TSTP Solution File: LCL490+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL490+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:52:38 EDT 2022
% Result : Theorem 238.40s 238.59s
% Output : CNFRefutation 238.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 133
% Number of leaves : 378
% Syntax : Number of formulae : 1890 ( 981 unt; 0 def)
% Number of atoms : 3187 (2026 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 2573 (1276 ~;1259 |; 15 &)
% ( 16 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 17 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 17 con; 0-2 aty)
% Number of variables : 3548 ( 130 sgn 79 !; 17 ?)
% 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(or_1,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ) ).
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_or_1,conjecture,
or_1 ).
fof(subgoal_0,plain,
or_1,
inference(strip,[],[hilbert_or_1]) ).
fof(negate_0_0,plain,
~ or_1,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ or_1
<=> ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y))) ),
inference(canonicalize,[],[or_1]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(skolemFOFtoCNF_X_9,or(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_9)))
| or_1 )
& ( ~ or_1
| is_a_theorem(implies(X,or(X,Y))) ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_X_9,or(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_9)))
| or_1 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ or_1,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,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_5,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_4]) ).
fof(normalize_0_6,plain,
! [P,Q,R] :
( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
r4,
inference(canonicalize,[],[principia_r4]) ).
fof(normalize_0_8,plain,
( ~ op_implies_or
| ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[op_implies_or]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
op_implies_or,
inference(canonicalize,[],[principia_op_implies_or]) ).
fof(normalize_0_11,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_12,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_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
modus_ponens,
inference(canonicalize,[],[principia_modus_ponens]) ).
fof(normalize_0_15,plain,
( ~ r3
<=> ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[r3]) ).
fof(normalize_0_16,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_15]) ).
fof(normalize_0_17,plain,
! [P,Q] :
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
r3,
inference(canonicalize,[],[principia_r3]) ).
fof(normalize_0_19,plain,
( ~ r2
<=> ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[r2]) ).
fof(normalize_0_20,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_19]) ).
fof(normalize_0_21,plain,
! [P,Q] :
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
r2,
inference(canonicalize,[],[principia_r2]) ).
fof(normalize_0_23,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_24,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
op_or,
inference(canonicalize,[],[hilbert_op_or]) ).
fof(normalize_0_26,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_27,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
op_implies_and,
inference(canonicalize,[],[hilbert_op_implies_and]) ).
fof(normalize_0_29,plain,
( ~ r1
<=> ? [P] : ~ is_a_theorem(implies(or(P,P),P)) ),
inference(canonicalize,[],[r1]) ).
fof(normalize_0_30,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_29]) ).
fof(normalize_0_31,plain,
! [P] :
( ~ r1
| is_a_theorem(implies(or(P,P),P)) ),
inference(conjunct,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
r1,
inference(canonicalize,[],[principia_r1]) ).
fof(normalize_0_33,plain,
( ~ op_and
| ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[op_and]) ).
fof(normalize_0_34,plain,
! [X,Y] :
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
op_and,
inference(canonicalize,[],[principia_op_and]) ).
fof(normalize_0_36,plain,
( ~ substitution_of_equivalents
<=> ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_37,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_36]) ).
fof(normalize_0_38,plain,
! [X,Y] :
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(conjunct,[],[normalize_0_37]) ).
fof(normalize_0_39,plain,
substitution_of_equivalents,
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_40,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_41,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_40]) ).
fof(normalize_0_42,plain,
op_equiv,
inference(canonicalize,[],[hilbert_op_equiv]) ).
fof(normalize_0_43,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_44,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_43]) ).
fof(normalize_0_45,plain,
! [P,Q,R] :
( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(conjunct,[],[normalize_0_44]) ).
fof(normalize_0_46,plain,
r5,
inference(canonicalize,[],[principia_r5]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_X_9,or(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_9)))
| or_1 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ or_1,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(skolemFOFtoCNF_X_9,or(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_9))),
inference(resolve,[$cnf( or_1 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
r4,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))),
inference(resolve,[$cnf( r4 )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(or(X_103,or(not(X),X_105)),or(not(X),or(X_103,X_105)))),
inference(subst,[],[refute_0_5:[bind(P,$fot(X_103)),bind(Q,$fot(not(X))),bind(R,$fot(X_105))]]) ).
cnf(refute_0_7,plain,
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
implies(X,Y) = or(not(X),Y),
inference(resolve,[$cnf( op_implies_or )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
implies(X,or(X_103,X_105)) = or(not(X),or(X_103,X_105)),
inference(subst,[],[refute_0_9:[bind(Y,$fot(or(X_103,X_105)))]]) ).
cnf(refute_0_11,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_12,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_13,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( implies(X,or(X_103,X_105)) != or(not(X),or(X_103,X_105))
| or(not(X),or(X_103,X_105)) = implies(X,or(X_103,X_105)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,or(X_103,X_105)))),bind(Y0,$fot(or(not(X),or(X_103,X_105))))]]) ).
cnf(refute_0_15,plain,
or(not(X),or(X_103,X_105)) = implies(X,or(X_103,X_105)),
inference(resolve,[$cnf( $equal(implies(X,or(X_103,X_105)),or(not(X),or(X_103,X_105))) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
( or(not(X),or(X_103,X_105)) != implies(X,or(X_103,X_105))
| ~ is_a_theorem(implies(or(X_103,or(not(X),X_105)),or(not(X),or(X_103,X_105))))
| is_a_theorem(implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_103,or(not(X),X_105)),or(not(X),or(X_103,X_105)))) ),[0,1],$fot(implies(X,or(X_103,X_105)))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(or(X_103,or(not(X),X_105)),or(not(X),or(X_103,X_105))))
| is_a_theorem(implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_103,X_105)),implies(X,or(X_103,X_105))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_103,or(not(X),X_105)),or(not(X),or(X_103,X_105)))) )],[refute_0_6,refute_0_17]) ).
cnf(refute_0_19,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_20,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[refute_0_9,refute_0_19]) ).
cnf(refute_0_21,plain,
or(not(X),X_105) = implies(X,X_105),
inference(subst,[],[refute_0_20:[bind(Y,$fot(X_105))]]) ).
cnf(refute_0_22,plain,
or(X_103,or(not(X),X_105)) = or(X_103,or(not(X),X_105)),
introduced(tautology,[refl,[$fot(or(X_103,or(not(X),X_105)))]]) ).
cnf(refute_0_23,plain,
( or(X_103,or(not(X),X_105)) != or(X_103,or(not(X),X_105))
| or(not(X),X_105) != implies(X,X_105)
| or(X_103,or(not(X),X_105)) = or(X_103,implies(X,X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_103,or(not(X),X_105)),or(X_103,or(not(X),X_105))) ),[1,1],$fot(implies(X,X_105))]]) ).
cnf(refute_0_24,plain,
( or(not(X),X_105) != implies(X,X_105)
| or(X_103,or(not(X),X_105)) = or(X_103,implies(X,X_105)) ),
inference(resolve,[$cnf( $equal(or(X_103,or(not(X),X_105)),or(X_103,or(not(X),X_105))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
or(X_103,or(not(X),X_105)) = or(X_103,implies(X,X_105)),
inference(resolve,[$cnf( $equal(or(not(X),X_105),implies(X,X_105)) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105))) = implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105))),
introduced(tautology,[refl,[$fot(implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105))))]]) ).
cnf(refute_0_27,plain,
( implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105))) != implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105)))
| or(X_103,or(not(X),X_105)) != or(X_103,implies(X,X_105))
| implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105))) = implies(or(X_103,implies(X,X_105)),implies(X,or(X_103,X_105))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105))),implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105)))) ),[1,0],$fot(or(X_103,implies(X,X_105)))]]) ).
cnf(refute_0_28,plain,
( or(X_103,or(not(X),X_105)) != or(X_103,implies(X,X_105))
| implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105))) = implies(or(X_103,implies(X,X_105)),implies(X,or(X_103,X_105))) ),
inference(resolve,[$cnf( $equal(implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105))),implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105))) = implies(or(X_103,implies(X,X_105)),implies(X,or(X_103,X_105))),
inference(resolve,[$cnf( $equal(or(X_103,or(not(X),X_105)),or(X_103,implies(X,X_105))) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105))) != implies(or(X_103,implies(X,X_105)),implies(X,or(X_103,X_105)))
| ~ is_a_theorem(implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105))))
| is_a_theorem(implies(or(X_103,implies(X,X_105)),implies(X,or(X_103,X_105)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105)))) ),[0],$fot(implies(or(X_103,implies(X,X_105)),implies(X,or(X_103,X_105))))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105))))
| is_a_theorem(implies(or(X_103,implies(X,X_105)),implies(X,or(X_103,X_105)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105))),implies(or(X_103,implies(X,X_105)),implies(X,or(X_103,X_105)))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(or(X_103,implies(X,X_105)),implies(X,or(X_103,X_105)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_103,or(not(X),X_105)),implies(X,or(X_103,X_105)))) )],[refute_0_18,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_34,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_34,refute_0_33]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(or(X_103,implies(X,X_105)),implies(X,or(X_103,X_105))))
| ~ is_a_theorem(or(X_103,implies(X,X_105)))
| is_a_theorem(implies(X,or(X_103,X_105))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(or(X_103,implies(X,X_105)))),bind(Y,$fot(implies(X,or(X_103,X_105))))]]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(or(X_103,implies(X,X_105)))
| is_a_theorem(implies(X,or(X_103,X_105))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_103,implies(X,X_105)),implies(X,or(X_103,X_105)))) )],[refute_0_32,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(or(and(X_12405,equiv(X_12407,X_12407)),implies(X_12405,X_12406)))
| is_a_theorem(implies(X_12405,or(and(X_12405,equiv(X_12407,X_12407)),X_12406))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_12405)),bind(X_103,$fot(and(X_12405,equiv(X_12407,X_12407)))),bind(X_105,$fot(X_12406))]]) ).
cnf(refute_0_39,plain,
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_40,plain,
r3,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(or(P,Q),or(Q,P))),
inference(resolve,[$cnf( r3 )],[refute_0_40,refute_0_39]) ).
cnf(refute_0_42,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_35:[bind(X,$fot(or(P,Q))),bind(Y,$fot(or(Q,P)))]]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(or(P,Q))
| is_a_theorem(or(Q,P)) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,Q),or(Q,P))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(or(X_4519,equiv(X_4518,X_4518)))
| is_a_theorem(or(equiv(X_4518,X_4518),X_4519)) ),
inference(subst,[],[refute_0_43:[bind(P,$fot(X_4519)),bind(Q,$fot(equiv(X_4518,X_4518)))]]) ).
cnf(refute_0_45,plain,
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_46,plain,
r2,
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(Q,or(P,Q))),
inference(resolve,[$cnf( r2 )],[refute_0_46,refute_0_45]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(not(X_10),or(P,not(X_10)))),
inference(subst,[],[refute_0_47:[bind(Q,$fot(not(X_10)))]]) ).
cnf(refute_0_49,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_50,plain,
op_or,
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_51,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_50,refute_0_49]) ).
cnf(refute_0_52,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_53,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_54,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_53,refute_0_52]) ).
cnf(refute_0_55,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_56,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_56:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_58,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_59,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_51,refute_0_59]) ).
cnf(refute_0_61,plain,
or(X_10,or(P,not(X_10))) = implies(not(X_10),or(P,not(X_10))),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_10)),bind(Y,$fot(or(P,not(X_10))))]]) ).
cnf(refute_0_62,plain,
( or(X_10,or(P,not(X_10))) != implies(not(X_10),or(P,not(X_10)))
| implies(not(X_10),or(P,not(X_10))) = or(X_10,or(P,not(X_10))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X_10,or(P,not(X_10))))),bind(Y0,$fot(implies(not(X_10),or(P,not(X_10)))))]]) ).
cnf(refute_0_63,plain,
implies(not(X_10),or(P,not(X_10))) = or(X_10,or(P,not(X_10))),
inference(resolve,[$cnf( $equal(or(X_10,or(P,not(X_10))),implies(not(X_10),or(P,not(X_10)))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( implies(not(X_10),or(P,not(X_10))) != or(X_10,or(P,not(X_10)))
| ~ is_a_theorem(implies(not(X_10),or(P,not(X_10))))
| is_a_theorem(or(X_10,or(P,not(X_10)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X_10),or(P,not(X_10)))) ),[0],$fot(or(X_10,or(P,not(X_10))))]]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(implies(not(X_10),or(P,not(X_10))))
| is_a_theorem(or(X_10,or(P,not(X_10)))) ),
inference(resolve,[$cnf( $equal(implies(not(X_10),or(P,not(X_10))),or(X_10,or(P,not(X_10)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
is_a_theorem(or(X_10,or(P,not(X_10)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_10),or(P,not(X_10)))) )],[refute_0_48,refute_0_65]) ).
cnf(refute_0_67,plain,
is_a_theorem(or(not(X),or(X_39,not(not(X))))),
inference(subst,[],[refute_0_66:[bind(P,$fot(X_39)),bind(X_10,$fot(not(X)))]]) ).
cnf(refute_0_68,plain,
implies(X,or(X_39,not(not(X)))) = or(not(X),or(X_39,not(not(X)))),
inference(subst,[],[refute_0_9:[bind(Y,$fot(or(X_39,not(not(X)))))]]) ).
cnf(refute_0_69,plain,
( implies(X,or(X_39,not(not(X)))) != or(not(X),or(X_39,not(not(X))))
| or(not(X),or(X_39,not(not(X)))) = implies(X,or(X_39,not(not(X)))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,or(X_39,not(not(X)))))),bind(Y0,$fot(or(not(X),or(X_39,not(not(X))))))]]) ).
cnf(refute_0_70,plain,
or(not(X),or(X_39,not(not(X)))) = implies(X,or(X_39,not(not(X)))),
inference(resolve,[$cnf( $equal(implies(X,or(X_39,not(not(X)))),or(not(X),or(X_39,not(not(X))))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( or(not(X),or(X_39,not(not(X)))) != implies(X,or(X_39,not(not(X))))
| ~ is_a_theorem(or(not(X),or(X_39,not(not(X)))))
| is_a_theorem(implies(X,or(X_39,not(not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X),or(X_39,not(not(X))))) ),[0],$fot(implies(X,or(X_39,not(not(X)))))]]) ).
cnf(refute_0_72,plain,
( ~ is_a_theorem(or(not(X),or(X_39,not(not(X)))))
| is_a_theorem(implies(X,or(X_39,not(not(X))))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_39,not(not(X)))),implies(X,or(X_39,not(not(X))))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(X,or(X_39,not(not(X))))),
inference(resolve,[$cnf( is_a_theorem(or(not(X),or(X_39,not(not(X))))) )],[refute_0_67,refute_0_72]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(not(X),or(X_42,not(not(not(X)))))),
inference(subst,[],[refute_0_73:[bind(X,$fot(not(X))),bind(X_39,$fot(X_42))]]) ).
cnf(refute_0_75,plain,
or(X,or(X_42,not(not(not(X))))) = implies(not(X),or(X_42,not(not(not(X))))),
inference(subst,[],[refute_0_60:[bind(Y,$fot(or(X_42,not(not(not(X))))))]]) ).
cnf(refute_0_76,plain,
( or(X,or(X_42,not(not(not(X))))) != implies(not(X),or(X_42,not(not(not(X)))))
| implies(not(X),or(X_42,not(not(not(X))))) = or(X,or(X_42,not(not(not(X))))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,or(X_42,not(not(not(X))))))),bind(Y0,$fot(implies(not(X),or(X_42,not(not(not(X)))))))]]) ).
cnf(refute_0_77,plain,
implies(not(X),or(X_42,not(not(not(X))))) = or(X,or(X_42,not(not(not(X))))),
inference(resolve,[$cnf( $equal(or(X,or(X_42,not(not(not(X))))),implies(not(X),or(X_42,not(not(not(X)))))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
( implies(not(X),or(X_42,not(not(not(X))))) != or(X,or(X_42,not(not(not(X)))))
| ~ is_a_theorem(implies(not(X),or(X_42,not(not(not(X))))))
| is_a_theorem(or(X,or(X_42,not(not(not(X)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X),or(X_42,not(not(not(X)))))) ),[0],$fot(or(X,or(X_42,not(not(not(X))))))]]) ).
cnf(refute_0_79,plain,
( ~ is_a_theorem(implies(not(X),or(X_42,not(not(not(X))))))
| is_a_theorem(or(X,or(X_42,not(not(not(X)))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),or(X_42,not(not(not(X))))),or(X,or(X_42,not(not(not(X)))))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
is_a_theorem(or(X,or(X_42,not(not(not(X)))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X),or(X_42,not(not(not(X)))))) )],[refute_0_74,refute_0_79]) ).
cnf(refute_0_81,plain,
is_a_theorem(or(not(X),or(X_57,not(not(not(not(X))))))),
inference(subst,[],[refute_0_80:[bind(X,$fot(not(X))),bind(X_42,$fot(X_57))]]) ).
cnf(refute_0_82,plain,
implies(X,or(X_57,not(not(not(not(X)))))) = or(not(X),or(X_57,not(not(not(not(X)))))),
inference(subst,[],[refute_0_9:[bind(Y,$fot(or(X_57,not(not(not(not(X)))))))]]) ).
cnf(refute_0_83,plain,
( implies(X,or(X_57,not(not(not(not(X)))))) != or(not(X),or(X_57,not(not(not(not(X))))))
| or(not(X),or(X_57,not(not(not(not(X)))))) = implies(X,or(X_57,not(not(not(not(X)))))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,or(X_57,not(not(not(not(X)))))))),bind(Y0,$fot(or(not(X),or(X_57,not(not(not(not(X))))))))]]) ).
cnf(refute_0_84,plain,
or(not(X),or(X_57,not(not(not(not(X)))))) = implies(X,or(X_57,not(not(not(not(X)))))),
inference(resolve,[$cnf( $equal(implies(X,or(X_57,not(not(not(not(X)))))),or(not(X),or(X_57,not(not(not(not(X))))))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
( or(not(X),or(X_57,not(not(not(not(X)))))) != implies(X,or(X_57,not(not(not(not(X))))))
| ~ is_a_theorem(or(not(X),or(X_57,not(not(not(not(X)))))))
| is_a_theorem(implies(X,or(X_57,not(not(not(not(X))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X),or(X_57,not(not(not(not(X))))))) ),[0],$fot(implies(X,or(X_57,not(not(not(not(X)))))))]]) ).
cnf(refute_0_86,plain,
( ~ is_a_theorem(or(not(X),or(X_57,not(not(not(not(X)))))))
| is_a_theorem(implies(X,or(X_57,not(not(not(not(X))))))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_57,not(not(not(not(X)))))),implies(X,or(X_57,not(not(not(not(X))))))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
is_a_theorem(implies(X,or(X_57,not(not(not(not(X))))))),
inference(resolve,[$cnf( is_a_theorem(or(not(X),or(X_57,not(not(not(not(X))))))) )],[refute_0_81,refute_0_86]) ).
cnf(refute_0_88,plain,
is_a_theorem(implies(X_155,or(X_57,not(not(not(not(X_155))))))),
inference(subst,[],[refute_0_87:[bind(X,$fot(X_155))]]) ).
cnf(refute_0_89,plain,
( ~ is_a_theorem(X_155)
| ~ is_a_theorem(implies(X_155,or(X_57,not(not(not(not(X_155)))))))
| is_a_theorem(or(X_57,not(not(not(not(X_155)))))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(X_155)),bind(Y,$fot(or(X_57,not(not(not(not(X_155)))))))]]) ).
cnf(refute_0_90,plain,
( ~ is_a_theorem(X_155)
| is_a_theorem(or(X_57,not(not(not(not(X_155)))))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_155,or(X_57,not(not(not(not(X_155))))))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( ~ is_a_theorem(equiv(X_4516,X_4516))
| is_a_theorem(or(X_57,not(not(not(not(equiv(X_4516,X_4516))))))) ),
inference(subst,[],[refute_0_90:[bind(X_155,$fot(equiv(X_4516,X_4516)))]]) ).
cnf(refute_0_92,plain,
( ~ is_a_theorem(X_214)
| ~ is_a_theorem(implies(X_214,and(X_214,X_214)))
| is_a_theorem(and(X_214,X_214)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(X_214)),bind(Y,$fot(and(X_214,X_214)))]]) ).
cnf(refute_0_93,plain,
( ~ r1
| is_a_theorem(implies(or(P,P),P)) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_94,plain,
r1,
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_95,plain,
is_a_theorem(implies(or(P,P),P)),
inference(resolve,[$cnf( r1 )],[refute_0_94,refute_0_93]) ).
cnf(refute_0_96,plain,
is_a_theorem(implies(or(not(X_1),not(X_1)),not(X_1))),
inference(subst,[],[refute_0_95:[bind(P,$fot(not(X_1)))]]) ).
cnf(refute_0_97,plain,
implies(X_1,not(X_1)) = or(not(X_1),not(X_1)),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_1)),bind(Y,$fot(not(X_1)))]]) ).
cnf(refute_0_98,plain,
( implies(X_1,not(X_1)) != or(not(X_1),not(X_1))
| or(not(X_1),not(X_1)) = implies(X_1,not(X_1)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X_1,not(X_1)))),bind(Y0,$fot(or(not(X_1),not(X_1))))]]) ).
cnf(refute_0_99,plain,
or(not(X_1),not(X_1)) = implies(X_1,not(X_1)),
inference(resolve,[$cnf( $equal(implies(X_1,not(X_1)),or(not(X_1),not(X_1))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
( or(not(X_1),not(X_1)) != implies(X_1,not(X_1))
| ~ is_a_theorem(implies(or(not(X_1),not(X_1)),not(X_1)))
| is_a_theorem(implies(implies(X_1,not(X_1)),not(X_1))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X_1),not(X_1)),not(X_1))) ),[0,0],$fot(implies(X_1,not(X_1)))]]) ).
cnf(refute_0_101,plain,
( ~ is_a_theorem(implies(or(not(X_1),not(X_1)),not(X_1)))
| is_a_theorem(implies(implies(X_1,not(X_1)),not(X_1))) ),
inference(resolve,[$cnf( $equal(or(not(X_1),not(X_1)),implies(X_1,not(X_1))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
is_a_theorem(implies(implies(X_1,not(X_1)),not(X_1))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X_1),not(X_1)),not(X_1))) )],[refute_0_96,refute_0_101]) ).
cnf(refute_0_103,plain,
is_a_theorem(implies(implies(not(X_10),not(not(X_10))),not(not(X_10)))),
inference(subst,[],[refute_0_102:[bind(X_1,$fot(not(X_10)))]]) ).
cnf(refute_0_104,plain,
or(X_10,not(not(X_10))) = implies(not(X_10),not(not(X_10))),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_10)),bind(Y,$fot(not(not(X_10))))]]) ).
cnf(refute_0_105,plain,
( or(X_10,not(not(X_10))) != implies(not(X_10),not(not(X_10)))
| implies(not(X_10),not(not(X_10))) = or(X_10,not(not(X_10))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X_10,not(not(X_10))))),bind(Y0,$fot(implies(not(X_10),not(not(X_10)))))]]) ).
cnf(refute_0_106,plain,
implies(not(X_10),not(not(X_10))) = or(X_10,not(not(X_10))),
inference(resolve,[$cnf( $equal(or(X_10,not(not(X_10))),implies(not(X_10),not(not(X_10)))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
( implies(not(X_10),not(not(X_10))) != or(X_10,not(not(X_10)))
| ~ is_a_theorem(implies(implies(not(X_10),not(not(X_10))),not(not(X_10))))
| is_a_theorem(implies(or(X_10,not(not(X_10))),not(not(X_10)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X_10),not(not(X_10))),not(not(X_10)))) ),[0,0],$fot(or(X_10,not(not(X_10))))]]) ).
cnf(refute_0_108,plain,
( ~ is_a_theorem(implies(implies(not(X_10),not(not(X_10))),not(not(X_10))))
| is_a_theorem(implies(or(X_10,not(not(X_10))),not(not(X_10)))) ),
inference(resolve,[$cnf( $equal(implies(not(X_10),not(not(X_10))),or(X_10,not(not(X_10)))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
is_a_theorem(implies(or(X_10,not(not(X_10))),not(not(X_10)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_10),not(not(X_10))),not(not(X_10)))) )],[refute_0_103,refute_0_108]) ).
cnf(refute_0_110,plain,
is_a_theorem(implies(or(not(X),not(not(not(X)))),not(not(not(X))))),
inference(subst,[],[refute_0_109:[bind(X_10,$fot(not(X)))]]) ).
cnf(refute_0_111,plain,
implies(X,not(not(not(X)))) = or(not(X),not(not(not(X)))),
inference(subst,[],[refute_0_9:[bind(Y,$fot(not(not(not(X)))))]]) ).
cnf(refute_0_112,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_13:[bind(X0,$fot(implies(X,not(not(not(X)))))),bind(Y0,$fot(or(not(X),not(not(not(X))))))]]) ).
cnf(refute_0_113,plain,
or(not(X),not(not(not(X)))) = implies(X,not(not(not(X)))),
inference(resolve,[$cnf( $equal(implies(X,not(not(not(X)))),or(not(X),not(not(not(X))))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
( or(not(X),not(not(not(X)))) != implies(X,not(not(not(X))))
| ~ is_a_theorem(implies(or(not(X),not(not(not(X)))),not(not(not(X)))))
| is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),not(not(not(X)))),not(not(not(X))))) ),[0,0],$fot(implies(X,not(not(not(X)))))]]) ).
cnf(refute_0_115,plain,
( ~ is_a_theorem(implies(or(not(X),not(not(not(X)))),not(not(not(X)))))
| is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(not(not(X)))),implies(X,not(not(not(X))))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),not(not(not(X)))),not(not(not(X))))) )],[refute_0_110,refute_0_115]) ).
cnf(refute_0_117,plain,
implies(implies(X_16,not(X_17)),Y) = or(not(implies(X_16,not(X_17))),Y),
inference(subst,[],[refute_0_9:[bind(X,$fot(implies(X_16,not(X_17))))]]) ).
cnf(refute_0_118,plain,
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_119,plain,
op_and,
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_120,plain,
and(X,Y) = not(or(not(X),not(Y))),
inference(resolve,[$cnf( op_and )],[refute_0_119,refute_0_118]) ).
cnf(refute_0_121,plain,
or(not(X),not(Y)) = implies(X,not(Y)),
inference(subst,[],[refute_0_20:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_122,plain,
not(or(not(X),not(Y))) = not(or(not(X),not(Y))),
introduced(tautology,[refl,[$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_123,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_124,plain,
( or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
not(or(not(X),not(Y))) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),implies(X,not(Y))) )],[refute_0_121,refute_0_124]) ).
cnf(refute_0_126,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) != not(implies(X,not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,Y),not(implies(X,not(Y)))) ),[0],$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_127,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(implies(X,not(Y)))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
and(X,Y) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[refute_0_120,refute_0_127]) ).
cnf(refute_0_129,plain,
and(X_16,X_17) = not(implies(X_16,not(X_17))),
inference(subst,[],[refute_0_128:[bind(X,$fot(X_16)),bind(Y,$fot(X_17))]]) ).
cnf(refute_0_130,plain,
( and(X_16,X_17) != not(implies(X_16,not(X_17)))
| not(implies(X_16,not(X_17))) = and(X_16,X_17) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(X_16,X_17))),bind(Y0,$fot(not(implies(X_16,not(X_17)))))]]) ).
cnf(refute_0_131,plain,
not(implies(X_16,not(X_17))) = and(X_16,X_17),
inference(resolve,[$cnf( $equal(and(X_16,X_17),not(implies(X_16,not(X_17)))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
( implies(implies(X_16,not(X_17)),Y) != or(not(implies(X_16,not(X_17))),Y)
| not(implies(X_16,not(X_17))) != and(X_16,X_17)
| implies(implies(X_16,not(X_17)),Y) = or(and(X_16,X_17),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,not(X_17)),Y),or(not(implies(X_16,not(X_17))),Y)) ),[1,0],$fot(and(X_16,X_17))]]) ).
cnf(refute_0_133,plain,
( implies(implies(X_16,not(X_17)),Y) != or(not(implies(X_16,not(X_17))),Y)
| implies(implies(X_16,not(X_17)),Y) = or(and(X_16,X_17),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_16,not(X_17))),and(X_16,X_17)) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
implies(implies(X_16,not(X_17)),Y) = or(and(X_16,X_17),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_16,not(X_17)),Y),or(not(implies(X_16,not(X_17))),Y)) )],[refute_0_117,refute_0_133]) ).
cnf(refute_0_135,plain,
implies(implies(X,not(X)),not(not(not(X)))) = or(and(X,X),not(not(not(X)))),
inference(subst,[],[refute_0_134:[bind(Y,$fot(not(not(not(X))))),bind(X_16,$fot(X)),bind(X_17,$fot(X))]]) ).
cnf(refute_0_136,plain,
or(and(X,not(Y)),X_11) = implies(not(and(X,not(Y))),X_11),
inference(subst,[],[refute_0_60:[bind(X,$fot(and(X,not(Y)))),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_137,plain,
( not(and(X,not(Y))) != implies(X,Y)
| or(and(X,not(Y)),X_11) != implies(not(and(X,not(Y))),X_11)
| or(and(X,not(Y)),X_11) = implies(implies(X,Y),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X,not(Y)),X_11),implies(not(and(X,not(Y))),X_11)) ),[1,0],$fot(implies(X,Y))]]) ).
cnf(refute_0_138,plain,
( or(and(X,not(Y)),X_11) != implies(not(and(X,not(Y))),X_11)
| or(and(X,not(Y)),X_11) = implies(implies(X,Y),X_11) ),
inference(resolve,[$cnf( $equal(not(and(X,not(Y))),implies(X,Y)) )],[refute_0_56,refute_0_137]) ).
cnf(refute_0_139,plain,
or(and(X,not(Y)),X_11) = implies(implies(X,Y),X_11),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),X_11),implies(not(and(X,not(Y))),X_11)) )],[refute_0_136,refute_0_138]) ).
cnf(refute_0_140,plain,
or(and(X,not(not(X))),not(not(not(X)))) = implies(implies(X,not(X)),not(not(not(X)))),
inference(subst,[],[refute_0_139:[bind(Y,$fot(not(X))),bind(X_11,$fot(not(not(not(X)))))]]) ).
cnf(refute_0_141,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_142,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_13,refute_0_141]) ).
cnf(refute_0_143,plain,
( implies(implies(X,not(X)),not(not(not(X)))) != or(and(X,X),not(not(not(X))))
| or(and(X,not(not(X))),not(not(not(X)))) != implies(implies(X,not(X)),not(not(not(X))))
| or(and(X,not(not(X))),not(not(not(X)))) = or(and(X,X),not(not(not(X)))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(or(and(X,not(not(X))),not(not(not(X)))))),bind(Y0,$fot(implies(implies(X,not(X)),not(not(not(X)))))),bind(Z,$fot(or(and(X,X),not(not(not(X))))))]]) ).
cnf(refute_0_144,plain,
( implies(implies(X,not(X)),not(not(not(X)))) != or(and(X,X),not(not(not(X))))
| or(and(X,not(not(X))),not(not(not(X)))) = or(and(X,X),not(not(not(X)))) ),
inference(resolve,[$cnf( $equal(or(and(X,not(not(X))),not(not(not(X)))),implies(implies(X,not(X)),not(not(not(X))))) )],[refute_0_140,refute_0_143]) ).
cnf(refute_0_145,plain,
or(and(X,not(not(X))),not(not(not(X)))) = or(and(X,X),not(not(not(X)))),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X)),not(not(not(X)))),or(and(X,X),not(not(not(X))))) )],[refute_0_135,refute_0_144]) ).
cnf(refute_0_146,plain,
implies(implies(X,not(not(not(X)))),not(not(not(X)))) = or(and(X,not(not(X))),not(not(not(X)))),
inference(subst,[],[refute_0_134:[bind(Y,$fot(not(not(not(X))))),bind(X_16,$fot(X)),bind(X_17,$fot(not(not(X))))]]) ).
cnf(refute_0_147,plain,
( implies(implies(X,not(not(not(X)))),not(not(not(X)))) != or(and(X,not(not(X))),not(not(not(X))))
| or(and(X,not(not(X))),not(not(not(X)))) != or(and(X,X),not(not(not(X))))
| implies(implies(X,not(not(not(X)))),not(not(not(X)))) = or(and(X,X),not(not(not(X)))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(implies(X,not(not(not(X)))),not(not(not(X)))))),bind(Y0,$fot(or(and(X,not(not(X))),not(not(not(X)))))),bind(Z,$fot(or(and(X,X),not(not(not(X))))))]]) ).
cnf(refute_0_148,plain,
( or(and(X,not(not(X))),not(not(not(X)))) != or(and(X,X),not(not(not(X))))
| implies(implies(X,not(not(not(X)))),not(not(not(X)))) = or(and(X,X),not(not(not(X)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(not(not(X)))),not(not(not(X)))),or(and(X,not(not(X))),not(not(not(X))))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
implies(implies(X,not(not(not(X)))),not(not(not(X)))) = or(and(X,X),not(not(not(X)))),
inference(resolve,[$cnf( $equal(or(and(X,not(not(X))),not(not(not(X)))),or(and(X,X),not(not(not(X))))) )],[refute_0_145,refute_0_148]) ).
cnf(refute_0_150,plain,
( implies(implies(X,not(not(not(X)))),not(not(not(X)))) != or(and(X,X),not(not(not(X))))
| ~ is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X)))))
| is_a_theorem(or(and(X,X),not(not(not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X))))) ),[0],$fot(or(and(X,X),not(not(not(X)))))]]) ).
cnf(refute_0_151,plain,
( ~ is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X)))))
| is_a_theorem(or(and(X,X),not(not(not(X))))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(not(not(X)))),not(not(not(X)))),or(and(X,X),not(not(not(X))))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
is_a_theorem(or(and(X,X),not(not(not(X))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X))))) )],[refute_0_116,refute_0_151]) ).
cnf(refute_0_153,plain,
is_a_theorem(or(and(not(X_91),not(X_91)),not(not(not(not(X_91)))))),
inference(subst,[],[refute_0_152:[bind(X,$fot(not(X_91)))]]) ).
cnf(refute_0_154,plain,
or(and(not(X_91),not(X_91)),not(not(not(not(X_91))))) = implies(implies(not(X_91),X_91),not(not(not(not(X_91))))),
inference(subst,[],[refute_0_139:[bind(X,$fot(not(X_91))),bind(Y,$fot(X_91)),bind(X_11,$fot(not(not(not(not(X_91))))))]]) ).
cnf(refute_0_155,plain,
( or(and(not(X_91),not(X_91)),not(not(not(not(X_91))))) != implies(implies(not(X_91),X_91),not(not(not(not(X_91)))))
| ~ is_a_theorem(or(and(not(X_91),not(X_91)),not(not(not(not(X_91))))))
| is_a_theorem(implies(implies(not(X_91),X_91),not(not(not(not(X_91)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(X_91),not(X_91)),not(not(not(not(X_91)))))) ),[0],$fot(implies(implies(not(X_91),X_91),not(not(not(not(X_91))))))]]) ).
cnf(refute_0_156,plain,
( ~ is_a_theorem(or(and(not(X_91),not(X_91)),not(not(not(not(X_91))))))
| is_a_theorem(implies(implies(not(X_91),X_91),not(not(not(not(X_91)))))) ),
inference(resolve,[$cnf( $equal(or(and(not(X_91),not(X_91)),not(not(not(not(X_91))))),implies(implies(not(X_91),X_91),not(not(not(not(X_91)))))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
is_a_theorem(implies(implies(not(X_91),X_91),not(not(not(not(X_91)))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(X_91),not(X_91)),not(not(not(not(X_91)))))) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_159,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[refute_0_60,refute_0_158]) ).
cnf(refute_0_160,plain,
implies(not(X_91),X_91) = or(X_91,X_91),
inference(subst,[],[refute_0_159:[bind(X,$fot(X_91)),bind(Y,$fot(X_91))]]) ).
cnf(refute_0_161,plain,
implies(implies(not(X_91),X_91),not(not(not(not(X_91))))) = implies(implies(not(X_91),X_91),not(not(not(not(X_91))))),
introduced(tautology,[refl,[$fot(implies(implies(not(X_91),X_91),not(not(not(not(X_91))))))]]) ).
cnf(refute_0_162,plain,
( implies(implies(not(X_91),X_91),not(not(not(not(X_91))))) != implies(implies(not(X_91),X_91),not(not(not(not(X_91)))))
| implies(not(X_91),X_91) != or(X_91,X_91)
| implies(implies(not(X_91),X_91),not(not(not(not(X_91))))) = implies(or(X_91,X_91),not(not(not(not(X_91))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_91),X_91),not(not(not(not(X_91))))),implies(implies(not(X_91),X_91),not(not(not(not(X_91)))))) ),[1,0],$fot(or(X_91,X_91))]]) ).
cnf(refute_0_163,plain,
( implies(not(X_91),X_91) != or(X_91,X_91)
| implies(implies(not(X_91),X_91),not(not(not(not(X_91))))) = implies(or(X_91,X_91),not(not(not(not(X_91))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_91),X_91),not(not(not(not(X_91))))),implies(implies(not(X_91),X_91),not(not(not(not(X_91)))))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
implies(implies(not(X_91),X_91),not(not(not(not(X_91))))) = implies(or(X_91,X_91),not(not(not(not(X_91))))),
inference(resolve,[$cnf( $equal(implies(not(X_91),X_91),or(X_91,X_91)) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
( implies(implies(not(X_91),X_91),not(not(not(not(X_91))))) != implies(or(X_91,X_91),not(not(not(not(X_91)))))
| ~ is_a_theorem(implies(implies(not(X_91),X_91),not(not(not(not(X_91))))))
| is_a_theorem(implies(or(X_91,X_91),not(not(not(not(X_91)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X_91),X_91),not(not(not(not(X_91)))))) ),[0],$fot(implies(or(X_91,X_91),not(not(not(not(X_91))))))]]) ).
cnf(refute_0_166,plain,
( ~ is_a_theorem(implies(implies(not(X_91),X_91),not(not(not(not(X_91))))))
| is_a_theorem(implies(or(X_91,X_91),not(not(not(not(X_91)))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_91),X_91),not(not(not(not(X_91))))),implies(or(X_91,X_91),not(not(not(not(X_91)))))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
is_a_theorem(implies(or(X_91,X_91),not(not(not(not(X_91)))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_91),X_91),not(not(not(not(X_91)))))) )],[refute_0_157,refute_0_166]) ).
cnf(refute_0_168,plain,
is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(X))))))),
inference(subst,[],[refute_0_167:[bind(X_91,$fot(not(X)))]]) ).
cnf(refute_0_169,plain,
implies(X,not(X)) = or(not(X),not(X)),
inference(subst,[],[refute_0_9:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_170,plain,
( implies(X,not(X)) != or(not(X),not(X))
| or(not(X),not(X)) = implies(X,not(X)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,not(X)))),bind(Y0,$fot(or(not(X),not(X))))]]) ).
cnf(refute_0_171,plain,
or(not(X),not(X)) = implies(X,not(X)),
inference(resolve,[$cnf( $equal(implies(X,not(X)),or(not(X),not(X))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
( or(not(X),not(X)) != implies(X,not(X))
| ~ is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(X)))))))
| is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(X))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(X))))))) ),[0,0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_173,plain,
( ~ is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(X)))))))
| is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(X))))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(X))))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(X))))))) )],[refute_0_168,refute_0_173]) ).
cnf(refute_0_175,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_134:[bind(Y,$fot(not(not(not(not(not(X))))))),bind(X_16,$fot(X)),bind(X_17,$fot(X))]]) ).
cnf(refute_0_176,plain,
( implies(implies(X,not(X)),not(not(not(not(not(X)))))) != or(and(X,X),not(not(not(not(not(X))))))
| ~ is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(X)))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(X))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(X))))))) ),[0],$fot(or(and(X,X),not(not(not(not(not(X)))))))]]) ).
cnf(refute_0_177,plain,
( ~ is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(X)))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(X))))))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X)),not(not(not(not(not(X)))))),or(and(X,X),not(not(not(not(not(X))))))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
is_a_theorem(or(and(X,X),not(not(not(not(not(X))))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(X))))))) )],[refute_0_174,refute_0_177]) ).
cnf(refute_0_179,plain,
is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(X))))))))),
inference(subst,[],[refute_0_178:[bind(X,$fot(not(not(X))))]]) ).
cnf(refute_0_180,plain,
and(not(X),X_17) = not(implies(not(X),not(X_17))),
inference(subst,[],[refute_0_128:[bind(X,$fot(not(X))),bind(Y,$fot(X_17))]]) ).
cnf(refute_0_181,plain,
or(X,not(X_17)) = implies(not(X),not(X_17)),
inference(subst,[],[refute_0_60:[bind(Y,$fot(not(X_17)))]]) ).
cnf(refute_0_182,plain,
( or(X,not(X_17)) != implies(not(X),not(X_17))
| implies(not(X),not(X_17)) = or(X,not(X_17)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,not(X_17)))),bind(Y0,$fot(implies(not(X),not(X_17))))]]) ).
cnf(refute_0_183,plain,
implies(not(X),not(X_17)) = or(X,not(X_17)),
inference(resolve,[$cnf( $equal(or(X,not(X_17)),implies(not(X),not(X_17))) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
( and(not(X),X_17) != not(implies(not(X),not(X_17)))
| implies(not(X),not(X_17)) != or(X,not(X_17))
| and(not(X),X_17) = not(or(X,not(X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(X),X_17),not(implies(not(X),not(X_17)))) ),[1,0],$fot(or(X,not(X_17)))]]) ).
cnf(refute_0_185,plain,
( and(not(X),X_17) != not(implies(not(X),not(X_17)))
| and(not(X),X_17) = not(or(X,not(X_17))) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X_17)),or(X,not(X_17))) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
and(not(X),X_17) = not(or(X,not(X_17))),
inference(resolve,[$cnf( $equal(and(not(X),X_17),not(implies(not(X),not(X_17)))) )],[refute_0_180,refute_0_185]) ).
cnf(refute_0_187,plain,
and(not(not(X)),X_20) = not(or(not(X),not(X_20))),
inference(subst,[],[refute_0_186:[bind(X,$fot(not(X))),bind(X_17,$fot(X_20))]]) ).
cnf(refute_0_188,plain,
implies(X,not(X_20)) = or(not(X),not(X_20)),
inference(subst,[],[refute_0_9:[bind(Y,$fot(not(X_20)))]]) ).
cnf(refute_0_189,plain,
( implies(X,not(X_20)) != or(not(X),not(X_20))
| or(not(X),not(X_20)) = implies(X,not(X_20)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,not(X_20)))),bind(Y0,$fot(or(not(X),not(X_20))))]]) ).
cnf(refute_0_190,plain,
or(not(X),not(X_20)) = implies(X,not(X_20)),
inference(resolve,[$cnf( $equal(implies(X,not(X_20)),or(not(X),not(X_20))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
( and(not(not(X)),X_20) != not(or(not(X),not(X_20)))
| or(not(X),not(X_20)) != implies(X,not(X_20))
| and(not(not(X)),X_20) = not(implies(X,not(X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X)),X_20),not(or(not(X),not(X_20)))) ),[1,0],$fot(implies(X,not(X_20)))]]) ).
cnf(refute_0_192,plain,
( and(not(not(X)),X_20) != not(or(not(X),not(X_20)))
| and(not(not(X)),X_20) = not(implies(X,not(X_20))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_20)),implies(X,not(X_20))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
and(not(not(X)),X_20) = not(implies(X,not(X_20))),
inference(resolve,[$cnf( $equal(and(not(not(X)),X_20),not(or(not(X),not(X_20)))) )],[refute_0_187,refute_0_192]) ).
cnf(refute_0_194,plain,
( and(X,Y) != not(implies(X,not(Y)))
| not(implies(X,not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(implies(X,not(Y)))))]]) ).
cnf(refute_0_195,plain,
not(implies(X,not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(implies(X,not(Y)))) )],[refute_0_128,refute_0_194]) ).
cnf(refute_0_196,plain,
not(implies(X,not(X_20))) = and(X,X_20),
inference(subst,[],[refute_0_195:[bind(Y,$fot(X_20))]]) ).
cnf(refute_0_197,plain,
( and(not(not(X)),X_20) != not(implies(X,not(X_20)))
| not(implies(X,not(X_20))) != and(X,X_20)
| and(not(not(X)),X_20) = and(X,X_20) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(not(not(X)),X_20),and(X,X_20)) ),[0],$fot(not(implies(X,not(X_20))))]]) ).
cnf(refute_0_198,plain,
( and(not(not(X)),X_20) != not(implies(X,not(X_20)))
| and(not(not(X)),X_20) = and(X,X_20) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(X_20))),and(X,X_20)) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
and(not(not(X)),X_20) = and(X,X_20),
inference(resolve,[$cnf( $equal(and(not(not(X)),X_20),not(implies(X,not(X_20)))) )],[refute_0_193,refute_0_198]) ).
cnf(refute_0_200,plain,
and(not(not(X)),not(not(X))) = and(X,not(not(X))),
inference(subst,[],[refute_0_199:[bind(X_20,$fot(not(not(X))))]]) ).
cnf(refute_0_201,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_202,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( $equal(and(not(not(X)),not(not(X))),and(X,not(not(X)))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X))))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(X))))))))) )],[refute_0_179,refute_0_202]) ).
cnf(refute_0_204,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_134:[bind(Y,$fot(not(not(not(not(not(not(not(X))))))))),bind(X_16,$fot(X)),bind(X_17,$fot(X))]]) ).
cnf(refute_0_205,plain,
or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))) = implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))),
inference(subst,[],[refute_0_139:[bind(Y,$fot(not(X))),bind(X_11,$fot(not(not(not(not(not(not(not(X)))))))))]]) ).
cnf(refute_0_206,plain,
( implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))) != or(and(X,X),not(not(not(not(not(not(not(X))))))))
| or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))) != implies(implies(X,not(X)),not(not(not(not(not(not(not(X))))))))
| or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))) = or(and(X,X),not(not(not(not(not(not(not(X)))))))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))))),bind(Y0,$fot(implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))))),bind(Z,$fot(or(and(X,X),not(not(not(not(not(not(not(X))))))))))]]) ).
cnf(refute_0_207,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( $equal(or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))),implies(implies(X,not(X)),not(not(not(not(not(not(not(X))))))))) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))) = or(and(X,X),not(not(not(not(not(not(not(X)))))))),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))),or(and(X,X),not(not(not(not(not(not(not(X))))))))) )],[refute_0_204,refute_0_207]) ).
cnf(refute_0_209,plain,
( or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))) != or(and(X,X),not(not(not(not(not(not(not(X))))))))
| ~ is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(X))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X))))))))) ),[0],$fot(or(and(X,X),not(not(not(not(not(not(not(X)))))))))]]) ).
cnf(refute_0_210,plain,
( ~ is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(X))))))))) ),
inference(resolve,[$cnf( $equal(or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))),or(and(X,X),not(not(not(not(not(not(not(X))))))))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(X))))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X))))))))) )],[refute_0_203,refute_0_210]) ).
cnf(refute_0_212,plain,
( ~ is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(X)))))))))
| is_a_theorem(or(not(not(not(not(not(not(not(X))))))),and(X,X))) ),
inference(subst,[],[refute_0_43:[bind(P,$fot(and(X,X))),bind(Q,$fot(not(not(not(not(not(not(not(X)))))))))]]) ).
cnf(refute_0_213,plain,
is_a_theorem(or(not(not(not(not(not(not(not(X))))))),and(X,X))),
inference(resolve,[$cnf( is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(X))))))))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
or(not(X),and(X,X)) = implies(X,and(X,X)),
inference(subst,[],[refute_0_20:[bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_215,plain,
implies(not(not(X)),and(X,X)) = or(not(X),and(X,X)),
inference(subst,[],[refute_0_159:[bind(X,$fot(not(X))),bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_216,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_142:[bind(X0,$fot(implies(not(not(X)),and(X,X)))),bind(Y0,$fot(or(not(X),and(X,X)))),bind(Z,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_217,plain,
( or(not(X),and(X,X)) != implies(X,and(X,X))
| implies(not(not(X)),and(X,X)) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(implies(not(not(X)),and(X,X)),or(not(X),and(X,X))) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
implies(not(not(X)),and(X,X)) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(or(not(X),and(X,X)),implies(X,and(X,X))) )],[refute_0_214,refute_0_217]) ).
cnf(refute_0_219,plain,
or(not(not(not(X))),and(X,X)) = implies(not(not(X)),and(X,X)),
inference(subst,[],[refute_0_20:[bind(X,$fot(not(not(X)))),bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_220,plain,
( implies(not(not(X)),and(X,X)) != implies(X,and(X,X))
| or(not(not(not(X))),and(X,X)) != implies(not(not(X)),and(X,X))
| or(not(not(not(X))),and(X,X)) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(or(not(not(not(X))),and(X,X)))),bind(Y0,$fot(implies(not(not(X)),and(X,X)))),bind(Z,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_221,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( $equal(or(not(not(not(X))),and(X,X)),implies(not(not(X)),and(X,X))) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
or(not(not(not(X))),and(X,X)) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(implies(not(not(X)),and(X,X)),implies(X,and(X,X))) )],[refute_0_218,refute_0_221]) ).
cnf(refute_0_223,plain,
implies(not(not(not(not(X)))),and(X,X)) = or(not(not(not(X))),and(X,X)),
inference(subst,[],[refute_0_159:[bind(X,$fot(not(not(not(X))))),bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_224,plain,
( implies(not(not(not(not(X)))),and(X,X)) != or(not(not(not(X))),and(X,X))
| or(not(not(not(X))),and(X,X)) != implies(X,and(X,X))
| implies(not(not(not(not(X)))),and(X,X)) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(not(not(not(not(X)))),and(X,X)))),bind(Y0,$fot(or(not(not(not(X))),and(X,X)))),bind(Z,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_225,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( $equal(implies(not(not(not(not(X)))),and(X,X)),or(not(not(not(X))),and(X,X))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
implies(not(not(not(not(X)))),and(X,X)) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(or(not(not(not(X))),and(X,X)),implies(X,and(X,X))) )],[refute_0_222,refute_0_225]) ).
cnf(refute_0_227,plain,
or(not(not(not(not(not(X))))),and(X,X)) = implies(not(not(not(not(X)))),and(X,X)),
inference(subst,[],[refute_0_20:[bind(X,$fot(not(not(not(not(X)))))),bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_228,plain,
( implies(not(not(not(not(X)))),and(X,X)) != implies(X,and(X,X))
| or(not(not(not(not(not(X))))),and(X,X)) != implies(not(not(not(not(X)))),and(X,X))
| or(not(not(not(not(not(X))))),and(X,X)) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(or(not(not(not(not(not(X))))),and(X,X)))),bind(Y0,$fot(implies(not(not(not(not(X)))),and(X,X)))),bind(Z,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_229,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( $equal(or(not(not(not(not(not(X))))),and(X,X)),implies(not(not(not(not(X)))),and(X,X))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
or(not(not(not(not(not(X))))),and(X,X)) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(X)))),and(X,X)),implies(X,and(X,X))) )],[refute_0_226,refute_0_229]) ).
cnf(refute_0_231,plain,
implies(not(not(not(not(not(not(X)))))),and(X,X)) = or(not(not(not(not(not(X))))),and(X,X)),
inference(subst,[],[refute_0_159:[bind(X,$fot(not(not(not(not(not(X))))))),bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_232,plain,
( implies(not(not(not(not(not(not(X)))))),and(X,X)) != or(not(not(not(not(not(X))))),and(X,X))
| or(not(not(not(not(not(X))))),and(X,X)) != implies(X,and(X,X))
| implies(not(not(not(not(not(not(X)))))),and(X,X)) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(not(not(not(not(not(not(X)))))),and(X,X)))),bind(Y0,$fot(or(not(not(not(not(not(X))))),and(X,X)))),bind(Z,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_233,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( $equal(implies(not(not(not(not(not(not(X)))))),and(X,X)),or(not(not(not(not(not(X))))),and(X,X))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
implies(not(not(not(not(not(not(X)))))),and(X,X)) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(X))))),and(X,X)),implies(X,and(X,X))) )],[refute_0_230,refute_0_233]) ).
cnf(refute_0_235,plain,
or(not(not(not(not(not(not(not(X))))))),and(X,X)) = implies(not(not(not(not(not(not(X)))))),and(X,X)),
inference(subst,[],[refute_0_20:[bind(X,$fot(not(not(not(not(not(not(X)))))))),bind(Y,$fot(and(X,X)))]]) ).
cnf(refute_0_236,plain,
( implies(not(not(not(not(not(not(X)))))),and(X,X)) != implies(X,and(X,X))
| or(not(not(not(not(not(not(not(X))))))),and(X,X)) != implies(not(not(not(not(not(not(X)))))),and(X,X))
| or(not(not(not(not(not(not(not(X))))))),and(X,X)) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(or(not(not(not(not(not(not(not(X))))))),and(X,X)))),bind(Y0,$fot(implies(not(not(not(not(not(not(X)))))),and(X,X)))),bind(Z,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_237,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( $equal(or(not(not(not(not(not(not(not(X))))))),and(X,X)),implies(not(not(not(not(not(not(X)))))),and(X,X))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
or(not(not(not(not(not(not(not(X))))))),and(X,X)) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(X)))))),and(X,X)),implies(X,and(X,X))) )],[refute_0_234,refute_0_237]) ).
cnf(refute_0_239,plain,
( or(not(not(not(not(not(not(not(X))))))),and(X,X)) != implies(X,and(X,X))
| ~ is_a_theorem(or(not(not(not(not(not(not(not(X))))))),and(X,X)))
| is_a_theorem(implies(X,and(X,X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(not(not(not(not(not(not(X))))))),and(X,X))) ),[0],$fot(implies(X,and(X,X)))]]) ).
cnf(refute_0_240,plain,
( ~ is_a_theorem(or(not(not(not(not(not(not(not(X))))))),and(X,X)))
| is_a_theorem(implies(X,and(X,X))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(not(X))))))),and(X,X)),implies(X,and(X,X))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
is_a_theorem(implies(X,and(X,X))),
inference(resolve,[$cnf( is_a_theorem(or(not(not(not(not(not(not(not(X))))))),and(X,X))) )],[refute_0_213,refute_0_240]) ).
cnf(refute_0_242,plain,
is_a_theorem(implies(X_214,and(X_214,X_214))),
inference(subst,[],[refute_0_241:[bind(X,$fot(X_214))]]) ).
cnf(refute_0_243,plain,
( ~ is_a_theorem(X_214)
| is_a_theorem(and(X_214,X_214)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_214,and(X_214,X_214))) )],[refute_0_242,refute_0_92]) ).
cnf(refute_0_244,plain,
( ~ is_a_theorem(implies(X_4515,X_4515))
| is_a_theorem(and(implies(X_4515,X_4515),implies(X_4515,X_4515))) ),
inference(subst,[],[refute_0_243:[bind(X_214,$fot(implies(X_4515,X_4515)))]]) ).
cnf(refute_0_245,plain,
( ~ is_a_theorem(or(X_4514,not(X_4514)))
| is_a_theorem(or(not(X_4514),X_4514)) ),
inference(subst,[],[refute_0_43:[bind(P,$fot(X_4514)),bind(Q,$fot(not(X_4514)))]]) ).
cnf(refute_0_246,plain,
is_a_theorem(implies(or(X_156,X_156),X_156)),
inference(subst,[],[refute_0_95:[bind(P,$fot(X_156))]]) ).
cnf(refute_0_247,plain,
( ~ is_a_theorem(implies(or(X_156,X_156),X_156))
| ~ is_a_theorem(or(X_156,X_156))
| is_a_theorem(X_156) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(or(X_156,X_156))),bind(Y,$fot(X_156))]]) ).
cnf(refute_0_248,plain,
( ~ is_a_theorem(or(X_156,X_156))
| is_a_theorem(X_156) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_156,X_156),X_156)) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
( ~ is_a_theorem(or(or(X_4513,not(X_4513)),or(X_4513,not(X_4513))))
| is_a_theorem(or(X_4513,not(X_4513))) ),
inference(subst,[],[refute_0_248:[bind(X_156,$fot(or(X_4513,not(X_4513))))]]) ).
cnf(refute_0_250,plain,
( ~ is_a_theorem(or(X_103,implies(X,not(X_103))))
| is_a_theorem(implies(X,or(X_103,not(X_103)))) ),
inference(subst,[],[refute_0_37:[bind(X_105,$fot(not(X_103)))]]) ).
cnf(refute_0_251,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_252,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_253,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_252,refute_0_251]) ).
cnf(refute_0_254,plain,
( ~ is_a_theorem(equiv(or(X_918,implies(X_917,not(X_918))),or(X_918,not(and(X_917,X_918)))))
| or(X_918,implies(X_917,not(X_918))) = or(X_918,not(and(X_917,X_918))) ),
inference(subst,[],[refute_0_253:[bind(X,$fot(or(X_918,implies(X_917,not(X_918))))),bind(Y,$fot(or(X_918,not(and(X_917,X_918)))))]]) ).
cnf(refute_0_255,plain,
is_a_theorem(implies(X_7,or(not(X),X_7))),
inference(subst,[],[refute_0_47:[bind(P,$fot(not(X))),bind(Q,$fot(X_7))]]) ).
cnf(refute_0_256,plain,
implies(X,X_7) = or(not(X),X_7),
inference(subst,[],[refute_0_9:[bind(Y,$fot(X_7))]]) ).
cnf(refute_0_257,plain,
( implies(X,X_7) != or(not(X),X_7)
| or(not(X),X_7) = implies(X,X_7) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,X_7))),bind(Y0,$fot(or(not(X),X_7)))]]) ).
cnf(refute_0_258,plain,
or(not(X),X_7) = implies(X,X_7),
inference(resolve,[$cnf( $equal(implies(X,X_7),or(not(X),X_7)) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
( or(not(X),X_7) != implies(X,X_7)
| ~ is_a_theorem(implies(X_7,or(not(X),X_7)))
| is_a_theorem(implies(X_7,implies(X,X_7))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_7,or(not(X),X_7))) ),[0,1],$fot(implies(X,X_7))]]) ).
cnf(refute_0_260,plain,
( ~ is_a_theorem(implies(X_7,or(not(X),X_7)))
| is_a_theorem(implies(X_7,implies(X,X_7))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_7),implies(X,X_7)) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
is_a_theorem(implies(X_7,implies(X,X_7))),
inference(resolve,[$cnf( is_a_theorem(implies(X_7,or(not(X),X_7))) )],[refute_0_255,refute_0_260]) ).
cnf(refute_0_262,plain,
is_a_theorem(implies(not(X_10),implies(X,not(X_10)))),
inference(subst,[],[refute_0_261:[bind(X_7,$fot(not(X_10)))]]) ).
cnf(refute_0_263,plain,
or(X_10,implies(X,not(X_10))) = implies(not(X_10),implies(X,not(X_10))),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_10)),bind(Y,$fot(implies(X,not(X_10))))]]) ).
cnf(refute_0_264,plain,
( or(X_10,implies(X,not(X_10))) != implies(not(X_10),implies(X,not(X_10)))
| implies(not(X_10),implies(X,not(X_10))) = or(X_10,implies(X,not(X_10))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X_10,implies(X,not(X_10))))),bind(Y0,$fot(implies(not(X_10),implies(X,not(X_10)))))]]) ).
cnf(refute_0_265,plain,
implies(not(X_10),implies(X,not(X_10))) = or(X_10,implies(X,not(X_10))),
inference(resolve,[$cnf( $equal(or(X_10,implies(X,not(X_10))),implies(not(X_10),implies(X,not(X_10)))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
( implies(not(X_10),implies(X,not(X_10))) != or(X_10,implies(X,not(X_10)))
| ~ is_a_theorem(implies(not(X_10),implies(X,not(X_10))))
| is_a_theorem(or(X_10,implies(X,not(X_10)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X_10),implies(X,not(X_10)))) ),[0],$fot(or(X_10,implies(X,not(X_10))))]]) ).
cnf(refute_0_267,plain,
( ~ is_a_theorem(implies(not(X_10),implies(X,not(X_10))))
| is_a_theorem(or(X_10,implies(X,not(X_10)))) ),
inference(resolve,[$cnf( $equal(implies(not(X_10),implies(X,not(X_10))),or(X_10,implies(X,not(X_10)))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
is_a_theorem(or(X_10,implies(X,not(X_10)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_10),implies(X,not(X_10)))) )],[refute_0_262,refute_0_267]) ).
cnf(refute_0_269,plain,
is_a_theorem(implies(X_155,implies(X,X_155))),
inference(subst,[],[refute_0_261:[bind(X_7,$fot(X_155))]]) ).
cnf(refute_0_270,plain,
( ~ is_a_theorem(X_155)
| ~ is_a_theorem(implies(X_155,implies(X,X_155)))
| is_a_theorem(implies(X,X_155)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(X_155)),bind(Y,$fot(implies(X,X_155)))]]) ).
cnf(refute_0_271,plain,
( ~ is_a_theorem(X_155)
| is_a_theorem(implies(X,X_155)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_155,implies(X,X_155))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
( ~ is_a_theorem(or(X_10,implies(X,not(X_10))))
| is_a_theorem(implies(X_241,or(X_10,implies(X,not(X_10))))) ),
inference(subst,[],[refute_0_271:[bind(X,$fot(X_241)),bind(X_155,$fot(or(X_10,implies(X,not(X_10)))))]]) ).
cnf(refute_0_273,plain,
is_a_theorem(implies(X_241,or(X_10,implies(X,not(X_10))))),
inference(resolve,[$cnf( is_a_theorem(or(X_10,implies(X,not(X_10)))) )],[refute_0_268,refute_0_272]) ).
cnf(refute_0_274,plain,
is_a_theorem(implies(or(X_10,implies(X,not(X_10))),or(X_10,implies(X,not(X_10))))),
inference(subst,[],[refute_0_273:[bind(X_241,$fot(or(X_10,implies(X,not(X_10)))))]]) ).
cnf(refute_0_275,plain,
( ~ is_a_theorem(implies(X_219,X_219))
| ~ is_a_theorem(implies(implies(X_219,X_219),equiv(X_219,X_219)))
| is_a_theorem(equiv(X_219,X_219)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(implies(X_219,X_219))),bind(Y,$fot(equiv(X_219,X_219)))]]) ).
cnf(refute_0_276,plain,
is_a_theorem(implies(or(and(X_44,not(X_45)),and(X_44,not(X_45))),and(X_44,not(X_45)))),
inference(subst,[],[refute_0_95:[bind(P,$fot(and(X_44,not(X_45))))]]) ).
cnf(refute_0_277,plain,
implies(X,and(X_4,not(X_5))) = not(and(X,not(and(X_4,not(X_5))))),
inference(subst,[],[refute_0_54:[bind(Y,$fot(and(X_4,not(X_5))))]]) ).
cnf(refute_0_278,plain,
implies(X_4,X_5) = not(and(X_4,not(X_5))),
inference(subst,[],[refute_0_54:[bind(X,$fot(X_4)),bind(Y,$fot(X_5))]]) ).
cnf(refute_0_279,plain,
( implies(X_4,X_5) != not(and(X_4,not(X_5)))
| not(and(X_4,not(X_5))) = implies(X_4,X_5) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X_4,X_5))),bind(Y0,$fot(not(and(X_4,not(X_5)))))]]) ).
cnf(refute_0_280,plain,
not(and(X_4,not(X_5))) = implies(X_4,X_5),
inference(resolve,[$cnf( $equal(implies(X_4,X_5),not(and(X_4,not(X_5)))) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
( implies(X,and(X_4,not(X_5))) != not(and(X,not(and(X_4,not(X_5)))))
| not(and(X_4,not(X_5))) != implies(X_4,X_5)
| implies(X,and(X_4,not(X_5))) = not(and(X,implies(X_4,X_5))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,and(X_4,not(X_5))),not(and(X,not(and(X_4,not(X_5)))))) ),[1,0,1],$fot(implies(X_4,X_5))]]) ).
cnf(refute_0_282,plain,
( implies(X,and(X_4,not(X_5))) != not(and(X,not(and(X_4,not(X_5)))))
| implies(X,and(X_4,not(X_5))) = not(and(X,implies(X_4,X_5))) ),
inference(resolve,[$cnf( $equal(not(and(X_4,not(X_5))),implies(X_4,X_5)) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
implies(X,and(X_4,not(X_5))) = not(and(X,implies(X_4,X_5))),
inference(resolve,[$cnf( $equal(implies(X,and(X_4,not(X_5))),not(and(X,not(and(X_4,not(X_5)))))) )],[refute_0_277,refute_0_282]) ).
cnf(refute_0_284,plain,
implies(or(and(X_44,not(X_45)),and(X_44,not(X_45))),and(X_44,not(X_45))) = not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))),
inference(subst,[],[refute_0_283:[bind(X,$fot(or(and(X_44,not(X_45)),and(X_44,not(X_45))))),bind(X_4,$fot(X_44)),bind(X_5,$fot(X_45))]]) ).
cnf(refute_0_285,plain,
( implies(or(and(X_44,not(X_45)),and(X_44,not(X_45))),and(X_44,not(X_45))) != not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)))
| ~ is_a_theorem(implies(or(and(X_44,not(X_45)),and(X_44,not(X_45))),and(X_44,not(X_45))))
| is_a_theorem(not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(and(X_44,not(X_45)),and(X_44,not(X_45))),and(X_44,not(X_45)))) ),[0],$fot(not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))))]]) ).
cnf(refute_0_286,plain,
( ~ is_a_theorem(implies(or(and(X_44,not(X_45)),and(X_44,not(X_45))),and(X_44,not(X_45))))
| is_a_theorem(not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)))) ),
inference(resolve,[$cnf( $equal(implies(or(and(X_44,not(X_45)),and(X_44,not(X_45))),and(X_44,not(X_45))),not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)))) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
is_a_theorem(not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(and(X_44,not(X_45)),and(X_44,not(X_45))),and(X_44,not(X_45)))) )],[refute_0_276,refute_0_286]) ).
cnf(refute_0_288,plain,
or(X,and(X_44,not(X_45))) = implies(not(X),and(X_44,not(X_45))),
inference(subst,[],[refute_0_60:[bind(Y,$fot(and(X_44,not(X_45))))]]) ).
cnf(refute_0_289,plain,
implies(not(X),and(X_44,not(X_45))) = not(and(not(X),implies(X_44,X_45))),
inference(subst,[],[refute_0_283:[bind(X,$fot(not(X))),bind(X_4,$fot(X_44)),bind(X_5,$fot(X_45))]]) ).
cnf(refute_0_290,plain,
( implies(not(X),and(X_44,not(X_45))) != not(and(not(X),implies(X_44,X_45)))
| or(X,and(X_44,not(X_45))) != implies(not(X),and(X_44,not(X_45)))
| or(X,and(X_44,not(X_45))) = not(and(not(X),implies(X_44,X_45))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,and(X_44,not(X_45))),implies(not(X),and(X_44,not(X_45)))) ),[1],$fot(not(and(not(X),implies(X_44,X_45))))]]) ).
cnf(refute_0_291,plain,
( or(X,and(X_44,not(X_45))) != implies(not(X),and(X_44,not(X_45)))
| or(X,and(X_44,not(X_45))) = not(and(not(X),implies(X_44,X_45))) ),
inference(resolve,[$cnf( $equal(implies(not(X),and(X_44,not(X_45))),not(and(not(X),implies(X_44,X_45)))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
or(X,and(X_44,not(X_45))) = not(and(not(X),implies(X_44,X_45))),
inference(resolve,[$cnf( $equal(or(X,and(X_44,not(X_45))),implies(not(X),and(X_44,not(X_45)))) )],[refute_0_288,refute_0_291]) ).
cnf(refute_0_293,plain,
( or(X,and(X_44,not(X_45))) != not(and(not(X),implies(X_44,X_45)))
| not(and(not(X),implies(X_44,X_45))) = or(X,and(X_44,not(X_45))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,and(X_44,not(X_45))))),bind(Y0,$fot(not(and(not(X),implies(X_44,X_45)))))]]) ).
cnf(refute_0_294,plain,
not(and(not(X),implies(X_44,X_45))) = or(X,and(X_44,not(X_45))),
inference(resolve,[$cnf( $equal(or(X,and(X_44,not(X_45))),not(and(not(X),implies(X_44,X_45)))) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
not(and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45))) = or(and(implies(X_44,X_45),implies(X_44,X_45)),and(X_44,not(X_45))),
inference(subst,[],[refute_0_294:[bind(X,$fot(and(implies(X_44,X_45),implies(X_44,X_45))))]]) ).
cnf(refute_0_296,plain,
implies(implies(X_44,X_45),and(X_44,not(X_45))) = not(and(implies(X_44,X_45),implies(X_44,X_45))),
inference(subst,[],[refute_0_283:[bind(X,$fot(implies(X_44,X_45))),bind(X_4,$fot(X_44)),bind(X_5,$fot(X_45))]]) ).
cnf(refute_0_297,plain,
or(and(X_44,not(X_45)),and(X_44,not(X_45))) = implies(implies(X_44,X_45),and(X_44,not(X_45))),
inference(subst,[],[refute_0_139:[bind(X,$fot(X_44)),bind(Y,$fot(X_45)),bind(X_11,$fot(and(X_44,not(X_45))))]]) ).
cnf(refute_0_298,plain,
( implies(implies(X_44,X_45),and(X_44,not(X_45))) != not(and(implies(X_44,X_45),implies(X_44,X_45)))
| or(and(X_44,not(X_45)),and(X_44,not(X_45))) != implies(implies(X_44,X_45),and(X_44,not(X_45)))
| or(and(X_44,not(X_45)),and(X_44,not(X_45))) = not(and(implies(X_44,X_45),implies(X_44,X_45))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(or(and(X_44,not(X_45)),and(X_44,not(X_45))))),bind(Y0,$fot(implies(implies(X_44,X_45),and(X_44,not(X_45))))),bind(Z,$fot(not(and(implies(X_44,X_45),implies(X_44,X_45)))))]]) ).
cnf(refute_0_299,plain,
( implies(implies(X_44,X_45),and(X_44,not(X_45))) != not(and(implies(X_44,X_45),implies(X_44,X_45)))
| or(and(X_44,not(X_45)),and(X_44,not(X_45))) = not(and(implies(X_44,X_45),implies(X_44,X_45))) ),
inference(resolve,[$cnf( $equal(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(implies(X_44,X_45),and(X_44,not(X_45)))) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
or(and(X_44,not(X_45)),and(X_44,not(X_45))) = not(and(implies(X_44,X_45),implies(X_44,X_45))),
inference(resolve,[$cnf( $equal(implies(implies(X_44,X_45),and(X_44,not(X_45))),not(and(implies(X_44,X_45),implies(X_44,X_45)))) )],[refute_0_296,refute_0_299]) ).
cnf(refute_0_301,plain,
and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)) = and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)),
introduced(tautology,[refl,[$fot(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)))]]) ).
