TSTP Solution File: LCL524+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL524+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 12:52:54 EDT 2022
% Result : Theorem 30.22s 30.39s
% Output : CNFRefutation 30.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 81
% Syntax : Number of formulae : 412 ( 207 unt; 0 def)
% Number of atoms : 715 ( 321 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 583 ( 280 ~; 254 |; 19 &)
% ( 24 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 20 ( 17 usr; 17 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 21 con; 0-2 aty)
% Number of variables : 547 ( 8 sgn 83 !; 21 ?)
% 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_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(km5_op_possibly,axiom,
op_possibly ).
fof(km5_axiom_M,axiom,
axiom_M ).
fof(km5_axiom_5,axiom,
axiom_5 ).
fof(km4b_axiom_B,conjecture,
axiom_B ).
fof(subgoal_0,plain,
axiom_B,
inference(strip,[],[km4b_axiom_B]) ).
fof(negate_0_0,plain,
~ axiom_B,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ axiom_B
<=> ? [X] : ~ is_a_theorem(implies(X,necessarily(possibly(X)))) ),
inference(canonicalize,[],[axiom_B]) ).
fof(normalize_0_1,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_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22))))
| axiom_B ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ axiom_B,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ substitution_of_equivalents
<=> ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_5,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_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
substitution_of_equivalents,
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_8,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_9,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_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
modus_ponens,
inference(canonicalize,[],[hilbert_modus_ponens]) ).
fof(normalize_0_12,plain,
( ~ axiom_5
<=> ? [X] : ~ is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_0_13,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_12]) ).
fof(normalize_0_14,plain,
! [X] :
( ~ axiom_5
| is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
axiom_5,
inference(canonicalize,[],[km5_axiom_5]) ).
fof(normalize_0_16,plain,
( ~ and_3
<=> ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[and_3]) ).
fof(normalize_0_17,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_16]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
and_3,
inference(canonicalize,[],[hilbert_and_3]) ).
fof(normalize_0_20,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_21,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
op_equiv,
inference(canonicalize,[],[hilbert_op_equiv]) ).
fof(normalize_0_23,plain,
( ~ axiom_M
<=> ? [X] : ~ is_a_theorem(implies(necessarily(X),X)) ),
inference(canonicalize,[],[axiom_M]) ).
fof(normalize_0_24,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_23]) ).
fof(normalize_0_25,plain,
! [X] :
( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
axiom_M,
inference(canonicalize,[],[km5_axiom_M]) ).
fof(normalize_0_27,plain,
( ~ modus_tollens
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(canonicalize,[],[modus_tollens]) ).
fof(normalize_0_28,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_27]) ).
fof(normalize_0_29,plain,
! [X,Y] :
( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(conjunct,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
modus_tollens,
inference(canonicalize,[],[hilbert_modus_tollens]) ).
fof(normalize_0_31,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_32,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
op_or,
inference(canonicalize,[],[hilbert_op_or]) ).
fof(normalize_0_34,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_35,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
op_implies_and,
inference(canonicalize,[],[hilbert_op_implies_and]) ).
fof(normalize_0_37,plain,
( ~ implies_2
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[implies_2]) ).
fof(normalize_0_38,plain,
! [X,Y] :
( ( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )
& ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_4,implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)),implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)))
| implies_2 ) ),
inference(clausify,[],[normalize_0_37]) ).
fof(normalize_0_39,plain,
! [X,Y] :
( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
implies_2,
inference(canonicalize,[],[hilbert_implies_2]) ).
fof(normalize_0_41,plain,
( ~ and_2
<=> ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[and_2]) ).
fof(normalize_0_42,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_41]) ).
fof(normalize_0_43,plain,
! [X,Y] :
( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) ),
inference(conjunct,[],[normalize_0_42]) ).
fof(normalize_0_44,plain,
and_2,
inference(canonicalize,[],[hilbert_and_2]) ).
fof(normalize_0_45,plain,
( ~ or_1
<=> ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y))) ),
inference(canonicalize,[],[or_1]) ).
fof(normalize_0_46,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_45]) ).
fof(normalize_0_47,plain,
! [X,Y] :
( ~ or_1
| is_a_theorem(implies(X,or(X,Y))) ),
inference(conjunct,[],[normalize_0_46]) ).
fof(normalize_0_48,plain,
or_1,
inference(canonicalize,[],[hilbert_or_1]) ).
fof(normalize_0_49,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_50,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_49]) ).
fof(normalize_0_51,plain,
! [X,Y] :
( ~ equivalence_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
inference(conjunct,[],[normalize_0_50]) ).
fof(normalize_0_52,plain,
equivalence_3,
inference(canonicalize,[],[hilbert_equivalence_3]) ).
fof(normalize_0_53,plain,
( ~ or_2
<=> ? [X,Y] : ~ is_a_theorem(implies(Y,or(X,Y))) ),
inference(canonicalize,[],[or_2]) ).
fof(normalize_0_54,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_53]) ).
fof(normalize_0_55,plain,
! [X,Y] :
( ~ or_2
| is_a_theorem(implies(Y,or(X,Y))) ),
inference(conjunct,[],[normalize_0_54]) ).
fof(normalize_0_56,plain,
or_2,
inference(canonicalize,[],[hilbert_or_2]) ).
fof(normalize_0_57,plain,
( ~ op_possibly
| ! [X] : possibly(X) = not(necessarily(not(X))) ),
inference(canonicalize,[],[op_possibly]) ).
fof(normalize_0_58,plain,
! [X] :
( ~ op_possibly
| possibly(X) = not(necessarily(not(X))) ),
inference(clausify,[],[normalize_0_57]) ).
fof(normalize_0_59,plain,
op_possibly,
inference(canonicalize,[],[km5_op_possibly]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22))))
| axiom_B ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ axiom_B,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22)))),
inference(resolve,[$cnf( axiom_B )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(equiv(possibly(X_1004),necessarily(possibly(X_1004))))
| possibly(X_1004) = necessarily(possibly(X_1004)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(possibly(X_1004))),bind(Y,$fot(necessarily(possibly(X_1004))))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(implies(necessarily(possibly(X_1003)),possibly(X_1003)),equiv(possibly(X_1003),necessarily(possibly(X_1003)))))
| ~ is_a_theorem(implies(necessarily(possibly(X_1003)),possibly(X_1003)))
| is_a_theorem(equiv(possibly(X_1003),necessarily(possibly(X_1003)))) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(implies(necessarily(possibly(X_1003)),possibly(X_1003)))),bind(Y,$fot(equiv(possibly(X_1003),necessarily(possibly(X_1003)))))]]) ).
cnf(refute_0_11,plain,
( ~ axiom_5
| is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
axiom_5,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(possibly(X),necessarily(possibly(X)))),
inference(resolve,[$cnf( axiom_5 )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_15,plain,
and_3,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(X,implies(Y,and(X,Y)))),
inference(resolve,[$cnf( and_3 )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(X_402,implies(Y,and(X_402,Y)))),
inference(subst,[],[refute_0_16:[bind(X,$fot(X_402))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(X_402)
| ~ is_a_theorem(implies(X_402,implies(Y,and(X_402,Y))))
| is_a_theorem(implies(Y,and(X_402,Y))) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_402)),bind(Y,$fot(implies(Y,and(X_402,Y))))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(X_402)
| is_a_theorem(implies(Y,and(X_402,Y))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_402,implies(Y,and(X_402,Y)))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(possibly(X),necessarily(possibly(X))))
| is_a_theorem(implies(X_411,and(implies(possibly(X),necessarily(possibly(X))),X_411))) ),
inference(subst,[],[refute_0_19:[bind(Y,$fot(X_411)),bind(X_402,$fot(implies(possibly(X),necessarily(possibly(X)))))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(X_411,and(implies(possibly(X),necessarily(possibly(X))),X_411))),
inference(resolve,[$cnf( is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) )],[refute_0_13,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(necessarily(possibly(X_1001)),possibly(X_1001)),and(implies(possibly(X_1001),necessarily(possibly(X_1001))),implies(necessarily(possibly(X_1001)),possibly(X_1001))))),
inference(subst,[],[refute_0_21:[bind(X,$fot(X_1001)),bind(X_411,$fot(implies(necessarily(possibly(X_1001)),possibly(X_1001))))]]) ).
cnf(refute_0_23,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_24,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_25,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_24,refute_0_23]) ).
cnf(refute_0_26,plain,
equiv(possibly(X_1001),necessarily(possibly(X_1001))) = and(implies(possibly(X_1001),necessarily(possibly(X_1001))),implies(necessarily(possibly(X_1001)),possibly(X_1001))),
inference(subst,[],[refute_0_25:[bind(X,$fot(possibly(X_1001))),bind(Y,$fot(necessarily(possibly(X_1001))))]]) ).
cnf(refute_0_27,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_28,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_29,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( equiv(possibly(X_1001),necessarily(possibly(X_1001))) != and(implies(possibly(X_1001),necessarily(possibly(X_1001))),implies(necessarily(possibly(X_1001)),possibly(X_1001)))
| and(implies(possibly(X_1001),necessarily(possibly(X_1001))),implies(necessarily(possibly(X_1001)),possibly(X_1001))) = equiv(possibly(X_1001),necessarily(possibly(X_1001))) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(equiv(possibly(X_1001),necessarily(possibly(X_1001))))),bind(Y0,$fot(and(implies(possibly(X_1001),necessarily(possibly(X_1001))),implies(necessarily(possibly(X_1001)),possibly(X_1001)))))]]) ).
cnf(refute_0_31,plain,
and(implies(possibly(X_1001),necessarily(possibly(X_1001))),implies(necessarily(possibly(X_1001)),possibly(X_1001))) = equiv(possibly(X_1001),necessarily(possibly(X_1001))),
inference(resolve,[$cnf( $equal(equiv(possibly(X_1001),necessarily(possibly(X_1001))),and(implies(possibly(X_1001),necessarily(possibly(X_1001))),implies(necessarily(possibly(X_1001)),possibly(X_1001)))) )],[refute_0_26,refute_0_30]) ).
