TSTP Solution File: LCL537+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL537+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 12:52:59 EDT 2022
% Result : Theorem 125.72s 125.93s
% Output : CNFRefutation 125.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 77
% Syntax : Number of formulae : 392 ( 195 unt; 0 def)
% Number of atoms : 684 ( 290 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 559 ( 267 ~; 240 |; 20 &)
% ( 26 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 21 ( 18 usr; 18 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 22 con; 0-2 aty)
% Number of variables : 489 ( 8 sgn 86 !; 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(equivalence_3,axiom,
( equivalence_3
<=> ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(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(hilbert_equivalence_3,axiom,
equivalence_3 ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents ).
fof(axiom_M,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ) ).
fof(axiom_4,axiom,
( axiom_4
<=> ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) ) ).
fof(axiom_B,axiom,
( axiom_B
<=> ! [X] : is_a_theorem(implies(X,necessarily(possibly(X)))) ) ).
fof(axiom_5,axiom,
( axiom_5
<=> ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ) ).
fof(op_possibly,axiom,
( op_possibly
=> ! [X] : possibly(X) = not(necessarily(not(X))) ) ).
fof(km4b_op_possibly,axiom,
op_possibly ).
fof(km4b_axiom_M,axiom,
axiom_M ).
fof(km4b_axiom_4,axiom,
axiom_4 ).
fof(km4b_axiom_B,axiom,
axiom_B ).
fof(km5_axiom_5,conjecture,
axiom_5 ).
fof(subgoal_0,plain,
axiom_5,
inference(strip,[],[km5_axiom_5]) ).
fof(negate_0_0,plain,
~ axiom_5,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ axiom_5
<=> ? [X] : ~ is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_0_1,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_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(possibly(skolemFOFtoCNF_X_23),necessarily(possibly(skolemFOFtoCNF_X_23))))
| axiom_5 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ axiom_5,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ axiom_B
<=> ? [X] : ~ is_a_theorem(implies(X,necessarily(possibly(X)))) ),
inference(canonicalize,[],[axiom_B]) ).
fof(normalize_0_5,plain,
! [X] :
( ( ~ axiom_B
| is_a_theorem(implies(X,necessarily(possibly(X)))) )
& ( ~ is_a_theorem(implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22))))
| axiom_B ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X] :
( ~ axiom_B
| is_a_theorem(implies(X,necessarily(possibly(X)))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
axiom_B,
inference(canonicalize,[],[km4b_axiom_B]) ).
fof(normalize_0_8,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
op_or,
inference(canonicalize,[],[hilbert_op_or]) ).
fof(normalize_0_11,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
op_implies_and,
inference(canonicalize,[],[hilbert_op_implies_and]) ).
fof(normalize_0_14,plain,
( ~ op_possibly
| ! [X] : possibly(X) = not(necessarily(not(X))) ),
inference(canonicalize,[],[op_possibly]) ).
fof(normalize_0_15,plain,
! [X] :
( ~ op_possibly
| possibly(X) = not(necessarily(not(X))) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
op_possibly,
inference(canonicalize,[],[km4b_op_possibly]) ).
fof(normalize_0_17,plain,
( ~ substitution_of_equivalents
<=> ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_18,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_17]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
substitution_of_equivalents,
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_21,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_22,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_21]) ).
fof(normalize_0_23,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
modus_ponens,
inference(canonicalize,[],[hilbert_modus_ponens]) ).
fof(normalize_0_25,plain,
( ~ or_2
<=> ? [X,Y] : ~ is_a_theorem(implies(Y,or(X,Y))) ),
inference(canonicalize,[],[or_2]) ).
fof(normalize_0_26,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_25]) ).
fof(normalize_0_27,plain,
! [X,Y] :
( ~ or_2
| is_a_theorem(implies(Y,or(X,Y))) ),
inference(conjunct,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
or_2,
inference(canonicalize,[],[hilbert_or_2]) ).
fof(normalize_0_29,plain,
( ~ and_3
<=> ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[and_3]) ).
fof(normalize_0_30,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_29]) ).
fof(normalize_0_31,plain,
! [X,Y] :
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(conjunct,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
and_3,
inference(canonicalize,[],[hilbert_and_3]) ).
fof(normalize_0_33,plain,
( ~ implies_2
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[implies_2]) ).
fof(normalize_0_34,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_33]) ).
fof(normalize_0_35,plain,
! [X,Y] :
( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(conjunct,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
implies_2,
inference(canonicalize,[],[hilbert_implies_2]) ).
fof(normalize_0_37,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_38,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_37]) ).
fof(normalize_0_39,plain,
op_equiv,
inference(canonicalize,[],[hilbert_op_equiv]) ).
fof(normalize_0_40,plain,
( ~ and_2
<=> ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[and_2]) ).
fof(normalize_0_41,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_40]) ).
fof(normalize_0_42,plain,
! [X,Y] :
( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) ),
inference(conjunct,[],[normalize_0_41]) ).
fof(normalize_0_43,plain,
and_2,
inference(canonicalize,[],[hilbert_and_2]) ).
fof(normalize_0_44,plain,
( ~ equivalence_3
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
inference(canonicalize,[],[equivalence_3]) ).
fof(normalize_0_45,plain,
! [X,Y] :
( ( ~ equivalence_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) )
& ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_14,skolemFOFtoCNF_Y_14),implies(implies(skolemFOFtoCNF_Y_14,skolemFOFtoCNF_X_14),equiv(skolemFOFtoCNF_X_14,skolemFOFtoCNF_Y_14))))
| equivalence_3 ) ),
inference(clausify,[],[normalize_0_44]) ).
fof(normalize_0_46,plain,
! [X,Y] :
( ~ equivalence_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
inference(conjunct,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
equivalence_3,
inference(canonicalize,[],[hilbert_equivalence_3]) ).
fof(normalize_0_48,plain,
( ~ modus_tollens
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(canonicalize,[],[modus_tollens]) ).
fof(normalize_0_49,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_48]) ).
fof(normalize_0_50,plain,
! [X,Y] :
( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(conjunct,[],[normalize_0_49]) ).
fof(normalize_0_51,plain,
modus_tollens,
inference(canonicalize,[],[hilbert_modus_tollens]) ).
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,
( ~ axiom_4
<=> ? [X] : ~ is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) ),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_0_57,plain,
! [X] :
( ( ~ axiom_4
| is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) )
& ( ~ is_a_theorem(implies(necessarily(skolemFOFtoCNF_X_21),necessarily(necessarily(skolemFOFtoCNF_X_21))))
| axiom_4 ) ),
inference(clausify,[],[normalize_0_56]) ).
fof(normalize_0_58,plain,
! [X] :
( ~ axiom_4
| is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) ),
inference(conjunct,[],[normalize_0_57]) ).
fof(normalize_0_59,plain,
axiom_4,
inference(canonicalize,[],[km4b_axiom_4]) ).
fof(normalize_0_60,plain,
( ~ axiom_M
<=> ? [X] : ~ is_a_theorem(implies(necessarily(X),X)) ),
inference(canonicalize,[],[axiom_M]) ).
fof(normalize_0_61,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_60]) ).
fof(normalize_0_62,plain,
! [X] :
( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) ),
inference(conjunct,[],[normalize_0_61]) ).
fof(normalize_0_63,plain,
axiom_M,
inference(canonicalize,[],[km4b_axiom_M]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(possibly(skolemFOFtoCNF_X_23),necessarily(possibly(skolemFOFtoCNF_X_23))))
| axiom_5 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ axiom_5,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(possibly(skolemFOFtoCNF_X_23),necessarily(possibly(skolemFOFtoCNF_X_23)))),
inference(resolve,[$cnf( axiom_5 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ axiom_B
| is_a_theorem(implies(X,necessarily(possibly(X)))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
axiom_B,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(X,necessarily(possibly(X)))),
inference(resolve,[$cnf( axiom_B )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(not(X_15),necessarily(possibly(not(X_15))))),
inference(subst,[],[refute_0_5:[bind(X,$fot(not(X_15)))]]) ).
cnf(refute_0_7,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
op_or,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_12,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_14,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_15,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_17,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_17:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_19,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_20,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_9,refute_0_20]) ).
cnf(refute_0_22,plain,
or(X_15,necessarily(possibly(not(X_15)))) = implies(not(X_15),necessarily(possibly(not(X_15)))),
inference(subst,[],[refute_0_21:[bind(X,$fot(X_15)),bind(Y,$fot(necessarily(possibly(not(X_15)))))]]) ).
cnf(refute_0_23,plain,
( or(X_15,necessarily(possibly(not(X_15)))) != implies(not(X_15),necessarily(possibly(not(X_15))))
| implies(not(X_15),necessarily(possibly(not(X_15)))) = or(X_15,necessarily(possibly(not(X_15)))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X_15,necessarily(possibly(not(X_15)))))),bind(Y0,$fot(implies(not(X_15),necessarily(possibly(not(X_15))))))]]) ).
cnf(refute_0_24,plain,
implies(not(X_15),necessarily(possibly(not(X_15)))) = or(X_15,necessarily(possibly(not(X_15)))),
inference(resolve,[$cnf( $equal(or(X_15,necessarily(possibly(not(X_15)))),implies(not(X_15),necessarily(possibly(not(X_15))))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( implies(not(X_15),necessarily(possibly(not(X_15)))) != or(X_15,necessarily(possibly(not(X_15))))
| ~ is_a_theorem(implies(not(X_15),necessarily(possibly(not(X_15)))))
| is_a_theorem(or(X_15,necessarily(possibly(not(X_15))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X_15),necessarily(possibly(not(X_15))))) ),[0],$fot(or(X_15,necessarily(possibly(not(X_15)))))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(not(X_15),necessarily(possibly(not(X_15)))))
| is_a_theorem(or(X_15,necessarily(possibly(not(X_15))))) ),
inference(resolve,[$cnf( $equal(implies(not(X_15),necessarily(possibly(not(X_15)))),or(X_15,necessarily(possibly(not(X_15))))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
is_a_theorem(or(X_15,necessarily(possibly(not(X_15))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_15),necessarily(possibly(not(X_15))))) )],[refute_0_6,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ op_possibly
| possibly(X) = not(necessarily(not(X))) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_29,plain,
op_possibly,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_30,plain,
possibly(X) = not(necessarily(not(X))),
inference(resolve,[$cnf( op_possibly )],[refute_0_29,refute_0_28]) ).
