TSTP Solution File: LCL497+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL497+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 12:52:44 EDT 2022
% Result : Theorem 242.92s 243.05s
% Output : CNFRefutation 243.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 151
% Number of leaves : 325
% Syntax : Number of formulae : 1443 ( 743 unt; 0 def)
% Number of atoms : 2456 (1592 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 2007 ( 994 ~; 976 |; 15 &)
% ( 16 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 16 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 17 con; 0-2 aty)
% Number of variables : 2880 ( 83 sgn 73 !; 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(cn2,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ) ).
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_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(luka_op_or,axiom,
op_or ).
fof(luka_op_equiv,axiom,
op_equiv ).
fof(luka_cn2,conjecture,
cn2 ).
fof(subgoal_0,plain,
cn2,
inference(strip,[],[luka_cn2]) ).
fof(negate_0_0,plain,
~ cn2,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ cn2
<=> ? [P,Q] : ~ is_a_theorem(implies(P,implies(not(P),Q))) ),
inference(canonicalize,[],[cn2]) ).
fof(normalize_0_1,plain,
! [P,Q] :
( ( ~ cn2
| is_a_theorem(implies(P,implies(not(P),Q))) )
& ( ~ is_a_theorem(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)))
| cn2 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)))
| cn2 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ cn2,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
op_or,
inference(canonicalize,[],[luka_op_or]) ).
fof(normalize_0_7,plain,
( ~ op_and
| ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[op_and]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
op_and,
inference(canonicalize,[],[principia_op_and]) ).
fof(normalize_0_10,plain,
( ~ op_implies_or
| ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[op_implies_or]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
op_implies_or,
inference(canonicalize,[],[principia_op_implies_or]) ).
fof(normalize_0_13,plain,
( ~ substitution_of_equivalents
<=> ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_14,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_13]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
substitution_of_equivalents,
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_17,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_18,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_17]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
modus_ponens,
inference(canonicalize,[],[principia_modus_ponens]) ).
fof(normalize_0_21,plain,
( ~ r3
<=> ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[r3]) ).
fof(normalize_0_22,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_21]) ).
fof(normalize_0_23,plain,
! [P,Q] :
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(conjunct,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
r3,
inference(canonicalize,[],[principia_r3]) ).
fof(normalize_0_25,plain,
( ~ r1
<=> ? [P] : ~ is_a_theorem(implies(or(P,P),P)) ),
inference(canonicalize,[],[r1]) ).
fof(normalize_0_26,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_25]) ).
fof(normalize_0_27,plain,
! [P] :
( ~ r1
| is_a_theorem(implies(or(P,P),P)) ),
inference(conjunct,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
r1,
inference(canonicalize,[],[principia_r1]) ).
fof(normalize_0_29,plain,
( ~ r2
<=> ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[r2]) ).
fof(normalize_0_30,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_29]) ).
fof(normalize_0_31,plain,
! [P,Q] :
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(conjunct,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
r2,
inference(canonicalize,[],[principia_r2]) ).
fof(normalize_0_33,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_34,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_33]) ).
fof(normalize_0_35,plain,
! [P,Q,R] :
( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(conjunct,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
r4,
inference(canonicalize,[],[principia_r4]) ).
fof(normalize_0_37,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_38,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_37]) ).
fof(normalize_0_39,plain,
op_equiv,
inference(canonicalize,[],[luka_op_equiv]) ).
fof(normalize_0_40,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_41,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_40]) ).
fof(normalize_0_42,plain,
! [P,Q,R] :
( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(conjunct,[],[normalize_0_41]) ).
fof(normalize_0_43,plain,
r5,
inference(canonicalize,[],[principia_r5]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)))
| cn2 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ cn2,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3))),
inference(resolve,[$cnf( cn2 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
op_or,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
or(implies(X_10,not(X_11)),Y) = not(and(not(implies(X_10,not(X_11))),not(Y))),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(X_10,not(X_11))))]]) ).
cnf(refute_0_7,plain,
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
op_and,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,plain,
and(X,Y) = not(or(not(X),not(Y))),
inference(resolve,[$cnf( op_and )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_12,plain,
implies(X,Y) = or(not(X),Y),
inference(resolve,[$cnf( op_implies_or )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_14,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_15,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_17,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
or(not(X),not(Y)) = implies(X,not(Y)),
inference(subst,[],[refute_0_17:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_19,plain,
not(or(not(X),not(Y))) = not(or(not(X),not(Y))),
introduced(tautology,[refl,[$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_20,plain,
( not(or(not(X),not(Y))) != not(or(not(X),not(Y)))
| or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) ),[1,0],$fot(implies(X,not(Y)))]]) ).
cnf(refute_0_21,plain,
( or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
not(or(not(X),not(Y))) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),implies(X,not(Y))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) != not(implies(X,not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,Y),not(implies(X,not(Y)))) ),[0],$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_24,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(implies(X,not(Y)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
and(X,Y) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[refute_0_9,refute_0_24]) ).
cnf(refute_0_26,plain,
and(X_10,X_11) = not(implies(X_10,not(X_11))),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_27,plain,
( and(X_10,X_11) != not(implies(X_10,not(X_11)))
| not(implies(X_10,not(X_11))) = and(X_10,X_11) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(X_10,X_11))),bind(Y0,$fot(not(implies(X_10,not(X_11)))))]]) ).
cnf(refute_0_28,plain,
not(implies(X_10,not(X_11))) = and(X_10,X_11),
inference(resolve,[$cnf( $equal(and(X_10,X_11),not(implies(X_10,not(X_11)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( not(implies(X_10,not(X_11))) != and(X_10,X_11)
| or(implies(X_10,not(X_11)),Y) != not(and(not(implies(X_10,not(X_11))),not(Y)))
| or(implies(X_10,not(X_11)),Y) = not(and(and(X_10,X_11),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(X_10,not(X_11)),Y),not(and(not(implies(X_10,not(X_11))),not(Y)))) ),[1,0,0],$fot(and(X_10,X_11))]]) ).
cnf(refute_0_30,plain,
( or(implies(X_10,not(X_11)),Y) != not(and(not(implies(X_10,not(X_11))),not(Y)))
| or(implies(X_10,not(X_11)),Y) = not(and(and(X_10,X_11),not(Y))) ),
inference(resolve,[$cnf( $equal(not(implies(X_10,not(X_11))),and(X_10,X_11)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
or(implies(X_10,not(X_11)),Y) = not(and(and(X_10,X_11),not(Y))),
inference(resolve,[$cnf( $equal(or(implies(X_10,not(X_11)),Y),not(and(not(implies(X_10,not(X_11))),not(Y)))) )],[refute_0_6,refute_0_30]) ).
cnf(refute_0_32,plain,
or(implies(not(X_93),not(not(X_94))),Y) = not(and(and(not(X_93),not(X_94)),not(Y))),
inference(subst,[],[refute_0_31:[bind(X_10,$fot(not(X_93))),bind(X_11,$fot(not(X_94)))]]) ).
cnf(refute_0_33,plain,
and(and(not(X_43),not(X_44)),Y) = not(implies(and(not(X_43),not(X_44)),not(Y))),
inference(subst,[],[refute_0_25:[bind(X,$fot(and(not(X_43),not(X_44))))]]) ).
cnf(refute_0_34,plain,
implies(and(not(X),not(Y)),X_6) = or(not(and(not(X),not(Y))),X_6),
inference(subst,[],[refute_0_12:[bind(X,$fot(and(not(X),not(Y)))),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_35,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| not(and(not(X),not(Y))) = or(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(not(and(not(X),not(Y)))))]]) ).
cnf(refute_0_36,plain,
not(and(not(X),not(Y))) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_5,refute_0_35]) ).
cnf(refute_0_37,plain,
( implies(and(not(X),not(Y)),X_6) != or(not(and(not(X),not(Y))),X_6)
| not(and(not(X),not(Y))) != or(X,Y)
| implies(and(not(X),not(Y)),X_6) = or(or(X,Y),X_6) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(not(X),not(Y)),X_6),or(not(and(not(X),not(Y))),X_6)) ),[1,0],$fot(or(X,Y))]]) ).