cnf(refute_0_32,plain,
( and(implies(possibly(X_1001),necessarily(possibly(X_1001))),implies(necessarily(possibly(X_1001)),possibly(X_1001))) != equiv(possibly(X_1001),necessarily(possibly(X_1001)))
| ~ is_a_theorem(implies(implies(necessarily(possibly(X_1001)),possibly(X_1001)),and(implies(possibly(X_1001),necessarily(possibly(X_1001))),implies(necessarily(possibly(X_1001)),possibly(X_1001)))))
| is_a_theorem(implies(implies(necessarily(possibly(X_1001)),possibly(X_1001)),equiv(possibly(X_1001),necessarily(possibly(X_1001))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(necessarily(possibly(X_1001)),possibly(X_1001)),and(implies(possibly(X_1001),necessarily(possibly(X_1001))),implies(necessarily(possibly(X_1001)),possibly(X_1001))))) ),[0,1],$fot(equiv(possibly(X_1001),necessarily(possibly(X_1001))))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(implies(necessarily(possibly(X_1001)),possibly(X_1001)),and(implies(possibly(X_1001),necessarily(possibly(X_1001))),implies(necessarily(possibly(X_1001)),possibly(X_1001)))))
| is_a_theorem(implies(implies(necessarily(possibly(X_1001)),possibly(X_1001)),equiv(possibly(X_1001),necessarily(possibly(X_1001))))) ),
inference(resolve,[$cnf( $equal(and(implies(possibly(X_1001),necessarily(possibly(X_1001))),implies(necessarily(possibly(X_1001)),possibly(X_1001))),equiv(possibly(X_1001),necessarily(possibly(X_1001)))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
is_a_theorem(implies(implies(necessarily(possibly(X_1001)),possibly(X_1001)),equiv(possibly(X_1001),necessarily(possibly(X_1001))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(necessarily(possibly(X_1001)),possibly(X_1001)),and(implies(possibly(X_1001),necessarily(possibly(X_1001))),implies(necessarily(possibly(X_1001)),possibly(X_1001))))) )],[refute_0_22,refute_0_33]) ).
cnf(refute_0_35,plain,
is_a_theorem(implies(implies(necessarily(possibly(X_1003)),possibly(X_1003)),equiv(possibly(X_1003),necessarily(possibly(X_1003))))),
inference(subst,[],[refute_0_34:[bind(X_1001,$fot(X_1003))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(necessarily(possibly(X_1003)),possibly(X_1003)))
| is_a_theorem(equiv(possibly(X_1003),necessarily(possibly(X_1003)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(necessarily(possibly(X_1003)),possibly(X_1003)),equiv(possibly(X_1003),necessarily(possibly(X_1003))))) )],[refute_0_35,refute_0_10]) ).
cnf(refute_0_37,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_38,plain,
axiom_M,
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(necessarily(X),X)),
inference(resolve,[$cnf( axiom_M )],[refute_0_38,refute_0_37]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(necessarily(possibly(X_1003)),possibly(X_1003))),
inference(subst,[],[refute_0_39:[bind(X,$fot(possibly(X_1003)))]]) ).
cnf(refute_0_41,plain,
is_a_theorem(equiv(possibly(X_1003),necessarily(possibly(X_1003)))),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(possibly(X_1003)),possibly(X_1003))) )],[refute_0_40,refute_0_36]) ).
cnf(refute_0_42,plain,
is_a_theorem(equiv(possibly(X_1004),necessarily(possibly(X_1004)))),
inference(subst,[],[refute_0_41:[bind(X_1003,$fot(X_1004))]]) ).
cnf(refute_0_43,plain,
possibly(X_1004) = necessarily(possibly(X_1004)),
inference(resolve,[$cnf( is_a_theorem(equiv(possibly(X_1004),necessarily(possibly(X_1004)))) )],[refute_0_42,refute_0_6]) ).
cnf(refute_0_44,plain,
( possibly(X_1004) != necessarily(possibly(X_1004))
| necessarily(possibly(X_1004)) = possibly(X_1004) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(possibly(X_1004))),bind(Y0,$fot(necessarily(possibly(X_1004))))]]) ).
cnf(refute_0_45,plain,
necessarily(possibly(X_1004)) = possibly(X_1004),
inference(resolve,[$cnf( $equal(possibly(X_1004),necessarily(possibly(X_1004))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
necessarily(possibly(skolemFOFtoCNF_X_22)) = possibly(skolemFOFtoCNF_X_22),
inference(subst,[],[refute_0_45:[bind(X_1004,$fot(skolemFOFtoCNF_X_22))]]) ).
cnf(refute_0_47,plain,
implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22))) = implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22))),
introduced(tautology,[refl,[$fot(implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22))))]]) ).
cnf(refute_0_48,plain,
( implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22))) != implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22)))
| necessarily(possibly(skolemFOFtoCNF_X_22)) != possibly(skolemFOFtoCNF_X_22)
| implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22))) = implies(skolemFOFtoCNF_X_22,possibly(skolemFOFtoCNF_X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22))),implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22)))) ),[1,1],$fot(possibly(skolemFOFtoCNF_X_22))]]) ).
cnf(refute_0_49,plain,
( necessarily(possibly(skolemFOFtoCNF_X_22)) != possibly(skolemFOFtoCNF_X_22)
| implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22))) = implies(skolemFOFtoCNF_X_22,possibly(skolemFOFtoCNF_X_22)) ),
inference(resolve,[$cnf( $equal(implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22))),implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22)))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22))) = implies(skolemFOFtoCNF_X_22,possibly(skolemFOFtoCNF_X_22)),
inference(resolve,[$cnf( $equal(necessarily(possibly(skolemFOFtoCNF_X_22)),possibly(skolemFOFtoCNF_X_22)) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
( implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22))) != implies(skolemFOFtoCNF_X_22,possibly(skolemFOFtoCNF_X_22))
| ~ is_a_theorem(implies(skolemFOFtoCNF_X_22,possibly(skolemFOFtoCNF_X_22)))
| is_a_theorem(implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22)))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22)))) ),[0],$fot(implies(skolemFOFtoCNF_X_22,possibly(skolemFOFtoCNF_X_22)))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_X_22,possibly(skolemFOFtoCNF_X_22)))
| is_a_theorem(implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22)))) ),
inference(resolve,[$cnf( $equal(implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22))),implies(skolemFOFtoCNF_X_22,possibly(skolemFOFtoCNF_X_22))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
~ is_a_theorem(implies(skolemFOFtoCNF_X_22,possibly(skolemFOFtoCNF_X_22))),
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_X_22,necessarily(possibly(skolemFOFtoCNF_X_22)))) )],[refute_0_52,refute_0_2]) ).
cnf(refute_0_54,plain,
( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_55,plain,
modus_tollens,
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))),
inference(resolve,[$cnf( modus_tollens )],[refute_0_55,refute_0_54]) ).
cnf(refute_0_57,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_58,plain,
op_or,
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_59,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_58,refute_0_57]) ).
cnf(refute_0_60,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_61,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_62,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_61,refute_0_60]) ).
cnf(refute_0_63,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_64,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_64:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_66,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_67,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_59,refute_0_67]) ).
cnf(refute_0_69,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_70,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
implies(not(Y),not(X)) = or(Y,not(X)),
inference(subst,[],[refute_0_70:[bind(X,$fot(Y)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_72,plain,
implies(implies(not(Y),not(X)),implies(X,Y)) = implies(implies(not(Y),not(X)),implies(X,Y)),
introduced(tautology,[refl,[$fot(implies(implies(not(Y),not(X)),implies(X,Y)))]]) ).
cnf(refute_0_73,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_74,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( $equal(implies(implies(not(Y),not(X)),implies(X,Y)),implies(implies(not(Y),not(X)),implies(X,Y))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
implies(implies(not(Y),not(X)),implies(X,Y)) = implies(or(Y,not(X)),implies(X,Y)),
inference(resolve,[$cnf( $equal(implies(not(Y),not(X)),or(Y,not(X))) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
( implies(implies(not(Y),not(X)),implies(X,Y)) != implies(or(Y,not(X)),implies(X,Y))
| ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| is_a_theorem(implies(or(Y,not(X)),implies(X,Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),[0],$fot(implies(or(Y,not(X)),implies(X,Y)))]]) ).
cnf(refute_0_77,plain,
( ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| is_a_theorem(implies(or(Y,not(X)),implies(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),not(X)),implies(X,Y)),implies(or(Y,not(X)),implies(X,Y))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(or(Y,not(X)),implies(X,Y))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )],[refute_0_56,refute_0_77]) ).
cnf(refute_0_79,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_9:[bind(X,$fot(or(Y,not(X)))),bind(Y,$fot(implies(X,Y)))]]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(or(Y,not(X)))
| is_a_theorem(implies(X,Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(Y,not(X)),implies(X,Y))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
( ~ is_a_theorem(or(possibly(X_5954),not(X_5954)))
| is_a_theorem(implies(X_5954,possibly(X_5954))) ),
inference(subst,[],[refute_0_80:[bind(X,$fot(X_5954)),bind(Y,$fot(possibly(X_5954)))]]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(necessarily(and(X_227,not(X_228))),and(X_227,not(X_228)))),
inference(subst,[],[refute_0_39:[bind(X,$fot(and(X_227,not(X_228))))]]) ).
cnf(refute_0_83,plain,
implies(X,and(X_17,not(X_18))) = not(and(X,not(and(X_17,not(X_18))))),
inference(subst,[],[refute_0_62:[bind(Y,$fot(and(X_17,not(X_18))))]]) ).
cnf(refute_0_84,plain,
implies(X_17,X_18) = not(and(X_17,not(X_18))),
inference(subst,[],[refute_0_62:[bind(X,$fot(X_17)),bind(Y,$fot(X_18))]]) ).
cnf(refute_0_85,plain,
( implies(X_17,X_18) != not(and(X_17,not(X_18)))
| not(and(X_17,not(X_18))) = implies(X_17,X_18) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(implies(X_17,X_18))),bind(Y0,$fot(not(and(X_17,not(X_18)))))]]) ).
cnf(refute_0_86,plain,
not(and(X_17,not(X_18))) = implies(X_17,X_18),
inference(resolve,[$cnf( $equal(implies(X_17,X_18),not(and(X_17,not(X_18)))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
( implies(X,and(X_17,not(X_18))) != not(and(X,not(and(X_17,not(X_18)))))
| not(and(X_17,not(X_18))) != implies(X_17,X_18)
| implies(X,and(X_17,not(X_18))) = not(and(X,implies(X_17,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,and(X_17,not(X_18))),not(and(X,not(and(X_17,not(X_18)))))) ),[1,0,1],$fot(implies(X_17,X_18))]]) ).
cnf(refute_0_88,plain,
( implies(X,and(X_17,not(X_18))) != not(and(X,not(and(X_17,not(X_18)))))
| implies(X,and(X_17,not(X_18))) = not(and(X,implies(X_17,X_18))) ),
inference(resolve,[$cnf( $equal(not(and(X_17,not(X_18))),implies(X_17,X_18)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
implies(X,and(X_17,not(X_18))) = not(and(X,implies(X_17,X_18))),
inference(resolve,[$cnf( $equal(implies(X,and(X_17,not(X_18))),not(and(X,not(and(X_17,not(X_18)))))) )],[refute_0_83,refute_0_88]) ).