cnf(refute_0_31,plain,
possibly(not(X_11930)) = not(necessarily(not(not(X_11930)))),
inference(subst,[],[refute_0_30:[bind(X,$fot(not(X_11930)))]]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_33,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_33,refute_0_32]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(equiv(X_11928,not(not(X_11928))))
| X_11928 = not(not(X_11928)) ),
inference(subst,[],[refute_0_34:[bind(X,$fot(X_11928)),bind(Y,$fot(not(not(X_11928))))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_37,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_37,refute_0_36]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(implies(or(not(X_11927),X_11927),equiv(X_11927,not(not(X_11927)))))
| ~ is_a_theorem(or(not(X_11927),X_11927))
| is_a_theorem(equiv(X_11927,not(not(X_11927)))) ),
inference(subst,[],[refute_0_38:[bind(X,$fot(or(not(X_11927),X_11927))),bind(Y,$fot(equiv(X_11927,not(not(X_11927)))))]]) ).
cnf(refute_0_40,plain,
( ~ or_2
| is_a_theorem(implies(Y,or(X,Y))) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_41,plain,
or_2,
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(Y,or(X,Y))),
inference(resolve,[$cnf( or_2 )],[refute_0_41,refute_0_40]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(Y,or(Y,Y))),
inference(subst,[],[refute_0_42:[bind(X,$fot(Y))]]) ).
cnf(refute_0_44,plain,
implies(not(Y),Y) = not(and(not(Y),not(Y))),
inference(subst,[],[refute_0_12:[bind(X,$fot(not(Y)))]]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(equiv(X_2394,and(X_2394,X_2394)))
| X_2394 = and(X_2394,X_2394) ),
inference(subst,[],[refute_0_34:[bind(X,$fot(X_2394)),bind(Y,$fot(and(X_2394,X_2394)))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(and(X_2393,X_2393),X_2393))
| ~ is_a_theorem(implies(implies(and(X_2393,X_2393),X_2393),equiv(X_2393,and(X_2393,X_2393))))
| is_a_theorem(equiv(X_2393,and(X_2393,X_2393))) ),
inference(subst,[],[refute_0_38:[bind(X,$fot(implies(and(X_2393,X_2393),X_2393))),bind(Y,$fot(equiv(X_2393,and(X_2393,X_2393))))]]) ).
cnf(refute_0_47,plain,
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_48,plain,
and_3,
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(X,implies(Y,and(X,Y)))),
inference(resolve,[$cnf( and_3 )],[refute_0_48,refute_0_47]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(X_417,implies(Y,and(X_417,Y)))),
inference(subst,[],[refute_0_49:[bind(X,$fot(X_417))]]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(X_417)
| ~ is_a_theorem(implies(X_417,implies(Y,and(X_417,Y))))
| is_a_theorem(implies(Y,and(X_417,Y))) ),
inference(subst,[],[refute_0_38:[bind(X,$fot(X_417)),bind(Y,$fot(implies(Y,and(X_417,Y))))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(X_417)
| is_a_theorem(implies(Y,and(X_417,Y))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_417,implies(Y,and(X_417,Y)))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(implies(X_2117,and(X_2117,X_2117)))
| is_a_theorem(implies(Y,and(implies(X_2117,and(X_2117,X_2117)),Y))) ),
inference(subst,[],[refute_0_52:[bind(X_417,$fot(implies(X_2117,and(X_2117,X_2117))))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(X_2114,implies(X_2114,and(X_2114,X_2114)))),
inference(subst,[],[refute_0_49:[bind(X,$fot(X_2114)),bind(Y,$fot(X_2114))]]) ).
cnf(refute_0_55,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_56,plain,
implies_2,
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))),
inference(resolve,[$cnf( implies_2 )],[refute_0_56,refute_0_55]) ).
cnf(refute_0_58,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_38:[bind(X,$fot(implies(X,implies(X,Y)))),bind(Y,$fot(implies(X,Y)))]]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(implies(X,implies(X,Y)))
| is_a_theorem(implies(X,Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(implies(X_2114,implies(X_2114,and(X_2114,X_2114))))
| is_a_theorem(implies(X_2114,and(X_2114,X_2114))) ),
inference(subst,[],[refute_0_59:[bind(X,$fot(X_2114)),bind(Y,$fot(and(X_2114,X_2114)))]]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(X_2114,and(X_2114,X_2114))),
inference(resolve,[$cnf( is_a_theorem(implies(X_2114,implies(X_2114,and(X_2114,X_2114)))) )],[refute_0_54,refute_0_60]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(X_2117,and(X_2117,X_2117))),
inference(subst,[],[refute_0_61:[bind(X_2114,$fot(X_2117))]]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(Y,and(implies(X_2117,and(X_2117,X_2117)),Y))),
inference(resolve,[$cnf( is_a_theorem(implies(X_2117,and(X_2117,X_2117))) )],[refute_0_62,refute_0_53]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(implies(and(X_2392,X_2392),X_2392),and(implies(X_2392,and(X_2392,X_2392)),implies(and(X_2392,X_2392),X_2392)))),
inference(subst,[],[refute_0_63:[bind(Y,$fot(implies(and(X_2392,X_2392),X_2392))),bind(X_2117,$fot(X_2392))]]) ).
cnf(refute_0_65,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_66,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_67,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_66,refute_0_65]) ).
cnf(refute_0_68,plain,
equiv(X_2392,and(X_2392,X_2392)) = and(implies(X_2392,and(X_2392,X_2392)),implies(and(X_2392,X_2392),X_2392)),
inference(subst,[],[refute_0_67:[bind(X,$fot(X_2392)),bind(Y,$fot(and(X_2392,X_2392)))]]) ).
cnf(refute_0_69,plain,
( equiv(X_2392,and(X_2392,X_2392)) != and(implies(X_2392,and(X_2392,X_2392)),implies(and(X_2392,X_2392),X_2392))
| and(implies(X_2392,and(X_2392,X_2392)),implies(and(X_2392,X_2392),X_2392)) = equiv(X_2392,and(X_2392,X_2392)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(X_2392,and(X_2392,X_2392)))),bind(Y0,$fot(and(implies(X_2392,and(X_2392,X_2392)),implies(and(X_2392,X_2392),X_2392))))]]) ).
cnf(refute_0_70,plain,
and(implies(X_2392,and(X_2392,X_2392)),implies(and(X_2392,X_2392),X_2392)) = equiv(X_2392,and(X_2392,X_2392)),
inference(resolve,[$cnf( $equal(equiv(X_2392,and(X_2392,X_2392)),and(implies(X_2392,and(X_2392,X_2392)),implies(and(X_2392,X_2392),X_2392))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( and(implies(X_2392,and(X_2392,X_2392)),implies(and(X_2392,X_2392),X_2392)) != equiv(X_2392,and(X_2392,X_2392))
| ~ is_a_theorem(implies(implies(and(X_2392,X_2392),X_2392),and(implies(X_2392,and(X_2392,X_2392)),implies(and(X_2392,X_2392),X_2392))))
| is_a_theorem(implies(implies(and(X_2392,X_2392),X_2392),equiv(X_2392,and(X_2392,X_2392)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(and(X_2392,X_2392),X_2392),and(implies(X_2392,and(X_2392,X_2392)),implies(and(X_2392,X_2392),X_2392)))) ),[0,1],$fot(equiv(X_2392,and(X_2392,X_2392)))]]) ).
cnf(refute_0_72,plain,
( ~ is_a_theorem(implies(implies(and(X_2392,X_2392),X_2392),and(implies(X_2392,and(X_2392,X_2392)),implies(and(X_2392,X_2392),X_2392))))
| is_a_theorem(implies(implies(and(X_2392,X_2392),X_2392),equiv(X_2392,and(X_2392,X_2392)))) ),
inference(resolve,[$cnf( $equal(and(implies(X_2392,and(X_2392,X_2392)),implies(and(X_2392,X_2392),X_2392)),equiv(X_2392,and(X_2392,X_2392))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(implies(and(X_2392,X_2392),X_2392),equiv(X_2392,and(X_2392,X_2392)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_2392,X_2392),X_2392),and(implies(X_2392,and(X_2392,X_2392)),implies(and(X_2392,X_2392),X_2392)))) )],[refute_0_64,refute_0_72]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(implies(and(X_2393,X_2393),X_2393),equiv(X_2393,and(X_2393,X_2393)))),
inference(subst,[],[refute_0_73:[bind(X_2392,$fot(X_2393))]]) ).
cnf(refute_0_75,plain,
( ~ is_a_theorem(implies(and(X_2393,X_2393),X_2393))
| is_a_theorem(equiv(X_2393,and(X_2393,X_2393))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_2393,X_2393),X_2393),equiv(X_2393,and(X_2393,X_2393)))) )],[refute_0_74,refute_0_46]) ).
cnf(refute_0_76,plain,
( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_77,plain,
and_2,
inference(canonicalize,[],[normalize_0_43]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(and(X,Y),Y)),
inference(resolve,[$cnf( and_2 )],[refute_0_77,refute_0_76]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(and(X_2393,X_2393),X_2393)),
inference(subst,[],[refute_0_78:[bind(X,$fot(X_2393)),bind(Y,$fot(X_2393))]]) ).
cnf(refute_0_80,plain,
is_a_theorem(equiv(X_2393,and(X_2393,X_2393))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_2393,X_2393),X_2393)) )],[refute_0_79,refute_0_75]) ).
cnf(refute_0_81,plain,
is_a_theorem(equiv(X_2394,and(X_2394,X_2394))),
inference(subst,[],[refute_0_80:[bind(X_2393,$fot(X_2394))]]) ).
cnf(refute_0_82,plain,
X_2394 = and(X_2394,X_2394),
inference(resolve,[$cnf( is_a_theorem(equiv(X_2394,and(X_2394,X_2394))) )],[refute_0_81,refute_0_45]) ).
