TSTP Solution File: LCL486+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL486+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 12:52:36 EDT 2022
% Result : Theorem 28.62s 28.78s
% Output : CNFRefutation 28.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 79
% Syntax : Number of formulae : 470 ( 236 unt; 0 def)
% Number of atoms : 813 ( 438 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 665 ( 322 ~; 305 |; 15 &)
% ( 16 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 17 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 18 con; 0-2 aty)
% Number of variables : 759 ( 6 sgn 81 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ) ).
fof(implies_3,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ) ).
fof(r1,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ) ).
fof(r2,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ) ).
fof(r3,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ) ).
fof(r4,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ) ).
fof(r5,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ) ).
fof(op_and,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ).
fof(principia_op_implies_or,axiom,
op_implies_or ).
fof(principia_op_and,axiom,
op_and ).
fof(principia_op_equiv,axiom,
op_equiv ).
fof(principia_modus_ponens,axiom,
modus_ponens ).
fof(principia_r1,axiom,
r1 ).
fof(principia_r2,axiom,
r2 ).
fof(principia_r3,axiom,
r3 ).
fof(principia_r4,axiom,
r4 ).
fof(principia_r5,axiom,
r5 ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents ).
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_implies_3,conjecture,
implies_3 ).
fof(subgoal_0,plain,
implies_3,
inference(strip,[],[hilbert_implies_3]) ).
fof(negate_0_0,plain,
~ implies_3,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ implies_3
<=> ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
inference(canonicalize,[],[implies_3]) ).
fof(normalize_0_1,plain,
! [X,Y,Z] :
( ( ~ implies_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )
& ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_5,skolemFOFtoCNF_Y_5),implies(implies(skolemFOFtoCNF_Y_5,skolemFOFtoCNF_Z),implies(skolemFOFtoCNF_X_5,skolemFOFtoCNF_Z))))
| implies_3 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_5,skolemFOFtoCNF_Y_5),implies(implies(skolemFOFtoCNF_Y_5,skolemFOFtoCNF_Z),implies(skolemFOFtoCNF_X_5,skolemFOFtoCNF_Z))))
| implies_3 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ implies_3,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ r5
<=> ? [P,Q,R] : ~ is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(canonicalize,[],[r5]) ).
fof(normalize_0_5,plain,
! [P,Q,R] :
( ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_3),implies(or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_Q_7),or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_R_3))))
| r5 )
& ( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [P,Q,R] :
( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
r5,
inference(canonicalize,[],[principia_r5]) ).
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_implies_or
| ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[op_implies_or]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
op_implies_or,
inference(canonicalize,[],[principia_op_implies_or]) ).
fof(normalize_0_17,plain,
( ~ op_and
| ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[op_and]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
op_and,
inference(canonicalize,[],[principia_op_and]) ).
fof(normalize_0_20,plain,
( ~ r4
<=> ? [P,Q,R] : ~ is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(canonicalize,[],[r4]) ).
fof(normalize_0_21,plain,
! [P,Q,R] :
( ( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_9,or(skolemFOFtoCNF_Q_6,skolemFOFtoCNF_R_2)),or(skolemFOFtoCNF_Q_6,or(skolemFOFtoCNF_P_9,skolemFOFtoCNF_R_2))))
| r4 )
& ( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [P,Q,R] :
( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
r4,
inference(canonicalize,[],[principia_r4]) ).
fof(normalize_0_24,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_25,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_24]) ).
fof(normalize_0_26,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
modus_ponens,
inference(canonicalize,[],[principia_modus_ponens]) ).
fof(normalize_0_28,plain,
( ~ substitution_of_equivalents
<=> ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_29,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_28]) ).
fof(normalize_0_30,plain,
! [X,Y] :
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(conjunct,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
substitution_of_equivalents,
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_32,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_33,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
op_equiv,
inference(canonicalize,[],[hilbert_op_equiv]) ).
fof(normalize_0_35,plain,
( ~ r1
<=> ? [P] : ~ is_a_theorem(implies(or(P,P),P)) ),
inference(canonicalize,[],[r1]) ).
fof(normalize_0_36,plain,
! [P] :
( ( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6))
| r1 )
& ( ~ r1
| is_a_theorem(implies(or(P,P),P)) ) ),
inference(clausify,[],[normalize_0_35]) ).
fof(normalize_0_37,plain,
! [P] :
( ~ r1
| is_a_theorem(implies(or(P,P),P)) ),
inference(conjunct,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
r1,
inference(canonicalize,[],[principia_r1]) ).
fof(normalize_0_39,plain,
( ~ r3
<=> ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[r3]) ).
fof(normalize_0_40,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_5),or(skolemFOFtoCNF_Q_5,skolemFOFtoCNF_P_8)))
| r3 )
& ( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ) ),
inference(clausify,[],[normalize_0_39]) ).
fof(normalize_0_41,plain,
! [P,Q] :
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(conjunct,[],[normalize_0_40]) ).
fof(normalize_0_42,plain,
r3,
inference(canonicalize,[],[principia_r3]) ).
fof(normalize_0_43,plain,
( ~ r2
<=> ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[r2]) ).
fof(normalize_0_44,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(skolemFOFtoCNF_Q_4,or(skolemFOFtoCNF_P_7,skolemFOFtoCNF_Q_4)))
| r2 )
& ( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ) ),
inference(clausify,[],[normalize_0_43]) ).
fof(normalize_0_45,plain,
! [P,Q] :
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(conjunct,[],[normalize_0_44]) ).
fof(normalize_0_46,plain,
r2,
inference(canonicalize,[],[principia_r2]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_5,skolemFOFtoCNF_Y_5),implies(implies(skolemFOFtoCNF_Y_5,skolemFOFtoCNF_Z),implies(skolemFOFtoCNF_X_5,skolemFOFtoCNF_Z))))
| implies_3 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ implies_3,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_5,skolemFOFtoCNF_Y_5),implies(implies(skolemFOFtoCNF_Y_5,skolemFOFtoCNF_Z),implies(skolemFOFtoCNF_X_5,skolemFOFtoCNF_Z)))),
inference(resolve,[$cnf( implies_3 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
r5,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))),
inference(resolve,[$cnf( r5 )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(not(X),X_143),implies(or(X_141,not(X)),or(X_141,X_143)))),
inference(subst,[],[refute_0_5:[bind(P,$fot(X_141)),bind(Q,$fot(not(X))),bind(R,$fot(X_143))]]) ).
cnf(refute_0_7,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
op_or,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$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( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_9,refute_0_20]) ).
cnf(refute_0_22,plain,
or(X,X_143) = implies(not(X),X_143),
inference(subst,[],[refute_0_21:[bind(Y,$fot(X_143))]]) ).
cnf(refute_0_23,plain,
( or(X,X_143) != implies(not(X),X_143)
| implies(not(X),X_143) = or(X,X_143) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_143))),bind(Y0,$fot(implies(not(X),X_143)))]]) ).
cnf(refute_0_24,plain,
implies(not(X),X_143) = or(X,X_143),
inference(resolve,[$cnf( $equal(or(X,X_143),implies(not(X),X_143)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( implies(not(X),X_143) != or(X,X_143)
| ~ is_a_theorem(implies(implies(not(X),X_143),implies(or(X_141,not(X)),or(X_141,X_143))))
| is_a_theorem(implies(or(X,X_143),implies(or(X_141,not(X)),or(X_141,X_143)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X),X_143),implies(or(X_141,not(X)),or(X_141,X_143)))) ),[0,0],$fot(or(X,X_143))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(implies(not(X),X_143),implies(or(X_141,not(X)),or(X_141,X_143))))
| is_a_theorem(implies(or(X,X_143),implies(or(X_141,not(X)),or(X_141,X_143)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_143),or(X,X_143)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(or(X,X_143),implies(or(X_141,not(X)),or(X_141,X_143)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X_143),implies(or(X_141,not(X)),or(X_141,X_143)))) )],[refute_0_6,refute_0_26]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(or(X_489,X_491),implies(or(not(X),not(X_489)),or(not(X),X_491)))),
inference(subst,[],[refute_0_27:[bind(X,$fot(X_489)),bind(X_141,$fot(not(X))),bind(X_143,$fot(X_491))]]) ).
cnf(refute_0_29,plain,
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_30,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_31,plain,
implies(X,Y) = or(not(X),Y),
inference(resolve,[$cnf( op_implies_or )],[refute_0_30,refute_0_29]) ).
cnf(refute_0_32,plain,
implies(X,X_491) = or(not(X),X_491),
inference(subst,[],[refute_0_31:[bind(Y,$fot(X_491))]]) ).
cnf(refute_0_33,plain,
( implies(X,X_491) != or(not(X),X_491)
| or(not(X),X_491) = implies(X,X_491) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_491))),bind(Y0,$fot(or(not(X),X_491)))]]) ).
cnf(refute_0_34,plain,
or(not(X),X_491) = implies(X,X_491),
inference(resolve,[$cnf( $equal(implies(X,X_491),or(not(X),X_491)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( or(not(X),X_491) != implies(X,X_491)
| ~ is_a_theorem(implies(or(X_489,X_491),implies(or(not(X),not(X_489)),or(not(X),X_491))))
| is_a_theorem(implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_489,X_491),implies(or(not(X),not(X_489)),or(not(X),X_491)))) ),[0,1,1],$fot(implies(X,X_491))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(or(X_489,X_491),implies(or(not(X),not(X_489)),or(not(X),X_491))))
| is_a_theorem(implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_491),implies(X,X_491)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_489,X_491),implies(or(not(X),not(X_489)),or(not(X),X_491)))) )],[refute_0_28,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(implies(X_10,not(X_11)),Y) = or(not(implies(X_10,not(X_11))),Y),
inference(subst,[],[refute_0_31:[bind(X,$fot(implies(X_10,not(X_11))))]]) ).
cnf(refute_0_39,plain,
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_40,plain,
op_and,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_41,plain,
and(X,Y) = not(or(not(X),not(Y))),
inference(resolve,[$cnf( op_and )],[refute_0_40,refute_0_39]) ).
cnf(refute_0_42,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_43,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[refute_0_31,refute_0_42]) ).
cnf(refute_0_44,plain,
or(not(X),not(Y)) = implies(X,not(Y)),
inference(subst,[],[refute_0_43:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_45,plain,
not(or(not(X),not(Y))) = not(or(not(X),not(Y))),
introduced(tautology,[refl,[$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_46,plain,
( not(or(not(X),not(Y))) != not(or(not(X),not(Y)))
| or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) ),[1,0],$fot(implies(X,not(Y)))]]) ).
cnf(refute_0_47,plain,
( or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
not(or(not(X),not(Y))) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),implies(X,not(Y))) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) != not(implies(X,not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,Y),not(implies(X,not(Y)))) ),[0],$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_50,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(implies(X,not(Y)))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
and(X,Y) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[refute_0_41,refute_0_50]) ).
cnf(refute_0_52,plain,
and(X_10,X_11) = not(implies(X_10,not(X_11))),
inference(subst,[],[refute_0_51:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_53,plain,
( and(X_10,X_11) != not(implies(X_10,not(X_11)))
| not(implies(X_10,not(X_11))) = and(X_10,X_11) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(X_10,X_11))),bind(Y0,$fot(not(implies(X_10,not(X_11)))))]]) ).
cnf(refute_0_54,plain,
not(implies(X_10,not(X_11))) = and(X_10,X_11),
inference(resolve,[$cnf( $equal(and(X_10,X_11),not(implies(X_10,not(X_11)))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( implies(implies(X_10,not(X_11)),Y) != or(not(implies(X_10,not(X_11))),Y)
| not(implies(X_10,not(X_11))) != and(X_10,X_11)
| implies(implies(X_10,not(X_11)),Y) = or(and(X_10,X_11),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_10,not(X_11)),Y),or(not(implies(X_10,not(X_11))),Y)) ),[1,0],$fot(and(X_10,X_11))]]) ).
cnf(refute_0_56,plain,
( implies(implies(X_10,not(X_11)),Y) != or(not(implies(X_10,not(X_11))),Y)
| implies(implies(X_10,not(X_11)),Y) = or(and(X_10,X_11),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_10,not(X_11))),and(X_10,X_11)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
implies(implies(X_10,not(X_11)),Y) = or(and(X_10,X_11),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_10,not(X_11)),Y),or(not(implies(X_10,not(X_11))),Y)) )],[refute_0_38,refute_0_56]) ).
cnf(refute_0_58,plain,
implies(implies(X,not(X_489)),implies(X,X_491)) = or(and(X,X_489),implies(X,X_491)),
inference(subst,[],[refute_0_57:[bind(Y,$fot(implies(X,X_491))),bind(X_10,$fot(X)),bind(X_11,$fot(X_489))]]) ).
cnf(refute_0_59,plain,
or(not(X),not(X_489)) = implies(X,not(X_489)),
inference(subst,[],[refute_0_43:[bind(Y,$fot(not(X_489)))]]) ).
cnf(refute_0_60,plain,
implies(or(not(X),not(X_489)),implies(X,X_491)) = implies(or(not(X),not(X_489)),implies(X,X_491)),
introduced(tautology,[refl,[$fot(implies(or(not(X),not(X_489)),implies(X,X_491)))]]) ).