cnf(refute_0_38,plain,
( implies(and(not(X),not(Y)),X_6) != or(not(and(not(X),not(Y))),X_6)
| implies(and(not(X),not(Y)),X_6) = or(or(X,Y),X_6) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),or(X,Y)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
implies(and(not(X),not(Y)),X_6) = or(or(X,Y),X_6),
inference(resolve,[$cnf( $equal(implies(and(not(X),not(Y)),X_6),or(not(and(not(X),not(Y))),X_6)) )],[refute_0_34,refute_0_38]) ).
cnf(refute_0_40,plain,
implies(and(not(X_43),not(X_44)),not(Y)) = or(or(X_43,X_44),not(Y)),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_43)),bind(Y,$fot(X_44)),bind(X_6,$fot(not(Y)))]]) ).
cnf(refute_0_41,plain,
( and(and(not(X_43),not(X_44)),Y) != not(implies(and(not(X_43),not(X_44)),not(Y)))
| implies(and(not(X_43),not(X_44)),not(Y)) != or(or(X_43,X_44),not(Y))
| and(and(not(X_43),not(X_44)),Y) = not(or(or(X_43,X_44),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(not(X_43),not(X_44)),Y),not(implies(and(not(X_43),not(X_44)),not(Y)))) ),[1,0],$fot(or(or(X_43,X_44),not(Y)))]]) ).
cnf(refute_0_42,plain,
( and(and(not(X_43),not(X_44)),Y) != not(implies(and(not(X_43),not(X_44)),not(Y)))
| and(and(not(X_43),not(X_44)),Y) = not(or(or(X_43,X_44),not(Y))) ),
inference(resolve,[$cnf( $equal(implies(and(not(X_43),not(X_44)),not(Y)),or(or(X_43,X_44),not(Y))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
and(and(not(X_43),not(X_44)),Y) = not(or(or(X_43,X_44),not(Y))),
inference(resolve,[$cnf( $equal(and(and(not(X_43),not(X_44)),Y),not(implies(and(not(X_43),not(X_44)),not(Y)))) )],[refute_0_33,refute_0_42]) ).
cnf(refute_0_44,plain,
and(and(not(X_93),not(X_94)),not(Y)) = not(or(or(X_93,X_94),not(not(Y)))),
inference(subst,[],[refute_0_43:[bind(Y,$fot(not(Y))),bind(X_43,$fot(X_93)),bind(X_44,$fot(X_94))]]) ).
cnf(refute_0_45,plain,
( and(and(not(X_93),not(X_94)),not(Y)) != not(or(or(X_93,X_94),not(not(Y))))
| or(implies(not(X_93),not(not(X_94))),Y) != not(and(and(not(X_93),not(X_94)),not(Y)))
| or(implies(not(X_93),not(not(X_94))),Y) = not(not(or(or(X_93,X_94),not(not(Y))))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(not(X_93),not(not(X_94))),Y),not(and(and(not(X_93),not(X_94)),not(Y)))) ),[1,0],$fot(not(or(or(X_93,X_94),not(not(Y)))))]]) ).
cnf(refute_0_46,plain,
( or(implies(not(X_93),not(not(X_94))),Y) != not(and(and(not(X_93),not(X_94)),not(Y)))
| or(implies(not(X_93),not(not(X_94))),Y) = not(not(or(or(X_93,X_94),not(not(Y))))) ),
inference(resolve,[$cnf( $equal(and(and(not(X_93),not(X_94)),not(Y)),not(or(or(X_93,X_94),not(not(Y))))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
or(implies(not(X_93),not(not(X_94))),Y) = not(not(or(or(X_93,X_94),not(not(Y))))),
inference(resolve,[$cnf( $equal(or(implies(not(X_93),not(not(X_94))),Y),not(and(and(not(X_93),not(X_94)),not(Y)))) )],[refute_0_32,refute_0_46]) ).
cnf(refute_0_48,plain,
or(implies(not(X_94),not(not(X_94))),Y) = not(not(or(or(X_94,X_94),not(not(Y))))),
inference(subst,[],[refute_0_47:[bind(X_93,$fot(X_94))]]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_50,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_50,refute_0_49]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(equiv(or(X_27414,X_27414),X_27414))
| or(X_27414,X_27414) = X_27414 ),
inference(subst,[],[refute_0_51:[bind(X,$fot(or(X_27414,X_27414))),bind(Y,$fot(X_27414))]]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_54,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_54,refute_0_53]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(implies(X_27413,or(X_27413,X_27413)))
| ~ is_a_theorem(implies(implies(X_27413,or(X_27413,X_27413)),equiv(or(X_27413,X_27413),X_27413)))
| is_a_theorem(equiv(or(X_27413,X_27413),X_27413)) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(implies(X_27413,or(X_27413,X_27413)))),bind(Y,$fot(equiv(or(X_27413,X_27413),X_27413)))]]) ).
cnf(refute_0_57,plain,
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_58,plain,
r3,
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_59,plain,
is_a_theorem(implies(or(P,Q),or(Q,P))),
inference(resolve,[$cnf( r3 )],[refute_0_58,refute_0_57]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ is_a_theorem(or(P,Q))
| is_a_theorem(or(Q,P)) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(or(P,Q))),bind(Y,$fot(or(Q,P)))]]) ).
cnf(refute_0_61,plain,
( ~ is_a_theorem(or(P,Q))
| is_a_theorem(or(Q,P)) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,Q),or(Q,P))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ is_a_theorem(or(equiv(or(X_25052,X_25052),X_25052),not(implies(X_25052,or(X_25052,X_25052)))))
| is_a_theorem(or(not(implies(X_25052,or(X_25052,X_25052))),equiv(or(X_25052,X_25052),X_25052))) ),
inference(subst,[],[refute_0_61:[bind(P,$fot(equiv(or(X_25052,X_25052),X_25052))),bind(Q,$fot(not(implies(X_25052,or(X_25052,X_25052)))))]]) ).
cnf(refute_0_63,plain,
( ~ r1
| is_a_theorem(implies(or(P,P),P)) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_64,plain,
r1,
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(or(P,P),P)),
inference(resolve,[$cnf( r1 )],[refute_0_64,refute_0_63]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(X_3653)
| ~ is_a_theorem(implies(X_3653,implies(implies(X_3653,X_3654),X_3654)))
| is_a_theorem(implies(implies(X_3653,X_3654),X_3654)) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(X_3653)),bind(Y,$fot(implies(implies(X_3653,X_3654),X_3654)))]]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(or(X_171,X_171),X_171)),
inference(subst,[],[refute_0_65:[bind(P,$fot(X_171))]]) ).
cnf(refute_0_68,plain,
( ~ is_a_theorem(implies(or(X_171,X_171),X_171))
| ~ is_a_theorem(or(X_171,X_171))
| is_a_theorem(X_171) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(or(X_171,X_171))),bind(Y,$fot(X_171))]]) ).
cnf(refute_0_69,plain,
( ~ is_a_theorem(or(X_171,X_171))
| is_a_theorem(X_171) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_171,X_171),X_171)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( ~ is_a_theorem(or(implies(X_2830,X_2830),implies(X_2830,X_2830)))
| is_a_theorem(implies(X_2830,X_2830)) ),
inference(subst,[],[refute_0_69:[bind(X_171,$fot(implies(X_2830,X_2830)))]]) ).
cnf(refute_0_71,plain,
( ~ is_a_theorem(or(or(X_2709,X_2710),implies(X_2711,X_2711)))
| is_a_theorem(or(implies(X_2711,X_2711),or(X_2709,X_2710))) ),
inference(subst,[],[refute_0_61:[bind(P,$fot(or(X_2709,X_2710))),bind(Q,$fot(implies(X_2711,X_2711)))]]) ).
cnf(refute_0_72,plain,
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_73,plain,
r2,
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(Q,or(P,Q))),
inference(resolve,[$cnf( r2 )],[refute_0_73,refute_0_72]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(Q,or(not(X_5),Q))),
inference(subst,[],[refute_0_74:[bind(P,$fot(not(X_5)))]]) ).
cnf(refute_0_76,plain,
implies(X_5,Q) = or(not(X_5),Q),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_5)),bind(Y,$fot(Q))]]) ).
cnf(refute_0_77,plain,
( implies(X_5,Q) != or(not(X_5),Q)
| or(not(X_5),Q) = implies(X_5,Q) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X_5,Q))),bind(Y0,$fot(or(not(X_5),Q)))]]) ).