cnf(refute_0_83,plain,
not(Y) = and(not(Y),not(Y)),
inference(subst,[],[refute_0_82:[bind(X_2394,$fot(not(Y)))]]) ).
cnf(refute_0_84,plain,
( not(Y) != and(not(Y),not(Y))
| and(not(Y),not(Y)) = not(Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(not(Y))),bind(Y0,$fot(and(not(Y),not(Y))))]]) ).
cnf(refute_0_85,plain,
and(not(Y),not(Y)) = not(Y),
inference(resolve,[$cnf( $equal(not(Y),and(not(Y),not(Y))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( and(not(Y),not(Y)) != not(Y)
| implies(not(Y),Y) != not(and(not(Y),not(Y)))
| implies(not(Y),Y) = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(Y),Y),not(and(not(Y),not(Y)))) ),[1,0],$fot(not(Y))]]) ).
cnf(refute_0_87,plain,
( implies(not(Y),Y) != not(and(not(Y),not(Y)))
| implies(not(Y),Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(and(not(Y),not(Y)),not(Y)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
implies(not(Y),Y) = not(not(Y)),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),not(and(not(Y),not(Y)))) )],[refute_0_44,refute_0_87]) ).
cnf(refute_0_89,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_90,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[refute_0_21,refute_0_89]) ).
cnf(refute_0_91,plain,
implies(not(Y),Y) = or(Y,Y),
inference(subst,[],[refute_0_90:[bind(X,$fot(Y))]]) ).
cnf(refute_0_92,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_93,plain,
( implies(not(Y),Y) != not(not(Y))
| or(Y,Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),or(Y,Y)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
or(Y,Y) = not(not(Y)),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),not(not(Y))) )],[refute_0_88,refute_0_93]) ).
cnf(refute_0_95,plain,
( or(Y,Y) != not(not(Y))
| ~ is_a_theorem(implies(Y,or(Y,Y)))
| is_a_theorem(implies(Y,not(not(Y)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(Y,or(Y,Y))) ),[0,1],$fot(not(not(Y)))]]) ).
cnf(refute_0_96,plain,
( ~ is_a_theorem(implies(Y,or(Y,Y)))
| is_a_theorem(implies(Y,not(not(Y)))) ),
inference(resolve,[$cnf( $equal(or(Y,Y),not(not(Y))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
is_a_theorem(implies(Y,not(not(Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(Y,or(Y,Y))) )],[refute_0_43,refute_0_96]) ).
cnf(refute_0_98,plain,
is_a_theorem(implies(X_11925,not(not(X_11925)))),
inference(subst,[],[refute_0_97:[bind(Y,$fot(X_11925))]]) ).
cnf(refute_0_99,plain,
( ~ equivalence_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_100,plain,
equivalence_3,
inference(canonicalize,[],[normalize_0_47]) ).
cnf(refute_0_101,plain,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))),
inference(resolve,[$cnf( equivalence_3 )],[refute_0_100,refute_0_99]) ).
cnf(refute_0_102,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))
| is_a_theorem(implies(implies(Y,X),equiv(X,Y))) ),
inference(subst,[],[refute_0_38:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,X),equiv(X,Y))))]]) ).
cnf(refute_0_103,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,X),equiv(X,Y))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
( ~ is_a_theorem(implies(X_11925,not(not(X_11925))))
| is_a_theorem(implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925))))) ),
inference(subst,[],[refute_0_103:[bind(X,$fot(X_11925)),bind(Y,$fot(not(not(X_11925))))]]) ).
cnf(refute_0_105,plain,
is_a_theorem(implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_11925,not(not(X_11925)))) )],[refute_0_98,refute_0_104]) ).
cnf(refute_0_106,plain,
implies(not(not(X_11925)),X_11925) = or(not(X_11925),X_11925),
inference(subst,[],[refute_0_90:[bind(X,$fot(not(X_11925))),bind(Y,$fot(X_11925))]]) ).
cnf(refute_0_107,plain,
implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925)))) = implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925)))),
introduced(tautology,[refl,[$fot(implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925)))))]]) ).
cnf(refute_0_108,plain,
( implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925)))) != implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925))))
| implies(not(not(X_11925)),X_11925) != or(not(X_11925),X_11925)
| implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925)))) = implies(or(not(X_11925),X_11925),equiv(X_11925,not(not(X_11925)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925)))),implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925))))) ),[1,0],$fot(or(not(X_11925),X_11925))]]) ).
cnf(refute_0_109,plain,
( implies(not(not(X_11925)),X_11925) != or(not(X_11925),X_11925)
| implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925)))) = implies(or(not(X_11925),X_11925),equiv(X_11925,not(not(X_11925)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925)))),implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925))))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925)))) = implies(or(not(X_11925),X_11925),equiv(X_11925,not(not(X_11925)))),
inference(resolve,[$cnf( $equal(implies(not(not(X_11925)),X_11925),or(not(X_11925),X_11925)) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
( implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925)))) != implies(or(not(X_11925),X_11925),equiv(X_11925,not(not(X_11925))))
| ~ is_a_theorem(implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925)))))
| is_a_theorem(implies(or(not(X_11925),X_11925),equiv(X_11925,not(not(X_11925))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925))))) ),[0],$fot(implies(or(not(X_11925),X_11925),equiv(X_11925,not(not(X_11925)))))]]) ).
cnf(refute_0_112,plain,
( ~ is_a_theorem(implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925)))))
| is_a_theorem(implies(or(not(X_11925),X_11925),equiv(X_11925,not(not(X_11925))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925)))),implies(or(not(X_11925),X_11925),equiv(X_11925,not(not(X_11925))))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
is_a_theorem(implies(or(not(X_11925),X_11925),equiv(X_11925,not(not(X_11925))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(X_11925)),X_11925),equiv(X_11925,not(not(X_11925))))) )],[refute_0_105,refute_0_112]) ).
cnf(refute_0_114,plain,
is_a_theorem(implies(or(not(X_11927),X_11927),equiv(X_11927,not(not(X_11927))))),
inference(subst,[],[refute_0_113:[bind(X_11925,$fot(X_11927))]]) ).
cnf(refute_0_115,plain,
( ~ is_a_theorem(or(not(X_11927),X_11927))
| is_a_theorem(equiv(X_11927,not(not(X_11927)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X_11927),X_11927),equiv(X_11927,not(not(X_11927))))) )],[refute_0_114,refute_0_39]) ).
cnf(refute_0_116,plain,
( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(canonicalize,[],[normalize_0_50]) ).
cnf(refute_0_117,plain,
modus_tollens,
inference(canonicalize,[],[normalize_0_51]) ).
cnf(refute_0_118,plain,
is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))),
inference(resolve,[$cnf( modus_tollens )],[refute_0_117,refute_0_116]) ).
cnf(refute_0_119,plain,
implies(not(Y),not(X)) = or(Y,not(X)),
inference(subst,[],[refute_0_90:[bind(X,$fot(Y)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_120,plain,
implies(implies(not(Y),not(X)),implies(X,Y)) = implies(implies(not(Y),not(X)),implies(X,Y)),
introduced(tautology,[refl,[$fot(implies(implies(not(Y),not(X)),implies(X,Y)))]]) ).
cnf(refute_0_121,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_122,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( $equal(implies(implies(not(Y),not(X)),implies(X,Y)),implies(implies(not(Y),not(X)),implies(X,Y))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
implies(implies(not(Y),not(X)),implies(X,Y)) = implies(or(Y,not(X)),implies(X,Y)),
inference(resolve,[$cnf( $equal(implies(not(Y),not(X)),or(Y,not(X))) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
( implies(implies(not(Y),not(X)),implies(X,Y)) != implies(or(Y,not(X)),implies(X,Y))
| ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| is_a_theorem(implies(or(Y,not(X)),implies(X,Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),[0],$fot(implies(or(Y,not(X)),implies(X,Y)))]]) ).
cnf(refute_0_125,plain,
( ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| is_a_theorem(implies(or(Y,not(X)),implies(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),not(X)),implies(X,Y)),implies(or(Y,not(X)),implies(X,Y))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
is_a_theorem(implies(or(Y,not(X)),implies(X,Y))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )],[refute_0_118,refute_0_125]) ).
cnf(refute_0_127,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_38:[bind(X,$fot(or(Y,not(X)))),bind(Y,$fot(implies(X,Y)))]]) ).
cnf(refute_0_128,plain,
( ~ is_a_theorem(or(Y,not(X)))
| is_a_theorem(implies(X,Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(Y,not(X)),implies(X,Y))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
( ~ is_a_theorem(or(X_2503,not(not(not(X_2503)))))
| is_a_theorem(implies(not(not(X_2503)),X_2503)) ),
inference(subst,[],[refute_0_128:[bind(X,$fot(not(not(X_2503)))),bind(Y,$fot(X_2503))]]) ).
cnf(refute_0_130,plain,
( ~ or_1
| is_a_theorem(implies(X,or(X,Y))) ),
inference(canonicalize,[],[normalize_0_54]) ).
cnf(refute_0_131,plain,
or_1,
inference(canonicalize,[],[normalize_0_55]) ).
cnf(refute_0_132,plain,
is_a_theorem(implies(X,or(X,Y))),
inference(resolve,[$cnf( or_1 )],[refute_0_131,refute_0_130]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(not(X_15),or(not(X_15),Y))),
inference(subst,[],[refute_0_132:[bind(X,$fot(not(X_15)))]]) ).
cnf(refute_0_134,plain,
or(X_15,or(not(X_15),Y)) = implies(not(X_15),or(not(X_15),Y)),
inference(subst,[],[refute_0_21:[bind(X,$fot(X_15)),bind(Y,$fot(or(not(X_15),Y)))]]) ).
cnf(refute_0_135,plain,
( or(X_15,or(not(X_15),Y)) != implies(not(X_15),or(not(X_15),Y))
| implies(not(X_15),or(not(X_15),Y)) = or(X_15,or(not(X_15),Y)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X_15,or(not(X_15),Y)))),bind(Y0,$fot(implies(not(X_15),or(not(X_15),Y))))]]) ).