cnf(refute_0_61,plain,
( implies(or(not(X),not(X_489)),implies(X,X_491)) != implies(or(not(X),not(X_489)),implies(X,X_491))
| or(not(X),not(X_489)) != implies(X,not(X_489))
| implies(or(not(X),not(X_489)),implies(X,X_491)) = implies(implies(X,not(X_489)),implies(X,X_491)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),not(X_489)),implies(X,X_491)),implies(or(not(X),not(X_489)),implies(X,X_491))) ),[1,0],$fot(implies(X,not(X_489)))]]) ).
cnf(refute_0_62,plain,
( or(not(X),not(X_489)) != implies(X,not(X_489))
| implies(or(not(X),not(X_489)),implies(X,X_491)) = implies(implies(X,not(X_489)),implies(X,X_491)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),not(X_489)),implies(X,X_491)),implies(or(not(X),not(X_489)),implies(X,X_491))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
implies(or(not(X),not(X_489)),implies(X,X_491)) = implies(implies(X,not(X_489)),implies(X,X_491)),
inference(resolve,[$cnf( $equal(or(not(X),not(X_489)),implies(X,not(X_489))) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_65,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_15,refute_0_64]) ).
cnf(refute_0_66,plain,
( implies(implies(X,not(X_489)),implies(X,X_491)) != or(and(X,X_489),implies(X,X_491))
| implies(or(not(X),not(X_489)),implies(X,X_491)) != implies(implies(X,not(X_489)),implies(X,X_491))
| implies(or(not(X),not(X_489)),implies(X,X_491)) = or(and(X,X_489),implies(X,X_491)) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(implies(or(not(X),not(X_489)),implies(X,X_491)))),bind(Y0,$fot(implies(implies(X,not(X_489)),implies(X,X_491)))),bind(Z0,$fot(or(and(X,X_489),implies(X,X_491))))]]) ).
cnf(refute_0_67,plain,
( implies(implies(X,not(X_489)),implies(X,X_491)) != or(and(X,X_489),implies(X,X_491))
| implies(or(not(X),not(X_489)),implies(X,X_491)) = or(and(X,X_489),implies(X,X_491)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),not(X_489)),implies(X,X_491)),implies(implies(X,not(X_489)),implies(X,X_491))) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
implies(or(not(X),not(X_489)),implies(X,X_491)) = or(and(X,X_489),implies(X,X_491)),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X_489)),implies(X,X_491)),or(and(X,X_489),implies(X,X_491))) )],[refute_0_58,refute_0_67]) ).
cnf(refute_0_69,plain,
implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491))) = implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491))),
introduced(tautology,[refl,[$fot(implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491))))]]) ).
cnf(refute_0_70,plain,
( implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491))) != implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491)))
| implies(or(not(X),not(X_489)),implies(X,X_491)) != or(and(X,X_489),implies(X,X_491))
| implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491))) = implies(or(X_489,X_491),or(and(X,X_489),implies(X,X_491))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491))),implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491)))) ),[1,1],$fot(or(and(X,X_489),implies(X,X_491)))]]) ).
cnf(refute_0_71,plain,
( implies(or(not(X),not(X_489)),implies(X,X_491)) != or(and(X,X_489),implies(X,X_491))
| implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491))) = implies(or(X_489,X_491),or(and(X,X_489),implies(X,X_491))) ),
inference(resolve,[$cnf( $equal(implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491))),implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491)))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491))) = implies(or(X_489,X_491),or(and(X,X_489),implies(X,X_491))),
inference(resolve,[$cnf( $equal(implies(or(not(X),not(X_489)),implies(X,X_491)),or(and(X,X_489),implies(X,X_491))) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
( implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491))) != implies(or(X_489,X_491),or(and(X,X_489),implies(X,X_491)))
| ~ is_a_theorem(implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491))))
| is_a_theorem(implies(or(X_489,X_491),or(and(X,X_489),implies(X,X_491)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491)))) ),[0],$fot(implies(or(X_489,X_491),or(and(X,X_489),implies(X,X_491))))]]) ).
cnf(refute_0_74,plain,
( ~ is_a_theorem(implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491))))
| is_a_theorem(implies(or(X_489,X_491),or(and(X,X_489),implies(X,X_491)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491))),implies(or(X_489,X_491),or(and(X,X_489),implies(X,X_491)))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(or(X_489,X_491),or(and(X,X_489),implies(X,X_491)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_489,X_491),implies(or(not(X),not(X_489)),implies(X,X_491)))) )],[refute_0_37,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_77,plain,
r4,
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))),
inference(resolve,[$cnf( r4 )],[refute_0_77,refute_0_76]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(or(not(X),or(X_139,X_140)),or(X_139,or(not(X),X_140)))),
inference(subst,[],[refute_0_78:[bind(P,$fot(not(X))),bind(Q,$fot(X_139)),bind(R,$fot(X_140))]]) ).
cnf(refute_0_80,plain,
implies(X,X_140) = or(not(X),X_140),
inference(subst,[],[refute_0_31:[bind(Y,$fot(X_140))]]) ).
cnf(refute_0_81,plain,
( implies(X,X_140) != or(not(X),X_140)
| or(not(X),X_140) = implies(X,X_140) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_140))),bind(Y0,$fot(or(not(X),X_140)))]]) ).
cnf(refute_0_82,plain,
or(not(X),X_140) = implies(X,X_140),
inference(resolve,[$cnf( $equal(implies(X,X_140),or(not(X),X_140)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
( or(not(X),X_140) != implies(X,X_140)
| ~ is_a_theorem(implies(or(not(X),or(X_139,X_140)),or(X_139,or(not(X),X_140))))
| is_a_theorem(implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),or(X_139,X_140)),or(X_139,or(not(X),X_140)))) ),[0,1,1],$fot(implies(X,X_140))]]) ).
cnf(refute_0_84,plain,
( ~ is_a_theorem(implies(or(not(X),or(X_139,X_140)),or(X_139,or(not(X),X_140))))
| is_a_theorem(implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_140),implies(X,X_140)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
is_a_theorem(implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),or(X_139,X_140)),or(X_139,or(not(X),X_140)))) )],[refute_0_79,refute_0_84]) ).
cnf(refute_0_86,plain,
or(not(X),or(X_139,X_140)) = implies(X,or(X_139,X_140)),
inference(subst,[],[refute_0_43:[bind(Y,$fot(or(X_139,X_140)))]]) ).
cnf(refute_0_87,plain,
implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140))) = implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140))))]]) ).
cnf(refute_0_88,plain,
( implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140))) != implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140)))
| or(not(X),or(X_139,X_140)) != implies(X,or(X_139,X_140))
| implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140))) = implies(implies(X,or(X_139,X_140)),or(X_139,implies(X,X_140))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140))),implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140)))) ),[1,0],$fot(implies(X,or(X_139,X_140)))]]) ).
cnf(refute_0_89,plain,
( or(not(X),or(X_139,X_140)) != implies(X,or(X_139,X_140))
| implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140))) = implies(implies(X,or(X_139,X_140)),or(X_139,implies(X,X_140))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140))),implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140)))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140))) = implies(implies(X,or(X_139,X_140)),or(X_139,implies(X,X_140))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_139,X_140)),implies(X,or(X_139,X_140))) )],[refute_0_86,refute_0_89]) ).
cnf(refute_0_91,plain,
( implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140))) != implies(implies(X,or(X_139,X_140)),or(X_139,implies(X,X_140)))
| ~ is_a_theorem(implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140))))
| is_a_theorem(implies(implies(X,or(X_139,X_140)),or(X_139,implies(X,X_140)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140)))) ),[0],$fot(implies(implies(X,or(X_139,X_140)),or(X_139,implies(X,X_140))))]]) ).
cnf(refute_0_92,plain,
( ~ is_a_theorem(implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140))))
| is_a_theorem(implies(implies(X,or(X_139,X_140)),or(X_139,implies(X,X_140)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140))),implies(implies(X,or(X_139,X_140)),or(X_139,implies(X,X_140)))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
is_a_theorem(implies(implies(X,or(X_139,X_140)),or(X_139,implies(X,X_140)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),or(X_139,X_140)),or(X_139,implies(X,X_140)))) )],[refute_0_85,refute_0_92]) ).
cnf(refute_0_94,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_95,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_96,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_95,refute_0_94]) ).
cnf(refute_0_97,plain,
( ~ is_a_theorem(implies(X,or(X_139,X_140)))
| ~ is_a_theorem(implies(implies(X,or(X_139,X_140)),or(X_139,implies(X,X_140))))
| is_a_theorem(or(X_139,implies(X,X_140))) ),
inference(subst,[],[refute_0_96:[bind(X,$fot(implies(X,or(X_139,X_140)))),bind(Y,$fot(or(X_139,implies(X,X_140))))]]) ).
cnf(refute_0_98,plain,
( ~ is_a_theorem(implies(X,or(X_139,X_140)))
| is_a_theorem(or(X_139,implies(X,X_140))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,or(X_139,X_140)),or(X_139,implies(X,X_140)))) )],[refute_0_93,refute_0_97]) ).
cnf(refute_0_99,plain,
( ~ is_a_theorem(implies(or(X_489,X_491),or(and(X,X_489),implies(X,X_491))))
| is_a_theorem(or(and(X,X_489),implies(or(X_489,X_491),implies(X,X_491)))) ),
inference(subst,[],[refute_0_98:[bind(X,$fot(or(X_489,X_491))),bind(X_139,$fot(and(X,X_489))),bind(X_140,$fot(implies(X,X_491)))]]) ).
cnf(refute_0_100,plain,
is_a_theorem(or(and(X,X_489),implies(or(X_489,X_491),implies(X,X_491)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_489,X_491),or(and(X,X_489),implies(X,X_491)))) )],[refute_0_75,refute_0_99]) ).
cnf(refute_0_101,plain,
is_a_theorem(or(and(X_4744,not(X)),implies(or(not(X),X_4746),implies(X_4744,X_4746)))),
inference(subst,[],[refute_0_100:[bind(X,$fot(X_4744)),bind(X_489,$fot(not(X))),bind(X_491,$fot(X_4746))]]) ).
cnf(refute_0_102,plain,
implies(X,X_4746) = or(not(X),X_4746),
inference(subst,[],[refute_0_31:[bind(Y,$fot(X_4746))]]) ).
cnf(refute_0_103,plain,
( implies(X,X_4746) != or(not(X),X_4746)
| or(not(X),X_4746) = implies(X,X_4746) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_4746))),bind(Y0,$fot(or(not(X),X_4746)))]]) ).
cnf(refute_0_104,plain,
or(not(X),X_4746) = implies(X,X_4746),
inference(resolve,[$cnf( $equal(implies(X,X_4746),or(not(X),X_4746)) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
( or(not(X),X_4746) != implies(X,X_4746)
| ~ is_a_theorem(or(and(X_4744,not(X)),implies(or(not(X),X_4746),implies(X_4744,X_4746))))
| is_a_theorem(or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_4744,not(X)),implies(or(not(X),X_4746),implies(X_4744,X_4746)))) ),[0,1,0],$fot(implies(X,X_4746))]]) ).
cnf(refute_0_106,plain,
( ~ is_a_theorem(or(and(X_4744,not(X)),implies(or(not(X),X_4746),implies(X_4744,X_4746))))
| is_a_theorem(or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_4746),implies(X,X_4746)) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
is_a_theorem(or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746)))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_4744,not(X)),implies(or(not(X),X_4746),implies(X_4744,X_4746)))) )],[refute_0_101,refute_0_106]) ).
cnf(refute_0_108,plain,
or(not(implies(X_4744,X)),implies(implies(X,X_4746),implies(X_4744,X_4746))) = implies(implies(X_4744,X),implies(implies(X,X_4746),implies(X_4744,X_4746))),
inference(subst,[],[refute_0_43:[bind(X,$fot(implies(X_4744,X))),bind(Y,$fot(implies(implies(X,X_4746),implies(X_4744,X_4746))))]]) ).
cnf(refute_0_109,plain,
and(X,not(X_2700)) = not(implies(X,not(not(X_2700)))),
inference(subst,[],[refute_0_51:[bind(Y,$fot(not(X_2700)))]]) ).
cnf(refute_0_110,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_111,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_112,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_111,refute_0_110]) ).
cnf(refute_0_113,plain,
( ~ is_a_theorem(equiv(X,not(not(X_82))))
| X = not(not(X_82)) ),
inference(subst,[],[refute_0_112:[bind(Y,$fot(not(not(X_82))))]]) ).
cnf(refute_0_114,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_115,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_116,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_115,refute_0_114]) ).
cnf(refute_0_117,plain,
equiv(X_43,not(X)) = and(implies(X_43,not(X)),implies(not(X),X_43)),
inference(subst,[],[refute_0_116:[bind(X,$fot(X_43)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_118,plain,
or(X,X_43) = implies(not(X),X_43),
inference(subst,[],[refute_0_21:[bind(Y,$fot(X_43))]]) ).