cnf(refute_0_302,plain,
( and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)) != and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))
| or(and(X_44,not(X_45)),and(X_44,not(X_45))) != not(and(implies(X_44,X_45),implies(X_44,X_45)))
| and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)) = and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45)) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)),and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))) ),[1,0],$fot(not(and(implies(X_44,X_45),implies(X_44,X_45))))]]) ).
cnf(refute_0_303,plain,
( or(and(X_44,not(X_45)),and(X_44,not(X_45))) != not(and(implies(X_44,X_45),implies(X_44,X_45)))
| and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)) = and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45)) ),
inference(resolve,[$cnf( $equal(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)),and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)) = and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45)),
inference(resolve,[$cnf( $equal(or(and(X_44,not(X_45)),and(X_44,not(X_45))),not(and(implies(X_44,X_45),implies(X_44,X_45)))) )],[refute_0_300,refute_0_303]) ).
cnf(refute_0_305,plain,
not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))) = not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))),
introduced(tautology,[refl,[$fot(not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))))]]) ).
cnf(refute_0_306,plain,
( and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)) != and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45))
| not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))) != not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)))
| not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))) = not(and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))),not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)))) ),[1,0],$fot(and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45)))]]) ).
cnf(refute_0_307,plain,
( and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)) != and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45))
| not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))) = not(and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45))) ),
inference(resolve,[$cnf( $equal(not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))),not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)))) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))) = not(and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45))),
inference(resolve,[$cnf( $equal(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)),and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45))) )],[refute_0_304,refute_0_307]) ).
cnf(refute_0_309,plain,
( not(and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45))) != or(and(implies(X_44,X_45),implies(X_44,X_45)),and(X_44,not(X_45)))
| not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))) != not(and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45)))
| not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))) = or(and(implies(X_44,X_45),implies(X_44,X_45)),and(X_44,not(X_45))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))))),bind(Y0,$fot(not(and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45))))),bind(Z,$fot(or(and(implies(X_44,X_45),implies(X_44,X_45)),and(X_44,not(X_45)))))]]) ).
cnf(refute_0_310,plain,
( not(and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45))) != or(and(implies(X_44,X_45),implies(X_44,X_45)),and(X_44,not(X_45)))
| not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))) = or(and(implies(X_44,X_45),implies(X_44,X_45)),and(X_44,not(X_45))) ),
inference(resolve,[$cnf( $equal(not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))),not(and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45)))) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))) = or(and(implies(X_44,X_45),implies(X_44,X_45)),and(X_44,not(X_45))),
inference(resolve,[$cnf( $equal(not(and(not(and(implies(X_44,X_45),implies(X_44,X_45))),implies(X_44,X_45))),or(and(implies(X_44,X_45),implies(X_44,X_45)),and(X_44,not(X_45)))) )],[refute_0_295,refute_0_310]) ).
cnf(refute_0_312,plain,
( not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))) != or(and(implies(X_44,X_45),implies(X_44,X_45)),and(X_44,not(X_45)))
| ~ is_a_theorem(not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))))
| is_a_theorem(or(and(implies(X_44,X_45),implies(X_44,X_45)),and(X_44,not(X_45)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)))) ),[0],$fot(or(and(implies(X_44,X_45),implies(X_44,X_45)),and(X_44,not(X_45))))]]) ).
cnf(refute_0_313,plain,
( ~ is_a_theorem(not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))))
| is_a_theorem(or(and(implies(X_44,X_45),implies(X_44,X_45)),and(X_44,not(X_45)))) ),
inference(resolve,[$cnf( $equal(not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45))),or(and(implies(X_44,X_45),implies(X_44,X_45)),and(X_44,not(X_45)))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
is_a_theorem(or(and(implies(X_44,X_45),implies(X_44,X_45)),and(X_44,not(X_45)))),
inference(resolve,[$cnf( is_a_theorem(not(and(or(and(X_44,not(X_45)),and(X_44,not(X_45))),implies(X_44,X_45)))) )],[refute_0_287,refute_0_313]) ).
cnf(refute_0_315,plain,
is_a_theorem(or(and(implies(X_58,X_58),implies(X_58,X_58)),and(X_58,not(X_58)))),
inference(subst,[],[refute_0_314:[bind(X_44,$fot(X_58)),bind(X_45,$fot(X_58))]]) ).
cnf(refute_0_316,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_41]) ).
cnf(refute_0_317,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_318,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_317,refute_0_316]) ).
cnf(refute_0_319,plain,
equiv(X_58,X_58) = and(implies(X_58,X_58),implies(X_58,X_58)),
inference(subst,[],[refute_0_318:[bind(X,$fot(X_58)),bind(Y,$fot(X_58))]]) ).
cnf(refute_0_320,plain,
( equiv(X_58,X_58) != and(implies(X_58,X_58),implies(X_58,X_58))
| and(implies(X_58,X_58),implies(X_58,X_58)) = equiv(X_58,X_58) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(X_58,X_58))),bind(Y0,$fot(and(implies(X_58,X_58),implies(X_58,X_58))))]]) ).
cnf(refute_0_321,plain,
and(implies(X_58,X_58),implies(X_58,X_58)) = equiv(X_58,X_58),
inference(resolve,[$cnf( $equal(equiv(X_58,X_58),and(implies(X_58,X_58),implies(X_58,X_58))) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
( and(implies(X_58,X_58),implies(X_58,X_58)) != equiv(X_58,X_58)
| ~ is_a_theorem(or(and(implies(X_58,X_58),implies(X_58,X_58)),and(X_58,not(X_58))))
| is_a_theorem(or(equiv(X_58,X_58),and(X_58,not(X_58)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(implies(X_58,X_58),implies(X_58,X_58)),and(X_58,not(X_58)))) ),[0,0],$fot(equiv(X_58,X_58))]]) ).
cnf(refute_0_323,plain,
( ~ is_a_theorem(or(and(implies(X_58,X_58),implies(X_58,X_58)),and(X_58,not(X_58))))
| is_a_theorem(or(equiv(X_58,X_58),and(X_58,not(X_58)))) ),
inference(resolve,[$cnf( $equal(and(implies(X_58,X_58),implies(X_58,X_58)),equiv(X_58,X_58)) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
is_a_theorem(or(equiv(X_58,X_58),and(X_58,not(X_58)))),
inference(resolve,[$cnf( is_a_theorem(or(and(implies(X_58,X_58),implies(X_58,X_58)),and(X_58,not(X_58)))) )],[refute_0_315,refute_0_323]) ).
cnf(refute_0_325,plain,
( ~ is_a_theorem(or(equiv(X_58,X_58),and(X_58,not(X_58))))
| is_a_theorem(or(and(X_58,not(X_58)),equiv(X_58,X_58))) ),
inference(subst,[],[refute_0_43:[bind(P,$fot(equiv(X_58,X_58))),bind(Q,$fot(and(X_58,not(X_58))))]]) ).
cnf(refute_0_326,plain,
is_a_theorem(or(and(X_58,not(X_58)),equiv(X_58,X_58))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(X_58,X_58),and(X_58,not(X_58)))) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
or(and(X_58,not(X_58)),equiv(X_58,X_58)) = implies(implies(X_58,X_58),equiv(X_58,X_58)),
inference(subst,[],[refute_0_139:[bind(X,$fot(X_58)),bind(Y,$fot(X_58)),bind(X_11,$fot(equiv(X_58,X_58)))]]) ).
cnf(refute_0_328,plain,
( or(and(X_58,not(X_58)),equiv(X_58,X_58)) != implies(implies(X_58,X_58),equiv(X_58,X_58))
| ~ is_a_theorem(or(and(X_58,not(X_58)),equiv(X_58,X_58)))
| is_a_theorem(implies(implies(X_58,X_58),equiv(X_58,X_58))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_58,not(X_58)),equiv(X_58,X_58))) ),[0],$fot(implies(implies(X_58,X_58),equiv(X_58,X_58)))]]) ).
cnf(refute_0_329,plain,
( ~ is_a_theorem(or(and(X_58,not(X_58)),equiv(X_58,X_58)))
| is_a_theorem(implies(implies(X_58,X_58),equiv(X_58,X_58))) ),
inference(resolve,[$cnf( $equal(or(and(X_58,not(X_58)),equiv(X_58,X_58)),implies(implies(X_58,X_58),equiv(X_58,X_58))) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
is_a_theorem(implies(implies(X_58,X_58),equiv(X_58,X_58))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_58,not(X_58)),equiv(X_58,X_58))) )],[refute_0_326,refute_0_329]) ).
cnf(refute_0_331,plain,
is_a_theorem(implies(implies(X_219,X_219),equiv(X_219,X_219))),
inference(subst,[],[refute_0_330:[bind(X_58,$fot(X_219))]]) ).
cnf(refute_0_332,plain,
( ~ is_a_theorem(implies(X_219,X_219))
| is_a_theorem(equiv(X_219,X_219)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_219,X_219),equiv(X_219,X_219))) )],[refute_0_331,refute_0_275]) ).
cnf(refute_0_333,plain,
( ~ is_a_theorem(implies(or(X_10,implies(X,not(X_10))),or(X_10,implies(X,not(X_10)))))
| is_a_theorem(equiv(or(X_10,implies(X,not(X_10))),or(X_10,implies(X,not(X_10))))) ),
inference(subst,[],[refute_0_332:[bind(X_219,$fot(or(X_10,implies(X,not(X_10)))))]]) ).
cnf(refute_0_334,plain,
is_a_theorem(equiv(or(X_10,implies(X,not(X_10))),or(X_10,implies(X,not(X_10))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_10,implies(X,not(X_10))),or(X_10,implies(X,not(X_10))))) )],[refute_0_274,refute_0_333]) ).
cnf(refute_0_335,plain,
and(not(not(implies(X_29,not(X)))),or(X,X_29)) = and(implies(X_29,not(X)),or(X,X_29)),
inference(subst,[],[refute_0_199:[bind(X,$fot(implies(X_29,not(X)))),bind(X_20,$fot(or(X,X_29)))]]) ).
cnf(refute_0_336,plain,
equiv(X_29,not(X)) = and(implies(X_29,not(X)),implies(not(X),X_29)),
inference(subst,[],[refute_0_318:[bind(X,$fot(X_29)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_337,plain,
or(X,X_29) = implies(not(X),X_29),
inference(subst,[],[refute_0_60:[bind(Y,$fot(X_29))]]) ).
cnf(refute_0_338,plain,
( or(X,X_29) != implies(not(X),X_29)
| implies(not(X),X_29) = or(X,X_29) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,X_29))),bind(Y0,$fot(implies(not(X),X_29)))]]) ).
cnf(refute_0_339,plain,
implies(not(X),X_29) = or(X,X_29),
inference(resolve,[$cnf( $equal(or(X,X_29),implies(not(X),X_29)) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
( equiv(X_29,not(X)) != and(implies(X_29,not(X)),implies(not(X),X_29))
| implies(not(X),X_29) != or(X,X_29)
| equiv(X_29,not(X)) = and(implies(X_29,not(X)),or(X,X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_29,not(X)),and(implies(X_29,not(X)),implies(not(X),X_29))) ),[1,1],$fot(or(X,X_29))]]) ).
cnf(refute_0_341,plain,
( equiv(X_29,not(X)) != and(implies(X_29,not(X)),implies(not(X),X_29))
| equiv(X_29,not(X)) = and(implies(X_29,not(X)),or(X,X_29)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_29),or(X,X_29)) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
equiv(X_29,not(X)) = and(implies(X_29,not(X)),or(X,X_29)),
inference(resolve,[$cnf( $equal(equiv(X_29,not(X)),and(implies(X_29,not(X)),implies(not(X),X_29))) )],[refute_0_336,refute_0_341]) ).
cnf(refute_0_343,plain,
( equiv(X_29,not(X)) != and(implies(X_29,not(X)),or(X,X_29))
| and(implies(X_29,not(X)),or(X,X_29)) = equiv(X_29,not(X)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(X_29,not(X)))),bind(Y0,$fot(and(implies(X_29,not(X)),or(X,X_29))))]]) ).
cnf(refute_0_344,plain,
and(implies(X_29,not(X)),or(X,X_29)) = equiv(X_29,not(X)),
inference(resolve,[$cnf( $equal(equiv(X_29,not(X)),and(implies(X_29,not(X)),or(X,X_29))) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
( and(implies(X_29,not(X)),or(X,X_29)) != equiv(X_29,not(X))
| and(not(not(implies(X_29,not(X)))),or(X,X_29)) != and(implies(X_29,not(X)),or(X,X_29))
| and(not(not(implies(X_29,not(X)))),or(X,X_29)) = equiv(X_29,not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(implies(X_29,not(X)))),or(X,X_29)),and(implies(X_29,not(X)),or(X,X_29))) ),[1],$fot(equiv(X_29,not(X)))]]) ).
cnf(refute_0_346,plain,
( and(not(not(implies(X_29,not(X)))),or(X,X_29)) != and(implies(X_29,not(X)),or(X,X_29))
| and(not(not(implies(X_29,not(X)))),or(X,X_29)) = equiv(X_29,not(X)) ),
inference(resolve,[$cnf( $equal(and(implies(X_29,not(X)),or(X,X_29)),equiv(X_29,not(X))) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
and(not(not(implies(X_29,not(X)))),or(X,X_29)) = equiv(X_29,not(X)),
inference(resolve,[$cnf( $equal(and(not(not(implies(X_29,not(X)))),or(X,X_29)),and(implies(X_29,not(X)),or(X,X_29))) )],[refute_0_335,refute_0_346]) ).
cnf(refute_0_348,plain,
and(not(not(implies(X,not(Y)))),X_89) = and(implies(X,not(Y)),X_89),
inference(subst,[],[refute_0_199:[bind(X,$fot(implies(X,not(Y)))),bind(X_20,$fot(X_89))]]) ).
cnf(refute_0_349,plain,
( and(not(not(implies(X,not(Y)))),X_89) != and(implies(X,not(Y)),X_89)
| not(implies(X,not(Y))) != and(X,Y)
| and(not(and(X,Y)),X_89) = and(implies(X,not(Y)),X_89) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(implies(X,not(Y)))),X_89),and(implies(X,not(Y)),X_89)) ),[0,0,0],$fot(and(X,Y))]]) ).
cnf(refute_0_350,plain,
( and(not(not(implies(X,not(Y)))),X_89) != and(implies(X,not(Y)),X_89)
| and(not(and(X,Y)),X_89) = and(implies(X,not(Y)),X_89) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_195,refute_0_349]) ).
cnf(refute_0_351,plain,
and(not(and(X,Y)),X_89) = and(implies(X,not(Y)),X_89),
inference(resolve,[$cnf( $equal(and(not(not(implies(X,not(Y)))),X_89),and(implies(X,not(Y)),X_89)) )],[refute_0_348,refute_0_350]) ).
cnf(refute_0_352,plain,
( and(not(and(X,Y)),X_89) != and(implies(X,not(Y)),X_89)
| and(implies(X,not(Y)),X_89) = and(not(and(X,Y)),X_89) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(not(and(X,Y)),X_89))),bind(Y0,$fot(and(implies(X,not(Y)),X_89)))]]) ).
cnf(refute_0_353,plain,
and(implies(X,not(Y)),X_89) = and(not(and(X,Y)),X_89),
inference(resolve,[$cnf( $equal(and(not(and(X,Y)),X_89),and(implies(X,not(Y)),X_89)) )],[refute_0_351,refute_0_352]) ).
cnf(refute_0_354,plain,
and(implies(X_29,not(X)),or(X,X_29)) = and(not(and(X_29,X)),or(X,X_29)),
inference(subst,[],[refute_0_353:[bind(X,$fot(X_29)),bind(Y,$fot(X)),bind(X_89,$fot(or(X,X_29)))]]) ).
cnf(refute_0_355,plain,
( and(implies(X_29,not(X)),or(X,X_29)) != and(not(and(X_29,X)),or(X,X_29))
| and(not(not(implies(X_29,not(X)))),or(X,X_29)) != and(implies(X_29,not(X)),or(X,X_29))
| and(not(not(implies(X_29,not(X)))),or(X,X_29)) = and(not(and(X_29,X)),or(X,X_29)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(and(not(not(implies(X_29,not(X)))),or(X,X_29)))),bind(Y0,$fot(and(implies(X_29,not(X)),or(X,X_29)))),bind(Z,$fot(and(not(and(X_29,X)),or(X,X_29))))]]) ).
cnf(refute_0_356,plain,
( and(implies(X_29,not(X)),or(X,X_29)) != and(not(and(X_29,X)),or(X,X_29))
| and(not(not(implies(X_29,not(X)))),or(X,X_29)) = and(not(and(X_29,X)),or(X,X_29)) ),
inference(resolve,[$cnf( $equal(and(not(not(implies(X_29,not(X)))),or(X,X_29)),and(implies(X_29,not(X)),or(X,X_29))) )],[refute_0_335,refute_0_355]) ).
cnf(refute_0_357,plain,
and(not(not(implies(X_29,not(X)))),or(X,X_29)) = and(not(and(X_29,X)),or(X,X_29)),
inference(resolve,[$cnf( $equal(and(implies(X_29,not(X)),or(X,X_29)),and(not(and(X_29,X)),or(X,X_29))) )],[refute_0_354,refute_0_356]) ).
cnf(refute_0_358,plain,
( and(not(not(implies(X_29,not(X)))),or(X,X_29)) != and(not(and(X_29,X)),or(X,X_29))
| and(not(not(implies(X_29,not(X)))),or(X,X_29)) != equiv(X_29,not(X))
| and(not(and(X_29,X)),or(X,X_29)) = equiv(X_29,not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(implies(X_29,not(X)))),or(X,X_29)),equiv(X_29,not(X))) ),[0],$fot(and(not(and(X_29,X)),or(X,X_29)))]]) ).
cnf(refute_0_359,plain,
( and(not(not(implies(X_29,not(X)))),or(X,X_29)) != equiv(X_29,not(X))
| and(not(and(X_29,X)),or(X,X_29)) = equiv(X_29,not(X)) ),
inference(resolve,[$cnf( $equal(and(not(not(implies(X_29,not(X)))),or(X,X_29)),and(not(and(X_29,X)),or(X,X_29))) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
and(not(and(X_29,X)),or(X,X_29)) = equiv(X_29,not(X)),
inference(resolve,[$cnf( $equal(and(not(not(implies(X_29,not(X)))),or(X,X_29)),equiv(X_29,not(X))) )],[refute_0_347,refute_0_359]) ).
cnf(refute_0_361,plain,
and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)) = equiv(X_29,not(and(not(X_906),and(X_907,X_908)))),
inference(subst,[],[refute_0_360:[bind(X,$fot(and(not(X_906),and(X_907,X_908))))]]) ).
cnf(refute_0_362,plain,
or(X,implies(X_81,not(X_82))) = implies(not(X),implies(X_81,not(X_82))),
inference(subst,[],[refute_0_60:[bind(Y,$fot(implies(X_81,not(X_82))))]]) ).
cnf(refute_0_363,plain,
implies(X,implies(X_16,not(X_17))) = not(and(X,not(implies(X_16,not(X_17))))),
inference(subst,[],[refute_0_54:[bind(Y,$fot(implies(X_16,not(X_17))))]]) ).
cnf(refute_0_364,plain,
( implies(X,implies(X_16,not(X_17))) != not(and(X,not(implies(X_16,not(X_17)))))
| not(implies(X_16,not(X_17))) != and(X_16,X_17)
| implies(X,implies(X_16,not(X_17))) = not(and(X,and(X_16,X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,implies(X_16,not(X_17))),not(and(X,not(implies(X_16,not(X_17)))))) ),[1,0,1],$fot(and(X_16,X_17))]]) ).
cnf(refute_0_365,plain,
( implies(X,implies(X_16,not(X_17))) != not(and(X,not(implies(X_16,not(X_17)))))
| implies(X,implies(X_16,not(X_17))) = not(and(X,and(X_16,X_17))) ),
inference(resolve,[$cnf( $equal(not(implies(X_16,not(X_17))),and(X_16,X_17)) )],[refute_0_131,refute_0_364]) ).
cnf(refute_0_366,plain,
implies(X,implies(X_16,not(X_17))) = not(and(X,and(X_16,X_17))),
inference(resolve,[$cnf( $equal(implies(X,implies(X_16,not(X_17))),not(and(X,not(implies(X_16,not(X_17)))))) )],[refute_0_363,refute_0_365]) ).
cnf(refute_0_367,plain,
implies(not(X),implies(X_81,not(X_82))) = not(and(not(X),and(X_81,X_82))),
inference(subst,[],[refute_0_366:[bind(X,$fot(not(X))),bind(X_16,$fot(X_81)),bind(X_17,$fot(X_82))]]) ).
cnf(refute_0_368,plain,
( implies(not(X),implies(X_81,not(X_82))) != not(and(not(X),and(X_81,X_82)))
| or(X,implies(X_81,not(X_82))) != implies(not(X),implies(X_81,not(X_82)))
| or(X,implies(X_81,not(X_82))) = not(and(not(X),and(X_81,X_82))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,implies(X_81,not(X_82))),implies(not(X),implies(X_81,not(X_82)))) ),[1],$fot(not(and(not(X),and(X_81,X_82))))]]) ).
cnf(refute_0_369,plain,
( or(X,implies(X_81,not(X_82))) != implies(not(X),implies(X_81,not(X_82)))
| or(X,implies(X_81,not(X_82))) = not(and(not(X),and(X_81,X_82))) ),
inference(resolve,[$cnf( $equal(implies(not(X),implies(X_81,not(X_82))),not(and(not(X),and(X_81,X_82)))) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
or(X,implies(X_81,not(X_82))) = not(and(not(X),and(X_81,X_82))),
inference(resolve,[$cnf( $equal(or(X,implies(X_81,not(X_82))),implies(not(X),implies(X_81,not(X_82)))) )],[refute_0_362,refute_0_369]) ).
cnf(refute_0_371,plain,
or(X_906,implies(X_907,not(X_908))) = not(and(not(X_906),and(X_907,X_908))),
inference(subst,[],[refute_0_370:[bind(X,$fot(X_906)),bind(X_81,$fot(X_907)),bind(X_82,$fot(X_908))]]) ).
cnf(refute_0_372,plain,
( or(X_906,implies(X_907,not(X_908))) != not(and(not(X_906),and(X_907,X_908)))
| not(and(not(X_906),and(X_907,X_908))) = or(X_906,implies(X_907,not(X_908))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X_906,implies(X_907,not(X_908))))),bind(Y0,$fot(not(and(not(X_906),and(X_907,X_908)))))]]) ).
cnf(refute_0_373,plain,
not(and(not(X_906),and(X_907,X_908))) = or(X_906,implies(X_907,not(X_908))),
inference(resolve,[$cnf( $equal(or(X_906,implies(X_907,not(X_908))),not(and(not(X_906),and(X_907,X_908)))) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
( and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)) != equiv(X_29,not(and(not(X_906),and(X_907,X_908))))
| not(and(not(X_906),and(X_907,X_908))) != or(X_906,implies(X_907,not(X_908)))
| and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)) = equiv(X_29,or(X_906,implies(X_907,not(X_908)))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)),equiv(X_29,not(and(not(X_906),and(X_907,X_908))))) ),[1,1],$fot(or(X_906,implies(X_907,not(X_908))))]]) ).
cnf(refute_0_375,plain,
( and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)) != equiv(X_29,not(and(not(X_906),and(X_907,X_908))))
| and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)) = equiv(X_29,or(X_906,implies(X_907,not(X_908)))) ),
inference(resolve,[$cnf( $equal(not(and(not(X_906),and(X_907,X_908))),or(X_906,implies(X_907,not(X_908)))) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)) = equiv(X_29,or(X_906,implies(X_907,not(X_908)))),
inference(resolve,[$cnf( $equal(and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)),equiv(X_29,not(and(not(X_906),and(X_907,X_908))))) )],[refute_0_361,refute_0_375]) ).
cnf(refute_0_377,plain,
equiv(X_35,not(not(X))) = and(implies(X_35,not(not(X))),or(not(X),X_35)),
inference(subst,[],[refute_0_342:[bind(X,$fot(not(X))),bind(X_29,$fot(X_35))]]) ).
cnf(refute_0_378,plain,
implies(X,X_35) = or(not(X),X_35),
inference(subst,[],[refute_0_9:[bind(Y,$fot(X_35))]]) ).
cnf(refute_0_379,plain,
( implies(X,X_35) != or(not(X),X_35)
| or(not(X),X_35) = implies(X,X_35) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,X_35))),bind(Y0,$fot(or(not(X),X_35)))]]) ).
cnf(refute_0_380,plain,
or(not(X),X_35) = implies(X,X_35),
inference(resolve,[$cnf( $equal(implies(X,X_35),or(not(X),X_35)) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
( equiv(X_35,not(not(X))) != and(implies(X_35,not(not(X))),or(not(X),X_35))
| or(not(X),X_35) != implies(X,X_35)
| equiv(X_35,not(not(X))) = and(implies(X_35,not(not(X))),implies(X,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_35,not(not(X))),and(implies(X_35,not(not(X))),or(not(X),X_35))) ),[1,1],$fot(implies(X,X_35))]]) ).
cnf(refute_0_382,plain,
( equiv(X_35,not(not(X))) != and(implies(X_35,not(not(X))),or(not(X),X_35))
| equiv(X_35,not(not(X))) = and(implies(X_35,not(not(X))),implies(X,X_35)) ),
inference(resolve,[$cnf( $equal(or(not(X),X_35),implies(X,X_35)) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
equiv(X_35,not(not(X))) = and(implies(X_35,not(not(X))),implies(X,X_35)),
inference(resolve,[$cnf( $equal(equiv(X_35,not(not(X))),and(implies(X_35,not(not(X))),or(not(X),X_35))) )],[refute_0_377,refute_0_382]) ).
cnf(refute_0_384,plain,
equiv(X_74,not(not(or(X,not(X_17))))) = and(implies(X_74,not(not(or(X,not(X_17))))),implies(or(X,not(X_17)),X_74)),
inference(subst,[],[refute_0_383:[bind(X,$fot(or(X,not(X_17)))),bind(X_35,$fot(X_74))]]) ).
cnf(refute_0_385,plain,
( and(not(X),X_17) != not(or(X,not(X_17)))
| not(or(X,not(X_17))) = and(not(X),X_17) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(not(X),X_17))),bind(Y0,$fot(not(or(X,not(X_17)))))]]) ).
cnf(refute_0_386,plain,
not(or(X,not(X_17))) = and(not(X),X_17),
inference(resolve,[$cnf( $equal(and(not(X),X_17),not(or(X,not(X_17)))) )],[refute_0_186,refute_0_385]) ).
cnf(refute_0_387,plain,
( equiv(X_74,not(not(or(X,not(X_17))))) != and(implies(X_74,not(not(or(X,not(X_17))))),implies(or(X,not(X_17)),X_74))
| not(or(X,not(X_17))) != and(not(X),X_17)
| equiv(X_74,not(not(or(X,not(X_17))))) = and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_74,not(not(or(X,not(X_17))))),and(implies(X_74,not(not(or(X,not(X_17))))),implies(or(X,not(X_17)),X_74))) ),[1,0,1,0],$fot(and(not(X),X_17))]]) ).
cnf(refute_0_388,plain,
( equiv(X_74,not(not(or(X,not(X_17))))) != and(implies(X_74,not(not(or(X,not(X_17))))),implies(or(X,not(X_17)),X_74))
| equiv(X_74,not(not(or(X,not(X_17))))) = and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) ),
inference(resolve,[$cnf( $equal(not(or(X,not(X_17))),and(not(X),X_17)) )],[refute_0_386,refute_0_387]) ).
cnf(refute_0_389,plain,
equiv(X_74,not(not(or(X,not(X_17))))) = and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74)),
inference(resolve,[$cnf( $equal(equiv(X_74,not(not(or(X,not(X_17))))),and(implies(X_74,not(not(or(X,not(X_17))))),implies(or(X,not(X_17)),X_74))) )],[refute_0_384,refute_0_388]) ).
cnf(refute_0_390,plain,
not(not(or(X,not(X_17)))) = not(not(or(X,not(X_17)))),
introduced(tautology,[refl,[$fot(not(not(or(X,not(X_17)))))]]) ).
cnf(refute_0_391,plain,
( not(not(or(X,not(X_17)))) != not(not(or(X,not(X_17))))
| not(or(X,not(X_17))) != and(not(X),X_17)
| not(not(or(X,not(X_17)))) = not(and(not(X),X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(or(X,not(X_17)))),not(not(or(X,not(X_17))))) ),[1,0],$fot(and(not(X),X_17))]]) ).
cnf(refute_0_392,plain,
( not(or(X,not(X_17))) != and(not(X),X_17)
| not(not(or(X,not(X_17)))) = not(and(not(X),X_17)) ),
inference(resolve,[$cnf( $equal(not(not(or(X,not(X_17)))),not(not(or(X,not(X_17))))) )],[refute_0_390,refute_0_391]) ).
cnf(refute_0_393,plain,
not(not(or(X,not(X_17)))) = not(and(not(X),X_17)),
inference(resolve,[$cnf( $equal(not(or(X,not(X_17))),and(not(X),X_17)) )],[refute_0_386,refute_0_392]) ).
cnf(refute_0_394,plain,
equiv(X_74,not(not(or(X,not(X_17))))) = equiv(X_74,not(not(or(X,not(X_17))))),
introduced(tautology,[refl,[$fot(equiv(X_74,not(not(or(X,not(X_17))))))]]) ).
cnf(refute_0_395,plain,
( equiv(X_74,not(not(or(X,not(X_17))))) != equiv(X_74,not(not(or(X,not(X_17)))))
| not(not(or(X,not(X_17)))) != not(and(not(X),X_17))
| equiv(X_74,not(not(or(X,not(X_17))))) = equiv(X_74,not(and(not(X),X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_74,not(not(or(X,not(X_17))))),equiv(X_74,not(not(or(X,not(X_17)))))) ),[1,1],$fot(not(and(not(X),X_17)))]]) ).
cnf(refute_0_396,plain,
( not(not(or(X,not(X_17)))) != not(and(not(X),X_17))
| equiv(X_74,not(not(or(X,not(X_17))))) = equiv(X_74,not(and(not(X),X_17))) ),
inference(resolve,[$cnf( $equal(equiv(X_74,not(not(or(X,not(X_17))))),equiv(X_74,not(not(or(X,not(X_17)))))) )],[refute_0_394,refute_0_395]) ).
cnf(refute_0_397,plain,
equiv(X_74,not(not(or(X,not(X_17))))) = equiv(X_74,not(and(not(X),X_17))),
inference(resolve,[$cnf( $equal(not(not(or(X,not(X_17)))),not(and(not(X),X_17))) )],[refute_0_393,refute_0_396]) ).
cnf(refute_0_398,plain,
( equiv(X_74,not(not(or(X,not(X_17))))) != and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74))
| equiv(X_74,not(not(or(X,not(X_17))))) != equiv(X_74,not(and(not(X),X_17)))
| equiv(X_74,not(and(not(X),X_17))) = and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_74,not(not(or(X,not(X_17))))),and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74))) ),[0],$fot(equiv(X_74,not(and(not(X),X_17))))]]) ).
cnf(refute_0_399,plain,
( equiv(X_74,not(not(or(X,not(X_17))))) != and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74))
| equiv(X_74,not(and(not(X),X_17))) = and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) ),
inference(resolve,[$cnf( $equal(equiv(X_74,not(not(or(X,not(X_17))))),equiv(X_74,not(and(not(X),X_17)))) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
equiv(X_74,not(and(not(X),X_17))) = and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74)),
inference(resolve,[$cnf( $equal(equiv(X_74,not(not(or(X,not(X_17))))),and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74))) )],[refute_0_389,refute_0_399]) ).
cnf(refute_0_401,plain,
( equiv(X,Y) != and(implies(X,Y),implies(Y,X))
| and(implies(X,Y),implies(Y,X)) = equiv(X,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(X,Y))),bind(Y0,$fot(and(implies(X,Y),implies(Y,X))))]]) ).
cnf(refute_0_402,plain,
and(implies(X,Y),implies(Y,X)) = equiv(X,Y),
inference(resolve,[$cnf( $equal(equiv(X,Y),and(implies(X,Y),implies(Y,X))) )],[refute_0_318,refute_0_401]) ).
cnf(refute_0_403,plain,
and(implies(X_74,or(X,not(X_17))),implies(or(X,not(X_17)),X_74)) = equiv(X_74,or(X,not(X_17))),
inference(subst,[],[refute_0_402:[bind(X,$fot(X_74)),bind(Y,$fot(or(X,not(X_17))))]]) ).
cnf(refute_0_404,plain,
implies(X,or(X_19,not(X_20))) = not(and(X,not(or(X_19,not(X_20))))),
inference(subst,[],[refute_0_54:[bind(Y,$fot(or(X_19,not(X_20))))]]) ).
cnf(refute_0_405,plain,
and(not(X_19),X_20) = not(or(X_19,not(X_20))),
inference(subst,[],[refute_0_186:[bind(X,$fot(X_19)),bind(X_17,$fot(X_20))]]) ).
cnf(refute_0_406,plain,
( and(not(X_19),X_20) != not(or(X_19,not(X_20)))
| not(or(X_19,not(X_20))) = and(not(X_19),X_20) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(not(X_19),X_20))),bind(Y0,$fot(not(or(X_19,not(X_20)))))]]) ).
cnf(refute_0_407,plain,
not(or(X_19,not(X_20))) = and(not(X_19),X_20),
inference(resolve,[$cnf( $equal(and(not(X_19),X_20),not(or(X_19,not(X_20)))) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
( implies(X,or(X_19,not(X_20))) != not(and(X,not(or(X_19,not(X_20)))))
| not(or(X_19,not(X_20))) != and(not(X_19),X_20)
| implies(X,or(X_19,not(X_20))) = not(and(X,and(not(X_19),X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,or(X_19,not(X_20))),not(and(X,not(or(X_19,not(X_20)))))) ),[1,0,1],$fot(and(not(X_19),X_20))]]) ).
cnf(refute_0_409,plain,
( implies(X,or(X_19,not(X_20))) != not(and(X,not(or(X_19,not(X_20)))))
| implies(X,or(X_19,not(X_20))) = not(and(X,and(not(X_19),X_20))) ),
inference(resolve,[$cnf( $equal(not(or(X_19,not(X_20))),and(not(X_19),X_20)) )],[refute_0_407,refute_0_408]) ).
cnf(refute_0_410,plain,
implies(X,or(X_19,not(X_20))) = not(and(X,and(not(X_19),X_20))),
inference(resolve,[$cnf( $equal(implies(X,or(X_19,not(X_20))),not(and(X,not(or(X_19,not(X_20)))))) )],[refute_0_404,refute_0_409]) ).
cnf(refute_0_411,plain,
( implies(X,or(X_19,not(X_20))) != not(and(X,and(not(X_19),X_20)))
| not(and(X,and(not(X_19),X_20))) = implies(X,or(X_19,not(X_20))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,or(X_19,not(X_20))))),bind(Y0,$fot(not(and(X,and(not(X_19),X_20)))))]]) ).
cnf(refute_0_412,plain,
not(and(X,and(not(X_19),X_20))) = implies(X,or(X_19,not(X_20))),
inference(resolve,[$cnf( $equal(implies(X,or(X_19,not(X_20))),not(and(X,and(not(X_19),X_20)))) )],[refute_0_410,refute_0_411]) ).
cnf(refute_0_413,plain,
not(and(X_74,and(not(X),X_17))) = implies(X_74,or(X,not(X_17))),
inference(subst,[],[refute_0_412:[bind(X,$fot(X_74)),bind(X_19,$fot(X)),bind(X_20,$fot(X_17))]]) ).
cnf(refute_0_414,plain,
and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) = and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)),
introduced(tautology,[refl,[$fot(and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)))]]) ).
cnf(refute_0_415,plain,
( and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) != and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74))
| not(and(X_74,and(not(X),X_17))) != implies(X_74,or(X,not(X_17)))
| and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) = and(implies(X_74,or(X,not(X_17))),implies(or(X,not(X_17)),X_74)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)),and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74))) ),[1,0],$fot(implies(X_74,or(X,not(X_17))))]]) ).
cnf(refute_0_416,plain,
( not(and(X_74,and(not(X),X_17))) != implies(X_74,or(X,not(X_17)))
| and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) = and(implies(X_74,or(X,not(X_17))),implies(or(X,not(X_17)),X_74)) ),
inference(resolve,[$cnf( $equal(and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)),and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74))) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) = and(implies(X_74,or(X,not(X_17))),implies(or(X,not(X_17)),X_74)),
inference(resolve,[$cnf( $equal(not(and(X_74,and(not(X),X_17))),implies(X_74,or(X,not(X_17)))) )],[refute_0_413,refute_0_416]) ).
cnf(refute_0_418,plain,
( and(implies(X_74,or(X,not(X_17))),implies(or(X,not(X_17)),X_74)) != equiv(X_74,or(X,not(X_17)))
| and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) != and(implies(X_74,or(X,not(X_17))),implies(or(X,not(X_17)),X_74))
| and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) = equiv(X_74,or(X,not(X_17))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)))),bind(Y0,$fot(and(implies(X_74,or(X,not(X_17))),implies(or(X,not(X_17)),X_74)))),bind(Z,$fot(equiv(X_74,or(X,not(X_17)))))]]) ).
cnf(refute_0_419,plain,
( and(implies(X_74,or(X,not(X_17))),implies(or(X,not(X_17)),X_74)) != equiv(X_74,or(X,not(X_17)))
| and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) = equiv(X_74,or(X,not(X_17))) ),
inference(resolve,[$cnf( $equal(and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)),and(implies(X_74,or(X,not(X_17))),implies(or(X,not(X_17)),X_74))) )],[refute_0_417,refute_0_418]) ).
cnf(refute_0_420,plain,
and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) = equiv(X_74,or(X,not(X_17))),
inference(resolve,[$cnf( $equal(and(implies(X_74,or(X,not(X_17))),implies(or(X,not(X_17)),X_74)),equiv(X_74,or(X,not(X_17)))) )],[refute_0_403,refute_0_419]) ).
cnf(refute_0_421,plain,
and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) = and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)),
inference(subst,[],[refute_0_353:[bind(X,$fot(X_74)),bind(Y,$fot(and(not(X),X_17))),bind(X_89,$fot(implies(or(X,not(X_17)),X_74)))]]) ).
cnf(refute_0_422,plain,
( and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) != and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74))
| and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) != equiv(X_74,or(X,not(X_17)))
| and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) = equiv(X_74,or(X,not(X_17))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74)))),bind(Y0,$fot(and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)))),bind(Z,$fot(equiv(X_74,or(X,not(X_17)))))]]) ).
cnf(refute_0_423,plain,
( and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) != equiv(X_74,or(X,not(X_17)))
| and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) = equiv(X_74,or(X,not(X_17))) ),
inference(resolve,[$cnf( $equal(and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74)),and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74))) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) = equiv(X_74,or(X,not(X_17))),
inference(resolve,[$cnf( $equal(and(not(and(X_74,and(not(X),X_17))),implies(or(X,not(X_17)),X_74)),equiv(X_74,or(X,not(X_17)))) )],[refute_0_420,refute_0_423]) ).
cnf(refute_0_425,plain,
( and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74)) != equiv(X_74,or(X,not(X_17)))
| equiv(X_74,not(and(not(X),X_17))) != and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74))
| equiv(X_74,not(and(not(X),X_17))) = equiv(X_74,or(X,not(X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_74,not(and(not(X),X_17))),and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74))) ),[1],$fot(equiv(X_74,or(X,not(X_17))))]]) ).
cnf(refute_0_426,plain,
( equiv(X_74,not(and(not(X),X_17))) != and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74))
| equiv(X_74,not(and(not(X),X_17))) = equiv(X_74,or(X,not(X_17))) ),
inference(resolve,[$cnf( $equal(and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74)),equiv(X_74,or(X,not(X_17)))) )],[refute_0_424,refute_0_425]) ).
cnf(refute_0_427,plain,
equiv(X_74,not(and(not(X),X_17))) = equiv(X_74,or(X,not(X_17))),
inference(resolve,[$cnf( $equal(equiv(X_74,not(and(not(X),X_17))),and(implies(X_74,not(and(not(X),X_17))),implies(or(X,not(X_17)),X_74))) )],[refute_0_400,refute_0_426]) ).
cnf(refute_0_428,plain,
equiv(X_29,not(and(not(X_906),and(X_907,X_908)))) = equiv(X_29,or(X_906,not(and(X_907,X_908)))),
inference(subst,[],[refute_0_427:[bind(X,$fot(X_906)),bind(X_17,$fot(and(X_907,X_908))),bind(X_74,$fot(X_29))]]) ).
cnf(refute_0_429,plain,
( and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)) != equiv(X_29,not(and(not(X_906),and(X_907,X_908))))
| equiv(X_29,not(and(not(X_906),and(X_907,X_908)))) != equiv(X_29,or(X_906,not(and(X_907,X_908))))
| and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)) = equiv(X_29,or(X_906,not(and(X_907,X_908)))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)))),bind(Y0,$fot(equiv(X_29,not(and(not(X_906),and(X_907,X_908)))))),bind(Z,$fot(equiv(X_29,or(X_906,not(and(X_907,X_908))))))]]) ).
cnf(refute_0_430,plain,
( equiv(X_29,not(and(not(X_906),and(X_907,X_908)))) != equiv(X_29,or(X_906,not(and(X_907,X_908))))
| and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)) = equiv(X_29,or(X_906,not(and(X_907,X_908)))) ),
inference(resolve,[$cnf( $equal(and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)),equiv(X_29,not(and(not(X_906),and(X_907,X_908))))) )],[refute_0_361,refute_0_429]) ).
cnf(refute_0_431,plain,
and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)) = equiv(X_29,or(X_906,not(and(X_907,X_908)))),
inference(resolve,[$cnf( $equal(equiv(X_29,not(and(not(X_906),and(X_907,X_908)))),equiv(X_29,or(X_906,not(and(X_907,X_908))))) )],[refute_0_428,refute_0_430]) ).
cnf(refute_0_432,plain,
( and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)) != equiv(X_29,or(X_906,implies(X_907,not(X_908))))
| and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)) != equiv(X_29,or(X_906,not(and(X_907,X_908))))
| equiv(X_29,or(X_906,not(and(X_907,X_908)))) = equiv(X_29,or(X_906,implies(X_907,not(X_908)))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)),equiv(X_29,or(X_906,implies(X_907,not(X_908))))) ),[0],$fot(equiv(X_29,or(X_906,not(and(X_907,X_908)))))]]) ).
cnf(refute_0_433,plain,
( and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)) != equiv(X_29,or(X_906,implies(X_907,not(X_908))))
| equiv(X_29,or(X_906,not(and(X_907,X_908)))) = equiv(X_29,or(X_906,implies(X_907,not(X_908)))) ),
inference(resolve,[$cnf( $equal(and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)),equiv(X_29,or(X_906,not(and(X_907,X_908))))) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
equiv(X_29,or(X_906,not(and(X_907,X_908)))) = equiv(X_29,or(X_906,implies(X_907,not(X_908)))),
inference(resolve,[$cnf( $equal(and(not(and(X_29,and(not(X_906),and(X_907,X_908)))),or(and(not(X_906),and(X_907,X_908)),X_29)),equiv(X_29,or(X_906,implies(X_907,not(X_908))))) )],[refute_0_376,refute_0_433]) ).
cnf(refute_0_435,plain,
( equiv(X_29,or(X_906,not(and(X_907,X_908)))) != equiv(X_29,or(X_906,implies(X_907,not(X_908))))
| equiv(X_29,or(X_906,implies(X_907,not(X_908)))) = equiv(X_29,or(X_906,not(and(X_907,X_908)))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(X_29,or(X_906,not(and(X_907,X_908)))))),bind(Y0,$fot(equiv(X_29,or(X_906,implies(X_907,not(X_908))))))]]) ).
cnf(refute_0_436,plain,
equiv(X_29,or(X_906,implies(X_907,not(X_908)))) = equiv(X_29,or(X_906,not(and(X_907,X_908)))),
inference(resolve,[$cnf( $equal(equiv(X_29,or(X_906,not(and(X_907,X_908)))),equiv(X_29,or(X_906,implies(X_907,not(X_908))))) )],[refute_0_434,refute_0_435]) ).
cnf(refute_0_437,plain,
equiv(or(X_10,implies(X,not(X_10))),or(X_10,implies(X,not(X_10)))) = equiv(or(X_10,implies(X,not(X_10))),or(X_10,not(and(X,X_10)))),
inference(subst,[],[refute_0_436:[bind(X_29,$fot(or(X_10,implies(X,not(X_10))))),bind(X_906,$fot(X_10)),bind(X_907,$fot(X)),bind(X_908,$fot(X_10))]]) ).
cnf(refute_0_438,plain,
( equiv(or(X_10,implies(X,not(X_10))),or(X_10,implies(X,not(X_10)))) != equiv(or(X_10,implies(X,not(X_10))),or(X_10,not(and(X,X_10))))
| ~ is_a_theorem(equiv(or(X_10,implies(X,not(X_10))),or(X_10,implies(X,not(X_10)))))
| is_a_theorem(equiv(or(X_10,implies(X,not(X_10))),or(X_10,not(and(X,X_10))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(equiv(or(X_10,implies(X,not(X_10))),or(X_10,implies(X,not(X_10))))) ),[0],$fot(equiv(or(X_10,implies(X,not(X_10))),or(X_10,not(and(X,X_10)))))]]) ).
cnf(refute_0_439,plain,
( ~ is_a_theorem(equiv(or(X_10,implies(X,not(X_10))),or(X_10,implies(X,not(X_10)))))
| is_a_theorem(equiv(or(X_10,implies(X,not(X_10))),or(X_10,not(and(X,X_10))))) ),
inference(resolve,[$cnf( $equal(equiv(or(X_10,implies(X,not(X_10))),or(X_10,implies(X,not(X_10)))),equiv(or(X_10,implies(X,not(X_10))),or(X_10,not(and(X,X_10))))) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
is_a_theorem(equiv(or(X_10,implies(X,not(X_10))),or(X_10,not(and(X,X_10))))),
inference(resolve,[$cnf( is_a_theorem(equiv(or(X_10,implies(X,not(X_10))),or(X_10,implies(X,not(X_10))))) )],[refute_0_334,refute_0_439]) ).
cnf(refute_0_441,plain,
is_a_theorem(equiv(or(X_918,implies(X_917,not(X_918))),or(X_918,not(and(X_917,X_918))))),
inference(subst,[],[refute_0_440:[bind(X,$fot(X_917)),bind(X_10,$fot(X_918))]]) ).
cnf(refute_0_442,plain,
or(X_918,implies(X_917,not(X_918))) = or(X_918,not(and(X_917,X_918))),
inference(resolve,[$cnf( is_a_theorem(equiv(or(X_918,implies(X_917,not(X_918))),or(X_918,not(and(X_917,X_918))))) )],[refute_0_441,refute_0_254]) ).
cnf(refute_0_443,plain,
or(X_103,implies(X,not(X_103))) = or(X_103,not(and(X,X_103))),
inference(subst,[],[refute_0_442:[bind(X_917,$fot(X)),bind(X_918,$fot(X_103))]]) ).
cnf(refute_0_444,plain,
( or(X_103,implies(X,not(X_103))) != or(X_103,not(and(X,X_103)))
| ~ is_a_theorem(or(X_103,not(and(X,X_103))))
| is_a_theorem(or(X_103,implies(X,not(X_103)))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(or(X_103,implies(X,not(X_103)))) ),[0],$fot(or(X_103,not(and(X,X_103))))]]) ).
cnf(refute_0_445,plain,
( ~ is_a_theorem(or(X_103,not(and(X,X_103))))
| is_a_theorem(or(X_103,implies(X,not(X_103)))) ),
inference(resolve,[$cnf( $equal(or(X_103,implies(X,not(X_103))),or(X_103,not(and(X,X_103)))) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
( ~ is_a_theorem(or(X_103,not(and(X,X_103))))
| is_a_theorem(implies(X,or(X_103,not(X_103)))) ),
inference(resolve,[$cnf( is_a_theorem(or(X_103,implies(X,not(X_103)))) )],[refute_0_445,refute_0_250]) ).
cnf(refute_0_447,plain,
is_a_theorem(implies(not(X),or(X_154,not(not(not(not(not(X)))))))),
inference(subst,[],[refute_0_87:[bind(X,$fot(not(X))),bind(X_57,$fot(X_154))]]) ).
cnf(refute_0_448,plain,
or(X,or(X_154,not(not(not(not(not(X))))))) = implies(not(X),or(X_154,not(not(not(not(not(X))))))),
inference(subst,[],[refute_0_60:[bind(Y,$fot(or(X_154,not(not(not(not(not(X))))))))]]) ).
cnf(refute_0_449,plain,
( or(X,or(X_154,not(not(not(not(not(X))))))) != implies(not(X),or(X_154,not(not(not(not(not(X)))))))
| implies(not(X),or(X_154,not(not(not(not(not(X))))))) = or(X,or(X_154,not(not(not(not(not(X))))))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,or(X_154,not(not(not(not(not(X))))))))),bind(Y0,$fot(implies(not(X),or(X_154,not(not(not(not(not(X)))))))))]]) ).
cnf(refute_0_450,plain,
implies(not(X),or(X_154,not(not(not(not(not(X))))))) = or(X,or(X_154,not(not(not(not(not(X))))))),
inference(resolve,[$cnf( $equal(or(X,or(X_154,not(not(not(not(not(X))))))),implies(not(X),or(X_154,not(not(not(not(not(X)))))))) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
( implies(not(X),or(X_154,not(not(not(not(not(X))))))) != or(X,or(X_154,not(not(not(not(not(X)))))))
| ~ is_a_theorem(implies(not(X),or(X_154,not(not(not(not(not(X))))))))
| is_a_theorem(or(X,or(X_154,not(not(not(not(not(X)))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X),or(X_154,not(not(not(not(not(X)))))))) ),[0],$fot(or(X,or(X_154,not(not(not(not(not(X))))))))]]) ).
cnf(refute_0_452,plain,
( ~ is_a_theorem(implies(not(X),or(X_154,not(not(not(not(not(X))))))))
| is_a_theorem(or(X,or(X_154,not(not(not(not(not(X)))))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),or(X_154,not(not(not(not(not(X))))))),or(X,or(X_154,not(not(not(not(not(X)))))))) )],[refute_0_450,refute_0_451]) ).
cnf(refute_0_453,plain,
is_a_theorem(or(X,or(X_154,not(not(not(not(not(X)))))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X),or(X_154,not(not(not(not(not(X)))))))) )],[refute_0_447,refute_0_452]) ).
cnf(refute_0_454,plain,
is_a_theorem(or(X_172,or(not(X),not(not(not(not(not(X_172)))))))),
inference(subst,[],[refute_0_453:[bind(X,$fot(X_172)),bind(X_154,$fot(not(X)))]]) ).
cnf(refute_0_455,plain,
implies(X,not(not(not(not(not(X_172)))))) = or(not(X),not(not(not(not(not(X_172)))))),
inference(subst,[],[refute_0_9:[bind(Y,$fot(not(not(not(not(not(X_172)))))))]]) ).
cnf(refute_0_456,plain,
( implies(X,not(not(not(not(not(X_172)))))) != or(not(X),not(not(not(not(not(X_172))))))
| or(not(X),not(not(not(not(not(X_172)))))) = implies(X,not(not(not(not(not(X_172)))))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,not(not(not(not(not(X_172)))))))),bind(Y0,$fot(or(not(X),not(not(not(not(not(X_172))))))))]]) ).
cnf(refute_0_457,plain,
or(not(X),not(not(not(not(not(X_172)))))) = implies(X,not(not(not(not(not(X_172)))))),
inference(resolve,[$cnf( $equal(implies(X,not(not(not(not(not(X_172)))))),or(not(X),not(not(not(not(not(X_172))))))) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
( or(not(X),not(not(not(not(not(X_172)))))) != implies(X,not(not(not(not(not(X_172))))))
| ~ is_a_theorem(or(X_172,or(not(X),not(not(not(not(not(X_172))))))))
| is_a_theorem(or(X_172,implies(X,not(not(not(not(not(X_172)))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_172,or(not(X),not(not(not(not(not(X_172)))))))) ),[0,1],$fot(implies(X,not(not(not(not(not(X_172)))))))]]) ).
cnf(refute_0_459,plain,
( ~ is_a_theorem(or(X_172,or(not(X),not(not(not(not(not(X_172))))))))
| is_a_theorem(or(X_172,implies(X,not(not(not(not(not(X_172)))))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(not(not(not(not(X_172)))))),implies(X,not(not(not(not(not(X_172))))))) )],[refute_0_457,refute_0_458]) ).
cnf(refute_0_460,plain,
is_a_theorem(or(X_172,implies(X,not(not(not(not(not(X_172)))))))),
inference(resolve,[$cnf( is_a_theorem(or(X_172,or(not(X),not(not(not(not(not(X_172)))))))) )],[refute_0_454,refute_0_459]) ).
cnf(refute_0_461,plain,
is_a_theorem(or(X_212,implies(X,not(not(not(not(not(X_212)))))))),
inference(subst,[],[refute_0_460:[bind(X_172,$fot(X_212))]]) ).
cnf(refute_0_462,plain,
( ~ is_a_theorem(or(X_212,implies(X,not(not(not(not(not(X_212))))))))
| is_a_theorem(or(implies(X,not(not(not(not(not(X_212)))))),X_212)) ),
inference(subst,[],[refute_0_43:[bind(P,$fot(X_212)),bind(Q,$fot(implies(X,not(not(not(not(not(X_212))))))))]]) ).
cnf(refute_0_463,plain,
is_a_theorem(or(implies(X,not(not(not(not(not(X_212)))))),X_212)),
inference(resolve,[$cnf( is_a_theorem(or(X_212,implies(X,not(not(not(not(not(X_212)))))))) )],[refute_0_461,refute_0_462]) ).
cnf(refute_0_464,plain,
or(implies(X_16,not(X_17)),Y) = implies(not(implies(X_16,not(X_17))),Y),
inference(subst,[],[refute_0_60:[bind(X,$fot(implies(X_16,not(X_17))))]]) ).
cnf(refute_0_465,plain,
( not(implies(X_16,not(X_17))) != and(X_16,X_17)
| or(implies(X_16,not(X_17)),Y) != implies(not(implies(X_16,not(X_17))),Y)
| or(implies(X_16,not(X_17)),Y) = implies(and(X_16,X_17),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(X_16,not(X_17)),Y),implies(not(implies(X_16,not(X_17))),Y)) ),[1,0],$fot(and(X_16,X_17))]]) ).
cnf(refute_0_466,plain,
( or(implies(X_16,not(X_17)),Y) != implies(not(implies(X_16,not(X_17))),Y)
| or(implies(X_16,not(X_17)),Y) = implies(and(X_16,X_17),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_16,not(X_17))),and(X_16,X_17)) )],[refute_0_131,refute_0_465]) ).
cnf(refute_0_467,plain,
or(implies(X_16,not(X_17)),Y) = implies(and(X_16,X_17),Y),
inference(resolve,[$cnf( $equal(or(implies(X_16,not(X_17)),Y),implies(not(implies(X_16,not(X_17))),Y)) )],[refute_0_464,refute_0_466]) ).
cnf(refute_0_468,plain,
or(implies(X,not(X_212)),X_212) = implies(and(X,X_212),X_212),
inference(subst,[],[refute_0_467:[bind(Y,$fot(X_212)),bind(X_16,$fot(X)),bind(X_17,$fot(X_212))]]) ).
cnf(refute_0_469,plain,
implies(and(X_4,not(X_5)),Y) = or(not(and(X_4,not(X_5))),Y),
inference(subst,[],[refute_0_9:[bind(X,$fot(and(X_4,not(X_5))))]]) ).
cnf(refute_0_470,plain,
( implies(and(X_4,not(X_5)),Y) != or(not(and(X_4,not(X_5))),Y)
| not(and(X_4,not(X_5))) != implies(X_4,X_5)
| implies(and(X_4,not(X_5)),Y) = or(implies(X_4,X_5),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(X_4,not(X_5)),Y),or(not(and(X_4,not(X_5))),Y)) ),[1,0],$fot(implies(X_4,X_5))]]) ).
cnf(refute_0_471,plain,
( implies(and(X_4,not(X_5)),Y) != or(not(and(X_4,not(X_5))),Y)
| implies(and(X_4,not(X_5)),Y) = or(implies(X_4,X_5),Y) ),
inference(resolve,[$cnf( $equal(not(and(X_4,not(X_5))),implies(X_4,X_5)) )],[refute_0_280,refute_0_470]) ).
cnf(refute_0_472,plain,
implies(and(X_4,not(X_5)),Y) = or(implies(X_4,X_5),Y),
inference(resolve,[$cnf( $equal(implies(and(X_4,not(X_5)),Y),or(not(and(X_4,not(X_5))),Y)) )],[refute_0_469,refute_0_471]) ).
cnf(refute_0_473,plain,
implies(and(X,not(not(X_212))),X_212) = or(implies(X,not(X_212)),X_212),
inference(subst,[],[refute_0_472:[bind(Y,$fot(X_212)),bind(X_4,$fot(X)),bind(X_5,$fot(not(X_212)))]]) ).
cnf(refute_0_474,plain,
( implies(and(X,not(not(X_212))),X_212) != or(implies(X,not(X_212)),X_212)
| or(implies(X,not(X_212)),X_212) != implies(and(X,X_212),X_212)
| implies(and(X,not(not(X_212))),X_212) = implies(and(X,X_212),X_212) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(and(X,not(not(X_212))),X_212))),bind(Y0,$fot(or(implies(X,not(X_212)),X_212))),bind(Z,$fot(implies(and(X,X_212),X_212)))]]) ).
cnf(refute_0_475,plain,
( or(implies(X,not(X_212)),X_212) != implies(and(X,X_212),X_212)
| implies(and(X,not(not(X_212))),X_212) = implies(and(X,X_212),X_212) ),
inference(resolve,[$cnf( $equal(implies(and(X,not(not(X_212))),X_212),or(implies(X,not(X_212)),X_212)) )],[refute_0_473,refute_0_474]) ).
cnf(refute_0_476,plain,
implies(and(X,not(not(X_212))),X_212) = implies(and(X,X_212),X_212),
inference(resolve,[$cnf( $equal(or(implies(X,not(X_212)),X_212),implies(and(X,X_212),X_212)) )],[refute_0_468,refute_0_475]) ).
cnf(refute_0_477,plain,
or(implies(X,not(not(not(X_212)))),X_212) = implies(and(X,not(not(X_212))),X_212),
inference(subst,[],[refute_0_467:[bind(Y,$fot(X_212)),bind(X_16,$fot(X)),bind(X_17,$fot(not(not(X_212))))]]) ).
cnf(refute_0_478,plain,
( implies(and(X,not(not(X_212))),X_212) != implies(and(X,X_212),X_212)
| or(implies(X,not(not(not(X_212)))),X_212) != implies(and(X,not(not(X_212))),X_212)
| or(implies(X,not(not(not(X_212)))),X_212) = implies(and(X,X_212),X_212) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(or(implies(X,not(not(not(X_212)))),X_212))),bind(Y0,$fot(implies(and(X,not(not(X_212))),X_212))),bind(Z,$fot(implies(and(X,X_212),X_212)))]]) ).
cnf(refute_0_479,plain,
( implies(and(X,not(not(X_212))),X_212) != implies(and(X,X_212),X_212)
| or(implies(X,not(not(not(X_212)))),X_212) = implies(and(X,X_212),X_212) ),
inference(resolve,[$cnf( $equal(or(implies(X,not(not(not(X_212)))),X_212),implies(and(X,not(not(X_212))),X_212)) )],[refute_0_477,refute_0_478]) ).
cnf(refute_0_480,plain,
or(implies(X,not(not(not(X_212)))),X_212) = implies(and(X,X_212),X_212),
inference(resolve,[$cnf( $equal(implies(and(X,not(not(X_212))),X_212),implies(and(X,X_212),X_212)) )],[refute_0_476,refute_0_479]) ).
cnf(refute_0_481,plain,
implies(and(X,not(not(not(not(X_212))))),X_212) = or(implies(X,not(not(not(X_212)))),X_212),
inference(subst,[],[refute_0_472:[bind(Y,$fot(X_212)),bind(X_4,$fot(X)),bind(X_5,$fot(not(not(not(X_212)))))]]) ).
cnf(refute_0_482,plain,
( implies(and(X,not(not(not(not(X_212))))),X_212) != or(implies(X,not(not(not(X_212)))),X_212)
| or(implies(X,not(not(not(X_212)))),X_212) != implies(and(X,X_212),X_212)
| implies(and(X,not(not(not(not(X_212))))),X_212) = implies(and(X,X_212),X_212) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(and(X,not(not(not(not(X_212))))),X_212))),bind(Y0,$fot(or(implies(X,not(not(not(X_212)))),X_212))),bind(Z,$fot(implies(and(X,X_212),X_212)))]]) ).
cnf(refute_0_483,plain,
( or(implies(X,not(not(not(X_212)))),X_212) != implies(and(X,X_212),X_212)
| implies(and(X,not(not(not(not(X_212))))),X_212) = implies(and(X,X_212),X_212) ),
inference(resolve,[$cnf( $equal(implies(and(X,not(not(not(not(X_212))))),X_212),or(implies(X,not(not(not(X_212)))),X_212)) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
implies(and(X,not(not(not(not(X_212))))),X_212) = implies(and(X,X_212),X_212),
inference(resolve,[$cnf( $equal(or(implies(X,not(not(not(X_212)))),X_212),implies(and(X,X_212),X_212)) )],[refute_0_480,refute_0_483]) ).
cnf(refute_0_485,plain,
or(implies(X,not(not(not(not(not(X_212)))))),X_212) = implies(and(X,not(not(not(not(X_212))))),X_212),
inference(subst,[],[refute_0_467:[bind(Y,$fot(X_212)),bind(X_16,$fot(X)),bind(X_17,$fot(not(not(not(not(X_212))))))]]) ).
cnf(refute_0_486,plain,
( implies(and(X,not(not(not(not(X_212))))),X_212) != implies(and(X,X_212),X_212)
| or(implies(X,not(not(not(not(not(X_212)))))),X_212) != implies(and(X,not(not(not(not(X_212))))),X_212)
| or(implies(X,not(not(not(not(not(X_212)))))),X_212) = implies(and(X,X_212),X_212) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(or(implies(X,not(not(not(not(not(X_212)))))),X_212))),bind(Y0,$fot(implies(and(X,not(not(not(not(X_212))))),X_212))),bind(Z,$fot(implies(and(X,X_212),X_212)))]]) ).
cnf(refute_0_487,plain,
( implies(and(X,not(not(not(not(X_212))))),X_212) != implies(and(X,X_212),X_212)
| or(implies(X,not(not(not(not(not(X_212)))))),X_212) = implies(and(X,X_212),X_212) ),
inference(resolve,[$cnf( $equal(or(implies(X,not(not(not(not(not(X_212)))))),X_212),implies(and(X,not(not(not(not(X_212))))),X_212)) )],[refute_0_485,refute_0_486]) ).
cnf(refute_0_488,plain,
or(implies(X,not(not(not(not(not(X_212)))))),X_212) = implies(and(X,X_212),X_212),
inference(resolve,[$cnf( $equal(implies(and(X,not(not(not(not(X_212))))),X_212),implies(and(X,X_212),X_212)) )],[refute_0_484,refute_0_487]) ).
cnf(refute_0_489,plain,
( or(implies(X,not(not(not(not(not(X_212)))))),X_212) != implies(and(X,X_212),X_212)
| ~ is_a_theorem(or(implies(X,not(not(not(not(not(X_212)))))),X_212))
| is_a_theorem(implies(and(X,X_212),X_212)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(X,not(not(not(not(not(X_212)))))),X_212)) ),[0],$fot(implies(and(X,X_212),X_212))]]) ).
cnf(refute_0_490,plain,
( ~ is_a_theorem(or(implies(X,not(not(not(not(not(X_212)))))),X_212))
| is_a_theorem(implies(and(X,X_212),X_212)) ),
inference(resolve,[$cnf( $equal(or(implies(X,not(not(not(not(not(X_212)))))),X_212),implies(and(X,X_212),X_212)) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
is_a_theorem(implies(and(X,X_212),X_212)),
inference(resolve,[$cnf( is_a_theorem(or(implies(X,not(not(not(not(not(X_212)))))),X_212)) )],[refute_0_463,refute_0_490]) ).
cnf(refute_0_492,plain,
is_a_theorem(implies(and(X,X_419),X_419)),
inference(subst,[],[refute_0_491:[bind(X_212,$fot(X_419))]]) ).
cnf(refute_0_493,plain,
is_a_theorem(implies(or(not(X),X_24),or(X_24,not(X)))),
inference(subst,[],[refute_0_41:[bind(P,$fot(not(X))),bind(Q,$fot(X_24))]]) ).
cnf(refute_0_494,plain,
implies(X,X_24) = or(not(X),X_24),
inference(subst,[],[refute_0_9:[bind(Y,$fot(X_24))]]) ).
cnf(refute_0_495,plain,
( implies(X,X_24) != or(not(X),X_24)
| or(not(X),X_24) = implies(X,X_24) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,X_24))),bind(Y0,$fot(or(not(X),X_24)))]]) ).
cnf(refute_0_496,plain,
or(not(X),X_24) = implies(X,X_24),
inference(resolve,[$cnf( $equal(implies(X,X_24),or(not(X),X_24)) )],[refute_0_494,refute_0_495]) ).
cnf(refute_0_497,plain,
( or(not(X),X_24) != implies(X,X_24)
| ~ is_a_theorem(implies(or(not(X),X_24),or(X_24,not(X))))
| is_a_theorem(implies(implies(X,X_24),or(X_24,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),X_24),or(X_24,not(X)))) ),[0,0],$fot(implies(X,X_24))]]) ).
cnf(refute_0_498,plain,
( ~ is_a_theorem(implies(or(not(X),X_24),or(X_24,not(X))))
| is_a_theorem(implies(implies(X,X_24),or(X_24,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_24),implies(X,X_24)) )],[refute_0_496,refute_0_497]) ).
cnf(refute_0_499,plain,
is_a_theorem(implies(implies(X,X_24),or(X_24,not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),X_24),or(X_24,not(X)))) )],[refute_0_493,refute_0_498]) ).
cnf(refute_0_500,plain,
( ~ is_a_theorem(implies(X,X_24))
| ~ is_a_theorem(implies(implies(X,X_24),or(X_24,not(X))))
| is_a_theorem(or(X_24,not(X))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(implies(X,X_24))),bind(Y,$fot(or(X_24,not(X))))]]) ).
cnf(refute_0_501,plain,
( ~ is_a_theorem(implies(X,X_24))
| is_a_theorem(or(X_24,not(X))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,X_24),or(X_24,not(X)))) )],[refute_0_499,refute_0_500]) ).
cnf(refute_0_502,plain,
( ~ is_a_theorem(implies(and(X,X_419),X_419))
| is_a_theorem(or(X_419,not(and(X,X_419)))) ),
inference(subst,[],[refute_0_501:[bind(X,$fot(and(X,X_419))),bind(X_24,$fot(X_419))]]) ).
cnf(refute_0_503,plain,
is_a_theorem(or(X_419,not(and(X,X_419)))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X,X_419),X_419)) )],[refute_0_492,refute_0_502]) ).
cnf(refute_0_504,plain,
is_a_theorem(or(X_103,not(and(X,X_103)))),
inference(subst,[],[refute_0_503:[bind(X_419,$fot(X_103))]]) ).
cnf(refute_0_505,plain,
is_a_theorem(implies(X,or(X_103,not(X_103)))),
inference(resolve,[$cnf( is_a_theorem(or(X_103,not(and(X,X_103)))) )],[refute_0_504,refute_0_446]) ).
cnf(refute_0_506,plain,
is_a_theorem(implies(not(X),or(X_4511,not(X_4511)))),
inference(subst,[],[refute_0_505:[bind(X,$fot(not(X))),bind(X_103,$fot(X_4511))]]) ).
cnf(refute_0_507,plain,
or(X,or(X_4511,not(X_4511))) = implies(not(X),or(X_4511,not(X_4511))),
inference(subst,[],[refute_0_60:[bind(Y,$fot(or(X_4511,not(X_4511))))]]) ).
cnf(refute_0_508,plain,
( or(X,or(X_4511,not(X_4511))) != implies(not(X),or(X_4511,not(X_4511)))
| implies(not(X),or(X_4511,not(X_4511))) = or(X,or(X_4511,not(X_4511))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,or(X_4511,not(X_4511))))),bind(Y0,$fot(implies(not(X),or(X_4511,not(X_4511)))))]]) ).
cnf(refute_0_509,plain,
implies(not(X),or(X_4511,not(X_4511))) = or(X,or(X_4511,not(X_4511))),
inference(resolve,[$cnf( $equal(or(X,or(X_4511,not(X_4511))),implies(not(X),or(X_4511,not(X_4511)))) )],[refute_0_507,refute_0_508]) ).
cnf(refute_0_510,plain,
( implies(not(X),or(X_4511,not(X_4511))) != or(X,or(X_4511,not(X_4511)))
| ~ is_a_theorem(implies(not(X),or(X_4511,not(X_4511))))
| is_a_theorem(or(X,or(X_4511,not(X_4511)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X),or(X_4511,not(X_4511)))) ),[0],$fot(or(X,or(X_4511,not(X_4511))))]]) ).
cnf(refute_0_511,plain,
( ~ is_a_theorem(implies(not(X),or(X_4511,not(X_4511))))
| is_a_theorem(or(X,or(X_4511,not(X_4511)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),or(X_4511,not(X_4511))),or(X,or(X_4511,not(X_4511)))) )],[refute_0_509,refute_0_510]) ).
cnf(refute_0_512,plain,
is_a_theorem(or(X,or(X_4511,not(X_4511)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X),or(X_4511,not(X_4511)))) )],[refute_0_506,refute_0_511]) ).
cnf(refute_0_513,plain,
is_a_theorem(or(or(X_4513,not(X_4513)),or(X_4513,not(X_4513)))),
inference(subst,[],[refute_0_512:[bind(X,$fot(or(X_4513,not(X_4513)))),bind(X_4511,$fot(X_4513))]]) ).
cnf(refute_0_514,plain,
is_a_theorem(or(X_4513,not(X_4513))),
inference(resolve,[$cnf( is_a_theorem(or(or(X_4513,not(X_4513)),or(X_4513,not(X_4513)))) )],[refute_0_513,refute_0_249]) ).
cnf(refute_0_515,plain,
is_a_theorem(or(X_4514,not(X_4514))),
inference(subst,[],[refute_0_514:[bind(X_4513,$fot(X_4514))]]) ).
cnf(refute_0_516,plain,
is_a_theorem(or(not(X_4514),X_4514)),
inference(resolve,[$cnf( is_a_theorem(or(X_4514,not(X_4514))) )],[refute_0_515,refute_0_245]) ).