cnf(refute_0_136,plain,
implies(not(X_15),or(not(X_15),Y)) = or(X_15,or(not(X_15),Y)),
inference(resolve,[$cnf( $equal(or(X_15,or(not(X_15),Y)),implies(not(X_15),or(not(X_15),Y))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
( implies(not(X_15),or(not(X_15),Y)) != or(X_15,or(not(X_15),Y))
| ~ is_a_theorem(implies(not(X_15),or(not(X_15),Y)))
| is_a_theorem(or(X_15,or(not(X_15),Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X_15),or(not(X_15),Y))) ),[0],$fot(or(X_15,or(not(X_15),Y)))]]) ).
cnf(refute_0_138,plain,
( ~ is_a_theorem(implies(not(X_15),or(not(X_15),Y)))
| is_a_theorem(or(X_15,or(not(X_15),Y))) ),
inference(resolve,[$cnf( $equal(implies(not(X_15),or(not(X_15),Y)),or(X_15,or(not(X_15),Y))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
is_a_theorem(or(X_15,or(not(X_15),Y))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_15),or(not(X_15),Y))) )],[refute_0_133,refute_0_138]) ).
cnf(refute_0_140,plain,
is_a_theorem(or(X_15,or(not(X_15),not(X_15)))),
inference(subst,[],[refute_0_139:[bind(Y,$fot(not(X_15)))]]) ).
cnf(refute_0_141,plain,
or(not(X_15),not(X_15)) = not(not(not(X_15))),
inference(subst,[],[refute_0_94:[bind(Y,$fot(not(X_15)))]]) ).
cnf(refute_0_142,plain,
( or(not(X_15),not(X_15)) != not(not(not(X_15)))
| ~ is_a_theorem(or(X_15,or(not(X_15),not(X_15))))
| is_a_theorem(or(X_15,not(not(not(X_15))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_15,or(not(X_15),not(X_15)))) ),[0,1],$fot(not(not(not(X_15))))]]) ).
cnf(refute_0_143,plain,
( ~ is_a_theorem(or(X_15,or(not(X_15),not(X_15))))
| is_a_theorem(or(X_15,not(not(not(X_15))))) ),
inference(resolve,[$cnf( $equal(or(not(X_15),not(X_15)),not(not(not(X_15)))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
is_a_theorem(or(X_15,not(not(not(X_15))))),
inference(resolve,[$cnf( is_a_theorem(or(X_15,or(not(X_15),not(X_15)))) )],[refute_0_140,refute_0_143]) ).
cnf(refute_0_145,plain,
is_a_theorem(or(X_2503,not(not(not(X_2503))))),
inference(subst,[],[refute_0_144:[bind(X_15,$fot(X_2503))]]) ).
cnf(refute_0_146,plain,
is_a_theorem(implies(not(not(X_2503)),X_2503)),
inference(resolve,[$cnf( is_a_theorem(or(X_2503,not(not(not(X_2503))))) )],[refute_0_145,refute_0_129]) ).
cnf(refute_0_147,plain,
implies(not(not(X_2503)),X_2503) = or(not(X_2503),X_2503),
inference(subst,[],[refute_0_90:[bind(X,$fot(not(X_2503))),bind(Y,$fot(X_2503))]]) ).
cnf(refute_0_148,plain,
( implies(not(not(X_2503)),X_2503) != or(not(X_2503),X_2503)
| ~ is_a_theorem(implies(not(not(X_2503)),X_2503))
| is_a_theorem(or(not(X_2503),X_2503)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(not(X_2503)),X_2503)) ),[0],$fot(or(not(X_2503),X_2503))]]) ).
cnf(refute_0_149,plain,
( ~ is_a_theorem(implies(not(not(X_2503)),X_2503))
| is_a_theorem(or(not(X_2503),X_2503)) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_2503)),X_2503),or(not(X_2503),X_2503)) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
is_a_theorem(or(not(X_2503),X_2503)),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_2503)),X_2503)) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
is_a_theorem(or(not(X_11927),X_11927)),
inference(subst,[],[refute_0_150:[bind(X_2503,$fot(X_11927))]]) ).
cnf(refute_0_152,plain,
is_a_theorem(equiv(X_11927,not(not(X_11927)))),
inference(resolve,[$cnf( is_a_theorem(or(not(X_11927),X_11927)) )],[refute_0_151,refute_0_115]) ).
cnf(refute_0_153,plain,
is_a_theorem(equiv(X_11928,not(not(X_11928)))),
inference(subst,[],[refute_0_152:[bind(X_11927,$fot(X_11928))]]) ).
cnf(refute_0_154,plain,
X_11928 = not(not(X_11928)),
inference(resolve,[$cnf( is_a_theorem(equiv(X_11928,not(not(X_11928)))) )],[refute_0_153,refute_0_35]) ).
cnf(refute_0_155,plain,
X_11930 = not(not(X_11930)),
inference(subst,[],[refute_0_154:[bind(X_11928,$fot(X_11930))]]) ).
cnf(refute_0_156,plain,
( X_11930 != not(not(X_11930))
| not(not(X_11930)) = X_11930 ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(X_11930)),bind(Y0,$fot(not(not(X_11930))))]]) ).
cnf(refute_0_157,plain,
not(not(X_11930)) = X_11930,
inference(resolve,[$cnf( $equal(X_11930,not(not(X_11930))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
( not(not(X_11930)) != X_11930
| possibly(not(X_11930)) != not(necessarily(not(not(X_11930))))
| possibly(not(X_11930)) = not(necessarily(X_11930)) ),
introduced(tautology,[equality,[$cnf( $equal(possibly(not(X_11930)),not(necessarily(not(not(X_11930))))) ),[1,0,0],$fot(X_11930)]]) ).
cnf(refute_0_159,plain,
( possibly(not(X_11930)) != not(necessarily(not(not(X_11930))))
| possibly(not(X_11930)) = not(necessarily(X_11930)) ),
inference(resolve,[$cnf( $equal(not(not(X_11930)),X_11930) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
possibly(not(X_11930)) = not(necessarily(X_11930)),
inference(resolve,[$cnf( $equal(possibly(not(X_11930)),not(necessarily(not(not(X_11930))))) )],[refute_0_31,refute_0_159]) ).
cnf(refute_0_161,plain,
possibly(not(X_15)) = not(necessarily(X_15)),
inference(subst,[],[refute_0_160:[bind(X_11930,$fot(X_15))]]) ).
cnf(refute_0_162,plain,
necessarily(possibly(not(X_15))) = necessarily(possibly(not(X_15))),
introduced(tautology,[refl,[$fot(necessarily(possibly(not(X_15))))]]) ).
cnf(refute_0_163,plain,
( necessarily(possibly(not(X_15))) != necessarily(possibly(not(X_15)))
| possibly(not(X_15)) != not(necessarily(X_15))
| necessarily(possibly(not(X_15))) = necessarily(not(necessarily(X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(necessarily(possibly(not(X_15))),necessarily(possibly(not(X_15)))) ),[1,0],$fot(not(necessarily(X_15)))]]) ).
cnf(refute_0_164,plain,
( possibly(not(X_15)) != not(necessarily(X_15))
| necessarily(possibly(not(X_15))) = necessarily(not(necessarily(X_15))) ),
inference(resolve,[$cnf( $equal(necessarily(possibly(not(X_15))),necessarily(possibly(not(X_15)))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
necessarily(possibly(not(X_15))) = necessarily(not(necessarily(X_15))),
inference(resolve,[$cnf( $equal(possibly(not(X_15)),not(necessarily(X_15))) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
or(X_15,necessarily(possibly(not(X_15)))) = or(X_15,necessarily(possibly(not(X_15)))),
introduced(tautology,[refl,[$fot(or(X_15,necessarily(possibly(not(X_15)))))]]) ).
cnf(refute_0_167,plain,
( necessarily(possibly(not(X_15))) != necessarily(not(necessarily(X_15)))
| or(X_15,necessarily(possibly(not(X_15)))) != or(X_15,necessarily(possibly(not(X_15))))
| or(X_15,necessarily(possibly(not(X_15)))) = or(X_15,necessarily(not(necessarily(X_15)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_15,necessarily(possibly(not(X_15)))),or(X_15,necessarily(possibly(not(X_15))))) ),[1,1],$fot(necessarily(not(necessarily(X_15))))]]) ).
cnf(refute_0_168,plain,
( necessarily(possibly(not(X_15))) != necessarily(not(necessarily(X_15)))
| or(X_15,necessarily(possibly(not(X_15)))) = or(X_15,necessarily(not(necessarily(X_15)))) ),
inference(resolve,[$cnf( $equal(or(X_15,necessarily(possibly(not(X_15)))),or(X_15,necessarily(possibly(not(X_15))))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
or(X_15,necessarily(possibly(not(X_15)))) = or(X_15,necessarily(not(necessarily(X_15)))),
inference(resolve,[$cnf( $equal(necessarily(possibly(not(X_15))),necessarily(not(necessarily(X_15)))) )],[refute_0_165,refute_0_168]) ).
cnf(refute_0_170,plain,
( or(X_15,necessarily(possibly(not(X_15)))) != or(X_15,necessarily(not(necessarily(X_15))))
| ~ is_a_theorem(or(X_15,necessarily(possibly(not(X_15)))))
| is_a_theorem(or(X_15,necessarily(not(necessarily(X_15))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_15,necessarily(possibly(not(X_15))))) ),[0],$fot(or(X_15,necessarily(not(necessarily(X_15)))))]]) ).
cnf(refute_0_171,plain,
( ~ is_a_theorem(or(X_15,necessarily(possibly(not(X_15)))))
| is_a_theorem(or(X_15,necessarily(not(necessarily(X_15))))) ),
inference(resolve,[$cnf( $equal(or(X_15,necessarily(possibly(not(X_15)))),or(X_15,necessarily(not(necessarily(X_15))))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
is_a_theorem(or(X_15,necessarily(not(necessarily(X_15))))),
inference(resolve,[$cnf( is_a_theorem(or(X_15,necessarily(possibly(not(X_15))))) )],[refute_0_27,refute_0_171]) ).