cnf(refute_0_90,plain,
implies(necessarily(and(X_227,not(X_228))),and(X_227,not(X_228))) = not(and(necessarily(and(X_227,not(X_228))),implies(X_227,X_228))),
inference(subst,[],[refute_0_89:[bind(X,$fot(necessarily(and(X_227,not(X_228))))),bind(X_17,$fot(X_227)),bind(X_18,$fot(X_228))]]) ).
cnf(refute_0_91,plain,
( implies(necessarily(and(X_227,not(X_228))),and(X_227,not(X_228))) != not(and(necessarily(and(X_227,not(X_228))),implies(X_227,X_228)))
| ~ is_a_theorem(implies(necessarily(and(X_227,not(X_228))),and(X_227,not(X_228))))
| is_a_theorem(not(and(necessarily(and(X_227,not(X_228))),implies(X_227,X_228)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(necessarily(and(X_227,not(X_228))),and(X_227,not(X_228)))) ),[0],$fot(not(and(necessarily(and(X_227,not(X_228))),implies(X_227,X_228))))]]) ).
cnf(refute_0_92,plain,
( ~ is_a_theorem(implies(necessarily(and(X_227,not(X_228))),and(X_227,not(X_228))))
| is_a_theorem(not(and(necessarily(and(X_227,not(X_228))),implies(X_227,X_228)))) ),
inference(resolve,[$cnf( $equal(implies(necessarily(and(X_227,not(X_228))),and(X_227,not(X_228))),not(and(necessarily(and(X_227,not(X_228))),implies(X_227,X_228)))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
is_a_theorem(not(and(necessarily(and(X_227,not(X_228))),implies(X_227,X_228)))),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(and(X_227,not(X_228))),and(X_227,not(X_228)))) )],[refute_0_82,refute_0_92]) ).
cnf(refute_0_94,plain,
is_a_theorem(not(and(necessarily(and(not(X),not(X_381))),implies(not(X),X_381)))),
inference(subst,[],[refute_0_93:[bind(X_227,$fot(not(X))),bind(X_228,$fot(X_381))]]) ).
cnf(refute_0_95,plain,
or(X,X_381) = implies(not(X),X_381),
inference(subst,[],[refute_0_68:[bind(Y,$fot(X_381))]]) ).
cnf(refute_0_96,plain,
( or(X,X_381) != implies(not(X),X_381)
| implies(not(X),X_381) = or(X,X_381) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(or(X,X_381))),bind(Y0,$fot(implies(not(X),X_381)))]]) ).
cnf(refute_0_97,plain,
implies(not(X),X_381) = or(X,X_381),
inference(resolve,[$cnf( $equal(or(X,X_381),implies(not(X),X_381)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
( implies(not(X),X_381) != or(X,X_381)
| ~ is_a_theorem(not(and(necessarily(and(not(X),not(X_381))),implies(not(X),X_381))))
| is_a_theorem(not(and(necessarily(and(not(X),not(X_381))),or(X,X_381)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(necessarily(and(not(X),not(X_381))),implies(not(X),X_381)))) ),[0,0,1],$fot(or(X,X_381))]]) ).
cnf(refute_0_99,plain,
( ~ is_a_theorem(not(and(necessarily(and(not(X),not(X_381))),implies(not(X),X_381))))
| is_a_theorem(not(and(necessarily(and(not(X),not(X_381))),or(X,X_381)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_381),or(X,X_381)) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
is_a_theorem(not(and(necessarily(and(not(X),not(X_381))),or(X,X_381)))),
inference(resolve,[$cnf( is_a_theorem(not(and(necessarily(and(not(X),not(X_381))),implies(not(X),X_381)))) )],[refute_0_94,refute_0_99]) ).
cnf(refute_0_101,plain,
is_a_theorem(not(and(necessarily(and(not(X_381),not(X_381))),or(X_381,X_381)))),
inference(subst,[],[refute_0_100:[bind(X,$fot(X_381))]]) ).
cnf(refute_0_102,plain,
implies(not(Y),Y) = not(and(not(Y),not(Y))),
inference(subst,[],[refute_0_62:[bind(X,$fot(not(Y)))]]) ).
cnf(refute_0_103,plain,
( ~ is_a_theorem(equiv(X_1618,and(X_1618,X_1618)))
| X_1618 = and(X_1618,X_1618) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_1618)),bind(Y,$fot(and(X_1618,X_1618)))]]) ).
cnf(refute_0_104,plain,
( ~ is_a_theorem(implies(and(X_1617,X_1617),X_1617))
| ~ is_a_theorem(implies(implies(and(X_1617,X_1617),X_1617),equiv(X_1617,and(X_1617,X_1617))))
| is_a_theorem(equiv(X_1617,and(X_1617,X_1617))) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(implies(and(X_1617,X_1617),X_1617))),bind(Y,$fot(equiv(X_1617,and(X_1617,X_1617))))]]) ).
cnf(refute_0_105,plain,
( ~ is_a_theorem(implies(X_1494,and(X_1494,X_1494)))
| is_a_theorem(implies(Y,and(implies(X_1494,and(X_1494,X_1494)),Y))) ),
inference(subst,[],[refute_0_19:[bind(X_402,$fot(implies(X_1494,and(X_1494,X_1494))))]]) ).
cnf(refute_0_106,plain,
is_a_theorem(implies(X_1490,implies(X_1490,and(X_1490,X_1490)))),
inference(subst,[],[refute_0_16:[bind(X,$fot(X_1490)),bind(Y,$fot(X_1490))]]) ).
cnf(refute_0_107,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_108,plain,
implies_2,
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_109,plain,
is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))),
inference(resolve,[$cnf( implies_2 )],[refute_0_108,refute_0_107]) ).
cnf(refute_0_110,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_9:[bind(X,$fot(implies(X,implies(X,Y)))),bind(Y,$fot(implies(X,Y)))]]) ).
cnf(refute_0_111,plain,
( ~ is_a_theorem(implies(X,implies(X,Y)))
| is_a_theorem(implies(X,Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( ~ is_a_theorem(implies(X_1490,implies(X_1490,and(X_1490,X_1490))))
| is_a_theorem(implies(X_1490,and(X_1490,X_1490))) ),
inference(subst,[],[refute_0_111:[bind(X,$fot(X_1490)),bind(Y,$fot(and(X_1490,X_1490)))]]) ).
cnf(refute_0_113,plain,
is_a_theorem(implies(X_1490,and(X_1490,X_1490))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1490,implies(X_1490,and(X_1490,X_1490)))) )],[refute_0_106,refute_0_112]) ).
cnf(refute_0_114,plain,
is_a_theorem(implies(X_1494,and(X_1494,X_1494))),
inference(subst,[],[refute_0_113:[bind(X_1490,$fot(X_1494))]]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(Y,and(implies(X_1494,and(X_1494,X_1494)),Y))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1494,and(X_1494,X_1494))) )],[refute_0_114,refute_0_105]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(implies(and(X_1616,X_1616),X_1616),and(implies(X_1616,and(X_1616,X_1616)),implies(and(X_1616,X_1616),X_1616)))),
inference(subst,[],[refute_0_115:[bind(Y,$fot(implies(and(X_1616,X_1616),X_1616))),bind(X_1494,$fot(X_1616))]]) ).
cnf(refute_0_117,plain,
equiv(X_1616,and(X_1616,X_1616)) = and(implies(X_1616,and(X_1616,X_1616)),implies(and(X_1616,X_1616),X_1616)),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_1616)),bind(Y,$fot(and(X_1616,X_1616)))]]) ).
cnf(refute_0_118,plain,
( equiv(X_1616,and(X_1616,X_1616)) != and(implies(X_1616,and(X_1616,X_1616)),implies(and(X_1616,X_1616),X_1616))
| and(implies(X_1616,and(X_1616,X_1616)),implies(and(X_1616,X_1616),X_1616)) = equiv(X_1616,and(X_1616,X_1616)) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(equiv(X_1616,and(X_1616,X_1616)))),bind(Y0,$fot(and(implies(X_1616,and(X_1616,X_1616)),implies(and(X_1616,X_1616),X_1616))))]]) ).
cnf(refute_0_119,plain,
and(implies(X_1616,and(X_1616,X_1616)),implies(and(X_1616,X_1616),X_1616)) = equiv(X_1616,and(X_1616,X_1616)),
inference(resolve,[$cnf( $equal(equiv(X_1616,and(X_1616,X_1616)),and(implies(X_1616,and(X_1616,X_1616)),implies(and(X_1616,X_1616),X_1616))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
( and(implies(X_1616,and(X_1616,X_1616)),implies(and(X_1616,X_1616),X_1616)) != equiv(X_1616,and(X_1616,X_1616))
| ~ is_a_theorem(implies(implies(and(X_1616,X_1616),X_1616),and(implies(X_1616,and(X_1616,X_1616)),implies(and(X_1616,X_1616),X_1616))))
| is_a_theorem(implies(implies(and(X_1616,X_1616),X_1616),equiv(X_1616,and(X_1616,X_1616)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(and(X_1616,X_1616),X_1616),and(implies(X_1616,and(X_1616,X_1616)),implies(and(X_1616,X_1616),X_1616)))) ),[0,1],$fot(equiv(X_1616,and(X_1616,X_1616)))]]) ).
cnf(refute_0_121,plain,
( ~ is_a_theorem(implies(implies(and(X_1616,X_1616),X_1616),and(implies(X_1616,and(X_1616,X_1616)),implies(and(X_1616,X_1616),X_1616))))
| is_a_theorem(implies(implies(and(X_1616,X_1616),X_1616),equiv(X_1616,and(X_1616,X_1616)))) ),
inference(resolve,[$cnf( $equal(and(implies(X_1616,and(X_1616,X_1616)),implies(and(X_1616,X_1616),X_1616)),equiv(X_1616,and(X_1616,X_1616))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
is_a_theorem(implies(implies(and(X_1616,X_1616),X_1616),equiv(X_1616,and(X_1616,X_1616)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_1616,X_1616),X_1616),and(implies(X_1616,and(X_1616,X_1616)),implies(and(X_1616,X_1616),X_1616)))) )],[refute_0_116,refute_0_121]) ).