cnf(refute_0_78,plain,
or(not(X_5),Q) = implies(X_5,Q),
inference(resolve,[$cnf( $equal(implies(X_5,Q),or(not(X_5),Q)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( or(not(X_5),Q) != implies(X_5,Q)
| ~ is_a_theorem(implies(Q,or(not(X_5),Q)))
| is_a_theorem(implies(Q,implies(X_5,Q))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(Q,or(not(X_5),Q))) ),[0,1],$fot(implies(X_5,Q))]]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(implies(Q,or(not(X_5),Q)))
| is_a_theorem(implies(Q,implies(X_5,Q))) ),
inference(resolve,[$cnf( $equal(or(not(X_5),Q),implies(X_5,Q)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
is_a_theorem(implies(Q,implies(X_5,Q))),
inference(resolve,[$cnf( is_a_theorem(implies(Q,or(not(X_5),Q))) )],[refute_0_75,refute_0_80]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(X_2665,implies(X_2663,X_2665))),
inference(subst,[],[refute_0_81:[bind(Q,$fot(X_2665)),bind(X_5,$fot(X_2663))]]) ).
cnf(refute_0_83,plain,
( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_84,plain,
r4,
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_85,plain,
is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))),
inference(resolve,[$cnf( r4 )],[refute_0_84,refute_0_83]) ).
cnf(refute_0_86,plain,
is_a_theorem(implies(or(not(X),or(X_72,X_73)),or(X_72,or(not(X),X_73)))),
inference(subst,[],[refute_0_85:[bind(P,$fot(not(X))),bind(Q,$fot(X_72)),bind(R,$fot(X_73))]]) ).
cnf(refute_0_87,plain,
implies(X,X_73) = or(not(X),X_73),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_73))]]) ).
cnf(refute_0_88,plain,
( implies(X,X_73) != or(not(X),X_73)
| or(not(X),X_73) = implies(X,X_73) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_73))),bind(Y0,$fot(or(not(X),X_73)))]]) ).
cnf(refute_0_89,plain,
or(not(X),X_73) = implies(X,X_73),
inference(resolve,[$cnf( $equal(implies(X,X_73),or(not(X),X_73)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( or(not(X),X_73) != implies(X,X_73)
| ~ is_a_theorem(implies(or(not(X),or(X_72,X_73)),or(X_72,or(not(X),X_73))))
| is_a_theorem(implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),or(X_72,X_73)),or(X_72,or(not(X),X_73)))) ),[0,1,1],$fot(implies(X,X_73))]]) ).
cnf(refute_0_91,plain,
( ~ is_a_theorem(implies(or(not(X),or(X_72,X_73)),or(X_72,or(not(X),X_73))))
| is_a_theorem(implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_73),implies(X,X_73)) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
is_a_theorem(implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),or(X_72,X_73)),or(X_72,or(not(X),X_73)))) )],[refute_0_86,refute_0_91]) ).
cnf(refute_0_93,plain,
or(not(X),or(X_72,X_73)) = implies(X,or(X_72,X_73)),
inference(subst,[],[refute_0_17:[bind(Y,$fot(or(X_72,X_73)))]]) ).
cnf(refute_0_94,plain,
implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73))) = implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73))))]]) ).
cnf(refute_0_95,plain,
( implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73))) != implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73)))
| or(not(X),or(X_72,X_73)) != implies(X,or(X_72,X_73))
| implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73))) = implies(implies(X,or(X_72,X_73)),or(X_72,implies(X,X_73))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73))),implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73)))) ),[1,0],$fot(implies(X,or(X_72,X_73)))]]) ).
cnf(refute_0_96,plain,
( or(not(X),or(X_72,X_73)) != implies(X,or(X_72,X_73))
| implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73))) = implies(implies(X,or(X_72,X_73)),or(X_72,implies(X,X_73))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73))),implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73)))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73))) = implies(implies(X,or(X_72,X_73)),or(X_72,implies(X,X_73))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_72,X_73)),implies(X,or(X_72,X_73))) )],[refute_0_93,refute_0_96]) ).
cnf(refute_0_98,plain,
( implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73))) != implies(implies(X,or(X_72,X_73)),or(X_72,implies(X,X_73)))
| ~ is_a_theorem(implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73))))
| is_a_theorem(implies(implies(X,or(X_72,X_73)),or(X_72,implies(X,X_73)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73)))) ),[0],$fot(implies(implies(X,or(X_72,X_73)),or(X_72,implies(X,X_73))))]]) ).
cnf(refute_0_99,plain,
( ~ is_a_theorem(implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73))))
| is_a_theorem(implies(implies(X,or(X_72,X_73)),or(X_72,implies(X,X_73)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73))),implies(implies(X,or(X_72,X_73)),or(X_72,implies(X,X_73)))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
is_a_theorem(implies(implies(X,or(X_72,X_73)),or(X_72,implies(X,X_73)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),or(X_72,X_73)),or(X_72,implies(X,X_73)))) )],[refute_0_92,refute_0_99]) ).
cnf(refute_0_101,plain,
is_a_theorem(implies(implies(X_80,or(not(X),X_82)),or(not(X),implies(X_80,X_82)))),
inference(subst,[],[refute_0_100:[bind(X,$fot(X_80)),bind(X_72,$fot(not(X))),bind(X_73,$fot(X_82))]]) ).
cnf(refute_0_102,plain,
implies(X,implies(X_80,X_82)) = or(not(X),implies(X_80,X_82)),
inference(subst,[],[refute_0_12:[bind(Y,$fot(implies(X_80,X_82)))]]) ).
cnf(refute_0_103,plain,
( implies(X,implies(X_80,X_82)) != or(not(X),implies(X_80,X_82))
| or(not(X),implies(X_80,X_82)) = implies(X,implies(X_80,X_82)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,implies(X_80,X_82)))),bind(Y0,$fot(or(not(X),implies(X_80,X_82))))]]) ).
cnf(refute_0_104,plain,
or(not(X),implies(X_80,X_82)) = implies(X,implies(X_80,X_82)),
inference(resolve,[$cnf( $equal(implies(X,implies(X_80,X_82)),or(not(X),implies(X_80,X_82))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
( or(not(X),implies(X_80,X_82)) != implies(X,implies(X_80,X_82))
| ~ is_a_theorem(implies(implies(X_80,or(not(X),X_82)),or(not(X),implies(X_80,X_82))))
| is_a_theorem(implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_80,or(not(X),X_82)),or(not(X),implies(X_80,X_82)))) ),[0,1],$fot(implies(X,implies(X_80,X_82)))]]) ).
cnf(refute_0_106,plain,
( ~ is_a_theorem(implies(implies(X_80,or(not(X),X_82)),or(not(X),implies(X_80,X_82))))
| is_a_theorem(implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82)))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_80,X_82)),implies(X,implies(X_80,X_82))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
is_a_theorem(implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_80,or(not(X),X_82)),or(not(X),implies(X_80,X_82)))) )],[refute_0_101,refute_0_106]) ).
cnf(refute_0_108,plain,
or(not(X),X_82) = implies(X,X_82),
inference(subst,[],[refute_0_17:[bind(Y,$fot(X_82))]]) ).
cnf(refute_0_109,plain,
implies(X_80,or(not(X),X_82)) = implies(X_80,or(not(X),X_82)),
introduced(tautology,[refl,[$fot(implies(X_80,or(not(X),X_82)))]]) ).
cnf(refute_0_110,plain,
( implies(X_80,or(not(X),X_82)) != implies(X_80,or(not(X),X_82))
| or(not(X),X_82) != implies(X,X_82)
| implies(X_80,or(not(X),X_82)) = implies(X_80,implies(X,X_82)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_80,or(not(X),X_82)),implies(X_80,or(not(X),X_82))) ),[1,1],$fot(implies(X,X_82))]]) ).
cnf(refute_0_111,plain,
( or(not(X),X_82) != implies(X,X_82)
| implies(X_80,or(not(X),X_82)) = implies(X_80,implies(X,X_82)) ),
inference(resolve,[$cnf( $equal(implies(X_80,or(not(X),X_82)),implies(X_80,or(not(X),X_82))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
implies(X_80,or(not(X),X_82)) = implies(X_80,implies(X,X_82)),
inference(resolve,[$cnf( $equal(or(not(X),X_82),implies(X,X_82)) )],[refute_0_108,refute_0_111]) ).