cnf(refute_0_173,plain,
is_a_theorem(or(necessarily(not(X)),necessarily(not(necessarily(necessarily(not(X))))))),
inference(subst,[],[refute_0_172:[bind(X_15,$fot(necessarily(not(X))))]]) ).
cnf(refute_0_174,plain,
or(necessarily(not(X)),X_16) = implies(not(necessarily(not(X))),X_16),
inference(subst,[],[refute_0_21:[bind(X,$fot(necessarily(not(X)))),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_175,plain,
( possibly(X) != not(necessarily(not(X)))
| not(necessarily(not(X))) = possibly(X) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(possibly(X))),bind(Y0,$fot(not(necessarily(not(X)))))]]) ).
cnf(refute_0_176,plain,
not(necessarily(not(X))) = possibly(X),
inference(resolve,[$cnf( $equal(possibly(X),not(necessarily(not(X)))) )],[refute_0_30,refute_0_175]) ).
cnf(refute_0_177,plain,
( not(necessarily(not(X))) != possibly(X)
| or(necessarily(not(X)),X_16) != implies(not(necessarily(not(X))),X_16)
| or(necessarily(not(X)),X_16) = implies(possibly(X),X_16) ),
introduced(tautology,[equality,[$cnf( $equal(or(necessarily(not(X)),X_16),implies(not(necessarily(not(X))),X_16)) ),[1,0],$fot(possibly(X))]]) ).
cnf(refute_0_178,plain,
( or(necessarily(not(X)),X_16) != implies(not(necessarily(not(X))),X_16)
| or(necessarily(not(X)),X_16) = implies(possibly(X),X_16) ),
inference(resolve,[$cnf( $equal(not(necessarily(not(X))),possibly(X)) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
or(necessarily(not(X)),X_16) = implies(possibly(X),X_16),
inference(resolve,[$cnf( $equal(or(necessarily(not(X)),X_16),implies(not(necessarily(not(X))),X_16)) )],[refute_0_174,refute_0_178]) ).
cnf(refute_0_180,plain,
or(necessarily(not(X)),necessarily(not(necessarily(necessarily(not(X)))))) = implies(possibly(X),necessarily(not(necessarily(necessarily(not(X)))))),
inference(subst,[],[refute_0_179:[bind(X_16,$fot(necessarily(not(necessarily(necessarily(not(X)))))))]]) ).
cnf(refute_0_181,plain,
( or(necessarily(not(X)),necessarily(not(necessarily(necessarily(not(X)))))) != implies(possibly(X),necessarily(not(necessarily(necessarily(not(X))))))
| ~ is_a_theorem(or(necessarily(not(X)),necessarily(not(necessarily(necessarily(not(X)))))))
| is_a_theorem(implies(possibly(X),necessarily(not(necessarily(necessarily(not(X))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(necessarily(not(X)),necessarily(not(necessarily(necessarily(not(X))))))) ),[0],$fot(implies(possibly(X),necessarily(not(necessarily(necessarily(not(X)))))))]]) ).
cnf(refute_0_182,plain,
( ~ is_a_theorem(or(necessarily(not(X)),necessarily(not(necessarily(necessarily(not(X)))))))
| is_a_theorem(implies(possibly(X),necessarily(not(necessarily(necessarily(not(X))))))) ),
inference(resolve,[$cnf( $equal(or(necessarily(not(X)),necessarily(not(necessarily(necessarily(not(X)))))),implies(possibly(X),necessarily(not(necessarily(necessarily(not(X))))))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
is_a_theorem(implies(possibly(X),necessarily(not(necessarily(necessarily(not(X))))))),
inference(resolve,[$cnf( is_a_theorem(or(necessarily(not(X)),necessarily(not(necessarily(necessarily(not(X))))))) )],[refute_0_173,refute_0_182]) ).
cnf(refute_0_184,plain,
( X_11928 != not(not(X_11928))
| not(not(X_11928)) = X_11928 ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(X_11928)),bind(Y0,$fot(not(not(X_11928))))]]) ).
cnf(refute_0_185,plain,
not(not(X_11928)) = X_11928,
inference(resolve,[$cnf( $equal(X_11928,not(not(X_11928))) )],[refute_0_154,refute_0_184]) ).
cnf(refute_0_186,plain,
not(not(implies(possibly(X),necessarily(possibly(X))))) = implies(possibly(X),necessarily(possibly(X))),
inference(subst,[],[refute_0_185:[bind(X_11928,$fot(implies(possibly(X),necessarily(possibly(X)))))]]) ).
cnf(refute_0_187,plain,
or(and(X_41,not(X_42)),Y) = implies(not(and(X_41,not(X_42))),Y),
inference(subst,[],[refute_0_21:[bind(X,$fot(and(X_41,not(X_42))))]]) ).
cnf(refute_0_188,plain,
implies(X_41,X_42) = not(and(X_41,not(X_42))),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_41)),bind(Y,$fot(X_42))]]) ).
cnf(refute_0_189,plain,
( implies(X_41,X_42) != not(and(X_41,not(X_42)))
| not(and(X_41,not(X_42))) = implies(X_41,X_42) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X_41,X_42))),bind(Y0,$fot(not(and(X_41,not(X_42)))))]]) ).
cnf(refute_0_190,plain,
not(and(X_41,not(X_42))) = implies(X_41,X_42),
inference(resolve,[$cnf( $equal(implies(X_41,X_42),not(and(X_41,not(X_42)))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
( not(and(X_41,not(X_42))) != implies(X_41,X_42)
| or(and(X_41,not(X_42)),Y) != implies(not(and(X_41,not(X_42))),Y)
| or(and(X_41,not(X_42)),Y) = implies(implies(X_41,X_42),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_41,not(X_42)),Y),implies(not(and(X_41,not(X_42))),Y)) ),[1,0],$fot(implies(X_41,X_42))]]) ).
cnf(refute_0_192,plain,
( or(and(X_41,not(X_42)),Y) != implies(not(and(X_41,not(X_42))),Y)
| or(and(X_41,not(X_42)),Y) = implies(implies(X_41,X_42),Y) ),
inference(resolve,[$cnf( $equal(not(and(X_41,not(X_42))),implies(X_41,X_42)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
or(and(X_41,not(X_42)),Y) = implies(implies(X_41,X_42),Y),
inference(resolve,[$cnf( $equal(or(and(X_41,not(X_42)),Y),implies(not(and(X_41,not(X_42))),Y)) )],[refute_0_187,refute_0_192]) ).
cnf(refute_0_194,plain,
or(and(X_41,not(X_42)),and(X_41,not(X_42))) = implies(implies(X_41,X_42),and(X_41,not(X_42))),
inference(subst,[],[refute_0_193:[bind(Y,$fot(and(X_41,not(X_42))))]]) ).
cnf(refute_0_195,plain,
not(not(Y)) = Y,
inference(subst,[],[refute_0_185:[bind(X_11928,$fot(Y))]]) ).
cnf(refute_0_196,plain,
( not(not(Y)) != Y
| or(Y,Y) != not(not(Y))
| or(Y,Y) = Y ),
introduced(tautology,[equality,[$cnf( $equal(or(Y,Y),not(not(Y))) ),[1],$fot(Y)]]) ).
cnf(refute_0_197,plain,
( or(Y,Y) != not(not(Y))
| or(Y,Y) = Y ),
inference(resolve,[$cnf( $equal(not(not(Y)),Y) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
or(Y,Y) = Y,
inference(resolve,[$cnf( $equal(or(Y,Y),not(not(Y))) )],[refute_0_94,refute_0_197]) ).
cnf(refute_0_199,plain,
or(and(X_41,not(X_42)),and(X_41,not(X_42))) = and(X_41,not(X_42)),
inference(subst,[],[refute_0_198:[bind(Y,$fot(and(X_41,not(X_42))))]]) ).
cnf(refute_0_200,plain,
( or(and(X_41,not(X_42)),and(X_41,not(X_42))) != and(X_41,not(X_42))
| or(and(X_41,not(X_42)),and(X_41,not(X_42))) != implies(implies(X_41,X_42),and(X_41,not(X_42)))
| and(X_41,not(X_42)) = implies(implies(X_41,X_42),and(X_41,not(X_42))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_41,not(X_42)),and(X_41,not(X_42))),implies(implies(X_41,X_42),and(X_41,not(X_42)))) ),[0],$fot(and(X_41,not(X_42)))]]) ).
cnf(refute_0_201,plain,
( or(and(X_41,not(X_42)),and(X_41,not(X_42))) != implies(implies(X_41,X_42),and(X_41,not(X_42)))
| and(X_41,not(X_42)) = implies(implies(X_41,X_42),and(X_41,not(X_42))) ),
inference(resolve,[$cnf( $equal(or(and(X_41,not(X_42)),and(X_41,not(X_42))),and(X_41,not(X_42))) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
and(X_41,not(X_42)) = implies(implies(X_41,X_42),and(X_41,not(X_42))),
inference(resolve,[$cnf( $equal(or(and(X_41,not(X_42)),and(X_41,not(X_42))),implies(implies(X_41,X_42),and(X_41,not(X_42)))) )],[refute_0_194,refute_0_201]) ).
cnf(refute_0_203,plain,
( X_2394 != and(X_2394,X_2394)
| and(X_2394,X_2394) = X_2394 ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(X_2394)),bind(Y0,$fot(and(X_2394,X_2394)))]]) ).
cnf(refute_0_204,plain,
and(X_2394,X_2394) = X_2394,
inference(resolve,[$cnf( $equal(X_2394,and(X_2394,X_2394)) )],[refute_0_82,refute_0_203]) ).
cnf(refute_0_205,plain,
and(implies(X_41,X_42),implies(X_41,X_42)) = implies(X_41,X_42),
inference(subst,[],[refute_0_204:[bind(X_2394,$fot(implies(X_41,X_42)))]]) ).
cnf(refute_0_206,plain,
not(and(implies(X_41,X_42),implies(X_41,X_42))) = not(and(implies(X_41,X_42),implies(X_41,X_42))),
introduced(tautology,[refl,[$fot(not(and(implies(X_41,X_42),implies(X_41,X_42))))]]) ).