cnf(refute_0_123,plain,
is_a_theorem(implies(implies(and(X_1617,X_1617),X_1617),equiv(X_1617,and(X_1617,X_1617)))),
inference(subst,[],[refute_0_122:[bind(X_1616,$fot(X_1617))]]) ).
cnf(refute_0_124,plain,
( ~ is_a_theorem(implies(and(X_1617,X_1617),X_1617))
| is_a_theorem(equiv(X_1617,and(X_1617,X_1617))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_1617,X_1617),X_1617),equiv(X_1617,and(X_1617,X_1617)))) )],[refute_0_123,refute_0_104]) ).
cnf(refute_0_125,plain,
( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[normalize_0_43]) ).
cnf(refute_0_126,plain,
and_2,
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_127,plain,
is_a_theorem(implies(and(X,Y),Y)),
inference(resolve,[$cnf( and_2 )],[refute_0_126,refute_0_125]) ).
cnf(refute_0_128,plain,
is_a_theorem(implies(and(X_1617,X_1617),X_1617)),
inference(subst,[],[refute_0_127:[bind(X,$fot(X_1617)),bind(Y,$fot(X_1617))]]) ).
cnf(refute_0_129,plain,
is_a_theorem(equiv(X_1617,and(X_1617,X_1617))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_1617,X_1617),X_1617)) )],[refute_0_128,refute_0_124]) ).
cnf(refute_0_130,plain,
is_a_theorem(equiv(X_1618,and(X_1618,X_1618))),
inference(subst,[],[refute_0_129:[bind(X_1617,$fot(X_1618))]]) ).
cnf(refute_0_131,plain,
X_1618 = and(X_1618,X_1618),
inference(resolve,[$cnf( is_a_theorem(equiv(X_1618,and(X_1618,X_1618))) )],[refute_0_130,refute_0_103]) ).
cnf(refute_0_132,plain,
not(Y) = and(not(Y),not(Y)),
inference(subst,[],[refute_0_131:[bind(X_1618,$fot(not(Y)))]]) ).
cnf(refute_0_133,plain,
( not(Y) != and(not(Y),not(Y))
| and(not(Y),not(Y)) = not(Y) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(not(Y))),bind(Y0,$fot(and(not(Y),not(Y))))]]) ).
cnf(refute_0_134,plain,
and(not(Y),not(Y)) = not(Y),
inference(resolve,[$cnf( $equal(not(Y),and(not(Y),not(Y))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
( and(not(Y),not(Y)) != not(Y)
| implies(not(Y),Y) != not(and(not(Y),not(Y)))
| implies(not(Y),Y) = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(Y),Y),not(and(not(Y),not(Y)))) ),[1,0],$fot(not(Y))]]) ).
cnf(refute_0_136,plain,
( implies(not(Y),Y) != not(and(not(Y),not(Y)))
| implies(not(Y),Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(and(not(Y),not(Y)),not(Y)) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
implies(not(Y),Y) = not(not(Y)),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),not(and(not(Y),not(Y)))) )],[refute_0_102,refute_0_136]) ).
cnf(refute_0_138,plain,
implies(not(Y),Y) = or(Y,Y),
inference(subst,[],[refute_0_70:[bind(X,$fot(Y))]]) ).
cnf(refute_0_139,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_140,plain,
( implies(not(Y),Y) != not(not(Y))
| or(Y,Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),or(Y,Y)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
or(Y,Y) = not(not(Y)),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),not(not(Y))) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
( ~ is_a_theorem(equiv(not(not(X_2983)),X_2983))
| not(not(X_2983)) = X_2983 ),
inference(subst,[],[refute_0_5:[bind(X,$fot(not(not(X_2983)))),bind(Y,$fot(X_2983))]]) ).
cnf(refute_0_143,plain,
( ~ is_a_theorem(implies(X_2982,not(not(X_2982))))
| ~ is_a_theorem(implies(implies(X_2982,not(not(X_2982))),equiv(not(not(X_2982)),X_2982)))
| is_a_theorem(equiv(not(not(X_2982)),X_2982)) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(implies(X_2982,not(not(X_2982))))),bind(Y,$fot(equiv(not(not(X_2982)),X_2982)))]]) ).
cnf(refute_0_144,plain,
( ~ is_a_theorem(or(X_1695,not(not(not(X_1695)))))
| is_a_theorem(implies(not(not(X_1695)),X_1695)) ),
inference(subst,[],[refute_0_80:[bind(X,$fot(not(not(X_1695)))),bind(Y,$fot(X_1695))]]) ).
cnf(refute_0_145,plain,
( ~ or_1
| is_a_theorem(implies(X,or(X,Y))) ),
inference(canonicalize,[],[normalize_0_47]) ).
cnf(refute_0_146,plain,
or_1,
inference(canonicalize,[],[normalize_0_48]) ).
cnf(refute_0_147,plain,
is_a_theorem(implies(X,or(X,Y))),
inference(resolve,[$cnf( or_1 )],[refute_0_146,refute_0_145]) ).
cnf(refute_0_148,plain,
is_a_theorem(implies(not(X_25),or(not(X_25),Y))),
inference(subst,[],[refute_0_147:[bind(X,$fot(not(X_25)))]]) ).
cnf(refute_0_149,plain,
or(X_25,or(not(X_25),Y)) = implies(not(X_25),or(not(X_25),Y)),
inference(subst,[],[refute_0_68:[bind(X,$fot(X_25)),bind(Y,$fot(or(not(X_25),Y)))]]) ).
cnf(refute_0_150,plain,
( or(X_25,or(not(X_25),Y)) != implies(not(X_25),or(not(X_25),Y))
| implies(not(X_25),or(not(X_25),Y)) = or(X_25,or(not(X_25),Y)) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(or(X_25,or(not(X_25),Y)))),bind(Y0,$fot(implies(not(X_25),or(not(X_25),Y))))]]) ).
cnf(refute_0_151,plain,
implies(not(X_25),or(not(X_25),Y)) = or(X_25,or(not(X_25),Y)),
inference(resolve,[$cnf( $equal(or(X_25,or(not(X_25),Y)),implies(not(X_25),or(not(X_25),Y))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
( implies(not(X_25),or(not(X_25),Y)) != or(X_25,or(not(X_25),Y))
| ~ is_a_theorem(implies(not(X_25),or(not(X_25),Y)))
| is_a_theorem(or(X_25,or(not(X_25),Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X_25),or(not(X_25),Y))) ),[0],$fot(or(X_25,or(not(X_25),Y)))]]) ).
cnf(refute_0_153,plain,
( ~ is_a_theorem(implies(not(X_25),or(not(X_25),Y)))
| is_a_theorem(or(X_25,or(not(X_25),Y))) ),
inference(resolve,[$cnf( $equal(implies(not(X_25),or(not(X_25),Y)),or(X_25,or(not(X_25),Y))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
is_a_theorem(or(X_25,or(not(X_25),Y))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_25),or(not(X_25),Y))) )],[refute_0_148,refute_0_153]) ).
cnf(refute_0_155,plain,
is_a_theorem(or(X_25,or(not(X_25),not(X_25)))),
inference(subst,[],[refute_0_154:[bind(Y,$fot(not(X_25)))]]) ).
cnf(refute_0_156,plain,
or(not(X_25),not(X_25)) = not(not(not(X_25))),
inference(subst,[],[refute_0_141:[bind(Y,$fot(not(X_25)))]]) ).
cnf(refute_0_157,plain,
( or(not(X_25),not(X_25)) != not(not(not(X_25)))
| ~ is_a_theorem(or(X_25,or(not(X_25),not(X_25))))
| is_a_theorem(or(X_25,not(not(not(X_25))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_25,or(not(X_25),not(X_25)))) ),[0,1],$fot(not(not(not(X_25))))]]) ).
cnf(refute_0_158,plain,
( ~ is_a_theorem(or(X_25,or(not(X_25),not(X_25))))
| is_a_theorem(or(X_25,not(not(not(X_25))))) ),
inference(resolve,[$cnf( $equal(or(not(X_25),not(X_25)),not(not(not(X_25)))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
is_a_theorem(or(X_25,not(not(not(X_25))))),
inference(resolve,[$cnf( is_a_theorem(or(X_25,or(not(X_25),not(X_25)))) )],[refute_0_155,refute_0_158]) ).
cnf(refute_0_160,plain,
is_a_theorem(or(X_1695,not(not(not(X_1695))))),
inference(subst,[],[refute_0_159:[bind(X_25,$fot(X_1695))]]) ).
cnf(refute_0_161,plain,
is_a_theorem(implies(not(not(X_1695)),X_1695)),
inference(resolve,[$cnf( is_a_theorem(or(X_1695,not(not(not(X_1695))))) )],[refute_0_160,refute_0_144]) ).
cnf(refute_0_162,plain,
implies(not(not(X_1695)),X_1695) = or(not(X_1695),X_1695),
inference(subst,[],[refute_0_70:[bind(X,$fot(not(X_1695))),bind(Y,$fot(X_1695))]]) ).
cnf(refute_0_163,plain,
( implies(not(not(X_1695)),X_1695) != or(not(X_1695),X_1695)
| ~ is_a_theorem(implies(not(not(X_1695)),X_1695))
| is_a_theorem(or(not(X_1695),X_1695)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(not(X_1695)),X_1695)) ),[0],$fot(or(not(X_1695),X_1695))]]) ).
cnf(refute_0_164,plain,
( ~ is_a_theorem(implies(not(not(X_1695)),X_1695))
| is_a_theorem(or(not(X_1695),X_1695)) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_1695)),X_1695),or(not(X_1695),X_1695)) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
is_a_theorem(or(not(X_1695),X_1695)),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_1695)),X_1695)) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
is_a_theorem(or(not(X_2981),X_2981)),
inference(subst,[],[refute_0_165:[bind(X_1695,$fot(X_2981))]]) ).
cnf(refute_0_167,plain,
( ~ equivalence_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
inference(canonicalize,[],[normalize_0_51]) ).
cnf(refute_0_168,plain,
equivalence_3,
inference(canonicalize,[],[normalize_0_52]) ).
cnf(refute_0_169,plain,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))),
inference(resolve,[$cnf( equivalence_3 )],[refute_0_168,refute_0_167]) ).
cnf(refute_0_170,plain,
is_a_theorem(implies(implies(not(X),X_110),implies(implies(X_110,not(X)),equiv(not(X),X_110)))),
inference(subst,[],[refute_0_169:[bind(X,$fot(not(X))),bind(Y,$fot(X_110))]]) ).
cnf(refute_0_171,plain,
or(X,X_110) = implies(not(X),X_110),
inference(subst,[],[refute_0_68:[bind(Y,$fot(X_110))]]) ).