cnf(refute_0_119,plain,
( or(X,X_43) != implies(not(X),X_43)
| implies(not(X),X_43) = or(X,X_43) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_43))),bind(Y0,$fot(implies(not(X),X_43)))]]) ).
cnf(refute_0_120,plain,
implies(not(X),X_43) = or(X,X_43),
inference(resolve,[$cnf( $equal(or(X,X_43),implies(not(X),X_43)) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( equiv(X_43,not(X)) != and(implies(X_43,not(X)),implies(not(X),X_43))
| implies(not(X),X_43) != or(X,X_43)
| equiv(X_43,not(X)) = and(implies(X_43,not(X)),or(X,X_43)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_43,not(X)),and(implies(X_43,not(X)),implies(not(X),X_43))) ),[1,1],$fot(or(X,X_43))]]) ).
cnf(refute_0_122,plain,
( equiv(X_43,not(X)) != and(implies(X_43,not(X)),implies(not(X),X_43))
| equiv(X_43,not(X)) = and(implies(X_43,not(X)),or(X,X_43)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_43),or(X,X_43)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
equiv(X_43,not(X)) = and(implies(X_43,not(X)),or(X,X_43)),
inference(resolve,[$cnf( $equal(equiv(X_43,not(X)),and(implies(X_43,not(X)),implies(not(X),X_43))) )],[refute_0_117,refute_0_122]) ).
cnf(refute_0_124,plain,
equiv(X_51,not(not(X))) = and(implies(X_51,not(not(X))),or(not(X),X_51)),
inference(subst,[],[refute_0_123:[bind(X,$fot(not(X))),bind(X_43,$fot(X_51))]]) ).
cnf(refute_0_125,plain,
implies(X,X_51) = or(not(X),X_51),
inference(subst,[],[refute_0_31:[bind(Y,$fot(X_51))]]) ).
cnf(refute_0_126,plain,
( implies(X,X_51) != or(not(X),X_51)
| or(not(X),X_51) = implies(X,X_51) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_51))),bind(Y0,$fot(or(not(X),X_51)))]]) ).
cnf(refute_0_127,plain,
or(not(X),X_51) = implies(X,X_51),
inference(resolve,[$cnf( $equal(implies(X,X_51),or(not(X),X_51)) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
( equiv(X_51,not(not(X))) != and(implies(X_51,not(not(X))),or(not(X),X_51))
| or(not(X),X_51) != implies(X,X_51)
| equiv(X_51,not(not(X))) = and(implies(X_51,not(not(X))),implies(X,X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_51,not(not(X))),and(implies(X_51,not(not(X))),or(not(X),X_51))) ),[1,1],$fot(implies(X,X_51))]]) ).
cnf(refute_0_129,plain,
( equiv(X_51,not(not(X))) != and(implies(X_51,not(not(X))),or(not(X),X_51))
| equiv(X_51,not(not(X))) = and(implies(X_51,not(not(X))),implies(X,X_51)) ),
inference(resolve,[$cnf( $equal(or(not(X),X_51),implies(X,X_51)) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
equiv(X_51,not(not(X))) = and(implies(X_51,not(not(X))),implies(X,X_51)),
inference(resolve,[$cnf( $equal(equiv(X_51,not(not(X))),and(implies(X_51,not(not(X))),or(not(X),X_51))) )],[refute_0_124,refute_0_129]) ).
cnf(refute_0_131,plain,
( equiv(X,Y) != and(implies(X,Y),implies(Y,X))
| and(implies(X,Y),implies(Y,X)) = equiv(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(X,Y))),bind(Y0,$fot(and(implies(X,Y),implies(Y,X))))]]) ).
cnf(refute_0_132,plain,
and(implies(X,Y),implies(Y,X)) = equiv(X,Y),
inference(resolve,[$cnf( $equal(equiv(X,Y),and(implies(X,Y),implies(Y,X))) )],[refute_0_116,refute_0_131]) ).
cnf(refute_0_133,plain,
and(implies(X_51,X),implies(X,X_51)) = equiv(X_51,X),
inference(subst,[],[refute_0_132:[bind(X,$fot(X_51)),bind(Y,$fot(X))]]) ).
cnf(refute_0_134,plain,
not(and(X_51,not(X))) = implies(X_51,X),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_51)),bind(Y,$fot(X))]]) ).
cnf(refute_0_135,plain,
and(not(and(X_51,not(X))),implies(X,X_51)) = and(not(and(X_51,not(X))),implies(X,X_51)),
introduced(tautology,[refl,[$fot(and(not(and(X_51,not(X))),implies(X,X_51)))]]) ).
cnf(refute_0_136,plain,
( and(not(and(X_51,not(X))),implies(X,X_51)) != and(not(and(X_51,not(X))),implies(X,X_51))
| not(and(X_51,not(X))) != implies(X_51,X)
| and(not(and(X_51,not(X))),implies(X,X_51)) = and(implies(X_51,X),implies(X,X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(X_51,not(X))),implies(X,X_51)),and(not(and(X_51,not(X))),implies(X,X_51))) ),[1,0],$fot(implies(X_51,X))]]) ).
cnf(refute_0_137,plain,
( not(and(X_51,not(X))) != implies(X_51,X)
| and(not(and(X_51,not(X))),implies(X,X_51)) = and(implies(X_51,X),implies(X,X_51)) ),
inference(resolve,[$cnf( $equal(and(not(and(X_51,not(X))),implies(X,X_51)),and(not(and(X_51,not(X))),implies(X,X_51))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
and(not(and(X_51,not(X))),implies(X,X_51)) = and(implies(X_51,X),implies(X,X_51)),
inference(resolve,[$cnf( $equal(not(and(X_51,not(X))),implies(X_51,X)) )],[refute_0_134,refute_0_137]) ).
cnf(refute_0_139,plain,
( and(implies(X_51,X),implies(X,X_51)) != equiv(X_51,X)
| and(not(and(X_51,not(X))),implies(X,X_51)) != and(implies(X_51,X),implies(X,X_51))
| and(not(and(X_51,not(X))),implies(X,X_51)) = equiv(X_51,X) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(and(not(and(X_51,not(X))),implies(X,X_51)))),bind(Y0,$fot(and(implies(X_51,X),implies(X,X_51)))),bind(Z0,$fot(equiv(X_51,X)))]]) ).
cnf(refute_0_140,plain,
( and(implies(X_51,X),implies(X,X_51)) != equiv(X_51,X)
| and(not(and(X_51,not(X))),implies(X,X_51)) = equiv(X_51,X) ),
inference(resolve,[$cnf( $equal(and(not(and(X_51,not(X))),implies(X,X_51)),and(implies(X_51,X),implies(X,X_51))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
and(not(and(X_51,not(X))),implies(X,X_51)) = equiv(X_51,X),
inference(resolve,[$cnf( $equal(and(implies(X_51,X),implies(X,X_51)),equiv(X_51,X)) )],[refute_0_133,refute_0_140]) ).
cnf(refute_0_142,plain,
and(not(X),X_11) = not(implies(not(X),not(X_11))),
inference(subst,[],[refute_0_51:[bind(X,$fot(not(X))),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_143,plain,
or(X,not(X_11)) = implies(not(X),not(X_11)),
inference(subst,[],[refute_0_21:[bind(Y,$fot(not(X_11)))]]) ).
cnf(refute_0_144,plain,
( or(X,not(X_11)) != implies(not(X),not(X_11))
| implies(not(X),not(X_11)) = or(X,not(X_11)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,not(X_11)))),bind(Y0,$fot(implies(not(X),not(X_11))))]]) ).
cnf(refute_0_145,plain,
implies(not(X),not(X_11)) = or(X,not(X_11)),
inference(resolve,[$cnf( $equal(or(X,not(X_11)),implies(not(X),not(X_11))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
( and(not(X),X_11) != not(implies(not(X),not(X_11)))
| implies(not(X),not(X_11)) != or(X,not(X_11))
| and(not(X),X_11) = not(or(X,not(X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(X),X_11),not(implies(not(X),not(X_11)))) ),[1,0],$fot(or(X,not(X_11)))]]) ).
cnf(refute_0_147,plain,
( and(not(X),X_11) != not(implies(not(X),not(X_11)))
| and(not(X),X_11) = not(or(X,not(X_11))) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X_11)),or(X,not(X_11))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
and(not(X),X_11) = not(or(X,not(X_11))),
inference(resolve,[$cnf( $equal(and(not(X),X_11),not(implies(not(X),not(X_11)))) )],[refute_0_142,refute_0_147]) ).
cnf(refute_0_149,plain,
and(not(not(X)),X_57) = not(or(not(X),not(X_57))),
inference(subst,[],[refute_0_148:[bind(X,$fot(not(X))),bind(X_11,$fot(X_57))]]) ).
cnf(refute_0_150,plain,
implies(X,not(X_57)) = or(not(X),not(X_57)),
inference(subst,[],[refute_0_31:[bind(Y,$fot(not(X_57)))]]) ).
cnf(refute_0_151,plain,
( implies(X,not(X_57)) != or(not(X),not(X_57))
| or(not(X),not(X_57)) = implies(X,not(X_57)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,not(X_57)))),bind(Y0,$fot(or(not(X),not(X_57))))]]) ).
cnf(refute_0_152,plain,
or(not(X),not(X_57)) = implies(X,not(X_57)),
inference(resolve,[$cnf( $equal(implies(X,not(X_57)),or(not(X),not(X_57))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
( and(not(not(X)),X_57) != not(or(not(X),not(X_57)))
| or(not(X),not(X_57)) != implies(X,not(X_57))
| and(not(not(X)),X_57) = not(implies(X,not(X_57))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X)),X_57),not(or(not(X),not(X_57)))) ),[1,0],$fot(implies(X,not(X_57)))]]) ).
cnf(refute_0_154,plain,
( and(not(not(X)),X_57) != not(or(not(X),not(X_57)))
| and(not(not(X)),X_57) = not(implies(X,not(X_57))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_57)),implies(X,not(X_57))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
and(not(not(X)),X_57) = not(implies(X,not(X_57))),
inference(resolve,[$cnf( $equal(and(not(not(X)),X_57),not(or(not(X),not(X_57)))) )],[refute_0_149,refute_0_154]) ).
cnf(refute_0_156,plain,
( and(X,Y) != not(implies(X,not(Y)))
| not(implies(X,not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(implies(X,not(Y)))))]]) ).
cnf(refute_0_157,plain,
not(implies(X,not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(implies(X,not(Y)))) )],[refute_0_51,refute_0_156]) ).
cnf(refute_0_158,plain,
not(implies(X,not(X_57))) = and(X,X_57),
inference(subst,[],[refute_0_157:[bind(Y,$fot(X_57))]]) ).
cnf(refute_0_159,plain,
( and(not(not(X)),X_57) != not(implies(X,not(X_57)))
| not(implies(X,not(X_57))) != and(X,X_57)
| and(not(not(X)),X_57) = and(X,X_57) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(not(not(X)),X_57),and(X,X_57)) ),[0],$fot(not(implies(X,not(X_57))))]]) ).
cnf(refute_0_160,plain,
( and(not(not(X)),X_57) != not(implies(X,not(X_57)))
| and(not(not(X)),X_57) = and(X,X_57) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(X_57))),and(X,X_57)) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
and(not(not(X)),X_57) = and(X,X_57),
inference(resolve,[$cnf( $equal(and(not(not(X)),X_57),not(implies(X,not(X_57)))) )],[refute_0_155,refute_0_160]) ).
cnf(refute_0_162,plain,
and(not(not(implies(X,not(Y)))),X_59) = and(implies(X,not(Y)),X_59),
inference(subst,[],[refute_0_161:[bind(X,$fot(implies(X,not(Y)))),bind(X_57,$fot(X_59))]]) ).
cnf(refute_0_163,plain,
( and(not(not(implies(X,not(Y)))),X_59) != and(implies(X,not(Y)),X_59)
| not(implies(X,not(Y))) != and(X,Y)
| and(not(and(X,Y)),X_59) = and(implies(X,not(Y)),X_59) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(implies(X,not(Y)))),X_59),and(implies(X,not(Y)),X_59)) ),[0,0,0],$fot(and(X,Y))]]) ).
cnf(refute_0_164,plain,
( and(not(not(implies(X,not(Y)))),X_59) != and(implies(X,not(Y)),X_59)
| and(not(and(X,Y)),X_59) = and(implies(X,not(Y)),X_59) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_157,refute_0_163]) ).
cnf(refute_0_165,plain,
and(not(and(X,Y)),X_59) = and(implies(X,not(Y)),X_59),
inference(resolve,[$cnf( $equal(and(not(not(implies(X,not(Y)))),X_59),and(implies(X,not(Y)),X_59)) )],[refute_0_162,refute_0_164]) ).
cnf(refute_0_166,plain,
( and(not(and(X,Y)),X_59) != and(implies(X,not(Y)),X_59)
| and(implies(X,not(Y)),X_59) = and(not(and(X,Y)),X_59) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(not(and(X,Y)),X_59))),bind(Y0,$fot(and(implies(X,not(Y)),X_59)))]]) ).