cnf(refute_0_207,plain,
( and(implies(X_41,X_42),implies(X_41,X_42)) != implies(X_41,X_42)
| not(and(implies(X_41,X_42),implies(X_41,X_42))) != not(and(implies(X_41,X_42),implies(X_41,X_42)))
| not(and(implies(X_41,X_42),implies(X_41,X_42))) = not(implies(X_41,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(implies(X_41,X_42),implies(X_41,X_42))),not(and(implies(X_41,X_42),implies(X_41,X_42)))) ),[1,0],$fot(implies(X_41,X_42))]]) ).
cnf(refute_0_208,plain,
( and(implies(X_41,X_42),implies(X_41,X_42)) != implies(X_41,X_42)
| not(and(implies(X_41,X_42),implies(X_41,X_42))) = not(implies(X_41,X_42)) ),
inference(resolve,[$cnf( $equal(not(and(implies(X_41,X_42),implies(X_41,X_42))),not(and(implies(X_41,X_42),implies(X_41,X_42)))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
not(and(implies(X_41,X_42),implies(X_41,X_42))) = not(implies(X_41,X_42)),
inference(resolve,[$cnf( $equal(and(implies(X_41,X_42),implies(X_41,X_42)),implies(X_41,X_42)) )],[refute_0_205,refute_0_208]) ).
cnf(refute_0_210,plain,
implies(X,and(X_41,not(X_42))) = not(and(X,not(and(X_41,not(X_42))))),
inference(subst,[],[refute_0_12:[bind(Y,$fot(and(X_41,not(X_42))))]]) ).
cnf(refute_0_211,plain,
( implies(X,and(X_41,not(X_42))) != not(and(X,not(and(X_41,not(X_42)))))
| not(and(X_41,not(X_42))) != implies(X_41,X_42)
| implies(X,and(X_41,not(X_42))) = not(and(X,implies(X_41,X_42))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,and(X_41,not(X_42))),not(and(X,not(and(X_41,not(X_42)))))) ),[1,0,1],$fot(implies(X_41,X_42))]]) ).
cnf(refute_0_212,plain,
( implies(X,and(X_41,not(X_42))) != not(and(X,not(and(X_41,not(X_42)))))
| implies(X,and(X_41,not(X_42))) = not(and(X,implies(X_41,X_42))) ),
inference(resolve,[$cnf( $equal(not(and(X_41,not(X_42))),implies(X_41,X_42)) )],[refute_0_190,refute_0_211]) ).
cnf(refute_0_213,plain,
implies(X,and(X_41,not(X_42))) = not(and(X,implies(X_41,X_42))),
inference(resolve,[$cnf( $equal(implies(X,and(X_41,not(X_42))),not(and(X,not(and(X_41,not(X_42)))))) )],[refute_0_210,refute_0_212]) ).
cnf(refute_0_214,plain,
implies(implies(X_41,X_42),and(X_41,not(X_42))) = not(and(implies(X_41,X_42),implies(X_41,X_42))),
inference(subst,[],[refute_0_213:[bind(X,$fot(implies(X_41,X_42)))]]) ).
cnf(refute_0_215,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_216,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_15,refute_0_215]) ).
cnf(refute_0_217,plain,
( implies(implies(X_41,X_42),and(X_41,not(X_42))) != not(and(implies(X_41,X_42),implies(X_41,X_42)))
| not(and(implies(X_41,X_42),implies(X_41,X_42))) != not(implies(X_41,X_42))
| implies(implies(X_41,X_42),and(X_41,not(X_42))) = not(implies(X_41,X_42)) ),
inference(subst,[],[refute_0_216:[bind(X0,$fot(implies(implies(X_41,X_42),and(X_41,not(X_42))))),bind(Y0,$fot(not(and(implies(X_41,X_42),implies(X_41,X_42))))),bind(Z,$fot(not(implies(X_41,X_42))))]]) ).
cnf(refute_0_218,plain,
( not(and(implies(X_41,X_42),implies(X_41,X_42))) != not(implies(X_41,X_42))
| implies(implies(X_41,X_42),and(X_41,not(X_42))) = not(implies(X_41,X_42)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_41,X_42),and(X_41,not(X_42))),not(and(implies(X_41,X_42),implies(X_41,X_42)))) )],[refute_0_214,refute_0_217]) ).
cnf(refute_0_219,plain,
implies(implies(X_41,X_42),and(X_41,not(X_42))) = not(implies(X_41,X_42)),
inference(resolve,[$cnf( $equal(not(and(implies(X_41,X_42),implies(X_41,X_42))),not(implies(X_41,X_42))) )],[refute_0_209,refute_0_218]) ).
cnf(refute_0_220,plain,
( and(X_41,not(X_42)) != implies(implies(X_41,X_42),and(X_41,not(X_42)))
| implies(implies(X_41,X_42),and(X_41,not(X_42))) != not(implies(X_41,X_42))
| and(X_41,not(X_42)) = not(implies(X_41,X_42)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_41,not(X_42)),not(implies(X_41,X_42))) ),[0],$fot(implies(implies(X_41,X_42),and(X_41,not(X_42))))]]) ).
cnf(refute_0_221,plain,
( and(X_41,not(X_42)) != implies(implies(X_41,X_42),and(X_41,not(X_42)))
| and(X_41,not(X_42)) = not(implies(X_41,X_42)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_41,X_42),and(X_41,not(X_42))),not(implies(X_41,X_42))) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
and(X_41,not(X_42)) = not(implies(X_41,X_42)),
inference(resolve,[$cnf( $equal(and(X_41,not(X_42)),implies(implies(X_41,X_42),and(X_41,not(X_42)))) )],[refute_0_202,refute_0_221]) ).
cnf(refute_0_223,plain,
and(possibly(X),not(necessarily(possibly(X)))) = not(implies(possibly(X),necessarily(possibly(X)))),
inference(subst,[],[refute_0_222:[bind(X_41,$fot(possibly(X))),bind(X_42,$fot(necessarily(possibly(X))))]]) ).
cnf(refute_0_224,plain,
possibly(necessarily(not(X_1))) = not(necessarily(not(necessarily(not(X_1))))),
inference(subst,[],[refute_0_30:[bind(X,$fot(necessarily(not(X_1))))]]) ).
cnf(refute_0_225,plain,
possibly(X_1) = not(necessarily(not(X_1))),
inference(subst,[],[refute_0_30:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_226,plain,
( possibly(X_1) != not(necessarily(not(X_1)))
| not(necessarily(not(X_1))) = possibly(X_1) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(possibly(X_1))),bind(Y0,$fot(not(necessarily(not(X_1)))))]]) ).
cnf(refute_0_227,plain,
not(necessarily(not(X_1))) = possibly(X_1),
inference(resolve,[$cnf( $equal(possibly(X_1),not(necessarily(not(X_1)))) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
( not(necessarily(not(X_1))) != possibly(X_1)
| possibly(necessarily(not(X_1))) != not(necessarily(not(necessarily(not(X_1)))))
| possibly(necessarily(not(X_1))) = not(necessarily(possibly(X_1))) ),
introduced(tautology,[equality,[$cnf( $equal(possibly(necessarily(not(X_1))),not(necessarily(not(necessarily(not(X_1)))))) ),[1,0,0],$fot(possibly(X_1))]]) ).
cnf(refute_0_229,plain,
( possibly(necessarily(not(X_1))) != not(necessarily(not(necessarily(not(X_1)))))
| possibly(necessarily(not(X_1))) = not(necessarily(possibly(X_1))) ),
inference(resolve,[$cnf( $equal(not(necessarily(not(X_1))),possibly(X_1)) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
possibly(necessarily(not(X_1))) = not(necessarily(possibly(X_1))),
inference(resolve,[$cnf( $equal(possibly(necessarily(not(X_1))),not(necessarily(not(necessarily(not(X_1)))))) )],[refute_0_224,refute_0_229]) ).
cnf(refute_0_231,plain,
possibly(necessarily(not(X))) = not(necessarily(possibly(X))),
inference(subst,[],[refute_0_230:[bind(X_1,$fot(X))]]) ).
cnf(refute_0_232,plain,
( ~ is_a_theorem(equiv(necessarily(X_4890),necessarily(necessarily(X_4890))))
| necessarily(X_4890) = necessarily(necessarily(X_4890)) ),
inference(subst,[],[refute_0_34:[bind(X,$fot(necessarily(X_4890))),bind(Y,$fot(necessarily(necessarily(X_4890))))]]) ).
cnf(refute_0_233,plain,
( ~ is_a_theorem(implies(implies(necessarily(necessarily(X_4889)),necessarily(X_4889)),equiv(necessarily(X_4889),necessarily(necessarily(X_4889)))))
| ~ is_a_theorem(implies(necessarily(necessarily(X_4889)),necessarily(X_4889)))
| is_a_theorem(equiv(necessarily(X_4889),necessarily(necessarily(X_4889)))) ),
inference(subst,[],[refute_0_38:[bind(X,$fot(implies(necessarily(necessarily(X_4889)),necessarily(X_4889)))),bind(Y,$fot(equiv(necessarily(X_4889),necessarily(necessarily(X_4889)))))]]) ).
cnf(refute_0_234,plain,
( ~ axiom_4
| is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) ),
inference(canonicalize,[],[normalize_0_58]) ).
cnf(refute_0_235,plain,
axiom_4,
inference(canonicalize,[],[normalize_0_59]) ).
cnf(refute_0_236,plain,
is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))),
inference(resolve,[$cnf( axiom_4 )],[refute_0_235,refute_0_234]) ).
cnf(refute_0_237,plain,
( ~ is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))
| is_a_theorem(implies(X_900,and(implies(necessarily(X),necessarily(necessarily(X))),X_900))) ),
inference(subst,[],[refute_0_52:[bind(Y,$fot(X_900)),bind(X_417,$fot(implies(necessarily(X),necessarily(necessarily(X)))))]]) ).