cnf(refute_0_172,plain,
( or(X,X_110) != implies(not(X),X_110)
| implies(not(X),X_110) = or(X,X_110) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(or(X,X_110))),bind(Y0,$fot(implies(not(X),X_110)))]]) ).
cnf(refute_0_173,plain,
implies(not(X),X_110) = or(X,X_110),
inference(resolve,[$cnf( $equal(or(X,X_110),implies(not(X),X_110)) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
( implies(not(X),X_110) != or(X,X_110)
| ~ is_a_theorem(implies(implies(not(X),X_110),implies(implies(X_110,not(X)),equiv(not(X),X_110))))
| is_a_theorem(implies(or(X,X_110),implies(implies(X_110,not(X)),equiv(not(X),X_110)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X),X_110),implies(implies(X_110,not(X)),equiv(not(X),X_110)))) ),[0,0],$fot(or(X,X_110))]]) ).
cnf(refute_0_175,plain,
( ~ is_a_theorem(implies(implies(not(X),X_110),implies(implies(X_110,not(X)),equiv(not(X),X_110))))
| is_a_theorem(implies(or(X,X_110),implies(implies(X_110,not(X)),equiv(not(X),X_110)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_110),or(X,X_110)) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
is_a_theorem(implies(or(X,X_110),implies(implies(X_110,not(X)),equiv(not(X),X_110)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X_110),implies(implies(X_110,not(X)),equiv(not(X),X_110)))) )],[refute_0_170,refute_0_175]) ).
cnf(refute_0_177,plain,
( ~ is_a_theorem(implies(or(X,X_110),implies(implies(X_110,not(X)),equiv(not(X),X_110))))
| ~ is_a_theorem(or(X,X_110))
| is_a_theorem(implies(implies(X_110,not(X)),equiv(not(X),X_110))) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(or(X,X_110))),bind(Y,$fot(implies(implies(X_110,not(X)),equiv(not(X),X_110))))]]) ).
cnf(refute_0_178,plain,
( ~ is_a_theorem(or(X,X_110))
| is_a_theorem(implies(implies(X_110,not(X)),equiv(not(X),X_110))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X,X_110),implies(implies(X_110,not(X)),equiv(not(X),X_110)))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
( ~ is_a_theorem(or(not(X_2981),X_2981))
| is_a_theorem(implies(implies(X_2981,not(not(X_2981))),equiv(not(not(X_2981)),X_2981))) ),
inference(subst,[],[refute_0_178:[bind(X,$fot(not(X_2981))),bind(X_110,$fot(X_2981))]]) ).
cnf(refute_0_180,plain,
is_a_theorem(implies(implies(X_2981,not(not(X_2981))),equiv(not(not(X_2981)),X_2981))),
inference(resolve,[$cnf( is_a_theorem(or(not(X_2981),X_2981)) )],[refute_0_166,refute_0_179]) ).
cnf(refute_0_181,plain,
is_a_theorem(implies(implies(X_2982,not(not(X_2982))),equiv(not(not(X_2982)),X_2982))),
inference(subst,[],[refute_0_180:[bind(X_2981,$fot(X_2982))]]) ).
cnf(refute_0_182,plain,
( ~ is_a_theorem(implies(X_2982,not(not(X_2982))))
| is_a_theorem(equiv(not(not(X_2982)),X_2982)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2982,not(not(X_2982))),equiv(not(not(X_2982)),X_2982))) )],[refute_0_181,refute_0_143]) ).
cnf(refute_0_183,plain,
( ~ or_2
| is_a_theorem(implies(Y,or(X,Y))) ),
inference(canonicalize,[],[normalize_0_55]) ).
cnf(refute_0_184,plain,
or_2,
inference(canonicalize,[],[normalize_0_56]) ).
cnf(refute_0_185,plain,
is_a_theorem(implies(Y,or(X,Y))),
inference(resolve,[$cnf( or_2 )],[refute_0_184,refute_0_183]) ).
cnf(refute_0_186,plain,
is_a_theorem(implies(Y,or(Y,Y))),
inference(subst,[],[refute_0_185:[bind(X,$fot(Y))]]) ).
cnf(refute_0_187,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_188,plain,
( ~ is_a_theorem(implies(Y,or(Y,Y)))
| is_a_theorem(implies(Y,not(not(Y)))) ),
inference(resolve,[$cnf( $equal(or(Y,Y),not(not(Y))) )],[refute_0_141,refute_0_187]) ).
cnf(refute_0_189,plain,
is_a_theorem(implies(Y,not(not(Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(Y,or(Y,Y))) )],[refute_0_186,refute_0_188]) ).
cnf(refute_0_190,plain,
is_a_theorem(implies(X_2982,not(not(X_2982)))),
inference(subst,[],[refute_0_189:[bind(Y,$fot(X_2982))]]) ).
cnf(refute_0_191,plain,
is_a_theorem(equiv(not(not(X_2982)),X_2982)),
inference(resolve,[$cnf( is_a_theorem(implies(X_2982,not(not(X_2982)))) )],[refute_0_190,refute_0_182]) ).
cnf(refute_0_192,plain,
is_a_theorem(equiv(not(not(X_2983)),X_2983)),
inference(subst,[],[refute_0_191:[bind(X_2982,$fot(X_2983))]]) ).
cnf(refute_0_193,plain,
not(not(X_2983)) = X_2983,
inference(resolve,[$cnf( is_a_theorem(equiv(not(not(X_2983)),X_2983)) )],[refute_0_192,refute_0_142]) ).
cnf(refute_0_194,plain,
not(not(Y)) = Y,
inference(subst,[],[refute_0_193:[bind(X_2983,$fot(Y))]]) ).
cnf(refute_0_195,plain,
( not(not(Y)) != Y
| or(Y,Y) != not(not(Y))
| or(Y,Y) = Y ),
introduced(tautology,[equality,[$cnf( $equal(or(Y,Y),not(not(Y))) ),[1],$fot(Y)]]) ).
cnf(refute_0_196,plain,
( or(Y,Y) != not(not(Y))
| or(Y,Y) = Y ),
inference(resolve,[$cnf( $equal(not(not(Y)),Y) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
or(Y,Y) = Y,
inference(resolve,[$cnf( $equal(or(Y,Y),not(not(Y))) )],[refute_0_141,refute_0_196]) ).
cnf(refute_0_198,plain,
or(X_381,X_381) = X_381,
inference(subst,[],[refute_0_197:[bind(Y,$fot(X_381))]]) ).
cnf(refute_0_199,plain,
( or(X_381,X_381) != X_381
| ~ is_a_theorem(not(and(necessarily(and(not(X_381),not(X_381))),or(X_381,X_381))))
| is_a_theorem(not(and(necessarily(and(not(X_381),not(X_381))),X_381))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(necessarily(and(not(X_381),not(X_381))),or(X_381,X_381)))) ),[0,0,1],$fot(X_381)]]) ).
cnf(refute_0_200,plain,
( ~ is_a_theorem(not(and(necessarily(and(not(X_381),not(X_381))),or(X_381,X_381))))
| is_a_theorem(not(and(necessarily(and(not(X_381),not(X_381))),X_381))) ),
inference(resolve,[$cnf( $equal(or(X_381,X_381),X_381) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
is_a_theorem(not(and(necessarily(and(not(X_381),not(X_381))),X_381))),
inference(resolve,[$cnf( is_a_theorem(not(and(necessarily(and(not(X_381),not(X_381))),or(X_381,X_381)))) )],[refute_0_101,refute_0_200]) ).
cnf(refute_0_202,plain,
implies(not(X_381),X_381) = or(X_381,X_381),
inference(subst,[],[refute_0_70:[bind(X,$fot(X_381)),bind(Y,$fot(X_381))]]) ).
cnf(refute_0_203,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_204,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_29,refute_0_203]) ).
cnf(refute_0_205,plain,
( implies(not(X_381),X_381) != or(X_381,X_381)
| or(X_381,X_381) != X_381
| implies(not(X_381),X_381) = X_381 ),
inference(subst,[],[refute_0_204:[bind(X0,$fot(implies(not(X_381),X_381))),bind(Y0,$fot(or(X_381,X_381))),bind(Z,$fot(X_381))]]) ).
cnf(refute_0_206,plain,
( or(X_381,X_381) != X_381
| implies(not(X_381),X_381) = X_381 ),
inference(resolve,[$cnf( $equal(implies(not(X_381),X_381),or(X_381,X_381)) )],[refute_0_202,refute_0_205]) ).
cnf(refute_0_207,plain,
implies(not(X_381),X_381) = X_381,
inference(resolve,[$cnf( $equal(or(X_381,X_381),X_381) )],[refute_0_198,refute_0_206]) ).
cnf(refute_0_208,plain,
not(implies(not(X_381),X_381)) = not(implies(not(X_381),X_381)),
introduced(tautology,[refl,[$fot(not(implies(not(X_381),X_381)))]]) ).
cnf(refute_0_209,plain,
( implies(not(X_381),X_381) != X_381
| not(implies(not(X_381),X_381)) != not(implies(not(X_381),X_381))
| not(implies(not(X_381),X_381)) = not(X_381) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(X_381),X_381)),not(implies(not(X_381),X_381))) ),[1,0],$fot(X_381)]]) ).
cnf(refute_0_210,plain,
( implies(not(X_381),X_381) != X_381
| not(implies(not(X_381),X_381)) = not(X_381) ),
inference(resolve,[$cnf( $equal(not(implies(not(X_381),X_381)),not(implies(not(X_381),X_381))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
not(implies(not(X_381),X_381)) = not(X_381),
inference(resolve,[$cnf( $equal(implies(not(X_381),X_381),X_381) )],[refute_0_207,refute_0_210]) ).
cnf(refute_0_212,plain,
or(and(X,not(Y)),X_26) = implies(not(and(X,not(Y))),X_26),
inference(subst,[],[refute_0_68:[bind(X,$fot(and(X,not(Y)))),bind(Y,$fot(X_26))]]) ).
cnf(refute_0_213,plain,
( not(and(X,not(Y))) != implies(X,Y)
| or(and(X,not(Y)),X_26) != implies(not(and(X,not(Y))),X_26)
| or(and(X,not(Y)),X_26) = implies(implies(X,Y),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X,not(Y)),X_26),implies(not(and(X,not(Y))),X_26)) ),[1,0],$fot(implies(X,Y))]]) ).