cnf(refute_0_113,plain,
implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82))) = implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82))),
introduced(tautology,[refl,[$fot(implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82))))]]) ).
cnf(refute_0_114,plain,
( implies(X_80,or(not(X),X_82)) != implies(X_80,implies(X,X_82))
| implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82))) != implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82)))
| implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82))) = implies(implies(X_80,implies(X,X_82)),implies(X,implies(X_80,X_82))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82))),implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82)))) ),[1,0],$fot(implies(X_80,implies(X,X_82)))]]) ).
cnf(refute_0_115,plain,
( implies(X_80,or(not(X),X_82)) != implies(X_80,implies(X,X_82))
| implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82))) = implies(implies(X_80,implies(X,X_82)),implies(X,implies(X_80,X_82))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82))),implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82)))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82))) = implies(implies(X_80,implies(X,X_82)),implies(X,implies(X_80,X_82))),
inference(resolve,[$cnf( $equal(implies(X_80,or(not(X),X_82)),implies(X_80,implies(X,X_82))) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
( implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82))) != implies(implies(X_80,implies(X,X_82)),implies(X,implies(X_80,X_82)))
| ~ is_a_theorem(implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82))))
| is_a_theorem(implies(implies(X_80,implies(X,X_82)),implies(X,implies(X_80,X_82)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82)))) ),[0],$fot(implies(implies(X_80,implies(X,X_82)),implies(X,implies(X_80,X_82))))]]) ).
cnf(refute_0_118,plain,
( ~ is_a_theorem(implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82))))
| is_a_theorem(implies(implies(X_80,implies(X,X_82)),implies(X,implies(X_80,X_82)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82))),implies(implies(X_80,implies(X,X_82)),implies(X,implies(X_80,X_82)))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
is_a_theorem(implies(implies(X_80,implies(X,X_82)),implies(X,implies(X_80,X_82)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_80,or(not(X),X_82)),implies(X,implies(X_80,X_82)))) )],[refute_0_107,refute_0_118]) ).
cnf(refute_0_120,plain,
( ~ is_a_theorem(implies(X_80,implies(X,X_82)))
| ~ is_a_theorem(implies(implies(X_80,implies(X,X_82)),implies(X,implies(X_80,X_82))))
| is_a_theorem(implies(X,implies(X_80,X_82))) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(implies(X_80,implies(X,X_82)))),bind(Y,$fot(implies(X,implies(X_80,X_82))))]]) ).
cnf(refute_0_121,plain,
( ~ is_a_theorem(implies(X_80,implies(X,X_82)))
| is_a_theorem(implies(X,implies(X_80,X_82))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_80,implies(X,X_82)),implies(X,implies(X_80,X_82)))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
( ~ is_a_theorem(implies(X_2665,implies(X_2663,X_2665)))
| is_a_theorem(implies(X_2663,implies(X_2665,X_2665))) ),
inference(subst,[],[refute_0_121:[bind(X,$fot(X_2663)),bind(X_80,$fot(X_2665)),bind(X_82,$fot(X_2665))]]) ).
cnf(refute_0_123,plain,
is_a_theorem(implies(X_2663,implies(X_2665,X_2665))),
inference(resolve,[$cnf( is_a_theorem(implies(X_2665,implies(X_2663,X_2665))) )],[refute_0_82,refute_0_122]) ).
cnf(refute_0_124,plain,
is_a_theorem(implies(and(not(X),not(Y)),implies(X_2667,X_2667))),
inference(subst,[],[refute_0_123:[bind(X_2663,$fot(and(not(X),not(Y)))),bind(X_2665,$fot(X_2667))]]) ).
cnf(refute_0_125,plain,
implies(and(not(X),not(Y)),implies(X_2667,X_2667)) = or(or(X,Y),implies(X_2667,X_2667)),
inference(subst,[],[refute_0_39:[bind(X_6,$fot(implies(X_2667,X_2667)))]]) ).
cnf(refute_0_126,plain,
( implies(and(not(X),not(Y)),implies(X_2667,X_2667)) != or(or(X,Y),implies(X_2667,X_2667))
| ~ is_a_theorem(implies(and(not(X),not(Y)),implies(X_2667,X_2667)))
| is_a_theorem(or(or(X,Y),implies(X_2667,X_2667))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(not(X),not(Y)),implies(X_2667,X_2667))) ),[0],$fot(or(or(X,Y),implies(X_2667,X_2667)))]]) ).
cnf(refute_0_127,plain,
( ~ is_a_theorem(implies(and(not(X),not(Y)),implies(X_2667,X_2667)))
| is_a_theorem(or(or(X,Y),implies(X_2667,X_2667))) ),
inference(resolve,[$cnf( $equal(implies(and(not(X),not(Y)),implies(X_2667,X_2667)),or(or(X,Y),implies(X_2667,X_2667))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
is_a_theorem(or(or(X,Y),implies(X_2667,X_2667))),
inference(resolve,[$cnf( is_a_theorem(implies(and(not(X),not(Y)),implies(X_2667,X_2667))) )],[refute_0_124,refute_0_127]) ).
cnf(refute_0_129,plain,
is_a_theorem(or(or(X_2709,X_2710),implies(X_2711,X_2711))),
inference(subst,[],[refute_0_128:[bind(X,$fot(X_2709)),bind(Y,$fot(X_2710)),bind(X_2667,$fot(X_2711))]]) ).
cnf(refute_0_130,plain,
is_a_theorem(or(implies(X_2711,X_2711),or(X_2709,X_2710))),
inference(resolve,[$cnf( is_a_theorem(or(or(X_2709,X_2710),implies(X_2711,X_2711))) )],[refute_0_129,refute_0_71]) ).
cnf(refute_0_131,plain,
is_a_theorem(or(implies(X_2828,X_2828),or(not(X),X_2827))),
inference(subst,[],[refute_0_130:[bind(X_2709,$fot(not(X))),bind(X_2710,$fot(X_2827)),bind(X_2711,$fot(X_2828))]]) ).
cnf(refute_0_132,plain,
implies(X,X_2827) = or(not(X),X_2827),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_2827))]]) ).
cnf(refute_0_133,plain,
( implies(X,X_2827) != or(not(X),X_2827)
| or(not(X),X_2827) = implies(X,X_2827) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_2827))),bind(Y0,$fot(or(not(X),X_2827)))]]) ).
cnf(refute_0_134,plain,
or(not(X),X_2827) = implies(X,X_2827),
inference(resolve,[$cnf( $equal(implies(X,X_2827),or(not(X),X_2827)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
( or(not(X),X_2827) != implies(X,X_2827)
| ~ is_a_theorem(or(implies(X_2828,X_2828),or(not(X),X_2827)))
| is_a_theorem(or(implies(X_2828,X_2828),implies(X,X_2827))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(X_2828,X_2828),or(not(X),X_2827))) ),[0,1],$fot(implies(X,X_2827))]]) ).
cnf(refute_0_136,plain,
( ~ is_a_theorem(or(implies(X_2828,X_2828),or(not(X),X_2827)))
| is_a_theorem(or(implies(X_2828,X_2828),implies(X,X_2827))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_2827),implies(X,X_2827)) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
is_a_theorem(or(implies(X_2828,X_2828),implies(X,X_2827))),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_2828,X_2828),or(not(X),X_2827))) )],[refute_0_131,refute_0_136]) ).
cnf(refute_0_138,plain,
is_a_theorem(or(implies(X_2830,X_2830),implies(X_2830,X_2830))),
inference(subst,[],[refute_0_137:[bind(X,$fot(X_2830)),bind(X_2827,$fot(X_2830)),bind(X_2828,$fot(X_2830))]]) ).
cnf(refute_0_139,plain,
is_a_theorem(implies(X_2830,X_2830)),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_2830,X_2830),implies(X_2830,X_2830))) )],[refute_0_138,refute_0_70]) ).
cnf(refute_0_140,plain,
is_a_theorem(implies(or(X_3612,X_3613),or(X_3612,X_3613))),
inference(subst,[],[refute_0_139:[bind(X_2830,$fot(or(X_3612,X_3613)))]]) ).