cnf(refute_0_238,plain,
is_a_theorem(implies(X_900,and(implies(necessarily(X),necessarily(necessarily(X))),X_900))),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
is_a_theorem(implies(implies(necessarily(necessarily(X_4887)),necessarily(X_4887)),and(implies(necessarily(X_4887),necessarily(necessarily(X_4887))),implies(necessarily(necessarily(X_4887)),necessarily(X_4887))))),
inference(subst,[],[refute_0_238:[bind(X,$fot(X_4887)),bind(X_900,$fot(implies(necessarily(necessarily(X_4887)),necessarily(X_4887))))]]) ).
cnf(refute_0_240,plain,
equiv(necessarily(X_4887),necessarily(necessarily(X_4887))) = and(implies(necessarily(X_4887),necessarily(necessarily(X_4887))),implies(necessarily(necessarily(X_4887)),necessarily(X_4887))),
inference(subst,[],[refute_0_67:[bind(X,$fot(necessarily(X_4887))),bind(Y,$fot(necessarily(necessarily(X_4887))))]]) ).
cnf(refute_0_241,plain,
( equiv(necessarily(X_4887),necessarily(necessarily(X_4887))) != and(implies(necessarily(X_4887),necessarily(necessarily(X_4887))),implies(necessarily(necessarily(X_4887)),necessarily(X_4887)))
| and(implies(necessarily(X_4887),necessarily(necessarily(X_4887))),implies(necessarily(necessarily(X_4887)),necessarily(X_4887))) = equiv(necessarily(X_4887),necessarily(necessarily(X_4887))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(necessarily(X_4887),necessarily(necessarily(X_4887))))),bind(Y0,$fot(and(implies(necessarily(X_4887),necessarily(necessarily(X_4887))),implies(necessarily(necessarily(X_4887)),necessarily(X_4887)))))]]) ).
cnf(refute_0_242,plain,
and(implies(necessarily(X_4887),necessarily(necessarily(X_4887))),implies(necessarily(necessarily(X_4887)),necessarily(X_4887))) = equiv(necessarily(X_4887),necessarily(necessarily(X_4887))),
inference(resolve,[$cnf( $equal(equiv(necessarily(X_4887),necessarily(necessarily(X_4887))),and(implies(necessarily(X_4887),necessarily(necessarily(X_4887))),implies(necessarily(necessarily(X_4887)),necessarily(X_4887)))) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
( and(implies(necessarily(X_4887),necessarily(necessarily(X_4887))),implies(necessarily(necessarily(X_4887)),necessarily(X_4887))) != equiv(necessarily(X_4887),necessarily(necessarily(X_4887)))
| ~ is_a_theorem(implies(implies(necessarily(necessarily(X_4887)),necessarily(X_4887)),and(implies(necessarily(X_4887),necessarily(necessarily(X_4887))),implies(necessarily(necessarily(X_4887)),necessarily(X_4887)))))
| is_a_theorem(implies(implies(necessarily(necessarily(X_4887)),necessarily(X_4887)),equiv(necessarily(X_4887),necessarily(necessarily(X_4887))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(necessarily(necessarily(X_4887)),necessarily(X_4887)),and(implies(necessarily(X_4887),necessarily(necessarily(X_4887))),implies(necessarily(necessarily(X_4887)),necessarily(X_4887))))) ),[0,1],$fot(equiv(necessarily(X_4887),necessarily(necessarily(X_4887))))]]) ).
cnf(refute_0_244,plain,
( ~ is_a_theorem(implies(implies(necessarily(necessarily(X_4887)),necessarily(X_4887)),and(implies(necessarily(X_4887),necessarily(necessarily(X_4887))),implies(necessarily(necessarily(X_4887)),necessarily(X_4887)))))
| is_a_theorem(implies(implies(necessarily(necessarily(X_4887)),necessarily(X_4887)),equiv(necessarily(X_4887),necessarily(necessarily(X_4887))))) ),
inference(resolve,[$cnf( $equal(and(implies(necessarily(X_4887),necessarily(necessarily(X_4887))),implies(necessarily(necessarily(X_4887)),necessarily(X_4887))),equiv(necessarily(X_4887),necessarily(necessarily(X_4887)))) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
is_a_theorem(implies(implies(necessarily(necessarily(X_4887)),necessarily(X_4887)),equiv(necessarily(X_4887),necessarily(necessarily(X_4887))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(necessarily(necessarily(X_4887)),necessarily(X_4887)),and(implies(necessarily(X_4887),necessarily(necessarily(X_4887))),implies(necessarily(necessarily(X_4887)),necessarily(X_4887))))) )],[refute_0_239,refute_0_244]) ).
cnf(refute_0_246,plain,
is_a_theorem(implies(implies(necessarily(necessarily(X_4889)),necessarily(X_4889)),equiv(necessarily(X_4889),necessarily(necessarily(X_4889))))),
inference(subst,[],[refute_0_245:[bind(X_4887,$fot(X_4889))]]) ).
cnf(refute_0_247,plain,
( ~ is_a_theorem(implies(necessarily(necessarily(X_4889)),necessarily(X_4889)))
| is_a_theorem(equiv(necessarily(X_4889),necessarily(necessarily(X_4889)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(necessarily(necessarily(X_4889)),necessarily(X_4889)),equiv(necessarily(X_4889),necessarily(necessarily(X_4889))))) )],[refute_0_246,refute_0_233]) ).
cnf(refute_0_248,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) ),
inference(canonicalize,[],[normalize_0_62]) ).
cnf(refute_0_249,plain,
axiom_M,
inference(canonicalize,[],[normalize_0_63]) ).
cnf(refute_0_250,plain,
is_a_theorem(implies(necessarily(X),X)),
inference(resolve,[$cnf( axiom_M )],[refute_0_249,refute_0_248]) ).
cnf(refute_0_251,plain,
is_a_theorem(implies(necessarily(necessarily(X_4889)),necessarily(X_4889))),
inference(subst,[],[refute_0_250:[bind(X,$fot(necessarily(X_4889)))]]) ).
cnf(refute_0_252,plain,
is_a_theorem(equiv(necessarily(X_4889),necessarily(necessarily(X_4889)))),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(necessarily(X_4889)),necessarily(X_4889))) )],[refute_0_251,refute_0_247]) ).
cnf(refute_0_253,plain,
is_a_theorem(equiv(necessarily(X_4890),necessarily(necessarily(X_4890)))),
inference(subst,[],[refute_0_252:[bind(X_4889,$fot(X_4890))]]) ).
cnf(refute_0_254,plain,
necessarily(X_4890) = necessarily(necessarily(X_4890)),
inference(resolve,[$cnf( is_a_theorem(equiv(necessarily(X_4890),necessarily(necessarily(X_4890)))) )],[refute_0_253,refute_0_232]) ).
cnf(refute_0_255,plain,
( necessarily(X_4890) != necessarily(necessarily(X_4890))
| necessarily(necessarily(X_4890)) = necessarily(X_4890) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(necessarily(X_4890))),bind(Y0,$fot(necessarily(necessarily(X_4890))))]]) ).
cnf(refute_0_256,plain,
necessarily(necessarily(X_4890)) = necessarily(X_4890),
inference(resolve,[$cnf( $equal(necessarily(X_4890),necessarily(necessarily(X_4890))) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
necessarily(necessarily(not(X))) = necessarily(not(X)),
inference(subst,[],[refute_0_256:[bind(X_4890,$fot(not(X)))]]) ).
cnf(refute_0_258,plain,
possibly(necessarily(necessarily(not(X)))) = possibly(necessarily(necessarily(not(X)))),
introduced(tautology,[refl,[$fot(possibly(necessarily(necessarily(not(X)))))]]) ).
cnf(refute_0_259,plain,
( necessarily(necessarily(not(X))) != necessarily(not(X))
| possibly(necessarily(necessarily(not(X)))) != possibly(necessarily(necessarily(not(X))))
| possibly(necessarily(necessarily(not(X)))) = possibly(necessarily(not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(possibly(necessarily(necessarily(not(X)))),possibly(necessarily(necessarily(not(X))))) ),[1,0],$fot(necessarily(not(X)))]]) ).
cnf(refute_0_260,plain,
( necessarily(necessarily(not(X))) != necessarily(not(X))
| possibly(necessarily(necessarily(not(X)))) = possibly(necessarily(not(X))) ),
inference(resolve,[$cnf( $equal(possibly(necessarily(necessarily(not(X)))),possibly(necessarily(necessarily(not(X))))) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
possibly(necessarily(necessarily(not(X)))) = possibly(necessarily(not(X))),
inference(resolve,[$cnf( $equal(necessarily(necessarily(not(X))),necessarily(not(X))) )],[refute_0_257,refute_0_260]) ).
cnf(refute_0_262,plain,
( possibly(necessarily(necessarily(not(X)))) != possibly(necessarily(not(X)))
| possibly(necessarily(not(X))) != not(necessarily(possibly(X)))
| possibly(necessarily(necessarily(not(X)))) = not(necessarily(possibly(X))) ),
inference(subst,[],[refute_0_216:[bind(X0,$fot(possibly(necessarily(necessarily(not(X)))))),bind(Y0,$fot(possibly(necessarily(not(X))))),bind(Z,$fot(not(necessarily(possibly(X)))))]]) ).
cnf(refute_0_263,plain,
( possibly(necessarily(not(X))) != not(necessarily(possibly(X)))
| possibly(necessarily(necessarily(not(X)))) = not(necessarily(possibly(X))) ),
inference(resolve,[$cnf( $equal(possibly(necessarily(necessarily(not(X)))),possibly(necessarily(not(X)))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
possibly(necessarily(necessarily(not(X)))) = not(necessarily(possibly(X))),
inference(resolve,[$cnf( $equal(possibly(necessarily(not(X))),not(necessarily(possibly(X)))) )],[refute_0_231,refute_0_263]) ).
cnf(refute_0_265,plain,
and(possibly(X),possibly(necessarily(necessarily(not(X))))) = and(possibly(X),possibly(necessarily(necessarily(not(X))))),
introduced(tautology,[refl,[$fot(and(possibly(X),possibly(necessarily(necessarily(not(X))))))]]) ).