cnf(refute_0_517,plain,
or(not(X_4514),X_4514) = implies(X_4514,X_4514),
inference(subst,[],[refute_0_20:[bind(X,$fot(X_4514)),bind(Y,$fot(X_4514))]]) ).
cnf(refute_0_518,plain,
( or(not(X_4514),X_4514) != implies(X_4514,X_4514)
| ~ is_a_theorem(or(not(X_4514),X_4514))
| is_a_theorem(implies(X_4514,X_4514)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X_4514),X_4514)) ),[0],$fot(implies(X_4514,X_4514))]]) ).
cnf(refute_0_519,plain,
( ~ is_a_theorem(or(not(X_4514),X_4514))
| is_a_theorem(implies(X_4514,X_4514)) ),
inference(resolve,[$cnf( $equal(or(not(X_4514),X_4514),implies(X_4514,X_4514)) )],[refute_0_517,refute_0_518]) ).
cnf(refute_0_520,plain,
is_a_theorem(implies(X_4514,X_4514)),
inference(resolve,[$cnf( is_a_theorem(or(not(X_4514),X_4514)) )],[refute_0_516,refute_0_519]) ).
cnf(refute_0_521,plain,
is_a_theorem(implies(X_4515,X_4515)),
inference(subst,[],[refute_0_520:[bind(X_4514,$fot(X_4515))]]) ).
cnf(refute_0_522,plain,
is_a_theorem(and(implies(X_4515,X_4515),implies(X_4515,X_4515))),
inference(resolve,[$cnf( is_a_theorem(implies(X_4515,X_4515)) )],[refute_0_521,refute_0_244]) ).
cnf(refute_0_523,plain,
and(implies(X_4515,X_4515),implies(X_4515,X_4515)) = equiv(X_4515,X_4515),
inference(subst,[],[refute_0_402:[bind(X,$fot(X_4515)),bind(Y,$fot(X_4515))]]) ).
cnf(refute_0_524,plain,
( and(implies(X_4515,X_4515),implies(X_4515,X_4515)) != equiv(X_4515,X_4515)
| ~ is_a_theorem(and(implies(X_4515,X_4515),implies(X_4515,X_4515)))
| is_a_theorem(equiv(X_4515,X_4515)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(and(implies(X_4515,X_4515),implies(X_4515,X_4515))) ),[0],$fot(equiv(X_4515,X_4515))]]) ).
cnf(refute_0_525,plain,
( ~ is_a_theorem(and(implies(X_4515,X_4515),implies(X_4515,X_4515)))
| is_a_theorem(equiv(X_4515,X_4515)) ),
inference(resolve,[$cnf( $equal(and(implies(X_4515,X_4515),implies(X_4515,X_4515)),equiv(X_4515,X_4515)) )],[refute_0_523,refute_0_524]) ).
cnf(refute_0_526,plain,
is_a_theorem(equiv(X_4515,X_4515)),
inference(resolve,[$cnf( is_a_theorem(and(implies(X_4515,X_4515),implies(X_4515,X_4515))) )],[refute_0_522,refute_0_525]) ).
cnf(refute_0_527,plain,
is_a_theorem(equiv(X_4516,X_4516)),
inference(subst,[],[refute_0_526:[bind(X_4515,$fot(X_4516))]]) ).
cnf(refute_0_528,plain,
is_a_theorem(or(X_57,not(not(not(not(equiv(X_4516,X_4516))))))),
inference(resolve,[$cnf( is_a_theorem(equiv(X_4516,X_4516)) )],[refute_0_527,refute_0_91]) ).
cnf(refute_0_529,plain,
and(Y,Y) = not(implies(Y,not(Y))),
inference(subst,[],[refute_0_128:[bind(X,$fot(Y))]]) ).
cnf(refute_0_530,plain,
implies(not(Y),Y) = not(and(not(Y),not(Y))),
inference(subst,[],[refute_0_54:[bind(X,$fot(not(Y)))]]) ).
cnf(refute_0_531,plain,
( ~ is_a_theorem(equiv(and(not(X_655),not(X_655)),not(or(X_655,X_655))))
| and(not(X_655),not(X_655)) = not(or(X_655,X_655)) ),
inference(subst,[],[refute_0_253:[bind(X,$fot(and(not(X_655),not(X_655)))),bind(Y,$fot(not(or(X_655,X_655))))]]) ).
cnf(refute_0_532,plain,
( ~ is_a_theorem(or(or(X_424,X_423),not(or(X_423,X_424))))
| is_a_theorem(and(or(or(X_424,X_423),not(or(X_423,X_424))),or(or(X_424,X_423),not(or(X_423,X_424))))) ),
inference(subst,[],[refute_0_243:[bind(X_214,$fot(or(or(X_424,X_423),not(or(X_423,X_424)))))]]) ).
cnf(refute_0_533,plain,
( ~ is_a_theorem(implies(or(P,Q),or(Q,P)))
| is_a_theorem(or(or(Q,P),not(or(P,Q)))) ),
inference(subst,[],[refute_0_501:[bind(X,$fot(or(P,Q))),bind(X_24,$fot(or(Q,P)))]]) ).
cnf(refute_0_534,plain,
is_a_theorem(or(or(Q,P),not(or(P,Q)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,Q),or(Q,P))) )],[refute_0_41,refute_0_533]) ).
cnf(refute_0_535,plain,
is_a_theorem(or(or(X_424,X_423),not(or(X_423,X_424)))),
inference(subst,[],[refute_0_534:[bind(P,$fot(X_423)),bind(Q,$fot(X_424))]]) ).
cnf(refute_0_536,plain,
is_a_theorem(and(or(or(X_424,X_423),not(or(X_423,X_424))),or(or(X_424,X_423),not(or(X_423,X_424))))),
inference(resolve,[$cnf( is_a_theorem(or(or(X_424,X_423),not(or(X_423,X_424)))) )],[refute_0_535,refute_0_532]) ).
cnf(refute_0_537,plain,
is_a_theorem(and(or(or(X_651,X_651),not(or(X_651,X_651))),or(or(X_651,X_651),not(or(X_651,X_651))))),
inference(subst,[],[refute_0_536:[bind(X_423,$fot(X_651)),bind(X_424,$fot(X_651))]]) ).
cnf(refute_0_538,plain,
equiv(not(X),not(X_34)) = and(implies(not(X),not(X_34)),or(X_34,not(X))),
inference(subst,[],[refute_0_342:[bind(X,$fot(X_34)),bind(X_29,$fot(not(X)))]]) ).
cnf(refute_0_539,plain,
or(X,not(X_34)) = implies(not(X),not(X_34)),
inference(subst,[],[refute_0_60:[bind(Y,$fot(not(X_34)))]]) ).
cnf(refute_0_540,plain,
( or(X,not(X_34)) != implies(not(X),not(X_34))
| implies(not(X),not(X_34)) = or(X,not(X_34)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,not(X_34)))),bind(Y0,$fot(implies(not(X),not(X_34))))]]) ).
cnf(refute_0_541,plain,
implies(not(X),not(X_34)) = or(X,not(X_34)),
inference(resolve,[$cnf( $equal(or(X,not(X_34)),implies(not(X),not(X_34))) )],[refute_0_539,refute_0_540]) ).
cnf(refute_0_542,plain,
( equiv(not(X),not(X_34)) != and(implies(not(X),not(X_34)),or(X_34,not(X)))
| implies(not(X),not(X_34)) != or(X,not(X_34))
| equiv(not(X),not(X_34)) = and(or(X,not(X_34)),or(X_34,not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X),not(X_34)),and(implies(not(X),not(X_34)),or(X_34,not(X)))) ),[1,0],$fot(or(X,not(X_34)))]]) ).
cnf(refute_0_543,plain,
( equiv(not(X),not(X_34)) != and(implies(not(X),not(X_34)),or(X_34,not(X)))
| equiv(not(X),not(X_34)) = and(or(X,not(X_34)),or(X_34,not(X))) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X_34)),or(X,not(X_34))) )],[refute_0_541,refute_0_542]) ).
cnf(refute_0_544,plain,
equiv(not(X),not(X_34)) = and(or(X,not(X_34)),or(X_34,not(X))),
inference(resolve,[$cnf( $equal(equiv(not(X),not(X_34)),and(implies(not(X),not(X_34)),or(X_34,not(X)))) )],[refute_0_538,refute_0_543]) ).
cnf(refute_0_545,plain,
equiv(not(or(X_651,X_651)),not(or(X_651,X_651))) = and(or(or(X_651,X_651),not(or(X_651,X_651))),or(or(X_651,X_651),not(or(X_651,X_651)))),
inference(subst,[],[refute_0_544:[bind(X,$fot(or(X_651,X_651))),bind(X_34,$fot(or(X_651,X_651)))]]) ).
cnf(refute_0_546,plain,
( equiv(not(or(X_651,X_651)),not(or(X_651,X_651))) != and(or(or(X_651,X_651),not(or(X_651,X_651))),or(or(X_651,X_651),not(or(X_651,X_651))))
| and(or(or(X_651,X_651),not(or(X_651,X_651))),or(or(X_651,X_651),not(or(X_651,X_651)))) = equiv(not(or(X_651,X_651)),not(or(X_651,X_651))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(not(or(X_651,X_651)),not(or(X_651,X_651))))),bind(Y0,$fot(and(or(or(X_651,X_651),not(or(X_651,X_651))),or(or(X_651,X_651),not(or(X_651,X_651))))))]]) ).
cnf(refute_0_547,plain,
and(or(or(X_651,X_651),not(or(X_651,X_651))),or(or(X_651,X_651),not(or(X_651,X_651)))) = equiv(not(or(X_651,X_651)),not(or(X_651,X_651))),
inference(resolve,[$cnf( $equal(equiv(not(or(X_651,X_651)),not(or(X_651,X_651))),and(or(or(X_651,X_651),not(or(X_651,X_651))),or(or(X_651,X_651),not(or(X_651,X_651))))) )],[refute_0_545,refute_0_546]) ).
cnf(refute_0_548,plain,
( and(or(or(X_651,X_651),not(or(X_651,X_651))),or(or(X_651,X_651),not(or(X_651,X_651)))) != equiv(not(or(X_651,X_651)),not(or(X_651,X_651)))
| ~ is_a_theorem(and(or(or(X_651,X_651),not(or(X_651,X_651))),or(or(X_651,X_651),not(or(X_651,X_651)))))
| is_a_theorem(equiv(not(or(X_651,X_651)),not(or(X_651,X_651)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(and(or(or(X_651,X_651),not(or(X_651,X_651))),or(or(X_651,X_651),not(or(X_651,X_651))))) ),[0],$fot(equiv(not(or(X_651,X_651)),not(or(X_651,X_651))))]]) ).
cnf(refute_0_549,plain,
( ~ is_a_theorem(and(or(or(X_651,X_651),not(or(X_651,X_651))),or(or(X_651,X_651),not(or(X_651,X_651)))))
| is_a_theorem(equiv(not(or(X_651,X_651)),not(or(X_651,X_651)))) ),
inference(resolve,[$cnf( $equal(and(or(or(X_651,X_651),not(or(X_651,X_651))),or(or(X_651,X_651),not(or(X_651,X_651)))),equiv(not(or(X_651,X_651)),not(or(X_651,X_651)))) )],[refute_0_547,refute_0_548]) ).
cnf(refute_0_550,plain,
is_a_theorem(equiv(not(or(X_651,X_651)),not(or(X_651,X_651)))),
inference(resolve,[$cnf( is_a_theorem(and(or(or(X_651,X_651),not(or(X_651,X_651))),or(or(X_651,X_651),not(or(X_651,X_651))))) )],[refute_0_537,refute_0_549]) ).
cnf(refute_0_551,plain,
is_a_theorem(equiv(not(or(not(X),not(X))),not(or(not(X),not(X))))),
inference(subst,[],[refute_0_550:[bind(X_651,$fot(not(X)))]]) ).
cnf(refute_0_552,plain,
( or(not(X),not(X)) != implies(X,not(X))
| ~ is_a_theorem(equiv(not(or(not(X),not(X))),not(or(not(X),not(X)))))
| is_a_theorem(equiv(not(or(not(X),not(X))),not(implies(X,not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(equiv(not(or(not(X),not(X))),not(or(not(X),not(X))))) ),[0,1,0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_553,plain,
( ~ is_a_theorem(equiv(not(or(not(X),not(X))),not(or(not(X),not(X)))))
| is_a_theorem(equiv(not(or(not(X),not(X))),not(implies(X,not(X))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_171,refute_0_552]) ).
cnf(refute_0_554,plain,
is_a_theorem(equiv(not(or(not(X),not(X))),not(implies(X,not(X))))),
inference(resolve,[$cnf( is_a_theorem(equiv(not(or(not(X),not(X))),not(or(not(X),not(X))))) )],[refute_0_551,refute_0_553]) ).
cnf(refute_0_555,plain,
not(implies(X,not(X))) = and(X,X),
inference(subst,[],[refute_0_195:[bind(Y,$fot(X))]]) ).
cnf(refute_0_556,plain,
equiv(and(X,X),not(implies(X,not(X)))) = equiv(and(X,X),not(implies(X,not(X)))),
introduced(tautology,[refl,[$fot(equiv(and(X,X),not(implies(X,not(X)))))]]) ).
cnf(refute_0_557,plain,
( equiv(and(X,X),not(implies(X,not(X)))) != equiv(and(X,X),not(implies(X,not(X))))
| not(implies(X,not(X))) != and(X,X)
| equiv(and(X,X),not(implies(X,not(X)))) = equiv(and(X,X),and(X,X)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(and(X,X),not(implies(X,not(X)))),equiv(and(X,X),not(implies(X,not(X))))) ),[1,1],$fot(and(X,X))]]) ).
cnf(refute_0_558,plain,
( not(implies(X,not(X))) != and(X,X)
| equiv(and(X,X),not(implies(X,not(X)))) = equiv(and(X,X),and(X,X)) ),
inference(resolve,[$cnf( $equal(equiv(and(X,X),not(implies(X,not(X)))),equiv(and(X,X),not(implies(X,not(X))))) )],[refute_0_556,refute_0_557]) ).
cnf(refute_0_559,plain,
equiv(and(X,X),not(implies(X,not(X)))) = equiv(and(X,X),and(X,X)),
inference(resolve,[$cnf( $equal(not(implies(X,not(X))),and(X,X)) )],[refute_0_555,refute_0_558]) ).
cnf(refute_0_560,plain,
and(not(not(X)),X) = and(X,X),
inference(subst,[],[refute_0_199:[bind(X_20,$fot(X))]]) ).
cnf(refute_0_561,plain,
not(or(not(X),not(X))) = and(not(not(X)),X),
inference(subst,[],[refute_0_386:[bind(X,$fot(not(X))),bind(X_17,$fot(X))]]) ).
cnf(refute_0_562,plain,
( and(not(not(X)),X) != and(X,X)
| not(or(not(X),not(X))) != and(not(not(X)),X)
| not(or(not(X),not(X))) = and(X,X) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(not(or(not(X),not(X))))),bind(Y0,$fot(and(not(not(X)),X))),bind(Z,$fot(and(X,X)))]]) ).
cnf(refute_0_563,plain,
( and(not(not(X)),X) != and(X,X)
| not(or(not(X),not(X))) = and(X,X) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(X))),and(not(not(X)),X)) )],[refute_0_561,refute_0_562]) ).
cnf(refute_0_564,plain,
not(or(not(X),not(X))) = and(X,X),
inference(resolve,[$cnf( $equal(and(not(not(X)),X),and(X,X)) )],[refute_0_560,refute_0_563]) ).
cnf(refute_0_565,plain,
equiv(not(or(not(X),not(X))),not(implies(X,not(X)))) = equiv(not(or(not(X),not(X))),not(implies(X,not(X)))),
introduced(tautology,[refl,[$fot(equiv(not(or(not(X),not(X))),not(implies(X,not(X)))))]]) ).
cnf(refute_0_566,plain,
( equiv(not(or(not(X),not(X))),not(implies(X,not(X)))) != equiv(not(or(not(X),not(X))),not(implies(X,not(X))))
| not(or(not(X),not(X))) != and(X,X)
| equiv(not(or(not(X),not(X))),not(implies(X,not(X)))) = equiv(and(X,X),not(implies(X,not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(or(not(X),not(X))),not(implies(X,not(X)))),equiv(not(or(not(X),not(X))),not(implies(X,not(X))))) ),[1,0],$fot(and(X,X))]]) ).
cnf(refute_0_567,plain,
( not(or(not(X),not(X))) != and(X,X)
| equiv(not(or(not(X),not(X))),not(implies(X,not(X)))) = equiv(and(X,X),not(implies(X,not(X)))) ),
inference(resolve,[$cnf( $equal(equiv(not(or(not(X),not(X))),not(implies(X,not(X)))),equiv(not(or(not(X),not(X))),not(implies(X,not(X))))) )],[refute_0_565,refute_0_566]) ).
cnf(refute_0_568,plain,
equiv(not(or(not(X),not(X))),not(implies(X,not(X)))) = equiv(and(X,X),not(implies(X,not(X)))),
inference(resolve,[$cnf( $equal(not(or(not(X),not(X))),and(X,X)) )],[refute_0_564,refute_0_567]) ).
cnf(refute_0_569,plain,
( equiv(and(X,X),not(implies(X,not(X)))) != equiv(and(X,X),and(X,X))
| equiv(not(or(not(X),not(X))),not(implies(X,not(X)))) != equiv(and(X,X),not(implies(X,not(X))))
| equiv(not(or(not(X),not(X))),not(implies(X,not(X)))) = equiv(and(X,X),and(X,X)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(equiv(not(or(not(X),not(X))),not(implies(X,not(X)))))),bind(Y0,$fot(equiv(and(X,X),not(implies(X,not(X)))))),bind(Z,$fot(equiv(and(X,X),and(X,X))))]]) ).
cnf(refute_0_570,plain,
( equiv(and(X,X),not(implies(X,not(X)))) != equiv(and(X,X),and(X,X))
| equiv(not(or(not(X),not(X))),not(implies(X,not(X)))) = equiv(and(X,X),and(X,X)) ),
inference(resolve,[$cnf( $equal(equiv(not(or(not(X),not(X))),not(implies(X,not(X)))),equiv(and(X,X),not(implies(X,not(X))))) )],[refute_0_568,refute_0_569]) ).
cnf(refute_0_571,plain,
equiv(not(or(not(X),not(X))),not(implies(X,not(X)))) = equiv(and(X,X),and(X,X)),
inference(resolve,[$cnf( $equal(equiv(and(X,X),not(implies(X,not(X)))),equiv(and(X,X),and(X,X))) )],[refute_0_559,refute_0_570]) ).
cnf(refute_0_572,plain,
( equiv(not(or(not(X),not(X))),not(implies(X,not(X)))) != equiv(and(X,X),and(X,X))
| ~ is_a_theorem(equiv(not(or(not(X),not(X))),not(implies(X,not(X)))))
| is_a_theorem(equiv(and(X,X),and(X,X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(equiv(not(or(not(X),not(X))),not(implies(X,not(X))))) ),[0],$fot(equiv(and(X,X),and(X,X)))]]) ).
cnf(refute_0_573,plain,
( ~ is_a_theorem(equiv(not(or(not(X),not(X))),not(implies(X,not(X)))))
| is_a_theorem(equiv(and(X,X),and(X,X))) ),
inference(resolve,[$cnf( $equal(equiv(not(or(not(X),not(X))),not(implies(X,not(X)))),equiv(and(X,X),and(X,X))) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
is_a_theorem(equiv(and(X,X),and(X,X))),
inference(resolve,[$cnf( is_a_theorem(equiv(not(or(not(X),not(X))),not(implies(X,not(X))))) )],[refute_0_554,refute_0_573]) ).
cnf(refute_0_575,plain,
is_a_theorem(equiv(and(not(X_45),not(X_45)),and(not(X_45),not(X_45)))),
inference(subst,[],[refute_0_574:[bind(X,$fot(not(X_45)))]]) ).
cnf(refute_0_576,plain,
equiv(X,and(X_44,not(X_45))) = and(implies(X,and(X_44,not(X_45))),implies(and(X_44,not(X_45)),X)),
inference(subst,[],[refute_0_318:[bind(Y,$fot(and(X_44,not(X_45))))]]) ).
cnf(refute_0_577,plain,
implies(X,and(X_44,not(X_45))) = not(and(X,implies(X_44,X_45))),
inference(subst,[],[refute_0_283:[bind(X_4,$fot(X_44)),bind(X_5,$fot(X_45))]]) ).
cnf(refute_0_578,plain,
( equiv(X,and(X_44,not(X_45))) != and(implies(X,and(X_44,not(X_45))),implies(and(X_44,not(X_45)),X))
| implies(X,and(X_44,not(X_45))) != not(and(X,implies(X_44,X_45)))
| equiv(X,and(X_44,not(X_45))) = and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X,and(X_44,not(X_45))),and(implies(X,and(X_44,not(X_45))),implies(and(X_44,not(X_45)),X))) ),[1,0],$fot(not(and(X,implies(X_44,X_45))))]]) ).
cnf(refute_0_579,plain,
( equiv(X,and(X_44,not(X_45))) != and(implies(X,and(X_44,not(X_45))),implies(and(X_44,not(X_45)),X))
| equiv(X,and(X_44,not(X_45))) = and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X)) ),
inference(resolve,[$cnf( $equal(implies(X,and(X_44,not(X_45))),not(and(X,implies(X_44,X_45)))) )],[refute_0_577,refute_0_578]) ).
cnf(refute_0_580,plain,
equiv(X,and(X_44,not(X_45))) = and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X)),
inference(resolve,[$cnf( $equal(equiv(X,and(X_44,not(X_45))),and(implies(X,and(X_44,not(X_45))),implies(and(X_44,not(X_45)),X))) )],[refute_0_576,refute_0_579]) ).
cnf(refute_0_581,plain,
implies(and(X_44,not(X_45)),X) = or(implies(X_44,X_45),X),
inference(subst,[],[refute_0_472:[bind(Y,$fot(X)),bind(X_4,$fot(X_44)),bind(X_5,$fot(X_45))]]) ).
cnf(refute_0_582,plain,
and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X)) = and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X)),
introduced(tautology,[refl,[$fot(and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X)))]]) ).
cnf(refute_0_583,plain,
( and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X)) != and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X))
| implies(and(X_44,not(X_45)),X) != or(implies(X_44,X_45),X)
| and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X)) = and(not(and(X,implies(X_44,X_45))),or(implies(X_44,X_45),X)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X)),and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X))) ),[1,1],$fot(or(implies(X_44,X_45),X))]]) ).
cnf(refute_0_584,plain,
( implies(and(X_44,not(X_45)),X) != or(implies(X_44,X_45),X)
| and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X)) = and(not(and(X,implies(X_44,X_45))),or(implies(X_44,X_45),X)) ),
inference(resolve,[$cnf( $equal(and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X)),and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X))) )],[refute_0_582,refute_0_583]) ).
cnf(refute_0_585,plain,
and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X)) = and(not(and(X,implies(X_44,X_45))),or(implies(X_44,X_45),X)),
inference(resolve,[$cnf( $equal(implies(and(X_44,not(X_45)),X),or(implies(X_44,X_45),X)) )],[refute_0_581,refute_0_584]) ).
cnf(refute_0_586,plain,
( and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X)) != and(not(and(X,implies(X_44,X_45))),or(implies(X_44,X_45),X))
| equiv(X,and(X_44,not(X_45))) != and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X))
| equiv(X,and(X_44,not(X_45))) = and(not(and(X,implies(X_44,X_45))),or(implies(X_44,X_45),X)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X,and(X_44,not(X_45))),and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X))) ),[1],$fot(and(not(and(X,implies(X_44,X_45))),or(implies(X_44,X_45),X)))]]) ).
cnf(refute_0_587,plain,
( equiv(X,and(X_44,not(X_45))) != and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X))
| equiv(X,and(X_44,not(X_45))) = and(not(and(X,implies(X_44,X_45))),or(implies(X_44,X_45),X)) ),
inference(resolve,[$cnf( $equal(and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X)),and(not(and(X,implies(X_44,X_45))),or(implies(X_44,X_45),X))) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
equiv(X,and(X_44,not(X_45))) = and(not(and(X,implies(X_44,X_45))),or(implies(X_44,X_45),X)),
inference(resolve,[$cnf( $equal(equiv(X,and(X_44,not(X_45))),and(not(and(X,implies(X_44,X_45))),implies(and(X_44,not(X_45)),X))) )],[refute_0_580,refute_0_587]) ).
cnf(refute_0_589,plain,
and(not(and(X,implies(X_44,X_45))),or(implies(X_44,X_45),X)) = equiv(X,not(implies(X_44,X_45))),
inference(subst,[],[refute_0_360:[bind(X,$fot(implies(X_44,X_45))),bind(X_29,$fot(X))]]) ).
cnf(refute_0_590,plain,
( and(not(and(X,implies(X_44,X_45))),or(implies(X_44,X_45),X)) != equiv(X,not(implies(X_44,X_45)))
| equiv(X,and(X_44,not(X_45))) != and(not(and(X,implies(X_44,X_45))),or(implies(X_44,X_45),X))
| equiv(X,and(X_44,not(X_45))) = equiv(X,not(implies(X_44,X_45))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X,and(X_44,not(X_45))),and(not(and(X,implies(X_44,X_45))),or(implies(X_44,X_45),X))) ),[1],$fot(equiv(X,not(implies(X_44,X_45))))]]) ).
cnf(refute_0_591,plain,
( equiv(X,and(X_44,not(X_45))) != and(not(and(X,implies(X_44,X_45))),or(implies(X_44,X_45),X))
| equiv(X,and(X_44,not(X_45))) = equiv(X,not(implies(X_44,X_45))) ),
inference(resolve,[$cnf( $equal(and(not(and(X,implies(X_44,X_45))),or(implies(X_44,X_45),X)),equiv(X,not(implies(X_44,X_45)))) )],[refute_0_589,refute_0_590]) ).
cnf(refute_0_592,plain,
equiv(X,and(X_44,not(X_45))) = equiv(X,not(implies(X_44,X_45))),
inference(resolve,[$cnf( $equal(equiv(X,and(X_44,not(X_45))),and(not(and(X,implies(X_44,X_45))),or(implies(X_44,X_45),X))) )],[refute_0_588,refute_0_591]) ).
cnf(refute_0_593,plain,
equiv(and(not(X_45),not(X_45)),and(not(X_45),not(X_45))) = equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45))),
inference(subst,[],[refute_0_592:[bind(X,$fot(and(not(X_45),not(X_45)))),bind(X_44,$fot(not(X_45)))]]) ).
cnf(refute_0_594,plain,
( equiv(and(not(X_45),not(X_45)),and(not(X_45),not(X_45))) != equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45)))
| ~ is_a_theorem(equiv(and(not(X_45),not(X_45)),and(not(X_45),not(X_45))))
| is_a_theorem(equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(equiv(and(not(X_45),not(X_45)),and(not(X_45),not(X_45)))) ),[0],$fot(equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45))))]]) ).
cnf(refute_0_595,plain,
( ~ is_a_theorem(equiv(and(not(X_45),not(X_45)),and(not(X_45),not(X_45))))
| is_a_theorem(equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45)))) ),
inference(resolve,[$cnf( $equal(equiv(and(not(X_45),not(X_45)),and(not(X_45),not(X_45))),equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45)))) )],[refute_0_593,refute_0_594]) ).
cnf(refute_0_596,plain,
is_a_theorem(equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45)))),
inference(resolve,[$cnf( is_a_theorem(equiv(and(not(X_45),not(X_45)),and(not(X_45),not(X_45)))) )],[refute_0_575,refute_0_595]) ).
cnf(refute_0_597,plain,
implies(not(X_45),X_45) = or(X_45,X_45),
inference(subst,[],[refute_0_159:[bind(X,$fot(X_45)),bind(Y,$fot(X_45))]]) ).
cnf(refute_0_598,plain,
not(implies(not(X_45),X_45)) = not(implies(not(X_45),X_45)),
introduced(tautology,[refl,[$fot(not(implies(not(X_45),X_45)))]]) ).
cnf(refute_0_599,plain,
( implies(not(X_45),X_45) != or(X_45,X_45)
| not(implies(not(X_45),X_45)) != not(implies(not(X_45),X_45))
| not(implies(not(X_45),X_45)) = not(or(X_45,X_45)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(X_45),X_45)),not(implies(not(X_45),X_45))) ),[1,0],$fot(or(X_45,X_45))]]) ).
cnf(refute_0_600,plain,
( implies(not(X_45),X_45) != or(X_45,X_45)
| not(implies(not(X_45),X_45)) = not(or(X_45,X_45)) ),
inference(resolve,[$cnf( $equal(not(implies(not(X_45),X_45)),not(implies(not(X_45),X_45))) )],[refute_0_598,refute_0_599]) ).
cnf(refute_0_601,plain,
not(implies(not(X_45),X_45)) = not(or(X_45,X_45)),
inference(resolve,[$cnf( $equal(implies(not(X_45),X_45),or(X_45,X_45)) )],[refute_0_597,refute_0_600]) ).
cnf(refute_0_602,plain,
equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45))) = equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45))),
introduced(tautology,[refl,[$fot(equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45))))]]) ).
cnf(refute_0_603,plain,
( equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45))) != equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45)))
| not(implies(not(X_45),X_45)) != not(or(X_45,X_45))
| equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45))) = equiv(and(not(X_45),not(X_45)),not(or(X_45,X_45))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45))),equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45)))) ),[1,1],$fot(not(or(X_45,X_45)))]]) ).
cnf(refute_0_604,plain,
( not(implies(not(X_45),X_45)) != not(or(X_45,X_45))
| equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45))) = equiv(and(not(X_45),not(X_45)),not(or(X_45,X_45))) ),
inference(resolve,[$cnf( $equal(equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45))),equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45)))) )],[refute_0_602,refute_0_603]) ).
cnf(refute_0_605,plain,
equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45))) = equiv(and(not(X_45),not(X_45)),not(or(X_45,X_45))),
inference(resolve,[$cnf( $equal(not(implies(not(X_45),X_45)),not(or(X_45,X_45))) )],[refute_0_601,refute_0_604]) ).
cnf(refute_0_606,plain,
( equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45))) != equiv(and(not(X_45),not(X_45)),not(or(X_45,X_45)))
| ~ is_a_theorem(equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45))))
| is_a_theorem(equiv(and(not(X_45),not(X_45)),not(or(X_45,X_45)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45)))) ),[0],$fot(equiv(and(not(X_45),not(X_45)),not(or(X_45,X_45))))]]) ).
cnf(refute_0_607,plain,
( ~ is_a_theorem(equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45))))
| is_a_theorem(equiv(and(not(X_45),not(X_45)),not(or(X_45,X_45)))) ),
inference(resolve,[$cnf( $equal(equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45))),equiv(and(not(X_45),not(X_45)),not(or(X_45,X_45)))) )],[refute_0_605,refute_0_606]) ).
cnf(refute_0_608,plain,
is_a_theorem(equiv(and(not(X_45),not(X_45)),not(or(X_45,X_45)))),
inference(resolve,[$cnf( is_a_theorem(equiv(and(not(X_45),not(X_45)),not(implies(not(X_45),X_45)))) )],[refute_0_596,refute_0_607]) ).
cnf(refute_0_609,plain,
is_a_theorem(equiv(and(not(X_655),not(X_655)),not(or(X_655,X_655)))),
inference(subst,[],[refute_0_608:[bind(X_45,$fot(X_655))]]) ).
cnf(refute_0_610,plain,
and(not(X_655),not(X_655)) = not(or(X_655,X_655)),
inference(resolve,[$cnf( is_a_theorem(equiv(and(not(X_655),not(X_655)),not(or(X_655,X_655)))) )],[refute_0_609,refute_0_531]) ).
cnf(refute_0_611,plain,
and(not(Y),not(Y)) = not(or(Y,Y)),
inference(subst,[],[refute_0_610:[bind(X_655,$fot(Y))]]) ).
cnf(refute_0_612,plain,
( and(not(Y),not(Y)) != not(or(Y,Y))
| implies(not(Y),Y) != not(and(not(Y),not(Y)))
| implies(not(Y),Y) = not(not(or(Y,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(Y),Y),not(and(not(Y),not(Y)))) ),[1,0],$fot(not(or(Y,Y)))]]) ).
cnf(refute_0_613,plain,
( implies(not(Y),Y) != not(and(not(Y),not(Y)))
| implies(not(Y),Y) = not(not(or(Y,Y))) ),
inference(resolve,[$cnf( $equal(and(not(Y),not(Y)),not(or(Y,Y))) )],[refute_0_611,refute_0_612]) ).
cnf(refute_0_614,plain,
implies(not(Y),Y) = not(not(or(Y,Y))),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),not(and(not(Y),not(Y)))) )],[refute_0_530,refute_0_613]) ).
cnf(refute_0_615,plain,
implies(not(Y),Y) = or(Y,Y),
inference(subst,[],[refute_0_159:[bind(X,$fot(Y))]]) ).
cnf(refute_0_616,plain,
( implies(not(Y),Y) != not(not(or(Y,Y)))
| implies(not(Y),Y) != or(Y,Y)
| or(Y,Y) = not(not(or(Y,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(Y),Y),not(not(or(Y,Y)))) ),[0],$fot(or(Y,Y))]]) ).
cnf(refute_0_617,plain,
( implies(not(Y),Y) != not(not(or(Y,Y)))
| or(Y,Y) = not(not(or(Y,Y))) ),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),or(Y,Y)) )],[refute_0_615,refute_0_616]) ).
cnf(refute_0_618,plain,
or(Y,Y) = not(not(or(Y,Y))),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),not(not(or(Y,Y)))) )],[refute_0_614,refute_0_617]) ).
cnf(refute_0_619,plain,
or(not(X),not(X)) = not(not(or(not(X),not(X)))),
inference(subst,[],[refute_0_618:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_620,plain,
( or(not(X),not(X)) != implies(X,not(X))
| or(not(X),not(X)) != not(not(or(not(X),not(X))))
| or(not(X),not(X)) = not(not(implies(X,not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X),not(X)),not(not(or(not(X),not(X))))) ),[1,0,0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_621,plain,
( or(not(X),not(X)) != not(not(or(not(X),not(X))))
| or(not(X),not(X)) = not(not(implies(X,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_171,refute_0_620]) ).
cnf(refute_0_622,plain,
or(not(X),not(X)) = not(not(implies(X,not(X)))),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),not(not(or(not(X),not(X))))) )],[refute_0_619,refute_0_621]) ).
cnf(refute_0_623,plain,
( or(not(X),not(X)) != implies(X,not(X))
| or(not(X),not(X)) != not(not(implies(X,not(X))))
| implies(X,not(X)) = not(not(implies(X,not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X),not(X)),not(not(implies(X,not(X))))) ),[0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_624,plain,
( or(not(X),not(X)) != not(not(implies(X,not(X))))
| implies(X,not(X)) = not(not(implies(X,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_171,refute_0_623]) ).
cnf(refute_0_625,plain,
not(not(implies(X,not(X)))) = not(not(implies(X,not(X)))),
introduced(tautology,[refl,[$fot(not(not(implies(X,not(X)))))]]) ).
cnf(refute_0_626,plain,
( not(implies(X,not(X))) != and(X,X)
| not(not(implies(X,not(X)))) != not(not(implies(X,not(X))))
| not(not(implies(X,not(X)))) = not(and(X,X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(X,not(X)))),not(not(implies(X,not(X))))) ),[1,0],$fot(and(X,X))]]) ).
cnf(refute_0_627,plain,
( not(implies(X,not(X))) != and(X,X)
| not(not(implies(X,not(X)))) = not(and(X,X)) ),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(X)))),not(not(implies(X,not(X))))) )],[refute_0_625,refute_0_626]) ).
cnf(refute_0_628,plain,
not(not(implies(X,not(X)))) = not(and(X,X)),
inference(resolve,[$cnf( $equal(not(implies(X,not(X))),and(X,X)) )],[refute_0_555,refute_0_627]) ).
cnf(refute_0_629,plain,
( implies(X,not(X)) != not(not(implies(X,not(X))))
| not(not(implies(X,not(X)))) != not(and(X,X))
| implies(X,not(X)) = not(and(X,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,not(X)),not(and(X,X))) ),[0],$fot(not(not(implies(X,not(X)))))]]) ).
cnf(refute_0_630,plain,
( implies(X,not(X)) != not(not(implies(X,not(X))))
| implies(X,not(X)) = not(and(X,X)) ),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(X)))),not(and(X,X))) )],[refute_0_628,refute_0_629]) ).
cnf(refute_0_631,plain,
( or(not(X),not(X)) != not(not(implies(X,not(X))))
| implies(X,not(X)) = not(and(X,X)) ),
inference(resolve,[$cnf( $equal(implies(X,not(X)),not(not(implies(X,not(X))))) )],[refute_0_624,refute_0_630]) ).
cnf(refute_0_632,plain,
implies(X,not(X)) = not(and(X,X)),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),not(not(implies(X,not(X))))) )],[refute_0_622,refute_0_631]) ).
cnf(refute_0_633,plain,
implies(Y,not(Y)) = not(and(Y,Y)),
inference(subst,[],[refute_0_632:[bind(X,$fot(Y))]]) ).
cnf(refute_0_634,plain,
( and(Y,Y) != not(implies(Y,not(Y)))
| implies(Y,not(Y)) != not(and(Y,Y))
| and(Y,Y) = not(not(and(Y,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(Y,Y),not(implies(Y,not(Y)))) ),[1,0],$fot(not(and(Y,Y)))]]) ).
cnf(refute_0_635,plain,
( and(Y,Y) != not(implies(Y,not(Y)))
| and(Y,Y) = not(not(and(Y,Y))) ),
inference(resolve,[$cnf( $equal(implies(Y,not(Y)),not(and(Y,Y))) )],[refute_0_633,refute_0_634]) ).
cnf(refute_0_636,plain,
and(Y,Y) = not(not(and(Y,Y))),
inference(resolve,[$cnf( $equal(and(Y,Y),not(implies(Y,not(Y)))) )],[refute_0_529,refute_0_635]) ).
cnf(refute_0_637,plain,
and(implies(X,X),implies(X,X)) = not(not(and(implies(X,X),implies(X,X)))),
inference(subst,[],[refute_0_636:[bind(Y,$fot(implies(X,X)))]]) ).
cnf(refute_0_638,plain,
equiv(X,X) = and(implies(X,X),implies(X,X)),
inference(subst,[],[refute_0_318:[bind(Y,$fot(X))]]) ).
cnf(refute_0_639,plain,
( equiv(X,X) != and(implies(X,X),implies(X,X))
| and(implies(X,X),implies(X,X)) = equiv(X,X) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(X,X))),bind(Y0,$fot(and(implies(X,X),implies(X,X))))]]) ).
cnf(refute_0_640,plain,
and(implies(X,X),implies(X,X)) = equiv(X,X),
inference(resolve,[$cnf( $equal(equiv(X,X),and(implies(X,X),implies(X,X))) )],[refute_0_638,refute_0_639]) ).
cnf(refute_0_641,plain,
( and(implies(X,X),implies(X,X)) != equiv(X,X)
| and(implies(X,X),implies(X,X)) != not(not(and(implies(X,X),implies(X,X))))
| and(implies(X,X),implies(X,X)) = not(not(equiv(X,X))) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(X,X),implies(X,X)),not(not(and(implies(X,X),implies(X,X))))) ),[1,0,0],$fot(equiv(X,X))]]) ).
cnf(refute_0_642,plain,
( and(implies(X,X),implies(X,X)) != not(not(and(implies(X,X),implies(X,X))))
| and(implies(X,X),implies(X,X)) = not(not(equiv(X,X))) ),
inference(resolve,[$cnf( $equal(and(implies(X,X),implies(X,X)),equiv(X,X)) )],[refute_0_640,refute_0_641]) ).
cnf(refute_0_643,plain,
and(implies(X,X),implies(X,X)) = not(not(equiv(X,X))),
inference(resolve,[$cnf( $equal(and(implies(X,X),implies(X,X)),not(not(and(implies(X,X),implies(X,X))))) )],[refute_0_637,refute_0_642]) ).
cnf(refute_0_644,plain,
( and(implies(X,X),implies(X,X)) != equiv(X,X)
| and(implies(X,X),implies(X,X)) != not(not(equiv(X,X)))
| equiv(X,X) = not(not(equiv(X,X))) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(X,X),implies(X,X)),not(not(equiv(X,X)))) ),[0],$fot(equiv(X,X))]]) ).
cnf(refute_0_645,plain,
( and(implies(X,X),implies(X,X)) != not(not(equiv(X,X)))
| equiv(X,X) = not(not(equiv(X,X))) ),
inference(resolve,[$cnf( $equal(and(implies(X,X),implies(X,X)),equiv(X,X)) )],[refute_0_640,refute_0_644]) ).
cnf(refute_0_646,plain,
equiv(X,X) = not(not(equiv(X,X))),
inference(resolve,[$cnf( $equal(and(implies(X,X),implies(X,X)),not(not(equiv(X,X)))) )],[refute_0_643,refute_0_645]) ).
cnf(refute_0_647,plain,
( equiv(X,X) != not(not(equiv(X,X)))
| not(not(equiv(X,X))) = equiv(X,X) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(X,X))),bind(Y0,$fot(not(not(equiv(X,X)))))]]) ).
cnf(refute_0_648,plain,
not(not(equiv(X,X))) = equiv(X,X),
inference(resolve,[$cnf( $equal(equiv(X,X),not(not(equiv(X,X)))) )],[refute_0_646,refute_0_647]) ).
cnf(refute_0_649,plain,
not(not(equiv(X_4516,X_4516))) = equiv(X_4516,X_4516),
inference(subst,[],[refute_0_648:[bind(X,$fot(X_4516))]]) ).
cnf(refute_0_650,plain,
not(not(not(equiv(X_4516,X_4516)))) = not(not(not(equiv(X_4516,X_4516)))),
introduced(tautology,[refl,[$fot(not(not(not(equiv(X_4516,X_4516)))))]]) ).
cnf(refute_0_651,plain,
( not(not(equiv(X_4516,X_4516))) != equiv(X_4516,X_4516)
| not(not(not(equiv(X_4516,X_4516)))) != not(not(not(equiv(X_4516,X_4516))))
| not(not(not(equiv(X_4516,X_4516)))) = not(equiv(X_4516,X_4516)) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(not(equiv(X_4516,X_4516)))),not(not(not(equiv(X_4516,X_4516))))) ),[1,0],$fot(equiv(X_4516,X_4516))]]) ).
cnf(refute_0_652,plain,
( not(not(equiv(X_4516,X_4516))) != equiv(X_4516,X_4516)
| not(not(not(equiv(X_4516,X_4516)))) = not(equiv(X_4516,X_4516)) ),
inference(resolve,[$cnf( $equal(not(not(not(equiv(X_4516,X_4516)))),not(not(not(equiv(X_4516,X_4516))))) )],[refute_0_650,refute_0_651]) ).
cnf(refute_0_653,plain,
not(not(not(equiv(X_4516,X_4516)))) = not(equiv(X_4516,X_4516)),
inference(resolve,[$cnf( $equal(not(not(equiv(X_4516,X_4516))),equiv(X_4516,X_4516)) )],[refute_0_649,refute_0_652]) ).
cnf(refute_0_654,plain,
not(not(not(not(equiv(X_4516,X_4516))))) = not(not(not(not(equiv(X_4516,X_4516))))),
introduced(tautology,[refl,[$fot(not(not(not(not(equiv(X_4516,X_4516))))))]]) ).
cnf(refute_0_655,plain,
( not(not(not(equiv(X_4516,X_4516)))) != not(equiv(X_4516,X_4516))
| not(not(not(not(equiv(X_4516,X_4516))))) != not(not(not(not(equiv(X_4516,X_4516)))))
| not(not(not(not(equiv(X_4516,X_4516))))) = not(not(equiv(X_4516,X_4516))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(not(not(equiv(X_4516,X_4516))))),not(not(not(not(equiv(X_4516,X_4516)))))) ),[1,0],$fot(not(equiv(X_4516,X_4516)))]]) ).
cnf(refute_0_656,plain,
( not(not(not(equiv(X_4516,X_4516)))) != not(equiv(X_4516,X_4516))
| not(not(not(not(equiv(X_4516,X_4516))))) = not(not(equiv(X_4516,X_4516))) ),
inference(resolve,[$cnf( $equal(not(not(not(not(equiv(X_4516,X_4516))))),not(not(not(not(equiv(X_4516,X_4516)))))) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
not(not(not(not(equiv(X_4516,X_4516))))) = not(not(equiv(X_4516,X_4516))),
inference(resolve,[$cnf( $equal(not(not(not(equiv(X_4516,X_4516)))),not(equiv(X_4516,X_4516))) )],[refute_0_653,refute_0_656]) ).
cnf(refute_0_658,plain,
( not(not(equiv(X_4516,X_4516))) != equiv(X_4516,X_4516)
| not(not(not(not(equiv(X_4516,X_4516))))) != not(not(equiv(X_4516,X_4516)))
| not(not(not(not(equiv(X_4516,X_4516))))) = equiv(X_4516,X_4516) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(not(not(not(not(equiv(X_4516,X_4516))))))),bind(Y0,$fot(not(not(equiv(X_4516,X_4516))))),bind(Z,$fot(equiv(X_4516,X_4516)))]]) ).
cnf(refute_0_659,plain,
( not(not(equiv(X_4516,X_4516))) != equiv(X_4516,X_4516)
| not(not(not(not(equiv(X_4516,X_4516))))) = equiv(X_4516,X_4516) ),
inference(resolve,[$cnf( $equal(not(not(not(not(equiv(X_4516,X_4516))))),not(not(equiv(X_4516,X_4516)))) )],[refute_0_657,refute_0_658]) ).
cnf(refute_0_660,plain,
not(not(not(not(equiv(X_4516,X_4516))))) = equiv(X_4516,X_4516),
inference(resolve,[$cnf( $equal(not(not(equiv(X_4516,X_4516))),equiv(X_4516,X_4516)) )],[refute_0_649,refute_0_659]) ).
cnf(refute_0_661,plain,
or(X_57,not(not(not(not(equiv(X_4516,X_4516)))))) = or(X_57,not(not(not(not(equiv(X_4516,X_4516)))))),
introduced(tautology,[refl,[$fot(or(X_57,not(not(not(not(equiv(X_4516,X_4516)))))))]]) ).
cnf(refute_0_662,plain,
( not(not(not(not(equiv(X_4516,X_4516))))) != equiv(X_4516,X_4516)
| or(X_57,not(not(not(not(equiv(X_4516,X_4516)))))) != or(X_57,not(not(not(not(equiv(X_4516,X_4516))))))
| or(X_57,not(not(not(not(equiv(X_4516,X_4516)))))) = or(X_57,equiv(X_4516,X_4516)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_57,not(not(not(not(equiv(X_4516,X_4516)))))),or(X_57,not(not(not(not(equiv(X_4516,X_4516))))))) ),[1,1],$fot(equiv(X_4516,X_4516))]]) ).
cnf(refute_0_663,plain,
( not(not(not(not(equiv(X_4516,X_4516))))) != equiv(X_4516,X_4516)
| or(X_57,not(not(not(not(equiv(X_4516,X_4516)))))) = or(X_57,equiv(X_4516,X_4516)) ),
inference(resolve,[$cnf( $equal(or(X_57,not(not(not(not(equiv(X_4516,X_4516)))))),or(X_57,not(not(not(not(equiv(X_4516,X_4516))))))) )],[refute_0_661,refute_0_662]) ).
cnf(refute_0_664,plain,
or(X_57,not(not(not(not(equiv(X_4516,X_4516)))))) = or(X_57,equiv(X_4516,X_4516)),
inference(resolve,[$cnf( $equal(not(not(not(not(equiv(X_4516,X_4516))))),equiv(X_4516,X_4516)) )],[refute_0_660,refute_0_663]) ).
cnf(refute_0_665,plain,
( or(X_57,not(not(not(not(equiv(X_4516,X_4516)))))) != or(X_57,equiv(X_4516,X_4516))
| ~ is_a_theorem(or(X_57,not(not(not(not(equiv(X_4516,X_4516)))))))
| is_a_theorem(or(X_57,equiv(X_4516,X_4516))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_57,not(not(not(not(equiv(X_4516,X_4516))))))) ),[0],$fot(or(X_57,equiv(X_4516,X_4516)))]]) ).
cnf(refute_0_666,plain,
( ~ is_a_theorem(or(X_57,not(not(not(not(equiv(X_4516,X_4516)))))))
| is_a_theorem(or(X_57,equiv(X_4516,X_4516))) ),
inference(resolve,[$cnf( $equal(or(X_57,not(not(not(not(equiv(X_4516,X_4516)))))),or(X_57,equiv(X_4516,X_4516))) )],[refute_0_664,refute_0_665]) ).
cnf(refute_0_667,plain,
is_a_theorem(or(X_57,equiv(X_4516,X_4516))),
inference(resolve,[$cnf( is_a_theorem(or(X_57,not(not(not(not(equiv(X_4516,X_4516))))))) )],[refute_0_528,refute_0_666]) ).
cnf(refute_0_668,plain,
is_a_theorem(or(X_4519,equiv(X_4518,X_4518))),
inference(subst,[],[refute_0_667:[bind(X_4516,$fot(X_4518)),bind(X_57,$fot(X_4519))]]) ).
cnf(refute_0_669,plain,
is_a_theorem(or(equiv(X_4518,X_4518),X_4519)),
inference(resolve,[$cnf( is_a_theorem(or(X_4519,equiv(X_4518,X_4518))) )],[refute_0_668,refute_0_44]) ).
cnf(refute_0_670,plain,
is_a_theorem(or(equiv(X_4518,X_4518),X_12390)),
inference(subst,[],[refute_0_669:[bind(X_4519,$fot(X_12390))]]) ).
cnf(refute_0_671,plain,
( ~ is_a_theorem(implies(or(X_807,X_809),or(and(X_808,X_807),implies(X_808,X_809))))
| ~ is_a_theorem(or(X_807,X_809))
| is_a_theorem(or(and(X_808,X_807),implies(X_808,X_809))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(or(X_807,X_809))),bind(Y,$fot(or(and(X_808,X_807),implies(X_808,X_809))))]]) ).
cnf(refute_0_672,plain,
( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(canonicalize,[],[normalize_0_45]) ).
cnf(refute_0_673,plain,
r5,
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_674,plain,
is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))),
inference(resolve,[$cnf( r5 )],[refute_0_673,refute_0_672]) ).
cnf(refute_0_675,plain,
is_a_theorem(implies(implies(X_126,X_127),implies(or(not(X),X_126),or(not(X),X_127)))),
inference(subst,[],[refute_0_674:[bind(P,$fot(not(X))),bind(Q,$fot(X_126)),bind(R,$fot(X_127))]]) ).
cnf(refute_0_676,plain,
implies(X,X_127) = or(not(X),X_127),
inference(subst,[],[refute_0_9:[bind(Y,$fot(X_127))]]) ).
cnf(refute_0_677,plain,
( implies(X,X_127) != or(not(X),X_127)
| or(not(X),X_127) = implies(X,X_127) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,X_127))),bind(Y0,$fot(or(not(X),X_127)))]]) ).
cnf(refute_0_678,plain,
or(not(X),X_127) = implies(X,X_127),
inference(resolve,[$cnf( $equal(implies(X,X_127),or(not(X),X_127)) )],[refute_0_676,refute_0_677]) ).
cnf(refute_0_679,plain,
( or(not(X),X_127) != implies(X,X_127)
| ~ is_a_theorem(implies(implies(X_126,X_127),implies(or(not(X),X_126),or(not(X),X_127))))
| is_a_theorem(implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_126,X_127),implies(or(not(X),X_126),or(not(X),X_127)))) ),[0,1,1],$fot(implies(X,X_127))]]) ).
cnf(refute_0_680,plain,
( ~ is_a_theorem(implies(implies(X_126,X_127),implies(or(not(X),X_126),or(not(X),X_127))))
| is_a_theorem(implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_127),implies(X,X_127)) )],[refute_0_678,refute_0_679]) ).
cnf(refute_0_681,plain,
is_a_theorem(implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_126,X_127),implies(or(not(X),X_126),or(not(X),X_127)))) )],[refute_0_675,refute_0_680]) ).
cnf(refute_0_682,plain,
or(not(X),X_126) = implies(X,X_126),
inference(subst,[],[refute_0_20:[bind(Y,$fot(X_126))]]) ).
cnf(refute_0_683,plain,
implies(or(not(X),X_126),implies(X,X_127)) = implies(or(not(X),X_126),implies(X,X_127)),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_126),implies(X,X_127)))]]) ).
cnf(refute_0_684,plain,
( implies(or(not(X),X_126),implies(X,X_127)) != implies(or(not(X),X_126),implies(X,X_127))
| or(not(X),X_126) != implies(X,X_126)
| implies(or(not(X),X_126),implies(X,X_127)) = implies(implies(X,X_126),implies(X,X_127)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_126),implies(X,X_127)),implies(or(not(X),X_126),implies(X,X_127))) ),[1,0],$fot(implies(X,X_126))]]) ).
cnf(refute_0_685,plain,
( or(not(X),X_126) != implies(X,X_126)
| implies(or(not(X),X_126),implies(X,X_127)) = implies(implies(X,X_126),implies(X,X_127)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_126),implies(X,X_127)),implies(or(not(X),X_126),implies(X,X_127))) )],[refute_0_683,refute_0_684]) ).
cnf(refute_0_686,plain,
implies(or(not(X),X_126),implies(X,X_127)) = implies(implies(X,X_126),implies(X,X_127)),
inference(resolve,[$cnf( $equal(or(not(X),X_126),implies(X,X_126)) )],[refute_0_682,refute_0_685]) ).
cnf(refute_0_687,plain,
implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127))) = implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127))),
introduced(tautology,[refl,[$fot(implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127))))]]) ).
cnf(refute_0_688,plain,
( implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127))) != implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127)))
| implies(or(not(X),X_126),implies(X,X_127)) != implies(implies(X,X_126),implies(X,X_127))
| implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127))) = implies(implies(X_126,X_127),implies(implies(X,X_126),implies(X,X_127))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127))),implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127)))) ),[1,1],$fot(implies(implies(X,X_126),implies(X,X_127)))]]) ).
cnf(refute_0_689,plain,
( implies(or(not(X),X_126),implies(X,X_127)) != implies(implies(X,X_126),implies(X,X_127))
| implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127))) = implies(implies(X_126,X_127),implies(implies(X,X_126),implies(X,X_127))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127))),implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127)))) )],[refute_0_687,refute_0_688]) ).
cnf(refute_0_690,plain,
implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127))) = implies(implies(X_126,X_127),implies(implies(X,X_126),implies(X,X_127))),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_126),implies(X,X_127)),implies(implies(X,X_126),implies(X,X_127))) )],[refute_0_686,refute_0_689]) ).
cnf(refute_0_691,plain,
( implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127))) != implies(implies(X_126,X_127),implies(implies(X,X_126),implies(X,X_127)))
| ~ is_a_theorem(implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127))))
| is_a_theorem(implies(implies(X_126,X_127),implies(implies(X,X_126),implies(X,X_127)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127)))) ),[0],$fot(implies(implies(X_126,X_127),implies(implies(X,X_126),implies(X,X_127))))]]) ).
cnf(refute_0_692,plain,
( ~ is_a_theorem(implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127))))
| is_a_theorem(implies(implies(X_126,X_127),implies(implies(X,X_126),implies(X,X_127)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127))),implies(implies(X_126,X_127),implies(implies(X,X_126),implies(X,X_127)))) )],[refute_0_690,refute_0_691]) ).
cnf(refute_0_693,plain,
is_a_theorem(implies(implies(X_126,X_127),implies(implies(X,X_126),implies(X,X_127)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_126,X_127),implies(or(not(X),X_126),implies(X,X_127)))) )],[refute_0_681,refute_0_692]) ).
cnf(refute_0_694,plain,
is_a_theorem(implies(implies(not(X_17),X_302),implies(implies(X_300,not(X_17)),implies(X_300,X_302)))),
inference(subst,[],[refute_0_693:[bind(X,$fot(X_300)),bind(X_126,$fot(not(X_17))),bind(X_127,$fot(X_302))]]) ).
cnf(refute_0_695,plain,
implies(implies(X_300,not(X_17)),implies(X_300,X_302)) = or(and(X_300,X_17),implies(X_300,X_302)),
inference(subst,[],[refute_0_134:[bind(Y,$fot(implies(X_300,X_302))),bind(X_16,$fot(X_300))]]) ).
cnf(refute_0_696,plain,
( implies(implies(X_300,not(X_17)),implies(X_300,X_302)) != or(and(X_300,X_17),implies(X_300,X_302))
| ~ is_a_theorem(implies(implies(not(X_17),X_302),implies(implies(X_300,not(X_17)),implies(X_300,X_302))))
| is_a_theorem(implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X_17),X_302),implies(implies(X_300,not(X_17)),implies(X_300,X_302)))) ),[0,1],$fot(or(and(X_300,X_17),implies(X_300,X_302)))]]) ).
cnf(refute_0_697,plain,
( ~ is_a_theorem(implies(implies(not(X_17),X_302),implies(implies(X_300,not(X_17)),implies(X_300,X_302))))
| is_a_theorem(implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_300,not(X_17)),implies(X_300,X_302)),or(and(X_300,X_17),implies(X_300,X_302))) )],[refute_0_695,refute_0_696]) ).
cnf(refute_0_698,plain,
is_a_theorem(implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_17),X_302),implies(implies(X_300,not(X_17)),implies(X_300,X_302)))) )],[refute_0_694,refute_0_697]) ).
cnf(refute_0_699,plain,
implies(not(X_17),X_302) = or(X_17,X_302),
inference(subst,[],[refute_0_159:[bind(X,$fot(X_17)),bind(Y,$fot(X_302))]]) ).
cnf(refute_0_700,plain,
implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302))) = implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302))),
introduced(tautology,[refl,[$fot(implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302))))]]) ).
cnf(refute_0_701,plain,
( implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302))) != implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302)))
| implies(not(X_17),X_302) != or(X_17,X_302)
| implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302))) = implies(or(X_17,X_302),or(and(X_300,X_17),implies(X_300,X_302))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302))),implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302)))) ),[1,0],$fot(or(X_17,X_302))]]) ).
cnf(refute_0_702,plain,
( implies(not(X_17),X_302) != or(X_17,X_302)
| implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302))) = implies(or(X_17,X_302),or(and(X_300,X_17),implies(X_300,X_302))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302))),implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302)))) )],[refute_0_700,refute_0_701]) ).
cnf(refute_0_703,plain,
implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302))) = implies(or(X_17,X_302),or(and(X_300,X_17),implies(X_300,X_302))),
inference(resolve,[$cnf( $equal(implies(not(X_17),X_302),or(X_17,X_302)) )],[refute_0_699,refute_0_702]) ).
cnf(refute_0_704,plain,
( implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302))) != implies(or(X_17,X_302),or(and(X_300,X_17),implies(X_300,X_302)))
| ~ is_a_theorem(implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302))))
| is_a_theorem(implies(or(X_17,X_302),or(and(X_300,X_17),implies(X_300,X_302)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302)))) ),[0],$fot(implies(or(X_17,X_302),or(and(X_300,X_17),implies(X_300,X_302))))]]) ).
cnf(refute_0_705,plain,
( ~ is_a_theorem(implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302))))
| is_a_theorem(implies(or(X_17,X_302),or(and(X_300,X_17),implies(X_300,X_302)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302))),implies(or(X_17,X_302),or(and(X_300,X_17),implies(X_300,X_302)))) )],[refute_0_703,refute_0_704]) ).
cnf(refute_0_706,plain,
is_a_theorem(implies(or(X_17,X_302),or(and(X_300,X_17),implies(X_300,X_302)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_17),X_302),or(and(X_300,X_17),implies(X_300,X_302)))) )],[refute_0_698,refute_0_705]) ).
cnf(refute_0_707,plain,
is_a_theorem(implies(or(X_807,X_809),or(and(X_808,X_807),implies(X_808,X_809)))),
inference(subst,[],[refute_0_706:[bind(X_17,$fot(X_807)),bind(X_300,$fot(X_808)),bind(X_302,$fot(X_809))]]) ).
cnf(refute_0_708,plain,
( ~ is_a_theorem(or(X_807,X_809))
| is_a_theorem(or(and(X_808,X_807),implies(X_808,X_809))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_807,X_809),or(and(X_808,X_807),implies(X_808,X_809)))) )],[refute_0_707,refute_0_671]) ).
cnf(refute_0_709,plain,
( ~ is_a_theorem(or(equiv(X_4518,X_4518),X_12390))
| is_a_theorem(or(and(X_12389,equiv(X_4518,X_4518)),implies(X_12389,X_12390))) ),
inference(subst,[],[refute_0_708:[bind(X_807,$fot(equiv(X_4518,X_4518))),bind(X_808,$fot(X_12389)),bind(X_809,$fot(X_12390))]]) ).
cnf(refute_0_710,plain,
is_a_theorem(or(and(X_12389,equiv(X_4518,X_4518)),implies(X_12389,X_12390))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(X_4518,X_4518),X_12390)) )],[refute_0_670,refute_0_709]) ).
cnf(refute_0_711,plain,
is_a_theorem(or(and(X_12405,equiv(X_12407,X_12407)),implies(X_12405,X_12406))),
inference(subst,[],[refute_0_710:[bind(X_12389,$fot(X_12405)),bind(X_12390,$fot(X_12406)),bind(X_4518,$fot(X_12407))]]) ).
cnf(refute_0_712,plain,
is_a_theorem(implies(X_12405,or(and(X_12405,equiv(X_12407,X_12407)),X_12406))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_12405,equiv(X_12407,X_12407)),implies(X_12405,X_12406))) )],[refute_0_711,refute_0_38]) ).
cnf(refute_0_713,plain,
is_a_theorem(implies(X_12407,or(and(X_12407,equiv(X_12407,X_12407)),X_12406))),
inference(subst,[],[refute_0_712:[bind(X_12405,$fot(X_12407))]]) ).
cnf(refute_0_714,plain,
( ~ is_a_theorem(equiv(X_56113,and(X_56113,equiv(X_56113,X_56113))))
| X_56113 = and(X_56113,equiv(X_56113,X_56113)) ),
inference(subst,[],[refute_0_253:[bind(X,$fot(X_56113)),bind(Y,$fot(and(X_56113,equiv(X_56113,X_56113))))]]) ).
cnf(refute_0_715,plain,
( ~ is_a_theorem(implies(X_56112,and(X_56112,equiv(X_56112,X_56112))))
| ~ is_a_theorem(implies(implies(X_56112,and(X_56112,equiv(X_56112,X_56112))),equiv(X_56112,and(X_56112,equiv(X_56112,X_56112)))))
| is_a_theorem(equiv(X_56112,and(X_56112,equiv(X_56112,X_56112)))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(implies(X_56112,and(X_56112,equiv(X_56112,X_56112))))),bind(Y,$fot(equiv(X_56112,and(X_56112,equiv(X_56112,X_56112)))))]]) ).
cnf(refute_0_716,plain,
( ~ is_a_theorem(or(and(X_29144,implies(and(equiv(X_29147,X_29146),X_29146),X_29147)),implies(X_29144,X_29145)))
| is_a_theorem(implies(X_29144,or(and(X_29144,implies(and(equiv(X_29147,X_29146),X_29146),X_29147)),X_29145))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_29144)),bind(X_103,$fot(and(X_29144,implies(and(equiv(X_29147,X_29146),X_29146),X_29147)))),bind(X_105,$fot(X_29145))]]) ).
cnf(refute_0_717,plain,
( ~ is_a_theorem(or(X_7395,implies(and(equiv(X_7397,X_7396),X_7396),X_7397)))
| is_a_theorem(or(implies(and(equiv(X_7397,X_7396),X_7396),X_7397),X_7395)) ),
inference(subst,[],[refute_0_43:[bind(P,$fot(X_7395)),bind(Q,$fot(implies(and(equiv(X_7397,X_7396),X_7396),X_7397)))]]) ).
cnf(refute_0_718,plain,
is_a_theorem(implies(X_155,or(P,X_155))),
inference(subst,[],[refute_0_47:[bind(Q,$fot(X_155))]]) ).
cnf(refute_0_719,plain,
( ~ is_a_theorem(X_155)
| ~ is_a_theorem(implies(X_155,or(P,X_155)))
| is_a_theorem(or(P,X_155)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(X_155)),bind(Y,$fot(or(P,X_155)))]]) ).
cnf(refute_0_720,plain,
( ~ is_a_theorem(X_155)
| is_a_theorem(or(P,X_155)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_155,or(P,X_155))) )],[refute_0_718,refute_0_719]) ).
cnf(refute_0_721,plain,
( ~ is_a_theorem(implies(and(equiv(X_6547,X_6546),X_6546),X_6547))
| is_a_theorem(or(P,implies(and(equiv(X_6547,X_6546),X_6546),X_6547))) ),
inference(subst,[],[refute_0_720:[bind(X_155,$fot(implies(and(equiv(X_6547,X_6546),X_6546),X_6547)))]]) ).
cnf(refute_0_722,plain,
( ~ is_a_theorem(or(X_6537,implies(equiv(X_6537,X_6536),not(X_6536))))
| is_a_theorem(or(implies(equiv(X_6537,X_6536),not(X_6536)),X_6537)) ),
inference(subst,[],[refute_0_43:[bind(P,$fot(X_6537)),bind(Q,$fot(implies(equiv(X_6537,X_6536),not(X_6536))))]]) ).
cnf(refute_0_723,plain,
( ~ is_a_theorem(implies(and(X_3072,X_3071),or(X_3073,and(X_3071,X_3072))))
| is_a_theorem(or(or(X_3073,and(X_3071,X_3072)),not(and(X_3072,X_3071)))) ),
inference(subst,[],[refute_0_501:[bind(X,$fot(and(X_3072,X_3071))),bind(X_24,$fot(or(X_3073,and(X_3071,X_3072))))]]) ).
cnf(refute_0_724,plain,
is_a_theorem(implies(implies(not(X),X_26),or(X_26,not(not(X))))),
inference(subst,[],[refute_0_499:[bind(X,$fot(not(X))),bind(X_24,$fot(X_26))]]) ).
cnf(refute_0_725,plain,
or(X,X_26) = implies(not(X),X_26),
inference(subst,[],[refute_0_60:[bind(Y,$fot(X_26))]]) ).
cnf(refute_0_726,plain,
( or(X,X_26) != implies(not(X),X_26)
| implies(not(X),X_26) = or(X,X_26) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,X_26))),bind(Y0,$fot(implies(not(X),X_26)))]]) ).
cnf(refute_0_727,plain,
implies(not(X),X_26) = or(X,X_26),
inference(resolve,[$cnf( $equal(or(X,X_26),implies(not(X),X_26)) )],[refute_0_725,refute_0_726]) ).
cnf(refute_0_728,plain,
( implies(not(X),X_26) != or(X,X_26)
| ~ is_a_theorem(implies(implies(not(X),X_26),or(X_26,not(not(X)))))
| is_a_theorem(implies(or(X,X_26),or(X_26,not(not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X),X_26),or(X_26,not(not(X))))) ),[0,0],$fot(or(X,X_26))]]) ).
cnf(refute_0_729,plain,
( ~ is_a_theorem(implies(implies(not(X),X_26),or(X_26,not(not(X)))))
| is_a_theorem(implies(or(X,X_26),or(X_26,not(not(X))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_26),or(X,X_26)) )],[refute_0_727,refute_0_728]) ).
cnf(refute_0_730,plain,
is_a_theorem(implies(or(X,X_26),or(X_26,not(not(X))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X_26),or(X_26,not(not(X))))) )],[refute_0_724,refute_0_729]) ).
cnf(refute_0_731,plain,
is_a_theorem(implies(or(not(X),X_55),or(X_55,not(not(not(X)))))),
inference(subst,[],[refute_0_730:[bind(X,$fot(not(X))),bind(X_26,$fot(X_55))]]) ).
cnf(refute_0_732,plain,
implies(X,X_55) = or(not(X),X_55),
inference(subst,[],[refute_0_9:[bind(Y,$fot(X_55))]]) ).
cnf(refute_0_733,plain,
( implies(X,X_55) != or(not(X),X_55)
| or(not(X),X_55) = implies(X,X_55) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,X_55))),bind(Y0,$fot(or(not(X),X_55)))]]) ).
cnf(refute_0_734,plain,
or(not(X),X_55) = implies(X,X_55),
inference(resolve,[$cnf( $equal(implies(X,X_55),or(not(X),X_55)) )],[refute_0_732,refute_0_733]) ).
cnf(refute_0_735,plain,
( or(not(X),X_55) != implies(X,X_55)
| ~ is_a_theorem(implies(or(not(X),X_55),or(X_55,not(not(not(X))))))
| is_a_theorem(implies(implies(X,X_55),or(X_55,not(not(not(X)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),X_55),or(X_55,not(not(not(X)))))) ),[0,0],$fot(implies(X,X_55))]]) ).
cnf(refute_0_736,plain,
( ~ is_a_theorem(implies(or(not(X),X_55),or(X_55,not(not(not(X))))))
| is_a_theorem(implies(implies(X,X_55),or(X_55,not(not(not(X)))))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_55),implies(X,X_55)) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
is_a_theorem(implies(implies(X,X_55),or(X_55,not(not(not(X)))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),X_55),or(X_55,not(not(not(X)))))) )],[refute_0_731,refute_0_736]) ).
cnf(refute_0_738,plain,
is_a_theorem(implies(implies(X,not(X_117)),or(not(X_117),not(not(not(X)))))),
inference(subst,[],[refute_0_737:[bind(X_55,$fot(not(X_117)))]]) ).
cnf(refute_0_739,plain,
implies(implies(X,not(X_117)),or(not(X_117),not(not(not(X))))) = or(and(X,X_117),or(not(X_117),not(not(not(X))))),
inference(subst,[],[refute_0_134:[bind(Y,$fot(or(not(X_117),not(not(not(X)))))),bind(X_16,$fot(X)),bind(X_17,$fot(X_117))]]) ).
cnf(refute_0_740,plain,
( implies(implies(X,not(X_117)),or(not(X_117),not(not(not(X))))) != or(and(X,X_117),or(not(X_117),not(not(not(X)))))
| ~ is_a_theorem(implies(implies(X,not(X_117)),or(not(X_117),not(not(not(X))))))
| is_a_theorem(or(and(X,X_117),or(not(X_117),not(not(not(X)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,not(X_117)),or(not(X_117),not(not(not(X)))))) ),[0],$fot(or(and(X,X_117),or(not(X_117),not(not(not(X))))))]]) ).