cnf(refute_0_214,plain,
( or(and(X,not(Y)),X_26) != implies(not(and(X,not(Y))),X_26)
| or(and(X,not(Y)),X_26) = implies(implies(X,Y),X_26) ),
inference(resolve,[$cnf( $equal(not(and(X,not(Y))),implies(X,Y)) )],[refute_0_64,refute_0_213]) ).
cnf(refute_0_215,plain,
or(and(X,not(Y)),X_26) = implies(implies(X,Y),X_26),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),X_26),implies(not(and(X,not(Y))),X_26)) )],[refute_0_212,refute_0_214]) ).
cnf(refute_0_216,plain,
or(and(X,not(Y)),and(X,not(Y))) = implies(implies(X,Y),and(X,not(Y))),
inference(subst,[],[refute_0_215:[bind(X_26,$fot(and(X,not(Y))))]]) ).
cnf(refute_0_217,plain,
or(and(X,not(Y)),and(X,not(Y))) = and(X,not(Y)),
inference(subst,[],[refute_0_197:[bind(Y,$fot(and(X,not(Y))))]]) ).
cnf(refute_0_218,plain,
( or(and(X,not(Y)),and(X,not(Y))) != and(X,not(Y))
| or(and(X,not(Y)),and(X,not(Y))) != implies(implies(X,Y),and(X,not(Y)))
| and(X,not(Y)) = implies(implies(X,Y),and(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X,not(Y)),and(X,not(Y))),implies(implies(X,Y),and(X,not(Y)))) ),[0],$fot(and(X,not(Y)))]]) ).
cnf(refute_0_219,plain,
( or(and(X,not(Y)),and(X,not(Y))) != implies(implies(X,Y),and(X,not(Y)))
| and(X,not(Y)) = implies(implies(X,Y),and(X,not(Y))) ),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),and(X,not(Y))),and(X,not(Y))) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
and(X,not(Y)) = implies(implies(X,Y),and(X,not(Y))),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),and(X,not(Y))),implies(implies(X,Y),and(X,not(Y)))) )],[refute_0_216,refute_0_219]) ).
cnf(refute_0_221,plain,
( X_1618 != and(X_1618,X_1618)
| and(X_1618,X_1618) = X_1618 ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(X_1618)),bind(Y0,$fot(and(X_1618,X_1618)))]]) ).
cnf(refute_0_222,plain,
and(X_1618,X_1618) = X_1618,
inference(resolve,[$cnf( $equal(X_1618,and(X_1618,X_1618)) )],[refute_0_131,refute_0_221]) ).
cnf(refute_0_223,plain,
and(implies(X,Y),implies(X,Y)) = implies(X,Y),
inference(subst,[],[refute_0_222:[bind(X_1618,$fot(implies(X,Y)))]]) ).
cnf(refute_0_224,plain,
not(and(implies(X,Y),implies(X,Y))) = not(and(implies(X,Y),implies(X,Y))),
introduced(tautology,[refl,[$fot(not(and(implies(X,Y),implies(X,Y))))]]) ).
cnf(refute_0_225,plain,
( and(implies(X,Y),implies(X,Y)) != implies(X,Y)
| not(and(implies(X,Y),implies(X,Y))) != not(and(implies(X,Y),implies(X,Y)))
| not(and(implies(X,Y),implies(X,Y))) = not(implies(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(implies(X,Y),implies(X,Y))),not(and(implies(X,Y),implies(X,Y)))) ),[1,0],$fot(implies(X,Y))]]) ).
cnf(refute_0_226,plain,
( and(implies(X,Y),implies(X,Y)) != implies(X,Y)
| not(and(implies(X,Y),implies(X,Y))) = not(implies(X,Y)) ),
inference(resolve,[$cnf( $equal(not(and(implies(X,Y),implies(X,Y))),not(and(implies(X,Y),implies(X,Y)))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
not(and(implies(X,Y),implies(X,Y))) = not(implies(X,Y)),
inference(resolve,[$cnf( $equal(and(implies(X,Y),implies(X,Y)),implies(X,Y)) )],[refute_0_223,refute_0_226]) ).
cnf(refute_0_228,plain,
implies(implies(X,Y),and(X,not(Y))) = not(and(implies(X,Y),implies(X,Y))),
inference(subst,[],[refute_0_89:[bind(X,$fot(implies(X,Y))),bind(X_17,$fot(X)),bind(X_18,$fot(Y))]]) ).
cnf(refute_0_229,plain,
( implies(implies(X,Y),and(X,not(Y))) != not(and(implies(X,Y),implies(X,Y)))
| not(and(implies(X,Y),implies(X,Y))) != not(implies(X,Y))
| implies(implies(X,Y),and(X,not(Y))) = not(implies(X,Y)) ),
inference(subst,[],[refute_0_204:[bind(X0,$fot(implies(implies(X,Y),and(X,not(Y))))),bind(Y0,$fot(not(and(implies(X,Y),implies(X,Y))))),bind(Z,$fot(not(implies(X,Y))))]]) ).
cnf(refute_0_230,plain,
( not(and(implies(X,Y),implies(X,Y))) != not(implies(X,Y))
| implies(implies(X,Y),and(X,not(Y))) = not(implies(X,Y)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),and(X,not(Y))),not(and(implies(X,Y),implies(X,Y)))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
implies(implies(X,Y),and(X,not(Y))) = not(implies(X,Y)),
inference(resolve,[$cnf( $equal(not(and(implies(X,Y),implies(X,Y))),not(implies(X,Y))) )],[refute_0_227,refute_0_230]) ).
cnf(refute_0_232,plain,
( and(X,not(Y)) != implies(implies(X,Y),and(X,not(Y)))
| implies(implies(X,Y),and(X,not(Y))) != not(implies(X,Y))
| and(X,not(Y)) = not(implies(X,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,not(Y)),not(implies(X,Y))) ),[0],$fot(implies(implies(X,Y),and(X,not(Y))))]]) ).
cnf(refute_0_233,plain,
( and(X,not(Y)) != implies(implies(X,Y),and(X,not(Y)))
| and(X,not(Y)) = not(implies(X,Y)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),and(X,not(Y))),not(implies(X,Y))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
and(X,not(Y)) = not(implies(X,Y)),
inference(resolve,[$cnf( $equal(and(X,not(Y)),implies(implies(X,Y),and(X,not(Y)))) )],[refute_0_220,refute_0_233]) ).
cnf(refute_0_235,plain,
and(not(X_381),not(X_381)) = not(implies(not(X_381),X_381)),
inference(subst,[],[refute_0_234:[bind(X,$fot(not(X_381))),bind(Y,$fot(X_381))]]) ).
cnf(refute_0_236,plain,
( and(not(X_381),not(X_381)) != not(implies(not(X_381),X_381))
| not(implies(not(X_381),X_381)) != not(X_381)
| and(not(X_381),not(X_381)) = not(X_381) ),
inference(subst,[],[refute_0_204:[bind(X0,$fot(and(not(X_381),not(X_381)))),bind(Y0,$fot(not(implies(not(X_381),X_381)))),bind(Z,$fot(not(X_381)))]]) ).
cnf(refute_0_237,plain,
( not(implies(not(X_381),X_381)) != not(X_381)
| and(not(X_381),not(X_381)) = not(X_381) ),
inference(resolve,[$cnf( $equal(and(not(X_381),not(X_381)),not(implies(not(X_381),X_381))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
and(not(X_381),not(X_381)) = not(X_381),
inference(resolve,[$cnf( $equal(not(implies(not(X_381),X_381)),not(X_381)) )],[refute_0_211,refute_0_237]) ).
cnf(refute_0_239,plain,
necessarily(and(not(X_381),not(X_381))) = necessarily(and(not(X_381),not(X_381))),
introduced(tautology,[refl,[$fot(necessarily(and(not(X_381),not(X_381))))]]) ).
cnf(refute_0_240,plain,
( and(not(X_381),not(X_381)) != not(X_381)
| necessarily(and(not(X_381),not(X_381))) != necessarily(and(not(X_381),not(X_381)))
| necessarily(and(not(X_381),not(X_381))) = necessarily(not(X_381)) ),
introduced(tautology,[equality,[$cnf( $equal(necessarily(and(not(X_381),not(X_381))),necessarily(and(not(X_381),not(X_381)))) ),[1,0],$fot(not(X_381))]]) ).
cnf(refute_0_241,plain,
( and(not(X_381),not(X_381)) != not(X_381)
| necessarily(and(not(X_381),not(X_381))) = necessarily(not(X_381)) ),
inference(resolve,[$cnf( $equal(necessarily(and(not(X_381),not(X_381))),necessarily(and(not(X_381),not(X_381)))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
necessarily(and(not(X_381),not(X_381))) = necessarily(not(X_381)),
inference(resolve,[$cnf( $equal(and(not(X_381),not(X_381)),not(X_381)) )],[refute_0_238,refute_0_241]) ).
cnf(refute_0_243,plain,
and(necessarily(and(not(X_381),not(X_381))),X_381) = and(necessarily(and(not(X_381),not(X_381))),X_381),
introduced(tautology,[refl,[$fot(and(necessarily(and(not(X_381),not(X_381))),X_381))]]) ).
cnf(refute_0_244,plain,
( and(necessarily(and(not(X_381),not(X_381))),X_381) != and(necessarily(and(not(X_381),not(X_381))),X_381)
| necessarily(and(not(X_381),not(X_381))) != necessarily(not(X_381))
| and(necessarily(and(not(X_381),not(X_381))),X_381) = and(necessarily(not(X_381)),X_381) ),
introduced(tautology,[equality,[$cnf( $equal(and(necessarily(and(not(X_381),not(X_381))),X_381),and(necessarily(and(not(X_381),not(X_381))),X_381)) ),[1,0],$fot(necessarily(not(X_381)))]]) ).
cnf(refute_0_245,plain,
( necessarily(and(not(X_381),not(X_381))) != necessarily(not(X_381))
| and(necessarily(and(not(X_381),not(X_381))),X_381) = and(necessarily(not(X_381)),X_381) ),
inference(resolve,[$cnf( $equal(and(necessarily(and(not(X_381),not(X_381))),X_381),and(necessarily(and(not(X_381),not(X_381))),X_381)) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
and(necessarily(and(not(X_381),not(X_381))),X_381) = and(necessarily(not(X_381)),X_381),
inference(resolve,[$cnf( $equal(necessarily(and(not(X_381),not(X_381))),necessarily(not(X_381))) )],[refute_0_242,refute_0_245]) ).
cnf(refute_0_247,plain,
not(and(necessarily(and(not(X_381),not(X_381))),X_381)) = not(and(necessarily(and(not(X_381),not(X_381))),X_381)),
introduced(tautology,[refl,[$fot(not(and(necessarily(and(not(X_381),not(X_381))),X_381)))]]) ).