cnf(refute_0_266,plain,
( and(possibly(X),possibly(necessarily(necessarily(not(X))))) != and(possibly(X),possibly(necessarily(necessarily(not(X)))))
| possibly(necessarily(necessarily(not(X)))) != not(necessarily(possibly(X)))
| and(possibly(X),possibly(necessarily(necessarily(not(X))))) = and(possibly(X),not(necessarily(possibly(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(and(possibly(X),possibly(necessarily(necessarily(not(X))))),and(possibly(X),possibly(necessarily(necessarily(not(X)))))) ),[1,1],$fot(not(necessarily(possibly(X))))]]) ).
cnf(refute_0_267,plain,
( possibly(necessarily(necessarily(not(X)))) != not(necessarily(possibly(X)))
| and(possibly(X),possibly(necessarily(necessarily(not(X))))) = and(possibly(X),not(necessarily(possibly(X)))) ),
inference(resolve,[$cnf( $equal(and(possibly(X),possibly(necessarily(necessarily(not(X))))),and(possibly(X),possibly(necessarily(necessarily(not(X)))))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
and(possibly(X),possibly(necessarily(necessarily(not(X))))) = and(possibly(X),not(necessarily(possibly(X)))),
inference(resolve,[$cnf( $equal(possibly(necessarily(necessarily(not(X)))),not(necessarily(possibly(X)))) )],[refute_0_264,refute_0_267]) ).
cnf(refute_0_269,plain,
( and(possibly(X),not(necessarily(possibly(X)))) != not(implies(possibly(X),necessarily(possibly(X))))
| and(possibly(X),possibly(necessarily(necessarily(not(X))))) != and(possibly(X),not(necessarily(possibly(X))))
| and(possibly(X),possibly(necessarily(necessarily(not(X))))) = not(implies(possibly(X),necessarily(possibly(X)))) ),
inference(subst,[],[refute_0_216:[bind(X0,$fot(and(possibly(X),possibly(necessarily(necessarily(not(X))))))),bind(Y0,$fot(and(possibly(X),not(necessarily(possibly(X)))))),bind(Z,$fot(not(implies(possibly(X),necessarily(possibly(X))))))]]) ).
cnf(refute_0_270,plain,
( and(possibly(X),not(necessarily(possibly(X)))) != not(implies(possibly(X),necessarily(possibly(X))))
| and(possibly(X),possibly(necessarily(necessarily(not(X))))) = not(implies(possibly(X),necessarily(possibly(X)))) ),
inference(resolve,[$cnf( $equal(and(possibly(X),possibly(necessarily(necessarily(not(X))))),and(possibly(X),not(necessarily(possibly(X))))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
and(possibly(X),possibly(necessarily(necessarily(not(X))))) = not(implies(possibly(X),necessarily(possibly(X)))),
inference(resolve,[$cnf( $equal(and(possibly(X),not(necessarily(possibly(X)))),not(implies(possibly(X),necessarily(possibly(X))))) )],[refute_0_223,refute_0_270]) ).
cnf(refute_0_272,plain,
not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))) = not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))),
introduced(tautology,[refl,[$fot(not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))))]]) ).
cnf(refute_0_273,plain,
( and(possibly(X),possibly(necessarily(necessarily(not(X))))) != not(implies(possibly(X),necessarily(possibly(X))))
| not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))) != not(and(possibly(X),possibly(necessarily(necessarily(not(X))))))
| not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))) = not(not(implies(possibly(X),necessarily(possibly(X))))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))),not(and(possibly(X),possibly(necessarily(necessarily(not(X))))))) ),[1,0],$fot(not(implies(possibly(X),necessarily(possibly(X)))))]]) ).
cnf(refute_0_274,plain,
( and(possibly(X),possibly(necessarily(necessarily(not(X))))) != not(implies(possibly(X),necessarily(possibly(X))))
| not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))) = not(not(implies(possibly(X),necessarily(possibly(X))))) ),
inference(resolve,[$cnf( $equal(not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))),not(and(possibly(X),possibly(necessarily(necessarily(not(X))))))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))) = not(not(implies(possibly(X),necessarily(possibly(X))))),
inference(resolve,[$cnf( $equal(and(possibly(X),possibly(necessarily(necessarily(not(X))))),not(implies(possibly(X),necessarily(possibly(X))))) )],[refute_0_271,refute_0_274]) ).
cnf(refute_0_276,plain,
( not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))) != not(not(implies(possibly(X),necessarily(possibly(X)))))
| not(not(implies(possibly(X),necessarily(possibly(X))))) != implies(possibly(X),necessarily(possibly(X)))
| not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))) = implies(possibly(X),necessarily(possibly(X))) ),
inference(subst,[],[refute_0_216:[bind(X0,$fot(not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))))),bind(Y0,$fot(not(not(implies(possibly(X),necessarily(possibly(X))))))),bind(Z,$fot(implies(possibly(X),necessarily(possibly(X)))))]]) ).
cnf(refute_0_277,plain,
( not(not(implies(possibly(X),necessarily(possibly(X))))) != implies(possibly(X),necessarily(possibly(X)))
| not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))) = implies(possibly(X),necessarily(possibly(X))) ),
inference(resolve,[$cnf( $equal(not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))),not(not(implies(possibly(X),necessarily(possibly(X)))))) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))) = implies(possibly(X),necessarily(possibly(X))),
inference(resolve,[$cnf( $equal(not(not(implies(possibly(X),necessarily(possibly(X))))),implies(possibly(X),necessarily(possibly(X)))) )],[refute_0_186,refute_0_277]) ).
cnf(refute_0_279,plain,
implies(X_41,necessarily(not(X))) = not(and(X_41,not(necessarily(not(X))))),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_41)),bind(Y,$fot(necessarily(not(X))))]]) ).
cnf(refute_0_280,plain,
( implies(X_41,necessarily(not(X))) != not(and(X_41,not(necessarily(not(X)))))
| not(necessarily(not(X))) != possibly(X)
| implies(X_41,necessarily(not(X))) = not(and(X_41,possibly(X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_41,necessarily(not(X))),not(and(X_41,not(necessarily(not(X)))))) ),[1,0,1],$fot(possibly(X))]]) ).
cnf(refute_0_281,plain,
( implies(X_41,necessarily(not(X))) != not(and(X_41,not(necessarily(not(X)))))
| implies(X_41,necessarily(not(X))) = not(and(X_41,possibly(X))) ),
inference(resolve,[$cnf( $equal(not(necessarily(not(X))),possibly(X)) )],[refute_0_176,refute_0_280]) ).
cnf(refute_0_282,plain,
implies(X_41,necessarily(not(X))) = not(and(X_41,possibly(X))),
inference(resolve,[$cnf( $equal(implies(X_41,necessarily(not(X))),not(and(X_41,not(necessarily(not(X)))))) )],[refute_0_279,refute_0_281]) ).
cnf(refute_0_283,plain,
implies(possibly(X),necessarily(not(necessarily(necessarily(not(X)))))) = not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))),
inference(subst,[],[refute_0_282:[bind(X,$fot(necessarily(necessarily(not(X))))),bind(X_41,$fot(possibly(X)))]]) ).
cnf(refute_0_284,plain,
( implies(possibly(X),necessarily(not(necessarily(necessarily(not(X)))))) != not(and(possibly(X),possibly(necessarily(necessarily(not(X))))))
| not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))) != implies(possibly(X),necessarily(possibly(X)))
| implies(possibly(X),necessarily(not(necessarily(necessarily(not(X)))))) = implies(possibly(X),necessarily(possibly(X))) ),
inference(subst,[],[refute_0_216:[bind(X0,$fot(implies(possibly(X),necessarily(not(necessarily(necessarily(not(X)))))))),bind(Y0,$fot(not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))))),bind(Z,$fot(implies(possibly(X),necessarily(possibly(X)))))]]) ).
cnf(refute_0_285,plain,
( not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))) != implies(possibly(X),necessarily(possibly(X)))
| implies(possibly(X),necessarily(not(necessarily(necessarily(not(X)))))) = implies(possibly(X),necessarily(possibly(X))) ),
inference(resolve,[$cnf( $equal(implies(possibly(X),necessarily(not(necessarily(necessarily(not(X)))))),not(and(possibly(X),possibly(necessarily(necessarily(not(X))))))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
implies(possibly(X),necessarily(not(necessarily(necessarily(not(X)))))) = implies(possibly(X),necessarily(possibly(X))),
inference(resolve,[$cnf( $equal(not(and(possibly(X),possibly(necessarily(necessarily(not(X)))))),implies(possibly(X),necessarily(possibly(X)))) )],[refute_0_278,refute_0_285]) ).
cnf(refute_0_287,plain,
( implies(possibly(X),necessarily(not(necessarily(necessarily(not(X)))))) != implies(possibly(X),necessarily(possibly(X)))
| ~ is_a_theorem(implies(possibly(X),necessarily(not(necessarily(necessarily(not(X)))))))
| is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(possibly(X),necessarily(not(necessarily(necessarily(not(X))))))) ),[0],$fot(implies(possibly(X),necessarily(possibly(X))))]]) ).
cnf(refute_0_288,plain,
( ~ is_a_theorem(implies(possibly(X),necessarily(not(necessarily(necessarily(not(X)))))))
| is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
inference(resolve,[$cnf( $equal(implies(possibly(X),necessarily(not(necessarily(necessarily(not(X)))))),implies(possibly(X),necessarily(possibly(X)))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
is_a_theorem(implies(possibly(X),necessarily(possibly(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(possibly(X),necessarily(not(necessarily(necessarily(not(X))))))) )],[refute_0_183,refute_0_288]) ).
cnf(refute_0_290,plain,
is_a_theorem(implies(possibly(skolemFOFtoCNF_X_23),necessarily(possibly(skolemFOFtoCNF_X_23)))),
inference(subst,[],[refute_0_289:[bind(X,$fot(skolemFOFtoCNF_X_23))]]) ).
cnf(refute_0_291,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(possibly(skolemFOFtoCNF_X_23),necessarily(possibly(skolemFOFtoCNF_X_23)))) )],[refute_0_290,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL537+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jul 5 01:18:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 125.72/125.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 125.72/125.93
% 125.72/125.93 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 125.72/125.96
%------------------------------------------------------------------------------