cnf(refute_0_167,plain,
and(implies(X,not(Y)),X_59) = and(not(and(X,Y)),X_59),
inference(resolve,[$cnf( $equal(and(not(and(X,Y)),X_59),and(implies(X,not(Y)),X_59)) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
and(implies(X_51,not(not(X))),implies(X,X_51)) = and(not(and(X_51,not(X))),implies(X,X_51)),
inference(subst,[],[refute_0_167:[bind(X,$fot(X_51)),bind(Y,$fot(not(X))),bind(X_59,$fot(implies(X,X_51)))]]) ).
cnf(refute_0_169,plain,
( and(implies(X_51,not(not(X))),implies(X,X_51)) != and(not(and(X_51,not(X))),implies(X,X_51))
| and(not(and(X_51,not(X))),implies(X,X_51)) != equiv(X_51,X)
| and(implies(X_51,not(not(X))),implies(X,X_51)) = equiv(X_51,X) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(and(implies(X_51,not(not(X))),implies(X,X_51)))),bind(Y0,$fot(and(not(and(X_51,not(X))),implies(X,X_51)))),bind(Z0,$fot(equiv(X_51,X)))]]) ).
cnf(refute_0_170,plain,
( and(not(and(X_51,not(X))),implies(X,X_51)) != equiv(X_51,X)
| and(implies(X_51,not(not(X))),implies(X,X_51)) = equiv(X_51,X) ),
inference(resolve,[$cnf( $equal(and(implies(X_51,not(not(X))),implies(X,X_51)),and(not(and(X_51,not(X))),implies(X,X_51))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
and(implies(X_51,not(not(X))),implies(X,X_51)) = equiv(X_51,X),
inference(resolve,[$cnf( $equal(and(not(and(X_51,not(X))),implies(X,X_51)),equiv(X_51,X)) )],[refute_0_141,refute_0_170]) ).
cnf(refute_0_172,plain,
( and(implies(X_51,not(not(X))),implies(X,X_51)) != equiv(X_51,X)
| equiv(X_51,not(not(X))) != and(implies(X_51,not(not(X))),implies(X,X_51))
| equiv(X_51,not(not(X))) = equiv(X_51,X) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_51,not(not(X))),and(implies(X_51,not(not(X))),implies(X,X_51))) ),[1],$fot(equiv(X_51,X))]]) ).
cnf(refute_0_173,plain,
( equiv(X_51,not(not(X))) != and(implies(X_51,not(not(X))),implies(X,X_51))
| equiv(X_51,not(not(X))) = equiv(X_51,X) ),
inference(resolve,[$cnf( $equal(and(implies(X_51,not(not(X))),implies(X,X_51)),equiv(X_51,X)) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
equiv(X_51,not(not(X))) = equiv(X_51,X),
inference(resolve,[$cnf( $equal(equiv(X_51,not(not(X))),and(implies(X_51,not(not(X))),implies(X,X_51))) )],[refute_0_130,refute_0_173]) ).
cnf(refute_0_175,plain,
equiv(X,not(not(X_82))) = equiv(X,X_82),
inference(subst,[],[refute_0_174:[bind(X,$fot(X_82)),bind(X_51,$fot(X))]]) ).
cnf(refute_0_176,plain,
( equiv(X,not(not(X_82))) != equiv(X,X_82)
| ~ is_a_theorem(equiv(X,X_82))
| is_a_theorem(equiv(X,not(not(X_82)))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(equiv(X,not(not(X_82)))) ),[0],$fot(equiv(X,X_82))]]) ).
cnf(refute_0_177,plain,
( ~ is_a_theorem(equiv(X,X_82))
| is_a_theorem(equiv(X,not(not(X_82)))) ),
inference(resolve,[$cnf( $equal(equiv(X,not(not(X_82))),equiv(X,X_82)) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
( ~ is_a_theorem(equiv(X,X_82))
| X = not(not(X_82)) ),
inference(resolve,[$cnf( is_a_theorem(equiv(X,not(not(X_82)))) )],[refute_0_177,refute_0_113]) ).
cnf(refute_0_179,plain,
( ~ is_a_theorem(equiv(X_2699,X_2699))
| X_2699 = not(not(X_2699)) ),
inference(subst,[],[refute_0_178:[bind(X,$fot(X_2699)),bind(X_82,$fot(X_2699))]]) ).
cnf(refute_0_180,plain,
( ~ is_a_theorem(X_326)
| ~ is_a_theorem(implies(X_326,and(X_326,X_326)))
| is_a_theorem(and(X_326,X_326)) ),
inference(subst,[],[refute_0_96:[bind(X,$fot(X_326)),bind(Y,$fot(and(X_326,X_326)))]]) ).
cnf(refute_0_181,plain,
( ~ r1
| is_a_theorem(implies(or(P,P),P)) ),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_182,plain,
r1,
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_183,plain,
is_a_theorem(implies(or(P,P),P)),
inference(resolve,[$cnf( r1 )],[refute_0_182,refute_0_181]) ).
cnf(refute_0_184,plain,
is_a_theorem(implies(or(not(X_1),not(X_1)),not(X_1))),
inference(subst,[],[refute_0_183:[bind(P,$fot(not(X_1)))]]) ).
cnf(refute_0_185,plain,
implies(X_1,not(X_1)) = or(not(X_1),not(X_1)),
inference(subst,[],[refute_0_31:[bind(X,$fot(X_1)),bind(Y,$fot(not(X_1)))]]) ).
cnf(refute_0_186,plain,
( implies(X_1,not(X_1)) != or(not(X_1),not(X_1))
| or(not(X_1),not(X_1)) = implies(X_1,not(X_1)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X_1,not(X_1)))),bind(Y0,$fot(or(not(X_1),not(X_1))))]]) ).
cnf(refute_0_187,plain,
or(not(X_1),not(X_1)) = implies(X_1,not(X_1)),
inference(resolve,[$cnf( $equal(implies(X_1,not(X_1)),or(not(X_1),not(X_1))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
( or(not(X_1),not(X_1)) != implies(X_1,not(X_1))
| ~ is_a_theorem(implies(or(not(X_1),not(X_1)),not(X_1)))
| is_a_theorem(implies(implies(X_1,not(X_1)),not(X_1))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X_1),not(X_1)),not(X_1))) ),[0,0],$fot(implies(X_1,not(X_1)))]]) ).
cnf(refute_0_189,plain,
( ~ is_a_theorem(implies(or(not(X_1),not(X_1)),not(X_1)))
| is_a_theorem(implies(implies(X_1,not(X_1)),not(X_1))) ),
inference(resolve,[$cnf( $equal(or(not(X_1),not(X_1)),implies(X_1,not(X_1))) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
is_a_theorem(implies(implies(X_1,not(X_1)),not(X_1))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X_1),not(X_1)),not(X_1))) )],[refute_0_184,refute_0_189]) ).
cnf(refute_0_191,plain,
is_a_theorem(implies(implies(not(X_4),not(not(X_4))),not(not(X_4)))),
inference(subst,[],[refute_0_190:[bind(X_1,$fot(not(X_4)))]]) ).
cnf(refute_0_192,plain,
or(X_4,not(not(X_4))) = implies(not(X_4),not(not(X_4))),
inference(subst,[],[refute_0_21:[bind(X,$fot(X_4)),bind(Y,$fot(not(not(X_4))))]]) ).
cnf(refute_0_193,plain,
( or(X_4,not(not(X_4))) != implies(not(X_4),not(not(X_4)))
| implies(not(X_4),not(not(X_4))) = or(X_4,not(not(X_4))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X_4,not(not(X_4))))),bind(Y0,$fot(implies(not(X_4),not(not(X_4)))))]]) ).
cnf(refute_0_194,plain,
implies(not(X_4),not(not(X_4))) = or(X_4,not(not(X_4))),
inference(resolve,[$cnf( $equal(or(X_4,not(not(X_4))),implies(not(X_4),not(not(X_4)))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
( implies(not(X_4),not(not(X_4))) != or(X_4,not(not(X_4)))
| ~ is_a_theorem(implies(implies(not(X_4),not(not(X_4))),not(not(X_4))))
| is_a_theorem(implies(or(X_4,not(not(X_4))),not(not(X_4)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X_4),not(not(X_4))),not(not(X_4)))) ),[0,0],$fot(or(X_4,not(not(X_4))))]]) ).
cnf(refute_0_196,plain,
( ~ is_a_theorem(implies(implies(not(X_4),not(not(X_4))),not(not(X_4))))
| is_a_theorem(implies(or(X_4,not(not(X_4))),not(not(X_4)))) ),
inference(resolve,[$cnf( $equal(implies(not(X_4),not(not(X_4))),or(X_4,not(not(X_4)))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
is_a_theorem(implies(or(X_4,not(not(X_4))),not(not(X_4)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_4),not(not(X_4))),not(not(X_4)))) )],[refute_0_191,refute_0_196]) ).
cnf(refute_0_198,plain,
is_a_theorem(implies(or(not(X),not(not(not(X)))),not(not(not(X))))),
inference(subst,[],[refute_0_197:[bind(X_4,$fot(not(X)))]]) ).
cnf(refute_0_199,plain,
implies(X,not(not(not(X)))) = or(not(X),not(not(not(X)))),
inference(subst,[],[refute_0_31:[bind(Y,$fot(not(not(not(X)))))]]) ).
cnf(refute_0_200,plain,
( implies(X,not(not(not(X)))) != or(not(X),not(not(not(X))))
| or(not(X),not(not(not(X)))) = implies(X,not(not(not(X)))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,not(not(not(X)))))),bind(Y0,$fot(or(not(X),not(not(not(X))))))]]) ).
cnf(refute_0_201,plain,
or(not(X),not(not(not(X)))) = implies(X,not(not(not(X)))),
inference(resolve,[$cnf( $equal(implies(X,not(not(not(X)))),or(not(X),not(not(not(X))))) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
( or(not(X),not(not(not(X)))) != implies(X,not(not(not(X))))
| ~ is_a_theorem(implies(or(not(X),not(not(not(X)))),not(not(not(X)))))
| is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),not(not(not(X)))),not(not(not(X))))) ),[0,0],$fot(implies(X,not(not(not(X)))))]]) ).
cnf(refute_0_203,plain,
( ~ is_a_theorem(implies(or(not(X),not(not(not(X)))),not(not(not(X)))))
| is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(not(not(X)))),implies(X,not(not(not(X))))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),not(not(not(X)))),not(not(not(X))))) )],[refute_0_198,refute_0_203]) ).
cnf(refute_0_205,plain,
is_a_theorem(implies(implies(not(X),not(not(not(not(X))))),not(not(not(not(X)))))),
inference(subst,[],[refute_0_204:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_206,plain,
or(X,not(not(not(not(X))))) = implies(not(X),not(not(not(not(X))))),
inference(subst,[],[refute_0_21:[bind(Y,$fot(not(not(not(not(X))))))]]) ).
cnf(refute_0_207,plain,
( or(X,not(not(not(not(X))))) != implies(not(X),not(not(not(not(X)))))
| implies(not(X),not(not(not(not(X))))) = or(X,not(not(not(not(X))))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,not(not(not(not(X))))))),bind(Y0,$fot(implies(not(X),not(not(not(not(X)))))))]]) ).
cnf(refute_0_208,plain,
implies(not(X),not(not(not(not(X))))) = or(X,not(not(not(not(X))))),
inference(resolve,[$cnf( $equal(or(X,not(not(not(not(X))))),implies(not(X),not(not(not(not(X)))))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
( implies(not(X),not(not(not(not(X))))) != or(X,not(not(not(not(X)))))
| ~ is_a_theorem(implies(implies(not(X),not(not(not(not(X))))),not(not(not(not(X))))))
| is_a_theorem(implies(or(X,not(not(not(not(X))))),not(not(not(not(X)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X),not(not(not(not(X))))),not(not(not(not(X)))))) ),[0,0],$fot(or(X,not(not(not(not(X))))))]]) ).
cnf(refute_0_210,plain,
( ~ is_a_theorem(implies(implies(not(X),not(not(not(not(X))))),not(not(not(not(X))))))
| is_a_theorem(implies(or(X,not(not(not(not(X))))),not(not(not(not(X)))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(not(not(not(X))))),or(X,not(not(not(not(X)))))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
is_a_theorem(implies(or(X,not(not(not(not(X))))),not(not(not(not(X)))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(not(not(not(X))))),not(not(not(not(X)))))) )],[refute_0_205,refute_0_210]) ).
cnf(refute_0_212,plain,
is_a_theorem(implies(or(not(X),not(not(not(not(not(X)))))),not(not(not(not(not(X))))))),
inference(subst,[],[refute_0_211:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_213,plain,
implies(X,not(not(not(not(not(X)))))) = or(not(X),not(not(not(not(not(X)))))),
inference(subst,[],[refute_0_31:[bind(Y,$fot(not(not(not(not(not(X)))))))]]) ).
cnf(refute_0_214,plain,
( implies(X,not(not(not(not(not(X)))))) != or(not(X),not(not(not(not(not(X))))))
| or(not(X),not(not(not(not(not(X)))))) = implies(X,not(not(not(not(not(X)))))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,not(not(not(not(not(X)))))))),bind(Y0,$fot(or(not(X),not(not(not(not(not(X))))))))]]) ).