cnf(refute_0_741,plain,
( ~ is_a_theorem(implies(implies(X,not(X_117)),or(not(X_117),not(not(not(X))))))
| is_a_theorem(or(and(X,X_117),or(not(X_117),not(not(not(X)))))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X_117)),or(not(X_117),not(not(not(X))))),or(and(X,X_117),or(not(X_117),not(not(not(X)))))) )],[refute_0_739,refute_0_740]) ).
cnf(refute_0_742,plain,
is_a_theorem(or(and(X,X_117),or(not(X_117),not(not(not(X)))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,not(X_117)),or(not(X_117),not(not(not(X)))))) )],[refute_0_738,refute_0_741]) ).
cnf(refute_0_743,plain,
or(not(X_117),not(not(not(X)))) = implies(X_117,not(not(not(X)))),
inference(subst,[],[refute_0_20:[bind(X,$fot(X_117)),bind(Y,$fot(not(not(not(X)))))]]) ).
cnf(refute_0_744,plain,
or(and(X,X_117),or(not(X_117),not(not(not(X))))) = or(and(X,X_117),or(not(X_117),not(not(not(X))))),
introduced(tautology,[refl,[$fot(or(and(X,X_117),or(not(X_117),not(not(not(X))))))]]) ).
cnf(refute_0_745,plain,
( or(and(X,X_117),or(not(X_117),not(not(not(X))))) != or(and(X,X_117),or(not(X_117),not(not(not(X)))))
| or(not(X_117),not(not(not(X)))) != implies(X_117,not(not(not(X))))
| or(and(X,X_117),or(not(X_117),not(not(not(X))))) = or(and(X,X_117),implies(X_117,not(not(not(X))))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X,X_117),or(not(X_117),not(not(not(X))))),or(and(X,X_117),or(not(X_117),not(not(not(X)))))) ),[1,1],$fot(implies(X_117,not(not(not(X)))))]]) ).
cnf(refute_0_746,plain,
( or(not(X_117),not(not(not(X)))) != implies(X_117,not(not(not(X))))
| or(and(X,X_117),or(not(X_117),not(not(not(X))))) = or(and(X,X_117),implies(X_117,not(not(not(X))))) ),
inference(resolve,[$cnf( $equal(or(and(X,X_117),or(not(X_117),not(not(not(X))))),or(and(X,X_117),or(not(X_117),not(not(not(X)))))) )],[refute_0_744,refute_0_745]) ).
cnf(refute_0_747,plain,
or(and(X,X_117),or(not(X_117),not(not(not(X))))) = or(and(X,X_117),implies(X_117,not(not(not(X))))),
inference(resolve,[$cnf( $equal(or(not(X_117),not(not(not(X)))),implies(X_117,not(not(not(X))))) )],[refute_0_743,refute_0_746]) ).
cnf(refute_0_748,plain,
( or(and(X,X_117),or(not(X_117),not(not(not(X))))) != or(and(X,X_117),implies(X_117,not(not(not(X)))))
| ~ is_a_theorem(or(and(X,X_117),or(not(X_117),not(not(not(X))))))
| is_a_theorem(or(and(X,X_117),implies(X_117,not(not(not(X)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X,X_117),or(not(X_117),not(not(not(X)))))) ),[0],$fot(or(and(X,X_117),implies(X_117,not(not(not(X))))))]]) ).
cnf(refute_0_749,plain,
( ~ is_a_theorem(or(and(X,X_117),or(not(X_117),not(not(not(X))))))
| is_a_theorem(or(and(X,X_117),implies(X_117,not(not(not(X)))))) ),
inference(resolve,[$cnf( $equal(or(and(X,X_117),or(not(X_117),not(not(not(X))))),or(and(X,X_117),implies(X_117,not(not(not(X)))))) )],[refute_0_747,refute_0_748]) ).
cnf(refute_0_750,plain,
is_a_theorem(or(and(X,X_117),implies(X_117,not(not(not(X)))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X,X_117),or(not(X_117),not(not(not(X)))))) )],[refute_0_742,refute_0_749]) ).
cnf(refute_0_751,plain,
( ~ is_a_theorem(or(and(X,X_117),implies(X_117,not(not(not(X))))))
| is_a_theorem(or(implies(X_117,not(not(not(X)))),and(X,X_117))) ),
inference(subst,[],[refute_0_43:[bind(P,$fot(and(X,X_117))),bind(Q,$fot(implies(X_117,not(not(not(X))))))]]) ).
cnf(refute_0_752,plain,
is_a_theorem(or(implies(X_117,not(not(not(X)))),and(X,X_117))),
inference(resolve,[$cnf( is_a_theorem(or(and(X,X_117),implies(X_117,not(not(not(X)))))) )],[refute_0_750,refute_0_751]) ).
cnf(refute_0_753,plain,
or(implies(X_117,not(X)),and(X,X_117)) = implies(and(X_117,X),and(X,X_117)),
inference(subst,[],[refute_0_467:[bind(Y,$fot(and(X,X_117))),bind(X_16,$fot(X_117)),bind(X_17,$fot(X))]]) ).
cnf(refute_0_754,plain,
implies(and(X_117,not(not(X))),and(X,X_117)) = or(implies(X_117,not(X)),and(X,X_117)),
inference(subst,[],[refute_0_472:[bind(Y,$fot(and(X,X_117))),bind(X_4,$fot(X_117)),bind(X_5,$fot(not(X)))]]) ).
cnf(refute_0_755,plain,
( implies(and(X_117,not(not(X))),and(X,X_117)) != or(implies(X_117,not(X)),and(X,X_117))
| or(implies(X_117,not(X)),and(X,X_117)) != implies(and(X_117,X),and(X,X_117))
| implies(and(X_117,not(not(X))),and(X,X_117)) = implies(and(X_117,X),and(X,X_117)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(and(X_117,not(not(X))),and(X,X_117)))),bind(Y0,$fot(or(implies(X_117,not(X)),and(X,X_117)))),bind(Z,$fot(implies(and(X_117,X),and(X,X_117))))]]) ).
cnf(refute_0_756,plain,
( or(implies(X_117,not(X)),and(X,X_117)) != implies(and(X_117,X),and(X,X_117))
| implies(and(X_117,not(not(X))),and(X,X_117)) = implies(and(X_117,X),and(X,X_117)) ),
inference(resolve,[$cnf( $equal(implies(and(X_117,not(not(X))),and(X,X_117)),or(implies(X_117,not(X)),and(X,X_117))) )],[refute_0_754,refute_0_755]) ).
cnf(refute_0_757,plain,
implies(and(X_117,not(not(X))),and(X,X_117)) = implies(and(X_117,X),and(X,X_117)),
inference(resolve,[$cnf( $equal(or(implies(X_117,not(X)),and(X,X_117)),implies(and(X_117,X),and(X,X_117))) )],[refute_0_753,refute_0_756]) ).
cnf(refute_0_758,plain,
or(implies(X_117,not(not(not(X)))),and(X,X_117)) = implies(and(X_117,not(not(X))),and(X,X_117)),
inference(subst,[],[refute_0_467:[bind(Y,$fot(and(X,X_117))),bind(X_16,$fot(X_117)),bind(X_17,$fot(not(not(X))))]]) ).
cnf(refute_0_759,plain,
( implies(and(X_117,not(not(X))),and(X,X_117)) != implies(and(X_117,X),and(X,X_117))
| or(implies(X_117,not(not(not(X)))),and(X,X_117)) != implies(and(X_117,not(not(X))),and(X,X_117))
| or(implies(X_117,not(not(not(X)))),and(X,X_117)) = implies(and(X_117,X),and(X,X_117)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(or(implies(X_117,not(not(not(X)))),and(X,X_117)))),bind(Y0,$fot(implies(and(X_117,not(not(X))),and(X,X_117)))),bind(Z,$fot(implies(and(X_117,X),and(X,X_117))))]]) ).
cnf(refute_0_760,plain,
( implies(and(X_117,not(not(X))),and(X,X_117)) != implies(and(X_117,X),and(X,X_117))
| or(implies(X_117,not(not(not(X)))),and(X,X_117)) = implies(and(X_117,X),and(X,X_117)) ),
inference(resolve,[$cnf( $equal(or(implies(X_117,not(not(not(X)))),and(X,X_117)),implies(and(X_117,not(not(X))),and(X,X_117))) )],[refute_0_758,refute_0_759]) ).
cnf(refute_0_761,plain,
or(implies(X_117,not(not(not(X)))),and(X,X_117)) = implies(and(X_117,X),and(X,X_117)),
inference(resolve,[$cnf( $equal(implies(and(X_117,not(not(X))),and(X,X_117)),implies(and(X_117,X),and(X,X_117))) )],[refute_0_757,refute_0_760]) ).
cnf(refute_0_762,plain,
( or(implies(X_117,not(not(not(X)))),and(X,X_117)) != implies(and(X_117,X),and(X,X_117))
| ~ is_a_theorem(or(implies(X_117,not(not(not(X)))),and(X,X_117)))
| is_a_theorem(implies(and(X_117,X),and(X,X_117))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(X_117,not(not(not(X)))),and(X,X_117))) ),[0],$fot(implies(and(X_117,X),and(X,X_117)))]]) ).
cnf(refute_0_763,plain,
( ~ is_a_theorem(or(implies(X_117,not(not(not(X)))),and(X,X_117)))
| is_a_theorem(implies(and(X_117,X),and(X,X_117))) ),
inference(resolve,[$cnf( $equal(or(implies(X_117,not(not(not(X)))),and(X,X_117)),implies(and(X_117,X),and(X,X_117))) )],[refute_0_761,refute_0_762]) ).
cnf(refute_0_764,plain,
is_a_theorem(implies(and(X_117,X),and(X,X_117))),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_117,not(not(not(X)))),and(X,X_117))) )],[refute_0_752,refute_0_763]) ).
cnf(refute_0_765,plain,
( ~ is_a_theorem(implies(and(X_117,X),and(X,X_117)))
| is_a_theorem(or(X_258,implies(and(X_117,X),and(X,X_117)))) ),
inference(subst,[],[refute_0_720:[bind(P,$fot(X_258)),bind(X_155,$fot(implies(and(X_117,X),and(X,X_117))))]]) ).
cnf(refute_0_766,plain,
is_a_theorem(or(X_258,implies(and(X_117,X),and(X,X_117)))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_117,X),and(X,X_117))) )],[refute_0_764,refute_0_765]) ).
cnf(refute_0_767,plain,
is_a_theorem(or(X_2905,implies(and(X_117,X),and(X,X_117)))),
inference(subst,[],[refute_0_766:[bind(X_258,$fot(X_2905))]]) ).
cnf(refute_0_768,plain,
( ~ is_a_theorem(or(X_2905,implies(and(X_117,X),and(X,X_117))))
| is_a_theorem(implies(and(X_117,X),or(X_2905,and(X,X_117)))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(and(X_117,X))),bind(X_103,$fot(X_2905)),bind(X_105,$fot(and(X,X_117)))]]) ).
cnf(refute_0_769,plain,
is_a_theorem(implies(and(X_117,X),or(X_2905,and(X,X_117)))),
inference(resolve,[$cnf( is_a_theorem(or(X_2905,implies(and(X_117,X),and(X,X_117)))) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
is_a_theorem(implies(and(X_3072,X_3071),or(X_3073,and(X_3071,X_3072)))),
inference(subst,[],[refute_0_769:[bind(X,$fot(X_3071)),bind(X_117,$fot(X_3072)),bind(X_2905,$fot(X_3073))]]) ).
cnf(refute_0_771,plain,
is_a_theorem(or(or(X_3073,and(X_3071,X_3072)),not(and(X_3072,X_3071)))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_3072,X_3071),or(X_3073,and(X_3071,X_3072)))) )],[refute_0_770,refute_0_723]) ).
cnf(refute_0_772,plain,
is_a_theorem(or(or(X_6417,and(not(X),not(X_122))),not(and(not(X_122),not(X))))),
inference(subst,[],[refute_0_771:[bind(X_3071,$fot(not(X))),bind(X_3072,$fot(not(X_122))),bind(X_3073,$fot(X_6417))]]) ).
cnf(refute_0_773,plain,
or(X_120,and(not(X),not(X_122))) = not(and(not(X_120),implies(not(X),X_122))),
inference(subst,[],[refute_0_292:[bind(X,$fot(X_120)),bind(X_44,$fot(not(X))),bind(X_45,$fot(X_122))]]) ).
cnf(refute_0_774,plain,
or(X,X_122) = implies(not(X),X_122),
inference(subst,[],[refute_0_60:[bind(Y,$fot(X_122))]]) ).
cnf(refute_0_775,plain,
( or(X,X_122) != implies(not(X),X_122)
| implies(not(X),X_122) = or(X,X_122) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,X_122))),bind(Y0,$fot(implies(not(X),X_122)))]]) ).
cnf(refute_0_776,plain,
implies(not(X),X_122) = or(X,X_122),
inference(resolve,[$cnf( $equal(or(X,X_122),implies(not(X),X_122)) )],[refute_0_774,refute_0_775]) ).
cnf(refute_0_777,plain,
( implies(not(X),X_122) != or(X,X_122)
| or(X_120,and(not(X),not(X_122))) != not(and(not(X_120),implies(not(X),X_122)))
| or(X_120,and(not(X),not(X_122))) = not(and(not(X_120),or(X,X_122))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_120,and(not(X),not(X_122))),not(and(not(X_120),implies(not(X),X_122)))) ),[1,0,1],$fot(or(X,X_122))]]) ).
cnf(refute_0_778,plain,
( or(X_120,and(not(X),not(X_122))) != not(and(not(X_120),implies(not(X),X_122)))
| or(X_120,and(not(X),not(X_122))) = not(and(not(X_120),or(X,X_122))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_122),or(X,X_122)) )],[refute_0_776,refute_0_777]) ).
cnf(refute_0_779,plain,
or(X_120,and(not(X),not(X_122))) = not(and(not(X_120),or(X,X_122))),
inference(resolve,[$cnf( $equal(or(X_120,and(not(X),not(X_122))),not(and(not(X_120),implies(not(X),X_122)))) )],[refute_0_773,refute_0_778]) ).
cnf(refute_0_780,plain,
or(X_6417,and(not(X),not(X_122))) = not(and(not(X_6417),or(X,X_122))),
inference(subst,[],[refute_0_779:[bind(X_120,$fot(X_6417))]]) ).
cnf(refute_0_781,plain,
( or(X_6417,and(not(X),not(X_122))) != not(and(not(X_6417),or(X,X_122)))
| ~ is_a_theorem(or(or(X_6417,and(not(X),not(X_122))),not(and(not(X_122),not(X)))))
| is_a_theorem(or(not(and(not(X_6417),or(X,X_122))),not(and(not(X_122),not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(or(X_6417,and(not(X),not(X_122))),not(and(not(X_122),not(X))))) ),[0,0],$fot(not(and(not(X_6417),or(X,X_122))))]]) ).
cnf(refute_0_782,plain,
( ~ is_a_theorem(or(or(X_6417,and(not(X),not(X_122))),not(and(not(X_122),not(X)))))
| is_a_theorem(or(not(and(not(X_6417),or(X,X_122))),not(and(not(X_122),not(X))))) ),
inference(resolve,[$cnf( $equal(or(X_6417,and(not(X),not(X_122))),not(and(not(X_6417),or(X,X_122)))) )],[refute_0_780,refute_0_781]) ).
cnf(refute_0_783,plain,
is_a_theorem(or(not(and(not(X_6417),or(X,X_122))),not(and(not(X_122),not(X))))),
inference(resolve,[$cnf( is_a_theorem(or(or(X_6417,and(not(X),not(X_122))),not(and(not(X_122),not(X))))) )],[refute_0_772,refute_0_782]) ).
cnf(refute_0_784,plain,
implies(not(X_122),X) = or(X_122,X),
inference(subst,[],[refute_0_159:[bind(X,$fot(X_122)),bind(Y,$fot(X))]]) ).
cnf(refute_0_785,plain,
not(and(not(X_122),not(X))) = implies(not(X_122),X),
inference(subst,[],[refute_0_56:[bind(X,$fot(not(X_122))),bind(Y,$fot(X))]]) ).
cnf(refute_0_786,plain,
( implies(not(X_122),X) != or(X_122,X)
| not(and(not(X_122),not(X))) != implies(not(X_122),X)
| not(and(not(X_122),not(X))) = or(X_122,X) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(not(and(not(X_122),not(X))))),bind(Y0,$fot(implies(not(X_122),X))),bind(Z,$fot(or(X_122,X)))]]) ).
cnf(refute_0_787,plain,
( implies(not(X_122),X) != or(X_122,X)
| not(and(not(X_122),not(X))) = or(X_122,X) ),
inference(resolve,[$cnf( $equal(not(and(not(X_122),not(X))),implies(not(X_122),X)) )],[refute_0_785,refute_0_786]) ).
cnf(refute_0_788,plain,
not(and(not(X_122),not(X))) = or(X_122,X),
inference(resolve,[$cnf( $equal(implies(not(X_122),X),or(X_122,X)) )],[refute_0_784,refute_0_787]) ).
cnf(refute_0_789,plain,
implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X)))) = implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X)))),
introduced(tautology,[refl,[$fot(implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X)))))]]) ).
cnf(refute_0_790,plain,
( implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X)))) != implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X))))
| not(and(not(X_122),not(X))) != or(X_122,X)
| implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X)))) = implies(and(not(X_6417),or(X,X_122)),or(X_122,X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X)))),implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X))))) ),[1,1],$fot(or(X_122,X))]]) ).
cnf(refute_0_791,plain,
( not(and(not(X_122),not(X))) != or(X_122,X)
| implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X)))) = implies(and(not(X_6417),or(X,X_122)),or(X_122,X)) ),
inference(resolve,[$cnf( $equal(implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X)))),implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X))))) )],[refute_0_789,refute_0_790]) ).
cnf(refute_0_792,plain,
implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X)))) = implies(and(not(X_6417),or(X,X_122)),or(X_122,X)),
inference(resolve,[$cnf( $equal(not(and(not(X_122),not(X))),or(X_122,X)) )],[refute_0_788,refute_0_791]) ).
cnf(refute_0_793,plain,
or(not(and(not(X_6417),or(X,X_122))),not(and(not(X_122),not(X)))) = implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X)))),
inference(subst,[],[refute_0_20:[bind(X,$fot(and(not(X_6417),or(X,X_122)))),bind(Y,$fot(not(and(not(X_122),not(X)))))]]) ).
cnf(refute_0_794,plain,
( implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X)))) != implies(and(not(X_6417),or(X,X_122)),or(X_122,X))
| or(not(and(not(X_6417),or(X,X_122))),not(and(not(X_122),not(X)))) != implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X))))
| or(not(and(not(X_6417),or(X,X_122))),not(and(not(X_122),not(X)))) = implies(and(not(X_6417),or(X,X_122)),or(X_122,X)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(or(not(and(not(X_6417),or(X,X_122))),not(and(not(X_122),not(X)))))),bind(Y0,$fot(implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X)))))),bind(Z,$fot(implies(and(not(X_6417),or(X,X_122)),or(X_122,X))))]]) ).
cnf(refute_0_795,plain,
( implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X)))) != implies(and(not(X_6417),or(X,X_122)),or(X_122,X))
| or(not(and(not(X_6417),or(X,X_122))),not(and(not(X_122),not(X)))) = implies(and(not(X_6417),or(X,X_122)),or(X_122,X)) ),
inference(resolve,[$cnf( $equal(or(not(and(not(X_6417),or(X,X_122))),not(and(not(X_122),not(X)))),implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X))))) )],[refute_0_793,refute_0_794]) ).
cnf(refute_0_796,plain,
or(not(and(not(X_6417),or(X,X_122))),not(and(not(X_122),not(X)))) = implies(and(not(X_6417),or(X,X_122)),or(X_122,X)),
inference(resolve,[$cnf( $equal(implies(and(not(X_6417),or(X,X_122)),not(and(not(X_122),not(X)))),implies(and(not(X_6417),or(X,X_122)),or(X_122,X))) )],[refute_0_792,refute_0_795]) ).
cnf(refute_0_797,plain,
( or(not(and(not(X_6417),or(X,X_122))),not(and(not(X_122),not(X)))) != implies(and(not(X_6417),or(X,X_122)),or(X_122,X))
| ~ is_a_theorem(or(not(and(not(X_6417),or(X,X_122))),not(and(not(X_122),not(X)))))
| is_a_theorem(implies(and(not(X_6417),or(X,X_122)),or(X_122,X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(and(not(X_6417),or(X,X_122))),not(and(not(X_122),not(X))))) ),[0],$fot(implies(and(not(X_6417),or(X,X_122)),or(X_122,X)))]]) ).
cnf(refute_0_798,plain,
( ~ is_a_theorem(or(not(and(not(X_6417),or(X,X_122))),not(and(not(X_122),not(X)))))
| is_a_theorem(implies(and(not(X_6417),or(X,X_122)),or(X_122,X))) ),
inference(resolve,[$cnf( $equal(or(not(and(not(X_6417),or(X,X_122))),not(and(not(X_122),not(X)))),implies(and(not(X_6417),or(X,X_122)),or(X_122,X))) )],[refute_0_796,refute_0_797]) ).
cnf(refute_0_799,plain,
is_a_theorem(implies(and(not(X_6417),or(X,X_122)),or(X_122,X))),
inference(resolve,[$cnf( is_a_theorem(or(not(and(not(X_6417),or(X,X_122))),not(and(not(X_122),not(X))))) )],[refute_0_783,refute_0_798]) ).
cnf(refute_0_800,plain,
is_a_theorem(implies(and(not(and(X_6419,X_6418)),or(X_6418,X_6419)),or(X_6419,X_6418))),
inference(subst,[],[refute_0_799:[bind(X,$fot(X_6418)),bind(X_122,$fot(X_6419)),bind(X_6417,$fot(and(X_6419,X_6418)))]]) ).
cnf(refute_0_801,plain,
and(not(and(X_6419,X_6418)),or(X_6418,X_6419)) = equiv(X_6419,not(X_6418)),
inference(subst,[],[refute_0_360:[bind(X,$fot(X_6418)),bind(X_29,$fot(X_6419))]]) ).
cnf(refute_0_802,plain,
( and(not(and(X_6419,X_6418)),or(X_6418,X_6419)) != equiv(X_6419,not(X_6418))
| ~ is_a_theorem(implies(and(not(and(X_6419,X_6418)),or(X_6418,X_6419)),or(X_6419,X_6418)))
| is_a_theorem(implies(equiv(X_6419,not(X_6418)),or(X_6419,X_6418))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(not(and(X_6419,X_6418)),or(X_6418,X_6419)),or(X_6419,X_6418))) ),[0,0],$fot(equiv(X_6419,not(X_6418)))]]) ).
cnf(refute_0_803,plain,
( ~ is_a_theorem(implies(and(not(and(X_6419,X_6418)),or(X_6418,X_6419)),or(X_6419,X_6418)))
| is_a_theorem(implies(equiv(X_6419,not(X_6418)),or(X_6419,X_6418))) ),
inference(resolve,[$cnf( $equal(and(not(and(X_6419,X_6418)),or(X_6418,X_6419)),equiv(X_6419,not(X_6418))) )],[refute_0_801,refute_0_802]) ).
cnf(refute_0_804,plain,
is_a_theorem(implies(equiv(X_6419,not(X_6418)),or(X_6419,X_6418))),
inference(resolve,[$cnf( is_a_theorem(implies(and(not(and(X_6419,X_6418)),or(X_6418,X_6419)),or(X_6419,X_6418))) )],[refute_0_800,refute_0_803]) ).
cnf(refute_0_805,plain,
is_a_theorem(implies(equiv(X_6422,not(not(X))),or(X_6422,not(X)))),
inference(subst,[],[refute_0_804:[bind(X_6418,$fot(not(X))),bind(X_6419,$fot(X_6422))]]) ).
cnf(refute_0_806,plain,
and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) = and(implies(X_35,not(not(X))),implies(X,X_35)),
inference(subst,[],[refute_0_199:[bind(X,$fot(implies(X_35,not(not(X))))),bind(X_20,$fot(implies(X,X_35)))]]) ).
cnf(refute_0_807,plain,
( equiv(X_35,not(not(X))) != and(implies(X_35,not(not(X))),implies(X,X_35))
| and(implies(X_35,not(not(X))),implies(X,X_35)) = equiv(X_35,not(not(X))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(X_35,not(not(X))))),bind(Y0,$fot(and(implies(X_35,not(not(X))),implies(X,X_35))))]]) ).
cnf(refute_0_808,plain,
and(implies(X_35,not(not(X))),implies(X,X_35)) = equiv(X_35,not(not(X))),
inference(resolve,[$cnf( $equal(equiv(X_35,not(not(X))),and(implies(X_35,not(not(X))),implies(X,X_35))) )],[refute_0_383,refute_0_807]) ).
cnf(refute_0_809,plain,
( and(implies(X_35,not(not(X))),implies(X,X_35)) != equiv(X_35,not(not(X)))
| and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) != and(implies(X_35,not(not(X))),implies(X,X_35))
| and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) = equiv(X_35,not(not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)),and(implies(X_35,not(not(X))),implies(X,X_35))) ),[1],$fot(equiv(X_35,not(not(X))))]]) ).
cnf(refute_0_810,plain,
( and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) != and(implies(X_35,not(not(X))),implies(X,X_35))
| and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) = equiv(X_35,not(not(X))) ),
inference(resolve,[$cnf( $equal(and(implies(X_35,not(not(X))),implies(X,X_35)),equiv(X_35,not(not(X)))) )],[refute_0_808,refute_0_809]) ).
cnf(refute_0_811,plain,
and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) = equiv(X_35,not(not(X))),
inference(resolve,[$cnf( $equal(and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)),and(implies(X_35,not(not(X))),implies(X,X_35))) )],[refute_0_806,refute_0_810]) ).
cnf(refute_0_812,plain,
and(implies(X_35,X),implies(X,X_35)) = equiv(X_35,X),
inference(subst,[],[refute_0_402:[bind(X,$fot(X_35)),bind(Y,$fot(X))]]) ).
cnf(refute_0_813,plain,
not(and(X_35,not(X))) = implies(X_35,X),
inference(subst,[],[refute_0_56:[bind(X,$fot(X_35)),bind(Y,$fot(X))]]) ).
cnf(refute_0_814,plain,
and(not(and(X_35,not(X))),implies(X,X_35)) = and(not(and(X_35,not(X))),implies(X,X_35)),
introduced(tautology,[refl,[$fot(and(not(and(X_35,not(X))),implies(X,X_35)))]]) ).
cnf(refute_0_815,plain,
( and(not(and(X_35,not(X))),implies(X,X_35)) != and(not(and(X_35,not(X))),implies(X,X_35))
| not(and(X_35,not(X))) != implies(X_35,X)
| and(not(and(X_35,not(X))),implies(X,X_35)) = and(implies(X_35,X),implies(X,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(X_35,not(X))),implies(X,X_35)),and(not(and(X_35,not(X))),implies(X,X_35))) ),[1,0],$fot(implies(X_35,X))]]) ).
cnf(refute_0_816,plain,
( not(and(X_35,not(X))) != implies(X_35,X)
| and(not(and(X_35,not(X))),implies(X,X_35)) = and(implies(X_35,X),implies(X,X_35)) ),
inference(resolve,[$cnf( $equal(and(not(and(X_35,not(X))),implies(X,X_35)),and(not(and(X_35,not(X))),implies(X,X_35))) )],[refute_0_814,refute_0_815]) ).
cnf(refute_0_817,plain,
and(not(and(X_35,not(X))),implies(X,X_35)) = and(implies(X_35,X),implies(X,X_35)),
inference(resolve,[$cnf( $equal(not(and(X_35,not(X))),implies(X_35,X)) )],[refute_0_813,refute_0_816]) ).
cnf(refute_0_818,plain,
( and(implies(X_35,X),implies(X,X_35)) != equiv(X_35,X)
| and(not(and(X_35,not(X))),implies(X,X_35)) != and(implies(X_35,X),implies(X,X_35))
| and(not(and(X_35,not(X))),implies(X,X_35)) = equiv(X_35,X) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(and(not(and(X_35,not(X))),implies(X,X_35)))),bind(Y0,$fot(and(implies(X_35,X),implies(X,X_35)))),bind(Z,$fot(equiv(X_35,X)))]]) ).
cnf(refute_0_819,plain,
( and(implies(X_35,X),implies(X,X_35)) != equiv(X_35,X)
| and(not(and(X_35,not(X))),implies(X,X_35)) = equiv(X_35,X) ),
inference(resolve,[$cnf( $equal(and(not(and(X_35,not(X))),implies(X,X_35)),and(implies(X_35,X),implies(X,X_35))) )],[refute_0_817,refute_0_818]) ).
cnf(refute_0_820,plain,
and(not(and(X_35,not(X))),implies(X,X_35)) = equiv(X_35,X),
inference(resolve,[$cnf( $equal(and(implies(X_35,X),implies(X,X_35)),equiv(X_35,X)) )],[refute_0_812,refute_0_819]) ).
cnf(refute_0_821,plain,
and(implies(X_35,not(not(X))),implies(X,X_35)) = and(not(and(X_35,not(X))),implies(X,X_35)),
inference(subst,[],[refute_0_353:[bind(X,$fot(X_35)),bind(Y,$fot(not(X))),bind(X_89,$fot(implies(X,X_35)))]]) ).
cnf(refute_0_822,plain,
( and(implies(X_35,not(not(X))),implies(X,X_35)) != and(not(and(X_35,not(X))),implies(X,X_35))
| and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) != and(implies(X_35,not(not(X))),implies(X,X_35))
| and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) = and(not(and(X_35,not(X))),implies(X,X_35)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)))),bind(Y0,$fot(and(implies(X_35,not(not(X))),implies(X,X_35)))),bind(Z,$fot(and(not(and(X_35,not(X))),implies(X,X_35))))]]) ).
cnf(refute_0_823,plain,
( and(implies(X_35,not(not(X))),implies(X,X_35)) != and(not(and(X_35,not(X))),implies(X,X_35))
| and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) = and(not(and(X_35,not(X))),implies(X,X_35)) ),
inference(resolve,[$cnf( $equal(and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)),and(implies(X_35,not(not(X))),implies(X,X_35))) )],[refute_0_806,refute_0_822]) ).
cnf(refute_0_824,plain,
and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) = and(not(and(X_35,not(X))),implies(X,X_35)),
inference(resolve,[$cnf( $equal(and(implies(X_35,not(not(X))),implies(X,X_35)),and(not(and(X_35,not(X))),implies(X,X_35))) )],[refute_0_821,refute_0_823]) ).
cnf(refute_0_825,plain,
( and(not(and(X_35,not(X))),implies(X,X_35)) != equiv(X_35,X)
| and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) != and(not(and(X_35,not(X))),implies(X,X_35))
| and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) = equiv(X_35,X) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)))),bind(Y0,$fot(and(not(and(X_35,not(X))),implies(X,X_35)))),bind(Z,$fot(equiv(X_35,X)))]]) ).
cnf(refute_0_826,plain,
( and(not(and(X_35,not(X))),implies(X,X_35)) != equiv(X_35,X)
| and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) = equiv(X_35,X) ),
inference(resolve,[$cnf( $equal(and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)),and(not(and(X_35,not(X))),implies(X,X_35))) )],[refute_0_824,refute_0_825]) ).
cnf(refute_0_827,plain,
and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) = equiv(X_35,X),
inference(resolve,[$cnf( $equal(and(not(and(X_35,not(X))),implies(X,X_35)),equiv(X_35,X)) )],[refute_0_820,refute_0_826]) ).
cnf(refute_0_828,plain,
( and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) != equiv(X_35,X)
| and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) != equiv(X_35,not(not(X)))
| equiv(X_35,X) = equiv(X_35,not(not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)),equiv(X_35,not(not(X)))) ),[0],$fot(equiv(X_35,X))]]) ).
cnf(refute_0_829,plain,
( and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)) != equiv(X_35,not(not(X)))
| equiv(X_35,X) = equiv(X_35,not(not(X))) ),
inference(resolve,[$cnf( $equal(and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)),equiv(X_35,X)) )],[refute_0_827,refute_0_828]) ).
cnf(refute_0_830,plain,
equiv(X_35,X) = equiv(X_35,not(not(X))),
inference(resolve,[$cnf( $equal(and(not(not(implies(X_35,not(not(X))))),implies(X,X_35)),equiv(X_35,not(not(X)))) )],[refute_0_811,refute_0_829]) ).
cnf(refute_0_831,plain,
equiv(X_6422,X) = equiv(X_6422,not(not(X))),
inference(subst,[],[refute_0_830:[bind(X_35,$fot(X_6422))]]) ).
cnf(refute_0_832,plain,
( equiv(X_6422,X) != equiv(X_6422,not(not(X)))
| equiv(X_6422,not(not(X))) = equiv(X_6422,X) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(X_6422,X))),bind(Y0,$fot(equiv(X_6422,not(not(X)))))]]) ).
cnf(refute_0_833,plain,
equiv(X_6422,not(not(X))) = equiv(X_6422,X),
inference(resolve,[$cnf( $equal(equiv(X_6422,X),equiv(X_6422,not(not(X)))) )],[refute_0_831,refute_0_832]) ).
cnf(refute_0_834,plain,
( equiv(X_6422,not(not(X))) != equiv(X_6422,X)
| ~ is_a_theorem(implies(equiv(X_6422,not(not(X))),or(X_6422,not(X))))
| is_a_theorem(implies(equiv(X_6422,X),or(X_6422,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(equiv(X_6422,not(not(X))),or(X_6422,not(X)))) ),[0,0],$fot(equiv(X_6422,X))]]) ).
cnf(refute_0_835,plain,
( ~ is_a_theorem(implies(equiv(X_6422,not(not(X))),or(X_6422,not(X))))
| is_a_theorem(implies(equiv(X_6422,X),or(X_6422,not(X)))) ),
inference(resolve,[$cnf( $equal(equiv(X_6422,not(not(X))),equiv(X_6422,X)) )],[refute_0_833,refute_0_834]) ).
cnf(refute_0_836,plain,
is_a_theorem(implies(equiv(X_6422,X),or(X_6422,not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(equiv(X_6422,not(not(X))),or(X_6422,not(X)))) )],[refute_0_805,refute_0_835]) ).
cnf(refute_0_837,plain,
is_a_theorem(implies(equiv(X_6532,X),or(X_6532,not(X)))),
inference(subst,[],[refute_0_836:[bind(X_6422,$fot(X_6532))]]) ).
cnf(refute_0_838,plain,
is_a_theorem(implies(or(not(X),or(X_104,X_105)),or(X_104,or(not(X),X_105)))),
inference(subst,[],[refute_0_5:[bind(P,$fot(not(X))),bind(Q,$fot(X_104)),bind(R,$fot(X_105))]]) ).
cnf(refute_0_839,plain,
( or(not(X),X_105) != implies(X,X_105)
| ~ is_a_theorem(implies(or(not(X),or(X_104,X_105)),or(X_104,or(not(X),X_105))))
| is_a_theorem(implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),or(X_104,X_105)),or(X_104,or(not(X),X_105)))) ),[0,1,1],$fot(implies(X,X_105))]]) ).
cnf(refute_0_840,plain,
( ~ is_a_theorem(implies(or(not(X),or(X_104,X_105)),or(X_104,or(not(X),X_105))))
| is_a_theorem(implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_105),implies(X,X_105)) )],[refute_0_21,refute_0_839]) ).
cnf(refute_0_841,plain,
is_a_theorem(implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),or(X_104,X_105)),or(X_104,or(not(X),X_105)))) )],[refute_0_838,refute_0_840]) ).
cnf(refute_0_842,plain,
or(not(X),or(X_104,X_105)) = implies(X,or(X_104,X_105)),
inference(subst,[],[refute_0_20:[bind(Y,$fot(or(X_104,X_105)))]]) ).
cnf(refute_0_843,plain,
implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105))) = implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105))))]]) ).
cnf(refute_0_844,plain,
( implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105))) != implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105)))
| or(not(X),or(X_104,X_105)) != implies(X,or(X_104,X_105))
| implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105))) = implies(implies(X,or(X_104,X_105)),or(X_104,implies(X,X_105))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105))),implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105)))) ),[1,0],$fot(implies(X,or(X_104,X_105)))]]) ).
cnf(refute_0_845,plain,
( or(not(X),or(X_104,X_105)) != implies(X,or(X_104,X_105))
| implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105))) = implies(implies(X,or(X_104,X_105)),or(X_104,implies(X,X_105))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105))),implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105)))) )],[refute_0_843,refute_0_844]) ).
cnf(refute_0_846,plain,
implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105))) = implies(implies(X,or(X_104,X_105)),or(X_104,implies(X,X_105))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_104,X_105)),implies(X,or(X_104,X_105))) )],[refute_0_842,refute_0_845]) ).
cnf(refute_0_847,plain,
( implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105))) != implies(implies(X,or(X_104,X_105)),or(X_104,implies(X,X_105)))
| ~ is_a_theorem(implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105))))
| is_a_theorem(implies(implies(X,or(X_104,X_105)),or(X_104,implies(X,X_105)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105)))) ),[0],$fot(implies(implies(X,or(X_104,X_105)),or(X_104,implies(X,X_105))))]]) ).
cnf(refute_0_848,plain,
( ~ is_a_theorem(implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105))))
| is_a_theorem(implies(implies(X,or(X_104,X_105)),or(X_104,implies(X,X_105)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105))),implies(implies(X,or(X_104,X_105)),or(X_104,implies(X,X_105)))) )],[refute_0_846,refute_0_847]) ).
cnf(refute_0_849,plain,
is_a_theorem(implies(implies(X,or(X_104,X_105)),or(X_104,implies(X,X_105)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),or(X_104,X_105)),or(X_104,implies(X,X_105)))) )],[refute_0_841,refute_0_848]) ).
cnf(refute_0_850,plain,
( ~ is_a_theorem(implies(X,or(X_104,X_105)))
| ~ is_a_theorem(implies(implies(X,or(X_104,X_105)),or(X_104,implies(X,X_105))))
| is_a_theorem(or(X_104,implies(X,X_105))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(implies(X,or(X_104,X_105)))),bind(Y,$fot(or(X_104,implies(X,X_105))))]]) ).
cnf(refute_0_851,plain,
( ~ is_a_theorem(implies(X,or(X_104,X_105)))
| is_a_theorem(or(X_104,implies(X,X_105))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,or(X_104,X_105)),or(X_104,implies(X,X_105)))) )],[refute_0_849,refute_0_850]) ).
cnf(refute_0_852,plain,
( ~ is_a_theorem(implies(equiv(X_6532,X),or(X_6532,not(X))))
| is_a_theorem(or(X_6532,implies(equiv(X_6532,X),not(X)))) ),
inference(subst,[],[refute_0_851:[bind(X,$fot(equiv(X_6532,X))),bind(X_104,$fot(X_6532)),bind(X_105,$fot(not(X)))]]) ).
cnf(refute_0_853,plain,
is_a_theorem(or(X_6532,implies(equiv(X_6532,X),not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(equiv(X_6532,X),or(X_6532,not(X)))) )],[refute_0_837,refute_0_852]) ).
cnf(refute_0_854,plain,
is_a_theorem(or(X_6537,implies(equiv(X_6537,X_6536),not(X_6536)))),
inference(subst,[],[refute_0_853:[bind(X,$fot(X_6536)),bind(X_6532,$fot(X_6537))]]) ).
cnf(refute_0_855,plain,
is_a_theorem(or(implies(equiv(X_6537,X_6536),not(X_6536)),X_6537)),
inference(resolve,[$cnf( is_a_theorem(or(X_6537,implies(equiv(X_6537,X_6536),not(X_6536)))) )],[refute_0_854,refute_0_722]) ).
cnf(refute_0_856,plain,
or(implies(equiv(X_6537,X_6536),not(X_6536)),X_6537) = implies(and(equiv(X_6537,X_6536),X_6536),X_6537),
inference(subst,[],[refute_0_467:[bind(Y,$fot(X_6537)),bind(X_16,$fot(equiv(X_6537,X_6536))),bind(X_17,$fot(X_6536))]]) ).
cnf(refute_0_857,plain,
( or(implies(equiv(X_6537,X_6536),not(X_6536)),X_6537) != implies(and(equiv(X_6537,X_6536),X_6536),X_6537)
| ~ is_a_theorem(or(implies(equiv(X_6537,X_6536),not(X_6536)),X_6537))
| is_a_theorem(implies(and(equiv(X_6537,X_6536),X_6536),X_6537)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(equiv(X_6537,X_6536),not(X_6536)),X_6537)) ),[0],$fot(implies(and(equiv(X_6537,X_6536),X_6536),X_6537))]]) ).
cnf(refute_0_858,plain,
( ~ is_a_theorem(or(implies(equiv(X_6537,X_6536),not(X_6536)),X_6537))
| is_a_theorem(implies(and(equiv(X_6537,X_6536),X_6536),X_6537)) ),
inference(resolve,[$cnf( $equal(or(implies(equiv(X_6537,X_6536),not(X_6536)),X_6537),implies(and(equiv(X_6537,X_6536),X_6536),X_6537)) )],[refute_0_856,refute_0_857]) ).
cnf(refute_0_859,plain,
is_a_theorem(implies(and(equiv(X_6537,X_6536),X_6536),X_6537)),
inference(resolve,[$cnf( is_a_theorem(or(implies(equiv(X_6537,X_6536),not(X_6536)),X_6537)) )],[refute_0_855,refute_0_858]) ).
cnf(refute_0_860,plain,
is_a_theorem(implies(and(equiv(X_6547,X_6546),X_6546),X_6547)),
inference(subst,[],[refute_0_859:[bind(X_6536,$fot(X_6546)),bind(X_6537,$fot(X_6547))]]) ).
cnf(refute_0_861,plain,
is_a_theorem(or(P,implies(and(equiv(X_6547,X_6546),X_6546),X_6547))),
inference(resolve,[$cnf( is_a_theorem(implies(and(equiv(X_6547,X_6546),X_6546),X_6547)) )],[refute_0_860,refute_0_721]) ).
cnf(refute_0_862,plain,
is_a_theorem(or(X_7395,implies(and(equiv(X_7397,X_7396),X_7396),X_7397))),
inference(subst,[],[refute_0_861:[bind(P,$fot(X_7395)),bind(X_6546,$fot(X_7396)),bind(X_6547,$fot(X_7397))]]) ).
cnf(refute_0_863,plain,
is_a_theorem(or(implies(and(equiv(X_7397,X_7396),X_7396),X_7397),X_7395)),
inference(resolve,[$cnf( is_a_theorem(or(X_7395,implies(and(equiv(X_7397,X_7396),X_7396),X_7397))) )],[refute_0_862,refute_0_717]) ).
cnf(refute_0_864,plain,
is_a_theorem(or(implies(and(equiv(X_7397,X_7396),X_7396),X_7397),X_28760)),
inference(subst,[],[refute_0_863:[bind(X_7395,$fot(X_28760))]]) ).
cnf(refute_0_865,plain,
( ~ is_a_theorem(implies(or(X_192,X_194),implies(or(X_193,not(X_192)),or(X_193,X_194))))
| ~ is_a_theorem(or(X_192,X_194))
| is_a_theorem(implies(or(X_193,not(X_192)),or(X_193,X_194))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(or(X_192,X_194))),bind(Y,$fot(implies(or(X_193,not(X_192)),or(X_193,X_194))))]]) ).
cnf(refute_0_866,plain,
is_a_theorem(implies(implies(not(X),X_127),implies(or(X_125,not(X)),or(X_125,X_127)))),
inference(subst,[],[refute_0_674:[bind(P,$fot(X_125)),bind(Q,$fot(not(X))),bind(R,$fot(X_127))]]) ).
cnf(refute_0_867,plain,
or(X,X_127) = implies(not(X),X_127),
inference(subst,[],[refute_0_60:[bind(Y,$fot(X_127))]]) ).
cnf(refute_0_868,plain,
( or(X,X_127) != implies(not(X),X_127)
| implies(not(X),X_127) = or(X,X_127) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,X_127))),bind(Y0,$fot(implies(not(X),X_127)))]]) ).
cnf(refute_0_869,plain,
implies(not(X),X_127) = or(X,X_127),
inference(resolve,[$cnf( $equal(or(X,X_127),implies(not(X),X_127)) )],[refute_0_867,refute_0_868]) ).
cnf(refute_0_870,plain,
( implies(not(X),X_127) != or(X,X_127)
| ~ is_a_theorem(implies(implies(not(X),X_127),implies(or(X_125,not(X)),or(X_125,X_127))))
| is_a_theorem(implies(or(X,X_127),implies(or(X_125,not(X)),or(X_125,X_127)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X),X_127),implies(or(X_125,not(X)),or(X_125,X_127)))) ),[0,0],$fot(or(X,X_127))]]) ).
cnf(refute_0_871,plain,
( ~ is_a_theorem(implies(implies(not(X),X_127),implies(or(X_125,not(X)),or(X_125,X_127))))
| is_a_theorem(implies(or(X,X_127),implies(or(X_125,not(X)),or(X_125,X_127)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_127),or(X,X_127)) )],[refute_0_869,refute_0_870]) ).
cnf(refute_0_872,plain,
is_a_theorem(implies(or(X,X_127),implies(or(X_125,not(X)),or(X_125,X_127)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X_127),implies(or(X_125,not(X)),or(X_125,X_127)))) )],[refute_0_866,refute_0_871]) ).
cnf(refute_0_873,plain,
is_a_theorem(implies(or(X_192,X_194),implies(or(X_193,not(X_192)),or(X_193,X_194)))),
inference(subst,[],[refute_0_872:[bind(X,$fot(X_192)),bind(X_125,$fot(X_193)),bind(X_127,$fot(X_194))]]) ).
cnf(refute_0_874,plain,
( ~ is_a_theorem(or(X_192,X_194))
| is_a_theorem(implies(or(X_193,not(X_192)),or(X_193,X_194))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_192,X_194),implies(or(X_193,not(X_192)),or(X_193,X_194)))) )],[refute_0_873,refute_0_865]) ).
cnf(refute_0_875,plain,
( ~ is_a_theorem(or(implies(and(equiv(X_7397,X_7396),X_7396),X_7397),X_28760))
| is_a_theorem(implies(or(X_28759,not(implies(and(equiv(X_7397,X_7396),X_7396),X_7397))),or(X_28759,X_28760))) ),
inference(subst,[],[refute_0_874:[bind(X_192,$fot(implies(and(equiv(X_7397,X_7396),X_7396),X_7397))),bind(X_193,$fot(X_28759)),bind(X_194,$fot(X_28760))]]) ).
cnf(refute_0_876,plain,
is_a_theorem(implies(or(X_28759,not(implies(and(equiv(X_7397,X_7396),X_7396),X_7397))),or(X_28759,X_28760))),
inference(resolve,[$cnf( is_a_theorem(or(implies(and(equiv(X_7397,X_7396),X_7396),X_7397),X_28760)) )],[refute_0_864,refute_0_875]) ).
cnf(refute_0_877,plain,
is_a_theorem(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),or(not(X),X_28789))),
inference(subst,[],[refute_0_876:[bind(X_28759,$fot(not(X))),bind(X_28760,$fot(X_28789)),bind(X_7396,$fot(X_28790)),bind(X_7397,$fot(X_28791))]]) ).
cnf(refute_0_878,plain,
implies(X,X_28789) = or(not(X),X_28789),
inference(subst,[],[refute_0_9:[bind(Y,$fot(X_28789))]]) ).
cnf(refute_0_879,plain,
( implies(X,X_28789) != or(not(X),X_28789)
| or(not(X),X_28789) = implies(X,X_28789) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,X_28789))),bind(Y0,$fot(or(not(X),X_28789)))]]) ).
cnf(refute_0_880,plain,
or(not(X),X_28789) = implies(X,X_28789),
inference(resolve,[$cnf( $equal(implies(X,X_28789),or(not(X),X_28789)) )],[refute_0_878,refute_0_879]) ).
cnf(refute_0_881,plain,
( or(not(X),X_28789) != implies(X,X_28789)
| ~ is_a_theorem(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),or(not(X),X_28789)))
| is_a_theorem(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),or(not(X),X_28789))) ),[0,1],$fot(implies(X,X_28789))]]) ).
cnf(refute_0_882,plain,
( ~ is_a_theorem(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),or(not(X),X_28789)))
| is_a_theorem(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_28789),implies(X,X_28789)) )],[refute_0_880,refute_0_881]) ).
cnf(refute_0_883,plain,
is_a_theorem(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),or(not(X),X_28789))) )],[refute_0_877,refute_0_882]) ).
cnf(refute_0_884,plain,
implies(not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)) = or(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)),implies(X,X_28789)),
inference(subst,[],[refute_0_159:[bind(X,$fot(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)))),bind(Y,$fot(implies(X,X_28789)))]]) ).
cnf(refute_0_885,plain,
and(not(not(X)),not(X_9550)) = and(X,not(X_9550)),
inference(subst,[],[refute_0_199:[bind(X_20,$fot(not(X_9550)))]]) ).
cnf(refute_0_886,plain,
( ~ is_a_theorem(equiv(and(not(X_9547),not(X_9548)),not(or(X_9547,X_9548))))
| and(not(X_9547),not(X_9548)) = not(or(X_9547,X_9548)) ),
inference(subst,[],[refute_0_253:[bind(X,$fot(and(not(X_9547),not(X_9548)))),bind(Y,$fot(not(or(X_9547,X_9548))))]]) ).
cnf(refute_0_887,plain,
( ~ is_a_theorem(implies(or(or(X_9545,X_9546),not(or(X_9545,X_9546))),equiv(and(not(X_9545),not(X_9546)),not(or(X_9545,X_9546)))))
| ~ is_a_theorem(or(or(X_9545,X_9546),not(or(X_9545,X_9546))))
| is_a_theorem(equiv(and(not(X_9545),not(X_9546)),not(or(X_9545,X_9546)))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(or(or(X_9545,X_9546),not(or(X_9545,X_9546))))),bind(Y,$fot(equiv(and(not(X_9545),not(X_9546)),not(or(X_9545,X_9546)))))]]) ).
cnf(refute_0_888,plain,
is_a_theorem(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),and(X_585,not(X_586))))),
inference(subst,[],[refute_0_330:[bind(X_58,$fot(and(X_585,not(X_586))))]]) ).
cnf(refute_0_889,plain,
equiv(and(X_585,not(X_586)),and(X_585,not(X_586))) = equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))),
inference(subst,[],[refute_0_592:[bind(X,$fot(and(X_585,not(X_586)))),bind(X_44,$fot(X_585)),bind(X_45,$fot(X_586))]]) ).
cnf(refute_0_890,plain,
( equiv(and(X_585,not(X_586)),and(X_585,not(X_586))) != equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))
| ~ is_a_theorem(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),and(X_585,not(X_586)))))
| is_a_theorem(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),and(X_585,not(X_586))))) ),[0,1],$fot(equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))]]) ).
cnf(refute_0_891,plain,
( ~ is_a_theorem(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),and(X_585,not(X_586)))))
| is_a_theorem(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))) ),
inference(resolve,[$cnf( $equal(equiv(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) )],[refute_0_889,refute_0_890]) ).
cnf(refute_0_892,plain,
is_a_theorem(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),and(X_585,not(X_586))))) )],[refute_0_888,refute_0_891]) ).
cnf(refute_0_893,plain,
or(and(not(X_120),implies(X_121,X_122)),Y) = implies(not(and(not(X_120),implies(X_121,X_122))),Y),
inference(subst,[],[refute_0_60:[bind(X,$fot(and(not(X_120),implies(X_121,X_122))))]]) ).
cnf(refute_0_894,plain,
or(X_120,and(X_121,not(X_122))) = not(and(not(X_120),implies(X_121,X_122))),
inference(subst,[],[refute_0_292:[bind(X,$fot(X_120)),bind(X_44,$fot(X_121)),bind(X_45,$fot(X_122))]]) ).
cnf(refute_0_895,plain,
( or(X_120,and(X_121,not(X_122))) != not(and(not(X_120),implies(X_121,X_122)))
| not(and(not(X_120),implies(X_121,X_122))) = or(X_120,and(X_121,not(X_122))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X_120,and(X_121,not(X_122))))),bind(Y0,$fot(not(and(not(X_120),implies(X_121,X_122)))))]]) ).
cnf(refute_0_896,plain,
not(and(not(X_120),implies(X_121,X_122))) = or(X_120,and(X_121,not(X_122))),
inference(resolve,[$cnf( $equal(or(X_120,and(X_121,not(X_122))),not(and(not(X_120),implies(X_121,X_122)))) )],[refute_0_894,refute_0_895]) ).
cnf(refute_0_897,plain,
( not(and(not(X_120),implies(X_121,X_122))) != or(X_120,and(X_121,not(X_122)))
| or(and(not(X_120),implies(X_121,X_122)),Y) != implies(not(and(not(X_120),implies(X_121,X_122))),Y)
| or(and(not(X_120),implies(X_121,X_122)),Y) = implies(or(X_120,and(X_121,not(X_122))),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_120),implies(X_121,X_122)),Y),implies(not(and(not(X_120),implies(X_121,X_122))),Y)) ),[1,0],$fot(or(X_120,and(X_121,not(X_122))))]]) ).
cnf(refute_0_898,plain,
( or(and(not(X_120),implies(X_121,X_122)),Y) != implies(not(and(not(X_120),implies(X_121,X_122))),Y)
| or(and(not(X_120),implies(X_121,X_122)),Y) = implies(or(X_120,and(X_121,not(X_122))),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X_120),implies(X_121,X_122))),or(X_120,and(X_121,not(X_122)))) )],[refute_0_896,refute_0_897]) ).
cnf(refute_0_899,plain,
or(and(not(X_120),implies(X_121,X_122)),Y) = implies(or(X_120,and(X_121,not(X_122))),Y),
inference(resolve,[$cnf( $equal(or(and(not(X_120),implies(X_121,X_122)),Y),implies(not(and(not(X_120),implies(X_121,X_122))),Y)) )],[refute_0_893,refute_0_898]) ).
cnf(refute_0_900,plain,
implies(or(X_19,not(X_20)),Y) = or(not(or(X_19,not(X_20))),Y),
inference(subst,[],[refute_0_9:[bind(X,$fot(or(X_19,not(X_20))))]]) ).
cnf(refute_0_901,plain,
( implies(or(X_19,not(X_20)),Y) != or(not(or(X_19,not(X_20))),Y)
| not(or(X_19,not(X_20))) != and(not(X_19),X_20)
| implies(or(X_19,not(X_20)),Y) = or(and(not(X_19),X_20),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_19,not(X_20)),Y),or(not(or(X_19,not(X_20))),Y)) ),[1,0],$fot(and(not(X_19),X_20))]]) ).
cnf(refute_0_902,plain,
( implies(or(X_19,not(X_20)),Y) != or(not(or(X_19,not(X_20))),Y)
| implies(or(X_19,not(X_20)),Y) = or(and(not(X_19),X_20),Y) ),
inference(resolve,[$cnf( $equal(not(or(X_19,not(X_20))),and(not(X_19),X_20)) )],[refute_0_407,refute_0_901]) ).
cnf(refute_0_903,plain,
implies(or(X_19,not(X_20)),Y) = or(and(not(X_19),X_20),Y),
inference(resolve,[$cnf( $equal(implies(or(X_19,not(X_20)),Y),or(not(or(X_19,not(X_20))),Y)) )],[refute_0_900,refute_0_902]) ).
cnf(refute_0_904,plain,
( implies(or(X_19,not(X_20)),Y) != or(and(not(X_19),X_20),Y)
| or(and(not(X_19),X_20),Y) = implies(or(X_19,not(X_20)),Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(or(X_19,not(X_20)),Y))),bind(Y0,$fot(or(and(not(X_19),X_20),Y)))]]) ).
cnf(refute_0_905,plain,
or(and(not(X_19),X_20),Y) = implies(or(X_19,not(X_20)),Y),
inference(resolve,[$cnf( $equal(implies(or(X_19,not(X_20)),Y),or(and(not(X_19),X_20),Y)) )],[refute_0_903,refute_0_904]) ).
cnf(refute_0_906,plain,
or(and(not(X_120),implies(X_121,X_122)),Y) = implies(or(X_120,not(implies(X_121,X_122))),Y),
inference(subst,[],[refute_0_905:[bind(X_19,$fot(X_120)),bind(X_20,$fot(implies(X_121,X_122)))]]) ).
cnf(refute_0_907,plain,
( or(and(not(X_120),implies(X_121,X_122)),Y) != implies(or(X_120,and(X_121,not(X_122))),Y)
| or(and(not(X_120),implies(X_121,X_122)),Y) != implies(or(X_120,not(implies(X_121,X_122))),Y)
| implies(or(X_120,not(implies(X_121,X_122))),Y) = implies(or(X_120,and(X_121,not(X_122))),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_120),implies(X_121,X_122)),Y),implies(or(X_120,and(X_121,not(X_122))),Y)) ),[0],$fot(implies(or(X_120,not(implies(X_121,X_122))),Y))]]) ).
cnf(refute_0_908,plain,
( or(and(not(X_120),implies(X_121,X_122)),Y) != implies(or(X_120,and(X_121,not(X_122))),Y)
| implies(or(X_120,not(implies(X_121,X_122))),Y) = implies(or(X_120,and(X_121,not(X_122))),Y) ),
inference(resolve,[$cnf( $equal(or(and(not(X_120),implies(X_121,X_122)),Y),implies(or(X_120,not(implies(X_121,X_122))),Y)) )],[refute_0_906,refute_0_907]) ).
cnf(refute_0_909,plain,
implies(or(X_120,not(implies(X_121,X_122))),Y) = implies(or(X_120,and(X_121,not(X_122))),Y),
inference(resolve,[$cnf( $equal(or(and(not(X_120),implies(X_121,X_122)),Y),implies(or(X_120,and(X_121,not(X_122))),Y)) )],[refute_0_899,refute_0_908]) ).
cnf(refute_0_910,plain,
( implies(or(X_120,not(implies(X_121,X_122))),Y) != implies(or(X_120,and(X_121,not(X_122))),Y)
| implies(or(X_120,and(X_121,not(X_122))),Y) = implies(or(X_120,not(implies(X_121,X_122))),Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(or(X_120,not(implies(X_121,X_122))),Y))),bind(Y0,$fot(implies(or(X_120,and(X_121,not(X_122))),Y)))]]) ).
cnf(refute_0_911,plain,
implies(or(X_120,and(X_121,not(X_122))),Y) = implies(or(X_120,not(implies(X_121,X_122))),Y),
inference(resolve,[$cnf( $equal(implies(or(X_120,not(implies(X_121,X_122))),Y),implies(or(X_120,and(X_121,not(X_122))),Y)) )],[refute_0_909,refute_0_910]) ).
cnf(refute_0_912,plain,
implies(or(implies(X_585,X_586),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) = implies(or(implies(X_585,X_586),not(implies(X_585,X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))),
inference(subst,[],[refute_0_911:[bind(Y,$fot(equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))),bind(X_120,$fot(implies(X_585,X_586))),bind(X_121,$fot(X_585)),bind(X_122,$fot(X_586))]]) ).
cnf(refute_0_913,plain,
implies(and(X_585,not(X_586)),and(X_585,not(X_586))) = or(implies(X_585,X_586),and(X_585,not(X_586))),
inference(subst,[],[refute_0_472:[bind(Y,$fot(and(X_585,not(X_586)))),bind(X_4,$fot(X_585)),bind(X_5,$fot(X_586))]]) ).
cnf(refute_0_914,plain,
implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) = implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))),
introduced(tautology,[refl,[$fot(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))))]]) ).
cnf(refute_0_915,plain,
( implies(and(X_585,not(X_586)),and(X_585,not(X_586))) != or(implies(X_585,X_586),and(X_585,not(X_586)))
| implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) != implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))
| implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) = implies(or(implies(X_585,X_586),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))),implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))) ),[1,0],$fot(or(implies(X_585,X_586),and(X_585,not(X_586))))]]) ).
cnf(refute_0_916,plain,
( implies(and(X_585,not(X_586)),and(X_585,not(X_586))) != or(implies(X_585,X_586),and(X_585,not(X_586)))
| implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) = implies(or(implies(X_585,X_586),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) ),
inference(resolve,[$cnf( $equal(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))),implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))) )],[refute_0_914,refute_0_915]) ).
cnf(refute_0_917,plain,
implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) = implies(or(implies(X_585,X_586),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))),
inference(resolve,[$cnf( $equal(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),or(implies(X_585,X_586),and(X_585,not(X_586)))) )],[refute_0_913,refute_0_916]) ).
cnf(refute_0_918,plain,
( implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) != implies(or(implies(X_585,X_586),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))
| implies(or(implies(X_585,X_586),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) != implies(or(implies(X_585,X_586),not(implies(X_585,X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))
| implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) = implies(or(implies(X_585,X_586),not(implies(X_585,X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))))),bind(Y0,$fot(implies(or(implies(X_585,X_586),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))))),bind(Z,$fot(implies(or(implies(X_585,X_586),not(implies(X_585,X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))))]]) ).
cnf(refute_0_919,plain,
( implies(or(implies(X_585,X_586),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) != implies(or(implies(X_585,X_586),not(implies(X_585,X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))
| implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) = implies(or(implies(X_585,X_586),not(implies(X_585,X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) ),
inference(resolve,[$cnf( $equal(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))),implies(or(implies(X_585,X_586),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))) )],[refute_0_917,refute_0_918]) ).
cnf(refute_0_920,plain,
implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) = implies(or(implies(X_585,X_586),not(implies(X_585,X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))),
inference(resolve,[$cnf( $equal(implies(or(implies(X_585,X_586),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))),implies(or(implies(X_585,X_586),not(implies(X_585,X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))) )],[refute_0_912,refute_0_919]) ).
cnf(refute_0_921,plain,
( implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))) != implies(or(implies(X_585,X_586),not(implies(X_585,X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))
| ~ is_a_theorem(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))))
| is_a_theorem(implies(or(implies(X_585,X_586),not(implies(X_585,X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))) ),[0],$fot(implies(or(implies(X_585,X_586),not(implies(X_585,X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))))]]) ).
cnf(refute_0_922,plain,
( ~ is_a_theorem(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))))
| is_a_theorem(implies(or(implies(X_585,X_586),not(implies(X_585,X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))) ),
inference(resolve,[$cnf( $equal(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586)))),implies(or(implies(X_585,X_586),not(implies(X_585,X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))) )],[refute_0_920,refute_0_921]) ).
cnf(refute_0_923,plain,
is_a_theorem(implies(or(implies(X_585,X_586),not(implies(X_585,X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_585,not(X_586)),and(X_585,not(X_586))),equiv(and(X_585,not(X_586)),not(implies(X_585,X_586))))) )],[refute_0_892,refute_0_922]) ).
cnf(refute_0_924,plain,
is_a_theorem(implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(implies(not(X),X_1840))))),
inference(subst,[],[refute_0_923:[bind(X_585,$fot(not(X))),bind(X_586,$fot(X_1840))]]) ).
cnf(refute_0_925,plain,
or(X,X_1840) = implies(not(X),X_1840),
inference(subst,[],[refute_0_60:[bind(Y,$fot(X_1840))]]) ).
cnf(refute_0_926,plain,
( or(X,X_1840) != implies(not(X),X_1840)
| implies(not(X),X_1840) = or(X,X_1840) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,X_1840))),bind(Y0,$fot(implies(not(X),X_1840)))]]) ).
cnf(refute_0_927,plain,
implies(not(X),X_1840) = or(X,X_1840),
inference(resolve,[$cnf( $equal(or(X,X_1840),implies(not(X),X_1840)) )],[refute_0_925,refute_0_926]) ).
cnf(refute_0_928,plain,
( implies(not(X),X_1840) != or(X,X_1840)
| ~ is_a_theorem(implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(implies(not(X),X_1840)))))
| is_a_theorem(implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(implies(not(X),X_1840))))) ),[0,1,1,0],$fot(or(X,X_1840))]]) ).
cnf(refute_0_929,plain,
( ~ is_a_theorem(implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(implies(not(X),X_1840)))))
| is_a_theorem(implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_1840),or(X,X_1840)) )],[refute_0_927,refute_0_928]) ).
cnf(refute_0_930,plain,
is_a_theorem(implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(implies(not(X),X_1840))))) )],[refute_0_924,refute_0_929]) ).
cnf(refute_0_931,plain,
not(implies(not(X),X_1840)) = not(implies(not(X),X_1840)),
introduced(tautology,[refl,[$fot(not(implies(not(X),X_1840)))]]) ).
cnf(refute_0_932,plain,
( implies(not(X),X_1840) != or(X,X_1840)
| not(implies(not(X),X_1840)) != not(implies(not(X),X_1840))
| not(implies(not(X),X_1840)) = not(or(X,X_1840)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(X),X_1840)),not(implies(not(X),X_1840))) ),[1,0],$fot(or(X,X_1840))]]) ).
cnf(refute_0_933,plain,
( implies(not(X),X_1840) != or(X,X_1840)
| not(implies(not(X),X_1840)) = not(or(X,X_1840)) ),
inference(resolve,[$cnf( $equal(not(implies(not(X),X_1840)),not(implies(not(X),X_1840))) )],[refute_0_931,refute_0_932]) ).
cnf(refute_0_934,plain,
not(implies(not(X),X_1840)) = not(or(X,X_1840)),
inference(resolve,[$cnf( $equal(implies(not(X),X_1840),or(X,X_1840)) )],[refute_0_927,refute_0_933]) ).
cnf(refute_0_935,plain,
or(or(X,X_1840),not(implies(not(X),X_1840))) = or(or(X,X_1840),not(implies(not(X),X_1840))),
introduced(tautology,[refl,[$fot(or(or(X,X_1840),not(implies(not(X),X_1840))))]]) ).
cnf(refute_0_936,plain,
( not(implies(not(X),X_1840)) != not(or(X,X_1840))
| or(or(X,X_1840),not(implies(not(X),X_1840))) != or(or(X,X_1840),not(implies(not(X),X_1840)))
| or(or(X,X_1840),not(implies(not(X),X_1840))) = or(or(X,X_1840),not(or(X,X_1840))) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(X,X_1840),not(implies(not(X),X_1840))),or(or(X,X_1840),not(implies(not(X),X_1840)))) ),[1,1],$fot(not(or(X,X_1840)))]]) ).
cnf(refute_0_937,plain,
( not(implies(not(X),X_1840)) != not(or(X,X_1840))
| or(or(X,X_1840),not(implies(not(X),X_1840))) = or(or(X,X_1840),not(or(X,X_1840))) ),
inference(resolve,[$cnf( $equal(or(or(X,X_1840),not(implies(not(X),X_1840))),or(or(X,X_1840),not(implies(not(X),X_1840)))) )],[refute_0_935,refute_0_936]) ).
cnf(refute_0_938,plain,
or(or(X,X_1840),not(implies(not(X),X_1840))) = or(or(X,X_1840),not(or(X,X_1840))),
inference(resolve,[$cnf( $equal(not(implies(not(X),X_1840)),not(or(X,X_1840))) )],[refute_0_934,refute_0_937]) ).
cnf(refute_0_939,plain,
or(implies(not(X),X_1840),not(implies(not(X),X_1840))) = or(implies(not(X),X_1840),not(implies(not(X),X_1840))),
introduced(tautology,[refl,[$fot(or(implies(not(X),X_1840),not(implies(not(X),X_1840))))]]) ).
cnf(refute_0_940,plain,
( implies(not(X),X_1840) != or(X,X_1840)
| or(implies(not(X),X_1840),not(implies(not(X),X_1840))) != or(implies(not(X),X_1840),not(implies(not(X),X_1840)))
| or(implies(not(X),X_1840),not(implies(not(X),X_1840))) = or(or(X,X_1840),not(implies(not(X),X_1840))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),or(implies(not(X),X_1840),not(implies(not(X),X_1840)))) ),[1,0],$fot(or(X,X_1840))]]) ).
cnf(refute_0_941,plain,
( implies(not(X),X_1840) != or(X,X_1840)
| or(implies(not(X),X_1840),not(implies(not(X),X_1840))) = or(or(X,X_1840),not(implies(not(X),X_1840))) ),
inference(resolve,[$cnf( $equal(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),or(implies(not(X),X_1840),not(implies(not(X),X_1840)))) )],[refute_0_939,refute_0_940]) ).
cnf(refute_0_942,plain,
or(implies(not(X),X_1840),not(implies(not(X),X_1840))) = or(or(X,X_1840),not(implies(not(X),X_1840))),
inference(resolve,[$cnf( $equal(implies(not(X),X_1840),or(X,X_1840)) )],[refute_0_927,refute_0_941]) ).
cnf(refute_0_943,plain,
( or(implies(not(X),X_1840),not(implies(not(X),X_1840))) != or(or(X,X_1840),not(implies(not(X),X_1840)))
| or(or(X,X_1840),not(implies(not(X),X_1840))) != or(or(X,X_1840),not(or(X,X_1840)))
| or(implies(not(X),X_1840),not(implies(not(X),X_1840))) = or(or(X,X_1840),not(or(X,X_1840))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(or(implies(not(X),X_1840),not(implies(not(X),X_1840))))),bind(Y0,$fot(or(or(X,X_1840),not(implies(not(X),X_1840))))),bind(Z,$fot(or(or(X,X_1840),not(or(X,X_1840)))))]]) ).
cnf(refute_0_944,plain,
( or(or(X,X_1840),not(implies(not(X),X_1840))) != or(or(X,X_1840),not(or(X,X_1840)))
| or(implies(not(X),X_1840),not(implies(not(X),X_1840))) = or(or(X,X_1840),not(or(X,X_1840))) ),
inference(resolve,[$cnf( $equal(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),or(or(X,X_1840),not(implies(not(X),X_1840)))) )],[refute_0_942,refute_0_943]) ).
cnf(refute_0_945,plain,
or(implies(not(X),X_1840),not(implies(not(X),X_1840))) = or(or(X,X_1840),not(or(X,X_1840))),
inference(resolve,[$cnf( $equal(or(or(X,X_1840),not(implies(not(X),X_1840))),or(or(X,X_1840),not(or(X,X_1840)))) )],[refute_0_938,refute_0_944]) ).
cnf(refute_0_946,plain,
implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))) = implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))),
introduced(tautology,[refl,[$fot(implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))))]]) ).
cnf(refute_0_947,plain,
( implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))) != implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840))))
| or(implies(not(X),X_1840),not(implies(not(X),X_1840))) != or(or(X,X_1840),not(or(X,X_1840)))
| implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))) = implies(or(or(X,X_1840),not(or(X,X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))),implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840))))) ),[1,0],$fot(or(or(X,X_1840),not(or(X,X_1840))))]]) ).
cnf(refute_0_948,plain,
( or(implies(not(X),X_1840),not(implies(not(X),X_1840))) != or(or(X,X_1840),not(or(X,X_1840)))
| implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))) = implies(or(or(X,X_1840),not(or(X,X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))) ),
inference(resolve,[$cnf( $equal(implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))),implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840))))) )],[refute_0_946,refute_0_947]) ).