cnf(refute_0_248,plain,
( and(necessarily(and(not(X_381),not(X_381))),X_381) != and(necessarily(not(X_381)),X_381)
| not(and(necessarily(and(not(X_381),not(X_381))),X_381)) != not(and(necessarily(and(not(X_381),not(X_381))),X_381))
| not(and(necessarily(and(not(X_381),not(X_381))),X_381)) = not(and(necessarily(not(X_381)),X_381)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(necessarily(and(not(X_381),not(X_381))),X_381)),not(and(necessarily(and(not(X_381),not(X_381))),X_381))) ),[1,0],$fot(and(necessarily(not(X_381)),X_381))]]) ).
cnf(refute_0_249,plain,
( and(necessarily(and(not(X_381),not(X_381))),X_381) != and(necessarily(not(X_381)),X_381)
| not(and(necessarily(and(not(X_381),not(X_381))),X_381)) = not(and(necessarily(not(X_381)),X_381)) ),
inference(resolve,[$cnf( $equal(not(and(necessarily(and(not(X_381),not(X_381))),X_381)),not(and(necessarily(and(not(X_381),not(X_381))),X_381))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
not(and(necessarily(and(not(X_381),not(X_381))),X_381)) = not(and(necessarily(not(X_381)),X_381)),
inference(resolve,[$cnf( $equal(and(necessarily(and(not(X_381),not(X_381))),X_381),and(necessarily(not(X_381)),X_381)) )],[refute_0_246,refute_0_249]) ).
cnf(refute_0_251,plain,
( not(and(necessarily(and(not(X_381),not(X_381))),X_381)) != not(and(necessarily(not(X_381)),X_381))
| ~ is_a_theorem(not(and(necessarily(and(not(X_381),not(X_381))),X_381)))
| is_a_theorem(not(and(necessarily(not(X_381)),X_381))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(necessarily(and(not(X_381),not(X_381))),X_381))) ),[0],$fot(not(and(necessarily(not(X_381)),X_381)))]]) ).
cnf(refute_0_252,plain,
( ~ is_a_theorem(not(and(necessarily(and(not(X_381),not(X_381))),X_381)))
| is_a_theorem(not(and(necessarily(not(X_381)),X_381))) ),
inference(resolve,[$cnf( $equal(not(and(necessarily(and(not(X_381),not(X_381))),X_381)),not(and(necessarily(not(X_381)),X_381))) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
is_a_theorem(not(and(necessarily(not(X_381)),X_381))),
inference(resolve,[$cnf( is_a_theorem(not(and(necessarily(and(not(X_381),not(X_381))),X_381))) )],[refute_0_201,refute_0_252]) ).
cnf(refute_0_254,plain,
or(X,not(X_3315)) = implies(not(X),not(X_3315)),
inference(subst,[],[refute_0_68:[bind(Y,$fot(not(X_3315)))]]) ).
cnf(refute_0_255,plain,
not(not(implies(X_3314,not(X_3313)))) = implies(X_3314,not(X_3313)),
inference(subst,[],[refute_0_193:[bind(X_2983,$fot(implies(X_3314,not(X_3313))))]]) ).
cnf(refute_0_256,plain,
and(X_3309,not(not(X_2983))) = not(implies(X_3309,not(X_2983))),
inference(subst,[],[refute_0_234:[bind(X,$fot(X_3309)),bind(Y,$fot(not(X_2983)))]]) ).
cnf(refute_0_257,plain,
( and(X_3309,not(not(X_2983))) != not(implies(X_3309,not(X_2983)))
| not(not(X_2983)) != X_2983
| and(X_3309,X_2983) = not(implies(X_3309,not(X_2983))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_3309,not(not(X_2983))),not(implies(X_3309,not(X_2983)))) ),[0,1],$fot(X_2983)]]) ).
cnf(refute_0_258,plain,
( and(X_3309,not(not(X_2983))) != not(implies(X_3309,not(X_2983)))
| and(X_3309,X_2983) = not(implies(X_3309,not(X_2983))) ),
inference(resolve,[$cnf( $equal(not(not(X_2983)),X_2983) )],[refute_0_193,refute_0_257]) ).
cnf(refute_0_259,plain,
and(X_3309,X_2983) = not(implies(X_3309,not(X_2983))),
inference(resolve,[$cnf( $equal(and(X_3309,not(not(X_2983))),not(implies(X_3309,not(X_2983)))) )],[refute_0_256,refute_0_258]) ).
cnf(refute_0_260,plain,
and(X_3314,X_3313) = not(implies(X_3314,not(X_3313))),
inference(subst,[],[refute_0_259:[bind(X_2983,$fot(X_3313)),bind(X_3309,$fot(X_3314))]]) ).
cnf(refute_0_261,plain,
( and(X_3314,X_3313) != not(implies(X_3314,not(X_3313)))
| not(implies(X_3314,not(X_3313))) = and(X_3314,X_3313) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(and(X_3314,X_3313))),bind(Y0,$fot(not(implies(X_3314,not(X_3313)))))]]) ).
cnf(refute_0_262,plain,
not(implies(X_3314,not(X_3313))) = and(X_3314,X_3313),
inference(resolve,[$cnf( $equal(and(X_3314,X_3313),not(implies(X_3314,not(X_3313)))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
( not(implies(X_3314,not(X_3313))) != and(X_3314,X_3313)
| not(not(implies(X_3314,not(X_3313)))) != implies(X_3314,not(X_3313))
| not(and(X_3314,X_3313)) = implies(X_3314,not(X_3313)) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(X_3314,not(X_3313)))),implies(X_3314,not(X_3313))) ),[0,0],$fot(and(X_3314,X_3313))]]) ).
cnf(refute_0_264,plain,
( not(not(implies(X_3314,not(X_3313)))) != implies(X_3314,not(X_3313))
| not(and(X_3314,X_3313)) = implies(X_3314,not(X_3313)) ),
inference(resolve,[$cnf( $equal(not(implies(X_3314,not(X_3313))),and(X_3314,X_3313)) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
not(and(X_3314,X_3313)) = implies(X_3314,not(X_3313)),
inference(resolve,[$cnf( $equal(not(not(implies(X_3314,not(X_3313)))),implies(X_3314,not(X_3313))) )],[refute_0_255,refute_0_264]) ).
cnf(refute_0_266,plain,
not(and(not(X),X_3315)) = implies(not(X),not(X_3315)),
inference(subst,[],[refute_0_265:[bind(X_3313,$fot(X_3315)),bind(X_3314,$fot(not(X)))]]) ).
cnf(refute_0_267,plain,
( not(and(not(X),X_3315)) != implies(not(X),not(X_3315))
| implies(not(X),not(X_3315)) = not(and(not(X),X_3315)) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(not(and(not(X),X_3315)))),bind(Y0,$fot(implies(not(X),not(X_3315))))]]) ).
cnf(refute_0_268,plain,
implies(not(X),not(X_3315)) = not(and(not(X),X_3315)),
inference(resolve,[$cnf( $equal(not(and(not(X),X_3315)),implies(not(X),not(X_3315))) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
( implies(not(X),not(X_3315)) != not(and(not(X),X_3315))
| or(X,not(X_3315)) != implies(not(X),not(X_3315))
| or(X,not(X_3315)) = not(and(not(X),X_3315)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(X_3315)),implies(not(X),not(X_3315))) ),[1],$fot(not(and(not(X),X_3315)))]]) ).
cnf(refute_0_270,plain,
( or(X,not(X_3315)) != implies(not(X),not(X_3315))
| or(X,not(X_3315)) = not(and(not(X),X_3315)) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X_3315)),not(and(not(X),X_3315))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
or(X,not(X_3315)) = not(and(not(X),X_3315)),
inference(resolve,[$cnf( $equal(or(X,not(X_3315)),implies(not(X),not(X_3315))) )],[refute_0_254,refute_0_270]) ).
cnf(refute_0_272,plain,
or(possibly(X),not(X_5953)) = not(and(not(possibly(X)),X_5953)),
inference(subst,[],[refute_0_271:[bind(X,$fot(possibly(X))),bind(X_3315,$fot(X_5953))]]) ).
cnf(refute_0_273,plain,
or(necessarily(not(X)),X_26) = implies(not(necessarily(not(X))),X_26),
inference(subst,[],[refute_0_68:[bind(X,$fot(necessarily(not(X)))),bind(Y,$fot(X_26))]]) ).
cnf(refute_0_274,plain,
( ~ op_possibly
| possibly(X) = not(necessarily(not(X))) ),
inference(canonicalize,[],[normalize_0_58]) ).
cnf(refute_0_275,plain,
op_possibly,
inference(canonicalize,[],[normalize_0_59]) ).
cnf(refute_0_276,plain,
possibly(X) = not(necessarily(not(X))),
inference(resolve,[$cnf( op_possibly )],[refute_0_275,refute_0_274]) ).
cnf(refute_0_277,plain,
( possibly(X) != not(necessarily(not(X)))
| not(necessarily(not(X))) = possibly(X) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(possibly(X))),bind(Y0,$fot(not(necessarily(not(X)))))]]) ).
cnf(refute_0_278,plain,
not(necessarily(not(X))) = possibly(X),
inference(resolve,[$cnf( $equal(possibly(X),not(necessarily(not(X)))) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
( not(necessarily(not(X))) != possibly(X)
| or(necessarily(not(X)),X_26) != implies(not(necessarily(not(X))),X_26)
| or(necessarily(not(X)),X_26) = implies(possibly(X),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(or(necessarily(not(X)),X_26),implies(not(necessarily(not(X))),X_26)) ),[1,0],$fot(possibly(X))]]) ).
cnf(refute_0_280,plain,
( or(necessarily(not(X)),X_26) != implies(not(necessarily(not(X))),X_26)
| or(necessarily(not(X)),X_26) = implies(possibly(X),X_26) ),
inference(resolve,[$cnf( $equal(not(necessarily(not(X))),possibly(X)) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
or(necessarily(not(X)),X_26) = implies(possibly(X),X_26),
inference(resolve,[$cnf( $equal(or(necessarily(not(X)),X_26),implies(not(necessarily(not(X))),X_26)) )],[refute_0_273,refute_0_280]) ).
cnf(refute_0_282,plain,
or(necessarily(not(X)),necessarily(not(X))) = implies(possibly(X),necessarily(not(X))),
inference(subst,[],[refute_0_281:[bind(X_26,$fot(necessarily(not(X))))]]) ).