cnf(refute_0_215,plain,
or(not(X),not(not(not(not(not(X)))))) = implies(X,not(not(not(not(not(X)))))),
inference(resolve,[$cnf( $equal(implies(X,not(not(not(not(not(X)))))),or(not(X),not(not(not(not(not(X))))))) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
( or(not(X),not(not(not(not(not(X)))))) != implies(X,not(not(not(not(not(X))))))
| ~ is_a_theorem(implies(or(not(X),not(not(not(not(not(X)))))),not(not(not(not(not(X)))))))
| is_a_theorem(implies(implies(X,not(not(not(not(not(X)))))),not(not(not(not(not(X))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),not(not(not(not(not(X)))))),not(not(not(not(not(X))))))) ),[0,0],$fot(implies(X,not(not(not(not(not(X)))))))]]) ).
cnf(refute_0_217,plain,
( ~ is_a_theorem(implies(or(not(X),not(not(not(not(not(X)))))),not(not(not(not(not(X)))))))
| is_a_theorem(implies(implies(X,not(not(not(not(not(X)))))),not(not(not(not(not(X))))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(not(not(not(not(X)))))),implies(X,not(not(not(not(not(X))))))) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
is_a_theorem(implies(implies(X,not(not(not(not(not(X)))))),not(not(not(not(not(X))))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),not(not(not(not(not(X)))))),not(not(not(not(not(X))))))) )],[refute_0_212,refute_0_217]) ).
cnf(refute_0_219,plain,
implies(implies(X,not(not(not(not(not(X)))))),not(not(not(not(not(X)))))) = or(and(X,not(not(not(not(X))))),not(not(not(not(not(X)))))),
inference(subst,[],[refute_0_57:[bind(Y,$fot(not(not(not(not(not(X))))))),bind(X_10,$fot(X)),bind(X_11,$fot(not(not(not(not(X))))))]]) ).
cnf(refute_0_220,plain,
( implies(implies(X,not(not(not(not(not(X)))))),not(not(not(not(not(X)))))) != or(and(X,not(not(not(not(X))))),not(not(not(not(not(X))))))
| ~ is_a_theorem(implies(implies(X,not(not(not(not(not(X)))))),not(not(not(not(not(X)))))))
| is_a_theorem(or(and(X,not(not(not(not(X))))),not(not(not(not(not(X))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,not(not(not(not(not(X)))))),not(not(not(not(not(X))))))) ),[0],$fot(or(and(X,not(not(not(not(X))))),not(not(not(not(not(X)))))))]]) ).
cnf(refute_0_221,plain,
( ~ is_a_theorem(implies(implies(X,not(not(not(not(not(X)))))),not(not(not(not(not(X)))))))
| is_a_theorem(or(and(X,not(not(not(not(X))))),not(not(not(not(not(X))))))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(not(not(not(not(X)))))),not(not(not(not(not(X)))))),or(and(X,not(not(not(not(X))))),not(not(not(not(not(X))))))) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
is_a_theorem(or(and(X,not(not(not(not(X))))),not(not(not(not(not(X))))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,not(not(not(not(not(X)))))),not(not(not(not(not(X))))))) )],[refute_0_218,refute_0_221]) ).
cnf(refute_0_223,plain,
implies(implies(X,not(X)),not(not(not(not(not(X)))))) = or(and(X,X),not(not(not(not(not(X)))))),
inference(subst,[],[refute_0_57:[bind(Y,$fot(not(not(not(not(not(X))))))),bind(X_10,$fot(X)),bind(X_11,$fot(X))]]) ).
cnf(refute_0_224,plain,
or(and(X_25,not(X_26)),Y) = implies(not(and(X_25,not(X_26))),Y),
inference(subst,[],[refute_0_21:[bind(X,$fot(and(X_25,not(X_26))))]]) ).
cnf(refute_0_225,plain,
implies(X_25,X_26) = not(and(X_25,not(X_26))),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_25)),bind(Y,$fot(X_26))]]) ).
cnf(refute_0_226,plain,
( implies(X_25,X_26) != not(and(X_25,not(X_26)))
| not(and(X_25,not(X_26))) = implies(X_25,X_26) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X_25,X_26))),bind(Y0,$fot(not(and(X_25,not(X_26)))))]]) ).
cnf(refute_0_227,plain,
not(and(X_25,not(X_26))) = implies(X_25,X_26),
inference(resolve,[$cnf( $equal(implies(X_25,X_26),not(and(X_25,not(X_26)))) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
( not(and(X_25,not(X_26))) != implies(X_25,X_26)
| or(and(X_25,not(X_26)),Y) != implies(not(and(X_25,not(X_26))),Y)
| or(and(X_25,not(X_26)),Y) = implies(implies(X_25,X_26),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_25,not(X_26)),Y),implies(not(and(X_25,not(X_26))),Y)) ),[1,0],$fot(implies(X_25,X_26))]]) ).
cnf(refute_0_229,plain,
( or(and(X_25,not(X_26)),Y) != implies(not(and(X_25,not(X_26))),Y)
| or(and(X_25,not(X_26)),Y) = implies(implies(X_25,X_26),Y) ),
inference(resolve,[$cnf( $equal(not(and(X_25,not(X_26))),implies(X_25,X_26)) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
or(and(X_25,not(X_26)),Y) = implies(implies(X_25,X_26),Y),
inference(resolve,[$cnf( $equal(or(and(X_25,not(X_26)),Y),implies(not(and(X_25,not(X_26))),Y)) )],[refute_0_224,refute_0_229]) ).
cnf(refute_0_231,plain,
or(and(X,not(not(X))),not(not(not(not(not(X)))))) = implies(implies(X,not(X)),not(not(not(not(not(X)))))),
inference(subst,[],[refute_0_230:[bind(Y,$fot(not(not(not(not(not(X))))))),bind(X_25,$fot(X)),bind(X_26,$fot(not(X)))]]) ).
cnf(refute_0_232,plain,
( implies(implies(X,not(X)),not(not(not(not(not(X)))))) != or(and(X,X),not(not(not(not(not(X))))))
| or(and(X,not(not(X))),not(not(not(not(not(X)))))) != implies(implies(X,not(X)),not(not(not(not(not(X))))))
| or(and(X,not(not(X))),not(not(not(not(not(X)))))) = or(and(X,X),not(not(not(not(not(X)))))) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(or(and(X,not(not(X))),not(not(not(not(not(X)))))))),bind(Y0,$fot(implies(implies(X,not(X)),not(not(not(not(not(X)))))))),bind(Z0,$fot(or(and(X,X),not(not(not(not(not(X))))))))]]) ).
cnf(refute_0_233,plain,
( implies(implies(X,not(X)),not(not(not(not(not(X)))))) != or(and(X,X),not(not(not(not(not(X))))))
| or(and(X,not(not(X))),not(not(not(not(not(X)))))) = or(and(X,X),not(not(not(not(not(X)))))) ),
inference(resolve,[$cnf( $equal(or(and(X,not(not(X))),not(not(not(not(not(X)))))),implies(implies(X,not(X)),not(not(not(not(not(X))))))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
or(and(X,not(not(X))),not(not(not(not(not(X)))))) = or(and(X,X),not(not(not(not(not(X)))))),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X)),not(not(not(not(not(X)))))),or(and(X,X),not(not(not(not(not(X))))))) )],[refute_0_223,refute_0_233]) ).
cnf(refute_0_235,plain,
implies(implies(X,not(not(not(X)))),not(not(not(not(not(X)))))) = or(and(X,not(not(X))),not(not(not(not(not(X)))))),
inference(subst,[],[refute_0_57:[bind(Y,$fot(not(not(not(not(not(X))))))),bind(X_10,$fot(X)),bind(X_11,$fot(not(not(X))))]]) ).
cnf(refute_0_236,plain,
( implies(implies(X,not(not(not(X)))),not(not(not(not(not(X)))))) != or(and(X,not(not(X))),not(not(not(not(not(X))))))
| or(and(X,not(not(X))),not(not(not(not(not(X)))))) != or(and(X,X),not(not(not(not(not(X))))))
| implies(implies(X,not(not(not(X)))),not(not(not(not(not(X)))))) = or(and(X,X),not(not(not(not(not(X)))))) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(implies(implies(X,not(not(not(X)))),not(not(not(not(not(X)))))))),bind(Y0,$fot(or(and(X,not(not(X))),not(not(not(not(not(X)))))))),bind(Z0,$fot(or(and(X,X),not(not(not(not(not(X))))))))]]) ).
cnf(refute_0_237,plain,
( or(and(X,not(not(X))),not(not(not(not(not(X)))))) != or(and(X,X),not(not(not(not(not(X))))))
| implies(implies(X,not(not(not(X)))),not(not(not(not(not(X)))))) = or(and(X,X),not(not(not(not(not(X)))))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(not(not(X)))),not(not(not(not(not(X)))))),or(and(X,not(not(X))),not(not(not(not(not(X))))))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
implies(implies(X,not(not(not(X)))),not(not(not(not(not(X)))))) = or(and(X,X),not(not(not(not(not(X)))))),
inference(resolve,[$cnf( $equal(or(and(X,not(not(X))),not(not(not(not(not(X)))))),or(and(X,X),not(not(not(not(not(X))))))) )],[refute_0_234,refute_0_237]) ).
cnf(refute_0_239,plain,
or(and(X,not(not(not(not(X))))),not(not(not(not(not(X)))))) = implies(implies(X,not(not(not(X)))),not(not(not(not(not(X)))))),
inference(subst,[],[refute_0_230:[bind(Y,$fot(not(not(not(not(not(X))))))),bind(X_25,$fot(X)),bind(X_26,$fot(not(not(not(X)))))]]) ).
cnf(refute_0_240,plain,
( implies(implies(X,not(not(not(X)))),not(not(not(not(not(X)))))) != or(and(X,X),not(not(not(not(not(X))))))
| or(and(X,not(not(not(not(X))))),not(not(not(not(not(X)))))) != implies(implies(X,not(not(not(X)))),not(not(not(not(not(X))))))
| or(and(X,not(not(not(not(X))))),not(not(not(not(not(X)))))) = or(and(X,X),not(not(not(not(not(X)))))) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(or(and(X,not(not(not(not(X))))),not(not(not(not(not(X)))))))),bind(Y0,$fot(implies(implies(X,not(not(not(X)))),not(not(not(not(not(X)))))))),bind(Z0,$fot(or(and(X,X),not(not(not(not(not(X))))))))]]) ).
cnf(refute_0_241,plain,
( implies(implies(X,not(not(not(X)))),not(not(not(not(not(X)))))) != or(and(X,X),not(not(not(not(not(X))))))
| or(and(X,not(not(not(not(X))))),not(not(not(not(not(X)))))) = or(and(X,X),not(not(not(not(not(X)))))) ),
inference(resolve,[$cnf( $equal(or(and(X,not(not(not(not(X))))),not(not(not(not(not(X)))))),implies(implies(X,not(not(not(X)))),not(not(not(not(not(X))))))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
or(and(X,not(not(not(not(X))))),not(not(not(not(not(X)))))) = or(and(X,X),not(not(not(not(not(X)))))),
inference(resolve,[$cnf( $equal(implies(implies(X,not(not(not(X)))),not(not(not(not(not(X)))))),or(and(X,X),not(not(not(not(not(X))))))) )],[refute_0_238,refute_0_241]) ).
cnf(refute_0_243,plain,
( or(and(X,not(not(not(not(X))))),not(not(not(not(not(X)))))) != or(and(X,X),not(not(not(not(not(X))))))
| ~ is_a_theorem(or(and(X,not(not(not(not(X))))),not(not(not(not(not(X)))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(X))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X,not(not(not(not(X))))),not(not(not(not(not(X))))))) ),[0],$fot(or(and(X,X),not(not(not(not(not(X)))))))]]) ).
cnf(refute_0_244,plain,
( ~ is_a_theorem(or(and(X,not(not(not(not(X))))),not(not(not(not(not(X)))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(X))))))) ),
inference(resolve,[$cnf( $equal(or(and(X,not(not(not(not(X))))),not(not(not(not(not(X)))))),or(and(X,X),not(not(not(not(not(X))))))) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
is_a_theorem(or(and(X,X),not(not(not(not(not(X))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X,not(not(not(not(X))))),not(not(not(not(not(X))))))) )],[refute_0_222,refute_0_244]) ).
cnf(refute_0_246,plain,
is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(X))))))))),
inference(subst,[],[refute_0_245:[bind(X,$fot(not(not(X))))]]) ).
cnf(refute_0_247,plain,
and(not(not(X)),not(not(X))) = and(X,not(not(X))),
inference(subst,[],[refute_0_161:[bind(X_57,$fot(not(not(X))))]]) ).
cnf(refute_0_248,plain,
( and(not(not(X)),not(not(X))) != and(X,not(not(X)))
| ~ is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(X)))))))))
| is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(X))))))))) ),[0,0],$fot(and(X,not(not(X))))]]) ).