cnf(refute_0_141,plain,
( ~ is_a_theorem(implies(X,or(X_72,X_73)))
| ~ is_a_theorem(implies(implies(X,or(X_72,X_73)),or(X_72,implies(X,X_73))))
| is_a_theorem(or(X_72,implies(X,X_73))) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(implies(X,or(X_72,X_73)))),bind(Y,$fot(or(X_72,implies(X,X_73))))]]) ).
cnf(refute_0_142,plain,
( ~ is_a_theorem(implies(X,or(X_72,X_73)))
| is_a_theorem(or(X_72,implies(X,X_73))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,or(X_72,X_73)),or(X_72,implies(X,X_73)))) )],[refute_0_100,refute_0_141]) ).
cnf(refute_0_143,plain,
( ~ is_a_theorem(implies(or(X_3612,X_3613),or(X_3612,X_3613)))
| is_a_theorem(or(X_3612,implies(or(X_3612,X_3613),X_3613))) ),
inference(subst,[],[refute_0_142:[bind(X,$fot(or(X_3612,X_3613))),bind(X_72,$fot(X_3612)),bind(X_73,$fot(X_3613))]]) ).
cnf(refute_0_144,plain,
is_a_theorem(or(X_3612,implies(or(X_3612,X_3613),X_3613))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_3612,X_3613),or(X_3612,X_3613))) )],[refute_0_140,refute_0_143]) ).
cnf(refute_0_145,plain,
is_a_theorem(or(not(X),implies(or(not(X),X_3630),X_3630))),
inference(subst,[],[refute_0_144:[bind(X_3612,$fot(not(X))),bind(X_3613,$fot(X_3630))]]) ).
cnf(refute_0_146,plain,
implies(X,X_3630) = or(not(X),X_3630),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_3630))]]) ).
cnf(refute_0_147,plain,
( implies(X,X_3630) != or(not(X),X_3630)
| or(not(X),X_3630) = implies(X,X_3630) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_3630))),bind(Y0,$fot(or(not(X),X_3630)))]]) ).
cnf(refute_0_148,plain,
or(not(X),X_3630) = implies(X,X_3630),
inference(resolve,[$cnf( $equal(implies(X,X_3630),or(not(X),X_3630)) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
( or(not(X),X_3630) != implies(X,X_3630)
| ~ is_a_theorem(or(not(X),implies(or(not(X),X_3630),X_3630)))
| is_a_theorem(or(not(X),implies(implies(X,X_3630),X_3630))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X),implies(or(not(X),X_3630),X_3630))) ),[0,1,0],$fot(implies(X,X_3630))]]) ).
cnf(refute_0_150,plain,
( ~ is_a_theorem(or(not(X),implies(or(not(X),X_3630),X_3630)))
| is_a_theorem(or(not(X),implies(implies(X,X_3630),X_3630))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_3630),implies(X,X_3630)) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
is_a_theorem(or(not(X),implies(implies(X,X_3630),X_3630))),
inference(resolve,[$cnf( is_a_theorem(or(not(X),implies(or(not(X),X_3630),X_3630))) )],[refute_0_145,refute_0_150]) ).
cnf(refute_0_152,plain,
or(not(X),implies(implies(X,X_3630),X_3630)) = implies(X,implies(implies(X,X_3630),X_3630)),
inference(subst,[],[refute_0_17:[bind(Y,$fot(implies(implies(X,X_3630),X_3630)))]]) ).
cnf(refute_0_153,plain,
( or(not(X),implies(implies(X,X_3630),X_3630)) != implies(X,implies(implies(X,X_3630),X_3630))
| ~ is_a_theorem(or(not(X),implies(implies(X,X_3630),X_3630)))
| is_a_theorem(implies(X,implies(implies(X,X_3630),X_3630))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X),implies(implies(X,X_3630),X_3630))) ),[0],$fot(implies(X,implies(implies(X,X_3630),X_3630)))]]) ).
cnf(refute_0_154,plain,
( ~ is_a_theorem(or(not(X),implies(implies(X,X_3630),X_3630)))
| is_a_theorem(implies(X,implies(implies(X,X_3630),X_3630))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(implies(X,X_3630),X_3630)),implies(X,implies(implies(X,X_3630),X_3630))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
is_a_theorem(implies(X,implies(implies(X,X_3630),X_3630))),
inference(resolve,[$cnf( is_a_theorem(or(not(X),implies(implies(X,X_3630),X_3630))) )],[refute_0_151,refute_0_154]) ).
cnf(refute_0_156,plain,
is_a_theorem(implies(X_3653,implies(implies(X_3653,X_3654),X_3654))),
inference(subst,[],[refute_0_155:[bind(X,$fot(X_3653)),bind(X_3630,$fot(X_3654))]]) ).
cnf(refute_0_157,plain,
( ~ is_a_theorem(X_3653)
| is_a_theorem(implies(implies(X_3653,X_3654),X_3654)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_3653,implies(implies(X_3653,X_3654),X_3654))) )],[refute_0_156,refute_0_66]) ).
cnf(refute_0_158,plain,
( ~ is_a_theorem(implies(or(P,P),P))
| is_a_theorem(implies(implies(implies(or(P,P),P),X_24842),X_24842)) ),
inference(subst,[],[refute_0_157:[bind(X_3653,$fot(implies(or(P,P),P))),bind(X_3654,$fot(X_24842))]]) ).
cnf(refute_0_159,plain,
is_a_theorem(implies(implies(implies(or(P,P),P),X_24842),X_24842)),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,P),P)) )],[refute_0_65,refute_0_158]) ).
cnf(refute_0_160,plain,
is_a_theorem(implies(implies(implies(or(X_24879,X_24879),X_24879),not(X_11)),not(X_11))),
inference(subst,[],[refute_0_159:[bind(P,$fot(X_24879)),bind(X_24842,$fot(not(X_11)))]]) ).
cnf(refute_0_161,plain,
implies(implies(X_10,not(X_11)),Y) = or(not(implies(X_10,not(X_11))),Y),
inference(subst,[],[refute_0_12:[bind(X,$fot(implies(X_10,not(X_11))))]]) ).
cnf(refute_0_162,plain,
( implies(implies(X_10,not(X_11)),Y) != or(not(implies(X_10,not(X_11))),Y)
| not(implies(X_10,not(X_11))) != and(X_10,X_11)
| implies(implies(X_10,not(X_11)),Y) = or(and(X_10,X_11),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_10,not(X_11)),Y),or(not(implies(X_10,not(X_11))),Y)) ),[1,0],$fot(and(X_10,X_11))]]) ).
cnf(refute_0_163,plain,
( implies(implies(X_10,not(X_11)),Y) != or(not(implies(X_10,not(X_11))),Y)
| implies(implies(X_10,not(X_11)),Y) = or(and(X_10,X_11),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_10,not(X_11))),and(X_10,X_11)) )],[refute_0_28,refute_0_162]) ).
cnf(refute_0_164,plain,
implies(implies(X_10,not(X_11)),Y) = or(and(X_10,X_11),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_10,not(X_11)),Y),or(not(implies(X_10,not(X_11))),Y)) )],[refute_0_161,refute_0_163]) ).
cnf(refute_0_165,plain,
implies(implies(implies(or(X_24879,X_24879),X_24879),not(X_11)),not(X_11)) = or(and(implies(or(X_24879,X_24879),X_24879),X_11),not(X_11)),
inference(subst,[],[refute_0_164:[bind(Y,$fot(not(X_11))),bind(X_10,$fot(implies(or(X_24879,X_24879),X_24879)))]]) ).
cnf(refute_0_166,plain,
( implies(implies(implies(or(X_24879,X_24879),X_24879),not(X_11)),not(X_11)) != or(and(implies(or(X_24879,X_24879),X_24879),X_11),not(X_11))
| ~ is_a_theorem(implies(implies(implies(or(X_24879,X_24879),X_24879),not(X_11)),not(X_11)))
| is_a_theorem(or(and(implies(or(X_24879,X_24879),X_24879),X_11),not(X_11))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(implies(or(X_24879,X_24879),X_24879),not(X_11)),not(X_11))) ),[0],$fot(or(and(implies(or(X_24879,X_24879),X_24879),X_11),not(X_11)))]]) ).