cnf(refute_0_283,plain,
or(necessarily(not(X)),necessarily(not(X))) = necessarily(not(X)),
inference(subst,[],[refute_0_197:[bind(Y,$fot(necessarily(not(X))))]]) ).
cnf(refute_0_284,plain,
( or(necessarily(not(X)),necessarily(not(X))) != implies(possibly(X),necessarily(not(X)))
| or(necessarily(not(X)),necessarily(not(X))) != necessarily(not(X))
| necessarily(not(X)) = implies(possibly(X),necessarily(not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(or(necessarily(not(X)),necessarily(not(X))),implies(possibly(X),necessarily(not(X)))) ),[0],$fot(necessarily(not(X)))]]) ).
cnf(refute_0_285,plain,
( or(necessarily(not(X)),necessarily(not(X))) != implies(possibly(X),necessarily(not(X)))
| necessarily(not(X)) = implies(possibly(X),necessarily(not(X))) ),
inference(resolve,[$cnf( $equal(or(necessarily(not(X)),necessarily(not(X))),necessarily(not(X))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
necessarily(not(X)) = implies(possibly(X),necessarily(not(X))),
inference(resolve,[$cnf( $equal(or(necessarily(not(X)),necessarily(not(X))),implies(possibly(X),necessarily(not(X)))) )],[refute_0_282,refute_0_285]) ).
cnf(refute_0_287,plain,
and(possibly(X),possibly(X)) = possibly(X),
inference(subst,[],[refute_0_222:[bind(X_1618,$fot(possibly(X)))]]) ).
cnf(refute_0_288,plain,
not(and(possibly(X),possibly(X))) = not(and(possibly(X),possibly(X))),
introduced(tautology,[refl,[$fot(not(and(possibly(X),possibly(X))))]]) ).
cnf(refute_0_289,plain,
( and(possibly(X),possibly(X)) != possibly(X)
| not(and(possibly(X),possibly(X))) != not(and(possibly(X),possibly(X)))
| not(and(possibly(X),possibly(X))) = not(possibly(X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(possibly(X),possibly(X))),not(and(possibly(X),possibly(X)))) ),[1,0],$fot(possibly(X))]]) ).
cnf(refute_0_290,plain,
( and(possibly(X),possibly(X)) != possibly(X)
| not(and(possibly(X),possibly(X))) = not(possibly(X)) ),
inference(resolve,[$cnf( $equal(not(and(possibly(X),possibly(X))),not(and(possibly(X),possibly(X)))) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
not(and(possibly(X),possibly(X))) = not(possibly(X)),
inference(resolve,[$cnf( $equal(and(possibly(X),possibly(X)),possibly(X)) )],[refute_0_287,refute_0_290]) ).
cnf(refute_0_292,plain,
implies(X_17,necessarily(not(X))) = not(and(X_17,not(necessarily(not(X))))),
inference(subst,[],[refute_0_62:[bind(X,$fot(X_17)),bind(Y,$fot(necessarily(not(X))))]]) ).
cnf(refute_0_293,plain,
( implies(X_17,necessarily(not(X))) != not(and(X_17,not(necessarily(not(X)))))
| not(necessarily(not(X))) != possibly(X)
| implies(X_17,necessarily(not(X))) = not(and(X_17,possibly(X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_17,necessarily(not(X))),not(and(X_17,not(necessarily(not(X)))))) ),[1,0,1],$fot(possibly(X))]]) ).
cnf(refute_0_294,plain,
( implies(X_17,necessarily(not(X))) != not(and(X_17,not(necessarily(not(X)))))
| implies(X_17,necessarily(not(X))) = not(and(X_17,possibly(X))) ),
inference(resolve,[$cnf( $equal(not(necessarily(not(X))),possibly(X)) )],[refute_0_278,refute_0_293]) ).
cnf(refute_0_295,plain,
implies(X_17,necessarily(not(X))) = not(and(X_17,possibly(X))),
inference(resolve,[$cnf( $equal(implies(X_17,necessarily(not(X))),not(and(X_17,not(necessarily(not(X)))))) )],[refute_0_292,refute_0_294]) ).
cnf(refute_0_296,plain,
implies(possibly(X),necessarily(not(X))) = not(and(possibly(X),possibly(X))),
inference(subst,[],[refute_0_295:[bind(X_17,$fot(possibly(X)))]]) ).
cnf(refute_0_297,plain,
( implies(possibly(X),necessarily(not(X))) != not(and(possibly(X),possibly(X)))
| not(and(possibly(X),possibly(X))) != not(possibly(X))
| implies(possibly(X),necessarily(not(X))) = not(possibly(X)) ),
inference(subst,[],[refute_0_204:[bind(X0,$fot(implies(possibly(X),necessarily(not(X))))),bind(Y0,$fot(not(and(possibly(X),possibly(X))))),bind(Z,$fot(not(possibly(X))))]]) ).
cnf(refute_0_298,plain,
( not(and(possibly(X),possibly(X))) != not(possibly(X))
| implies(possibly(X),necessarily(not(X))) = not(possibly(X)) ),
inference(resolve,[$cnf( $equal(implies(possibly(X),necessarily(not(X))),not(and(possibly(X),possibly(X)))) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
implies(possibly(X),necessarily(not(X))) = not(possibly(X)),
inference(resolve,[$cnf( $equal(not(and(possibly(X),possibly(X))),not(possibly(X))) )],[refute_0_291,refute_0_298]) ).
cnf(refute_0_300,plain,
( implies(possibly(X),necessarily(not(X))) != not(possibly(X))
| necessarily(not(X)) != implies(possibly(X),necessarily(not(X)))
| necessarily(not(X)) = not(possibly(X)) ),
introduced(tautology,[equality,[$cnf( $equal(necessarily(not(X)),implies(possibly(X),necessarily(not(X)))) ),[1],$fot(not(possibly(X)))]]) ).
cnf(refute_0_301,plain,
( necessarily(not(X)) != implies(possibly(X),necessarily(not(X)))
| necessarily(not(X)) = not(possibly(X)) ),
inference(resolve,[$cnf( $equal(implies(possibly(X),necessarily(not(X))),not(possibly(X))) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
necessarily(not(X)) = not(possibly(X)),
inference(resolve,[$cnf( $equal(necessarily(not(X)),implies(possibly(X),necessarily(not(X)))) )],[refute_0_286,refute_0_301]) ).
cnf(refute_0_303,plain,
( necessarily(not(X)) != not(possibly(X))
| not(possibly(X)) = necessarily(not(X)) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(necessarily(not(X)))),bind(Y0,$fot(not(possibly(X))))]]) ).
cnf(refute_0_304,plain,
not(possibly(X)) = necessarily(not(X)),
inference(resolve,[$cnf( $equal(necessarily(not(X)),not(possibly(X))) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
( not(possibly(X)) != necessarily(not(X))
| or(possibly(X),not(X_5953)) != not(and(not(possibly(X)),X_5953))
| or(possibly(X),not(X_5953)) = not(and(necessarily(not(X)),X_5953)) ),
introduced(tautology,[equality,[$cnf( $equal(or(possibly(X),not(X_5953)),not(and(not(possibly(X)),X_5953))) ),[1,0,0],$fot(necessarily(not(X)))]]) ).
cnf(refute_0_306,plain,
( or(possibly(X),not(X_5953)) != not(and(not(possibly(X)),X_5953))
| or(possibly(X),not(X_5953)) = not(and(necessarily(not(X)),X_5953)) ),
inference(resolve,[$cnf( $equal(not(possibly(X)),necessarily(not(X))) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
or(possibly(X),not(X_5953)) = not(and(necessarily(not(X)),X_5953)),
inference(resolve,[$cnf( $equal(or(possibly(X),not(X_5953)),not(and(not(possibly(X)),X_5953))) )],[refute_0_272,refute_0_306]) ).
cnf(refute_0_308,plain,
( or(possibly(X),not(X_5953)) != not(and(necessarily(not(X)),X_5953))
| not(and(necessarily(not(X)),X_5953)) = or(possibly(X),not(X_5953)) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(or(possibly(X),not(X_5953)))),bind(Y0,$fot(not(and(necessarily(not(X)),X_5953))))]]) ).
cnf(refute_0_309,plain,
not(and(necessarily(not(X)),X_5953)) = or(possibly(X),not(X_5953)),
inference(resolve,[$cnf( $equal(or(possibly(X),not(X_5953)),not(and(necessarily(not(X)),X_5953))) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
not(and(necessarily(not(X_381)),X_381)) = or(possibly(X_381),not(X_381)),
inference(subst,[],[refute_0_309:[bind(X,$fot(X_381)),bind(X_5953,$fot(X_381))]]) ).
cnf(refute_0_311,plain,
( not(and(necessarily(not(X_381)),X_381)) != or(possibly(X_381),not(X_381))
| ~ is_a_theorem(not(and(necessarily(not(X_381)),X_381)))
| is_a_theorem(or(possibly(X_381),not(X_381))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(necessarily(not(X_381)),X_381))) ),[0],$fot(or(possibly(X_381),not(X_381)))]]) ).
cnf(refute_0_312,plain,
( ~ is_a_theorem(not(and(necessarily(not(X_381)),X_381)))
| is_a_theorem(or(possibly(X_381),not(X_381))) ),
inference(resolve,[$cnf( $equal(not(and(necessarily(not(X_381)),X_381)),or(possibly(X_381),not(X_381))) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
is_a_theorem(or(possibly(X_381),not(X_381))),
inference(resolve,[$cnf( is_a_theorem(not(and(necessarily(not(X_381)),X_381))) )],[refute_0_253,refute_0_312]) ).
cnf(refute_0_314,plain,
is_a_theorem(or(possibly(X_5954),not(X_5954))),
inference(subst,[],[refute_0_313:[bind(X_381,$fot(X_5954))]]) ).
cnf(refute_0_315,plain,
is_a_theorem(implies(X_5954,possibly(X_5954))),
inference(resolve,[$cnf( is_a_theorem(or(possibly(X_5954),not(X_5954))) )],[refute_0_314,refute_0_81]) ).
cnf(refute_0_316,plain,
is_a_theorem(implies(skolemFOFtoCNF_X_22,possibly(skolemFOFtoCNF_X_22))),
inference(subst,[],[refute_0_315:[bind(X_5954,$fot(skolemFOFtoCNF_X_22))]]) ).
cnf(refute_0_317,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_X_22,possibly(skolemFOFtoCNF_X_22))) )],[refute_0_316,refute_0_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL524+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sun Jul 3 03:45:50 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 30.22/30.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.22/30.39
% 30.22/30.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.26/30.43
%------------------------------------------------------------------------------