cnf(refute_0_249,plain,
( ~ is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(X)))))))))
| is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X))))))))) ),
inference(resolve,[$cnf( $equal(and(not(not(X)),not(not(X))),and(X,not(not(X)))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X))))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(X))))))))) )],[refute_0_246,refute_0_249]) ).
cnf(refute_0_251,plain,
implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))) = or(and(X,X),not(not(not(not(not(not(not(X)))))))),
inference(subst,[],[refute_0_57:[bind(Y,$fot(not(not(not(not(not(not(not(X))))))))),bind(X_10,$fot(X)),bind(X_11,$fot(X))]]) ).
cnf(refute_0_252,plain,
or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))) = implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))),
inference(subst,[],[refute_0_230:[bind(Y,$fot(not(not(not(not(not(not(not(X))))))))),bind(X_25,$fot(X)),bind(X_26,$fot(not(X)))]]) ).
cnf(refute_0_253,plain,
( implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))) != or(and(X,X),not(not(not(not(not(not(not(X))))))))
| or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))) != implies(implies(X,not(X)),not(not(not(not(not(not(not(X))))))))
| or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))) = or(and(X,X),not(not(not(not(not(not(not(X)))))))) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))))),bind(Y0,$fot(implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))))),bind(Z0,$fot(or(and(X,X),not(not(not(not(not(not(not(X))))))))))]]) ).
cnf(refute_0_254,plain,
( implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))) != or(and(X,X),not(not(not(not(not(not(not(X))))))))
| or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))) = or(and(X,X),not(not(not(not(not(not(not(X)))))))) ),
inference(resolve,[$cnf( $equal(or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))),implies(implies(X,not(X)),not(not(not(not(not(not(not(X))))))))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))) = or(and(X,X),not(not(not(not(not(not(not(X)))))))),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))),or(and(X,X),not(not(not(not(not(not(not(X))))))))) )],[refute_0_251,refute_0_254]) ).
cnf(refute_0_256,plain,
( or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))) != or(and(X,X),not(not(not(not(not(not(not(X))))))))
| ~ is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(X))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X))))))))) ),[0],$fot(or(and(X,X),not(not(not(not(not(not(not(X)))))))))]]) ).
cnf(refute_0_257,plain,
( ~ is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(X))))))))) ),
inference(resolve,[$cnf( $equal(or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))),or(and(X,X),not(not(not(not(not(not(not(X))))))))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(X))))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X))))))))) )],[refute_0_250,refute_0_257]) ).
cnf(refute_0_259,plain,
is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(not(not(X))))))))))),
inference(subst,[],[refute_0_258:[bind(X,$fot(not(not(X))))]]) ).
cnf(refute_0_260,plain,
( and(not(not(X)),not(not(X))) != and(X,not(not(X)))
| ~ is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(not(not(X)))))))))))
| is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(X))))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(not(not(X))))))))))) ),[0,0],$fot(and(X,not(not(X))))]]) ).
cnf(refute_0_261,plain,
( ~ is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(not(not(X)))))))))))
| is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(X))))))))))) ),
inference(resolve,[$cnf( $equal(and(not(not(X)),not(not(X))),and(X,not(not(X)))) )],[refute_0_247,refute_0_260]) ).
cnf(refute_0_262,plain,
is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(X))))))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(not(not(X))))))))))) )],[refute_0_259,refute_0_261]) ).
cnf(refute_0_263,plain,
implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X)))))))))) = or(and(X,X),not(not(not(not(not(not(not(not(not(X)))))))))),
inference(subst,[],[refute_0_57:[bind(Y,$fot(not(not(not(not(not(not(not(not(not(X))))))))))),bind(X_10,$fot(X)),bind(X_11,$fot(X))]]) ).
cnf(refute_0_264,plain,
or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(X)))))))))) = implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X)))))))))),
inference(subst,[],[refute_0_230:[bind(Y,$fot(not(not(not(not(not(not(not(not(not(X))))))))))),bind(X_25,$fot(X)),bind(X_26,$fot(not(X)))]]) ).
cnf(refute_0_265,plain,
( implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X)))))))))) != or(and(X,X),not(not(not(not(not(not(not(not(not(X))))))))))
| or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(X)))))))))) != implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X))))))))))
| or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(X)))))))))) = or(and(X,X),not(not(not(not(not(not(not(not(not(X)))))))))) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(X)))))))))))),bind(Y0,$fot(implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X)))))))))))),bind(Z0,$fot(or(and(X,X),not(not(not(not(not(not(not(not(not(X))))))))))))]]) ).
cnf(refute_0_266,plain,
( implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X)))))))))) != or(and(X,X),not(not(not(not(not(not(not(not(not(X))))))))))
| or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(X)))))))))) = or(and(X,X),not(not(not(not(not(not(not(not(not(X)))))))))) ),
inference(resolve,[$cnf( $equal(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(X)))))))))),implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X))))))))))) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(X)))))))))) = or(and(X,X),not(not(not(not(not(not(not(not(not(X)))))))))),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X)))))))))),or(and(X,X),not(not(not(not(not(not(not(not(not(X))))))))))) )],[refute_0_263,refute_0_266]) ).
cnf(refute_0_268,plain,
( or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(X)))))))))) != or(and(X,X),not(not(not(not(not(not(not(not(not(X))))))))))
| ~ is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(X)))))))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(not(not(X))))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(X))))))))))) ),[0],$fot(or(and(X,X),not(not(not(not(not(not(not(not(not(X)))))))))))]]) ).
cnf(refute_0_269,plain,
( ~ is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(X)))))))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(not(not(X))))))))))) ),
inference(resolve,[$cnf( $equal(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(X)))))))))),or(and(X,X),not(not(not(not(not(not(not(not(not(X))))))))))) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(not(not(X))))))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(X))))))))))) )],[refute_0_262,refute_0_269]) ).
cnf(refute_0_271,plain,
is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))),
inference(subst,[],[refute_0_270:[bind(X,$fot(not(not(X))))]]) ).
cnf(refute_0_272,plain,
( and(not(not(X)),not(not(X))) != and(X,not(not(X)))
| ~ is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))))
| is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))) ),[0,0],$fot(and(X,not(not(X))))]]) ).
cnf(refute_0_273,plain,
( ~ is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))))
| is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))) ),
inference(resolve,[$cnf( $equal(and(not(not(X)),not(not(X))),and(X,not(not(X)))) )],[refute_0_247,refute_0_272]) ).
cnf(refute_0_274,plain,
is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))) )],[refute_0_271,refute_0_273]) ).
cnf(refute_0_275,plain,
implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))) = or(and(X,X),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))),
inference(subst,[],[refute_0_57:[bind(Y,$fot(not(not(not(not(not(not(not(not(not(not(not(X))))))))))))),bind(X_10,$fot(X)),bind(X_11,$fot(X))]]) ).
cnf(refute_0_276,plain,
or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))) = implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))),
inference(subst,[],[refute_0_230:[bind(Y,$fot(not(not(not(not(not(not(not(not(not(not(not(X))))))))))))),bind(X_25,$fot(X)),bind(X_26,$fot(not(X)))]]) ).
cnf(refute_0_277,plain,
( implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))) != or(and(X,X),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))
| or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))) != implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))
| or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))) = or(and(X,X),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))))),bind(Y0,$fot(implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))))),bind(Z0,$fot(or(and(X,X),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))))]]) ).
cnf(refute_0_278,plain,
( implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))) != or(and(X,X),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))
| or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))) = or(and(X,X),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))) ),
inference(resolve,[$cnf( $equal(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))),implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))) = or(and(X,X),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))),or(and(X,X),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))) )],[refute_0_275,refute_0_278]) ).
cnf(refute_0_280,plain,
( or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))) != or(and(X,X),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))
| ~ is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))) ),[0],$fot(or(and(X,X),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))))]]) ).
cnf(refute_0_281,plain,
( ~ is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))) ),
inference(resolve,[$cnf( $equal(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))),or(and(X,X),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))) )],[refute_0_274,refute_0_281]) ).
cnf(refute_0_283,plain,
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[normalize_0_41]) ).
cnf(refute_0_284,plain,
r3,
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_285,plain,
is_a_theorem(implies(or(P,Q),or(Q,P))),
inference(resolve,[$cnf( r3 )],[refute_0_284,refute_0_283]) ).
cnf(refute_0_286,plain,
( ~ is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ is_a_theorem(or(P,Q))
| is_a_theorem(or(Q,P)) ),
inference(subst,[],[refute_0_96:[bind(X,$fot(or(P,Q))),bind(Y,$fot(or(Q,P)))]]) ).
cnf(refute_0_287,plain,
( ~ is_a_theorem(or(P,Q))
| is_a_theorem(or(Q,P)) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,Q),or(Q,P))) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
( ~ is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(not(not(not(not(X)))))))))))))
| is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(not(X))))))))))),and(X,X))) ),
inference(subst,[],[refute_0_287:[bind(P,$fot(and(X,X))),bind(Q,$fot(not(not(not(not(not(not(not(not(not(not(not(X)))))))))))))]]) ).
cnf(refute_0_289,plain,
is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(not(X))))))))))),and(X,X))),
inference(resolve,[$cnf( is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(not(not(not(not(X))))))))))))) )],[refute_0_282,refute_0_288]) ).
cnf(refute_0_290,plain,
or(not(X),and(X,X)) = implies(X,and(X,X)),
inference(subst,[],[refute_0_43:[bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_291,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_292,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[refute_0_21,refute_0_291]) ).
cnf(refute_0_293,plain,
implies(not(not(X)),and(X,X)) = or(not(X),and(X,X)),
inference(subst,[],[refute_0_292:[bind(X,$fot(not(X))),bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_294,plain,
( implies(not(not(X)),and(X,X)) != or(not(X),and(X,X))
| or(not(X),and(X,X)) != implies(X,and(X,X))
| implies(not(not(X)),and(X,X)) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(implies(not(not(X)),and(X,X)))),bind(Y0,$fot(or(not(X),and(X,X)))),bind(Z0,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_295,plain,
( or(not(X),and(X,X)) != implies(X,and(X,X))
| implies(not(not(X)),and(X,X)) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(implies(not(not(X)),and(X,X)),or(not(X),and(X,X))) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
implies(not(not(X)),and(X,X)) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(or(not(X),and(X,X)),implies(X,and(X,X))) )],[refute_0_290,refute_0_295]) ).
cnf(refute_0_297,plain,
or(not(not(not(X))),and(X,X)) = implies(not(not(X)),and(X,X)),
inference(subst,[],[refute_0_43:[bind(X,$fot(not(not(X)))),bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_298,plain,
( implies(not(not(X)),and(X,X)) != implies(X,and(X,X))
| or(not(not(not(X))),and(X,X)) != implies(not(not(X)),and(X,X))
| or(not(not(not(X))),and(X,X)) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(or(not(not(not(X))),and(X,X)))),bind(Y0,$fot(implies(not(not(X)),and(X,X)))),bind(Z0,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_299,plain,
( implies(not(not(X)),and(X,X)) != implies(X,and(X,X))
| or(not(not(not(X))),and(X,X)) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(or(not(not(not(X))),and(X,X)),implies(not(not(X)),and(X,X))) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
or(not(not(not(X))),and(X,X)) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(implies(not(not(X)),and(X,X)),implies(X,and(X,X))) )],[refute_0_296,refute_0_299]) ).
cnf(refute_0_301,plain,
implies(not(not(not(not(X)))),and(X,X)) = or(not(not(not(X))),and(X,X)),
inference(subst,[],[refute_0_292:[bind(X,$fot(not(not(not(X))))),bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_302,plain,
( implies(not(not(not(not(X)))),and(X,X)) != or(not(not(not(X))),and(X,X))
| or(not(not(not(X))),and(X,X)) != implies(X,and(X,X))
| implies(not(not(not(not(X)))),and(X,X)) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(implies(not(not(not(not(X)))),and(X,X)))),bind(Y0,$fot(or(not(not(not(X))),and(X,X)))),bind(Z0,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_303,plain,
( or(not(not(not(X))),and(X,X)) != implies(X,and(X,X))
| implies(not(not(not(not(X)))),and(X,X)) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(X)))),and(X,X)),or(not(not(not(X))),and(X,X))) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
implies(not(not(not(not(X)))),and(X,X)) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(or(not(not(not(X))),and(X,X)),implies(X,and(X,X))) )],[refute_0_300,refute_0_303]) ).
cnf(refute_0_305,plain,
or(not(not(not(not(not(X))))),and(X,X)) = implies(not(not(not(not(X)))),and(X,X)),
inference(subst,[],[refute_0_43:[bind(X,$fot(not(not(not(not(X)))))),bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_306,plain,
( implies(not(not(not(not(X)))),and(X,X)) != implies(X,and(X,X))
| or(not(not(not(not(not(X))))),and(X,X)) != implies(not(not(not(not(X)))),and(X,X))
| or(not(not(not(not(not(X))))),and(X,X)) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(or(not(not(not(not(not(X))))),and(X,X)))),bind(Y0,$fot(implies(not(not(not(not(X)))),and(X,X)))),bind(Z0,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_307,plain,
( implies(not(not(not(not(X)))),and(X,X)) != implies(X,and(X,X))
| or(not(not(not(not(not(X))))),and(X,X)) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(X))))),and(X,X)),implies(not(not(not(not(X)))),and(X,X))) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
or(not(not(not(not(not(X))))),and(X,X)) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(X)))),and(X,X)),implies(X,and(X,X))) )],[refute_0_304,refute_0_307]) ).