cnf(refute_0_949,plain,
implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))) = implies(or(or(X,X_1840),not(or(X,X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))),
inference(resolve,[$cnf( $equal(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),or(or(X,X_1840),not(or(X,X_1840)))) )],[refute_0_945,refute_0_948]) ).
cnf(refute_0_950,plain,
( implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))) != implies(or(or(X,X_1840),not(or(X,X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840))))
| ~ is_a_theorem(implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))))
| is_a_theorem(implies(or(or(X,X_1840),not(or(X,X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840))))) ),[0],$fot(implies(or(or(X,X_1840),not(or(X,X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))))]]) ).
cnf(refute_0_951,plain,
( ~ is_a_theorem(implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))))
| is_a_theorem(implies(or(or(X,X_1840),not(or(X,X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840))))) ),
inference(resolve,[$cnf( $equal(implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840)))),implies(or(or(X,X_1840),not(or(X,X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840))))) )],[refute_0_949,refute_0_950]) ).
cnf(refute_0_952,plain,
is_a_theorem(implies(or(or(X,X_1840),not(or(X,X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(implies(not(X),X_1840),not(implies(not(X),X_1840))),equiv(and(not(X),not(X_1840)),not(or(X,X_1840))))) )],[refute_0_930,refute_0_951]) ).
cnf(refute_0_953,plain,
is_a_theorem(implies(or(or(X_9545,X_9546),not(or(X_9545,X_9546))),equiv(and(not(X_9545),not(X_9546)),not(or(X_9545,X_9546))))),
inference(subst,[],[refute_0_952:[bind(X,$fot(X_9545)),bind(X_1840,$fot(X_9546))]]) ).
cnf(refute_0_954,plain,
( ~ is_a_theorem(or(or(X_9545,X_9546),not(or(X_9545,X_9546))))
| is_a_theorem(equiv(and(not(X_9545),not(X_9546)),not(or(X_9545,X_9546)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(or(X_9545,X_9546),not(or(X_9545,X_9546))),equiv(and(not(X_9545),not(X_9546)),not(or(X_9545,X_9546))))) )],[refute_0_953,refute_0_887]) ).
cnf(refute_0_955,plain,
is_a_theorem(or(or(X_9545,X_9546),not(or(X_9545,X_9546)))),
inference(subst,[],[refute_0_514:[bind(X_4513,$fot(or(X_9545,X_9546)))]]) ).
cnf(refute_0_956,plain,
is_a_theorem(equiv(and(not(X_9545),not(X_9546)),not(or(X_9545,X_9546)))),
inference(resolve,[$cnf( is_a_theorem(or(or(X_9545,X_9546),not(or(X_9545,X_9546)))) )],[refute_0_955,refute_0_954]) ).
cnf(refute_0_957,plain,
is_a_theorem(equiv(and(not(X_9547),not(X_9548)),not(or(X_9547,X_9548)))),
inference(subst,[],[refute_0_956:[bind(X_9545,$fot(X_9547)),bind(X_9546,$fot(X_9548))]]) ).
cnf(refute_0_958,plain,
and(not(X_9547),not(X_9548)) = not(or(X_9547,X_9548)),
inference(resolve,[$cnf( is_a_theorem(equiv(and(not(X_9547),not(X_9548)),not(or(X_9547,X_9548)))) )],[refute_0_957,refute_0_886]) ).
cnf(refute_0_959,plain,
and(not(not(X)),not(X_9550)) = not(or(not(X),X_9550)),
inference(subst,[],[refute_0_958:[bind(X_9547,$fot(not(X))),bind(X_9548,$fot(X_9550))]]) ).
cnf(refute_0_960,plain,
( and(not(not(X)),not(X_9550)) != and(X,not(X_9550))
| and(not(not(X)),not(X_9550)) != not(or(not(X),X_9550))
| not(or(not(X),X_9550)) = and(X,not(X_9550)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X)),not(X_9550)),and(X,not(X_9550))) ),[0],$fot(not(or(not(X),X_9550)))]]) ).
cnf(refute_0_961,plain,
( and(not(not(X)),not(X_9550)) != and(X,not(X_9550))
| not(or(not(X),X_9550)) = and(X,not(X_9550)) ),
inference(resolve,[$cnf( $equal(and(not(not(X)),not(X_9550)),not(or(not(X),X_9550))) )],[refute_0_959,refute_0_960]) ).
cnf(refute_0_962,plain,
not(or(not(X),X_9550)) = and(X,not(X_9550)),
inference(resolve,[$cnf( $equal(and(not(not(X)),not(X_9550)),and(X,not(X_9550))) )],[refute_0_885,refute_0_961]) ).
cnf(refute_0_963,plain,
or(not(X),X_9550) = implies(X,X_9550),
inference(subst,[],[refute_0_20:[bind(Y,$fot(X_9550))]]) ).
cnf(refute_0_964,plain,
not(or(not(X),X_9550)) = not(or(not(X),X_9550)),
introduced(tautology,[refl,[$fot(not(or(not(X),X_9550)))]]) ).
cnf(refute_0_965,plain,
( not(or(not(X),X_9550)) != not(or(not(X),X_9550))
| or(not(X),X_9550) != implies(X,X_9550)
| not(or(not(X),X_9550)) = not(implies(X,X_9550)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),X_9550)),not(or(not(X),X_9550))) ),[1,0],$fot(implies(X,X_9550))]]) ).
cnf(refute_0_966,plain,
( or(not(X),X_9550) != implies(X,X_9550)
| not(or(not(X),X_9550)) = not(implies(X,X_9550)) ),
inference(resolve,[$cnf( $equal(not(or(not(X),X_9550)),not(or(not(X),X_9550))) )],[refute_0_964,refute_0_965]) ).
cnf(refute_0_967,plain,
not(or(not(X),X_9550)) = not(implies(X,X_9550)),
inference(resolve,[$cnf( $equal(or(not(X),X_9550),implies(X,X_9550)) )],[refute_0_963,refute_0_966]) ).
cnf(refute_0_968,plain,
( not(or(not(X),X_9550)) != and(X,not(X_9550))
| not(or(not(X),X_9550)) != not(implies(X,X_9550))
| not(implies(X,X_9550)) = and(X,not(X_9550)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),X_9550)),and(X,not(X_9550))) ),[0],$fot(not(implies(X,X_9550)))]]) ).
cnf(refute_0_969,plain,
( not(or(not(X),X_9550)) != and(X,not(X_9550))
| not(implies(X,X_9550)) = and(X,not(X_9550)) ),
inference(resolve,[$cnf( $equal(not(or(not(X),X_9550)),not(implies(X,X_9550))) )],[refute_0_967,refute_0_968]) ).
cnf(refute_0_970,plain,
not(implies(X,X_9550)) = and(X,not(X_9550)),
inference(resolve,[$cnf( $equal(not(or(not(X),X_9550)),and(X,not(X_9550))) )],[refute_0_962,refute_0_969]) ).
cnf(refute_0_971,plain,
( not(implies(X,X_9550)) != and(X,not(X_9550))
| and(X,not(X_9550)) = not(implies(X,X_9550)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(implies(X,X_9550)))),bind(Y0,$fot(and(X,not(X_9550))))]]) ).
cnf(refute_0_972,plain,
and(X,not(X_9550)) = not(implies(X,X_9550)),
inference(resolve,[$cnf( $equal(not(implies(X,X_9550)),and(X,not(X_9550))) )],[refute_0_970,refute_0_971]) ).
cnf(refute_0_973,plain,
and(X,not(Y)) = not(implies(X,Y)),
inference(subst,[],[refute_0_972:[bind(X_9550,$fot(Y))]]) ).
cnf(refute_0_974,plain,
not(and(X,not(Y))) = not(and(X,not(Y))),
introduced(tautology,[refl,[$fot(not(and(X,not(Y))))]]) ).
cnf(refute_0_975,plain,
( and(X,not(Y)) != not(implies(X,Y))
| not(and(X,not(Y))) != not(and(X,not(Y)))
| not(and(X,not(Y))) = not(not(implies(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(X,not(Y))),not(and(X,not(Y)))) ),[1,0],$fot(not(implies(X,Y)))]]) ).
cnf(refute_0_976,plain,
( and(X,not(Y)) != not(implies(X,Y))
| not(and(X,not(Y))) = not(not(implies(X,Y))) ),
inference(resolve,[$cnf( $equal(not(and(X,not(Y))),not(and(X,not(Y)))) )],[refute_0_974,refute_0_975]) ).
cnf(refute_0_977,plain,
not(and(X,not(Y))) = not(not(implies(X,Y))),
inference(resolve,[$cnf( $equal(and(X,not(Y)),not(implies(X,Y))) )],[refute_0_973,refute_0_976]) ).
cnf(refute_0_978,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) != not(not(implies(X,Y)))
| implies(X,Y) = not(not(implies(X,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,Y),not(not(implies(X,Y)))) ),[0],$fot(not(and(X,not(Y))))]]) ).
cnf(refute_0_979,plain,
( implies(X,Y) != not(and(X,not(Y)))
| implies(X,Y) = not(not(implies(X,Y))) ),
inference(resolve,[$cnf( $equal(not(and(X,not(Y))),not(not(implies(X,Y)))) )],[refute_0_977,refute_0_978]) ).
cnf(refute_0_980,plain,
implies(X,Y) = not(not(implies(X,Y))),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_54,refute_0_979]) ).
cnf(refute_0_981,plain,
implies(X_9551,not(Y)) = not(not(implies(X_9551,not(Y)))),
inference(subst,[],[refute_0_980:[bind(X,$fot(X_9551)),bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_982,plain,
and(X_9551,Y) = not(implies(X_9551,not(Y))),
inference(subst,[],[refute_0_128:[bind(X,$fot(X_9551))]]) ).
cnf(refute_0_983,plain,
( and(X_9551,Y) != not(implies(X_9551,not(Y)))
| not(implies(X_9551,not(Y))) = and(X_9551,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(X_9551,Y))),bind(Y0,$fot(not(implies(X_9551,not(Y)))))]]) ).
cnf(refute_0_984,plain,
not(implies(X_9551,not(Y))) = and(X_9551,Y),
inference(resolve,[$cnf( $equal(and(X_9551,Y),not(implies(X_9551,not(Y)))) )],[refute_0_982,refute_0_983]) ).
cnf(refute_0_985,plain,
( implies(X_9551,not(Y)) != not(not(implies(X_9551,not(Y))))
| not(implies(X_9551,not(Y))) != and(X_9551,Y)
| implies(X_9551,not(Y)) = not(and(X_9551,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_9551,not(Y)),not(not(implies(X_9551,not(Y))))) ),[1,0],$fot(and(X_9551,Y))]]) ).
cnf(refute_0_986,plain,
( implies(X_9551,not(Y)) != not(not(implies(X_9551,not(Y))))
| implies(X_9551,not(Y)) = not(and(X_9551,Y)) ),
inference(resolve,[$cnf( $equal(not(implies(X_9551,not(Y))),and(X_9551,Y)) )],[refute_0_984,refute_0_985]) ).
cnf(refute_0_987,plain,
implies(X_9551,not(Y)) = not(and(X_9551,Y)),
inference(resolve,[$cnf( $equal(implies(X_9551,not(Y)),not(not(implies(X_9551,not(Y))))) )],[refute_0_981,refute_0_986]) ).
cnf(refute_0_988,plain,
implies(X,not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))) = not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),
inference(subst,[],[refute_0_987:[bind(Y,$fot(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),bind(X_9551,$fot(X))]]) ).
cnf(refute_0_989,plain,
or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))) = implies(X,not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),
inference(subst,[],[refute_0_20:[bind(Y,$fot(not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))))]]) ).
cnf(refute_0_990,plain,
( implies(X,not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))) != not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)))
| or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))) != implies(X,not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791)))
| or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))) = not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))))),bind(Y0,$fot(implies(X,not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))))),bind(Z,$fot(not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)))))]]) ).
cnf(refute_0_991,plain,
( implies(X,not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))) != not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)))
| or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))) = not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791)))) )],[refute_0_989,refute_0_990]) ).
cnf(refute_0_992,plain,
or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))) = not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),
inference(resolve,[$cnf( $equal(implies(X,not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)))) )],[refute_0_988,refute_0_991]) ).
cnf(refute_0_993,plain,
implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)) = implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)),
introduced(tautology,[refl,[$fot(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)))]]) ).
cnf(refute_0_994,plain,
( implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)) != implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789))
| or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))) != not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)))
| implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)) = implies(not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)),implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789))) ),[1,0],$fot(not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791))))]]) ).
cnf(refute_0_995,plain,
( or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))) != not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)))
| implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)) = implies(not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)),implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789))) )],[refute_0_993,refute_0_994]) ).
cnf(refute_0_996,plain,
implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)) = implies(not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)),
inference(resolve,[$cnf( $equal(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)))) )],[refute_0_992,refute_0_995]) ).
cnf(refute_0_997,plain,
( implies(not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)) != or(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)),implies(X,X_28789))
| implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)) != implies(not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789))
| implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)) = or(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)),implies(X,X_28789)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)))),bind(Y0,$fot(implies(not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)))),bind(Z,$fot(or(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)),implies(X,X_28789))))]]) ).
cnf(refute_0_998,plain,
( implies(not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)) != or(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)),implies(X,X_28789))
| implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)) = or(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)),implies(X,X_28789)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)),implies(not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789))) )],[refute_0_996,refute_0_997]) ).
cnf(refute_0_999,plain,
implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)) = or(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)),implies(X,X_28789)),
inference(resolve,[$cnf( $equal(implies(not(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)),or(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)),implies(X,X_28789))) )],[refute_0_884,refute_0_998]) ).
cnf(refute_0_1000,plain,
( implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)) != or(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)),implies(X,X_28789))
| ~ is_a_theorem(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)))
| is_a_theorem(or(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)),implies(X,X_28789))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789))) ),[0],$fot(or(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)),implies(X,X_28789)))]]) ).
cnf(refute_0_1001,plain,
( ~ is_a_theorem(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)))
| is_a_theorem(or(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)),implies(X,X_28789))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789)),or(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)),implies(X,X_28789))) )],[refute_0_999,refute_0_1000]) ).
cnf(refute_0_1002,plain,
is_a_theorem(or(and(X,implies(and(equiv(X_28791,X_28790),X_28790),X_28791)),implies(X,X_28789))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),not(implies(and(equiv(X_28791,X_28790),X_28790),X_28791))),implies(X,X_28789))) )],[refute_0_883,refute_0_1001]) ).
cnf(refute_0_1003,plain,
is_a_theorem(or(and(X_29144,implies(and(equiv(X_29147,X_29146),X_29146),X_29147)),implies(X_29144,X_29145))),
inference(subst,[],[refute_0_1002:[bind(X,$fot(X_29144)),bind(X_28789,$fot(X_29145)),bind(X_28790,$fot(X_29146)),bind(X_28791,$fot(X_29147))]]) ).
cnf(refute_0_1004,plain,
is_a_theorem(implies(X_29144,or(and(X_29144,implies(and(equiv(X_29147,X_29146),X_29146),X_29147)),X_29145))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_29144,implies(and(equiv(X_29147,X_29146),X_29146),X_29147)),implies(X_29144,X_29145))) )],[refute_0_1003,refute_0_716]) ).
cnf(refute_0_1005,plain,
is_a_theorem(implies(X_30033,or(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)),and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036))))),
inference(subst,[],[refute_0_1004:[bind(X_29144,$fot(X_30033)),bind(X_29145,$fot(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)))),bind(X_29146,$fot(X_30035)),bind(X_29147,$fot(X_30036))]]) ).
cnf(refute_0_1006,plain,
( ~ is_a_theorem(equiv(X_25347,or(X_25347,X_25347)))
| X_25347 = or(X_25347,X_25347) ),
inference(subst,[],[refute_0_253:[bind(X,$fot(X_25347)),bind(Y,$fot(or(X_25347,X_25347)))]]) ).
cnf(refute_0_1007,plain,
( ~ is_a_theorem(or(equiv(X_25346,or(X_25346,X_25346)),equiv(X_25346,or(X_25346,X_25346))))
| is_a_theorem(equiv(X_25346,or(X_25346,X_25346))) ),
inference(subst,[],[refute_0_248:[bind(X_156,$fot(equiv(X_25346,or(X_25346,X_25346))))]]) ).
cnf(refute_0_1008,plain,
( ~ is_a_theorem(implies(X_25344,or(X_25344,X_25344)))
| ~ is_a_theorem(implies(implies(X_25344,or(X_25344,X_25344)),or(equiv(X_25344,or(X_25344,X_25344)),X_25343)))
| is_a_theorem(or(equiv(X_25344,or(X_25344,X_25344)),X_25343)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(implies(X_25344,or(X_25344,X_25344)))),bind(Y,$fot(or(equiv(X_25344,or(X_25344,X_25344)),X_25343)))]]) ).
cnf(refute_0_1009,plain,
( ~ is_a_theorem(or(equiv(X_17197,or(X_17197,X_17197)),implies(implies(X_17197,or(X_17197,X_17197)),X_17196)))
| is_a_theorem(implies(implies(X_17197,or(X_17197,X_17197)),or(equiv(X_17197,or(X_17197,X_17197)),X_17196))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(implies(X_17197,or(X_17197,X_17197)))),bind(X_103,$fot(equiv(X_17197,or(X_17197,X_17197)))),bind(X_105,$fot(X_17196))]]) ).
cnf(refute_0_1010,plain,
( ~ is_a_theorem(or(X_265,implies(or(X_264,X_264),X_264)))
| is_a_theorem(or(implies(or(X_264,X_264),X_264),X_265)) ),
inference(subst,[],[refute_0_43:[bind(P,$fot(X_265)),bind(Q,$fot(implies(or(X_264,X_264),X_264)))]]) ).
cnf(refute_0_1011,plain,
( ~ is_a_theorem(implies(or(P,P),P))
| is_a_theorem(or(X_258,implies(or(P,P),P))) ),
inference(subst,[],[refute_0_720:[bind(P,$fot(X_258)),bind(X_155,$fot(implies(or(P,P),P)))]]) ).
cnf(refute_0_1012,plain,
is_a_theorem(or(X_258,implies(or(P,P),P))),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,P),P)) )],[refute_0_95,refute_0_1011]) ).
cnf(refute_0_1013,plain,
is_a_theorem(or(X_265,implies(or(X_264,X_264),X_264))),
inference(subst,[],[refute_0_1012:[bind(P,$fot(X_264)),bind(X_258,$fot(X_265))]]) ).
cnf(refute_0_1014,plain,
is_a_theorem(or(implies(or(X_264,X_264),X_264),X_265)),
inference(resolve,[$cnf( is_a_theorem(or(X_265,implies(or(X_264,X_264),X_264))) )],[refute_0_1013,refute_0_1010]) ).
cnf(refute_0_1015,plain,
is_a_theorem(or(implies(or(not(X),not(X)),not(X)),X_280)),
inference(subst,[],[refute_0_1014:[bind(X_264,$fot(not(X))),bind(X_265,$fot(X_280))]]) ).
cnf(refute_0_1016,plain,
( or(not(X),not(X)) != implies(X,not(X))
| ~ is_a_theorem(or(implies(or(not(X),not(X)),not(X)),X_280))
| is_a_theorem(or(implies(implies(X,not(X)),not(X)),X_280)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(or(not(X),not(X)),not(X)),X_280)) ),[0,0,0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_1017,plain,
( ~ is_a_theorem(or(implies(or(not(X),not(X)),not(X)),X_280))
| is_a_theorem(or(implies(implies(X,not(X)),not(X)),X_280)) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_171,refute_0_1016]) ).
cnf(refute_0_1018,plain,
is_a_theorem(or(implies(implies(X,not(X)),not(X)),X_280)),
inference(resolve,[$cnf( is_a_theorem(or(implies(or(not(X),not(X)),not(X)),X_280)) )],[refute_0_1015,refute_0_1017]) ).
cnf(refute_0_1019,plain,
and(implies(X,not(X)),X) = and(not(and(X,X)),X),
inference(subst,[],[refute_0_353:[bind(Y,$fot(X)),bind(X_89,$fot(X))]]) ).
cnf(refute_0_1020,plain,
implies(and(implies(X,not(X)),X),X_280) = implies(and(implies(X,not(X)),X),X_280),
introduced(tautology,[refl,[$fot(implies(and(implies(X,not(X)),X),X_280))]]) ).
cnf(refute_0_1021,plain,
( and(implies(X,not(X)),X) != and(not(and(X,X)),X)
| implies(and(implies(X,not(X)),X),X_280) != implies(and(implies(X,not(X)),X),X_280)
| implies(and(implies(X,not(X)),X),X_280) = implies(and(not(and(X,X)),X),X_280) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(implies(X,not(X)),X),X_280),implies(and(implies(X,not(X)),X),X_280)) ),[1,0],$fot(and(not(and(X,X)),X))]]) ).
cnf(refute_0_1022,plain,
( and(implies(X,not(X)),X) != and(not(and(X,X)),X)
| implies(and(implies(X,not(X)),X),X_280) = implies(and(not(and(X,X)),X),X_280) ),
inference(resolve,[$cnf( $equal(implies(and(implies(X,not(X)),X),X_280),implies(and(implies(X,not(X)),X),X_280)) )],[refute_0_1020,refute_0_1021]) ).
cnf(refute_0_1023,plain,
implies(and(implies(X,not(X)),X),X_280) = implies(and(not(and(X,X)),X),X_280),
inference(resolve,[$cnf( $equal(and(implies(X,not(X)),X),and(not(and(X,X)),X)) )],[refute_0_1019,refute_0_1022]) ).
cnf(refute_0_1024,plain,
or(implies(implies(X,not(X)),not(X)),X_280) = implies(and(implies(X,not(X)),X),X_280),
inference(subst,[],[refute_0_467:[bind(Y,$fot(X_280)),bind(X_16,$fot(implies(X,not(X)))),bind(X_17,$fot(X))]]) ).
cnf(refute_0_1025,plain,
( implies(and(implies(X,not(X)),X),X_280) != implies(and(not(and(X,X)),X),X_280)
| or(implies(implies(X,not(X)),not(X)),X_280) != implies(and(implies(X,not(X)),X),X_280)
| or(implies(implies(X,not(X)),not(X)),X_280) = implies(and(not(and(X,X)),X),X_280) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(or(implies(implies(X,not(X)),not(X)),X_280))),bind(Y0,$fot(implies(and(implies(X,not(X)),X),X_280))),bind(Z,$fot(implies(and(not(and(X,X)),X),X_280)))]]) ).
cnf(refute_0_1026,plain,
( implies(and(implies(X,not(X)),X),X_280) != implies(and(not(and(X,X)),X),X_280)
| or(implies(implies(X,not(X)),not(X)),X_280) = implies(and(not(and(X,X)),X),X_280) ),
inference(resolve,[$cnf( $equal(or(implies(implies(X,not(X)),not(X)),X_280),implies(and(implies(X,not(X)),X),X_280)) )],[refute_0_1024,refute_0_1025]) ).
cnf(refute_0_1027,plain,
or(implies(implies(X,not(X)),not(X)),X_280) = implies(and(not(and(X,X)),X),X_280),
inference(resolve,[$cnf( $equal(implies(and(implies(X,not(X)),X),X_280),implies(and(not(and(X,X)),X),X_280)) )],[refute_0_1023,refute_0_1026]) ).
cnf(refute_0_1028,plain,
( or(implies(implies(X,not(X)),not(X)),X_280) != implies(and(not(and(X,X)),X),X_280)
| ~ is_a_theorem(or(implies(implies(X,not(X)),not(X)),X_280))
| is_a_theorem(implies(and(not(and(X,X)),X),X_280)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(implies(X,not(X)),not(X)),X_280)) ),[0],$fot(implies(and(not(and(X,X)),X),X_280))]]) ).
cnf(refute_0_1029,plain,
( ~ is_a_theorem(or(implies(implies(X,not(X)),not(X)),X_280))
| is_a_theorem(implies(and(not(and(X,X)),X),X_280)) ),
inference(resolve,[$cnf( $equal(or(implies(implies(X,not(X)),not(X)),X_280),implies(and(not(and(X,X)),X),X_280)) )],[refute_0_1027,refute_0_1028]) ).
cnf(refute_0_1030,plain,
is_a_theorem(implies(and(not(and(X,X)),X),X_280)),
inference(resolve,[$cnf( is_a_theorem(or(implies(implies(X,not(X)),not(X)),X_280)) )],[refute_0_1018,refute_0_1029]) ).
cnf(refute_0_1031,plain,
is_a_theorem(implies(and(not(and(X,X)),X),X_12812)),
inference(subst,[],[refute_0_1030:[bind(X_280,$fot(X_12812))]]) ).
cnf(refute_0_1032,plain,
( ~ is_a_theorem(implies(Q,R))
| ~ is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| is_a_theorem(implies(or(P,Q),or(P,R))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(implies(Q,R))),bind(Y,$fot(implies(or(P,Q),or(P,R))))]]) ).
cnf(refute_0_1033,plain,
( ~ is_a_theorem(implies(Q,R))
| is_a_theorem(implies(or(P,Q),or(P,R))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )],[refute_0_674,refute_0_1032]) ).
cnf(refute_0_1034,plain,
( ~ is_a_theorem(implies(and(not(and(X,X)),X),X_12812))
| is_a_theorem(implies(or(X_12810,and(not(and(X,X)),X)),or(X_12810,X_12812))) ),
inference(subst,[],[refute_0_1033:[bind(P,$fot(X_12810)),bind(Q,$fot(and(not(and(X,X)),X))),bind(R,$fot(X_12812))]]) ).
cnf(refute_0_1035,plain,
is_a_theorem(implies(or(X_12810,and(not(and(X,X)),X)),or(X_12810,X_12812))),
inference(resolve,[$cnf( is_a_theorem(implies(and(not(and(X,X)),X),X_12812)) )],[refute_0_1031,refute_0_1034]) ).
cnf(refute_0_1036,plain,
is_a_theorem(implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),or(not(X),X_16162))),
inference(subst,[],[refute_0_1035:[bind(X,$fot(X_16160)),bind(X_12810,$fot(not(X))),bind(X_12812,$fot(X_16162))]]) ).
cnf(refute_0_1037,plain,
implies(X,X_16162) = or(not(X),X_16162),
inference(subst,[],[refute_0_9:[bind(Y,$fot(X_16162))]]) ).
cnf(refute_0_1038,plain,
( implies(X,X_16162) != or(not(X),X_16162)
| or(not(X),X_16162) = implies(X,X_16162) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,X_16162))),bind(Y0,$fot(or(not(X),X_16162)))]]) ).
cnf(refute_0_1039,plain,
or(not(X),X_16162) = implies(X,X_16162),
inference(resolve,[$cnf( $equal(implies(X,X_16162),or(not(X),X_16162)) )],[refute_0_1037,refute_0_1038]) ).
cnf(refute_0_1040,plain,
( or(not(X),X_16162) != implies(X,X_16162)
| ~ is_a_theorem(implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),or(not(X),X_16162)))
| is_a_theorem(implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),or(not(X),X_16162))) ),[0,1],$fot(implies(X,X_16162))]]) ).
cnf(refute_0_1041,plain,
( ~ is_a_theorem(implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),or(not(X),X_16162)))
| is_a_theorem(implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_16162),implies(X,X_16162)) )],[refute_0_1039,refute_0_1040]) ).
cnf(refute_0_1042,plain,
is_a_theorem(implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),or(not(X),X_16162))) )],[refute_0_1036,refute_0_1041]) ).
cnf(refute_0_1043,plain,
or(not(X),and(not(and(X_16160,X_16160)),X_16160)) = implies(X,and(not(and(X_16160,X_16160)),X_16160)),
inference(subst,[],[refute_0_20:[bind(Y,$fot(and(not(and(X_16160,X_16160)),X_16160)))]]) ).
cnf(refute_0_1044,plain,
implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)) = implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)),
introduced(tautology,[refl,[$fot(implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)))]]) ).
cnf(refute_0_1045,plain,
( implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)) != implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162))
| or(not(X),and(not(and(X_16160,X_16160)),X_16160)) != implies(X,and(not(and(X_16160,X_16160)),X_16160))
| implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)) = implies(implies(X,and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)),implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162))) ),[1,0],$fot(implies(X,and(not(and(X_16160,X_16160)),X_16160)))]]) ).
cnf(refute_0_1046,plain,
( or(not(X),and(not(and(X_16160,X_16160)),X_16160)) != implies(X,and(not(and(X_16160,X_16160)),X_16160))
| implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)) = implies(implies(X,and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)),implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162))) )],[refute_0_1044,refute_0_1045]) ).
cnf(refute_0_1047,plain,
implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)) = implies(implies(X,and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)),
inference(resolve,[$cnf( $equal(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,and(not(and(X_16160,X_16160)),X_16160))) )],[refute_0_1043,refute_0_1046]) ).
cnf(refute_0_1048,plain,
( implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)) != implies(implies(X,and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162))
| ~ is_a_theorem(implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)))
| is_a_theorem(implies(implies(X,and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162))) ),[0],$fot(implies(implies(X,and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)))]]) ).
cnf(refute_0_1049,plain,
( ~ is_a_theorem(implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)))
| is_a_theorem(implies(implies(X,and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162)),implies(implies(X,and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162))) )],[refute_0_1047,refute_0_1048]) ).
cnf(refute_0_1050,plain,
is_a_theorem(implies(implies(X,and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),and(not(and(X_16160,X_16160)),X_16160)),implies(X,X_16162))) )],[refute_0_1042,refute_0_1049]) ).
cnf(refute_0_1051,plain,
is_a_theorem(implies(implies(X_16170,and(not(and(not(X_9550),not(X_9550))),not(X_9550))),implies(X_16170,X_16172))),
inference(subst,[],[refute_0_1050:[bind(X,$fot(X_16170)),bind(X_16160,$fot(not(X_9550))),bind(X_16162,$fot(X_16172))]]) ).
cnf(refute_0_1052,plain,
not(implies(not(X_9550),X_9550)) = and(not(X_9550),not(X_9550)),
inference(subst,[],[refute_0_970:[bind(X,$fot(not(X_9550)))]]) ).
cnf(refute_0_1053,plain,
( not(implies(not(X_9550),X_9550)) != and(not(X_9550),not(X_9550))
| and(not(X_9550),not(X_9550)) = not(implies(not(X_9550),X_9550)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(implies(not(X_9550),X_9550)))),bind(Y0,$fot(and(not(X_9550),not(X_9550))))]]) ).
cnf(refute_0_1054,plain,
and(not(X_9550),not(X_9550)) = not(implies(not(X_9550),X_9550)),
inference(resolve,[$cnf( $equal(not(implies(not(X_9550),X_9550)),and(not(X_9550),not(X_9550))) )],[refute_0_1052,refute_0_1053]) ).
cnf(refute_0_1055,plain,
( and(not(X_9550),not(X_9550)) != not(implies(not(X_9550),X_9550))
| ~ is_a_theorem(implies(implies(X_16170,and(not(and(not(X_9550),not(X_9550))),not(X_9550))),implies(X_16170,X_16172)))
| is_a_theorem(implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_16170,and(not(and(not(X_9550),not(X_9550))),not(X_9550))),implies(X_16170,X_16172))) ),[0,0,1,0,0],$fot(not(implies(not(X_9550),X_9550)))]]) ).
cnf(refute_0_1056,plain,
( ~ is_a_theorem(implies(implies(X_16170,and(not(and(not(X_9550),not(X_9550))),not(X_9550))),implies(X_16170,X_16172)))
| is_a_theorem(implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172))) ),
inference(resolve,[$cnf( $equal(and(not(X_9550),not(X_9550)),not(implies(not(X_9550),X_9550))) )],[refute_0_1054,refute_0_1055]) ).
cnf(refute_0_1057,plain,
is_a_theorem(implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_16170,and(not(and(not(X_9550),not(X_9550))),not(X_9550))),implies(X_16170,X_16172))) )],[refute_0_1051,refute_0_1056]) ).
cnf(refute_0_1058,plain,
implies(not(and(X_16170,implies(or(X_9550,X_9550),X_9550))),implies(X_16170,X_16172)) = or(and(X_16170,implies(or(X_9550,X_9550),X_9550)),implies(X_16170,X_16172)),
inference(subst,[],[refute_0_159:[bind(X,$fot(and(X_16170,implies(or(X_9550,X_9550),X_9550)))),bind(Y,$fot(implies(X_16170,X_16172)))]]) ).
cnf(refute_0_1059,plain,
implies(X_16170,not(implies(or(X_9550,X_9550),X_9550))) = not(and(X_16170,implies(or(X_9550,X_9550),X_9550))),
inference(subst,[],[refute_0_987:[bind(Y,$fot(implies(or(X_9550,X_9550),X_9550))),bind(X_9551,$fot(X_16170))]]) ).
cnf(refute_0_1060,plain,
implies(not(X_9550),X_9550) = or(X_9550,X_9550),
inference(subst,[],[refute_0_159:[bind(X,$fot(X_9550)),bind(Y,$fot(X_9550))]]) ).
cnf(refute_0_1061,plain,
implies(implies(not(X_9550),X_9550),X_9550) = implies(implies(not(X_9550),X_9550),X_9550),
introduced(tautology,[refl,[$fot(implies(implies(not(X_9550),X_9550),X_9550))]]) ).
cnf(refute_0_1062,plain,
( implies(implies(not(X_9550),X_9550),X_9550) != implies(implies(not(X_9550),X_9550),X_9550)
| implies(not(X_9550),X_9550) != or(X_9550,X_9550)
| implies(implies(not(X_9550),X_9550),X_9550) = implies(or(X_9550,X_9550),X_9550) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_9550),X_9550),X_9550),implies(implies(not(X_9550),X_9550),X_9550)) ),[1,0],$fot(or(X_9550,X_9550))]]) ).
cnf(refute_0_1063,plain,
( implies(not(X_9550),X_9550) != or(X_9550,X_9550)
| implies(implies(not(X_9550),X_9550),X_9550) = implies(or(X_9550,X_9550),X_9550) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_9550),X_9550),X_9550),implies(implies(not(X_9550),X_9550),X_9550)) )],[refute_0_1061,refute_0_1062]) ).
cnf(refute_0_1064,plain,
implies(implies(not(X_9550),X_9550),X_9550) = implies(or(X_9550,X_9550),X_9550),
inference(resolve,[$cnf( $equal(implies(not(X_9550),X_9550),or(X_9550,X_9550)) )],[refute_0_1060,refute_0_1063]) ).
cnf(refute_0_1065,plain,
or(not(implies(not(X_9550),X_9550)),X_9550) = implies(implies(not(X_9550),X_9550),X_9550),
inference(subst,[],[refute_0_20:[bind(X,$fot(implies(not(X_9550),X_9550))),bind(Y,$fot(X_9550))]]) ).
cnf(refute_0_1066,plain,
implies(not(not(implies(not(X_9550),X_9550))),X_9550) = or(not(implies(not(X_9550),X_9550)),X_9550),
inference(subst,[],[refute_0_159:[bind(X,$fot(not(implies(not(X_9550),X_9550)))),bind(Y,$fot(X_9550))]]) ).
cnf(refute_0_1067,plain,
( implies(not(not(implies(not(X_9550),X_9550))),X_9550) != or(not(implies(not(X_9550),X_9550)),X_9550)
| or(not(implies(not(X_9550),X_9550)),X_9550) != implies(implies(not(X_9550),X_9550),X_9550)
| implies(not(not(implies(not(X_9550),X_9550))),X_9550) = implies(implies(not(X_9550),X_9550),X_9550) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(not(not(implies(not(X_9550),X_9550))),X_9550))),bind(Y0,$fot(or(not(implies(not(X_9550),X_9550)),X_9550))),bind(Z,$fot(implies(implies(not(X_9550),X_9550),X_9550)))]]) ).
cnf(refute_0_1068,plain,
( or(not(implies(not(X_9550),X_9550)),X_9550) != implies(implies(not(X_9550),X_9550),X_9550)
| implies(not(not(implies(not(X_9550),X_9550))),X_9550) = implies(implies(not(X_9550),X_9550),X_9550) ),
inference(resolve,[$cnf( $equal(implies(not(not(implies(not(X_9550),X_9550))),X_9550),or(not(implies(not(X_9550),X_9550)),X_9550)) )],[refute_0_1066,refute_0_1067]) ).
cnf(refute_0_1069,plain,
implies(not(not(implies(not(X_9550),X_9550))),X_9550) = implies(implies(not(X_9550),X_9550),X_9550),
inference(resolve,[$cnf( $equal(or(not(implies(not(X_9550),X_9550)),X_9550),implies(implies(not(X_9550),X_9550),X_9550)) )],[refute_0_1065,refute_0_1068]) ).
cnf(refute_0_1070,plain,
( implies(implies(not(X_9550),X_9550),X_9550) != implies(or(X_9550,X_9550),X_9550)
| implies(not(not(implies(not(X_9550),X_9550))),X_9550) != implies(implies(not(X_9550),X_9550),X_9550)
| implies(not(not(implies(not(X_9550),X_9550))),X_9550) = implies(or(X_9550,X_9550),X_9550) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(not(not(implies(not(X_9550),X_9550))),X_9550))),bind(Y0,$fot(implies(implies(not(X_9550),X_9550),X_9550))),bind(Z,$fot(implies(or(X_9550,X_9550),X_9550)))]]) ).
cnf(refute_0_1071,plain,
( implies(implies(not(X_9550),X_9550),X_9550) != implies(or(X_9550,X_9550),X_9550)
| implies(not(not(implies(not(X_9550),X_9550))),X_9550) = implies(or(X_9550,X_9550),X_9550) ),
inference(resolve,[$cnf( $equal(implies(not(not(implies(not(X_9550),X_9550))),X_9550),implies(implies(not(X_9550),X_9550),X_9550)) )],[refute_0_1069,refute_0_1070]) ).
cnf(refute_0_1072,plain,
implies(not(not(implies(not(X_9550),X_9550))),X_9550) = implies(or(X_9550,X_9550),X_9550),
inference(resolve,[$cnf( $equal(implies(implies(not(X_9550),X_9550),X_9550),implies(or(X_9550,X_9550),X_9550)) )],[refute_0_1064,refute_0_1071]) ).
cnf(refute_0_1073,plain,
not(implies(not(not(implies(not(X_9550),X_9550))),X_9550)) = not(implies(not(not(implies(not(X_9550),X_9550))),X_9550)),
introduced(tautology,[refl,[$fot(not(implies(not(not(implies(not(X_9550),X_9550))),X_9550)))]]) ).
cnf(refute_0_1074,plain,
( implies(not(not(implies(not(X_9550),X_9550))),X_9550) != implies(or(X_9550,X_9550),X_9550)
| not(implies(not(not(implies(not(X_9550),X_9550))),X_9550)) != not(implies(not(not(implies(not(X_9550),X_9550))),X_9550))
| not(implies(not(not(implies(not(X_9550),X_9550))),X_9550)) = not(implies(or(X_9550,X_9550),X_9550)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(not(implies(not(X_9550),X_9550))),X_9550)),not(implies(not(not(implies(not(X_9550),X_9550))),X_9550))) ),[1,0],$fot(implies(or(X_9550,X_9550),X_9550))]]) ).
cnf(refute_0_1075,plain,
( implies(not(not(implies(not(X_9550),X_9550))),X_9550) != implies(or(X_9550,X_9550),X_9550)
| not(implies(not(not(implies(not(X_9550),X_9550))),X_9550)) = not(implies(or(X_9550,X_9550),X_9550)) ),
inference(resolve,[$cnf( $equal(not(implies(not(not(implies(not(X_9550),X_9550))),X_9550)),not(implies(not(not(implies(not(X_9550),X_9550))),X_9550))) )],[refute_0_1073,refute_0_1074]) ).
cnf(refute_0_1076,plain,
not(implies(not(not(implies(not(X_9550),X_9550))),X_9550)) = not(implies(or(X_9550,X_9550),X_9550)),
inference(resolve,[$cnf( $equal(implies(not(not(implies(not(X_9550),X_9550))),X_9550),implies(or(X_9550,X_9550),X_9550)) )],[refute_0_1072,refute_0_1075]) ).
cnf(refute_0_1077,plain,
and(not(not(implies(not(X_9550),X_9550))),not(X_9550)) = not(implies(not(not(implies(not(X_9550),X_9550))),X_9550)),
inference(subst,[],[refute_0_972:[bind(X,$fot(not(not(implies(not(X_9550),X_9550)))))]]) ).
cnf(refute_0_1078,plain,
( and(not(not(implies(not(X_9550),X_9550))),not(X_9550)) != not(implies(not(not(implies(not(X_9550),X_9550))),X_9550))
| not(implies(not(not(implies(not(X_9550),X_9550))),X_9550)) != not(implies(or(X_9550,X_9550),X_9550))
| and(not(not(implies(not(X_9550),X_9550))),not(X_9550)) = not(implies(or(X_9550,X_9550),X_9550)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(and(not(not(implies(not(X_9550),X_9550))),not(X_9550)))),bind(Y0,$fot(not(implies(not(not(implies(not(X_9550),X_9550))),X_9550)))),bind(Z,$fot(not(implies(or(X_9550,X_9550),X_9550))))]]) ).
cnf(refute_0_1079,plain,
( not(implies(not(not(implies(not(X_9550),X_9550))),X_9550)) != not(implies(or(X_9550,X_9550),X_9550))
| and(not(not(implies(not(X_9550),X_9550))),not(X_9550)) = not(implies(or(X_9550,X_9550),X_9550)) ),
inference(resolve,[$cnf( $equal(and(not(not(implies(not(X_9550),X_9550))),not(X_9550)),not(implies(not(not(implies(not(X_9550),X_9550))),X_9550))) )],[refute_0_1077,refute_0_1078]) ).
cnf(refute_0_1080,plain,
and(not(not(implies(not(X_9550),X_9550))),not(X_9550)) = not(implies(or(X_9550,X_9550),X_9550)),
inference(resolve,[$cnf( $equal(not(implies(not(not(implies(not(X_9550),X_9550))),X_9550)),not(implies(or(X_9550,X_9550),X_9550))) )],[refute_0_1076,refute_0_1079]) ).
cnf(refute_0_1081,plain,
implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))) = implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),
introduced(tautology,[refl,[$fot(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))))]]) ).
cnf(refute_0_1082,plain,
( and(not(not(implies(not(X_9550),X_9550))),not(X_9550)) != not(implies(or(X_9550,X_9550),X_9550))
| implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))) != implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550)))
| implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))) = implies(X_16170,not(implies(or(X_9550,X_9550),X_9550))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550)))) ),[1,1],$fot(not(implies(or(X_9550,X_9550),X_9550)))]]) ).
cnf(refute_0_1083,plain,
( and(not(not(implies(not(X_9550),X_9550))),not(X_9550)) != not(implies(or(X_9550,X_9550),X_9550))
| implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))) = implies(X_16170,not(implies(or(X_9550,X_9550),X_9550))) ),
inference(resolve,[$cnf( $equal(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550)))) )],[refute_0_1081,refute_0_1082]) ).
cnf(refute_0_1084,plain,
implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))) = implies(X_16170,not(implies(or(X_9550,X_9550),X_9550))),
inference(resolve,[$cnf( $equal(and(not(not(implies(not(X_9550),X_9550))),not(X_9550)),not(implies(or(X_9550,X_9550),X_9550))) )],[refute_0_1080,refute_0_1083]) ).
cnf(refute_0_1085,plain,
( implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))) != implies(X_16170,not(implies(or(X_9550,X_9550),X_9550)))
| implies(X_16170,not(implies(or(X_9550,X_9550),X_9550))) != not(and(X_16170,implies(or(X_9550,X_9550),X_9550)))
| implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))) = not(and(X_16170,implies(or(X_9550,X_9550),X_9550))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))))),bind(Y0,$fot(implies(X_16170,not(implies(or(X_9550,X_9550),X_9550))))),bind(Z,$fot(not(and(X_16170,implies(or(X_9550,X_9550),X_9550)))))]]) ).
cnf(refute_0_1086,plain,
( implies(X_16170,not(implies(or(X_9550,X_9550),X_9550))) != not(and(X_16170,implies(or(X_9550,X_9550),X_9550)))
| implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))) = not(and(X_16170,implies(or(X_9550,X_9550),X_9550))) ),
inference(resolve,[$cnf( $equal(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,not(implies(or(X_9550,X_9550),X_9550)))) )],[refute_0_1084,refute_0_1085]) ).
cnf(refute_0_1087,plain,
implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))) = not(and(X_16170,implies(or(X_9550,X_9550),X_9550))),
inference(resolve,[$cnf( $equal(implies(X_16170,not(implies(or(X_9550,X_9550),X_9550))),not(and(X_16170,implies(or(X_9550,X_9550),X_9550)))) )],[refute_0_1059,refute_0_1086]) ).
cnf(refute_0_1088,plain,
implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)) = implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)),
introduced(tautology,[refl,[$fot(implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)))]]) ).
cnf(refute_0_1089,plain,
( implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))) != not(and(X_16170,implies(or(X_9550,X_9550),X_9550)))
| implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)) != implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172))
| implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)) = implies(not(and(X_16170,implies(or(X_9550,X_9550),X_9550))),implies(X_16170,X_16172)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)),implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172))) ),[1,0],$fot(not(and(X_16170,implies(or(X_9550,X_9550),X_9550))))]]) ).
cnf(refute_0_1090,plain,
( implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))) != not(and(X_16170,implies(or(X_9550,X_9550),X_9550)))
| implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)) = implies(not(and(X_16170,implies(or(X_9550,X_9550),X_9550))),implies(X_16170,X_16172)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)),implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172))) )],[refute_0_1088,refute_0_1089]) ).
cnf(refute_0_1091,plain,
implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)) = implies(not(and(X_16170,implies(or(X_9550,X_9550),X_9550))),implies(X_16170,X_16172)),
inference(resolve,[$cnf( $equal(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),not(and(X_16170,implies(or(X_9550,X_9550),X_9550)))) )],[refute_0_1087,refute_0_1090]) ).
cnf(refute_0_1092,plain,
( implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)) != implies(not(and(X_16170,implies(or(X_9550,X_9550),X_9550))),implies(X_16170,X_16172))
| implies(not(and(X_16170,implies(or(X_9550,X_9550),X_9550))),implies(X_16170,X_16172)) != or(and(X_16170,implies(or(X_9550,X_9550),X_9550)),implies(X_16170,X_16172))
| implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)) = or(and(X_16170,implies(or(X_9550,X_9550),X_9550)),implies(X_16170,X_16172)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)))),bind(Y0,$fot(implies(not(and(X_16170,implies(or(X_9550,X_9550),X_9550))),implies(X_16170,X_16172)))),bind(Z,$fot(or(and(X_16170,implies(or(X_9550,X_9550),X_9550)),implies(X_16170,X_16172))))]]) ).
cnf(refute_0_1093,plain,
( implies(not(and(X_16170,implies(or(X_9550,X_9550),X_9550))),implies(X_16170,X_16172)) != or(and(X_16170,implies(or(X_9550,X_9550),X_9550)),implies(X_16170,X_16172))
| implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)) = or(and(X_16170,implies(or(X_9550,X_9550),X_9550)),implies(X_16170,X_16172)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)),implies(not(and(X_16170,implies(or(X_9550,X_9550),X_9550))),implies(X_16170,X_16172))) )],[refute_0_1091,refute_0_1092]) ).
cnf(refute_0_1094,plain,
implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)) = or(and(X_16170,implies(or(X_9550,X_9550),X_9550)),implies(X_16170,X_16172)),
inference(resolve,[$cnf( $equal(implies(not(and(X_16170,implies(or(X_9550,X_9550),X_9550))),implies(X_16170,X_16172)),or(and(X_16170,implies(or(X_9550,X_9550),X_9550)),implies(X_16170,X_16172))) )],[refute_0_1058,refute_0_1093]) ).
cnf(refute_0_1095,plain,
( implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)) != or(and(X_16170,implies(or(X_9550,X_9550),X_9550)),implies(X_16170,X_16172))
| ~ is_a_theorem(implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)))
| is_a_theorem(or(and(X_16170,implies(or(X_9550,X_9550),X_9550)),implies(X_16170,X_16172))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172))) ),[0],$fot(or(and(X_16170,implies(or(X_9550,X_9550),X_9550)),implies(X_16170,X_16172)))]]) ).
cnf(refute_0_1096,plain,
( ~ is_a_theorem(implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)))
| is_a_theorem(or(and(X_16170,implies(or(X_9550,X_9550),X_9550)),implies(X_16170,X_16172))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172)),or(and(X_16170,implies(or(X_9550,X_9550),X_9550)),implies(X_16170,X_16172))) )],[refute_0_1094,refute_0_1095]) ).
cnf(refute_0_1097,plain,
is_a_theorem(or(and(X_16170,implies(or(X_9550,X_9550),X_9550)),implies(X_16170,X_16172))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_16170,and(not(not(implies(not(X_9550),X_9550))),not(X_9550))),implies(X_16170,X_16172))) )],[refute_0_1057,refute_0_1096]) ).
cnf(refute_0_1098,plain,
is_a_theorem(or(and(implies(X_16181,or(X_16181,X_16181)),implies(or(X_16181,X_16181),X_16181)),implies(implies(X_16181,or(X_16181,X_16181)),X_16180))),
inference(subst,[],[refute_0_1097:[bind(X_16170,$fot(implies(X_16181,or(X_16181,X_16181)))),bind(X_16172,$fot(X_16180)),bind(X_9550,$fot(X_16181))]]) ).
cnf(refute_0_1099,plain,
equiv(X_16181,or(X_16181,X_16181)) = and(implies(X_16181,or(X_16181,X_16181)),implies(or(X_16181,X_16181),X_16181)),
inference(subst,[],[refute_0_318:[bind(X,$fot(X_16181)),bind(Y,$fot(or(X_16181,X_16181)))]]) ).
cnf(refute_0_1100,plain,
( equiv(X_16181,or(X_16181,X_16181)) != and(implies(X_16181,or(X_16181,X_16181)),implies(or(X_16181,X_16181),X_16181))
| and(implies(X_16181,or(X_16181,X_16181)),implies(or(X_16181,X_16181),X_16181)) = equiv(X_16181,or(X_16181,X_16181)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(X_16181,or(X_16181,X_16181)))),bind(Y0,$fot(and(implies(X_16181,or(X_16181,X_16181)),implies(or(X_16181,X_16181),X_16181))))]]) ).
cnf(refute_0_1101,plain,
and(implies(X_16181,or(X_16181,X_16181)),implies(or(X_16181,X_16181),X_16181)) = equiv(X_16181,or(X_16181,X_16181)),
inference(resolve,[$cnf( $equal(equiv(X_16181,or(X_16181,X_16181)),and(implies(X_16181,or(X_16181,X_16181)),implies(or(X_16181,X_16181),X_16181))) )],[refute_0_1099,refute_0_1100]) ).
cnf(refute_0_1102,plain,
( and(implies(X_16181,or(X_16181,X_16181)),implies(or(X_16181,X_16181),X_16181)) != equiv(X_16181,or(X_16181,X_16181))
| ~ is_a_theorem(or(and(implies(X_16181,or(X_16181,X_16181)),implies(or(X_16181,X_16181),X_16181)),implies(implies(X_16181,or(X_16181,X_16181)),X_16180)))
| is_a_theorem(or(equiv(X_16181,or(X_16181,X_16181)),implies(implies(X_16181,or(X_16181,X_16181)),X_16180))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(implies(X_16181,or(X_16181,X_16181)),implies(or(X_16181,X_16181),X_16181)),implies(implies(X_16181,or(X_16181,X_16181)),X_16180))) ),[0,0],$fot(equiv(X_16181,or(X_16181,X_16181)))]]) ).
cnf(refute_0_1103,plain,
( ~ is_a_theorem(or(and(implies(X_16181,or(X_16181,X_16181)),implies(or(X_16181,X_16181),X_16181)),implies(implies(X_16181,or(X_16181,X_16181)),X_16180)))
| is_a_theorem(or(equiv(X_16181,or(X_16181,X_16181)),implies(implies(X_16181,or(X_16181,X_16181)),X_16180))) ),
inference(resolve,[$cnf( $equal(and(implies(X_16181,or(X_16181,X_16181)),implies(or(X_16181,X_16181),X_16181)),equiv(X_16181,or(X_16181,X_16181))) )],[refute_0_1101,refute_0_1102]) ).
cnf(refute_0_1104,plain,
is_a_theorem(or(equiv(X_16181,or(X_16181,X_16181)),implies(implies(X_16181,or(X_16181,X_16181)),X_16180))),
inference(resolve,[$cnf( is_a_theorem(or(and(implies(X_16181,or(X_16181,X_16181)),implies(or(X_16181,X_16181),X_16181)),implies(implies(X_16181,or(X_16181,X_16181)),X_16180))) )],[refute_0_1098,refute_0_1103]) ).
cnf(refute_0_1105,plain,
is_a_theorem(or(equiv(X_17197,or(X_17197,X_17197)),implies(implies(X_17197,or(X_17197,X_17197)),X_17196))),
inference(subst,[],[refute_0_1104:[bind(X_16180,$fot(X_17196)),bind(X_16181,$fot(X_17197))]]) ).
cnf(refute_0_1106,plain,
is_a_theorem(implies(implies(X_17197,or(X_17197,X_17197)),or(equiv(X_17197,or(X_17197,X_17197)),X_17196))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(X_17197,or(X_17197,X_17197)),implies(implies(X_17197,or(X_17197,X_17197)),X_17196))) )],[refute_0_1105,refute_0_1009]) ).
cnf(refute_0_1107,plain,
is_a_theorem(implies(implies(X_25344,or(X_25344,X_25344)),or(equiv(X_25344,or(X_25344,X_25344)),X_25343))),
inference(subst,[],[refute_0_1106:[bind(X_17196,$fot(X_25343)),bind(X_17197,$fot(X_25344))]]) ).
cnf(refute_0_1108,plain,
( ~ is_a_theorem(implies(X_25344,or(X_25344,X_25344)))
| is_a_theorem(or(equiv(X_25344,or(X_25344,X_25344)),X_25343)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_25344,or(X_25344,X_25344)),or(equiv(X_25344,or(X_25344,X_25344)),X_25343))) )],[refute_0_1107,refute_0_1008]) ).
cnf(refute_0_1109,plain,
is_a_theorem(implies(X_25344,or(X_25344,X_25344))),
inference(subst,[],[refute_0_47:[bind(P,$fot(X_25344)),bind(Q,$fot(X_25344))]]) ).
cnf(refute_0_1110,plain,
is_a_theorem(or(equiv(X_25344,or(X_25344,X_25344)),X_25343)),
inference(resolve,[$cnf( is_a_theorem(implies(X_25344,or(X_25344,X_25344))) )],[refute_0_1109,refute_0_1108]) ).
cnf(refute_0_1111,plain,
is_a_theorem(or(equiv(X_25346,or(X_25346,X_25346)),equiv(X_25346,or(X_25346,X_25346)))),
inference(subst,[],[refute_0_1110:[bind(X_25343,$fot(equiv(X_25346,or(X_25346,X_25346)))),bind(X_25344,$fot(X_25346))]]) ).
cnf(refute_0_1112,plain,
is_a_theorem(equiv(X_25346,or(X_25346,X_25346))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(X_25346,or(X_25346,X_25346)),equiv(X_25346,or(X_25346,X_25346)))) )],[refute_0_1111,refute_0_1007]) ).
cnf(refute_0_1113,plain,
is_a_theorem(equiv(X_25347,or(X_25347,X_25347))),
inference(subst,[],[refute_0_1112:[bind(X_25346,$fot(X_25347))]]) ).
cnf(refute_0_1114,plain,
X_25347 = or(X_25347,X_25347),
inference(resolve,[$cnf( is_a_theorem(equiv(X_25347,or(X_25347,X_25347))) )],[refute_0_1113,refute_0_1006]) ).
cnf(refute_0_1115,plain,
and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)) = or(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)),and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036))),
inference(subst,[],[refute_0_1114:[bind(X_25347,$fot(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036))))]]) ).
cnf(refute_0_1116,plain,
( and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)) != or(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)),and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)))
| or(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)),and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036))) = and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)))),bind(Y0,$fot(or(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)),and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)))))]]) ).
cnf(refute_0_1117,plain,
or(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)),and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036))) = and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)),
inference(resolve,[$cnf( $equal(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)),or(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)),and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)))) )],[refute_0_1115,refute_0_1116]) ).
cnf(refute_0_1118,plain,
( or(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)),and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036))) != and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036))
| ~ is_a_theorem(implies(X_30033,or(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)),and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)))))
| is_a_theorem(implies(X_30033,and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_30033,or(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)),and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036))))) ),[0,1],$fot(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)))]]) ).
cnf(refute_0_1119,plain,
( ~ is_a_theorem(implies(X_30033,or(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)),and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)))))
| is_a_theorem(implies(X_30033,and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)))) ),
inference(resolve,[$cnf( $equal(or(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)),and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036))),and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036))) )],[refute_0_1117,refute_0_1118]) ).
cnf(refute_0_1120,plain,
is_a_theorem(implies(X_30033,and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_30033,or(and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036)),and(X_30033,implies(and(equiv(X_30036,X_30035),X_30035),X_30036))))) )],[refute_0_1005,refute_0_1119]) ).
cnf(refute_0_1121,plain,
is_a_theorem(implies(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),and(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),implies(and(equiv(X_44336,X_44335),X_44335),X_44336)))),
inference(subst,[],[refute_0_1120:[bind(X_30033,$fot(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)))),bind(X_30035,$fot(X_44335)),bind(X_30036,$fot(X_44336))]]) ).
cnf(refute_0_1122,plain,
equiv(X_44336,and(equiv(X_44336,X_44335),X_44335)) = and(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),implies(and(equiv(X_44336,X_44335),X_44335),X_44336)),
inference(subst,[],[refute_0_318:[bind(X,$fot(X_44336)),bind(Y,$fot(and(equiv(X_44336,X_44335),X_44335)))]]) ).
cnf(refute_0_1123,plain,
( equiv(X_44336,and(equiv(X_44336,X_44335),X_44335)) != and(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),implies(and(equiv(X_44336,X_44335),X_44335),X_44336))
| and(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),implies(and(equiv(X_44336,X_44335),X_44335),X_44336)) = equiv(X_44336,and(equiv(X_44336,X_44335),X_44335)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(X_44336,and(equiv(X_44336,X_44335),X_44335)))),bind(Y0,$fot(and(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),implies(and(equiv(X_44336,X_44335),X_44335),X_44336))))]]) ).
cnf(refute_0_1124,plain,
and(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),implies(and(equiv(X_44336,X_44335),X_44335),X_44336)) = equiv(X_44336,and(equiv(X_44336,X_44335),X_44335)),
inference(resolve,[$cnf( $equal(equiv(X_44336,and(equiv(X_44336,X_44335),X_44335)),and(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),implies(and(equiv(X_44336,X_44335),X_44335),X_44336))) )],[refute_0_1122,refute_0_1123]) ).
cnf(refute_0_1125,plain,
( and(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),implies(and(equiv(X_44336,X_44335),X_44335),X_44336)) != equiv(X_44336,and(equiv(X_44336,X_44335),X_44335))
| ~ is_a_theorem(implies(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),and(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),implies(and(equiv(X_44336,X_44335),X_44335),X_44336))))
| is_a_theorem(implies(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),equiv(X_44336,and(equiv(X_44336,X_44335),X_44335)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),and(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),implies(and(equiv(X_44336,X_44335),X_44335),X_44336)))) ),[0,1],$fot(equiv(X_44336,and(equiv(X_44336,X_44335),X_44335)))]]) ).
cnf(refute_0_1126,plain,
( ~ is_a_theorem(implies(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),and(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),implies(and(equiv(X_44336,X_44335),X_44335),X_44336))))
| is_a_theorem(implies(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),equiv(X_44336,and(equiv(X_44336,X_44335),X_44335)))) ),
inference(resolve,[$cnf( $equal(and(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),implies(and(equiv(X_44336,X_44335),X_44335),X_44336)),equiv(X_44336,and(equiv(X_44336,X_44335),X_44335))) )],[refute_0_1124,refute_0_1125]) ).
cnf(refute_0_1127,plain,
is_a_theorem(implies(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),equiv(X_44336,and(equiv(X_44336,X_44335),X_44335)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),and(implies(X_44336,and(equiv(X_44336,X_44335),X_44335)),implies(and(equiv(X_44336,X_44335),X_44335),X_44336)))) )],[refute_0_1121,refute_0_1126]) ).
cnf(refute_0_1128,plain,
is_a_theorem(implies(implies(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))))),
inference(subst,[],[refute_0_1127:[bind(X_44335,$fot(equiv(X_44336,X_44336)))]]) ).
cnf(refute_0_1129,plain,
( ~ is_a_theorem(equiv(equiv(X_55981,equiv(X_55981,X_55981)),X_55981))
| equiv(X_55981,equiv(X_55981,X_55981)) = X_55981 ),
inference(subst,[],[refute_0_253:[bind(X,$fot(equiv(X_55981,equiv(X_55981,X_55981)))),bind(Y,$fot(X_55981))]]) ).
cnf(refute_0_1130,plain,
( ~ is_a_theorem(implies(equiv(X_55980,equiv(X_55980,X_55980)),X_55980))
| ~ is_a_theorem(implies(implies(equiv(X_55980,equiv(X_55980,X_55980)),X_55980),equiv(equiv(X_55980,equiv(X_55980,X_55980)),X_55980)))
| is_a_theorem(equiv(equiv(X_55980,equiv(X_55980,X_55980)),X_55980)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(implies(equiv(X_55980,equiv(X_55980,X_55980)),X_55980))),bind(Y,$fot(equiv(equiv(X_55980,equiv(X_55980,X_55980)),X_55980)))]]) ).
cnf(refute_0_1131,plain,
( ~ is_a_theorem(or(and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965)))),not(X_55966)))
| is_a_theorem(or(not(X_55966),and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965)))))) ),
inference(subst,[],[refute_0_43:[bind(P,$fot(and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965)))))),bind(Q,$fot(not(X_55966)))]]) ).
cnf(refute_0_1132,plain,
( ~ is_a_theorem(or(equiv(not(or(X_31173,X_31174)),not(equiv(X_31174,not(X_31173)))),and(X_31174,X_31173)))
| is_a_theorem(or(and(X_31174,X_31173),equiv(not(or(X_31173,X_31174)),not(equiv(X_31174,not(X_31173)))))) ),
inference(subst,[],[refute_0_43:[bind(P,$fot(equiv(not(or(X_31173,X_31174)),not(equiv(X_31174,not(X_31173)))))),bind(Q,$fot(and(X_31174,X_31173)))]]) ).
cnf(refute_0_1133,plain,
( ~ is_a_theorem(implies(or(X_31162,or(X_31161,not(X_31162))),or(equiv(not(X_31162),or(X_31161,not(X_31162))),X_31161)))
| ~ is_a_theorem(or(X_31162,or(X_31161,not(X_31162))))
| is_a_theorem(or(equiv(not(X_31162),or(X_31161,not(X_31162))),X_31161)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(or(X_31162,or(X_31161,not(X_31162))))),bind(Y,$fot(or(equiv(not(X_31162),or(X_31161,not(X_31162))),X_31161)))]]) ).
cnf(refute_0_1134,plain,
( ~ is_a_theorem(or(equiv(not(X_17382),or(X_17381,not(X_17382))),implies(or(X_17382,or(X_17381,not(X_17382))),X_17381)))
| is_a_theorem(implies(or(X_17382,or(X_17381,not(X_17382))),or(equiv(not(X_17382),or(X_17381,not(X_17382))),X_17381))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(or(X_17382,or(X_17381,not(X_17382))))),bind(X_103,$fot(equiv(not(X_17382),or(X_17381,not(X_17382))))),bind(X_105,$fot(X_17381))]]) ).
cnf(refute_0_1135,plain,
( ~ is_a_theorem(or(X_6550,implies(or(X_6550,X_6551),X_6551)))
| is_a_theorem(or(implies(or(X_6550,X_6551),X_6551),X_6550)) ),
inference(subst,[],[refute_0_43:[bind(P,$fot(X_6550)),bind(Q,$fot(implies(or(X_6550,X_6551),X_6551)))]]) ).
cnf(refute_0_1136,plain,
is_a_theorem(implies(or(X_6532,X_6533),or(X_6532,X_6533))),
inference(subst,[],[refute_0_520:[bind(X_4514,$fot(or(X_6532,X_6533)))]]) ).
cnf(refute_0_1137,plain,
( ~ is_a_theorem(implies(or(X_6532,X_6533),or(X_6532,X_6533)))
| is_a_theorem(or(X_6532,implies(or(X_6532,X_6533),X_6533))) ),
inference(subst,[],[refute_0_851:[bind(X,$fot(or(X_6532,X_6533))),bind(X_104,$fot(X_6532)),bind(X_105,$fot(X_6533))]]) ).
cnf(refute_0_1138,plain,
is_a_theorem(or(X_6532,implies(or(X_6532,X_6533),X_6533))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_6532,X_6533),or(X_6532,X_6533))) )],[refute_0_1136,refute_0_1137]) ).
cnf(refute_0_1139,plain,
is_a_theorem(or(X_6550,implies(or(X_6550,X_6551),X_6551))),
inference(subst,[],[refute_0_1138:[bind(X_6532,$fot(X_6550)),bind(X_6533,$fot(X_6551))]]) ).
cnf(refute_0_1140,plain,
is_a_theorem(or(implies(or(X_6550,X_6551),X_6551),X_6550)),
inference(resolve,[$cnf( is_a_theorem(or(X_6550,implies(or(X_6550,X_6551),X_6551))) )],[refute_0_1139,refute_0_1135]) ).
cnf(refute_0_1141,plain,
is_a_theorem(or(implies(or(X_6552,not(X_17)),not(X_17)),X_6552)),
inference(subst,[],[refute_0_1140:[bind(X_6550,$fot(X_6552)),bind(X_6551,$fot(not(X_17)))]]) ).
cnf(refute_0_1142,plain,
or(implies(or(X_6552,not(X_17)),not(X_17)),X_6552) = implies(and(or(X_6552,not(X_17)),X_17),X_6552),
inference(subst,[],[refute_0_467:[bind(Y,$fot(X_6552)),bind(X_16,$fot(or(X_6552,not(X_17))))]]) ).
cnf(refute_0_1143,plain,
( or(implies(or(X_6552,not(X_17)),not(X_17)),X_6552) != implies(and(or(X_6552,not(X_17)),X_17),X_6552)
| ~ is_a_theorem(or(implies(or(X_6552,not(X_17)),not(X_17)),X_6552))
| is_a_theorem(implies(and(or(X_6552,not(X_17)),X_17),X_6552)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(or(X_6552,not(X_17)),not(X_17)),X_6552)) ),[0],$fot(implies(and(or(X_6552,not(X_17)),X_17),X_6552))]]) ).
cnf(refute_0_1144,plain,
( ~ is_a_theorem(or(implies(or(X_6552,not(X_17)),not(X_17)),X_6552))
| is_a_theorem(implies(and(or(X_6552,not(X_17)),X_17),X_6552)) ),
inference(resolve,[$cnf( $equal(or(implies(or(X_6552,not(X_17)),not(X_17)),X_6552),implies(and(or(X_6552,not(X_17)),X_17),X_6552)) )],[refute_0_1142,refute_0_1143]) ).
cnf(refute_0_1145,plain,
is_a_theorem(implies(and(or(X_6552,not(X_17)),X_17),X_6552)),
inference(resolve,[$cnf( is_a_theorem(or(implies(or(X_6552,not(X_17)),not(X_17)),X_6552)) )],[refute_0_1141,refute_0_1144]) ).
cnf(refute_0_1146,plain,
is_a_theorem(implies(and(or(X_16359,not(X_17)),X_17),X_16359)),
inference(subst,[],[refute_0_1145:[bind(X_6552,$fot(X_16359))]]) ).
cnf(refute_0_1147,plain,
( ~ is_a_theorem(implies(X_301,X_302))
| ~ is_a_theorem(implies(implies(X_301,X_302),implies(implies(X_300,X_301),implies(X_300,X_302))))
| is_a_theorem(implies(implies(X_300,X_301),implies(X_300,X_302))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(implies(X_301,X_302))),bind(Y,$fot(implies(implies(X_300,X_301),implies(X_300,X_302))))]]) ).
cnf(refute_0_1148,plain,
is_a_theorem(implies(implies(X_301,X_302),implies(implies(X_300,X_301),implies(X_300,X_302)))),
inference(subst,[],[refute_0_693:[bind(X,$fot(X_300)),bind(X_126,$fot(X_301)),bind(X_127,$fot(X_302))]]) ).
cnf(refute_0_1149,plain,
( ~ is_a_theorem(implies(X_301,X_302))
| is_a_theorem(implies(implies(X_300,X_301),implies(X_300,X_302))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_301,X_302),implies(implies(X_300,X_301),implies(X_300,X_302)))) )],[refute_0_1148,refute_0_1147]) ).
cnf(refute_0_1150,plain,
( ~ is_a_theorem(implies(and(or(X_16359,not(X_17)),X_17),X_16359))
| is_a_theorem(implies(implies(X_16357,and(or(X_16359,not(X_17)),X_17)),implies(X_16357,X_16359))) ),
inference(subst,[],[refute_0_1149:[bind(X_300,$fot(X_16357)),bind(X_301,$fot(and(or(X_16359,not(X_17)),X_17))),bind(X_302,$fot(X_16359))]]) ).
cnf(refute_0_1151,plain,
is_a_theorem(implies(implies(X_16357,and(or(X_16359,not(X_17)),X_17)),implies(X_16357,X_16359))),
inference(resolve,[$cnf( is_a_theorem(implies(and(or(X_16359,not(X_17)),X_17),X_16359)) )],[refute_0_1146,refute_0_1150]) ).
cnf(refute_0_1152,plain,
is_a_theorem(implies(implies(or(X_16592,or(X_16591,not(X_16592))),and(or(X_16591,not(X_16592)),X_16592)),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591))),
inference(subst,[],[refute_0_1151:[bind(X_16357,$fot(or(X_16592,or(X_16591,not(X_16592))))),bind(X_16359,$fot(X_16591)),bind(X_17,$fot(X_16592))]]) ).
cnf(refute_0_1153,plain,
implies(or(X,X_30),and(X_30,X)) = not(not(implies(or(X,X_30),and(X_30,X)))),
inference(subst,[],[refute_0_980:[bind(X,$fot(or(X,X_30))),bind(Y,$fot(and(X_30,X)))]]) ).
cnf(refute_0_1154,plain,
equiv(not(X),X_30) = and(implies(not(X),X_30),implies(X_30,not(X))),
inference(subst,[],[refute_0_318:[bind(X,$fot(not(X))),bind(Y,$fot(X_30))]]) ).