cnf(refute_0_167,plain,
( ~ is_a_theorem(implies(implies(implies(or(X_24879,X_24879),X_24879),not(X_11)),not(X_11)))
| is_a_theorem(or(and(implies(or(X_24879,X_24879),X_24879),X_11),not(X_11))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(or(X_24879,X_24879),X_24879),not(X_11)),not(X_11)),or(and(implies(or(X_24879,X_24879),X_24879),X_11),not(X_11))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
is_a_theorem(or(and(implies(or(X_24879,X_24879),X_24879),X_11),not(X_11))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(or(X_24879,X_24879),X_24879),not(X_11)),not(X_11))) )],[refute_0_160,refute_0_167]) ).
cnf(refute_0_169,plain,
is_a_theorem(or(and(implies(or(X_25029,X_25029),X_25029),implies(X_25029,or(X_25029,X_25029))),not(implies(X_25029,or(X_25029,X_25029))))),
inference(subst,[],[refute_0_168:[bind(X_11,$fot(implies(X_25029,or(X_25029,X_25029)))),bind(X_24879,$fot(X_25029))]]) ).
cnf(refute_0_170,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_171,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_172,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_171,refute_0_170]) ).
cnf(refute_0_173,plain,
equiv(or(X_25029,X_25029),X_25029) = and(implies(or(X_25029,X_25029),X_25029),implies(X_25029,or(X_25029,X_25029))),
inference(subst,[],[refute_0_172:[bind(X,$fot(or(X_25029,X_25029))),bind(Y,$fot(X_25029))]]) ).
cnf(refute_0_174,plain,
( equiv(or(X_25029,X_25029),X_25029) != and(implies(or(X_25029,X_25029),X_25029),implies(X_25029,or(X_25029,X_25029)))
| and(implies(or(X_25029,X_25029),X_25029),implies(X_25029,or(X_25029,X_25029))) = equiv(or(X_25029,X_25029),X_25029) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(or(X_25029,X_25029),X_25029))),bind(Y0,$fot(and(implies(or(X_25029,X_25029),X_25029),implies(X_25029,or(X_25029,X_25029)))))]]) ).
cnf(refute_0_175,plain,
and(implies(or(X_25029,X_25029),X_25029),implies(X_25029,or(X_25029,X_25029))) = equiv(or(X_25029,X_25029),X_25029),
inference(resolve,[$cnf( $equal(equiv(or(X_25029,X_25029),X_25029),and(implies(or(X_25029,X_25029),X_25029),implies(X_25029,or(X_25029,X_25029)))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
( and(implies(or(X_25029,X_25029),X_25029),implies(X_25029,or(X_25029,X_25029))) != equiv(or(X_25029,X_25029),X_25029)
| ~ is_a_theorem(or(and(implies(or(X_25029,X_25029),X_25029),implies(X_25029,or(X_25029,X_25029))),not(implies(X_25029,or(X_25029,X_25029)))))
| is_a_theorem(or(equiv(or(X_25029,X_25029),X_25029),not(implies(X_25029,or(X_25029,X_25029))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(implies(or(X_25029,X_25029),X_25029),implies(X_25029,or(X_25029,X_25029))),not(implies(X_25029,or(X_25029,X_25029))))) ),[0,0],$fot(equiv(or(X_25029,X_25029),X_25029))]]) ).
cnf(refute_0_177,plain,
( ~ is_a_theorem(or(and(implies(or(X_25029,X_25029),X_25029),implies(X_25029,or(X_25029,X_25029))),not(implies(X_25029,or(X_25029,X_25029)))))
| is_a_theorem(or(equiv(or(X_25029,X_25029),X_25029),not(implies(X_25029,or(X_25029,X_25029))))) ),
inference(resolve,[$cnf( $equal(and(implies(or(X_25029,X_25029),X_25029),implies(X_25029,or(X_25029,X_25029))),equiv(or(X_25029,X_25029),X_25029)) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
is_a_theorem(or(equiv(or(X_25029,X_25029),X_25029),not(implies(X_25029,or(X_25029,X_25029))))),
inference(resolve,[$cnf( is_a_theorem(or(and(implies(or(X_25029,X_25029),X_25029),implies(X_25029,or(X_25029,X_25029))),not(implies(X_25029,or(X_25029,X_25029))))) )],[refute_0_169,refute_0_177]) ).
cnf(refute_0_179,plain,
is_a_theorem(or(equiv(or(X_25052,X_25052),X_25052),not(implies(X_25052,or(X_25052,X_25052))))),
inference(subst,[],[refute_0_178:[bind(X_25029,$fot(X_25052))]]) ).
cnf(refute_0_180,plain,
is_a_theorem(or(not(implies(X_25052,or(X_25052,X_25052))),equiv(or(X_25052,X_25052),X_25052))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(or(X_25052,X_25052),X_25052),not(implies(X_25052,or(X_25052,X_25052))))) )],[refute_0_179,refute_0_62]) ).
cnf(refute_0_181,plain,
or(not(implies(X_25052,or(X_25052,X_25052))),equiv(or(X_25052,X_25052),X_25052)) = implies(implies(X_25052,or(X_25052,X_25052)),equiv(or(X_25052,X_25052),X_25052)),
inference(subst,[],[refute_0_17:[bind(X,$fot(implies(X_25052,or(X_25052,X_25052)))),bind(Y,$fot(equiv(or(X_25052,X_25052),X_25052)))]]) ).
cnf(refute_0_182,plain,
( or(not(implies(X_25052,or(X_25052,X_25052))),equiv(or(X_25052,X_25052),X_25052)) != implies(implies(X_25052,or(X_25052,X_25052)),equiv(or(X_25052,X_25052),X_25052))
| ~ is_a_theorem(or(not(implies(X_25052,or(X_25052,X_25052))),equiv(or(X_25052,X_25052),X_25052)))
| is_a_theorem(implies(implies(X_25052,or(X_25052,X_25052)),equiv(or(X_25052,X_25052),X_25052))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(implies(X_25052,or(X_25052,X_25052))),equiv(or(X_25052,X_25052),X_25052))) ),[0],$fot(implies(implies(X_25052,or(X_25052,X_25052)),equiv(or(X_25052,X_25052),X_25052)))]]) ).
cnf(refute_0_183,plain,
( ~ is_a_theorem(or(not(implies(X_25052,or(X_25052,X_25052))),equiv(or(X_25052,X_25052),X_25052)))
| is_a_theorem(implies(implies(X_25052,or(X_25052,X_25052)),equiv(or(X_25052,X_25052),X_25052))) ),
inference(resolve,[$cnf( $equal(or(not(implies(X_25052,or(X_25052,X_25052))),equiv(or(X_25052,X_25052),X_25052)),implies(implies(X_25052,or(X_25052,X_25052)),equiv(or(X_25052,X_25052),X_25052))) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
is_a_theorem(implies(implies(X_25052,or(X_25052,X_25052)),equiv(or(X_25052,X_25052),X_25052))),
inference(resolve,[$cnf( is_a_theorem(or(not(implies(X_25052,or(X_25052,X_25052))),equiv(or(X_25052,X_25052),X_25052))) )],[refute_0_180,refute_0_183]) ).
cnf(refute_0_185,plain,
is_a_theorem(implies(implies(X_27413,or(X_27413,X_27413)),equiv(or(X_27413,X_27413),X_27413))),
inference(subst,[],[refute_0_184:[bind(X_25052,$fot(X_27413))]]) ).
cnf(refute_0_186,plain,
( ~ is_a_theorem(implies(X_27413,or(X_27413,X_27413)))
| is_a_theorem(equiv(or(X_27413,X_27413),X_27413)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_27413,or(X_27413,X_27413)),equiv(or(X_27413,X_27413),X_27413))) )],[refute_0_185,refute_0_56]) ).
cnf(refute_0_187,plain,
is_a_theorem(implies(X_27413,or(X_27413,X_27413))),
inference(subst,[],[refute_0_74:[bind(P,$fot(X_27413)),bind(Q,$fot(X_27413))]]) ).
cnf(refute_0_188,plain,
is_a_theorem(equiv(or(X_27413,X_27413),X_27413)),
inference(resolve,[$cnf( is_a_theorem(implies(X_27413,or(X_27413,X_27413))) )],[refute_0_187,refute_0_186]) ).
cnf(refute_0_189,plain,
is_a_theorem(equiv(or(X_27414,X_27414),X_27414)),
inference(subst,[],[refute_0_188:[bind(X_27413,$fot(X_27414))]]) ).
