or(X_8717,X_8717))))),
inference(subst,[],[refute_0_403:[bind(X_928,$fot(X_8717)),bind(X_929,$fot(X_8717))]]) ).
cnf(refute_0_405,plain,
or(X_8717,X_8717) = X_8717,
inference(subst,[],[refute_0_357:[bind(Y,$fot(X_8717))]]) ).
cnf(refute_0_406,plain,
( or(X_8717,X_8717) != X_8717
| ~ is_a_theorem(necessarily(or(possibly(or(X_8717,X_8717)),not(or(X_8717,X_8717)))))
| is_a_theorem(necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(necessarily(or(possibly(or(X_8717,X_8717)),not(or(X_8717,X_8717))))) ),[0,0,1,0],$fot(X_8717)]]) ).
cnf(refute_0_407,plain,
( ~ is_a_theorem(necessarily(or(possibly(or(X_8717,X_8717)),not(or(X_8717,X_8717)))))
| is_a_theorem(necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717)))) ),
inference(resolve,[$cnf( $equal(or(X_8717,X_8717),X_8717) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
is_a_theorem(necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717)))),
inference(resolve,[$cnf( is_a_theorem(necessarily(or(possibly(or(X_8717,X_8717)),not(or(X_8717,X_8717))))) )],[refute_0_404,refute_0_407]) ).
cnf(refute_0_409,plain,
possibly(or(X_8717,X_8717)) = possibly(or(X_8717,X_8717)),
introduced(tautology,[refl,[$fot(possibly(or(X_8717,X_8717)))]]) ).
cnf(refute_0_410,plain,
( or(X_8717,X_8717) != X_8717
| possibly(or(X_8717,X_8717)) != possibly(or(X_8717,X_8717))
| possibly(or(X_8717,X_8717)) = possibly(X_8717) ),
introduced(tautology,[equality,[$cnf( $equal(possibly(or(X_8717,X_8717)),possibly(or(X_8717,X_8717))) ),[1,0],$fot(X_8717)]]) ).
cnf(refute_0_411,plain,
( or(X_8717,X_8717) != X_8717
| possibly(or(X_8717,X_8717)) = possibly(X_8717) ),
inference(resolve,[$cnf( $equal(possibly(or(X_8717,X_8717)),possibly(or(X_8717,X_8717))) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
possibly(or(X_8717,X_8717)) = possibly(X_8717),
inference(resolve,[$cnf( $equal(or(X_8717,X_8717),X_8717) )],[refute_0_405,refute_0_411]) ).
cnf(refute_0_413,plain,
or(possibly(or(X_8717,X_8717)),not(X_8717)) = or(possibly(or(X_8717,X_8717)),not(X_8717)),
introduced(tautology,[refl,[$fot(or(possibly(or(X_8717,X_8717)),not(X_8717)))]]) ).
cnf(refute_0_414,plain,
( or(possibly(or(X_8717,X_8717)),not(X_8717)) != or(possibly(or(X_8717,X_8717)),not(X_8717))
| possibly(or(X_8717,X_8717)) != possibly(X_8717)
| or(possibly(or(X_8717,X_8717)),not(X_8717)) = or(possibly(X_8717),not(X_8717)) ),
introduced(tautology,[equality,[$cnf( $equal(or(possibly(or(X_8717,X_8717)),not(X_8717)),or(possibly(or(X_8717,X_8717)),not(X_8717))) ),[1,0],$fot(possibly(X_8717))]]) ).
cnf(refute_0_415,plain,
( possibly(or(X_8717,X_8717)) != possibly(X_8717)
| or(possibly(or(X_8717,X_8717)),not(X_8717)) = or(possibly(X_8717),not(X_8717)) ),
inference(resolve,[$cnf( $equal(or(possibly(or(X_8717,X_8717)),not(X_8717)),or(possibly(or(X_8717,X_8717)),not(X_8717))) )],[refute_0_413,refute_0_414]) ).
cnf(refute_0_416,plain,
or(possibly(or(X_8717,X_8717)),not(X_8717)) = or(possibly(X_8717),not(X_8717)),
inference(resolve,[$cnf( $equal(possibly(or(X_8717,X_8717)),possibly(X_8717)) )],[refute_0_412,refute_0_415]) ).
cnf(refute_0_417,plain,
necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717))) = necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717))),
introduced(tautology,[refl,[$fot(necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717))))]]) ).
cnf(refute_0_418,plain,
( necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717))) != necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717)))
| or(possibly(or(X_8717,X_8717)),not(X_8717)) != or(possibly(X_8717),not(X_8717))
| necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717))) = necessarily(or(possibly(X_8717),not(X_8717))) ),
introduced(tautology,[equality,[$cnf( $equal(necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717))),necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717)))) ),[1,0],$fot(or(possibly(X_8717),not(X_8717)))]]) ).