cnf(refute_0_309,plain,
implies(not(not(not(not(not(not(X)))))),and(X,X)) = or(not(not(not(not(not(X))))),and(X,X)),
inference(subst,[],[refute_0_292:[bind(X,$fot(not(not(not(not(not(X))))))),bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_310,plain,
( implies(not(not(not(not(not(not(X)))))),and(X,X)) != or(not(not(not(not(not(X))))),and(X,X))
| or(not(not(not(not(not(X))))),and(X,X)) != implies(X,and(X,X))
| implies(not(not(not(not(not(not(X)))))),and(X,X)) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(implies(not(not(not(not(not(not(X)))))),and(X,X)))),bind(Y0,$fot(or(not(not(not(not(not(X))))),and(X,X)))),bind(Z0,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_311,plain,
( or(not(not(not(not(not(X))))),and(X,X)) != implies(X,and(X,X))
| implies(not(not(not(not(not(not(X)))))),and(X,X)) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(X)))))),and(X,X)),or(not(not(not(not(not(X))))),and(X,X))) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
implies(not(not(not(not(not(not(X)))))),and(X,X)) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(X))))),and(X,X)),implies(X,and(X,X))) )],[refute_0_308,refute_0_311]) ).
cnf(refute_0_313,plain,
or(not(not(not(not(not(not(not(X))))))),and(X,X)) = implies(not(not(not(not(not(not(X)))))),and(X,X)),
inference(subst,[],[refute_0_43:[bind(X,$fot(not(not(not(not(not(not(X)))))))),bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_314,plain,
( implies(not(not(not(not(not(not(X)))))),and(X,X)) != implies(X,and(X,X))
| or(not(not(not(not(not(not(not(X))))))),and(X,X)) != implies(not(not(not(not(not(not(X)))))),and(X,X))
| or(not(not(not(not(not(not(not(X))))))),and(X,X)) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(or(not(not(not(not(not(not(not(X))))))),and(X,X)))),bind(Y0,$fot(implies(not(not(not(not(not(not(X)))))),and(X,X)))),bind(Z0,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_315,plain,
( implies(not(not(not(not(not(not(X)))))),and(X,X)) != implies(X,and(X,X))
| or(not(not(not(not(not(not(not(X))))))),and(X,X)) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(not(X))))))),and(X,X)),implies(not(not(not(not(not(not(X)))))),and(X,X))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
or(not(not(not(not(not(not(not(X))))))),and(X,X)) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(X)))))),and(X,X)),implies(X,and(X,X))) )],[refute_0_312,refute_0_315]) ).
cnf(refute_0_317,plain,
implies(not(not(not(not(not(not(not(not(X)))))))),and(X,X)) = or(not(not(not(not(not(not(not(X))))))),and(X,X)),
inference(subst,[],[refute_0_292:[bind(X,$fot(not(not(not(not(not(not(not(X))))))))),bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_318,plain,
( implies(not(not(not(not(not(not(not(not(X)))))))),and(X,X)) != or(not(not(not(not(not(not(not(X))))))),and(X,X))
| or(not(not(not(not(not(not(not(X))))))),and(X,X)) != implies(X,and(X,X))
| implies(not(not(not(not(not(not(not(not(X)))))))),and(X,X)) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(implies(not(not(not(not(not(not(not(not(X)))))))),and(X,X)))),bind(Y0,$fot(or(not(not(not(not(not(not(not(X))))))),and(X,X)))),bind(Z0,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_319,plain,
( or(not(not(not(not(not(not(not(X))))))),and(X,X)) != implies(X,and(X,X))
| implies(not(not(not(not(not(not(not(not(X)))))))),and(X,X)) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(not(not(X)))))))),and(X,X)),or(not(not(not(not(not(not(not(X))))))),and(X,X))) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
implies(not(not(not(not(not(not(not(not(X)))))))),and(X,X)) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(not(X))))))),and(X,X)),implies(X,and(X,X))) )],[refute_0_316,refute_0_319]) ).
cnf(refute_0_321,plain,
or(not(not(not(not(not(not(not(not(not(X))))))))),and(X,X)) = implies(not(not(not(not(not(not(not(not(X)))))))),and(X,X)),
inference(subst,[],[refute_0_43:[bind(X,$fot(not(not(not(not(not(not(not(not(X)))))))))),bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_322,plain,
( implies(not(not(not(not(not(not(not(not(X)))))))),and(X,X)) != implies(X,and(X,X))
| or(not(not(not(not(not(not(not(not(not(X))))))))),and(X,X)) != implies(not(not(not(not(not(not(not(not(X)))))))),and(X,X))
| or(not(not(not(not(not(not(not(not(not(X))))))))),and(X,X)) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(or(not(not(not(not(not(not(not(not(not(X))))))))),and(X,X)))),bind(Y0,$fot(implies(not(not(not(not(not(not(not(not(X)))))))),and(X,X)))),bind(Z0,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_323,plain,
( implies(not(not(not(not(not(not(not(not(X)))))))),and(X,X)) != implies(X,and(X,X))
| or(not(not(not(not(not(not(not(not(not(X))))))))),and(X,X)) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(not(not(not(X))))))))),and(X,X)),implies(not(not(not(not(not(not(not(not(X)))))))),and(X,X))) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
or(not(not(not(not(not(not(not(not(not(X))))))))),and(X,X)) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(not(not(X)))))))),and(X,X)),implies(X,and(X,X))) )],[refute_0_320,refute_0_323]) ).
cnf(refute_0_325,plain,
implies(not(not(not(not(not(not(not(not(not(not(X)))))))))),and(X,X)) = or(not(not(not(not(not(not(not(not(not(X))))))))),and(X,X)),
inference(subst,[],[refute_0_292:[bind(X,$fot(not(not(not(not(not(not(not(not(not(X))))))))))),bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_326,plain,
( implies(not(not(not(not(not(not(not(not(not(not(X)))))))))),and(X,X)) != or(not(not(not(not(not(not(not(not(not(X))))))))),and(X,X))
| or(not(not(not(not(not(not(not(not(not(X))))))))),and(X,X)) != implies(X,and(X,X))
| implies(not(not(not(not(not(not(not(not(not(not(X)))))))))),and(X,X)) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(implies(not(not(not(not(not(not(not(not(not(not(X)))))))))),and(X,X)))),bind(Y0,$fot(or(not(not(not(not(not(not(not(not(not(X))))))))),and(X,X)))),bind(Z0,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_327,plain,
( or(not(not(not(not(not(not(not(not(not(X))))))))),and(X,X)) != implies(X,and(X,X))
| implies(not(not(not(not(not(not(not(not(not(not(X)))))))))),and(X,X)) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(not(not(not(not(X)))))))))),and(X,X)),or(not(not(not(not(not(not(not(not(not(X))))))))),and(X,X))) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
implies(not(not(not(not(not(not(not(not(not(not(X)))))))))),and(X,X)) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(not(not(not(X))))))))),and(X,X)),implies(X,and(X,X))) )],[refute_0_324,refute_0_327]) ).
cnf(refute_0_329,plain,
or(not(not(not(not(not(not(not(not(not(not(not(X))))))))))),and(X,X)) = implies(not(not(not(not(not(not(not(not(not(not(X)))))))))),and(X,X)),
inference(subst,[],[refute_0_43:[bind(X,$fot(not(not(not(not(not(not(not(not(not(not(X)))))))))))),bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_330,plain,
( implies(not(not(not(not(not(not(not(not(not(not(X)))))))))),and(X,X)) != implies(X,and(X,X))
| or(not(not(not(not(not(not(not(not(not(not(not(X))))))))))),and(X,X)) != implies(not(not(not(not(not(not(not(not(not(not(X)))))))))),and(X,X))
| or(not(not(not(not(not(not(not(not(not(not(not(X))))))))))),and(X,X)) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(or(not(not(not(not(not(not(not(not(not(not(not(X))))))))))),and(X,X)))),bind(Y0,$fot(implies(not(not(not(not(not(not(not(not(not(not(X)))))))))),and(X,X)))),bind(Z0,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_331,plain,
( implies(not(not(not(not(not(not(not(not(not(not(X)))))))))),and(X,X)) != implies(X,and(X,X))
| or(not(not(not(not(not(not(not(not(not(not(not(X))))))))))),and(X,X)) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(not(not(not(not(not(X))))))))))),and(X,X)),implies(not(not(not(not(not(not(not(not(not(not(X)))))))))),and(X,X))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
or(not(not(not(not(not(not(not(not(not(not(not(X))))))))))),and(X,X)) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(not(not(not(not(X)))))))))),and(X,X)),implies(X,and(X,X))) )],[refute_0_328,refute_0_331]) ).
cnf(refute_0_333,plain,
( or(not(not(not(not(not(not(not(not(not(not(not(X))))))))))),and(X,X)) != implies(X,and(X,X))
| ~ is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(not(X))))))))))),and(X,X)))
| is_a_theorem(implies(X,and(X,X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(not(X))))))))))),and(X,X))) ),[0],$fot(implies(X,and(X,X)))]]) ).
cnf(refute_0_334,plain,
( ~ is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(not(X))))))))))),and(X,X)))
| is_a_theorem(implies(X,and(X,X))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(not(not(not(not(not(X))))))))))),and(X,X)),implies(X,and(X,X))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
is_a_theorem(implies(X,and(X,X))),
inference(resolve,[$cnf( is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(not(X))))))))))),and(X,X))) )],[refute_0_289,refute_0_334]) ).
cnf(refute_0_336,plain,
is_a_theorem(implies(X_326,and(X_326,X_326))),
inference(subst,[],[refute_0_335:[bind(X,$fot(X_326))]]) ).
cnf(refute_0_337,plain,
( ~ is_a_theorem(X_326)
| is_a_theorem(and(X_326,X_326)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_326,and(X_326,X_326))) )],[refute_0_336,refute_0_180]) ).
cnf(refute_0_338,plain,
( ~ is_a_theorem(implies(X_2697,X_2697))
| is_a_theorem(and(implies(X_2697,X_2697),implies(X_2697,X_2697))) ),
inference(subst,[],[refute_0_337:[bind(X_326,$fot(implies(X_2697,X_2697)))]]) ).
cnf(refute_0_339,plain,
( ~ is_a_theorem(or(X_2696,not(X_2696)))
| is_a_theorem(or(not(X_2696),X_2696)) ),
inference(subst,[],[refute_0_287:[bind(P,$fot(X_2696)),bind(Q,$fot(not(X_2696)))]]) ).
cnf(refute_0_340,plain,
is_a_theorem(implies(or(X_316,X_316),X_316)),
inference(subst,[],[refute_0_183:[bind(P,$fot(X_316))]]) ).
cnf(refute_0_341,plain,
( ~ is_a_theorem(implies(or(X_316,X_316),X_316))
| ~ is_a_theorem(or(X_316,X_316))
| is_a_theorem(X_316) ),
inference(subst,[],[refute_0_96:[bind(X,$fot(or(X_316,X_316))),bind(Y,$fot(X_316))]]) ).
cnf(refute_0_342,plain,
( ~ is_a_theorem(or(X_316,X_316))
| is_a_theorem(X_316) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_316,X_316),X_316)) )],[refute_0_340,refute_0_341]) ).
cnf(refute_0_343,plain,
( ~ is_a_theorem(or(or(X_2694,not(X_2694)),or(X_2694,not(X_2694))))
| is_a_theorem(or(X_2694,not(X_2694))) ),
inference(subst,[],[refute_0_342:[bind(X_316,$fot(or(X_2694,not(X_2694))))]]) ).
cnf(refute_0_344,plain,
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[normalize_0_45]) ).
cnf(refute_0_345,plain,
r2,
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_346,plain,
is_a_theorem(implies(Q,or(P,Q))),
inference(resolve,[$cnf( r2 )],[refute_0_345,refute_0_344]) ).
cnf(refute_0_347,plain,
is_a_theorem(implies(not(X),or(X_6,not(X)))),
inference(subst,[],[refute_0_346:[bind(P,$fot(X_6)),bind(Q,$fot(not(X)))]]) ).
cnf(refute_0_348,plain,
or(X,or(X_6,not(X))) = implies(not(X),or(X_6,not(X))),
inference(subst,[],[refute_0_21:[bind(Y,$fot(or(X_6,not(X))))]]) ).
cnf(refute_0_349,plain,
( or(X,or(X_6,not(X))) != implies(not(X),or(X_6,not(X)))
| implies(not(X),or(X_6,not(X))) = or(X,or(X_6,not(X))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,or(X_6,not(X))))),bind(Y0,$fot(implies(not(X),or(X_6,not(X)))))]]) ).