cnf(refute_0_190,plain,
or(X_27414,X_27414) = X_27414,
inference(resolve,[$cnf( is_a_theorem(equiv(or(X_27414,X_27414),X_27414)) )],[refute_0_189,refute_0_52]) ).
cnf(refute_0_191,plain,
or(X_94,X_94) = X_94,
inference(subst,[],[refute_0_190:[bind(X_27414,$fot(X_94))]]) ).
cnf(refute_0_192,plain,
( or(X_94,X_94) != X_94
| or(implies(not(X_94),not(not(X_94))),Y) != not(not(or(or(X_94,X_94),not(not(Y)))))
| or(implies(not(X_94),not(not(X_94))),Y) = not(not(or(X_94,not(not(Y))))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(not(X_94),not(not(X_94))),Y),not(not(or(or(X_94,X_94),not(not(Y)))))) ),[1,0,0,0],$fot(X_94)]]) ).
cnf(refute_0_193,plain,
( or(implies(not(X_94),not(not(X_94))),Y) != not(not(or(or(X_94,X_94),not(not(Y)))))
| or(implies(not(X_94),not(not(X_94))),Y) = not(not(or(X_94,not(not(Y))))) ),
inference(resolve,[$cnf( $equal(or(X_94,X_94),X_94) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
or(implies(not(X_94),not(not(X_94))),Y) = not(not(or(X_94,not(not(Y))))),
inference(resolve,[$cnf( $equal(or(implies(not(X_94),not(not(X_94))),Y),not(not(or(or(X_94,X_94),not(not(Y)))))) )],[refute_0_48,refute_0_193]) ).
cnf(refute_0_195,plain,
or(not(not(X_94)),Y) = implies(not(X_94),Y),
inference(subst,[],[refute_0_17:[bind(X,$fot(not(X_94)))]]) ).
cnf(refute_0_196,plain,
implies(X,not(X)) = or(not(X),not(X)),
inference(subst,[],[refute_0_12:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_197,plain,
or(not(X),not(X)) = not(X),
inference(subst,[],[refute_0_190:[bind(X_27414,$fot(not(X)))]]) ).
cnf(refute_0_198,plain,
( implies(X,not(X)) != or(not(X),not(X))
| or(not(X),not(X)) != not(X)
| implies(X,not(X)) = not(X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,not(X)),not(X)) ),[0],$fot(or(not(X),not(X)))]]) ).
cnf(refute_0_199,plain,
( implies(X,not(X)) != or(not(X),not(X))
| implies(X,not(X)) = not(X) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),not(X)) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
implies(X,not(X)) = not(X),
inference(resolve,[$cnf( $equal(implies(X,not(X)),or(not(X),not(X))) )],[refute_0_196,refute_0_199]) ).
cnf(refute_0_201,plain,
implies(not(X_94),not(not(X_94))) = not(not(X_94)),
inference(subst,[],[refute_0_200:[bind(X,$fot(not(X_94)))]]) ).
cnf(refute_0_202,plain,
or(implies(not(X_94),not(not(X_94))),Y) = or(implies(not(X_94),not(not(X_94))),Y),
introduced(tautology,[refl,[$fot(or(implies(not(X_94),not(not(X_94))),Y))]]) ).
cnf(refute_0_203,plain,
( implies(not(X_94),not(not(X_94))) != not(not(X_94))
| or(implies(not(X_94),not(not(X_94))),Y) != or(implies(not(X_94),not(not(X_94))),Y)
| or(implies(not(X_94),not(not(X_94))),Y) = or(not(not(X_94)),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(not(X_94),not(not(X_94))),Y),or(implies(not(X_94),not(not(X_94))),Y)) ),[1,0],$fot(not(not(X_94)))]]) ).
cnf(refute_0_204,plain,
( implies(not(X_94),not(not(X_94))) != not(not(X_94))
| or(implies(not(X_94),not(not(X_94))),Y) = or(not(not(X_94)),Y) ),
inference(resolve,[$cnf( $equal(or(implies(not(X_94),not(not(X_94))),Y),or(implies(not(X_94),not(not(X_94))),Y)) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
or(implies(not(X_94),not(not(X_94))),Y) = or(not(not(X_94)),Y),
inference(resolve,[$cnf( $equal(implies(not(X_94),not(not(X_94))),not(not(X_94))) )],[refute_0_201,refute_0_204]) ).
cnf(refute_0_206,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_207,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_15,refute_0_206]) ).
cnf(refute_0_208,plain,
( or(implies(not(X_94),not(not(X_94))),Y) != or(not(not(X_94)),Y)
| or(not(not(X_94)),Y) != implies(not(X_94),Y)
| or(implies(not(X_94),not(not(X_94))),Y) = implies(not(X_94),Y) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(or(implies(not(X_94),not(not(X_94))),Y))),bind(Y0,$fot(or(not(not(X_94)),Y))),bind(Z,$fot(implies(not(X_94),Y)))]]) ).
cnf(refute_0_209,plain,
( or(not(not(X_94)),Y) != implies(not(X_94),Y)
| or(implies(not(X_94),not(not(X_94))),Y) = implies(not(X_94),Y) ),
inference(resolve,[$cnf( $equal(or(implies(not(X_94),not(not(X_94))),Y),or(not(not(X_94)),Y)) )],[refute_0_205,refute_0_208]) ).
cnf(refute_0_210,plain,
or(implies(not(X_94),not(not(X_94))),Y) = implies(not(X_94),Y),
inference(resolve,[$cnf( $equal(or(not(not(X_94)),Y),implies(not(X_94),Y)) )],[refute_0_195,refute_0_209]) ).
cnf(refute_0_211,plain,
( or(implies(not(X_94),not(not(X_94))),Y) != implies(not(X_94),Y)
| or(implies(not(X_94),not(not(X_94))),Y) != not(not(or(X_94,not(not(Y)))))
| implies(not(X_94),Y) = not(not(or(X_94,not(not(Y))))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(not(X_94),not(not(X_94))),Y),not(not(or(X_94,not(not(Y)))))) ),[0],$fot(implies(not(X_94),Y))]]) ).
cnf(refute_0_212,plain,
( or(implies(not(X_94),not(not(X_94))),Y) != not(not(or(X_94,not(not(Y)))))
| implies(not(X_94),Y) = not(not(or(X_94,not(not(Y))))) ),
inference(resolve,[$cnf( $equal(or(implies(not(X_94),not(not(X_94))),Y),implies(not(X_94),Y)) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
implies(not(X_94),Y) = not(not(or(X_94,not(not(Y))))),
inference(resolve,[$cnf( $equal(or(implies(not(X_94),not(not(X_94))),Y),not(not(or(X_94,not(not(Y)))))) )],[refute_0_194,refute_0_212]) ).
cnf(refute_0_214,plain,
( ~ is_a_theorem(equiv(not(not(X_31803)),X_31803))
| not(not(X_31803)) = X_31803 ),
inference(subst,[],[refute_0_51:[bind(X,$fot(not(not(X_31803)))),bind(Y,$fot(X_31803))]]) ).
cnf(refute_0_215,plain,
( ~ is_a_theorem(implies(not(and(X_31802,not(X_31802))),equiv(not(not(X_31802)),X_31802)))
| ~ is_a_theorem(not(and(X_31802,not(X_31802))))
| is_a_theorem(equiv(not(not(X_31802)),X_31802)) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(not(and(X_31802,not(X_31802))))),bind(Y,$fot(equiv(not(not(X_31802)),X_31802)))]]) ).
cnf(refute_0_216,plain,
( ~ is_a_theorem(or(equiv(X_31774,not(not(X_31774))),and(X_31774,not(X_31774))))
| is_a_theorem(or(and(X_31774,not(X_31774)),equiv(X_31774,not(not(X_31774))))) ),
inference(subst,[],[refute_0_61:[bind(P,$fot(equiv(X_31774,not(not(X_31774))))),bind(Q,$fot(and(X_31774,not(X_31774))))]]) ).
cnf(refute_0_217,plain,
( ~ is_a_theorem(or(X_9782,implies(or(X_9783,X_9783),and(X_9783,X_9783))))
| is_a_theorem(or(implies(or(X_9783,X_9783),and(X_9783,X_9783)),X_9782)) ),
inference(subst,[],[refute_0_61:[bind(P,$fot(X_9782)),bind(Q,$fot(implies(or(X_9783,X_9783),and(X_9783,X_9783))))]]) ).