cnf(refute_0_1155,plain,
or(X,X_30) = implies(not(X),X_30),
inference(subst,[],[refute_0_60:[bind(Y,$fot(X_30))]]) ).
cnf(refute_0_1156,plain,
( or(X,X_30) != implies(not(X),X_30)
| implies(not(X),X_30) = or(X,X_30) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,X_30))),bind(Y0,$fot(implies(not(X),X_30)))]]) ).
cnf(refute_0_1157,plain,
implies(not(X),X_30) = or(X,X_30),
inference(resolve,[$cnf( $equal(or(X,X_30),implies(not(X),X_30)) )],[refute_0_1155,refute_0_1156]) ).
cnf(refute_0_1158,plain,
( equiv(not(X),X_30) != and(implies(not(X),X_30),implies(X_30,not(X)))
| implies(not(X),X_30) != or(X,X_30)
| equiv(not(X),X_30) = and(or(X,X_30),implies(X_30,not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X),X_30),and(implies(not(X),X_30),implies(X_30,not(X)))) ),[1,0],$fot(or(X,X_30))]]) ).
cnf(refute_0_1159,plain,
( equiv(not(X),X_30) != and(implies(not(X),X_30),implies(X_30,not(X)))
| equiv(not(X),X_30) = and(or(X,X_30),implies(X_30,not(X))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_30),or(X,X_30)) )],[refute_0_1157,refute_0_1158]) ).
cnf(refute_0_1160,plain,
equiv(not(X),X_30) = and(or(X,X_30),implies(X_30,not(X))),
inference(resolve,[$cnf( $equal(equiv(not(X),X_30),and(implies(not(X),X_30),implies(X_30,not(X)))) )],[refute_0_1154,refute_0_1159]) ).
cnf(refute_0_1161,plain,
and(X,implies(X_16,not(X_17))) = not(implies(X,not(implies(X_16,not(X_17))))),
inference(subst,[],[refute_0_128:[bind(Y,$fot(implies(X_16,not(X_17))))]]) ).
cnf(refute_0_1162,plain,
( and(X,implies(X_16,not(X_17))) != not(implies(X,not(implies(X_16,not(X_17)))))
| not(implies(X_16,not(X_17))) != and(X_16,X_17)
| and(X,implies(X_16,not(X_17))) = not(implies(X,and(X_16,X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,implies(X_16,not(X_17))),not(implies(X,not(implies(X_16,not(X_17)))))) ),[1,0,1],$fot(and(X_16,X_17))]]) ).
cnf(refute_0_1163,plain,
( and(X,implies(X_16,not(X_17))) != not(implies(X,not(implies(X_16,not(X_17)))))
| and(X,implies(X_16,not(X_17))) = not(implies(X,and(X_16,X_17))) ),
inference(resolve,[$cnf( $equal(not(implies(X_16,not(X_17))),and(X_16,X_17)) )],[refute_0_131,refute_0_1162]) ).
cnf(refute_0_1164,plain,
and(X,implies(X_16,not(X_17))) = not(implies(X,and(X_16,X_17))),
inference(resolve,[$cnf( $equal(and(X,implies(X_16,not(X_17))),not(implies(X,not(implies(X_16,not(X_17)))))) )],[refute_0_1161,refute_0_1163]) ).
cnf(refute_0_1165,plain,
and(or(X,X_30),implies(X_30,not(X))) = not(implies(or(X,X_30),and(X_30,X))),
inference(subst,[],[refute_0_1164:[bind(X,$fot(or(X,X_30))),bind(X_16,$fot(X_30)),bind(X_17,$fot(X))]]) ).
cnf(refute_0_1166,plain,
( and(or(X,X_30),implies(X_30,not(X))) != not(implies(or(X,X_30),and(X_30,X)))
| equiv(not(X),X_30) != and(or(X,X_30),implies(X_30,not(X)))
| equiv(not(X),X_30) = not(implies(or(X,X_30),and(X_30,X))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X),X_30),and(or(X,X_30),implies(X_30,not(X)))) ),[1],$fot(not(implies(or(X,X_30),and(X_30,X))))]]) ).
cnf(refute_0_1167,plain,
( equiv(not(X),X_30) != and(or(X,X_30),implies(X_30,not(X)))
| equiv(not(X),X_30) = not(implies(or(X,X_30),and(X_30,X))) ),
inference(resolve,[$cnf( $equal(and(or(X,X_30),implies(X_30,not(X))),not(implies(or(X,X_30),and(X_30,X)))) )],[refute_0_1165,refute_0_1166]) ).
cnf(refute_0_1168,plain,
equiv(not(X),X_30) = not(implies(or(X,X_30),and(X_30,X))),
inference(resolve,[$cnf( $equal(equiv(not(X),X_30),and(or(X,X_30),implies(X_30,not(X)))) )],[refute_0_1160,refute_0_1167]) ).
cnf(refute_0_1169,plain,
( equiv(not(X),X_30) != not(implies(or(X,X_30),and(X_30,X)))
| not(implies(or(X,X_30),and(X_30,X))) = equiv(not(X),X_30) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(not(X),X_30))),bind(Y0,$fot(not(implies(or(X,X_30),and(X_30,X)))))]]) ).
cnf(refute_0_1170,plain,
not(implies(or(X,X_30),and(X_30,X))) = equiv(not(X),X_30),
inference(resolve,[$cnf( $equal(equiv(not(X),X_30),not(implies(or(X,X_30),and(X_30,X)))) )],[refute_0_1168,refute_0_1169]) ).
cnf(refute_0_1171,plain,
( implies(or(X,X_30),and(X_30,X)) != not(not(implies(or(X,X_30),and(X_30,X))))
| not(implies(or(X,X_30),and(X_30,X))) != equiv(not(X),X_30)
| implies(or(X,X_30),and(X_30,X)) = not(equiv(not(X),X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X,X_30),and(X_30,X)),not(not(implies(or(X,X_30),and(X_30,X))))) ),[1,0],$fot(equiv(not(X),X_30))]]) ).
cnf(refute_0_1172,plain,
( implies(or(X,X_30),and(X_30,X)) != not(not(implies(or(X,X_30),and(X_30,X))))
| implies(or(X,X_30),and(X_30,X)) = not(equiv(not(X),X_30)) ),
inference(resolve,[$cnf( $equal(not(implies(or(X,X_30),and(X_30,X))),equiv(not(X),X_30)) )],[refute_0_1170,refute_0_1171]) ).
cnf(refute_0_1173,plain,
implies(or(X,X_30),and(X_30,X)) = not(equiv(not(X),X_30)),
inference(resolve,[$cnf( $equal(implies(or(X,X_30),and(X_30,X)),not(not(implies(or(X,X_30),and(X_30,X))))) )],[refute_0_1153,refute_0_1172]) ).
cnf(refute_0_1174,plain,
implies(or(X_16592,or(X_16591,not(X_16592))),and(or(X_16591,not(X_16592)),X_16592)) = not(equiv(not(X_16592),or(X_16591,not(X_16592)))),
inference(subst,[],[refute_0_1173:[bind(X,$fot(X_16592)),bind(X_30,$fot(or(X_16591,not(X_16592))))]]) ).
cnf(refute_0_1175,plain,
( implies(or(X_16592,or(X_16591,not(X_16592))),and(or(X_16591,not(X_16592)),X_16592)) != not(equiv(not(X_16592),or(X_16591,not(X_16592))))
| ~ is_a_theorem(implies(implies(or(X_16592,or(X_16591,not(X_16592))),and(or(X_16591,not(X_16592)),X_16592)),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591)))
| is_a_theorem(implies(not(equiv(not(X_16592),or(X_16591,not(X_16592)))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(or(X_16592,or(X_16591,not(X_16592))),and(or(X_16591,not(X_16592)),X_16592)),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591))) ),[0,0],$fot(not(equiv(not(X_16592),or(X_16591,not(X_16592)))))]]) ).
cnf(refute_0_1176,plain,
( ~ is_a_theorem(implies(implies(or(X_16592,or(X_16591,not(X_16592))),and(or(X_16591,not(X_16592)),X_16592)),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591)))
| is_a_theorem(implies(not(equiv(not(X_16592),or(X_16591,not(X_16592)))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591))) ),
inference(resolve,[$cnf( $equal(implies(or(X_16592,or(X_16591,not(X_16592))),and(or(X_16591,not(X_16592)),X_16592)),not(equiv(not(X_16592),or(X_16591,not(X_16592))))) )],[refute_0_1174,refute_0_1175]) ).
cnf(refute_0_1177,plain,
is_a_theorem(implies(not(equiv(not(X_16592),or(X_16591,not(X_16592)))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_16592,or(X_16591,not(X_16592))),and(or(X_16591,not(X_16592)),X_16592)),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591))) )],[refute_0_1152,refute_0_1176]) ).
cnf(refute_0_1178,plain,
implies(not(equiv(not(X_16592),or(X_16591,not(X_16592)))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591)) = or(equiv(not(X_16592),or(X_16591,not(X_16592))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591)),
inference(subst,[],[refute_0_159:[bind(X,$fot(equiv(not(X_16592),or(X_16591,not(X_16592))))),bind(Y,$fot(implies(or(X_16592,or(X_16591,not(X_16592))),X_16591)))]]) ).
cnf(refute_0_1179,plain,
( implies(not(equiv(not(X_16592),or(X_16591,not(X_16592)))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591)) != or(equiv(not(X_16592),or(X_16591,not(X_16592))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591))
| ~ is_a_theorem(implies(not(equiv(not(X_16592),or(X_16591,not(X_16592)))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591)))
| is_a_theorem(or(equiv(not(X_16592),or(X_16591,not(X_16592))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(equiv(not(X_16592),or(X_16591,not(X_16592)))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591))) ),[0],$fot(or(equiv(not(X_16592),or(X_16591,not(X_16592))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591)))]]) ).
cnf(refute_0_1180,plain,
( ~ is_a_theorem(implies(not(equiv(not(X_16592),or(X_16591,not(X_16592)))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591)))
| is_a_theorem(or(equiv(not(X_16592),or(X_16591,not(X_16592))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591))) ),
inference(resolve,[$cnf( $equal(implies(not(equiv(not(X_16592),or(X_16591,not(X_16592)))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591)),or(equiv(not(X_16592),or(X_16591,not(X_16592))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591))) )],[refute_0_1178,refute_0_1179]) ).
cnf(refute_0_1181,plain,
is_a_theorem(or(equiv(not(X_16592),or(X_16591,not(X_16592))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591))),
inference(resolve,[$cnf( is_a_theorem(implies(not(equiv(not(X_16592),or(X_16591,not(X_16592)))),implies(or(X_16592,or(X_16591,not(X_16592))),X_16591))) )],[refute_0_1177,refute_0_1180]) ).
cnf(refute_0_1182,plain,
is_a_theorem(or(equiv(not(X_17382),or(X_17381,not(X_17382))),implies(or(X_17382,or(X_17381,not(X_17382))),X_17381))),
inference(subst,[],[refute_0_1181:[bind(X_16591,$fot(X_17381)),bind(X_16592,$fot(X_17382))]]) ).
cnf(refute_0_1183,plain,
is_a_theorem(implies(or(X_17382,or(X_17381,not(X_17382))),or(equiv(not(X_17382),or(X_17381,not(X_17382))),X_17381))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(not(X_17382),or(X_17381,not(X_17382))),implies(or(X_17382,or(X_17381,not(X_17382))),X_17381))) )],[refute_0_1182,refute_0_1134]) ).
cnf(refute_0_1184,plain,
is_a_theorem(implies(or(X_31162,or(X_31161,not(X_31162))),or(equiv(not(X_31162),or(X_31161,not(X_31162))),X_31161))),
inference(subst,[],[refute_0_1183:[bind(X_17381,$fot(X_31161)),bind(X_17382,$fot(X_31162))]]) ).
cnf(refute_0_1185,plain,
( ~ is_a_theorem(or(X_31162,or(X_31161,not(X_31162))))
| is_a_theorem(or(equiv(not(X_31162),or(X_31161,not(X_31162))),X_31161)) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_31162,or(X_31161,not(X_31162))),or(equiv(not(X_31162),or(X_31161,not(X_31162))),X_31161))) )],[refute_0_1184,refute_0_1133]) ).
cnf(refute_0_1186,plain,
is_a_theorem(or(X_13,implies(not(X),not(X_13)))),
inference(subst,[],[refute_0_268:[bind(X,$fot(not(X))),bind(X_10,$fot(X_13))]]) ).
cnf(refute_0_1187,plain,
or(X,not(X_13)) = implies(not(X),not(X_13)),
inference(subst,[],[refute_0_60:[bind(Y,$fot(not(X_13)))]]) ).
cnf(refute_0_1188,plain,
( or(X,not(X_13)) != implies(not(X),not(X_13))
| implies(not(X),not(X_13)) = or(X,not(X_13)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,not(X_13)))),bind(Y0,$fot(implies(not(X),not(X_13))))]]) ).
cnf(refute_0_1189,plain,
implies(not(X),not(X_13)) = or(X,not(X_13)),
inference(resolve,[$cnf( $equal(or(X,not(X_13)),implies(not(X),not(X_13))) )],[refute_0_1187,refute_0_1188]) ).
cnf(refute_0_1190,plain,
( implies(not(X),not(X_13)) != or(X,not(X_13))
| ~ is_a_theorem(or(X_13,implies(not(X),not(X_13))))
| is_a_theorem(or(X_13,or(X,not(X_13)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_13,implies(not(X),not(X_13)))) ),[0,1],$fot(or(X,not(X_13)))]]) ).
cnf(refute_0_1191,plain,
( ~ is_a_theorem(or(X_13,implies(not(X),not(X_13))))
| is_a_theorem(or(X_13,or(X,not(X_13)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X_13)),or(X,not(X_13))) )],[refute_0_1189,refute_0_1190]) ).
cnf(refute_0_1192,plain,
is_a_theorem(or(X_13,or(X,not(X_13)))),
inference(resolve,[$cnf( is_a_theorem(or(X_13,implies(not(X),not(X_13)))) )],[refute_0_1186,refute_0_1191]) ).
cnf(refute_0_1193,plain,
is_a_theorem(or(X_31162,or(X_31161,not(X_31162)))),
inference(subst,[],[refute_0_1192:[bind(X,$fot(X_31161)),bind(X_13,$fot(X_31162))]]) ).
cnf(refute_0_1194,plain,
is_a_theorem(or(equiv(not(X_31162),or(X_31161,not(X_31162))),X_31161)),
inference(resolve,[$cnf( is_a_theorem(or(X_31162,or(X_31161,not(X_31162)))) )],[refute_0_1193,refute_0_1185]) ).
cnf(refute_0_1195,plain,
is_a_theorem(or(equiv(not(or(X,X_29)),or(and(X_29,X),not(or(X,X_29)))),and(X_29,X))),
inference(subst,[],[refute_0_1194:[bind(X_31161,$fot(and(X_29,X))),bind(X_31162,$fot(or(X,X_29)))]]) ).
cnf(refute_0_1196,plain,
implies(not(and(X_29,X)),not(or(X,X_29))) = not(and(not(and(X_29,X)),or(X,X_29))),
inference(subst,[],[refute_0_987:[bind(Y,$fot(or(X,X_29))),bind(X_9551,$fot(not(and(X_29,X))))]]) ).
cnf(refute_0_1197,plain,
( and(not(and(X_29,X)),or(X,X_29)) != equiv(X_29,not(X))
| implies(not(and(X_29,X)),not(or(X,X_29))) != not(and(not(and(X_29,X)),or(X,X_29)))
| implies(not(and(X_29,X)),not(or(X,X_29))) = not(equiv(X_29,not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(and(X_29,X)),not(or(X,X_29))),not(and(not(and(X_29,X)),or(X,X_29)))) ),[1,0],$fot(equiv(X_29,not(X)))]]) ).
cnf(refute_0_1198,plain,
( implies(not(and(X_29,X)),not(or(X,X_29))) != not(and(not(and(X_29,X)),or(X,X_29)))
| implies(not(and(X_29,X)),not(or(X,X_29))) = not(equiv(X_29,not(X))) ),
inference(resolve,[$cnf( $equal(and(not(and(X_29,X)),or(X,X_29)),equiv(X_29,not(X))) )],[refute_0_360,refute_0_1197]) ).
cnf(refute_0_1199,plain,
implies(not(and(X_29,X)),not(or(X,X_29))) = not(equiv(X_29,not(X))),
inference(resolve,[$cnf( $equal(implies(not(and(X_29,X)),not(or(X,X_29))),not(and(not(and(X_29,X)),or(X,X_29)))) )],[refute_0_1196,refute_0_1198]) ).
cnf(refute_0_1200,plain,
or(X,not(X_9554)) = implies(not(X),not(X_9554)),
inference(subst,[],[refute_0_60:[bind(Y,$fot(not(X_9554)))]]) ).
cnf(refute_0_1201,plain,
implies(not(X),not(X_9554)) = not(and(not(X),X_9554)),
inference(subst,[],[refute_0_987:[bind(Y,$fot(X_9554)),bind(X_9551,$fot(not(X)))]]) ).
cnf(refute_0_1202,plain,
( implies(not(X),not(X_9554)) != not(and(not(X),X_9554))
| or(X,not(X_9554)) != implies(not(X),not(X_9554))
| or(X,not(X_9554)) = not(and(not(X),X_9554)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(X_9554)),implies(not(X),not(X_9554))) ),[1],$fot(not(and(not(X),X_9554)))]]) ).
cnf(refute_0_1203,plain,
( or(X,not(X_9554)) != implies(not(X),not(X_9554))
| or(X,not(X_9554)) = not(and(not(X),X_9554)) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X_9554)),not(and(not(X),X_9554))) )],[refute_0_1201,refute_0_1202]) ).
cnf(refute_0_1204,plain,
or(X,not(X_9554)) = not(and(not(X),X_9554)),
inference(resolve,[$cnf( $equal(or(X,not(X_9554)),implies(not(X),not(X_9554))) )],[refute_0_1200,refute_0_1203]) ).
cnf(refute_0_1205,plain,
( or(X,not(X_9554)) != not(and(not(X),X_9554))
| not(and(not(X),X_9554)) = or(X,not(X_9554)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,not(X_9554)))),bind(Y0,$fot(not(and(not(X),X_9554))))]]) ).
cnf(refute_0_1206,plain,
not(and(not(X),X_9554)) = or(X,not(X_9554)),
inference(resolve,[$cnf( $equal(or(X,not(X_9554)),not(and(not(X),X_9554))) )],[refute_0_1204,refute_0_1205]) ).
cnf(refute_0_1207,plain,
not(and(not(and(X_29,X)),or(X,X_29))) = or(and(X_29,X),not(or(X,X_29))),
inference(subst,[],[refute_0_1206:[bind(X,$fot(and(X_29,X))),bind(X_9554,$fot(or(X,X_29)))]]) ).
cnf(refute_0_1208,plain,
( implies(not(and(X_29,X)),not(or(X,X_29))) != not(and(not(and(X_29,X)),or(X,X_29)))
| not(and(not(and(X_29,X)),or(X,X_29))) != or(and(X_29,X),not(or(X,X_29)))
| implies(not(and(X_29,X)),not(or(X,X_29))) = or(and(X_29,X),not(or(X,X_29))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(not(and(X_29,X)),not(or(X,X_29))))),bind(Y0,$fot(not(and(not(and(X_29,X)),or(X,X_29))))),bind(Z,$fot(or(and(X_29,X),not(or(X,X_29)))))]]) ).
cnf(refute_0_1209,plain,
( not(and(not(and(X_29,X)),or(X,X_29))) != or(and(X_29,X),not(or(X,X_29)))
| implies(not(and(X_29,X)),not(or(X,X_29))) = or(and(X_29,X),not(or(X,X_29))) ),
inference(resolve,[$cnf( $equal(implies(not(and(X_29,X)),not(or(X,X_29))),not(and(not(and(X_29,X)),or(X,X_29)))) )],[refute_0_1196,refute_0_1208]) ).
cnf(refute_0_1210,plain,
implies(not(and(X_29,X)),not(or(X,X_29))) = or(and(X_29,X),not(or(X,X_29))),
inference(resolve,[$cnf( $equal(not(and(not(and(X_29,X)),or(X,X_29))),or(and(X_29,X),not(or(X,X_29)))) )],[refute_0_1207,refute_0_1209]) ).
cnf(refute_0_1211,plain,
( implies(not(and(X_29,X)),not(or(X,X_29))) != not(equiv(X_29,not(X)))
| implies(not(and(X_29,X)),not(or(X,X_29))) != or(and(X_29,X),not(or(X,X_29)))
| or(and(X_29,X),not(or(X,X_29))) = not(equiv(X_29,not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(and(X_29,X)),not(or(X,X_29))),not(equiv(X_29,not(X)))) ),[0],$fot(or(and(X_29,X),not(or(X,X_29))))]]) ).
cnf(refute_0_1212,plain,
( implies(not(and(X_29,X)),not(or(X,X_29))) != not(equiv(X_29,not(X)))
| or(and(X_29,X),not(or(X,X_29))) = not(equiv(X_29,not(X))) ),
inference(resolve,[$cnf( $equal(implies(not(and(X_29,X)),not(or(X,X_29))),or(and(X_29,X),not(or(X,X_29)))) )],[refute_0_1210,refute_0_1211]) ).
cnf(refute_0_1213,plain,
or(and(X_29,X),not(or(X,X_29))) = not(equiv(X_29,not(X))),
inference(resolve,[$cnf( $equal(implies(not(and(X_29,X)),not(or(X,X_29))),not(equiv(X_29,not(X)))) )],[refute_0_1199,refute_0_1212]) ).
cnf(refute_0_1214,plain,
( or(and(X_29,X),not(or(X,X_29))) != not(equiv(X_29,not(X)))
| ~ is_a_theorem(or(equiv(not(or(X,X_29)),or(and(X_29,X),not(or(X,X_29)))),and(X_29,X)))
| is_a_theorem(or(equiv(not(or(X,X_29)),not(equiv(X_29,not(X)))),and(X_29,X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(equiv(not(or(X,X_29)),or(and(X_29,X),not(or(X,X_29)))),and(X_29,X))) ),[0,0,1],$fot(not(equiv(X_29,not(X))))]]) ).
cnf(refute_0_1215,plain,
( ~ is_a_theorem(or(equiv(not(or(X,X_29)),or(and(X_29,X),not(or(X,X_29)))),and(X_29,X)))
| is_a_theorem(or(equiv(not(or(X,X_29)),not(equiv(X_29,not(X)))),and(X_29,X))) ),
inference(resolve,[$cnf( $equal(or(and(X_29,X),not(or(X,X_29))),not(equiv(X_29,not(X)))) )],[refute_0_1213,refute_0_1214]) ).
cnf(refute_0_1216,plain,
is_a_theorem(or(equiv(not(or(X,X_29)),not(equiv(X_29,not(X)))),and(X_29,X))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(not(or(X,X_29)),or(and(X_29,X),not(or(X,X_29)))),and(X_29,X))) )],[refute_0_1195,refute_0_1215]) ).
cnf(refute_0_1217,plain,
is_a_theorem(or(equiv(not(or(X_31173,X_31174)),not(equiv(X_31174,not(X_31173)))),and(X_31174,X_31173))),
inference(subst,[],[refute_0_1216:[bind(X,$fot(X_31173)),bind(X_29,$fot(X_31174))]]) ).
cnf(refute_0_1218,plain,
is_a_theorem(or(and(X_31174,X_31173),equiv(not(or(X_31173,X_31174)),not(equiv(X_31174,not(X_31173)))))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(not(or(X_31173,X_31174)),not(equiv(X_31174,not(X_31173)))),and(X_31174,X_31173))) )],[refute_0_1217,refute_0_1132]) ).
cnf(refute_0_1219,plain,
is_a_theorem(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,not(not(X_10026))))))),
inference(subst,[],[refute_0_1218:[bind(X_31173,$fot(not(X_10026))),bind(X_31174,$fot(X_31182))]]) ).
cnf(refute_0_1220,plain,
is_a_theorem(equiv(X_10026,X_10026)),
inference(subst,[],[refute_0_526:[bind(X_4515,$fot(X_10026))]]) ).
cnf(refute_0_1221,plain,
( ~ is_a_theorem(equiv(X,not(not(X_137))))
| X = not(not(X_137)) ),
inference(subst,[],[refute_0_253:[bind(Y,$fot(not(not(X_137))))]]) ).
cnf(refute_0_1222,plain,
equiv(X,X_137) = equiv(X,not(not(X_137))),
inference(subst,[],[refute_0_830:[bind(X,$fot(X_137)),bind(X_35,$fot(X))]]) ).
cnf(refute_0_1223,plain,
( equiv(X,X_137) != equiv(X,not(not(X_137)))
| equiv(X,not(not(X_137))) = equiv(X,X_137) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(X,X_137))),bind(Y0,$fot(equiv(X,not(not(X_137)))))]]) ).
cnf(refute_0_1224,plain,
equiv(X,not(not(X_137))) = equiv(X,X_137),
inference(resolve,[$cnf( $equal(equiv(X,X_137),equiv(X,not(not(X_137)))) )],[refute_0_1222,refute_0_1223]) ).
cnf(refute_0_1225,plain,
( equiv(X,not(not(X_137))) != equiv(X,X_137)
| ~ is_a_theorem(equiv(X,X_137))
| is_a_theorem(equiv(X,not(not(X_137)))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(equiv(X,not(not(X_137)))) ),[0],$fot(equiv(X,X_137))]]) ).
cnf(refute_0_1226,plain,
( ~ is_a_theorem(equiv(X,X_137))
| is_a_theorem(equiv(X,not(not(X_137)))) ),
inference(resolve,[$cnf( $equal(equiv(X,not(not(X_137))),equiv(X,X_137)) )],[refute_0_1224,refute_0_1225]) ).
cnf(refute_0_1227,plain,
( ~ is_a_theorem(equiv(X,X_137))
| X = not(not(X_137)) ),
inference(resolve,[$cnf( is_a_theorem(equiv(X,not(not(X_137)))) )],[refute_0_1226,refute_0_1221]) ).
cnf(refute_0_1228,plain,
( ~ is_a_theorem(equiv(X_10026,X_10026))
| X_10026 = not(not(X_10026)) ),
inference(subst,[],[refute_0_1227:[bind(X,$fot(X_10026)),bind(X_137,$fot(X_10026))]]) ).
cnf(refute_0_1229,plain,
X_10026 = not(not(X_10026)),
inference(resolve,[$cnf( is_a_theorem(equiv(X_10026,X_10026)) )],[refute_0_1220,refute_0_1228]) ).
cnf(refute_0_1230,plain,
( X_10026 != not(not(X_10026))
| not(not(X_10026)) = X_10026 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(X_10026)),bind(Y0,$fot(not(not(X_10026))))]]) ).
cnf(refute_0_1231,plain,
not(not(X_10026)) = X_10026,
inference(resolve,[$cnf( $equal(X_10026,not(not(X_10026))) )],[refute_0_1229,refute_0_1230]) ).
cnf(refute_0_1232,plain,
( not(not(X_10026)) != X_10026
| ~ is_a_theorem(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,not(not(X_10026)))))))
| is_a_theorem(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,not(not(X_10026))))))) ),[0,1,1,0,1],$fot(X_10026)]]) ).
cnf(refute_0_1233,plain,
( ~ is_a_theorem(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,not(not(X_10026)))))))
| is_a_theorem(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))))) ),
inference(resolve,[$cnf( $equal(not(not(X_10026)),X_10026) )],[refute_0_1231,refute_0_1232]) ).
cnf(refute_0_1234,plain,
is_a_theorem(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,not(not(X_10026))))))) )],[refute_0_1219,refute_0_1233]) ).
cnf(refute_0_1235,plain,
or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))) = implies(implies(X_31182,X_10026),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))),
inference(subst,[],[refute_0_20:[bind(X,$fot(implies(X_31182,X_10026))),bind(Y,$fot(equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))))]]) ).
cnf(refute_0_1236,plain,
or(not(X_10026),X_31182) = implies(X_10026,X_31182),
inference(subst,[],[refute_0_20:[bind(X,$fot(X_10026)),bind(Y,$fot(X_31182))]]) ).
cnf(refute_0_1237,plain,
not(or(not(X_10026),X_31182)) = not(or(not(X_10026),X_31182)),
introduced(tautology,[refl,[$fot(not(or(not(X_10026),X_31182)))]]) ).
cnf(refute_0_1238,plain,
( not(or(not(X_10026),X_31182)) != not(or(not(X_10026),X_31182))
| or(not(X_10026),X_31182) != implies(X_10026,X_31182)
| not(or(not(X_10026),X_31182)) = not(implies(X_10026,X_31182)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X_10026),X_31182)),not(or(not(X_10026),X_31182))) ),[1,0],$fot(implies(X_10026,X_31182))]]) ).
cnf(refute_0_1239,plain,
( or(not(X_10026),X_31182) != implies(X_10026,X_31182)
| not(or(not(X_10026),X_31182)) = not(implies(X_10026,X_31182)) ),
inference(resolve,[$cnf( $equal(not(or(not(X_10026),X_31182)),not(or(not(X_10026),X_31182))) )],[refute_0_1237,refute_0_1238]) ).
cnf(refute_0_1240,plain,
not(or(not(X_10026),X_31182)) = not(implies(X_10026,X_31182)),
inference(resolve,[$cnf( $equal(or(not(X_10026),X_31182),implies(X_10026,X_31182)) )],[refute_0_1236,refute_0_1239]) ).
cnf(refute_0_1241,plain,
equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))) = equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))),
introduced(tautology,[refl,[$fot(equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))))]]) ).
cnf(refute_0_1242,plain,
( equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))) != equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))
| not(or(not(X_10026),X_31182)) != not(implies(X_10026,X_31182))
| equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))) = equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) ),[1,0],$fot(not(implies(X_10026,X_31182)))]]) ).
cnf(refute_0_1243,plain,
( not(or(not(X_10026),X_31182)) != not(implies(X_10026,X_31182))
| equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))) = equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))) ),
inference(resolve,[$cnf( $equal(equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) )],[refute_0_1241,refute_0_1242]) ).
cnf(refute_0_1244,plain,
equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))) = equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))),
inference(resolve,[$cnf( $equal(not(or(not(X_10026),X_31182)),not(implies(X_10026,X_31182))) )],[refute_0_1240,refute_0_1243]) ).
cnf(refute_0_1245,plain,
or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) = or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))),
introduced(tautology,[refl,[$fot(or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))))]]) ).
cnf(refute_0_1246,plain,
( equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))) != equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))
| or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) != or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))))
| or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) = or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))),or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))))) ),[1,1],$fot(equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))))]]) ).
cnf(refute_0_1247,plain,
( equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))) != equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))
| or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) = or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))) ),
inference(resolve,[$cnf( $equal(or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))),or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))))) )],[refute_0_1245,refute_0_1246]) ).
cnf(refute_0_1248,plain,
or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) = or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))),
inference(resolve,[$cnf( $equal(equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))) )],[refute_0_1244,refute_0_1247]) ).
cnf(refute_0_1249,plain,
and(X_31182,not(X_10026)) = not(implies(X_31182,X_10026)),
inference(subst,[],[refute_0_972:[bind(X,$fot(X_31182)),bind(X_9550,$fot(X_10026))]]) ).
cnf(refute_0_1250,plain,
or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) = or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))),
introduced(tautology,[refl,[$fot(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))))]]) ).
cnf(refute_0_1251,plain,
( and(X_31182,not(X_10026)) != not(implies(X_31182,X_10026))
| or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) != or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))))
| or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) = or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))),or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))))) ),[1,0],$fot(not(implies(X_31182,X_10026)))]]) ).
cnf(refute_0_1252,plain,
( and(X_31182,not(X_10026)) != not(implies(X_31182,X_10026))
| or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) = or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) ),
inference(resolve,[$cnf( $equal(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))),or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))))) )],[refute_0_1250,refute_0_1251]) ).
cnf(refute_0_1253,plain,
or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) = or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))),
inference(resolve,[$cnf( $equal(and(X_31182,not(X_10026)),not(implies(X_31182,X_10026))) )],[refute_0_1249,refute_0_1252]) ).
cnf(refute_0_1254,plain,
( or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) != or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))))
| or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) != or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))))
| or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) = or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))))),bind(Y0,$fot(or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))))),bind(Z,$fot(or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))))))]]) ).
cnf(refute_0_1255,plain,
( or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) != or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))))
| or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) = or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))) ),
inference(resolve,[$cnf( $equal(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))),or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))))) )],[refute_0_1253,refute_0_1254]) ).
cnf(refute_0_1256,plain,
or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) = or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))),
inference(resolve,[$cnf( $equal(or(not(implies(X_31182,X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))),or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))))) )],[refute_0_1248,refute_0_1255]) ).
cnf(refute_0_1257,plain,
( or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) != or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))))
| or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))) != implies(implies(X_31182,X_10026),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))))
| or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) = implies(implies(X_31182,X_10026),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))))),bind(Y0,$fot(or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))))),bind(Z,$fot(implies(implies(X_31182,X_10026),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))))))]]) ).
cnf(refute_0_1258,plain,
( or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))) != implies(implies(X_31182,X_10026),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))))
| or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) = implies(implies(X_31182,X_10026),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))) ),
inference(resolve,[$cnf( $equal(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))),or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))))) )],[refute_0_1256,refute_0_1257]) ).
cnf(refute_0_1259,plain,
or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) = implies(implies(X_31182,X_10026),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))),
inference(resolve,[$cnf( $equal(or(not(implies(X_31182,X_10026)),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))),implies(implies(X_31182,X_10026),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))))) )],[refute_0_1235,refute_0_1258]) ).
cnf(refute_0_1260,plain,
( or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))) != implies(implies(X_31182,X_10026),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))))
| ~ is_a_theorem(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))))
| is_a_theorem(implies(implies(X_31182,X_10026),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))))) ),[0],$fot(implies(implies(X_31182,X_10026),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026)))))]]) ).
cnf(refute_0_1261,plain,
( ~ is_a_theorem(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))))
| is_a_theorem(implies(implies(X_31182,X_10026),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))))) ),
inference(resolve,[$cnf( $equal(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026)))),implies(implies(X_31182,X_10026),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))))) )],[refute_0_1259,refute_0_1260]) ).
cnf(refute_0_1262,plain,
is_a_theorem(implies(implies(X_31182,X_10026),equiv(not(implies(X_10026,X_31182)),not(equiv(X_31182,X_10026))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_31182,not(X_10026)),equiv(not(or(not(X_10026),X_31182)),not(equiv(X_31182,X_10026))))) )],[refute_0_1234,refute_0_1261]) ).
cnf(refute_0_1263,plain,
is_a_theorem(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(equiv(not(X_31183),X_31183))))),
inference(subst,[],[refute_0_1262:[bind(X_10026,$fot(X_31183)),bind(X_31182,$fot(not(X_31183)))]]) ).
cnf(refute_0_1264,plain,
equiv(not(X_25350),X_25350) = not(not(equiv(not(X_25350),X_25350))),
inference(subst,[],[refute_0_1229:[bind(X_10026,$fot(equiv(not(X_25350),X_25350)))]]) ).
cnf(refute_0_1265,plain,
implies(or(X_30,X_30),and(X_30,X_30)) = not(equiv(not(X_30),X_30)),
inference(subst,[],[refute_0_1173:[bind(X,$fot(X_30))]]) ).
cnf(refute_0_1266,plain,
X_30 = or(X_30,X_30),
inference(subst,[],[refute_0_1114:[bind(X_25347,$fot(X_30))]]) ).
cnf(refute_0_1267,plain,
( X_30 != or(X_30,X_30)
| or(X_30,X_30) = X_30 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(X_30)),bind(Y0,$fot(or(X_30,X_30)))]]) ).
cnf(refute_0_1268,plain,
or(X_30,X_30) = X_30,
inference(resolve,[$cnf( $equal(X_30,or(X_30,X_30)) )],[refute_0_1266,refute_0_1267]) ).
cnf(refute_0_1269,plain,
( implies(or(X_30,X_30),and(X_30,X_30)) != not(equiv(not(X_30),X_30))
| or(X_30,X_30) != X_30
| implies(X_30,and(X_30,X_30)) = not(equiv(not(X_30),X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_30,X_30),and(X_30,X_30)),not(equiv(not(X_30),X_30))) ),[0,0],$fot(X_30)]]) ).
cnf(refute_0_1270,plain,
( implies(or(X_30,X_30),and(X_30,X_30)) != not(equiv(not(X_30),X_30))
| implies(X_30,and(X_30,X_30)) = not(equiv(not(X_30),X_30)) ),
inference(resolve,[$cnf( $equal(or(X_30,X_30),X_30) )],[refute_0_1268,refute_0_1269]) ).
cnf(refute_0_1271,plain,
implies(X_30,and(X_30,X_30)) = not(equiv(not(X_30),X_30)),
inference(resolve,[$cnf( $equal(implies(or(X_30,X_30),and(X_30,X_30)),not(equiv(not(X_30),X_30))) )],[refute_0_1265,refute_0_1270]) ).
cnf(refute_0_1272,plain,
and(not(not(X_17)),X_17) = not(or(not(X_17),not(X_17))),
inference(subst,[],[refute_0_186:[bind(X,$fot(not(X_17)))]]) ).
cnf(refute_0_1273,plain,
not(X_17) = or(not(X_17),not(X_17)),
inference(subst,[],[refute_0_1114:[bind(X_25347,$fot(not(X_17)))]]) ).
cnf(refute_0_1274,plain,
( not(X_17) != or(not(X_17),not(X_17))
| or(not(X_17),not(X_17)) = not(X_17) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(X_17))),bind(Y0,$fot(or(not(X_17),not(X_17))))]]) ).
cnf(refute_0_1275,plain,
or(not(X_17),not(X_17)) = not(X_17),
inference(resolve,[$cnf( $equal(not(X_17),or(not(X_17),not(X_17))) )],[refute_0_1273,refute_0_1274]) ).
cnf(refute_0_1276,plain,
( and(not(not(X_17)),X_17) != not(or(not(X_17),not(X_17)))
| or(not(X_17),not(X_17)) != not(X_17)
| and(not(not(X_17)),X_17) = not(not(X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X_17)),X_17),not(or(not(X_17),not(X_17)))) ),[1,0],$fot(not(X_17))]]) ).
cnf(refute_0_1277,plain,
( and(not(not(X_17)),X_17) != not(or(not(X_17),not(X_17)))
| and(not(not(X_17)),X_17) = not(not(X_17)) ),
inference(resolve,[$cnf( $equal(or(not(X_17),not(X_17)),not(X_17)) )],[refute_0_1275,refute_0_1276]) ).
cnf(refute_0_1278,plain,
and(not(not(X_17)),X_17) = not(not(X_17)),
inference(resolve,[$cnf( $equal(and(not(not(X_17)),X_17),not(or(not(X_17),not(X_17)))) )],[refute_0_1272,refute_0_1277]) ).
cnf(refute_0_1279,plain,
not(not(X_17)) = X_17,
inference(subst,[],[refute_0_1231:[bind(X_10026,$fot(X_17))]]) ).
cnf(refute_0_1280,plain,
and(not(not(X_17)),X_17) = and(not(not(X_17)),X_17),
introduced(tautology,[refl,[$fot(and(not(not(X_17)),X_17))]]) ).
cnf(refute_0_1281,plain,
( and(not(not(X_17)),X_17) != and(not(not(X_17)),X_17)
| not(not(X_17)) != X_17
| and(not(not(X_17)),X_17) = and(X_17,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X_17)),X_17),and(not(not(X_17)),X_17)) ),[1,0],$fot(X_17)]]) ).
cnf(refute_0_1282,plain,
( not(not(X_17)) != X_17
| and(not(not(X_17)),X_17) = and(X_17,X_17) ),
inference(resolve,[$cnf( $equal(and(not(not(X_17)),X_17),and(not(not(X_17)),X_17)) )],[refute_0_1280,refute_0_1281]) ).
cnf(refute_0_1283,plain,
and(not(not(X_17)),X_17) = and(X_17,X_17),
inference(resolve,[$cnf( $equal(not(not(X_17)),X_17) )],[refute_0_1279,refute_0_1282]) ).
cnf(refute_0_1284,plain,
( and(not(not(X_17)),X_17) != and(X_17,X_17)
| and(not(not(X_17)),X_17) != not(not(X_17))
| and(X_17,X_17) = not(not(X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X_17)),X_17),not(not(X_17))) ),[0],$fot(and(X_17,X_17))]]) ).
cnf(refute_0_1285,plain,
( and(not(not(X_17)),X_17) != not(not(X_17))
| and(X_17,X_17) = not(not(X_17)) ),
inference(resolve,[$cnf( $equal(and(not(not(X_17)),X_17),and(X_17,X_17)) )],[refute_0_1283,refute_0_1284]) ).
cnf(refute_0_1286,plain,
( and(X_17,X_17) != not(not(X_17))
| not(not(X_17)) != X_17
| and(X_17,X_17) = X_17 ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_17,X_17),X_17) ),[0],$fot(not(not(X_17)))]]) ).
cnf(refute_0_1287,plain,
( and(X_17,X_17) != not(not(X_17))
| and(X_17,X_17) = X_17 ),
inference(resolve,[$cnf( $equal(not(not(X_17)),X_17) )],[refute_0_1279,refute_0_1286]) ).
cnf(refute_0_1288,plain,
( and(not(not(X_17)),X_17) != not(not(X_17))
| and(X_17,X_17) = X_17 ),
inference(resolve,[$cnf( $equal(and(X_17,X_17),not(not(X_17))) )],[refute_0_1285,refute_0_1287]) ).
cnf(refute_0_1289,plain,
and(X_17,X_17) = X_17,
inference(resolve,[$cnf( $equal(and(not(not(X_17)),X_17),not(not(X_17))) )],[refute_0_1278,refute_0_1288]) ).
cnf(refute_0_1290,plain,
and(X_30,X_30) = X_30,
inference(subst,[],[refute_0_1289:[bind(X_17,$fot(X_30))]]) ).
cnf(refute_0_1291,plain,
implies(X_30,and(X_30,X_30)) = implies(X_30,and(X_30,X_30)),
introduced(tautology,[refl,[$fot(implies(X_30,and(X_30,X_30)))]]) ).
cnf(refute_0_1292,plain,
( and(X_30,X_30) != X_30
| implies(X_30,and(X_30,X_30)) != implies(X_30,and(X_30,X_30))
| implies(X_30,and(X_30,X_30)) = implies(X_30,X_30) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_30,and(X_30,X_30)),implies(X_30,and(X_30,X_30))) ),[1,1],$fot(X_30)]]) ).
cnf(refute_0_1293,plain,
( and(X_30,X_30) != X_30
| implies(X_30,and(X_30,X_30)) = implies(X_30,X_30) ),
inference(resolve,[$cnf( $equal(implies(X_30,and(X_30,X_30)),implies(X_30,and(X_30,X_30))) )],[refute_0_1291,refute_0_1292]) ).
cnf(refute_0_1294,plain,
implies(X_30,and(X_30,X_30)) = implies(X_30,X_30),
inference(resolve,[$cnf( $equal(and(X_30,X_30),X_30) )],[refute_0_1290,refute_0_1293]) ).
cnf(refute_0_1295,plain,
( implies(X_30,and(X_30,X_30)) != implies(X_30,X_30)
| implies(X_30,and(X_30,X_30)) != not(equiv(not(X_30),X_30))
| implies(X_30,X_30) = not(equiv(not(X_30),X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_30,and(X_30,X_30)),not(equiv(not(X_30),X_30))) ),[0],$fot(implies(X_30,X_30))]]) ).
cnf(refute_0_1296,plain,
( implies(X_30,and(X_30,X_30)) != not(equiv(not(X_30),X_30))
| implies(X_30,X_30) = not(equiv(not(X_30),X_30)) ),
inference(resolve,[$cnf( $equal(implies(X_30,and(X_30,X_30)),implies(X_30,X_30)) )],[refute_0_1294,refute_0_1295]) ).
cnf(refute_0_1297,plain,
implies(X_30,X_30) = not(equiv(not(X_30),X_30)),
inference(resolve,[$cnf( $equal(implies(X_30,and(X_30,X_30)),not(equiv(not(X_30),X_30))) )],[refute_0_1271,refute_0_1296]) ).
cnf(refute_0_1298,plain,
and(not(and(implies(X,Y),implies(Y,X))),or(implies(Y,X),implies(X,Y))) = equiv(implies(X,Y),not(implies(Y,X))),
inference(subst,[],[refute_0_360:[bind(X,$fot(implies(Y,X))),bind(X_29,$fot(implies(X,Y)))]]) ).
cnf(refute_0_1299,plain,
( and(implies(X,Y),implies(Y,X)) != equiv(X,Y)
| and(not(and(implies(X,Y),implies(Y,X))),or(implies(Y,X),implies(X,Y))) != equiv(implies(X,Y),not(implies(Y,X)))
| and(not(equiv(X,Y)),or(implies(Y,X),implies(X,Y))) = equiv(implies(X,Y),not(implies(Y,X))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(implies(X,Y),implies(Y,X))),or(implies(Y,X),implies(X,Y))),equiv(implies(X,Y),not(implies(Y,X)))) ),[0,0,0],$fot(equiv(X,Y))]]) ).
cnf(refute_0_1300,plain,
( and(not(and(implies(X,Y),implies(Y,X))),or(implies(Y,X),implies(X,Y))) != equiv(implies(X,Y),not(implies(Y,X)))
| and(not(equiv(X,Y)),or(implies(Y,X),implies(X,Y))) = equiv(implies(X,Y),not(implies(Y,X))) ),
inference(resolve,[$cnf( $equal(and(implies(X,Y),implies(Y,X)),equiv(X,Y)) )],[refute_0_402,refute_0_1299]) ).
cnf(refute_0_1301,plain,
and(not(equiv(X,Y)),or(implies(Y,X),implies(X,Y))) = equiv(implies(X,Y),not(implies(Y,X))),
inference(resolve,[$cnf( $equal(and(not(and(implies(X,Y),implies(Y,X))),or(implies(Y,X),implies(X,Y))),equiv(implies(X,Y),not(implies(Y,X)))) )],[refute_0_1298,refute_0_1300]) ).
cnf(refute_0_1302,plain,
and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),implies(not(X),X_1079))) = equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))),
inference(subst,[],[refute_0_1301:[bind(X,$fot(not(X))),bind(Y,$fot(X_1079))]]) ).
cnf(refute_0_1303,plain,
or(X,X_1079) = implies(not(X),X_1079),
inference(subst,[],[refute_0_60:[bind(Y,$fot(X_1079))]]) ).
cnf(refute_0_1304,plain,
( or(X,X_1079) != implies(not(X),X_1079)
| implies(not(X),X_1079) = or(X,X_1079) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,X_1079))),bind(Y0,$fot(implies(not(X),X_1079)))]]) ).
cnf(refute_0_1305,plain,
implies(not(X),X_1079) = or(X,X_1079),
inference(resolve,[$cnf( $equal(or(X,X_1079),implies(not(X),X_1079)) )],[refute_0_1303,refute_0_1304]) ).
cnf(refute_0_1306,plain,
( and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),implies(not(X),X_1079))) != equiv(implies(not(X),X_1079),not(implies(X_1079,not(X))))
| implies(not(X),X_1079) != or(X,X_1079)
| and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))) = equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),implies(not(X),X_1079))),equiv(implies(not(X),X_1079),not(implies(X_1079,not(X))))) ),[0,1,1],$fot(or(X,X_1079))]]) ).
cnf(refute_0_1307,plain,
( and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),implies(not(X),X_1079))) != equiv(implies(not(X),X_1079),not(implies(X_1079,not(X))))
| and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))) = equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_1079),or(X,X_1079)) )],[refute_0_1305,refute_0_1306]) ).
cnf(refute_0_1308,plain,
and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))) = equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),implies(not(X),X_1079))),equiv(implies(not(X),X_1079),not(implies(X_1079,not(X))))) )],[refute_0_1302,refute_0_1307]) ).
cnf(refute_0_1309,plain,
or(implies(X_1079,not(X)),or(X,X_1079)) = implies(and(X_1079,X),or(X,X_1079)),
inference(subst,[],[refute_0_467:[bind(Y,$fot(or(X,X_1079))),bind(X_16,$fot(X_1079)),bind(X_17,$fot(X))]]) ).
cnf(refute_0_1310,plain,
and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))) = and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))),
introduced(tautology,[refl,[$fot(and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))))]]) ).
cnf(refute_0_1311,plain,
( and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))) != and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079)))
| or(implies(X_1079,not(X)),or(X,X_1079)) != implies(and(X_1079,X),or(X,X_1079))
| and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))) = and(not(equiv(not(X),X_1079)),implies(and(X_1079,X),or(X,X_1079))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))),and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079)))) ),[1,1],$fot(implies(and(X_1079,X),or(X,X_1079)))]]) ).
cnf(refute_0_1312,plain,
( or(implies(X_1079,not(X)),or(X,X_1079)) != implies(and(X_1079,X),or(X,X_1079))
| and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))) = and(not(equiv(not(X),X_1079)),implies(and(X_1079,X),or(X,X_1079))) ),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))),and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079)))) )],[refute_0_1310,refute_0_1311]) ).
cnf(refute_0_1313,plain,
and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))) = and(not(equiv(not(X),X_1079)),implies(and(X_1079,X),or(X,X_1079))),
inference(resolve,[$cnf( $equal(or(implies(X_1079,not(X)),or(X,X_1079)),implies(and(X_1079,X),or(X,X_1079))) )],[refute_0_1309,refute_0_1312]) ).
cnf(refute_0_1314,plain,
( and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))) != and(not(equiv(not(X),X_1079)),implies(and(X_1079,X),or(X,X_1079)))
| and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))) != equiv(implies(not(X),X_1079),not(implies(X_1079,not(X))))
| and(not(equiv(not(X),X_1079)),implies(and(X_1079,X),or(X,X_1079))) = equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))),equiv(implies(not(X),X_1079),not(implies(X_1079,not(X))))) ),[0],$fot(and(not(equiv(not(X),X_1079)),implies(and(X_1079,X),or(X,X_1079))))]]) ).
cnf(refute_0_1315,plain,
( and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))) != equiv(implies(not(X),X_1079),not(implies(X_1079,not(X))))
| and(not(equiv(not(X),X_1079)),implies(and(X_1079,X),or(X,X_1079))) = equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))) ),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))),and(not(equiv(not(X),X_1079)),implies(and(X_1079,X),or(X,X_1079)))) )],[refute_0_1313,refute_0_1314]) ).
cnf(refute_0_1316,plain,
not(implies(X_1079,not(X))) = and(X_1079,X),
inference(subst,[],[refute_0_195:[bind(X,$fot(X_1079)),bind(Y,$fot(X))]]) ).
cnf(refute_0_1317,plain,
equiv(or(X,X_1079),not(implies(X_1079,not(X)))) = equiv(or(X,X_1079),not(implies(X_1079,not(X)))),
introduced(tautology,[refl,[$fot(equiv(or(X,X_1079),not(implies(X_1079,not(X)))))]]) ).
cnf(refute_0_1318,plain,
( equiv(or(X,X_1079),not(implies(X_1079,not(X)))) != equiv(or(X,X_1079),not(implies(X_1079,not(X))))
| not(implies(X_1079,not(X))) != and(X_1079,X)
| equiv(or(X,X_1079),not(implies(X_1079,not(X)))) = equiv(or(X,X_1079),and(X_1079,X)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(or(X,X_1079),not(implies(X_1079,not(X)))),equiv(or(X,X_1079),not(implies(X_1079,not(X))))) ),[1,1],$fot(and(X_1079,X))]]) ).
cnf(refute_0_1319,plain,
( not(implies(X_1079,not(X))) != and(X_1079,X)
| equiv(or(X,X_1079),not(implies(X_1079,not(X)))) = equiv(or(X,X_1079),and(X_1079,X)) ),
inference(resolve,[$cnf( $equal(equiv(or(X,X_1079),not(implies(X_1079,not(X)))),equiv(or(X,X_1079),not(implies(X_1079,not(X))))) )],[refute_0_1317,refute_0_1318]) ).
cnf(refute_0_1320,plain,
equiv(or(X,X_1079),not(implies(X_1079,not(X)))) = equiv(or(X,X_1079),and(X_1079,X)),
inference(resolve,[$cnf( $equal(not(implies(X_1079,not(X))),and(X_1079,X)) )],[refute_0_1316,refute_0_1319]) ).
cnf(refute_0_1321,plain,
equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))) = equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))),
introduced(tautology,[refl,[$fot(equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))))]]) ).
cnf(refute_0_1322,plain,
( equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))) != equiv(implies(not(X),X_1079),not(implies(X_1079,not(X))))
| implies(not(X),X_1079) != or(X,X_1079)
| equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))) = equiv(or(X,X_1079),not(implies(X_1079,not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))),equiv(implies(not(X),X_1079),not(implies(X_1079,not(X))))) ),[1,0],$fot(or(X,X_1079))]]) ).
cnf(refute_0_1323,plain,
( implies(not(X),X_1079) != or(X,X_1079)
| equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))) = equiv(or(X,X_1079),not(implies(X_1079,not(X)))) ),
inference(resolve,[$cnf( $equal(equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))),equiv(implies(not(X),X_1079),not(implies(X_1079,not(X))))) )],[refute_0_1321,refute_0_1322]) ).
cnf(refute_0_1324,plain,
equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))) = equiv(or(X,X_1079),not(implies(X_1079,not(X)))),
inference(resolve,[$cnf( $equal(implies(not(X),X_1079),or(X,X_1079)) )],[refute_0_1305,refute_0_1323]) ).
cnf(refute_0_1325,plain,
( equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))) != equiv(or(X,X_1079),not(implies(X_1079,not(X))))
| equiv(or(X,X_1079),not(implies(X_1079,not(X)))) != equiv(or(X,X_1079),and(X_1079,X))
| equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))) = equiv(or(X,X_1079),and(X_1079,X)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))))),bind(Y0,$fot(equiv(or(X,X_1079),not(implies(X_1079,not(X)))))),bind(Z,$fot(equiv(or(X,X_1079),and(X_1079,X))))]]) ).
cnf(refute_0_1326,plain,
( equiv(or(X,X_1079),not(implies(X_1079,not(X)))) != equiv(or(X,X_1079),and(X_1079,X))
| equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))) = equiv(or(X,X_1079),and(X_1079,X)) ),
inference(resolve,[$cnf( $equal(equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))),equiv(or(X,X_1079),not(implies(X_1079,not(X))))) )],[refute_0_1324,refute_0_1325]) ).
cnf(refute_0_1327,plain,
equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))) = equiv(or(X,X_1079),and(X_1079,X)),
inference(resolve,[$cnf( $equal(equiv(or(X,X_1079),not(implies(X_1079,not(X)))),equiv(or(X,X_1079),and(X_1079,X))) )],[refute_0_1320,refute_0_1326]) ).
cnf(refute_0_1328,plain,
( and(not(equiv(not(X),X_1079)),implies(and(X_1079,X),or(X,X_1079))) != equiv(implies(not(X),X_1079),not(implies(X_1079,not(X))))
| equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))) != equiv(or(X,X_1079),and(X_1079,X))
| and(not(equiv(not(X),X_1079)),implies(and(X_1079,X),or(X,X_1079))) = equiv(or(X,X_1079),and(X_1079,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(not(equiv(not(X),X_1079)),implies(and(X_1079,X),or(X,X_1079))),equiv(or(X,X_1079),and(X_1079,X))) ),[0],$fot(equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))))]]) ).
cnf(refute_0_1329,plain,
( and(not(equiv(not(X),X_1079)),implies(and(X_1079,X),or(X,X_1079))) != equiv(implies(not(X),X_1079),not(implies(X_1079,not(X))))
| and(not(equiv(not(X),X_1079)),implies(and(X_1079,X),or(X,X_1079))) = equiv(or(X,X_1079),and(X_1079,X)) ),
inference(resolve,[$cnf( $equal(equiv(implies(not(X),X_1079),not(implies(X_1079,not(X)))),equiv(or(X,X_1079),and(X_1079,X))) )],[refute_0_1327,refute_0_1328]) ).
cnf(refute_0_1330,plain,
( and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))) != equiv(implies(not(X),X_1079),not(implies(X_1079,not(X))))
| and(not(equiv(not(X),X_1079)),implies(and(X_1079,X),or(X,X_1079))) = equiv(or(X,X_1079),and(X_1079,X)) ),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X),X_1079)),implies(and(X_1079,X),or(X,X_1079))),equiv(implies(not(X),X_1079),not(implies(X_1079,not(X))))) )],[refute_0_1315,refute_0_1329]) ).
cnf(refute_0_1331,plain,
and(not(equiv(not(X),X_1079)),implies(and(X_1079,X),or(X,X_1079))) = equiv(or(X,X_1079),and(X_1079,X)),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X),X_1079)),or(implies(X_1079,not(X)),or(X,X_1079))),equiv(implies(not(X),X_1079),not(implies(X_1079,not(X))))) )],[refute_0_1308,refute_0_1330]) ).
cnf(refute_0_1332,plain,
and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),or(X_1079,X_1079))) = equiv(or(X_1079,X_1079),and(X_1079,X_1079)),
inference(subst,[],[refute_0_1331:[bind(X,$fot(X_1079))]]) ).
cnf(refute_0_1333,plain,
X_1079 = or(X_1079,X_1079),
inference(subst,[],[refute_0_1114:[bind(X_25347,$fot(X_1079))]]) ).
cnf(refute_0_1334,plain,
( X_1079 != or(X_1079,X_1079)
| or(X_1079,X_1079) = X_1079 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(X_1079)),bind(Y0,$fot(or(X_1079,X_1079)))]]) ).
cnf(refute_0_1335,plain,
or(X_1079,X_1079) = X_1079,
inference(resolve,[$cnf( $equal(X_1079,or(X_1079,X_1079)) )],[refute_0_1333,refute_0_1334]) ).
cnf(refute_0_1336,plain,
( and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),or(X_1079,X_1079))) != equiv(or(X_1079,X_1079),and(X_1079,X_1079))
| or(X_1079,X_1079) != X_1079
| and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) = equiv(or(X_1079,X_1079),and(X_1079,X_1079)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),or(X_1079,X_1079))),equiv(or(X_1079,X_1079),and(X_1079,X_1079))) ),[0,1,1],$fot(X_1079)]]) ).
cnf(refute_0_1337,plain,
( and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),or(X_1079,X_1079))) != equiv(or(X_1079,X_1079),and(X_1079,X_1079))
| and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) = equiv(or(X_1079,X_1079),and(X_1079,X_1079)) ),
inference(resolve,[$cnf( $equal(or(X_1079,X_1079),X_1079) )],[refute_0_1335,refute_0_1336]) ).
cnf(refute_0_1338,plain,
and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) = equiv(or(X_1079,X_1079),and(X_1079,X_1079)),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),or(X_1079,X_1079))),equiv(or(X_1079,X_1079),and(X_1079,X_1079))) )],[refute_0_1332,refute_0_1337]) ).
cnf(refute_0_1339,plain,
equiv(or(X_1079,X_1079),and(X_1079,X_1079)) = equiv(or(X_1079,X_1079),and(X_1079,X_1079)),
introduced(tautology,[refl,[$fot(equiv(or(X_1079,X_1079),and(X_1079,X_1079)))]]) ).
cnf(refute_0_1340,plain,
( equiv(or(X_1079,X_1079),and(X_1079,X_1079)) != equiv(or(X_1079,X_1079),and(X_1079,X_1079))
| or(X_1079,X_1079) != X_1079
| equiv(or(X_1079,X_1079),and(X_1079,X_1079)) = equiv(X_1079,and(X_1079,X_1079)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(or(X_1079,X_1079),and(X_1079,X_1079)),equiv(or(X_1079,X_1079),and(X_1079,X_1079))) ),[1,0],$fot(X_1079)]]) ).
cnf(refute_0_1341,plain,
( or(X_1079,X_1079) != X_1079
| equiv(or(X_1079,X_1079),and(X_1079,X_1079)) = equiv(X_1079,and(X_1079,X_1079)) ),
inference(resolve,[$cnf( $equal(equiv(or(X_1079,X_1079),and(X_1079,X_1079)),equiv(or(X_1079,X_1079),and(X_1079,X_1079))) )],[refute_0_1339,refute_0_1340]) ).
cnf(refute_0_1342,plain,
equiv(or(X_1079,X_1079),and(X_1079,X_1079)) = equiv(X_1079,and(X_1079,X_1079)),
inference(resolve,[$cnf( $equal(or(X_1079,X_1079),X_1079) )],[refute_0_1335,refute_0_1341]) ).
cnf(refute_0_1343,plain,
( and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) != equiv(or(X_1079,X_1079),and(X_1079,X_1079))
| equiv(or(X_1079,X_1079),and(X_1079,X_1079)) != equiv(X_1079,and(X_1079,X_1079))
| and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) = equiv(X_1079,and(X_1079,X_1079)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)),equiv(X_1079,and(X_1079,X_1079))) ),[0],$fot(equiv(or(X_1079,X_1079),and(X_1079,X_1079)))]]) ).
cnf(refute_0_1344,plain,
( and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) != equiv(or(X_1079,X_1079),and(X_1079,X_1079))
| and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) = equiv(X_1079,and(X_1079,X_1079)) ),
inference(resolve,[$cnf( $equal(equiv(or(X_1079,X_1079),and(X_1079,X_1079)),equiv(X_1079,and(X_1079,X_1079))) )],[refute_0_1342,refute_0_1343]) ).
cnf(refute_0_1345,plain,
and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) = equiv(X_1079,and(X_1079,X_1079)),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)),equiv(or(X_1079,X_1079),and(X_1079,X_1079))) )],[refute_0_1338,refute_0_1344]) ).
cnf(refute_0_1346,plain,
and(implies(X_1079,X_1079),implies(X_1079,X_1079)) = implies(X_1079,X_1079),
inference(subst,[],[refute_0_1289:[bind(X_17,$fot(implies(X_1079,X_1079)))]]) ).
cnf(refute_0_1347,plain,
or(or(X_19,not(X_20)),Y) = implies(not(or(X_19,not(X_20))),Y),
inference(subst,[],[refute_0_60:[bind(X,$fot(or(X_19,not(X_20))))]]) ).
cnf(refute_0_1348,plain,
( not(or(X_19,not(X_20))) != and(not(X_19),X_20)
| or(or(X_19,not(X_20)),Y) != implies(not(or(X_19,not(X_20))),Y)
| or(or(X_19,not(X_20)),Y) = implies(and(not(X_19),X_20),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(X_19,not(X_20)),Y),implies(not(or(X_19,not(X_20))),Y)) ),[1,0],$fot(and(not(X_19),X_20))]]) ).
cnf(refute_0_1349,plain,
( or(or(X_19,not(X_20)),Y) != implies(not(or(X_19,not(X_20))),Y)
| or(or(X_19,not(X_20)),Y) = implies(and(not(X_19),X_20),Y) ),
inference(resolve,[$cnf( $equal(not(or(X_19,not(X_20))),and(not(X_19),X_20)) )],[refute_0_407,refute_0_1348]) ).
cnf(refute_0_1350,plain,
or(or(X_19,not(X_20)),Y) = implies(and(not(X_19),X_20),Y),
inference(resolve,[$cnf( $equal(or(or(X_19,not(X_20)),Y),implies(not(or(X_19,not(X_20))),Y)) )],[refute_0_1347,refute_0_1349]) ).
cnf(refute_0_1351,plain,
or(or(not(X_20),not(X_20)),Y) = implies(and(not(not(X_20)),X_20),Y),
inference(subst,[],[refute_0_1350:[bind(X_19,$fot(not(X_20)))]]) ).
cnf(refute_0_1352,plain,
not(X_20) = or(not(X_20),not(X_20)),
inference(subst,[],[refute_0_1114:[bind(X_25347,$fot(not(X_20)))]]) ).
cnf(refute_0_1353,plain,
( not(X_20) != or(not(X_20),not(X_20))
| or(not(X_20),not(X_20)) = not(X_20) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(X_20))),bind(Y0,$fot(or(not(X_20),not(X_20))))]]) ).
cnf(refute_0_1354,plain,
or(not(X_20),not(X_20)) = not(X_20),
inference(resolve,[$cnf( $equal(not(X_20),or(not(X_20),not(X_20))) )],[refute_0_1352,refute_0_1353]) ).
cnf(refute_0_1355,plain,
( or(not(X_20),not(X_20)) != not(X_20)
| or(or(not(X_20),not(X_20)),Y) != implies(and(not(not(X_20)),X_20),Y)
| or(not(X_20),Y) = implies(and(not(not(X_20)),X_20),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(not(X_20),not(X_20)),Y),implies(and(not(not(X_20)),X_20),Y)) ),[0,0],$fot(not(X_20))]]) ).
cnf(refute_0_1356,plain,
( or(or(not(X_20),not(X_20)),Y) != implies(and(not(not(X_20)),X_20),Y)
| or(not(X_20),Y) = implies(and(not(not(X_20)),X_20),Y) ),
inference(resolve,[$cnf( $equal(or(not(X_20),not(X_20)),not(X_20)) )],[refute_0_1354,refute_0_1355]) ).
cnf(refute_0_1357,plain,
or(not(X_20),Y) = implies(and(not(not(X_20)),X_20),Y),
inference(resolve,[$cnf( $equal(or(or(not(X_20),not(X_20)),Y),implies(and(not(not(X_20)),X_20),Y)) )],[refute_0_1351,refute_0_1356]) ).
cnf(refute_0_1358,plain,
or(not(X_20),Y) = implies(X_20,Y),
inference(subst,[],[refute_0_20:[bind(X,$fot(X_20))]]) ).
cnf(refute_0_1359,plain,
( or(not(X_20),Y) != implies(X_20,Y)
| or(not(X_20),Y) != implies(and(not(not(X_20)),X_20),Y)
| implies(X_20,Y) = implies(and(not(not(X_20)),X_20),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X_20),Y),implies(and(not(not(X_20)),X_20),Y)) ),[0],$fot(implies(X_20,Y))]]) ).
cnf(refute_0_1360,plain,
( or(not(X_20),Y) != implies(and(not(not(X_20)),X_20),Y)
| implies(X_20,Y) = implies(and(not(not(X_20)),X_20),Y) ),
inference(resolve,[$cnf( $equal(or(not(X_20),Y),implies(X_20,Y)) )],[refute_0_1358,refute_0_1359]) ).
cnf(refute_0_1361,plain,
not(not(X_20)) = X_20,
inference(subst,[],[refute_0_1231:[bind(X_10026,$fot(X_20))]]) ).
cnf(refute_0_1362,plain,
and(not(not(X_20)),X_20) = and(not(not(X_20)),X_20),
introduced(tautology,[refl,[$fot(and(not(not(X_20)),X_20))]]) ).
cnf(refute_0_1363,plain,
( and(not(not(X_20)),X_20) != and(not(not(X_20)),X_20)
| not(not(X_20)) != X_20
| and(not(not(X_20)),X_20) = and(X_20,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X_20)),X_20),and(not(not(X_20)),X_20)) ),[1,0],$fot(X_20)]]) ).
cnf(refute_0_1364,plain,
( not(not(X_20)) != X_20
| and(not(not(X_20)),X_20) = and(X_20,X_20) ),
inference(resolve,[$cnf( $equal(and(not(not(X_20)),X_20),and(not(not(X_20)),X_20)) )],[refute_0_1362,refute_0_1363]) ).
cnf(refute_0_1365,plain,
and(not(not(X_20)),X_20) = and(X_20,X_20),
inference(resolve,[$cnf( $equal(not(not(X_20)),X_20) )],[refute_0_1361,refute_0_1364]) ).
cnf(refute_0_1366,plain,
implies(and(not(not(X_20)),X_20),Y) = implies(and(not(not(X_20)),X_20),Y),
introduced(tautology,[refl,[$fot(implies(and(not(not(X_20)),X_20),Y))]]) ).
cnf(refute_0_1367,plain,
( and(not(not(X_20)),X_20) != and(X_20,X_20)
| implies(and(not(not(X_20)),X_20),Y) != implies(and(not(not(X_20)),X_20),Y)
| implies(and(not(not(X_20)),X_20),Y) = implies(and(X_20,X_20),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(not(not(X_20)),X_20),Y),implies(and(not(not(X_20)),X_20),Y)) ),[1,0],$fot(and(X_20,X_20))]]) ).
cnf(refute_0_1368,plain,
( and(not(not(X_20)),X_20) != and(X_20,X_20)
| implies(and(not(not(X_20)),X_20),Y) = implies(and(X_20,X_20),Y) ),
inference(resolve,[$cnf( $equal(implies(and(not(not(X_20)),X_20),Y),implies(and(not(not(X_20)),X_20),Y)) )],[refute_0_1366,refute_0_1367]) ).
cnf(refute_0_1369,plain,
implies(and(not(not(X_20)),X_20),Y) = implies(and(X_20,X_20),Y),
inference(resolve,[$cnf( $equal(and(not(not(X_20)),X_20),and(X_20,X_20)) )],[refute_0_1365,refute_0_1368]) ).
cnf(refute_0_1370,plain,
( implies(X_20,Y) != implies(and(not(not(X_20)),X_20),Y)
| implies(and(not(not(X_20)),X_20),Y) != implies(and(X_20,X_20),Y)
| implies(X_20,Y) = implies(and(X_20,X_20),Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_20,Y),implies(and(X_20,X_20),Y)) ),[0],$fot(implies(and(not(not(X_20)),X_20),Y))]]) ).
cnf(refute_0_1371,plain,
( implies(X_20,Y) != implies(and(not(not(X_20)),X_20),Y)
| implies(X_20,Y) = implies(and(X_20,X_20),Y) ),
inference(resolve,[$cnf( $equal(implies(and(not(not(X_20)),X_20),Y),implies(and(X_20,X_20),Y)) )],[refute_0_1369,refute_0_1370]) ).
cnf(refute_0_1372,plain,
( or(not(X_20),Y) != implies(and(not(not(X_20)),X_20),Y)
| implies(X_20,Y) = implies(and(X_20,X_20),Y) ),
inference(resolve,[$cnf( $equal(implies(X_20,Y),implies(and(not(not(X_20)),X_20),Y)) )],[refute_0_1360,refute_0_1371]) ).
cnf(refute_0_1373,plain,
implies(X_20,Y) = implies(and(X_20,X_20),Y),
inference(resolve,[$cnf( $equal(or(not(X_20),Y),implies(and(not(not(X_20)),X_20),Y)) )],[refute_0_1357,refute_0_1372]) ).
cnf(refute_0_1374,plain,
( implies(X_20,Y) != implies(and(X_20,X_20),Y)
| implies(and(X_20,X_20),Y) = implies(X_20,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X_20,Y))),bind(Y0,$fot(implies(and(X_20,X_20),Y)))]]) ).