cnf(refute_0_350,plain,
implies(not(X),or(X_6,not(X))) = or(X,or(X_6,not(X))),
inference(resolve,[$cnf( $equal(or(X,or(X_6,not(X))),implies(not(X),or(X_6,not(X)))) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
( implies(not(X),or(X_6,not(X))) != or(X,or(X_6,not(X)))
| ~ is_a_theorem(implies(not(X),or(X_6,not(X))))
| is_a_theorem(or(X,or(X_6,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X),or(X_6,not(X)))) ),[0],$fot(or(X,or(X_6,not(X))))]]) ).
cnf(refute_0_352,plain,
( ~ is_a_theorem(implies(not(X),or(X_6,not(X))))
| is_a_theorem(or(X,or(X_6,not(X)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),or(X_6,not(X))),or(X,or(X_6,not(X)))) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
is_a_theorem(or(X,or(X_6,not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X),or(X_6,not(X)))) )],[refute_0_347,refute_0_352]) ).
cnf(refute_0_354,plain,
is_a_theorem(or(X_2691,or(X_2692,not(X_2691)))),
inference(subst,[],[refute_0_353:[bind(X,$fot(X_2691)),bind(X_6,$fot(X_2692))]]) ).
cnf(refute_0_355,plain,
( ~ is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| ~ is_a_theorem(or(P,or(Q,R)))
| is_a_theorem(or(Q,or(P,R))) ),
inference(subst,[],[refute_0_96:[bind(X,$fot(or(P,or(Q,R)))),bind(Y,$fot(or(Q,or(P,R))))]]) ).
cnf(refute_0_356,plain,
( ~ is_a_theorem(or(P,or(Q,R)))
| is_a_theorem(or(Q,or(P,R))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) )],[refute_0_78,refute_0_355]) ).
cnf(refute_0_357,plain,
( ~ is_a_theorem(or(X_2691,or(X_2692,not(X_2691))))
| is_a_theorem(or(X_2692,or(X_2691,not(X_2691)))) ),
inference(subst,[],[refute_0_356:[bind(P,$fot(X_2691)),bind(Q,$fot(X_2692)),bind(R,$fot(not(X_2691)))]]) ).
cnf(refute_0_358,plain,
is_a_theorem(or(X_2692,or(X_2691,not(X_2691)))),
inference(resolve,[$cnf( is_a_theorem(or(X_2691,or(X_2692,not(X_2691)))) )],[refute_0_354,refute_0_357]) ).
cnf(refute_0_359,plain,
is_a_theorem(or(or(X_2694,not(X_2694)),or(X_2694,not(X_2694)))),
inference(subst,[],[refute_0_358:[bind(X_2691,$fot(X_2694)),bind(X_2692,$fot(or(X_2694,not(X_2694))))]]) ).
cnf(refute_0_360,plain,
is_a_theorem(or(X_2694,not(X_2694))),
inference(resolve,[$cnf( is_a_theorem(or(or(X_2694,not(X_2694)),or(X_2694,not(X_2694)))) )],[refute_0_359,refute_0_343]) ).
cnf(refute_0_361,plain,
is_a_theorem(or(X_2696,not(X_2696))),
inference(subst,[],[refute_0_360:[bind(X_2694,$fot(X_2696))]]) ).
cnf(refute_0_362,plain,
is_a_theorem(or(not(X_2696),X_2696)),
inference(resolve,[$cnf( is_a_theorem(or(X_2696,not(X_2696))) )],[refute_0_361,refute_0_339]) ).
cnf(refute_0_363,plain,
or(not(X_2696),X_2696) = implies(X_2696,X_2696),
inference(subst,[],[refute_0_43:[bind(X,$fot(X_2696)),bind(Y,$fot(X_2696))]]) ).
cnf(refute_0_364,plain,
( or(not(X_2696),X_2696) != implies(X_2696,X_2696)
| ~ is_a_theorem(or(not(X_2696),X_2696))
| is_a_theorem(implies(X_2696,X_2696)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X_2696),X_2696)) ),[0],$fot(implies(X_2696,X_2696))]]) ).
cnf(refute_0_365,plain,
( ~ is_a_theorem(or(not(X_2696),X_2696))
| is_a_theorem(implies(X_2696,X_2696)) ),
inference(resolve,[$cnf( $equal(or(not(X_2696),X_2696),implies(X_2696,X_2696)) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
is_a_theorem(implies(X_2696,X_2696)),
inference(resolve,[$cnf( is_a_theorem(or(not(X_2696),X_2696)) )],[refute_0_362,refute_0_365]) ).
cnf(refute_0_367,plain,
is_a_theorem(implies(X_2697,X_2697)),
inference(subst,[],[refute_0_366:[bind(X_2696,$fot(X_2697))]]) ).
cnf(refute_0_368,plain,
is_a_theorem(and(implies(X_2697,X_2697),implies(X_2697,X_2697))),
inference(resolve,[$cnf( is_a_theorem(implies(X_2697,X_2697)) )],[refute_0_367,refute_0_338]) ).
cnf(refute_0_369,plain,
and(implies(X_2697,X_2697),implies(X_2697,X_2697)) = equiv(X_2697,X_2697),
inference(subst,[],[refute_0_132:[bind(X,$fot(X_2697)),bind(Y,$fot(X_2697))]]) ).
cnf(refute_0_370,plain,
( and(implies(X_2697,X_2697),implies(X_2697,X_2697)) != equiv(X_2697,X_2697)
| ~ is_a_theorem(and(implies(X_2697,X_2697),implies(X_2697,X_2697)))
| is_a_theorem(equiv(X_2697,X_2697)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(and(implies(X_2697,X_2697),implies(X_2697,X_2697))) ),[0],$fot(equiv(X_2697,X_2697))]]) ).
cnf(refute_0_371,plain,
( ~ is_a_theorem(and(implies(X_2697,X_2697),implies(X_2697,X_2697)))
| is_a_theorem(equiv(X_2697,X_2697)) ),
inference(resolve,[$cnf( $equal(and(implies(X_2697,X_2697),implies(X_2697,X_2697)),equiv(X_2697,X_2697)) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
is_a_theorem(equiv(X_2697,X_2697)),
inference(resolve,[$cnf( is_a_theorem(and(implies(X_2697,X_2697),implies(X_2697,X_2697))) )],[refute_0_368,refute_0_371]) ).
cnf(refute_0_373,plain,
is_a_theorem(equiv(X_2699,X_2699)),
inference(subst,[],[refute_0_372:[bind(X_2697,$fot(X_2699))]]) ).
cnf(refute_0_374,plain,
X_2699 = not(not(X_2699)),
inference(resolve,[$cnf( is_a_theorem(equiv(X_2699,X_2699)) )],[refute_0_373,refute_0_179]) ).
cnf(refute_0_375,plain,
X_2700 = not(not(X_2700)),
inference(subst,[],[refute_0_374:[bind(X_2699,$fot(X_2700))]]) ).
cnf(refute_0_376,plain,
( X_2700 != not(not(X_2700))
| not(not(X_2700)) = X_2700 ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(X_2700)),bind(Y0,$fot(not(not(X_2700))))]]) ).
cnf(refute_0_377,plain,
not(not(X_2700)) = X_2700,
inference(resolve,[$cnf( $equal(X_2700,not(not(X_2700))) )],[refute_0_375,refute_0_376]) ).
cnf(refute_0_378,plain,
( and(X,not(X_2700)) != not(implies(X,not(not(X_2700))))
| not(not(X_2700)) != X_2700
| and(X,not(X_2700)) = not(implies(X,X_2700)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,not(X_2700)),not(implies(X,not(not(X_2700))))) ),[1,0,1],$fot(X_2700)]]) ).
cnf(refute_0_379,plain,
( and(X,not(X_2700)) != not(implies(X,not(not(X_2700))))
| and(X,not(X_2700)) = not(implies(X,X_2700)) ),
inference(resolve,[$cnf( $equal(not(not(X_2700)),X_2700) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
and(X,not(X_2700)) = not(implies(X,X_2700)),
inference(resolve,[$cnf( $equal(and(X,not(X_2700)),not(implies(X,not(not(X_2700))))) )],[refute_0_109,refute_0_379]) ).
cnf(refute_0_381,plain,
and(X_4744,not(X)) = not(implies(X_4744,X)),
inference(subst,[],[refute_0_380:[bind(X,$fot(X_4744)),bind(X_2700,$fot(X))]]) ).
cnf(refute_0_382,plain,
or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))) = or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))),
introduced(tautology,[refl,[$fot(or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))))]]) ).
cnf(refute_0_383,plain,
( and(X_4744,not(X)) != not(implies(X_4744,X))
| or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))) != or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746)))
| or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))) = or(not(implies(X_4744,X)),implies(implies(X,X_4746),implies(X_4744,X_4746))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))),or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746)))) ),[1,0],$fot(not(implies(X_4744,X)))]]) ).
cnf(refute_0_384,plain,
( and(X_4744,not(X)) != not(implies(X_4744,X))
| or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))) = or(not(implies(X_4744,X)),implies(implies(X,X_4746),implies(X_4744,X_4746))) ),
inference(resolve,[$cnf( $equal(or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))),or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746)))) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))) = or(not(implies(X_4744,X)),implies(implies(X,X_4746),implies(X_4744,X_4746))),
inference(resolve,[$cnf( $equal(and(X_4744,not(X)),not(implies(X_4744,X))) )],[refute_0_381,refute_0_384]) ).
cnf(refute_0_386,plain,
( or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))) != or(not(implies(X_4744,X)),implies(implies(X,X_4746),implies(X_4744,X_4746)))
| or(not(implies(X_4744,X)),implies(implies(X,X_4746),implies(X_4744,X_4746))) != implies(implies(X_4744,X),implies(implies(X,X_4746),implies(X_4744,X_4746)))
| or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))) = implies(implies(X_4744,X),implies(implies(X,X_4746),implies(X_4744,X_4746))) ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))))),bind(Y0,$fot(or(not(implies(X_4744,X)),implies(implies(X,X_4746),implies(X_4744,X_4746))))),bind(Z0,$fot(implies(implies(X_4744,X),implies(implies(X,X_4746),implies(X_4744,X_4746)))))]]) ).
cnf(refute_0_387,plain,
( or(not(implies(X_4744,X)),implies(implies(X,X_4746),implies(X_4744,X_4746))) != implies(implies(X_4744,X),implies(implies(X,X_4746),implies(X_4744,X_4746)))
| or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))) = implies(implies(X_4744,X),implies(implies(X,X_4746),implies(X_4744,X_4746))) ),
inference(resolve,[$cnf( $equal(or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))),or(not(implies(X_4744,X)),implies(implies(X,X_4746),implies(X_4744,X_4746)))) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))) = implies(implies(X_4744,X),implies(implies(X,X_4746),implies(X_4744,X_4746))),
inference(resolve,[$cnf( $equal(or(not(implies(X_4744,X)),implies(implies(X,X_4746),implies(X_4744,X_4746))),implies(implies(X_4744,X),implies(implies(X,X_4746),implies(X_4744,X_4746)))) )],[refute_0_108,refute_0_387]) ).
cnf(refute_0_389,plain,
( or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))) != implies(implies(X_4744,X),implies(implies(X,X_4746),implies(X_4744,X_4746)))
| ~ is_a_theorem(or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))))
| is_a_theorem(implies(implies(X_4744,X),implies(implies(X,X_4746),implies(X_4744,X_4746)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746)))) ),[0],$fot(implies(implies(X_4744,X),implies(implies(X,X_4746),implies(X_4744,X_4746))))]]) ).
cnf(refute_0_390,plain,
( ~ is_a_theorem(or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))))
| is_a_theorem(implies(implies(X_4744,X),implies(implies(X,X_4746),implies(X_4744,X_4746)))) ),
inference(resolve,[$cnf( $equal(or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746))),implies(implies(X_4744,X),implies(implies(X,X_4746),implies(X_4744,X_4746)))) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
is_a_theorem(implies(implies(X_4744,X),implies(implies(X,X_4746),implies(X_4744,X_4746)))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_4744,not(X)),implies(implies(X,X_4746),implies(X_4744,X_4746)))) )],[refute_0_107,refute_0_390]) ).
cnf(refute_0_392,plain,
is_a_theorem(implies(implies(skolemFOFtoCNF_X_5,skolemFOFtoCNF_Y_5),implies(implies(skolemFOFtoCNF_Y_5,skolemFOFtoCNF_Z),implies(skolemFOFtoCNF_X_5,skolemFOFtoCNF_Z)))),
inference(subst,[],[refute_0_391:[bind(X,$fot(skolemFOFtoCNF_Y_5)),bind(X_4744,$fot(skolemFOFtoCNF_X_5)),bind(X_4746,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_393,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(skolemFOFtoCNF_X_5,skolemFOFtoCNF_Y_5),implies(implies(skolemFOFtoCNF_Y_5,skolemFOFtoCNF_Z),implies(skolemFOFtoCNF_X_5,skolemFOFtoCNF_Z)))) )],[refute_0_392,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL486+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 18:19:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 28.62/28.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.62/28.78
% 28.62/28.78 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 28.62/28.85
%------------------------------------------------------------------------------