cnf(refute_0_419,plain,
( or(possibly(or(X_8717,X_8717)),not(X_8717)) != or(possibly(X_8717),not(X_8717))
| necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717))) = necessarily(or(possibly(X_8717),not(X_8717))) ),
inference(resolve,[$cnf( $equal(necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717))),necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717)))) )],[refute_0_417,refute_0_418]) ).
cnf(refute_0_420,plain,
necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717))) = necessarily(or(possibly(X_8717),not(X_8717))),
inference(resolve,[$cnf( $equal(or(possibly(or(X_8717,X_8717)),not(X_8717)),or(possibly(X_8717),not(X_8717))) )],[refute_0_416,refute_0_419]) ).
cnf(refute_0_421,plain,
( necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717))) != necessarily(or(possibly(X_8717),not(X_8717)))
| ~ is_a_theorem(necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717))))
| is_a_theorem(necessarily(or(possibly(X_8717),not(X_8717)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717)))) ),[0],$fot(necessarily(or(possibly(X_8717),not(X_8717))))]]) ).
cnf(refute_0_422,plain,
( ~ is_a_theorem(necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717))))
| is_a_theorem(necessarily(or(possibly(X_8717),not(X_8717)))) ),
inference(resolve,[$cnf( $equal(necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717))),necessarily(or(possibly(X_8717),not(X_8717)))) )],[refute_0_420,refute_0_421]) ).
cnf(refute_0_423,plain,
is_a_theorem(necessarily(or(possibly(X_8717),not(X_8717)))),
inference(resolve,[$cnf( is_a_theorem(necessarily(or(possibly(or(X_8717,X_8717)),not(X_8717)))) )],[refute_0_408,refute_0_422]) ).
cnf(refute_0_424,plain,
is_a_theorem(necessarily(or(possibly(X_8718),not(X_8718)))),
inference(subst,[],[refute_0_423:[bind(X_8717,$fot(X_8718))]]) ).
cnf(refute_0_425,plain,
is_a_theorem(or(possibly(X_8718),not(X_8718))),
inference(resolve,[$cnf( is_a_theorem(necessarily(or(possibly(X_8718),not(X_8718)))) )],[refute_0_424,refute_0_47]) ).
cnf(refute_0_426,plain,
is_a_theorem(or(possibly(X_8719),not(X_8719))),
inference(subst,[],[refute_0_425:[bind(X_8718,$fot(X_8719))]]) ).
cnf(refute_0_427,plain,
is_a_theorem(implies(X_8719,possibly(X_8719))),
inference(resolve,[$cnf( is_a_theorem(or(possibly(X_8719),not(X_8719))) )],[refute_0_426,refute_0_40]) ).
cnf(refute_0_428,plain,
is_a_theorem(implies(X_8720,possibly(X_8720))),
inference(subst,[],[refute_0_427:[bind(X_8719,$fot(X_8720))]]) ).
cnf(refute_0_429,plain,
is_a_theorem(necessarily(implies(X_8720,possibly(X_8720)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_8720,possibly(X_8720))) )],[refute_0_428,refute_0_6]) ).
cnf(refute_0_430,plain,
necessarily(implies(X_8720,possibly(X_8720))) = strict_implies(X_8720,possibly(X_8720)),
inference(subst,[],[refute_0_290:[bind(X,$fot(X_8720)),bind(Y,$fot(possibly(X_8720)))]]) ).
cnf(refute_0_431,plain,
( necessarily(implies(X_8720,possibly(X_8720))) != strict_implies(X_8720,possibly(X_8720))
| ~ is_a_theorem(necessarily(implies(X_8720,possibly(X_8720))))
| is_a_theorem(strict_implies(X_8720,possibly(X_8720))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(necessarily(implies(X_8720,possibly(X_8720)))) ),[0],$fot(strict_implies(X_8720,possibly(X_8720)))]]) ).
cnf(refute_0_432,plain,
( ~ is_a_theorem(necessarily(implies(X_8720,possibly(X_8720))))
| is_a_theorem(strict_implies(X_8720,possibly(X_8720))) ),
inference(resolve,[$cnf( $equal(necessarily(implies(X_8720,possibly(X_8720))),strict_implies(X_8720,possibly(X_8720))) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
is_a_theorem(strict_implies(X_8720,possibly(X_8720))),
inference(resolve,[$cnf( is_a_theorem(necessarily(implies(X_8720,possibly(X_8720)))) )],[refute_0_429,refute_0_432]) ).
cnf(refute_0_434,plain,
is_a_theorem(strict_implies(skolemFOFtoCNF_X_32,possibly(skolemFOFtoCNF_X_32))),
inference(subst,[],[refute_0_433:[bind(X_8720,$fot(skolemFOFtoCNF_X_32))]]) ).
cnf(refute_0_435,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(strict_implies(skolemFOFtoCNF_X_32,possibly(skolemFOFtoCNF_X_32))) )],[refute_0_434,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL533+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 20:01:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 40.06/40.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 40.06/40.23
% 40.06/40.23 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 40.06/40.26
%------------------------------------------------------------------------------