cnf(refute_0_1375,plain,
implies(and(X_20,X_20),Y) = implies(X_20,Y),
inference(resolve,[$cnf( $equal(implies(X_20,Y),implies(and(X_20,X_20),Y)) )],[refute_0_1373,refute_0_1374]) ).
cnf(refute_0_1376,plain,
implies(and(X_1079,X_1079),X_1079) = implies(X_1079,X_1079),
inference(subst,[],[refute_0_1375:[bind(Y,$fot(X_1079)),bind(X_20,$fot(X_1079))]]) ).
cnf(refute_0_1377,plain,
and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079)) = and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079)),
introduced(tautology,[refl,[$fot(and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079)))]]) ).
cnf(refute_0_1378,plain,
( and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079)) != and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079))
| implies(and(X_1079,X_1079),X_1079) != implies(X_1079,X_1079)
| and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079)) = and(implies(X_1079,X_1079),implies(X_1079,X_1079)) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079)),and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079))) ),[1,1],$fot(implies(X_1079,X_1079))]]) ).
cnf(refute_0_1379,plain,
( implies(and(X_1079,X_1079),X_1079) != implies(X_1079,X_1079)
| and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079)) = and(implies(X_1079,X_1079),implies(X_1079,X_1079)) ),
inference(resolve,[$cnf( $equal(and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079)),and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079))) )],[refute_0_1377,refute_0_1378]) ).
cnf(refute_0_1380,plain,
and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079)) = and(implies(X_1079,X_1079),implies(X_1079,X_1079)),
inference(resolve,[$cnf( $equal(implies(and(X_1079,X_1079),X_1079),implies(X_1079,X_1079)) )],[refute_0_1376,refute_0_1379]) ).
cnf(refute_0_1381,plain,
( implies(X_30,X_30) != not(equiv(not(X_30),X_30))
| not(equiv(not(X_30),X_30)) = implies(X_30,X_30) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X_30,X_30))),bind(Y0,$fot(not(equiv(not(X_30),X_30))))]]) ).
cnf(refute_0_1382,plain,
not(equiv(not(X_30),X_30)) = implies(X_30,X_30),
inference(resolve,[$cnf( $equal(implies(X_30,X_30),not(equiv(not(X_30),X_30))) )],[refute_0_1297,refute_0_1381]) ).
cnf(refute_0_1383,plain,
not(equiv(not(X_1079),X_1079)) = implies(X_1079,X_1079),
inference(subst,[],[refute_0_1382:[bind(X_30,$fot(X_1079))]]) ).
cnf(refute_0_1384,plain,
and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) = and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)),
introduced(tautology,[refl,[$fot(and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)))]]) ).
cnf(refute_0_1385,plain,
( and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) != and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079))
| not(equiv(not(X_1079),X_1079)) != implies(X_1079,X_1079)
| and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) = and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)),and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079))) ),[1,0],$fot(implies(X_1079,X_1079))]]) ).
cnf(refute_0_1386,plain,
( not(equiv(not(X_1079),X_1079)) != implies(X_1079,X_1079)
| and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) = and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079)) ),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)),and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079))) )],[refute_0_1384,refute_0_1385]) ).
cnf(refute_0_1387,plain,
and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) = and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079)),
inference(resolve,[$cnf( $equal(not(equiv(not(X_1079),X_1079)),implies(X_1079,X_1079)) )],[refute_0_1383,refute_0_1386]) ).
cnf(refute_0_1388,plain,
( and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079)) != and(implies(X_1079,X_1079),implies(X_1079,X_1079))
| and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) != and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079))
| and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) = and(implies(X_1079,X_1079),implies(X_1079,X_1079)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)))),bind(Y0,$fot(and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079)))),bind(Z,$fot(and(implies(X_1079,X_1079),implies(X_1079,X_1079))))]]) ).
cnf(refute_0_1389,plain,
( and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079)) != and(implies(X_1079,X_1079),implies(X_1079,X_1079))
| and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) = and(implies(X_1079,X_1079),implies(X_1079,X_1079)) ),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)),and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079))) )],[refute_0_1387,refute_0_1388]) ).
cnf(refute_0_1390,plain,
and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) = and(implies(X_1079,X_1079),implies(X_1079,X_1079)),
inference(resolve,[$cnf( $equal(and(implies(X_1079,X_1079),implies(and(X_1079,X_1079),X_1079)),and(implies(X_1079,X_1079),implies(X_1079,X_1079))) )],[refute_0_1380,refute_0_1389]) ).
cnf(refute_0_1391,plain,
( and(implies(X_1079,X_1079),implies(X_1079,X_1079)) != implies(X_1079,X_1079)
| and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) != and(implies(X_1079,X_1079),implies(X_1079,X_1079))
| and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) = implies(X_1079,X_1079) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)))),bind(Y0,$fot(and(implies(X_1079,X_1079),implies(X_1079,X_1079)))),bind(Z,$fot(implies(X_1079,X_1079)))]]) ).
cnf(refute_0_1392,plain,
( and(implies(X_1079,X_1079),implies(X_1079,X_1079)) != implies(X_1079,X_1079)
| and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) = implies(X_1079,X_1079) ),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)),and(implies(X_1079,X_1079),implies(X_1079,X_1079))) )],[refute_0_1390,refute_0_1391]) ).
cnf(refute_0_1393,plain,
and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) = implies(X_1079,X_1079),
inference(resolve,[$cnf( $equal(and(implies(X_1079,X_1079),implies(X_1079,X_1079)),implies(X_1079,X_1079)) )],[refute_0_1346,refute_0_1392]) ).
cnf(refute_0_1394,plain,
( and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) != equiv(X_1079,and(X_1079,X_1079))
| and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) != implies(X_1079,X_1079)
| implies(X_1079,X_1079) = equiv(X_1079,and(X_1079,X_1079)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)),equiv(X_1079,and(X_1079,X_1079))) ),[0],$fot(implies(X_1079,X_1079))]]) ).
cnf(refute_0_1395,plain,
( and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) != equiv(X_1079,and(X_1079,X_1079))
| implies(X_1079,X_1079) = equiv(X_1079,and(X_1079,X_1079)) ),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)),implies(X_1079,X_1079)) )],[refute_0_1393,refute_0_1394]) ).
cnf(refute_0_1396,plain,
and(X_1079,X_1079) = X_1079,
inference(subst,[],[refute_0_1289:[bind(X_17,$fot(X_1079))]]) ).
cnf(refute_0_1397,plain,
equiv(X_1079,and(X_1079,X_1079)) = equiv(X_1079,and(X_1079,X_1079)),
introduced(tautology,[refl,[$fot(equiv(X_1079,and(X_1079,X_1079)))]]) ).
cnf(refute_0_1398,plain,
( and(X_1079,X_1079) != X_1079
| equiv(X_1079,and(X_1079,X_1079)) != equiv(X_1079,and(X_1079,X_1079))
| equiv(X_1079,and(X_1079,X_1079)) = equiv(X_1079,X_1079) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_1079,and(X_1079,X_1079)),equiv(X_1079,and(X_1079,X_1079))) ),[1,1],$fot(X_1079)]]) ).
cnf(refute_0_1399,plain,
( and(X_1079,X_1079) != X_1079
| equiv(X_1079,and(X_1079,X_1079)) = equiv(X_1079,X_1079) ),
inference(resolve,[$cnf( $equal(equiv(X_1079,and(X_1079,X_1079)),equiv(X_1079,and(X_1079,X_1079))) )],[refute_0_1397,refute_0_1398]) ).
cnf(refute_0_1400,plain,
equiv(X_1079,and(X_1079,X_1079)) = equiv(X_1079,X_1079),
inference(resolve,[$cnf( $equal(and(X_1079,X_1079),X_1079) )],[refute_0_1396,refute_0_1399]) ).
cnf(refute_0_1401,plain,
( equiv(X_1079,and(X_1079,X_1079)) != equiv(X_1079,X_1079)
| implies(X_1079,X_1079) != equiv(X_1079,and(X_1079,X_1079))
| implies(X_1079,X_1079) = equiv(X_1079,X_1079) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_1079,X_1079),equiv(X_1079,and(X_1079,X_1079))) ),[1],$fot(equiv(X_1079,X_1079))]]) ).
cnf(refute_0_1402,plain,
( implies(X_1079,X_1079) != equiv(X_1079,and(X_1079,X_1079))
| implies(X_1079,X_1079) = equiv(X_1079,X_1079) ),
inference(resolve,[$cnf( $equal(equiv(X_1079,and(X_1079,X_1079)),equiv(X_1079,X_1079)) )],[refute_0_1400,refute_0_1401]) ).
cnf(refute_0_1403,plain,
( and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)) != equiv(X_1079,and(X_1079,X_1079))
| implies(X_1079,X_1079) = equiv(X_1079,X_1079) ),
inference(resolve,[$cnf( $equal(implies(X_1079,X_1079),equiv(X_1079,and(X_1079,X_1079))) )],[refute_0_1395,refute_0_1402]) ).
cnf(refute_0_1404,plain,
implies(X_1079,X_1079) = equiv(X_1079,X_1079),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X_1079),X_1079)),implies(and(X_1079,X_1079),X_1079)),equiv(X_1079,and(X_1079,X_1079))) )],[refute_0_1345,refute_0_1403]) ).
cnf(refute_0_1405,plain,
implies(X_30,X_30) = equiv(X_30,X_30),
inference(subst,[],[refute_0_1404:[bind(X_1079,$fot(X_30))]]) ).
cnf(refute_0_1406,plain,
( implies(X_30,X_30) != equiv(X_30,X_30)
| implies(X_30,X_30) != not(equiv(not(X_30),X_30))
| equiv(X_30,X_30) = not(equiv(not(X_30),X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_30,X_30),not(equiv(not(X_30),X_30))) ),[0],$fot(equiv(X_30,X_30))]]) ).
cnf(refute_0_1407,plain,
( implies(X_30,X_30) != not(equiv(not(X_30),X_30))
| equiv(X_30,X_30) = not(equiv(not(X_30),X_30)) ),
inference(resolve,[$cnf( $equal(implies(X_30,X_30),equiv(X_30,X_30)) )],[refute_0_1405,refute_0_1406]) ).
cnf(refute_0_1408,plain,
equiv(X_30,X_30) = not(equiv(not(X_30),X_30)),
inference(resolve,[$cnf( $equal(implies(X_30,X_30),not(equiv(not(X_30),X_30))) )],[refute_0_1297,refute_0_1407]) ).
cnf(refute_0_1409,plain,
equiv(X_25350,X_25350) = not(equiv(not(X_25350),X_25350)),
inference(subst,[],[refute_0_1408:[bind(X_30,$fot(X_25350))]]) ).
cnf(refute_0_1410,plain,
( equiv(X_25350,X_25350) != not(equiv(not(X_25350),X_25350))
| not(equiv(not(X_25350),X_25350)) = equiv(X_25350,X_25350) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(X_25350,X_25350))),bind(Y0,$fot(not(equiv(not(X_25350),X_25350))))]]) ).
cnf(refute_0_1411,plain,
not(equiv(not(X_25350),X_25350)) = equiv(X_25350,X_25350),
inference(resolve,[$cnf( $equal(equiv(X_25350,X_25350),not(equiv(not(X_25350),X_25350))) )],[refute_0_1409,refute_0_1410]) ).
cnf(refute_0_1412,plain,
( equiv(not(X_25350),X_25350) != not(not(equiv(not(X_25350),X_25350)))
| not(equiv(not(X_25350),X_25350)) != equiv(X_25350,X_25350)
| equiv(not(X_25350),X_25350) = not(equiv(X_25350,X_25350)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X_25350),X_25350),not(not(equiv(not(X_25350),X_25350)))) ),[1,0],$fot(equiv(X_25350,X_25350))]]) ).
cnf(refute_0_1413,plain,
( equiv(not(X_25350),X_25350) != not(not(equiv(not(X_25350),X_25350)))
| equiv(not(X_25350),X_25350) = not(equiv(X_25350,X_25350)) ),
inference(resolve,[$cnf( $equal(not(equiv(not(X_25350),X_25350)),equiv(X_25350,X_25350)) )],[refute_0_1411,refute_0_1412]) ).
cnf(refute_0_1414,plain,
equiv(not(X_25350),X_25350) = not(equiv(X_25350,X_25350)),
inference(resolve,[$cnf( $equal(equiv(not(X_25350),X_25350),not(not(equiv(not(X_25350),X_25350)))) )],[refute_0_1264,refute_0_1413]) ).
cnf(refute_0_1415,plain,
equiv(not(X_31183),X_31183) = not(equiv(X_31183,X_31183)),
inference(subst,[],[refute_0_1414:[bind(X_25350,$fot(X_31183))]]) ).
cnf(refute_0_1416,plain,
( equiv(not(X_31183),X_31183) != not(equiv(X_31183,X_31183))
| ~ is_a_theorem(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(equiv(not(X_31183),X_31183)))))
| is_a_theorem(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(equiv(not(X_31183),X_31183))))) ),[0,1,1,0],$fot(not(equiv(X_31183,X_31183)))]]) ).
cnf(refute_0_1417,plain,
( ~ is_a_theorem(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(equiv(not(X_31183),X_31183)))))
| is_a_theorem(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))))) ),
inference(resolve,[$cnf( $equal(equiv(not(X_31183),X_31183),not(equiv(X_31183,X_31183))) )],[refute_0_1415,refute_0_1416]) ).
cnf(refute_0_1418,plain,
is_a_theorem(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(equiv(not(X_31183),X_31183))))) )],[refute_0_1263,refute_0_1417]) ).
cnf(refute_0_1419,plain,
not(not(equiv(X_31183,X_31183))) = equiv(X_31183,X_31183),
inference(subst,[],[refute_0_1231:[bind(X_10026,$fot(equiv(X_31183,X_31183)))]]) ).
cnf(refute_0_1420,plain,
equiv(X_31183,not(not(equiv(X_31183,X_31183)))) = equiv(X_31183,not(not(equiv(X_31183,X_31183)))),
introduced(tautology,[refl,[$fot(equiv(X_31183,not(not(equiv(X_31183,X_31183)))))]]) ).
cnf(refute_0_1421,plain,
( equiv(X_31183,not(not(equiv(X_31183,X_31183)))) != equiv(X_31183,not(not(equiv(X_31183,X_31183))))
| not(not(equiv(X_31183,X_31183))) != equiv(X_31183,X_31183)
| equiv(X_31183,not(not(equiv(X_31183,X_31183)))) = equiv(X_31183,equiv(X_31183,X_31183)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_31183,not(not(equiv(X_31183,X_31183)))),equiv(X_31183,not(not(equiv(X_31183,X_31183))))) ),[1,1],$fot(equiv(X_31183,X_31183))]]) ).
cnf(refute_0_1422,plain,
( not(not(equiv(X_31183,X_31183))) != equiv(X_31183,X_31183)
| equiv(X_31183,not(not(equiv(X_31183,X_31183)))) = equiv(X_31183,equiv(X_31183,X_31183)) ),
inference(resolve,[$cnf( $equal(equiv(X_31183,not(not(equiv(X_31183,X_31183)))),equiv(X_31183,not(not(equiv(X_31183,X_31183))))) )],[refute_0_1420,refute_0_1421]) ).
cnf(refute_0_1423,plain,
equiv(X_31183,not(not(equiv(X_31183,X_31183)))) = equiv(X_31183,equiv(X_31183,X_31183)),
inference(resolve,[$cnf( $equal(not(not(equiv(X_31183,X_31183))),equiv(X_31183,X_31183)) )],[refute_0_1419,refute_0_1422]) ).
cnf(refute_0_1424,plain,
not(not(X_31183)) = X_31183,
inference(subst,[],[refute_0_1231:[bind(X_10026,$fot(X_31183))]]) ).
cnf(refute_0_1425,plain,
and(X_31183,X_31183) = X_31183,
inference(subst,[],[refute_0_1289:[bind(X_17,$fot(X_31183))]]) ).
cnf(refute_0_1426,plain,
not(and(X_31183,X_31183)) = not(and(X_31183,X_31183)),
introduced(tautology,[refl,[$fot(not(and(X_31183,X_31183)))]]) ).
cnf(refute_0_1427,plain,
( and(X_31183,X_31183) != X_31183
| not(and(X_31183,X_31183)) != not(and(X_31183,X_31183))
| not(and(X_31183,X_31183)) = not(X_31183) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(X_31183,X_31183)),not(and(X_31183,X_31183))) ),[1,0],$fot(X_31183)]]) ).
cnf(refute_0_1428,plain,
( and(X_31183,X_31183) != X_31183
| not(and(X_31183,X_31183)) = not(X_31183) ),
inference(resolve,[$cnf( $equal(not(and(X_31183,X_31183)),not(and(X_31183,X_31183))) )],[refute_0_1426,refute_0_1427]) ).
cnf(refute_0_1429,plain,
not(and(X_31183,X_31183)) = not(X_31183),
inference(resolve,[$cnf( $equal(and(X_31183,X_31183),X_31183) )],[refute_0_1425,refute_0_1428]) ).
cnf(refute_0_1430,plain,
implies(X_31183,not(X_31183)) = not(and(X_31183,X_31183)),
inference(subst,[],[refute_0_987:[bind(Y,$fot(X_31183)),bind(X_9551,$fot(X_31183))]]) ).
cnf(refute_0_1431,plain,
( implies(X_31183,not(X_31183)) != not(and(X_31183,X_31183))
| not(and(X_31183,X_31183)) != not(X_31183)
| implies(X_31183,not(X_31183)) = not(X_31183) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(X_31183,not(X_31183)))),bind(Y0,$fot(not(and(X_31183,X_31183)))),bind(Z,$fot(not(X_31183)))]]) ).
cnf(refute_0_1432,plain,
( not(and(X_31183,X_31183)) != not(X_31183)
| implies(X_31183,not(X_31183)) = not(X_31183) ),
inference(resolve,[$cnf( $equal(implies(X_31183,not(X_31183)),not(and(X_31183,X_31183))) )],[refute_0_1430,refute_0_1431]) ).
cnf(refute_0_1433,plain,
implies(X_31183,not(X_31183)) = not(X_31183),
inference(resolve,[$cnf( $equal(not(and(X_31183,X_31183)),not(X_31183)) )],[refute_0_1429,refute_0_1432]) ).
cnf(refute_0_1434,plain,
not(implies(X_31183,not(X_31183))) = not(implies(X_31183,not(X_31183))),
introduced(tautology,[refl,[$fot(not(implies(X_31183,not(X_31183))))]]) ).
cnf(refute_0_1435,plain,
( implies(X_31183,not(X_31183)) != not(X_31183)
| not(implies(X_31183,not(X_31183))) != not(implies(X_31183,not(X_31183)))
| not(implies(X_31183,not(X_31183))) = not(not(X_31183)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_31183,not(X_31183))),not(implies(X_31183,not(X_31183)))) ),[1,0],$fot(not(X_31183))]]) ).
cnf(refute_0_1436,plain,
( implies(X_31183,not(X_31183)) != not(X_31183)
| not(implies(X_31183,not(X_31183))) = not(not(X_31183)) ),
inference(resolve,[$cnf( $equal(not(implies(X_31183,not(X_31183))),not(implies(X_31183,not(X_31183)))) )],[refute_0_1434,refute_0_1435]) ).
cnf(refute_0_1437,plain,
not(implies(X_31183,not(X_31183))) = not(not(X_31183)),
inference(resolve,[$cnf( $equal(implies(X_31183,not(X_31183)),not(X_31183)) )],[refute_0_1433,refute_0_1436]) ).
cnf(refute_0_1438,plain,
( not(implies(X_31183,not(X_31183))) != not(not(X_31183))
| not(not(X_31183)) != X_31183
| not(implies(X_31183,not(X_31183))) = X_31183 ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(not(implies(X_31183,not(X_31183))))),bind(Y0,$fot(not(not(X_31183)))),bind(Z,$fot(X_31183))]]) ).
cnf(refute_0_1439,plain,
( not(not(X_31183)) != X_31183
| not(implies(X_31183,not(X_31183))) = X_31183 ),
inference(resolve,[$cnf( $equal(not(implies(X_31183,not(X_31183))),not(not(X_31183))) )],[refute_0_1437,refute_0_1438]) ).
cnf(refute_0_1440,plain,
not(implies(X_31183,not(X_31183))) = X_31183,
inference(resolve,[$cnf( $equal(not(not(X_31183)),X_31183) )],[refute_0_1424,refute_0_1439]) ).
cnf(refute_0_1441,plain,
equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))) = equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))),
introduced(tautology,[refl,[$fot(equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))))]]) ).
cnf(refute_0_1442,plain,
( equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))) != equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))
| not(implies(X_31183,not(X_31183))) != X_31183
| equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))) = equiv(X_31183,not(not(equiv(X_31183,X_31183)))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) ),[1,0],$fot(X_31183)]]) ).
cnf(refute_0_1443,plain,
( not(implies(X_31183,not(X_31183))) != X_31183
| equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))) = equiv(X_31183,not(not(equiv(X_31183,X_31183)))) ),
inference(resolve,[$cnf( $equal(equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) )],[refute_0_1441,refute_0_1442]) ).
cnf(refute_0_1444,plain,
equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))) = equiv(X_31183,not(not(equiv(X_31183,X_31183)))),
inference(resolve,[$cnf( $equal(not(implies(X_31183,not(X_31183))),X_31183) )],[refute_0_1440,refute_0_1443]) ).
cnf(refute_0_1445,plain,
( equiv(X_31183,not(not(equiv(X_31183,X_31183)))) != equiv(X_31183,equiv(X_31183,X_31183))
| equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))) != equiv(X_31183,not(not(equiv(X_31183,X_31183))))
| equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))) = equiv(X_31183,equiv(X_31183,X_31183)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))))),bind(Y0,$fot(equiv(X_31183,not(not(equiv(X_31183,X_31183)))))),bind(Z,$fot(equiv(X_31183,equiv(X_31183,X_31183))))]]) ).
cnf(refute_0_1446,plain,
( equiv(X_31183,not(not(equiv(X_31183,X_31183)))) != equiv(X_31183,equiv(X_31183,X_31183))
| equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))) = equiv(X_31183,equiv(X_31183,X_31183)) ),
inference(resolve,[$cnf( $equal(equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))),equiv(X_31183,not(not(equiv(X_31183,X_31183))))) )],[refute_0_1444,refute_0_1445]) ).
cnf(refute_0_1447,plain,
equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))) = equiv(X_31183,equiv(X_31183,X_31183)),
inference(resolve,[$cnf( $equal(equiv(X_31183,not(not(equiv(X_31183,X_31183)))),equiv(X_31183,equiv(X_31183,X_31183))) )],[refute_0_1423,refute_0_1446]) ).
cnf(refute_0_1448,plain,
implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) = implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))),
introduced(tautology,[refl,[$fot(implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))))]]) ).
cnf(refute_0_1449,plain,
( equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))) != equiv(X_31183,equiv(X_31183,X_31183))
| implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) != implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))))
| implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) = implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))),implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))))) ),[1,1],$fot(equiv(X_31183,equiv(X_31183,X_31183)))]]) ).
cnf(refute_0_1450,plain,
( equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))) != equiv(X_31183,equiv(X_31183,X_31183))
| implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) = implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183))) ),
inference(resolve,[$cnf( $equal(implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))),implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))))) )],[refute_0_1448,refute_0_1449]) ).
cnf(refute_0_1451,plain,
implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) = implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183))),
inference(resolve,[$cnf( $equal(equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))),equiv(X_31183,equiv(X_31183,X_31183))) )],[refute_0_1447,refute_0_1450]) ).
cnf(refute_0_1452,plain,
( X_25347 != or(X_25347,X_25347)
| or(X_25347,X_25347) = X_25347 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(X_25347)),bind(Y0,$fot(or(X_25347,X_25347)))]]) ).
cnf(refute_0_1453,plain,
or(X_25347,X_25347) = X_25347,
inference(resolve,[$cnf( $equal(X_25347,or(X_25347,X_25347)) )],[refute_0_1114,refute_0_1452]) ).
cnf(refute_0_1454,plain,
or(X_31183,X_31183) = X_31183,
inference(subst,[],[refute_0_1453:[bind(X_25347,$fot(X_31183))]]) ).
cnf(refute_0_1455,plain,
implies(not(X_31183),X_31183) = or(X_31183,X_31183),
inference(subst,[],[refute_0_159:[bind(X,$fot(X_31183)),bind(Y,$fot(X_31183))]]) ).
cnf(refute_0_1456,plain,
( implies(not(X_31183),X_31183) != or(X_31183,X_31183)
| or(X_31183,X_31183) != X_31183
| implies(not(X_31183),X_31183) = X_31183 ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(not(X_31183),X_31183))),bind(Y0,$fot(or(X_31183,X_31183))),bind(Z,$fot(X_31183))]]) ).
cnf(refute_0_1457,plain,
( or(X_31183,X_31183) != X_31183
| implies(not(X_31183),X_31183) = X_31183 ),
inference(resolve,[$cnf( $equal(implies(not(X_31183),X_31183),or(X_31183,X_31183)) )],[refute_0_1455,refute_0_1456]) ).
cnf(refute_0_1458,plain,
implies(not(X_31183),X_31183) = X_31183,
inference(resolve,[$cnf( $equal(or(X_31183,X_31183),X_31183) )],[refute_0_1454,refute_0_1457]) ).
cnf(refute_0_1459,plain,
implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) = implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))),
introduced(tautology,[refl,[$fot(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))))]]) ).
cnf(refute_0_1460,plain,
( implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) != implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))))
| implies(not(X_31183),X_31183) != X_31183
| implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) = implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))),implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))))) ),[1,0],$fot(X_31183)]]) ).
cnf(refute_0_1461,plain,
( implies(not(X_31183),X_31183) != X_31183
| implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) = implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))),implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))))) )],[refute_0_1459,refute_0_1460]) ).
cnf(refute_0_1462,plain,
implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) = implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))),
inference(resolve,[$cnf( $equal(implies(not(X_31183),X_31183),X_31183) )],[refute_0_1458,refute_0_1461]) ).
cnf(refute_0_1463,plain,
( implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) != implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183)))
| implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) != implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))))
| implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) = implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))))),bind(Y0,$fot(implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))))),bind(Z,$fot(implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183)))))]]) ).
cnf(refute_0_1464,plain,
( implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) != implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183)))
| implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) = implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))),implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))))) )],[refute_0_1462,refute_0_1463]) ).
cnf(refute_0_1465,plain,
implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) = implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183))),
inference(resolve,[$cnf( $equal(implies(X_31183,equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))),implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183)))) )],[refute_0_1451,refute_0_1464]) ).
cnf(refute_0_1466,plain,
( implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))) != implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183)))
| ~ is_a_theorem(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))))
| is_a_theorem(implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))))) ),[0],$fot(implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183))))]]) ).
cnf(refute_0_1467,plain,
( ~ is_a_theorem(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))))
| is_a_theorem(implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183))))),implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183)))) )],[refute_0_1465,refute_0_1466]) ).
cnf(refute_0_1468,plain,
is_a_theorem(implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_31183),X_31183),equiv(not(implies(X_31183,not(X_31183))),not(not(equiv(X_31183,X_31183)))))) )],[refute_0_1418,refute_0_1467]) ).
cnf(refute_0_1469,plain,
( ~ is_a_theorem(X_2943)
| ~ is_a_theorem(implies(X_2943,or(and(X_2942,X_2943),not(X_2942))))
| is_a_theorem(or(and(X_2942,X_2943),not(X_2942))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(X_2943)),bind(Y,$fot(or(and(X_2942,X_2943),not(X_2942))))]]) ).
cnf(refute_0_1470,plain,
is_a_theorem(implies(implies(X_25,not(X)),or(not(X),not(X_25)))),
inference(subst,[],[refute_0_499:[bind(X,$fot(X_25)),bind(X_24,$fot(not(X)))]]) ).
cnf(refute_0_1471,plain,
implies(X,not(X_25)) = or(not(X),not(X_25)),
inference(subst,[],[refute_0_9:[bind(Y,$fot(not(X_25)))]]) ).
cnf(refute_0_1472,plain,
( implies(X,not(X_25)) != or(not(X),not(X_25))
| or(not(X),not(X_25)) = implies(X,not(X_25)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,not(X_25)))),bind(Y0,$fot(or(not(X),not(X_25))))]]) ).
cnf(refute_0_1473,plain,
or(not(X),not(X_25)) = implies(X,not(X_25)),
inference(resolve,[$cnf( $equal(implies(X,not(X_25)),or(not(X),not(X_25))) )],[refute_0_1471,refute_0_1472]) ).
cnf(refute_0_1474,plain,
( or(not(X),not(X_25)) != implies(X,not(X_25))
| ~ is_a_theorem(implies(implies(X_25,not(X)),or(not(X),not(X_25))))
| is_a_theorem(implies(implies(X_25,not(X)),implies(X,not(X_25)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_25,not(X)),or(not(X),not(X_25)))) ),[0,1],$fot(implies(X,not(X_25)))]]) ).
cnf(refute_0_1475,plain,
( ~ is_a_theorem(implies(implies(X_25,not(X)),or(not(X),not(X_25))))
| is_a_theorem(implies(implies(X_25,not(X)),implies(X,not(X_25)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_25)),implies(X,not(X_25))) )],[refute_0_1473,refute_0_1474]) ).
cnf(refute_0_1476,plain,
is_a_theorem(implies(implies(X_25,not(X)),implies(X,not(X_25)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_25,not(X)),or(not(X),not(X_25)))) )],[refute_0_1470,refute_0_1475]) ).
cnf(refute_0_1477,plain,
implies(implies(X_25,not(X)),implies(X,not(X_25))) = or(and(X_25,X),implies(X,not(X_25))),
inference(subst,[],[refute_0_134:[bind(Y,$fot(implies(X,not(X_25)))),bind(X_16,$fot(X_25)),bind(X_17,$fot(X))]]) ).
cnf(refute_0_1478,plain,
( implies(implies(X_25,not(X)),implies(X,not(X_25))) != or(and(X_25,X),implies(X,not(X_25)))
| ~ is_a_theorem(implies(implies(X_25,not(X)),implies(X,not(X_25))))
| is_a_theorem(or(and(X_25,X),implies(X,not(X_25)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_25,not(X)),implies(X,not(X_25)))) ),[0],$fot(or(and(X_25,X),implies(X,not(X_25))))]]) ).
cnf(refute_0_1479,plain,
( ~ is_a_theorem(implies(implies(X_25,not(X)),implies(X,not(X_25))))
| is_a_theorem(or(and(X_25,X),implies(X,not(X_25)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_25,not(X)),implies(X,not(X_25))),or(and(X_25,X),implies(X,not(X_25)))) )],[refute_0_1477,refute_0_1478]) ).
cnf(refute_0_1480,plain,
is_a_theorem(or(and(X_25,X),implies(X,not(X_25)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_25,not(X)),implies(X,not(X_25)))) )],[refute_0_1476,refute_0_1479]) ).
cnf(refute_0_1481,plain,
is_a_theorem(or(and(X_25,X_2904),implies(X_2904,not(X_25)))),
inference(subst,[],[refute_0_1480:[bind(X,$fot(X_2904))]]) ).
cnf(refute_0_1482,plain,
( ~ is_a_theorem(or(and(X_25,X_2904),implies(X_2904,not(X_25))))
| is_a_theorem(implies(X_2904,or(and(X_25,X_2904),not(X_25)))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_2904)),bind(X_103,$fot(and(X_25,X_2904))),bind(X_105,$fot(not(X_25)))]]) ).
cnf(refute_0_1483,plain,
is_a_theorem(implies(X_2904,or(and(X_25,X_2904),not(X_25)))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_25,X_2904),implies(X_2904,not(X_25)))) )],[refute_0_1481,refute_0_1482]) ).
cnf(refute_0_1484,plain,
is_a_theorem(implies(X_2943,or(and(X_2942,X_2943),not(X_2942)))),
inference(subst,[],[refute_0_1483:[bind(X_25,$fot(X_2942)),bind(X_2904,$fot(X_2943))]]) ).
cnf(refute_0_1485,plain,
( ~ is_a_theorem(X_2943)
| is_a_theorem(or(and(X_2942,X_2943),not(X_2942))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_2943,or(and(X_2942,X_2943),not(X_2942)))) )],[refute_0_1484,refute_0_1469]) ).
cnf(refute_0_1486,plain,
( ~ is_a_theorem(implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183))))
| is_a_theorem(or(and(X_34994,implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183)))),not(X_34994))) ),
inference(subst,[],[refute_0_1485:[bind(X_2942,$fot(X_34994)),bind(X_2943,$fot(implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183)))))]]) ).
cnf(refute_0_1487,plain,
is_a_theorem(or(and(X_34994,implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183)))),not(X_34994))),
inference(resolve,[$cnf( is_a_theorem(implies(X_31183,equiv(X_31183,equiv(X_31183,X_31183)))) )],[refute_0_1468,refute_0_1486]) ).
cnf(refute_0_1488,plain,
is_a_theorem(or(and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965)))),not(X_55966))),
inference(subst,[],[refute_0_1487:[bind(X_31183,$fot(X_55965)),bind(X_34994,$fot(X_55966))]]) ).
cnf(refute_0_1489,plain,
is_a_theorem(or(not(X_55966),and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965)))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965)))),not(X_55966))) )],[refute_0_1488,refute_0_1131]) ).
cnf(refute_0_1490,plain,
or(not(X_55966),and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965))))) = implies(X_55966,and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965))))),
inference(subst,[],[refute_0_20:[bind(X,$fot(X_55966)),bind(Y,$fot(and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965))))))]]) ).
cnf(refute_0_1491,plain,
( or(not(X_55966),and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965))))) != implies(X_55966,and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965)))))
| ~ is_a_theorem(or(not(X_55966),and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965))))))
| is_a_theorem(implies(X_55966,and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X_55966),and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965)))))) ),[0],$fot(implies(X_55966,and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965))))))]]) ).
cnf(refute_0_1492,plain,
( ~ is_a_theorem(or(not(X_55966),and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965))))))
| is_a_theorem(implies(X_55966,and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965)))))) ),
inference(resolve,[$cnf( $equal(or(not(X_55966),and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965))))),implies(X_55966,and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965)))))) )],[refute_0_1490,refute_0_1491]) ).
cnf(refute_0_1493,plain,
is_a_theorem(implies(X_55966,and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965)))))),
inference(resolve,[$cnf( is_a_theorem(or(not(X_55966),and(X_55966,implies(X_55965,equiv(X_55965,equiv(X_55965,X_55965)))))) )],[refute_0_1489,refute_0_1492]) ).
cnf(refute_0_1494,plain,
is_a_theorem(implies(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),and(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),implies(X_55968,equiv(X_55968,equiv(X_55968,X_55968)))))),
inference(subst,[],[refute_0_1493:[bind(X_55965,$fot(X_55968)),bind(X_55966,$fot(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968)))]]) ).
cnf(refute_0_1495,plain,
equiv(equiv(X_55968,equiv(X_55968,X_55968)),X_55968) = and(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),implies(X_55968,equiv(X_55968,equiv(X_55968,X_55968)))),
inference(subst,[],[refute_0_318:[bind(X,$fot(equiv(X_55968,equiv(X_55968,X_55968)))),bind(Y,$fot(X_55968))]]) ).
cnf(refute_0_1496,plain,
( equiv(equiv(X_55968,equiv(X_55968,X_55968)),X_55968) != and(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),implies(X_55968,equiv(X_55968,equiv(X_55968,X_55968))))
| and(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),implies(X_55968,equiv(X_55968,equiv(X_55968,X_55968)))) = equiv(equiv(X_55968,equiv(X_55968,X_55968)),X_55968) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(equiv(X_55968,equiv(X_55968,X_55968)),X_55968))),bind(Y0,$fot(and(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),implies(X_55968,equiv(X_55968,equiv(X_55968,X_55968))))))]]) ).
cnf(refute_0_1497,plain,
and(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),implies(X_55968,equiv(X_55968,equiv(X_55968,X_55968)))) = equiv(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),
inference(resolve,[$cnf( $equal(equiv(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),and(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),implies(X_55968,equiv(X_55968,equiv(X_55968,X_55968))))) )],[refute_0_1495,refute_0_1496]) ).
cnf(refute_0_1498,plain,
( and(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),implies(X_55968,equiv(X_55968,equiv(X_55968,X_55968)))) != equiv(equiv(X_55968,equiv(X_55968,X_55968)),X_55968)
| ~ is_a_theorem(implies(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),and(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),implies(X_55968,equiv(X_55968,equiv(X_55968,X_55968))))))
| is_a_theorem(implies(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),equiv(equiv(X_55968,equiv(X_55968,X_55968)),X_55968))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),and(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),implies(X_55968,equiv(X_55968,equiv(X_55968,X_55968)))))) ),[0,1],$fot(equiv(equiv(X_55968,equiv(X_55968,X_55968)),X_55968))]]) ).
cnf(refute_0_1499,plain,
( ~ is_a_theorem(implies(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),and(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),implies(X_55968,equiv(X_55968,equiv(X_55968,X_55968))))))
| is_a_theorem(implies(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),equiv(equiv(X_55968,equiv(X_55968,X_55968)),X_55968))) ),
inference(resolve,[$cnf( $equal(and(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),implies(X_55968,equiv(X_55968,equiv(X_55968,X_55968)))),equiv(equiv(X_55968,equiv(X_55968,X_55968)),X_55968)) )],[refute_0_1497,refute_0_1498]) ).
cnf(refute_0_1500,plain,
is_a_theorem(implies(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),equiv(equiv(X_55968,equiv(X_55968,X_55968)),X_55968))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),and(implies(equiv(X_55968,equiv(X_55968,X_55968)),X_55968),implies(X_55968,equiv(X_55968,equiv(X_55968,X_55968)))))) )],[refute_0_1494,refute_0_1499]) ).
cnf(refute_0_1501,plain,
is_a_theorem(implies(implies(equiv(X_55980,equiv(X_55980,X_55980)),X_55980),equiv(equiv(X_55980,equiv(X_55980,X_55980)),X_55980))),
inference(subst,[],[refute_0_1500:[bind(X_55968,$fot(X_55980))]]) ).
cnf(refute_0_1502,plain,
( ~ is_a_theorem(implies(equiv(X_55980,equiv(X_55980,X_55980)),X_55980))
| is_a_theorem(equiv(equiv(X_55980,equiv(X_55980,X_55980)),X_55980)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(equiv(X_55980,equiv(X_55980,X_55980)),X_55980),equiv(equiv(X_55980,equiv(X_55980,X_55980)),X_55980))) )],[refute_0_1501,refute_0_1130]) ).
cnf(refute_0_1503,plain,
( ~ is_a_theorem(implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137))
| is_a_theorem(implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137))) ),
inference(subst,[],[refute_0_271:[bind(X_155,$fot(implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)))]]) ).
cnf(refute_0_1504,plain,
( ~ is_a_theorem(equiv(X_10134,X_10134))
| ~ is_a_theorem(implies(equiv(X_10134,X_10134),implies(equiv(X_10135,implies(X_10134,X_10134)),X_10135)))
| is_a_theorem(implies(equiv(X_10135,implies(X_10134,X_10134)),X_10135)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(equiv(X_10134,X_10134))),bind(Y,$fot(implies(equiv(X_10135,implies(X_10134,X_10134)),X_10135)))]]) ).
cnf(refute_0_1505,plain,
( ~ is_a_theorem(implies(and(X_117,X),and(X,X_117)))
| is_a_theorem(or(and(X,X_117),not(and(X_117,X)))) ),
inference(subst,[],[refute_0_501:[bind(X,$fot(and(X_117,X))),bind(X_24,$fot(and(X,X_117)))]]) ).
cnf(refute_0_1506,plain,
is_a_theorem(or(and(X,X_117),not(and(X_117,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_117,X),and(X,X_117))) )],[refute_0_764,refute_0_1505]) ).
cnf(refute_0_1507,plain,
( ~ is_a_theorem(implies(not(X),X_156))
| ~ is_a_theorem(not(X))
| is_a_theorem(X_156) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(not(X))),bind(Y,$fot(X_156))]]) ).
cnf(refute_0_1508,plain,
or(X,X_156) = implies(not(X),X_156),
inference(subst,[],[refute_0_60:[bind(Y,$fot(X_156))]]) ).
cnf(refute_0_1509,plain,
( or(X,X_156) != implies(not(X),X_156)
| implies(not(X),X_156) = or(X,X_156) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,X_156))),bind(Y0,$fot(implies(not(X),X_156)))]]) ).
cnf(refute_0_1510,plain,
implies(not(X),X_156) = or(X,X_156),
inference(resolve,[$cnf( $equal(or(X,X_156),implies(not(X),X_156)) )],[refute_0_1508,refute_0_1509]) ).
cnf(refute_0_1511,plain,
( implies(not(X),X_156) != or(X,X_156)
| ~ is_a_theorem(or(X,X_156))
| is_a_theorem(implies(not(X),X_156)) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(implies(not(X),X_156)) ),[0],$fot(or(X,X_156))]]) ).
cnf(refute_0_1512,plain,
( ~ is_a_theorem(or(X,X_156))
| is_a_theorem(implies(not(X),X_156)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_156),or(X,X_156)) )],[refute_0_1510,refute_0_1511]) ).
cnf(refute_0_1513,plain,
( ~ is_a_theorem(not(X))
| ~ is_a_theorem(or(X,X_156))
| is_a_theorem(X_156) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(X),X_156)) )],[refute_0_1512,refute_0_1507]) ).
cnf(refute_0_1514,plain,
( ~ is_a_theorem(not(and(X,X_117)))
| ~ is_a_theorem(or(and(X,X_117),not(and(X_117,X))))
| is_a_theorem(not(and(X_117,X))) ),
inference(subst,[],[refute_0_1513:[bind(X,$fot(and(X,X_117))),bind(X_156,$fot(not(and(X_117,X))))]]) ).
cnf(refute_0_1515,plain,
( ~ is_a_theorem(not(and(X,X_117)))
| is_a_theorem(not(and(X_117,X))) ),
inference(resolve,[$cnf( is_a_theorem(or(and(X,X_117),not(and(X_117,X)))) )],[refute_0_1506,refute_0_1514]) ).
cnf(refute_0_1516,plain,
( ~ is_a_theorem(not(and(and(equiv(not(X_8736),X_8737),X_8736),and(X_8737,X_8737))))
| is_a_theorem(not(and(and(X_8737,X_8737),and(equiv(not(X_8736),X_8737),X_8736)))) ),
inference(subst,[],[refute_0_1515:[bind(X,$fot(and(equiv(not(X_8736),X_8737),X_8736))),bind(X_117,$fot(and(X_8737,X_8737)))]]) ).
cnf(refute_0_1517,plain,
( ~ is_a_theorem(or(implies(and(X_6783,or(X_6784,X_6785)),X_6785),X_6784))
| is_a_theorem(or(P,or(implies(and(X_6783,or(X_6784,X_6785)),X_6785),X_6784))) ),
inference(subst,[],[refute_0_720:[bind(X_155,$fot(or(implies(and(X_6783,or(X_6784,X_6785)),X_6785),X_6784)))]]) ).
cnf(refute_0_1518,plain,
( ~ is_a_theorem(or(X_6661,implies(and(X_6660,or(X_6661,X_6662)),X_6662)))
| is_a_theorem(or(implies(and(X_6660,or(X_6661,X_6662)),X_6662),X_6661)) ),
inference(subst,[],[refute_0_43:[bind(P,$fot(X_6661)),bind(Q,$fot(implies(and(X_6660,or(X_6661,X_6662)),X_6662)))]]) ).
cnf(refute_0_1519,plain,
is_a_theorem(implies(and(X,or(X_6532,X_6533)),or(X_6532,X_6533))),
inference(subst,[],[refute_0_491:[bind(X_212,$fot(or(X_6532,X_6533)))]]) ).
cnf(refute_0_1520,plain,
( ~ is_a_theorem(implies(and(X,or(X_6532,X_6533)),or(X_6532,X_6533)))
| is_a_theorem(or(X_6532,implies(and(X,or(X_6532,X_6533)),X_6533))) ),
inference(subst,[],[refute_0_851:[bind(X,$fot(and(X,or(X_6532,X_6533)))),bind(X_104,$fot(X_6532)),bind(X_105,$fot(X_6533))]]) ).
cnf(refute_0_1521,plain,
is_a_theorem(or(X_6532,implies(and(X,or(X_6532,X_6533)),X_6533))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X,or(X_6532,X_6533)),or(X_6532,X_6533))) )],[refute_0_1519,refute_0_1520]) ).
cnf(refute_0_1522,plain,
is_a_theorem(or(X_6661,implies(and(X_6660,or(X_6661,X_6662)),X_6662))),
inference(subst,[],[refute_0_1521:[bind(X,$fot(X_6660)),bind(X_6532,$fot(X_6661)),bind(X_6533,$fot(X_6662))]]) ).
cnf(refute_0_1523,plain,
is_a_theorem(or(implies(and(X_6660,or(X_6661,X_6662)),X_6662),X_6661)),
inference(resolve,[$cnf( is_a_theorem(or(X_6661,implies(and(X_6660,or(X_6661,X_6662)),X_6662))) )],[refute_0_1522,refute_0_1518]) ).
cnf(refute_0_1524,plain,
is_a_theorem(or(implies(and(X_6783,or(X_6784,X_6785)),X_6785),X_6784)),
inference(subst,[],[refute_0_1523:[bind(X_6660,$fot(X_6783)),bind(X_6661,$fot(X_6784)),bind(X_6662,$fot(X_6785))]]) ).
cnf(refute_0_1525,plain,
is_a_theorem(or(P,or(implies(and(X_6783,or(X_6784,X_6785)),X_6785),X_6784))),
inference(resolve,[$cnf( is_a_theorem(or(implies(and(X_6783,or(X_6784,X_6785)),X_6785),X_6784)) )],[refute_0_1524,refute_0_1517]) ).
cnf(refute_0_1526,plain,
is_a_theorem(or(X_7631,or(implies(and(X_6783,or(X_7633,X_6785)),X_6785),X_7633))),
inference(subst,[],[refute_0_1525:[bind(P,$fot(X_7631)),bind(X_6784,$fot(X_7633))]]) ).
cnf(refute_0_1527,plain,
( ~ is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| ~ is_a_theorem(or(P,or(Q,R)))
| is_a_theorem(or(Q,or(P,R))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(or(P,or(Q,R)))),bind(Y,$fot(or(Q,or(P,R))))]]) ).
cnf(refute_0_1528,plain,
( ~ is_a_theorem(or(P,or(Q,R)))
| is_a_theorem(or(Q,or(P,R))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) )],[refute_0_5,refute_0_1527]) ).
cnf(refute_0_1529,plain,
( ~ is_a_theorem(or(X_7631,or(implies(and(X_6783,or(X_7633,X_6785)),X_6785),X_7633)))
| is_a_theorem(or(implies(and(X_6783,or(X_7633,X_6785)),X_6785),or(X_7631,X_7633))) ),
inference(subst,[],[refute_0_1528:[bind(P,$fot(X_7631)),bind(Q,$fot(implies(and(X_6783,or(X_7633,X_6785)),X_6785))),bind(R,$fot(X_7633))]]) ).
cnf(refute_0_1530,plain,
is_a_theorem(or(implies(and(X_6783,or(X_7633,X_6785)),X_6785),or(X_7631,X_7633))),
inference(resolve,[$cnf( is_a_theorem(or(X_7631,or(implies(and(X_6783,or(X_7633,X_6785)),X_6785),X_7633))) )],[refute_0_1526,refute_0_1529]) ).
cnf(refute_0_1531,plain,
is_a_theorem(or(implies(and(X_7684,or(X_7687,X_7685)),X_7685),or(not(X),X_7687))),
inference(subst,[],[refute_0_1530:[bind(X_6783,$fot(X_7684)),bind(X_6785,$fot(X_7685)),bind(X_7631,$fot(not(X))),bind(X_7633,$fot(X_7687))]]) ).
cnf(refute_0_1532,plain,
implies(X,X_7687) = or(not(X),X_7687),
inference(subst,[],[refute_0_9:[bind(Y,$fot(X_7687))]]) ).
cnf(refute_0_1533,plain,
( implies(X,X_7687) != or(not(X),X_7687)
| or(not(X),X_7687) = implies(X,X_7687) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,X_7687))),bind(Y0,$fot(or(not(X),X_7687)))]]) ).
cnf(refute_0_1534,plain,
or(not(X),X_7687) = implies(X,X_7687),
inference(resolve,[$cnf( $equal(implies(X,X_7687),or(not(X),X_7687)) )],[refute_0_1532,refute_0_1533]) ).
cnf(refute_0_1535,plain,
( or(not(X),X_7687) != implies(X,X_7687)
| ~ is_a_theorem(or(implies(and(X_7684,or(X_7687,X_7685)),X_7685),or(not(X),X_7687)))
| is_a_theorem(or(implies(and(X_7684,or(X_7687,X_7685)),X_7685),implies(X,X_7687))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(and(X_7684,or(X_7687,X_7685)),X_7685),or(not(X),X_7687))) ),[0,1],$fot(implies(X,X_7687))]]) ).
cnf(refute_0_1536,plain,
( ~ is_a_theorem(or(implies(and(X_7684,or(X_7687,X_7685)),X_7685),or(not(X),X_7687)))
| is_a_theorem(or(implies(and(X_7684,or(X_7687,X_7685)),X_7685),implies(X,X_7687))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_7687),implies(X,X_7687)) )],[refute_0_1534,refute_0_1535]) ).
cnf(refute_0_1537,plain,
is_a_theorem(or(implies(and(X_7684,or(X_7687,X_7685)),X_7685),implies(X,X_7687))),
inference(resolve,[$cnf( is_a_theorem(or(implies(and(X_7684,or(X_7687,X_7685)),X_7685),or(not(X),X_7687))) )],[refute_0_1531,refute_0_1536]) ).
cnf(refute_0_1538,plain,
is_a_theorem(or(implies(and(not(and(X_7944,X_7945)),or(X_7945,X_7944)),X_7944),implies(X_7942,X_7945))),
inference(subst,[],[refute_0_1537:[bind(X,$fot(X_7942)),bind(X_7684,$fot(not(and(X_7944,X_7945)))),bind(X_7685,$fot(X_7944)),bind(X_7687,$fot(X_7945))]]) ).
cnf(refute_0_1539,plain,
and(not(and(X_7944,X_7945)),or(X_7945,X_7944)) = equiv(X_7944,not(X_7945)),
inference(subst,[],[refute_0_360:[bind(X,$fot(X_7945)),bind(X_29,$fot(X_7944))]]) ).
cnf(refute_0_1540,plain,
( and(not(and(X_7944,X_7945)),or(X_7945,X_7944)) != equiv(X_7944,not(X_7945))
| ~ is_a_theorem(or(implies(and(not(and(X_7944,X_7945)),or(X_7945,X_7944)),X_7944),implies(X_7942,X_7945)))
| is_a_theorem(or(implies(equiv(X_7944,not(X_7945)),X_7944),implies(X_7942,X_7945))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(and(not(and(X_7944,X_7945)),or(X_7945,X_7944)),X_7944),implies(X_7942,X_7945))) ),[0,0,0],$fot(equiv(X_7944,not(X_7945)))]]) ).
cnf(refute_0_1541,plain,
( ~ is_a_theorem(or(implies(and(not(and(X_7944,X_7945)),or(X_7945,X_7944)),X_7944),implies(X_7942,X_7945)))
| is_a_theorem(or(implies(equiv(X_7944,not(X_7945)),X_7944),implies(X_7942,X_7945))) ),
inference(resolve,[$cnf( $equal(and(not(and(X_7944,X_7945)),or(X_7945,X_7944)),equiv(X_7944,not(X_7945))) )],[refute_0_1539,refute_0_1540]) ).
cnf(refute_0_1542,plain,
is_a_theorem(or(implies(equiv(X_7944,not(X_7945)),X_7944),implies(X_7942,X_7945))),
inference(resolve,[$cnf( is_a_theorem(or(implies(and(not(and(X_7944,X_7945)),or(X_7945,X_7944)),X_7944),implies(X_7942,X_7945))) )],[refute_0_1538,refute_0_1541]) ).
cnf(refute_0_1543,plain,
is_a_theorem(or(implies(equiv(X_7947,not(not(X_7946))),X_7947),implies(X_7946,not(X_7946)))),
inference(subst,[],[refute_0_1542:[bind(X_7942,$fot(X_7946)),bind(X_7944,$fot(X_7947)),bind(X_7945,$fot(not(X_7946)))]]) ).
cnf(refute_0_1544,plain,
implies(X_7946,not(X_7946)) = not(and(X_7946,X_7946)),
inference(subst,[],[refute_0_632:[bind(X,$fot(X_7946))]]) ).
cnf(refute_0_1545,plain,
( implies(X_7946,not(X_7946)) != not(and(X_7946,X_7946))
| ~ is_a_theorem(or(implies(equiv(X_7947,not(not(X_7946))),X_7947),implies(X_7946,not(X_7946))))
| is_a_theorem(or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(equiv(X_7947,not(not(X_7946))),X_7947),implies(X_7946,not(X_7946)))) ),[0,1],$fot(not(and(X_7946,X_7946)))]]) ).
cnf(refute_0_1546,plain,
( ~ is_a_theorem(or(implies(equiv(X_7947,not(not(X_7946))),X_7947),implies(X_7946,not(X_7946))))
| is_a_theorem(or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946)))) ),
inference(resolve,[$cnf( $equal(implies(X_7946,not(X_7946)),not(and(X_7946,X_7946))) )],[refute_0_1544,refute_0_1545]) ).
cnf(refute_0_1547,plain,
is_a_theorem(or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946)))),
inference(resolve,[$cnf( is_a_theorem(or(implies(equiv(X_7947,not(not(X_7946))),X_7947),implies(X_7946,not(X_7946)))) )],[refute_0_1543,refute_0_1546]) ).
cnf(refute_0_1548,plain,
( equiv(X_35,X) != equiv(X_35,not(not(X)))
| equiv(X_35,not(not(X))) = equiv(X_35,X) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(X_35,X))),bind(Y0,$fot(equiv(X_35,not(not(X)))))]]) ).
cnf(refute_0_1549,plain,
equiv(X_35,not(not(X))) = equiv(X_35,X),
inference(resolve,[$cnf( $equal(equiv(X_35,X),equiv(X_35,not(not(X)))) )],[refute_0_830,refute_0_1548]) ).
cnf(refute_0_1550,plain,
equiv(X_7947,not(not(X_7946))) = equiv(X_7947,X_7946),
inference(subst,[],[refute_0_1549:[bind(X,$fot(X_7946)),bind(X_35,$fot(X_7947))]]) ).
cnf(refute_0_1551,plain,
implies(equiv(X_7947,not(not(X_7946))),X_7947) = implies(equiv(X_7947,not(not(X_7946))),X_7947),
introduced(tautology,[refl,[$fot(implies(equiv(X_7947,not(not(X_7946))),X_7947))]]) ).
cnf(refute_0_1552,plain,
( equiv(X_7947,not(not(X_7946))) != equiv(X_7947,X_7946)
| implies(equiv(X_7947,not(not(X_7946))),X_7947) != implies(equiv(X_7947,not(not(X_7946))),X_7947)
| implies(equiv(X_7947,not(not(X_7946))),X_7947) = implies(equiv(X_7947,X_7946),X_7947) ),
introduced(tautology,[equality,[$cnf( $equal(implies(equiv(X_7947,not(not(X_7946))),X_7947),implies(equiv(X_7947,not(not(X_7946))),X_7947)) ),[1,0],$fot(equiv(X_7947,X_7946))]]) ).
cnf(refute_0_1553,plain,
( equiv(X_7947,not(not(X_7946))) != equiv(X_7947,X_7946)
| implies(equiv(X_7947,not(not(X_7946))),X_7947) = implies(equiv(X_7947,X_7946),X_7947) ),
inference(resolve,[$cnf( $equal(implies(equiv(X_7947,not(not(X_7946))),X_7947),implies(equiv(X_7947,not(not(X_7946))),X_7947)) )],[refute_0_1551,refute_0_1552]) ).
cnf(refute_0_1554,plain,
implies(equiv(X_7947,not(not(X_7946))),X_7947) = implies(equiv(X_7947,X_7946),X_7947),
inference(resolve,[$cnf( $equal(equiv(X_7947,not(not(X_7946))),equiv(X_7947,X_7946)) )],[refute_0_1550,refute_0_1553]) ).
cnf(refute_0_1555,plain,
or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946))) = or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946))),
introduced(tautology,[refl,[$fot(or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946))))]]) ).
cnf(refute_0_1556,plain,
( implies(equiv(X_7947,not(not(X_7946))),X_7947) != implies(equiv(X_7947,X_7946),X_7947)
| or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946))) != or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946)))
| or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946))) = or(implies(equiv(X_7947,X_7946),X_7947),not(and(X_7946,X_7946))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946))),or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946)))) ),[1,0],$fot(implies(equiv(X_7947,X_7946),X_7947))]]) ).
cnf(refute_0_1557,plain,
( implies(equiv(X_7947,not(not(X_7946))),X_7947) != implies(equiv(X_7947,X_7946),X_7947)
| or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946))) = or(implies(equiv(X_7947,X_7946),X_7947),not(and(X_7946,X_7946))) ),
inference(resolve,[$cnf( $equal(or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946))),or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946)))) )],[refute_0_1555,refute_0_1556]) ).
cnf(refute_0_1558,plain,
or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946))) = or(implies(equiv(X_7947,X_7946),X_7947),not(and(X_7946,X_7946))),
inference(resolve,[$cnf( $equal(implies(equiv(X_7947,not(not(X_7946))),X_7947),implies(equiv(X_7947,X_7946),X_7947)) )],[refute_0_1554,refute_0_1557]) ).
cnf(refute_0_1559,plain,
( or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946))) != or(implies(equiv(X_7947,X_7946),X_7947),not(and(X_7946,X_7946)))
| ~ is_a_theorem(or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946))))
| is_a_theorem(or(implies(equiv(X_7947,X_7946),X_7947),not(and(X_7946,X_7946)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946)))) ),[0],$fot(or(implies(equiv(X_7947,X_7946),X_7947),not(and(X_7946,X_7946))))]]) ).
cnf(refute_0_1560,plain,
( ~ is_a_theorem(or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946))))
| is_a_theorem(or(implies(equiv(X_7947,X_7946),X_7947),not(and(X_7946,X_7946)))) ),
inference(resolve,[$cnf( $equal(or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946))),or(implies(equiv(X_7947,X_7946),X_7947),not(and(X_7946,X_7946)))) )],[refute_0_1558,refute_0_1559]) ).
cnf(refute_0_1561,plain,
is_a_theorem(or(implies(equiv(X_7947,X_7946),X_7947),not(and(X_7946,X_7946)))),
inference(resolve,[$cnf( is_a_theorem(or(implies(equiv(X_7947,not(not(X_7946))),X_7947),not(and(X_7946,X_7946)))) )],[refute_0_1547,refute_0_1560]) ).
cnf(refute_0_1562,plain,
is_a_theorem(or(implies(equiv(not(X_17),X_8734),not(X_17)),not(and(X_8734,X_8734)))),
inference(subst,[],[refute_0_1561:[bind(X_7946,$fot(X_8734)),bind(X_7947,$fot(not(X_17)))]]) ).
cnf(refute_0_1563,plain,
or(implies(equiv(not(X_17),X_8734),not(X_17)),not(and(X_8734,X_8734))) = implies(and(equiv(not(X_17),X_8734),X_17),not(and(X_8734,X_8734))),
inference(subst,[],[refute_0_467:[bind(Y,$fot(not(and(X_8734,X_8734)))),bind(X_16,$fot(equiv(not(X_17),X_8734)))]]) ).
cnf(refute_0_1564,plain,
( or(implies(equiv(not(X_17),X_8734),not(X_17)),not(and(X_8734,X_8734))) != implies(and(equiv(not(X_17),X_8734),X_17),not(and(X_8734,X_8734)))
| ~ is_a_theorem(or(implies(equiv(not(X_17),X_8734),not(X_17)),not(and(X_8734,X_8734))))
| is_a_theorem(implies(and(equiv(not(X_17),X_8734),X_17),not(and(X_8734,X_8734)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(equiv(not(X_17),X_8734),not(X_17)),not(and(X_8734,X_8734)))) ),[0],$fot(implies(and(equiv(not(X_17),X_8734),X_17),not(and(X_8734,X_8734))))]]) ).
cnf(refute_0_1565,plain,
( ~ is_a_theorem(or(implies(equiv(not(X_17),X_8734),not(X_17)),not(and(X_8734,X_8734))))
| is_a_theorem(implies(and(equiv(not(X_17),X_8734),X_17),not(and(X_8734,X_8734)))) ),
inference(resolve,[$cnf( $equal(or(implies(equiv(not(X_17),X_8734),not(X_17)),not(and(X_8734,X_8734))),implies(and(equiv(not(X_17),X_8734),X_17),not(and(X_8734,X_8734)))) )],[refute_0_1563,refute_0_1564]) ).
cnf(refute_0_1566,plain,
is_a_theorem(implies(and(equiv(not(X_17),X_8734),X_17),not(and(X_8734,X_8734)))),
inference(resolve,[$cnf( is_a_theorem(or(implies(equiv(not(X_17),X_8734),not(X_17)),not(and(X_8734,X_8734)))) )],[refute_0_1562,refute_0_1565]) ).
cnf(refute_0_1567,plain,
implies(X,implies(X_17,not(X_17))) = not(and(X,and(X_17,X_17))),
inference(subst,[],[refute_0_366:[bind(X_16,$fot(X_17))]]) ).
cnf(refute_0_1568,plain,
implies(X_17,not(X_17)) = not(and(X_17,X_17)),
inference(subst,[],[refute_0_632:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_1569,plain,
( implies(X,implies(X_17,not(X_17))) != not(and(X,and(X_17,X_17)))
| implies(X_17,not(X_17)) != not(and(X_17,X_17))
| implies(X,not(and(X_17,X_17))) = not(and(X,and(X_17,X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,implies(X_17,not(X_17))),not(and(X,and(X_17,X_17)))) ),[0,1],$fot(not(and(X_17,X_17)))]]) ).
cnf(refute_0_1570,plain,
( implies(X,implies(X_17,not(X_17))) != not(and(X,and(X_17,X_17)))
| implies(X,not(and(X_17,X_17))) = not(and(X,and(X_17,X_17))) ),
inference(resolve,[$cnf( $equal(implies(X_17,not(X_17)),not(and(X_17,X_17))) )],[refute_0_1568,refute_0_1569]) ).
cnf(refute_0_1571,plain,
implies(X,not(and(X_17,X_17))) = not(and(X,and(X_17,X_17))),
inference(resolve,[$cnf( $equal(implies(X,implies(X_17,not(X_17))),not(and(X,and(X_17,X_17)))) )],[refute_0_1567,refute_0_1570]) ).
cnf(refute_0_1572,plain,
implies(and(equiv(not(X_17),X_8734),X_17),not(and(X_8734,X_8734))) = not(and(and(equiv(not(X_17),X_8734),X_17),and(X_8734,X_8734))),
inference(subst,[],[refute_0_1571:[bind(X,$fot(and(equiv(not(X_17),X_8734),X_17))),bind(X_17,$fot(X_8734))]]) ).
cnf(refute_0_1573,plain,
( implies(and(equiv(not(X_17),X_8734),X_17),not(and(X_8734,X_8734))) != not(and(and(equiv(not(X_17),X_8734),X_17),and(X_8734,X_8734)))
| ~ is_a_theorem(implies(and(equiv(not(X_17),X_8734),X_17),not(and(X_8734,X_8734))))
| is_a_theorem(not(and(and(equiv(not(X_17),X_8734),X_17),and(X_8734,X_8734)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(equiv(not(X_17),X_8734),X_17),not(and(X_8734,X_8734)))) ),[0],$fot(not(and(and(equiv(not(X_17),X_8734),X_17),and(X_8734,X_8734))))]]) ).
cnf(refute_0_1574,plain,
( ~ is_a_theorem(implies(and(equiv(not(X_17),X_8734),X_17),not(and(X_8734,X_8734))))
| is_a_theorem(not(and(and(equiv(not(X_17),X_8734),X_17),and(X_8734,X_8734)))) ),
inference(resolve,[$cnf( $equal(implies(and(equiv(not(X_17),X_8734),X_17),not(and(X_8734,X_8734))),not(and(and(equiv(not(X_17),X_8734),X_17),and(X_8734,X_8734)))) )],[refute_0_1572,refute_0_1573]) ).
cnf(refute_0_1575,plain,
is_a_theorem(not(and(and(equiv(not(X_17),X_8734),X_17),and(X_8734,X_8734)))),
inference(resolve,[$cnf( is_a_theorem(implies(and(equiv(not(X_17),X_8734),X_17),not(and(X_8734,X_8734)))) )],[refute_0_1566,refute_0_1574]) ).
cnf(refute_0_1576,plain,
is_a_theorem(not(and(and(equiv(not(X_8736),X_8737),X_8736),and(X_8737,X_8737)))),
inference(subst,[],[refute_0_1575:[bind(X_17,$fot(X_8736)),bind(X_8734,$fot(X_8737))]]) ).
cnf(refute_0_1577,plain,
is_a_theorem(not(and(and(X_8737,X_8737),and(equiv(not(X_8736),X_8737),X_8736)))),
inference(resolve,[$cnf( is_a_theorem(not(and(and(equiv(not(X_8736),X_8737),X_8736),and(X_8737,X_8737)))) )],[refute_0_1576,refute_0_1516]) ).
cnf(refute_0_1578,plain,
is_a_theorem(not(and(and(X_8737,X_8737),and(equiv(not(not(X_10027)),X_8737),not(X_10027))))),
inference(subst,[],[refute_0_1577:[bind(X_8736,$fot(not(X_10027)))]]) ).
cnf(refute_0_1579,plain,
X_10027 = not(not(X_10027)),
inference(subst,[],[refute_0_1229:[bind(X_10026,$fot(X_10027))]]) ).
cnf(refute_0_1580,plain,
( X_10027 != not(not(X_10027))
| not(not(X_10027)) = X_10027 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(X_10027)),bind(Y0,$fot(not(not(X_10027))))]]) ).
cnf(refute_0_1581,plain,
not(not(X_10027)) = X_10027,
inference(resolve,[$cnf( $equal(X_10027,not(not(X_10027))) )],[refute_0_1579,refute_0_1580]) ).
cnf(refute_0_1582,plain,
( not(not(X_10027)) != X_10027
| ~ is_a_theorem(not(and(and(X_8737,X_8737),and(equiv(not(not(X_10027)),X_8737),not(X_10027)))))
| is_a_theorem(not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(and(X_8737,X_8737),and(equiv(not(not(X_10027)),X_8737),not(X_10027))))) ),[0,0,1,0,0],$fot(X_10027)]]) ).
cnf(refute_0_1583,plain,
( ~ is_a_theorem(not(and(and(X_8737,X_8737),and(equiv(not(not(X_10027)),X_8737),not(X_10027)))))
| is_a_theorem(not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))))) ),
inference(resolve,[$cnf( $equal(not(not(X_10027)),X_10027) )],[refute_0_1581,refute_0_1582]) ).
cnf(refute_0_1584,plain,
is_a_theorem(not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))))),
inference(resolve,[$cnf( is_a_theorem(not(and(and(X_8737,X_8737),and(equiv(not(not(X_10027)),X_8737),not(X_10027))))) )],[refute_0_1578,refute_0_1583]) ).
cnf(refute_0_1585,plain,
not(not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)))) = implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)),
inference(subst,[],[refute_0_1231:[bind(X_10026,$fot(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))))]]) ).
cnf(refute_0_1586,plain,
and(and(X_8737,X_8737),not(implies(equiv(X_10027,X_8737),X_10027))) = not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))),
inference(subst,[],[refute_0_972:[bind(X,$fot(and(X_8737,X_8737))),bind(X_9550,$fot(implies(equiv(X_10027,X_8737),X_10027)))]]) ).
cnf(refute_0_1587,plain,
and(equiv(X_10027,X_8737),not(X_10027)) = not(implies(equiv(X_10027,X_8737),X_10027)),
inference(subst,[],[refute_0_972:[bind(X,$fot(equiv(X_10027,X_8737))),bind(X_9550,$fot(X_10027))]]) ).
cnf(refute_0_1588,plain,
and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))) = and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))),
introduced(tautology,[refl,[$fot(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))))]]) ).
cnf(refute_0_1589,plain,
( and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))) != and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))
| and(equiv(X_10027,X_8737),not(X_10027)) != not(implies(equiv(X_10027,X_8737),X_10027))
| and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))) = and(and(X_8737,X_8737),not(implies(equiv(X_10027,X_8737),X_10027))) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))),and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))) ),[1,1],$fot(not(implies(equiv(X_10027,X_8737),X_10027)))]]) ).
cnf(refute_0_1590,plain,
( and(equiv(X_10027,X_8737),not(X_10027)) != not(implies(equiv(X_10027,X_8737),X_10027))
| and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))) = and(and(X_8737,X_8737),not(implies(equiv(X_10027,X_8737),X_10027))) ),
inference(resolve,[$cnf( $equal(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))),and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))) )],[refute_0_1588,refute_0_1589]) ).
cnf(refute_0_1591,plain,
and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))) = and(and(X_8737,X_8737),not(implies(equiv(X_10027,X_8737),X_10027))),
inference(resolve,[$cnf( $equal(and(equiv(X_10027,X_8737),not(X_10027)),not(implies(equiv(X_10027,X_8737),X_10027))) )],[refute_0_1587,refute_0_1590]) ).
cnf(refute_0_1592,plain,
( and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))) != and(and(X_8737,X_8737),not(implies(equiv(X_10027,X_8737),X_10027)))
| and(and(X_8737,X_8737),not(implies(equiv(X_10027,X_8737),X_10027))) != not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)))
| and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))) = not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))))),bind(Y0,$fot(and(and(X_8737,X_8737),not(implies(equiv(X_10027,X_8737),X_10027))))),bind(Z,$fot(not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)))))]]) ).
cnf(refute_0_1593,plain,
( and(and(X_8737,X_8737),not(implies(equiv(X_10027,X_8737),X_10027))) != not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)))
| and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))) = not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))) ),
inference(resolve,[$cnf( $equal(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))),and(and(X_8737,X_8737),not(implies(equiv(X_10027,X_8737),X_10027)))) )],[refute_0_1591,refute_0_1592]) ).
cnf(refute_0_1594,plain,
and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))) = not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))),
inference(resolve,[$cnf( $equal(and(and(X_8737,X_8737),not(implies(equiv(X_10027,X_8737),X_10027))),not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)))) )],[refute_0_1586,refute_0_1593]) ).
cnf(refute_0_1595,plain,
not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))) = not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))),
introduced(tautology,[refl,[$fot(not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))))]]) ).
cnf(refute_0_1596,plain,
( and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))) != not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)))
| not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))) != not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))))
| not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))) = not(not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))),not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))))) ),[1,0],$fot(not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))))]]) ).
cnf(refute_0_1597,plain,
( and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))) != not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)))
| not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))) = not(not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)))) ),
inference(resolve,[$cnf( $equal(not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))),not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))))) )],[refute_0_1595,refute_0_1596]) ).
cnf(refute_0_1598,plain,
not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))) = not(not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)))),
inference(resolve,[$cnf( $equal(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))),not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)))) )],[refute_0_1594,refute_0_1597]) ).
cnf(refute_0_1599,plain,
( not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))) != not(not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))))
| not(not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)))) != implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))
| not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))) = implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))))),bind(Y0,$fot(not(not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)))))),bind(Z,$fot(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))))]]) ).
cnf(refute_0_1600,plain,
( not(not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)))) != implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))
| not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))) = implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)) ),
inference(resolve,[$cnf( $equal(not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))),not(not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))))) )],[refute_0_1598,refute_0_1599]) ).
cnf(refute_0_1601,plain,
not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))) = implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)),
inference(resolve,[$cnf( $equal(not(not(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)))),implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))) )],[refute_0_1585,refute_0_1600]) ).
cnf(refute_0_1602,plain,
( not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))) != implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))
| ~ is_a_theorem(not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))))
| is_a_theorem(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))))) ),[0],$fot(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027)))]]) ).
cnf(refute_0_1603,plain,
( ~ is_a_theorem(not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))))
| is_a_theorem(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))) ),
inference(resolve,[$cnf( $equal(not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027)))),implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))) )],[refute_0_1601,refute_0_1602]) ).
cnf(refute_0_1604,plain,
is_a_theorem(implies(and(X_8737,X_8737),implies(equiv(X_10027,X_8737),X_10027))),
inference(resolve,[$cnf( is_a_theorem(not(and(and(X_8737,X_8737),and(equiv(X_10027,X_8737),not(X_10027))))) )],[refute_0_1584,refute_0_1603]) ).
cnf(refute_0_1605,plain,
is_a_theorem(implies(and(implies(X,X),implies(X,X)),implies(equiv(X_10115,implies(X,X)),X_10115))),
inference(subst,[],[refute_0_1604:[bind(X_10027,$fot(X_10115)),bind(X_8737,$fot(implies(X,X)))]]) ).
cnf(refute_0_1606,plain,
( and(implies(X,X),implies(X,X)) != equiv(X,X)
| ~ is_a_theorem(implies(and(implies(X,X),implies(X,X)),implies(equiv(X_10115,implies(X,X)),X_10115)))
| is_a_theorem(implies(equiv(X,X),implies(equiv(X_10115,implies(X,X)),X_10115))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(implies(X,X),implies(X,X)),implies(equiv(X_10115,implies(X,X)),X_10115))) ),[0,0],$fot(equiv(X,X))]]) ).
cnf(refute_0_1607,plain,
( ~ is_a_theorem(implies(and(implies(X,X),implies(X,X)),implies(equiv(X_10115,implies(X,X)),X_10115)))
| is_a_theorem(implies(equiv(X,X),implies(equiv(X_10115,implies(X,X)),X_10115))) ),
inference(resolve,[$cnf( $equal(and(implies(X,X),implies(X,X)),equiv(X,X)) )],[refute_0_640,refute_0_1606]) ).
cnf(refute_0_1608,plain,
is_a_theorem(implies(equiv(X,X),implies(equiv(X_10115,implies(X,X)),X_10115))),
inference(resolve,[$cnf( is_a_theorem(implies(and(implies(X,X),implies(X,X)),implies(equiv(X_10115,implies(X,X)),X_10115))) )],[refute_0_1605,refute_0_1607]) ).
cnf(refute_0_1609,plain,
is_a_theorem(implies(equiv(X_10134,X_10134),implies(equiv(X_10135,implies(X_10134,X_10134)),X_10135))),
inference(subst,[],[refute_0_1608:[bind(X,$fot(X_10134)),bind(X_10115,$fot(X_10135))]]) ).
cnf(refute_0_1610,plain,
( ~ is_a_theorem(equiv(X_10134,X_10134))
| is_a_theorem(implies(equiv(X_10135,implies(X_10134,X_10134)),X_10135)) ),
inference(resolve,[$cnf( is_a_theorem(implies(equiv(X_10134,X_10134),implies(equiv(X_10135,implies(X_10134,X_10134)),X_10135))) )],[refute_0_1609,refute_0_1504]) ).
cnf(refute_0_1611,plain,
is_a_theorem(equiv(X_10134,X_10134)),
inference(subst,[],[refute_0_526:[bind(X_4515,$fot(X_10134))]]) ).
cnf(refute_0_1612,plain,
is_a_theorem(implies(equiv(X_10135,implies(X_10134,X_10134)),X_10135)),
inference(resolve,[$cnf( is_a_theorem(equiv(X_10134,X_10134)) )],[refute_0_1611,refute_0_1610]) ).
cnf(refute_0_1613,plain,
is_a_theorem(implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)),
inference(subst,[],[refute_0_1612:[bind(X_10134,$fot(X_10136)),bind(X_10135,$fot(X_10137))]]) ).
cnf(refute_0_1614,plain,
is_a_theorem(implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137))),
inference(resolve,[$cnf( is_a_theorem(implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)) )],[refute_0_1613,refute_0_1503]) ).
cnf(refute_0_1615,plain,
implies(X_10136,X_10136) = equiv(X_10136,X_10136),
inference(subst,[],[refute_0_1404:[bind(X_1079,$fot(X_10136))]]) ).
cnf(refute_0_1616,plain,
equiv(X_10137,implies(X_10136,X_10136)) = equiv(X_10137,implies(X_10136,X_10136)),
introduced(tautology,[refl,[$fot(equiv(X_10137,implies(X_10136,X_10136)))]]) ).
cnf(refute_0_1617,plain,
( equiv(X_10137,implies(X_10136,X_10136)) != equiv(X_10137,implies(X_10136,X_10136))
| implies(X_10136,X_10136) != equiv(X_10136,X_10136)
| equiv(X_10137,implies(X_10136,X_10136)) = equiv(X_10137,equiv(X_10136,X_10136)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_10137,implies(X_10136,X_10136)),equiv(X_10137,implies(X_10136,X_10136))) ),[1,1],$fot(equiv(X_10136,X_10136))]]) ).
cnf(refute_0_1618,plain,
( implies(X_10136,X_10136) != equiv(X_10136,X_10136)
| equiv(X_10137,implies(X_10136,X_10136)) = equiv(X_10137,equiv(X_10136,X_10136)) ),
inference(resolve,[$cnf( $equal(equiv(X_10137,implies(X_10136,X_10136)),equiv(X_10137,implies(X_10136,X_10136))) )],[refute_0_1616,refute_0_1617]) ).
cnf(refute_0_1619,plain,
equiv(X_10137,implies(X_10136,X_10136)) = equiv(X_10137,equiv(X_10136,X_10136)),
inference(resolve,[$cnf( $equal(implies(X_10136,X_10136),equiv(X_10136,X_10136)) )],[refute_0_1615,refute_0_1618]) ).
cnf(refute_0_1620,plain,
implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137) = implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137),
introduced(tautology,[refl,[$fot(implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137))]]) ).
cnf(refute_0_1621,plain,
( equiv(X_10137,implies(X_10136,X_10136)) != equiv(X_10137,equiv(X_10136,X_10136))
| implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137) != implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)
| implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137) = implies(equiv(X_10137,equiv(X_10136,X_10136)),X_10137) ),
introduced(tautology,[equality,[$cnf( $equal(implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137),implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)) ),[1,0],$fot(equiv(X_10137,equiv(X_10136,X_10136)))]]) ).
cnf(refute_0_1622,plain,
( equiv(X_10137,implies(X_10136,X_10136)) != equiv(X_10137,equiv(X_10136,X_10136))
| implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137) = implies(equiv(X_10137,equiv(X_10136,X_10136)),X_10137) ),
inference(resolve,[$cnf( $equal(implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137),implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)) )],[refute_0_1620,refute_0_1621]) ).
cnf(refute_0_1623,plain,
implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137) = implies(equiv(X_10137,equiv(X_10136,X_10136)),X_10137),
inference(resolve,[$cnf( $equal(equiv(X_10137,implies(X_10136,X_10136)),equiv(X_10137,equiv(X_10136,X_10136))) )],[refute_0_1619,refute_0_1622]) ).
cnf(refute_0_1624,plain,
implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)) = implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)),
introduced(tautology,[refl,[$fot(implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)))]]) ).
cnf(refute_0_1625,plain,
( implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)) != implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137))
| implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137) != implies(equiv(X_10137,equiv(X_10136,X_10136)),X_10137)
| implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)) = implies(X,implies(equiv(X_10137,equiv(X_10136,X_10136)),X_10137)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)),implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137))) ),[1,1],$fot(implies(equiv(X_10137,equiv(X_10136,X_10136)),X_10137))]]) ).
cnf(refute_0_1626,plain,
( implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137) != implies(equiv(X_10137,equiv(X_10136,X_10136)),X_10137)
| implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)) = implies(X,implies(equiv(X_10137,equiv(X_10136,X_10136)),X_10137)) ),
inference(resolve,[$cnf( $equal(implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)),implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137))) )],[refute_0_1624,refute_0_1625]) ).
cnf(refute_0_1627,plain,
implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)) = implies(X,implies(equiv(X_10137,equiv(X_10136,X_10136)),X_10137)),
inference(resolve,[$cnf( $equal(implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137),implies(equiv(X_10137,equiv(X_10136,X_10136)),X_10137)) )],[refute_0_1623,refute_0_1626]) ).
cnf(refute_0_1628,plain,
( implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)) != implies(X,implies(equiv(X_10137,equiv(X_10136,X_10136)),X_10137))
| ~ is_a_theorem(implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)))
| is_a_theorem(implies(X,implies(equiv(X_10137,equiv(X_10136,X_10136)),X_10137))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137))) ),[0],$fot(implies(X,implies(equiv(X_10137,equiv(X_10136,X_10136)),X_10137)))]]) ).
cnf(refute_0_1629,plain,
( ~ is_a_theorem(implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)))
| is_a_theorem(implies(X,implies(equiv(X_10137,equiv(X_10136,X_10136)),X_10137))) ),
inference(resolve,[$cnf( $equal(implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137)),implies(X,implies(equiv(X_10137,equiv(X_10136,X_10136)),X_10137))) )],[refute_0_1627,refute_0_1628]) ).
cnf(refute_0_1630,plain,
is_a_theorem(implies(X,implies(equiv(X_10137,equiv(X_10136,X_10136)),X_10137))),
inference(resolve,[$cnf( is_a_theorem(implies(X,implies(equiv(X_10137,implies(X_10136,X_10136)),X_10137))) )],[refute_0_1614,refute_0_1629]) ).
cnf(refute_0_1631,plain,
is_a_theorem(implies(not(X),implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473))),
inference(subst,[],[refute_0_1630:[bind(X,$fot(not(X))),bind(X_10136,$fot(X_25472)),bind(X_10137,$fot(X_25473))]]) ).
cnf(refute_0_1632,plain,
or(X,implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473)) = implies(not(X),implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473)),
inference(subst,[],[refute_0_60:[bind(Y,$fot(implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473)))]]) ).
cnf(refute_0_1633,plain,
( or(X,implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473)) != implies(not(X),implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473))
| implies(not(X),implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473)) = or(X,implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473)))),bind(Y0,$fot(implies(not(X),implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473))))]]) ).
cnf(refute_0_1634,plain,
implies(not(X),implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473)) = or(X,implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473)),
inference(resolve,[$cnf( $equal(or(X,implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473)),implies(not(X),implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473))) )],[refute_0_1632,refute_0_1633]) ).
cnf(refute_0_1635,plain,
( implies(not(X),implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473)) != or(X,implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473))
| ~ is_a_theorem(implies(not(X),implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473)))
| is_a_theorem(or(X,implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X),implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473))) ),[0],$fot(or(X,implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473)))]]) ).
cnf(refute_0_1636,plain,
( ~ is_a_theorem(implies(not(X),implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473)))
| is_a_theorem(or(X,implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473))) ),
inference(resolve,[$cnf( $equal(implies(not(X),implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473)),or(X,implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473))) )],[refute_0_1634,refute_0_1635]) ).
cnf(refute_0_1637,plain,
is_a_theorem(or(X,implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X),implies(equiv(X_25473,equiv(X_25472,X_25472)),X_25473))) )],[refute_0_1631,refute_0_1636]) ).
cnf(refute_0_1638,plain,
is_a_theorem(or(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476),implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476))),
inference(subst,[],[refute_0_1637:[bind(X,$fot(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476))),bind(X_25472,$fot(X_25475)),bind(X_25473,$fot(X_25476))]]) ).
cnf(refute_0_1639,plain,
implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476) = or(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476),implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476)),
inference(subst,[],[refute_0_1114:[bind(X_25347,$fot(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476)))]]) ).
cnf(refute_0_1640,plain,
( implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476) != or(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476),implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476))
| or(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476),implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476)) = implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476))),bind(Y0,$fot(or(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476),implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476))))]]) ).
cnf(refute_0_1641,plain,
or(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476),implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476)) = implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476),
inference(resolve,[$cnf( $equal(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476),or(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476),implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476))) )],[refute_0_1639,refute_0_1640]) ).
cnf(refute_0_1642,plain,
( or(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476),implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476)) != implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476)
| ~ is_a_theorem(or(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476),implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476)))
| is_a_theorem(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476),implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476))) ),[0],$fot(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476))]]) ).
cnf(refute_0_1643,plain,
( ~ is_a_theorem(or(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476),implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476)))
| is_a_theorem(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476)) ),
inference(resolve,[$cnf( $equal(or(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476),implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476)),implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476)) )],[refute_0_1641,refute_0_1642]) ).
cnf(refute_0_1644,plain,
is_a_theorem(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476)),
inference(resolve,[$cnf( is_a_theorem(or(implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476),implies(equiv(X_25476,equiv(X_25475,X_25475)),X_25476))) )],[refute_0_1638,refute_0_1643]) ).
cnf(refute_0_1645,plain,
is_a_theorem(implies(equiv(X_55980,equiv(X_55980,X_55980)),X_55980)),
inference(subst,[],[refute_0_1644:[bind(X_25475,$fot(X_55980)),bind(X_25476,$fot(X_55980))]]) ).
cnf(refute_0_1646,plain,
is_a_theorem(equiv(equiv(X_55980,equiv(X_55980,X_55980)),X_55980)),
inference(resolve,[$cnf( is_a_theorem(implies(equiv(X_55980,equiv(X_55980,X_55980)),X_55980)) )],[refute_0_1645,refute_0_1502]) ).
cnf(refute_0_1647,plain,
is_a_theorem(equiv(equiv(X_55981,equiv(X_55981,X_55981)),X_55981)),
inference(subst,[],[refute_0_1646:[bind(X_55980,$fot(X_55981))]]) ).
cnf(refute_0_1648,plain,
equiv(X_55981,equiv(X_55981,X_55981)) = X_55981,
inference(resolve,[$cnf( is_a_theorem(equiv(equiv(X_55981,equiv(X_55981,X_55981)),X_55981)) )],[refute_0_1647,refute_0_1129]) ).
cnf(refute_0_1649,plain,
equiv(X_44336,equiv(X_44336,X_44336)) = X_44336,
inference(subst,[],[refute_0_1648:[bind(X_55981,$fot(X_44336))]]) ).
cnf(refute_0_1650,plain,
( equiv(X_44336,equiv(X_44336,X_44336)) != X_44336
| ~ is_a_theorem(implies(implies(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))))
| is_a_theorem(implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))))) ),[0,0,1,0],$fot(X_44336)]]) ).
cnf(refute_0_1651,plain,
( ~ is_a_theorem(implies(implies(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))))
| is_a_theorem(implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))))) ),
inference(resolve,[$cnf( $equal(equiv(X_44336,equiv(X_44336,X_44336)),X_44336) )],[refute_0_1649,refute_0_1650]) ).
cnf(refute_0_1652,plain,
is_a_theorem(implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))))) )],[refute_0_1128,refute_0_1651]) ).
cnf(refute_0_1653,plain,
and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)) = and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)),
introduced(tautology,[refl,[$fot(and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))]]) ).
cnf(refute_0_1654,plain,
( and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)) != and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))
| equiv(X_44336,equiv(X_44336,X_44336)) != X_44336
| and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)) = and(X_44336,equiv(X_44336,X_44336)) ),
introduced(tautology,[equality,[$cnf( $equal(and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)),and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))) ),[1,0],$fot(X_44336)]]) ).
cnf(refute_0_1655,plain,
( equiv(X_44336,equiv(X_44336,X_44336)) != X_44336
| and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)) = and(X_44336,equiv(X_44336,X_44336)) ),
inference(resolve,[$cnf( $equal(and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)),and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))) )],[refute_0_1653,refute_0_1654]) ).
cnf(refute_0_1656,plain,
and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)) = and(X_44336,equiv(X_44336,X_44336)),
inference(resolve,[$cnf( $equal(equiv(X_44336,equiv(X_44336,X_44336)),X_44336) )],[refute_0_1649,refute_0_1655]) ).
cnf(refute_0_1657,plain,
equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))) = equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))),
introduced(tautology,[refl,[$fot(equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))))]]) ).
cnf(refute_0_1658,plain,
( and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)) != and(X_44336,equiv(X_44336,X_44336))
| equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))) != equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))
| equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))) = equiv(X_44336,and(X_44336,equiv(X_44336,X_44336))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))) ),[1,1],$fot(and(X_44336,equiv(X_44336,X_44336)))]]) ).
cnf(refute_0_1659,plain,
( and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)) != and(X_44336,equiv(X_44336,X_44336))
| equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))) = equiv(X_44336,and(X_44336,equiv(X_44336,X_44336))) ),
inference(resolve,[$cnf( $equal(equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))) )],[refute_0_1657,refute_0_1658]) ).
cnf(refute_0_1660,plain,
equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))) = equiv(X_44336,and(X_44336,equiv(X_44336,X_44336))),
inference(resolve,[$cnf( $equal(and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)),and(X_44336,equiv(X_44336,X_44336))) )],[refute_0_1656,refute_0_1659]) ).
cnf(refute_0_1661,plain,
implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))) = implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))),
introduced(tautology,[refl,[$fot(implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))))]]) ).
cnf(refute_0_1662,plain,
( equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))) != equiv(X_44336,and(X_44336,equiv(X_44336,X_44336)))
| implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))) != implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))))
| implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))) = implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(X_44336,equiv(X_44336,X_44336)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))),implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))))) ),[1,1],$fot(equiv(X_44336,and(X_44336,equiv(X_44336,X_44336))))]]) ).
cnf(refute_0_1663,plain,
( equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))) != equiv(X_44336,and(X_44336,equiv(X_44336,X_44336)))
| implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))) = implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(X_44336,equiv(X_44336,X_44336)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))),implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))))) )],[refute_0_1661,refute_0_1662]) ).
cnf(refute_0_1664,plain,
implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))) = implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(X_44336,equiv(X_44336,X_44336)))),
inference(resolve,[$cnf( $equal(equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))),equiv(X_44336,and(X_44336,equiv(X_44336,X_44336)))) )],[refute_0_1660,refute_0_1663]) ).
cnf(refute_0_1665,plain,
( implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))) != implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(X_44336,equiv(X_44336,X_44336))))
| ~ is_a_theorem(implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))))
| is_a_theorem(implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(X_44336,equiv(X_44336,X_44336))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))))) ),[0],$fot(implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(X_44336,equiv(X_44336,X_44336)))))]]) ).
cnf(refute_0_1666,plain,
( ~ is_a_theorem(implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))))
| is_a_theorem(implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(X_44336,equiv(X_44336,X_44336))))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336)))),implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(X_44336,equiv(X_44336,X_44336))))) )],[refute_0_1664,refute_0_1665]) ).
cnf(refute_0_1667,plain,
is_a_theorem(implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(X_44336,equiv(X_44336,X_44336))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_44336,and(X_44336,equiv(X_44336,X_44336))),equiv(X_44336,and(equiv(X_44336,equiv(X_44336,X_44336)),equiv(X_44336,X_44336))))) )],[refute_0_1652,refute_0_1666]) ).
cnf(refute_0_1668,plain,
is_a_theorem(implies(implies(X_56112,and(X_56112,equiv(X_56112,X_56112))),equiv(X_56112,and(X_56112,equiv(X_56112,X_56112))))),
inference(subst,[],[refute_0_1667:[bind(X_44336,$fot(X_56112))]]) ).
cnf(refute_0_1669,plain,
( ~ is_a_theorem(implies(X_56112,and(X_56112,equiv(X_56112,X_56112))))
| is_a_theorem(equiv(X_56112,and(X_56112,equiv(X_56112,X_56112)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_56112,and(X_56112,equiv(X_56112,X_56112))),equiv(X_56112,and(X_56112,equiv(X_56112,X_56112))))) )],[refute_0_1668,refute_0_715]) ).
cnf(refute_0_1670,plain,
( ~ is_a_theorem(or(and(X_25375,equiv(X_25375,X_25375)),not(X_25375)))
| is_a_theorem(or(not(X_25375),and(X_25375,equiv(X_25375,X_25375)))) ),
inference(subst,[],[refute_0_43:[bind(P,$fot(and(X_25375,equiv(X_25375,X_25375)))),bind(Q,$fot(not(X_25375)))]]) ).
cnf(refute_0_1671,plain,
( ~ is_a_theorem(or(X_2981,not(and(X_2980,or(X_2981,X_2981)))))
| is_a_theorem(or(not(and(X_2980,or(X_2981,X_2981))),X_2981)) ),
inference(subst,[],[refute_0_43:[bind(P,$fot(X_2981)),bind(Q,$fot(not(and(X_2980,or(X_2981,X_2981)))))]]) ).
cnf(refute_0_1672,plain,
( ~ is_a_theorem(implies(X,and(X,X)))
| is_a_theorem(or(X_258,implies(X,and(X,X)))) ),
inference(subst,[],[refute_0_720:[bind(P,$fot(X_258)),bind(X_155,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_1673,plain,
is_a_theorem(or(X_258,implies(X,and(X,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(X,and(X,X))) )],[refute_0_241,refute_0_1672]) ).
cnf(refute_0_1674,plain,
is_a_theorem(or(X_2905,implies(X_2904,and(X_2904,X_2904)))),
inference(subst,[],[refute_0_1673:[bind(X,$fot(X_2904)),bind(X_258,$fot(X_2905))]]) ).
cnf(refute_0_1675,plain,
( ~ is_a_theorem(or(X_2905,implies(X_2904,and(X_2904,X_2904))))
| is_a_theorem(implies(X_2904,or(X_2905,and(X_2904,X_2904)))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_2904)),bind(X_103,$fot(X_2905)),bind(X_105,$fot(and(X_2904,X_2904)))]]) ).
cnf(refute_0_1676,plain,
is_a_theorem(implies(X_2904,or(X_2905,and(X_2904,X_2904)))),
inference(resolve,[$cnf( is_a_theorem(or(X_2905,implies(X_2904,and(X_2904,X_2904)))) )],[refute_0_1674,refute_0_1675]) ).
cnf(refute_0_1677,plain,
is_a_theorem(implies(not(X_655),or(X_2910,and(not(X_655),not(X_655))))),
inference(subst,[],[refute_0_1676:[bind(X_2904,$fot(not(X_655))),bind(X_2905,$fot(X_2910))]]) ).
cnf(refute_0_1678,plain,
( and(not(X_655),not(X_655)) != not(or(X_655,X_655))
| ~ is_a_theorem(implies(not(X_655),or(X_2910,and(not(X_655),not(X_655)))))
| is_a_theorem(implies(not(X_655),or(X_2910,not(or(X_655,X_655))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X_655),or(X_2910,and(not(X_655),not(X_655))))) ),[0,1,1],$fot(not(or(X_655,X_655)))]]) ).
cnf(refute_0_1679,plain,
( ~ is_a_theorem(implies(not(X_655),or(X_2910,and(not(X_655),not(X_655)))))
| is_a_theorem(implies(not(X_655),or(X_2910,not(or(X_655,X_655))))) ),
inference(resolve,[$cnf( $equal(and(not(X_655),not(X_655)),not(or(X_655,X_655))) )],[refute_0_610,refute_0_1678]) ).
cnf(refute_0_1680,plain,
is_a_theorem(implies(not(X_655),or(X_2910,not(or(X_655,X_655))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_655),or(X_2910,and(not(X_655),not(X_655))))) )],[refute_0_1677,refute_0_1679]) ).
cnf(refute_0_1681,plain,
implies(not(X_655),or(X_2910,not(or(X_655,X_655)))) = or(X_655,or(X_2910,not(or(X_655,X_655)))),
inference(subst,[],[refute_0_159:[bind(X,$fot(X_655)),bind(Y,$fot(or(X_2910,not(or(X_655,X_655)))))]]) ).
cnf(refute_0_1682,plain,
( implies(not(X_655),or(X_2910,not(or(X_655,X_655)))) != or(X_655,or(X_2910,not(or(X_655,X_655))))
| ~ is_a_theorem(implies(not(X_655),or(X_2910,not(or(X_655,X_655)))))
| is_a_theorem(or(X_655,or(X_2910,not(or(X_655,X_655))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X_655),or(X_2910,not(or(X_655,X_655))))) ),[0],$fot(or(X_655,or(X_2910,not(or(X_655,X_655)))))]]) ).
cnf(refute_0_1683,plain,
( ~ is_a_theorem(implies(not(X_655),or(X_2910,not(or(X_655,X_655)))))
| is_a_theorem(or(X_655,or(X_2910,not(or(X_655,X_655))))) ),
inference(resolve,[$cnf( $equal(implies(not(X_655),or(X_2910,not(or(X_655,X_655)))),or(X_655,or(X_2910,not(or(X_655,X_655))))) )],[refute_0_1681,refute_0_1682]) ).
cnf(refute_0_1684,plain,
is_a_theorem(or(X_655,or(X_2910,not(or(X_655,X_655))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_655),or(X_2910,not(or(X_655,X_655))))) )],[refute_0_1680,refute_0_1683]) ).
cnf(refute_0_1685,plain,
is_a_theorem(or(X_2935,or(not(X),not(or(X_2935,X_2935))))),
inference(subst,[],[refute_0_1684:[bind(X_2910,$fot(not(X))),bind(X_655,$fot(X_2935))]]) ).
cnf(refute_0_1686,plain,
implies(X,not(or(X_2935,X_2935))) = or(not(X),not(or(X_2935,X_2935))),
inference(subst,[],[refute_0_9:[bind(Y,$fot(not(or(X_2935,X_2935))))]]) ).
cnf(refute_0_1687,plain,
( implies(X,not(or(X_2935,X_2935))) != or(not(X),not(or(X_2935,X_2935)))
| or(not(X),not(or(X_2935,X_2935))) = implies(X,not(or(X_2935,X_2935))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,not(or(X_2935,X_2935))))),bind(Y0,$fot(or(not(X),not(or(X_2935,X_2935)))))]]) ).
cnf(refute_0_1688,plain,
or(not(X),not(or(X_2935,X_2935))) = implies(X,not(or(X_2935,X_2935))),
inference(resolve,[$cnf( $equal(implies(X,not(or(X_2935,X_2935))),or(not(X),not(or(X_2935,X_2935)))) )],[refute_0_1686,refute_0_1687]) ).
cnf(refute_0_1689,plain,
( or(not(X),not(or(X_2935,X_2935))) != implies(X,not(or(X_2935,X_2935)))
| ~ is_a_theorem(or(X_2935,or(not(X),not(or(X_2935,X_2935)))))
| is_a_theorem(or(X_2935,implies(X,not(or(X_2935,X_2935))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_2935,or(not(X),not(or(X_2935,X_2935))))) ),[0,1],$fot(implies(X,not(or(X_2935,X_2935))))]]) ).
cnf(refute_0_1690,plain,
( ~ is_a_theorem(or(X_2935,or(not(X),not(or(X_2935,X_2935)))))
| is_a_theorem(or(X_2935,implies(X,not(or(X_2935,X_2935))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(or(X_2935,X_2935))),implies(X,not(or(X_2935,X_2935)))) )],[refute_0_1688,refute_0_1689]) ).
cnf(refute_0_1691,plain,
is_a_theorem(or(X_2935,implies(X,not(or(X_2935,X_2935))))),
inference(resolve,[$cnf( is_a_theorem(or(X_2935,or(not(X),not(or(X_2935,X_2935))))) )],[refute_0_1685,refute_0_1690]) ).
cnf(refute_0_1692,plain,
implies(X,and(not(X_5),not(X_5))) = not(and(X,implies(not(X_5),X_5))),
inference(subst,[],[refute_0_283:[bind(X_4,$fot(not(X_5)))]]) ).
cnf(refute_0_1693,plain,
and(not(X_5),not(X_5)) = not(or(X_5,X_5)),
inference(subst,[],[refute_0_610:[bind(X_655,$fot(X_5))]]) ).
cnf(refute_0_1694,plain,
( and(not(X_5),not(X_5)) != not(or(X_5,X_5))
| implies(X,and(not(X_5),not(X_5))) != not(and(X,implies(not(X_5),X_5)))
| implies(X,not(or(X_5,X_5))) = not(and(X,implies(not(X_5),X_5))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,and(not(X_5),not(X_5))),not(and(X,implies(not(X_5),X_5)))) ),[0,1],$fot(not(or(X_5,X_5)))]]) ).
cnf(refute_0_1695,plain,
( implies(X,and(not(X_5),not(X_5))) != not(and(X,implies(not(X_5),X_5)))
| implies(X,not(or(X_5,X_5))) = not(and(X,implies(not(X_5),X_5))) ),
inference(resolve,[$cnf( $equal(and(not(X_5),not(X_5)),not(or(X_5,X_5))) )],[refute_0_1693,refute_0_1694]) ).
cnf(refute_0_1696,plain,
implies(X,not(or(X_5,X_5))) = not(and(X,implies(not(X_5),X_5))),
inference(resolve,[$cnf( $equal(implies(X,and(not(X_5),not(X_5))),not(and(X,implies(not(X_5),X_5)))) )],[refute_0_1692,refute_0_1695]) ).
cnf(refute_0_1697,plain,
implies(not(X_5),X_5) = or(X_5,X_5),
inference(subst,[],[refute_0_159:[bind(X,$fot(X_5)),bind(Y,$fot(X_5))]]) ).
cnf(refute_0_1698,plain,
and(X,implies(not(X_5),X_5)) = and(X,implies(not(X_5),X_5)),
introduced(tautology,[refl,[$fot(and(X,implies(not(X_5),X_5)))]]) ).
cnf(refute_0_1699,plain,
( and(X,implies(not(X_5),X_5)) != and(X,implies(not(X_5),X_5))
| implies(not(X_5),X_5) != or(X_5,X_5)
| and(X,implies(not(X_5),X_5)) = and(X,or(X_5,X_5)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,implies(not(X_5),X_5)),and(X,implies(not(X_5),X_5))) ),[1,1],$fot(or(X_5,X_5))]]) ).
cnf(refute_0_1700,plain,
( implies(not(X_5),X_5) != or(X_5,X_5)
| and(X,implies(not(X_5),X_5)) = and(X,or(X_5,X_5)) ),
inference(resolve,[$cnf( $equal(and(X,implies(not(X_5),X_5)),and(X,implies(not(X_5),X_5))) )],[refute_0_1698,refute_0_1699]) ).
cnf(refute_0_1701,plain,
and(X,implies(not(X_5),X_5)) = and(X,or(X_5,X_5)),
inference(resolve,[$cnf( $equal(implies(not(X_5),X_5),or(X_5,X_5)) )],[refute_0_1697,refute_0_1700]) ).
cnf(refute_0_1702,plain,
not(and(X,implies(not(X_5),X_5))) = not(and(X,implies(not(X_5),X_5))),
introduced(tautology,[refl,[$fot(not(and(X,implies(not(X_5),X_5))))]]) ).
cnf(refute_0_1703,plain,
( and(X,implies(not(X_5),X_5)) != and(X,or(X_5,X_5))
| not(and(X,implies(not(X_5),X_5))) != not(and(X,implies(not(X_5),X_5)))
| not(and(X,implies(not(X_5),X_5))) = not(and(X,or(X_5,X_5))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(X,implies(not(X_5),X_5))),not(and(X,implies(not(X_5),X_5)))) ),[1,0],$fot(and(X,or(X_5,X_5)))]]) ).
cnf(refute_0_1704,plain,
( and(X,implies(not(X_5),X_5)) != and(X,or(X_5,X_5))
| not(and(X,implies(not(X_5),X_5))) = not(and(X,or(X_5,X_5))) ),
inference(resolve,[$cnf( $equal(not(and(X,implies(not(X_5),X_5))),not(and(X,implies(not(X_5),X_5)))) )],[refute_0_1702,refute_0_1703]) ).
cnf(refute_0_1705,plain,
not(and(X,implies(not(X_5),X_5))) = not(and(X,or(X_5,X_5))),
inference(resolve,[$cnf( $equal(and(X,implies(not(X_5),X_5)),and(X,or(X_5,X_5))) )],[refute_0_1701,refute_0_1704]) ).
cnf(refute_0_1706,plain,
( implies(X,not(or(X_5,X_5))) != not(and(X,implies(not(X_5),X_5)))
| not(and(X,implies(not(X_5),X_5))) != not(and(X,or(X_5,X_5)))
| implies(X,not(or(X_5,X_5))) = not(and(X,or(X_5,X_5))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,not(or(X_5,X_5))),not(and(X,or(X_5,X_5)))) ),[0],$fot(not(and(X,implies(not(X_5),X_5))))]]) ).
cnf(refute_0_1707,plain,
( implies(X,not(or(X_5,X_5))) != not(and(X,implies(not(X_5),X_5)))
| implies(X,not(or(X_5,X_5))) = not(and(X,or(X_5,X_5))) ),
inference(resolve,[$cnf( $equal(not(and(X,implies(not(X_5),X_5))),not(and(X,or(X_5,X_5)))) )],[refute_0_1705,refute_0_1706]) ).
cnf(refute_0_1708,plain,
implies(X,not(or(X_5,X_5))) = not(and(X,or(X_5,X_5))),
inference(resolve,[$cnf( $equal(implies(X,not(or(X_5,X_5))),not(and(X,implies(not(X_5),X_5)))) )],[refute_0_1696,refute_0_1707]) ).
cnf(refute_0_1709,plain,
implies(X,not(or(X_2935,X_2935))) = not(and(X,or(X_2935,X_2935))),
inference(subst,[],[refute_0_1708:[bind(X_5,$fot(X_2935))]]) ).
cnf(refute_0_1710,plain,
or(X_2935,implies(X,not(or(X_2935,X_2935)))) = or(X_2935,implies(X,not(or(X_2935,X_2935)))),
introduced(tautology,[refl,[$fot(or(X_2935,implies(X,not(or(X_2935,X_2935)))))]]) ).
cnf(refute_0_1711,plain,
( implies(X,not(or(X_2935,X_2935))) != not(and(X,or(X_2935,X_2935)))
| or(X_2935,implies(X,not(or(X_2935,X_2935)))) != or(X_2935,implies(X,not(or(X_2935,X_2935))))
| or(X_2935,implies(X,not(or(X_2935,X_2935)))) = or(X_2935,not(and(X,or(X_2935,X_2935)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_2935,implies(X,not(or(X_2935,X_2935)))),or(X_2935,implies(X,not(or(X_2935,X_2935))))) ),[1,1],$fot(not(and(X,or(X_2935,X_2935))))]]) ).
cnf(refute_0_1712,plain,
( implies(X,not(or(X_2935,X_2935))) != not(and(X,or(X_2935,X_2935)))
| or(X_2935,implies(X,not(or(X_2935,X_2935)))) = or(X_2935,not(and(X,or(X_2935,X_2935)))) ),
inference(resolve,[$cnf( $equal(or(X_2935,implies(X,not(or(X_2935,X_2935)))),or(X_2935,implies(X,not(or(X_2935,X_2935))))) )],[refute_0_1710,refute_0_1711]) ).
cnf(refute_0_1713,plain,
or(X_2935,implies(X,not(or(X_2935,X_2935)))) = or(X_2935,not(and(X,or(X_2935,X_2935)))),
inference(resolve,[$cnf( $equal(implies(X,not(or(X_2935,X_2935))),not(and(X,or(X_2935,X_2935)))) )],[refute_0_1709,refute_0_1712]) ).
cnf(refute_0_1714,plain,
( or(X_2935,implies(X,not(or(X_2935,X_2935)))) != or(X_2935,not(and(X,or(X_2935,X_2935))))
| ~ is_a_theorem(or(X_2935,implies(X,not(or(X_2935,X_2935)))))
| is_a_theorem(or(X_2935,not(and(X,or(X_2935,X_2935))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_2935,implies(X,not(or(X_2935,X_2935))))) ),[0],$fot(or(X_2935,not(and(X,or(X_2935,X_2935)))))]]) ).
cnf(refute_0_1715,plain,
( ~ is_a_theorem(or(X_2935,implies(X,not(or(X_2935,X_2935)))))
| is_a_theorem(or(X_2935,not(and(X,or(X_2935,X_2935))))) ),
inference(resolve,[$cnf( $equal(or(X_2935,implies(X,not(or(X_2935,X_2935)))),or(X_2935,not(and(X,or(X_2935,X_2935))))) )],[refute_0_1713,refute_0_1714]) ).
cnf(refute_0_1716,plain,
is_a_theorem(or(X_2935,not(and(X,or(X_2935,X_2935))))),
inference(resolve,[$cnf( is_a_theorem(or(X_2935,implies(X,not(or(X_2935,X_2935))))) )],[refute_0_1691,refute_0_1715]) ).
cnf(refute_0_1717,plain,
is_a_theorem(or(X_2981,not(and(X_2980,or(X_2981,X_2981))))),
inference(subst,[],[refute_0_1716:[bind(X,$fot(X_2980)),bind(X_2935,$fot(X_2981))]]) ).
cnf(refute_0_1718,plain,
is_a_theorem(or(not(and(X_2980,or(X_2981,X_2981))),X_2981)),
inference(resolve,[$cnf( is_a_theorem(or(X_2981,not(and(X_2980,or(X_2981,X_2981))))) )],[refute_0_1717,refute_0_1671]) ).
cnf(refute_0_1719,plain,
or(not(and(X_2980,or(X_2981,X_2981))),X_2981) = implies(and(X_2980,or(X_2981,X_2981)),X_2981),
inference(subst,[],[refute_0_20:[bind(X,$fot(and(X_2980,or(X_2981,X_2981)))),bind(Y,$fot(X_2981))]]) ).
cnf(refute_0_1720,plain,
( or(not(and(X_2980,or(X_2981,X_2981))),X_2981) != implies(and(X_2980,or(X_2981,X_2981)),X_2981)
| ~ is_a_theorem(or(not(and(X_2980,or(X_2981,X_2981))),X_2981))
| is_a_theorem(implies(and(X_2980,or(X_2981,X_2981)),X_2981)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(and(X_2980,or(X_2981,X_2981))),X_2981)) ),[0],$fot(implies(and(X_2980,or(X_2981,X_2981)),X_2981))]]) ).
cnf(refute_0_1721,plain,
( ~ is_a_theorem(or(not(and(X_2980,or(X_2981,X_2981))),X_2981))
| is_a_theorem(implies(and(X_2980,or(X_2981,X_2981)),X_2981)) ),
inference(resolve,[$cnf( $equal(or(not(and(X_2980,or(X_2981,X_2981))),X_2981),implies(and(X_2980,or(X_2981,X_2981)),X_2981)) )],[refute_0_1719,refute_0_1720]) ).
cnf(refute_0_1722,plain,
is_a_theorem(implies(and(X_2980,or(X_2981,X_2981)),X_2981)),
inference(resolve,[$cnf( is_a_theorem(or(not(and(X_2980,or(X_2981,X_2981))),X_2981)) )],[refute_0_1718,refute_0_1721]) ).
cnf(refute_0_1723,plain,
is_a_theorem(implies(and(X_2980,or(X_12812,X_12812)),X_12812)),
inference(subst,[],[refute_0_1722:[bind(X_2981,$fot(X_12812))]]) ).
cnf(refute_0_1724,plain,
( ~ is_a_theorem(implies(and(X_2980,or(X_12812,X_12812)),X_12812))
| is_a_theorem(implies(or(X_12810,and(X_2980,or(X_12812,X_12812))),or(X_12810,X_12812))) ),
inference(subst,[],[refute_0_1033:[bind(P,$fot(X_12810)),bind(Q,$fot(and(X_2980,or(X_12812,X_12812)))),bind(R,$fot(X_12812))]]) ).
cnf(refute_0_1725,plain,
is_a_theorem(implies(or(X_12810,and(X_2980,or(X_12812,X_12812))),or(X_12810,X_12812))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_2980,or(X_12812,X_12812)),X_12812)) )],[refute_0_1723,refute_0_1724]) ).
cnf(refute_0_1726,plain,
is_a_theorem(implies(or(X_12817,and(or(X,not(not(X))),or(not(X),not(X)))),or(X_12817,not(X)))),
inference(subst,[],[refute_0_1725:[bind(X_12810,$fot(X_12817)),bind(X_12812,$fot(not(X))),bind(X_2980,$fot(or(X,not(not(X)))))]]) ).
cnf(refute_0_1727,plain,
equiv(not(X),not(not(X))) = and(or(X,not(not(X))),or(not(X),not(X))),
inference(subst,[],[refute_0_544:[bind(X_34,$fot(not(X)))]]) ).
cnf(refute_0_1728,plain,
( equiv(not(X),not(not(X))) != and(or(X,not(not(X))),or(not(X),not(X)))
| and(or(X,not(not(X))),or(not(X),not(X))) = equiv(not(X),not(not(X))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(not(X),not(not(X))))),bind(Y0,$fot(and(or(X,not(not(X))),or(not(X),not(X)))))]]) ).
cnf(refute_0_1729,plain,
and(or(X,not(not(X))),or(not(X),not(X))) = equiv(not(X),not(not(X))),
inference(resolve,[$cnf( $equal(equiv(not(X),not(not(X))),and(or(X,not(not(X))),or(not(X),not(X)))) )],[refute_0_1727,refute_0_1728]) ).
cnf(refute_0_1730,plain,
( and(or(X,not(not(X))),or(not(X),not(X))) != equiv(not(X),not(not(X)))
| ~ is_a_theorem(implies(or(X_12817,and(or(X,not(not(X))),or(not(X),not(X)))),or(X_12817,not(X))))
| is_a_theorem(implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_12817,and(or(X,not(not(X))),or(not(X),not(X)))),or(X_12817,not(X)))) ),[0,0,1],$fot(equiv(not(X),not(not(X))))]]) ).
cnf(refute_0_1731,plain,
( ~ is_a_theorem(implies(or(X_12817,and(or(X,not(not(X))),or(not(X),not(X)))),or(X_12817,not(X))))
| is_a_theorem(implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X)))) ),
inference(resolve,[$cnf( $equal(and(or(X,not(not(X))),or(not(X),not(X))),equiv(not(X),not(not(X)))) )],[refute_0_1729,refute_0_1730]) ).
cnf(refute_0_1732,plain,
is_a_theorem(implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_12817,and(or(X,not(not(X))),or(not(X),not(X)))),or(X_12817,not(X)))) )],[refute_0_1726,refute_0_1731]) ).
cnf(refute_0_1733,plain,
not(not(X)) = X,
inference(subst,[],[refute_0_1231:[bind(X_10026,$fot(X))]]) ).
cnf(refute_0_1734,plain,
equiv(not(X),not(not(X))) = equiv(not(X),not(not(X))),
introduced(tautology,[refl,[$fot(equiv(not(X),not(not(X))))]]) ).
cnf(refute_0_1735,plain,
( equiv(not(X),not(not(X))) != equiv(not(X),not(not(X)))
| not(not(X)) != X
| equiv(not(X),not(not(X))) = equiv(not(X),X) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X),not(not(X))),equiv(not(X),not(not(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_1736,plain,
( not(not(X)) != X
| equiv(not(X),not(not(X))) = equiv(not(X),X) ),
inference(resolve,[$cnf( $equal(equiv(not(X),not(not(X))),equiv(not(X),not(not(X)))) )],[refute_0_1734,refute_0_1735]) ).
cnf(refute_0_1737,plain,
equiv(not(X),not(not(X))) = equiv(not(X),X),
inference(resolve,[$cnf( $equal(not(not(X)),X) )],[refute_0_1733,refute_0_1736]) ).
cnf(refute_0_1738,plain,
or(X_12817,equiv(not(X),not(not(X)))) = or(X_12817,equiv(not(X),not(not(X)))),
introduced(tautology,[refl,[$fot(or(X_12817,equiv(not(X),not(not(X)))))]]) ).
cnf(refute_0_1739,plain,
( equiv(not(X),not(not(X))) != equiv(not(X),X)
| or(X_12817,equiv(not(X),not(not(X)))) != or(X_12817,equiv(not(X),not(not(X))))
| or(X_12817,equiv(not(X),not(not(X)))) = or(X_12817,equiv(not(X),X)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,equiv(not(X),not(not(X))))) ),[1,1],$fot(equiv(not(X),X))]]) ).
cnf(refute_0_1740,plain,
( equiv(not(X),not(not(X))) != equiv(not(X),X)
| or(X_12817,equiv(not(X),not(not(X)))) = or(X_12817,equiv(not(X),X)) ),
inference(resolve,[$cnf( $equal(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,equiv(not(X),not(not(X))))) )],[refute_0_1738,refute_0_1739]) ).
cnf(refute_0_1741,plain,
or(X_12817,equiv(not(X),not(not(X)))) = or(X_12817,equiv(not(X),X)),
inference(resolve,[$cnf( $equal(equiv(not(X),not(not(X))),equiv(not(X),X)) )],[refute_0_1737,refute_0_1740]) ).
cnf(refute_0_1742,plain,
implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X))) = implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X))),
introduced(tautology,[refl,[$fot(implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X))))]]) ).
cnf(refute_0_1743,plain,
( implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X))) != implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X)))
| or(X_12817,equiv(not(X),not(not(X)))) != or(X_12817,equiv(not(X),X))
| implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X))) = implies(or(X_12817,equiv(not(X),X)),or(X_12817,not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X))),implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X)))) ),[1,0],$fot(or(X_12817,equiv(not(X),X)))]]) ).
cnf(refute_0_1744,plain,
( or(X_12817,equiv(not(X),not(not(X)))) != or(X_12817,equiv(not(X),X))
| implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X))) = implies(or(X_12817,equiv(not(X),X)),or(X_12817,not(X))) ),
inference(resolve,[$cnf( $equal(implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X))),implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X)))) )],[refute_0_1742,refute_0_1743]) ).
cnf(refute_0_1745,plain,
implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X))) = implies(or(X_12817,equiv(not(X),X)),or(X_12817,not(X))),
inference(resolve,[$cnf( $equal(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,equiv(not(X),X))) )],[refute_0_1741,refute_0_1744]) ).
cnf(refute_0_1746,plain,
( implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X))) != implies(or(X_12817,equiv(not(X),X)),or(X_12817,not(X)))
| ~ is_a_theorem(implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X))))
| is_a_theorem(implies(or(X_12817,equiv(not(X),X)),or(X_12817,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X)))) ),[0],$fot(implies(or(X_12817,equiv(not(X),X)),or(X_12817,not(X))))]]) ).
cnf(refute_0_1747,plain,
( ~ is_a_theorem(implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X))))
| is_a_theorem(implies(or(X_12817,equiv(not(X),X)),or(X_12817,not(X)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X))),implies(or(X_12817,equiv(not(X),X)),or(X_12817,not(X)))) )],[refute_0_1745,refute_0_1746]) ).
cnf(refute_0_1748,plain,
is_a_theorem(implies(or(X_12817,equiv(not(X),X)),or(X_12817,not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_12817,equiv(not(X),not(not(X)))),or(X_12817,not(X)))) )],[refute_0_1732,refute_0_1747]) ).
cnf(refute_0_1749,plain,
is_a_theorem(implies(or(not(X),equiv(not(X),X)),or(not(X),not(X)))),
inference(subst,[],[refute_0_1748:[bind(X_12817,$fot(not(X)))]]) ).
cnf(refute_0_1750,plain,
not(X) = or(not(X),not(X)),
inference(subst,[],[refute_0_1114:[bind(X_25347,$fot(not(X)))]]) ).
cnf(refute_0_1751,plain,
( not(X) != or(not(X),not(X))
| or(not(X),not(X)) = not(X) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(X))),bind(Y0,$fot(or(not(X),not(X))))]]) ).
cnf(refute_0_1752,plain,
or(not(X),not(X)) = not(X),
inference(resolve,[$cnf( $equal(not(X),or(not(X),not(X))) )],[refute_0_1750,refute_0_1751]) ).
cnf(refute_0_1753,plain,
( or(not(X),not(X)) != not(X)
| ~ is_a_theorem(implies(or(not(X),equiv(not(X),X)),or(not(X),not(X))))
| is_a_theorem(implies(or(not(X),equiv(not(X),X)),not(X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),equiv(not(X),X)),or(not(X),not(X)))) ),[0,1],$fot(not(X))]]) ).
cnf(refute_0_1754,plain,
( ~ is_a_theorem(implies(or(not(X),equiv(not(X),X)),or(not(X),not(X))))
| is_a_theorem(implies(or(not(X),equiv(not(X),X)),not(X))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),not(X)) )],[refute_0_1752,refute_0_1753]) ).
cnf(refute_0_1755,plain,
is_a_theorem(implies(or(not(X),equiv(not(X),X)),not(X))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),equiv(not(X),X)),or(not(X),not(X)))) )],[refute_0_1749,refute_0_1754]) ).
cnf(refute_0_1756,plain,
or(not(X),equiv(not(X),X)) = implies(X,equiv(not(X),X)),
inference(subst,[],[refute_0_20:[bind(Y,$fot(equiv(not(X),X)))]]) ).
cnf(refute_0_1757,plain,
and(or(not(X),equiv(not(X),X)),X) = and(or(not(X),equiv(not(X),X)),X),
introduced(tautology,[refl,[$fot(and(or(not(X),equiv(not(X),X)),X))]]) ).
cnf(refute_0_1758,plain,
( and(or(not(X),equiv(not(X),X)),X) != and(or(not(X),equiv(not(X),X)),X)
| or(not(X),equiv(not(X),X)) != implies(X,equiv(not(X),X))
| and(or(not(X),equiv(not(X),X)),X) = and(implies(X,equiv(not(X),X)),X) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(not(X),equiv(not(X),X)),X),and(or(not(X),equiv(not(X),X)),X)) ),[1,0],$fot(implies(X,equiv(not(X),X)))]]) ).
cnf(refute_0_1759,plain,
( or(not(X),equiv(not(X),X)) != implies(X,equiv(not(X),X))
| and(or(not(X),equiv(not(X),X)),X) = and(implies(X,equiv(not(X),X)),X) ),
inference(resolve,[$cnf( $equal(and(or(not(X),equiv(not(X),X)),X),and(or(not(X),equiv(not(X),X)),X)) )],[refute_0_1757,refute_0_1758]) ).
cnf(refute_0_1760,plain,
and(or(not(X),equiv(not(X),X)),X) = and(implies(X,equiv(not(X),X)),X),
inference(resolve,[$cnf( $equal(or(not(X),equiv(not(X),X)),implies(X,equiv(not(X),X))) )],[refute_0_1756,refute_0_1759]) ).
cnf(refute_0_1761,plain,
not(and(or(not(X),equiv(not(X),X)),X)) = not(and(or(not(X),equiv(not(X),X)),X)),
introduced(tautology,[refl,[$fot(not(and(or(not(X),equiv(not(X),X)),X)))]]) ).
cnf(refute_0_1762,plain,
( and(or(not(X),equiv(not(X),X)),X) != and(implies(X,equiv(not(X),X)),X)
| not(and(or(not(X),equiv(not(X),X)),X)) != not(and(or(not(X),equiv(not(X),X)),X))
| not(and(or(not(X),equiv(not(X),X)),X)) = not(and(implies(X,equiv(not(X),X)),X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(or(not(X),equiv(not(X),X)),X)),not(and(or(not(X),equiv(not(X),X)),X))) ),[1,0],$fot(and(implies(X,equiv(not(X),X)),X))]]) ).
cnf(refute_0_1763,plain,
( and(or(not(X),equiv(not(X),X)),X) != and(implies(X,equiv(not(X),X)),X)
| not(and(or(not(X),equiv(not(X),X)),X)) = not(and(implies(X,equiv(not(X),X)),X)) ),
inference(resolve,[$cnf( $equal(not(and(or(not(X),equiv(not(X),X)),X)),not(and(or(not(X),equiv(not(X),X)),X))) )],[refute_0_1761,refute_0_1762]) ).
cnf(refute_0_1764,plain,
not(and(or(not(X),equiv(not(X),X)),X)) = not(and(implies(X,equiv(not(X),X)),X)),
inference(resolve,[$cnf( $equal(and(or(not(X),equiv(not(X),X)),X),and(implies(X,equiv(not(X),X)),X)) )],[refute_0_1760,refute_0_1763]) ).
cnf(refute_0_1765,plain,
implies(or(not(X),equiv(not(X),X)),not(X)) = not(and(or(not(X),equiv(not(X),X)),X)),
inference(subst,[],[refute_0_987:[bind(Y,$fot(X)),bind(X_9551,$fot(or(not(X),equiv(not(X),X))))]]) ).
cnf(refute_0_1766,plain,
( implies(or(not(X),equiv(not(X),X)),not(X)) != not(and(or(not(X),equiv(not(X),X)),X))
| not(and(or(not(X),equiv(not(X),X)),X)) != not(and(implies(X,equiv(not(X),X)),X))
| implies(or(not(X),equiv(not(X),X)),not(X)) = not(and(implies(X,equiv(not(X),X)),X)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(or(not(X),equiv(not(X),X)),not(X)))),bind(Y0,$fot(not(and(or(not(X),equiv(not(X),X)),X)))),bind(Z,$fot(not(and(implies(X,equiv(not(X),X)),X))))]]) ).
cnf(refute_0_1767,plain,
( not(and(or(not(X),equiv(not(X),X)),X)) != not(and(implies(X,equiv(not(X),X)),X))
| implies(or(not(X),equiv(not(X),X)),not(X)) = not(and(implies(X,equiv(not(X),X)),X)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),equiv(not(X),X)),not(X)),not(and(or(not(X),equiv(not(X),X)),X))) )],[refute_0_1765,refute_0_1766]) ).
cnf(refute_0_1768,plain,
implies(or(not(X),equiv(not(X),X)),not(X)) = not(and(implies(X,equiv(not(X),X)),X)),
inference(resolve,[$cnf( $equal(not(and(or(not(X),equiv(not(X),X)),X)),not(and(implies(X,equiv(not(X),X)),X))) )],[refute_0_1764,refute_0_1767]) ).
cnf(refute_0_1769,plain,
( implies(or(not(X),equiv(not(X),X)),not(X)) != not(and(implies(X,equiv(not(X),X)),X))
| ~ is_a_theorem(implies(or(not(X),equiv(not(X),X)),not(X)))
| is_a_theorem(not(and(implies(X,equiv(not(X),X)),X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),equiv(not(X),X)),not(X))) ),[0],$fot(not(and(implies(X,equiv(not(X),X)),X)))]]) ).
cnf(refute_0_1770,plain,
( ~ is_a_theorem(implies(or(not(X),equiv(not(X),X)),not(X)))
| is_a_theorem(not(and(implies(X,equiv(not(X),X)),X))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),equiv(not(X),X)),not(X)),not(and(implies(X,equiv(not(X),X)),X))) )],[refute_0_1768,refute_0_1769]) ).
cnf(refute_0_1771,plain,
is_a_theorem(not(and(implies(X,equiv(not(X),X)),X))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),equiv(not(X),X)),not(X))) )],[refute_0_1755,refute_0_1770]) ).
cnf(refute_0_1772,plain,
not(and(not(and(X,equiv(X,X))),X)) = or(and(X,equiv(X,X)),not(X)),
inference(subst,[],[refute_0_1206:[bind(X,$fot(and(X,equiv(X,X)))),bind(X_9554,$fot(X))]]) ).
cnf(refute_0_1773,plain,
implies(X,not(equiv(X,X))) = not(and(X,equiv(X,X))),
inference(subst,[],[refute_0_987:[bind(Y,$fot(equiv(X,X))),bind(X_9551,$fot(X))]]) ).
cnf(refute_0_1774,plain,
equiv(not(X),X) = not(equiv(X,X)),
inference(subst,[],[refute_0_1414:[bind(X_25350,$fot(X))]]) ).
cnf(refute_0_1775,plain,
implies(X,equiv(not(X),X)) = implies(X,equiv(not(X),X)),
introduced(tautology,[refl,[$fot(implies(X,equiv(not(X),X)))]]) ).
cnf(refute_0_1776,plain,
( equiv(not(X),X) != not(equiv(X,X))
| implies(X,equiv(not(X),X)) != implies(X,equiv(not(X),X))
| implies(X,equiv(not(X),X)) = implies(X,not(equiv(X,X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,equiv(not(X),X)),implies(X,equiv(not(X),X))) ),[1,1],$fot(not(equiv(X,X)))]]) ).
cnf(refute_0_1777,plain,
( equiv(not(X),X) != not(equiv(X,X))
| implies(X,equiv(not(X),X)) = implies(X,not(equiv(X,X))) ),
inference(resolve,[$cnf( $equal(implies(X,equiv(not(X),X)),implies(X,equiv(not(X),X))) )],[refute_0_1775,refute_0_1776]) ).
cnf(refute_0_1778,plain,
implies(X,equiv(not(X),X)) = implies(X,not(equiv(X,X))),
inference(resolve,[$cnf( $equal(equiv(not(X),X),not(equiv(X,X))) )],[refute_0_1774,refute_0_1777]) ).
cnf(refute_0_1779,plain,
( implies(X,equiv(not(X),X)) != implies(X,not(equiv(X,X)))
| implies(X,not(equiv(X,X))) != not(and(X,equiv(X,X)))
| implies(X,equiv(not(X),X)) = not(and(X,equiv(X,X))) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(implies(X,equiv(not(X),X)))),bind(Y0,$fot(implies(X,not(equiv(X,X))))),bind(Z,$fot(not(and(X,equiv(X,X)))))]]) ).
cnf(refute_0_1780,plain,
( implies(X,not(equiv(X,X))) != not(and(X,equiv(X,X)))
| implies(X,equiv(not(X),X)) = not(and(X,equiv(X,X))) ),
inference(resolve,[$cnf( $equal(implies(X,equiv(not(X),X)),implies(X,not(equiv(X,X)))) )],[refute_0_1778,refute_0_1779]) ).
cnf(refute_0_1781,plain,
implies(X,equiv(not(X),X)) = not(and(X,equiv(X,X))),
inference(resolve,[$cnf( $equal(implies(X,not(equiv(X,X))),not(and(X,equiv(X,X)))) )],[refute_0_1773,refute_0_1780]) ).
cnf(refute_0_1782,plain,
and(implies(X,equiv(not(X),X)),X) = and(implies(X,equiv(not(X),X)),X),
introduced(tautology,[refl,[$fot(and(implies(X,equiv(not(X),X)),X))]]) ).
cnf(refute_0_1783,plain,
( and(implies(X,equiv(not(X),X)),X) != and(implies(X,equiv(not(X),X)),X)
| implies(X,equiv(not(X),X)) != not(and(X,equiv(X,X)))
| and(implies(X,equiv(not(X),X)),X) = and(not(and(X,equiv(X,X))),X) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(X,equiv(not(X),X)),X),and(implies(X,equiv(not(X),X)),X)) ),[1,0],$fot(not(and(X,equiv(X,X))))]]) ).
cnf(refute_0_1784,plain,
( implies(X,equiv(not(X),X)) != not(and(X,equiv(X,X)))
| and(implies(X,equiv(not(X),X)),X) = and(not(and(X,equiv(X,X))),X) ),
inference(resolve,[$cnf( $equal(and(implies(X,equiv(not(X),X)),X),and(implies(X,equiv(not(X),X)),X)) )],[refute_0_1782,refute_0_1783]) ).
cnf(refute_0_1785,plain,
and(implies(X,equiv(not(X),X)),X) = and(not(and(X,equiv(X,X))),X),
inference(resolve,[$cnf( $equal(implies(X,equiv(not(X),X)),not(and(X,equiv(X,X)))) )],[refute_0_1781,refute_0_1784]) ).
cnf(refute_0_1786,plain,
not(and(implies(X,equiv(not(X),X)),X)) = not(and(implies(X,equiv(not(X),X)),X)),
introduced(tautology,[refl,[$fot(not(and(implies(X,equiv(not(X),X)),X)))]]) ).
cnf(refute_0_1787,plain,
( and(implies(X,equiv(not(X),X)),X) != and(not(and(X,equiv(X,X))),X)
| not(and(implies(X,equiv(not(X),X)),X)) != not(and(implies(X,equiv(not(X),X)),X))
| not(and(implies(X,equiv(not(X),X)),X)) = not(and(not(and(X,equiv(X,X))),X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(implies(X,equiv(not(X),X)),X)),not(and(implies(X,equiv(not(X),X)),X))) ),[1,0],$fot(and(not(and(X,equiv(X,X))),X))]]) ).
cnf(refute_0_1788,plain,
( and(implies(X,equiv(not(X),X)),X) != and(not(and(X,equiv(X,X))),X)
| not(and(implies(X,equiv(not(X),X)),X)) = not(and(not(and(X,equiv(X,X))),X)) ),
inference(resolve,[$cnf( $equal(not(and(implies(X,equiv(not(X),X)),X)),not(and(implies(X,equiv(not(X),X)),X))) )],[refute_0_1786,refute_0_1787]) ).
cnf(refute_0_1789,plain,
not(and(implies(X,equiv(not(X),X)),X)) = not(and(not(and(X,equiv(X,X))),X)),
inference(resolve,[$cnf( $equal(and(implies(X,equiv(not(X),X)),X),and(not(and(X,equiv(X,X))),X)) )],[refute_0_1785,refute_0_1788]) ).
cnf(refute_0_1790,plain,
( not(and(implies(X,equiv(not(X),X)),X)) != not(and(not(and(X,equiv(X,X))),X))
| not(and(not(and(X,equiv(X,X))),X)) != or(and(X,equiv(X,X)),not(X))
| not(and(implies(X,equiv(not(X),X)),X)) = or(and(X,equiv(X,X)),not(X)) ),
inference(subst,[],[refute_0_142:[bind(X0,$fot(not(and(implies(X,equiv(not(X),X)),X)))),bind(Y0,$fot(not(and(not(and(X,equiv(X,X))),X)))),bind(Z,$fot(or(and(X,equiv(X,X)),not(X))))]]) ).
cnf(refute_0_1791,plain,
( not(and(not(and(X,equiv(X,X))),X)) != or(and(X,equiv(X,X)),not(X))
| not(and(implies(X,equiv(not(X),X)),X)) = or(and(X,equiv(X,X)),not(X)) ),
inference(resolve,[$cnf( $equal(not(and(implies(X,equiv(not(X),X)),X)),not(and(not(and(X,equiv(X,X))),X))) )],[refute_0_1789,refute_0_1790]) ).
cnf(refute_0_1792,plain,
not(and(implies(X,equiv(not(X),X)),X)) = or(and(X,equiv(X,X)),not(X)),
inference(resolve,[$cnf( $equal(not(and(not(and(X,equiv(X,X))),X)),or(and(X,equiv(X,X)),not(X))) )],[refute_0_1772,refute_0_1791]) ).
cnf(refute_0_1793,plain,
( not(and(implies(X,equiv(not(X),X)),X)) != or(and(X,equiv(X,X)),not(X))
| ~ is_a_theorem(not(and(implies(X,equiv(not(X),X)),X)))
| is_a_theorem(or(and(X,equiv(X,X)),not(X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(implies(X,equiv(not(X),X)),X))) ),[0],$fot(or(and(X,equiv(X,X)),not(X)))]]) ).
cnf(refute_0_1794,plain,
( ~ is_a_theorem(not(and(implies(X,equiv(not(X),X)),X)))
| is_a_theorem(or(and(X,equiv(X,X)),not(X))) ),
inference(resolve,[$cnf( $equal(not(and(implies(X,equiv(not(X),X)),X)),or(and(X,equiv(X,X)),not(X))) )],[refute_0_1792,refute_0_1793]) ).
cnf(refute_0_1795,plain,
is_a_theorem(or(and(X,equiv(X,X)),not(X))),
inference(resolve,[$cnf( is_a_theorem(not(and(implies(X,equiv(not(X),X)),X))) )],[refute_0_1771,refute_0_1794]) ).
cnf(refute_0_1796,plain,
is_a_theorem(or(and(X_25375,equiv(X_25375,X_25375)),not(X_25375))),
inference(subst,[],[refute_0_1795:[bind(X,$fot(X_25375))]]) ).
cnf(refute_0_1797,plain,
is_a_theorem(or(not(X_25375),and(X_25375,equiv(X_25375,X_25375)))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_25375,equiv(X_25375,X_25375)),not(X_25375))) )],[refute_0_1796,refute_0_1670]) ).
cnf(refute_0_1798,plain,
or(not(X_25375),and(X_25375,equiv(X_25375,X_25375))) = implies(X_25375,and(X_25375,equiv(X_25375,X_25375))),
inference(subst,[],[refute_0_20:[bind(X,$fot(X_25375)),bind(Y,$fot(and(X_25375,equiv(X_25375,X_25375))))]]) ).
cnf(refute_0_1799,plain,
( or(not(X_25375),and(X_25375,equiv(X_25375,X_25375))) != implies(X_25375,and(X_25375,equiv(X_25375,X_25375)))
| ~ is_a_theorem(or(not(X_25375),and(X_25375,equiv(X_25375,X_25375))))
| is_a_theorem(implies(X_25375,and(X_25375,equiv(X_25375,X_25375)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X_25375),and(X_25375,equiv(X_25375,X_25375)))) ),[0],$fot(implies(X_25375,and(X_25375,equiv(X_25375,X_25375))))]]) ).
cnf(refute_0_1800,plain,
( ~ is_a_theorem(or(not(X_25375),and(X_25375,equiv(X_25375,X_25375))))
| is_a_theorem(implies(X_25375,and(X_25375,equiv(X_25375,X_25375)))) ),
inference(resolve,[$cnf( $equal(or(not(X_25375),and(X_25375,equiv(X_25375,X_25375))),implies(X_25375,and(X_25375,equiv(X_25375,X_25375)))) )],[refute_0_1798,refute_0_1799]) ).
cnf(refute_0_1801,plain,
is_a_theorem(implies(X_25375,and(X_25375,equiv(X_25375,X_25375)))),
inference(resolve,[$cnf( is_a_theorem(or(not(X_25375),and(X_25375,equiv(X_25375,X_25375)))) )],[refute_0_1797,refute_0_1800]) ).
cnf(refute_0_1802,plain,
is_a_theorem(implies(X_56112,and(X_56112,equiv(X_56112,X_56112)))),
inference(subst,[],[refute_0_1801:[bind(X_25375,$fot(X_56112))]]) ).
cnf(refute_0_1803,plain,
is_a_theorem(equiv(X_56112,and(X_56112,equiv(X_56112,X_56112)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_56112,and(X_56112,equiv(X_56112,X_56112)))) )],[refute_0_1802,refute_0_1669]) ).
cnf(refute_0_1804,plain,
is_a_theorem(equiv(X_56113,and(X_56113,equiv(X_56113,X_56113)))),
inference(subst,[],[refute_0_1803:[bind(X_56112,$fot(X_56113))]]) ).
cnf(refute_0_1805,plain,
X_56113 = and(X_56113,equiv(X_56113,X_56113)),
inference(resolve,[$cnf( is_a_theorem(equiv(X_56113,and(X_56113,equiv(X_56113,X_56113)))) )],[refute_0_1804,refute_0_714]) ).
cnf(refute_0_1806,plain,
X_12407 = and(X_12407,equiv(X_12407,X_12407)),
inference(subst,[],[refute_0_1805:[bind(X_56113,$fot(X_12407))]]) ).
cnf(refute_0_1807,plain,
( X_12407 != and(X_12407,equiv(X_12407,X_12407))
| and(X_12407,equiv(X_12407,X_12407)) = X_12407 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(X_12407)),bind(Y0,$fot(and(X_12407,equiv(X_12407,X_12407))))]]) ).
cnf(refute_0_1808,plain,
and(X_12407,equiv(X_12407,X_12407)) = X_12407,
inference(resolve,[$cnf( $equal(X_12407,and(X_12407,equiv(X_12407,X_12407))) )],[refute_0_1806,refute_0_1807]) ).
cnf(refute_0_1809,plain,
( and(X_12407,equiv(X_12407,X_12407)) != X_12407
| ~ is_a_theorem(implies(X_12407,or(and(X_12407,equiv(X_12407,X_12407)),X_12406)))
| is_a_theorem(implies(X_12407,or(X_12407,X_12406))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_12407,or(and(X_12407,equiv(X_12407,X_12407)),X_12406))) ),[0,1,0],$fot(X_12407)]]) ).
cnf(refute_0_1810,plain,
( ~ is_a_theorem(implies(X_12407,or(and(X_12407,equiv(X_12407,X_12407)),X_12406)))
| is_a_theorem(implies(X_12407,or(X_12407,X_12406))) ),
inference(resolve,[$cnf( $equal(and(X_12407,equiv(X_12407,X_12407)),X_12407) )],[refute_0_1808,refute_0_1809]) ).
cnf(refute_0_1811,plain,
is_a_theorem(implies(X_12407,or(X_12407,X_12406))),
inference(resolve,[$cnf( is_a_theorem(implies(X_12407,or(and(X_12407,equiv(X_12407,X_12407)),X_12406))) )],[refute_0_713,refute_0_1810]) ).
cnf(refute_0_1812,plain,
is_a_theorem(implies(skolemFOFtoCNF_X_9,or(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_9))),
inference(subst,[],[refute_0_1811:[bind(X_12406,$fot(skolemFOFtoCNF_Y_9)),bind(X_12407,$fot(skolemFOFtoCNF_X_9))]]) ).
cnf(refute_0_1813,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_X_9,or(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_9))) )],[refute_0_1812,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : LCL490+1 : TPTP v8.1.0. Released v3.3.0.
% 0.02/0.11 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 03:17:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 238.40/238.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 238.40/238.59
% 238.40/238.59 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 238.70/238.87
%------------------------------------------------------------------------------