cnf(refute_0_218,plain,
is_a_theorem(implies(X_170,or(P,X_170))),
inference(subst,[],[refute_0_74:[bind(Q,$fot(X_170))]]) ).
cnf(refute_0_219,plain,
( ~ is_a_theorem(X_170)
| ~ is_a_theorem(implies(X_170,or(P,X_170)))
| is_a_theorem(or(P,X_170)) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(X_170)),bind(Y,$fot(or(P,X_170)))]]) ).
cnf(refute_0_220,plain,
( ~ is_a_theorem(X_170)
| is_a_theorem(or(P,X_170)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_170,or(P,X_170))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
( ~ is_a_theorem(implies(or(X_9740,X_9740),and(X_9740,X_9740)))
| is_a_theorem(or(P,implies(or(X_9740,X_9740),and(X_9740,X_9740)))) ),
inference(subst,[],[refute_0_220:[bind(X_170,$fot(implies(or(X_9740,X_9740),and(X_9740,X_9740))))]]) ).
cnf(refute_0_222,plain,
is_a_theorem(implies(or(X_9739,X_9739),X_9739)),
inference(subst,[],[refute_0_65:[bind(P,$fot(X_9739))]]) ).
cnf(refute_0_223,plain,
( ~ is_a_theorem(implies(X_1439,X_1440))
| ~ is_a_theorem(implies(implies(X_1439,X_1440),implies(X_1439,and(X_1440,X_1440))))
| is_a_theorem(implies(X_1439,and(X_1440,X_1440))) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(implies(X_1439,X_1440))),bind(Y,$fot(implies(X_1439,and(X_1440,X_1440))))]]) ).
cnf(refute_0_224,plain,
is_a_theorem(implies(or(not(X_5),not(X_5)),not(X_5))),
inference(subst,[],[refute_0_65:[bind(P,$fot(not(X_5)))]]) ).
cnf(refute_0_225,plain,
implies(X_5,not(X_5)) = or(not(X_5),not(X_5)),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_5)),bind(Y,$fot(not(X_5)))]]) ).
cnf(refute_0_226,plain,
( implies(X_5,not(X_5)) != or(not(X_5),not(X_5))
| or(not(X_5),not(X_5)) = implies(X_5,not(X_5)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X_5,not(X_5)))),bind(Y0,$fot(or(not(X_5),not(X_5))))]]) ).
cnf(refute_0_227,plain,
or(not(X_5),not(X_5)) = implies(X_5,not(X_5)),
inference(resolve,[$cnf( $equal(implies(X_5,not(X_5)),or(not(X_5),not(X_5))) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
( or(not(X_5),not(X_5)) != implies(X_5,not(X_5))
| ~ is_a_theorem(implies(or(not(X_5),not(X_5)),not(X_5)))
| is_a_theorem(implies(implies(X_5,not(X_5)),not(X_5))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X_5),not(X_5)),not(X_5))) ),[0,0],$fot(implies(X_5,not(X_5)))]]) ).
cnf(refute_0_229,plain,
( ~ is_a_theorem(implies(or(not(X_5),not(X_5)),not(X_5)))
| is_a_theorem(implies(implies(X_5,not(X_5)),not(X_5))) ),
inference(resolve,[$cnf( $equal(or(not(X_5),not(X_5)),implies(X_5,not(X_5))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
is_a_theorem(implies(implies(X_5,not(X_5)),not(X_5))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X_5),not(X_5)),not(X_5))) )],[refute_0_224,refute_0_229]) ).
cnf(refute_0_231,plain,
implies(implies(X_5,not(X_5)),not(X_5)) = or(and(X_5,X_5),not(X_5)),
inference(subst,[],[refute_0_164:[bind(Y,$fot(not(X_5))),bind(X_10,$fot(X_5)),bind(X_11,$fot(X_5))]]) ).
cnf(refute_0_232,plain,
( implies(implies(X_5,not(X_5)),not(X_5)) != or(and(X_5,X_5),not(X_5))
| ~ is_a_theorem(implies(implies(X_5,not(X_5)),not(X_5)))
| is_a_theorem(or(and(X_5,X_5),not(X_5))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_5,not(X_5)),not(X_5))) ),[0],$fot(or(and(X_5,X_5),not(X_5)))]]) ).
cnf(refute_0_233,plain,
( ~ is_a_theorem(implies(implies(X_5,not(X_5)),not(X_5)))
| is_a_theorem(or(and(X_5,X_5),not(X_5))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_5,not(X_5)),not(X_5)),or(and(X_5,X_5),not(X_5))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
is_a_theorem(or(and(X_5,X_5),not(X_5))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_5,not(X_5)),not(X_5))) )],[refute_0_230,refute_0_233]) ).
cnf(refute_0_235,plain,
( ~ is_a_theorem(or(and(X_5,X_5),not(X_5)))
| is_a_theorem(or(not(X_5),and(X_5,X_5))) ),
inference(subst,[],[refute_0_61:[bind(P,$fot(and(X_5,X_5))),bind(Q,$fot(not(X_5)))]]) ).
cnf(refute_0_236,plain,
is_a_theorem(or(not(X_5),and(X_5,X_5))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_5,X_5),not(X_5))) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
or(not(X_5),and(X_5,X_5)) = implies(X_5,and(X_5,X_5)),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_5)),bind(Y,$fot(and(X_5,X_5)))]]) ).
cnf(refute_0_238,plain,
( or(not(X_5),and(X_5,X_5)) != implies(X_5,and(X_5,X_5))
| ~ is_a_theorem(or(not(X_5),and(X_5,X_5)))
| is_a_theorem(implies(X_5,and(X_5,X_5))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X_5),and(X_5,X_5))) ),[0],$fot(implies(X_5,and(X_5,X_5)))]]) ).
cnf(refute_0_239,plain,
( ~ is_a_theorem(or(not(X_5),and(X_5,X_5)))
| is_a_theorem(implies(X_5,and(X_5,X_5))) ),
inference(resolve,[$cnf( $equal(or(not(X_5),and(X_5,X_5)),implies(X_5,and(X_5,X_5))) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
is_a_theorem(implies(X_5,and(X_5,X_5))),
inference(resolve,[$cnf( is_a_theorem(or(not(X_5),and(X_5,X_5))) )],[refute_0_236,refute_0_239]) ).
cnf(refute_0_241,plain,
is_a_theorem(implies(X_1435,and(X_1435,X_1435))),
inference(subst,[],[refute_0_240:[bind(X_5,$fot(X_1435))]]) ).
cnf(refute_0_242,plain,
( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_243,plain,
r5,
inference(canonicalize,[],[normalize_0_43]) ).
cnf(refute_0_244,plain,
is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))),
inference(resolve,[$cnf( r5 )],[refute_0_243,refute_0_242]) ).
cnf(refute_0_245,plain,
is_a_theorem(implies(implies(X_39,X_40),implies(or(not(X),X_39),or(not(X),X_40)))),
inference(subst,[],[refute_0_244:[bind(P,$fot(not(X))),bind(Q,$fot(X_39)),bind(R,$fot(X_40))]]) ).
cnf(refute_0_246,plain,
implies(X,X_40) = or(not(X),X_40),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_40))]]) ).
cnf(refute_0_247,plain,
( implies(X,X_40) != or(not(X),X_40)
| or(not(X),X_40) = implies(X,X_40) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_40))),bind(Y0,$fot(or(not(X),X_40)))]]) ).
cnf(refute_0_248,plain,
or(not(X),X_40) = implies(X,X_40),
inference(resolve,[$cnf( $equal(implies(X,X_40),or(not(X),X_40)) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
( or(not(X),X_40) != implies(X,X_40)
| ~ is_a_theorem(implies(implies(X_39,X_40),implies(or(not(X),X_39),or(not(X),X_40))))
| is_a_theorem(implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_39,X_40),implies(or(not(X),X_39),or(not(X),X_40)))) ),[0,1,1],$fot(implies(X,X_40))]]) ).
cnf(refute_0_250,plain,
( ~ is_a_theorem(implies(implies(X_39,X_40),implies(or(not(X),X_39),or(not(X),X_40))))
| is_a_theorem(implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_40),implies(X,X_40)) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
is_a_theorem(implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_39,X_40),implies(or(not(X),X_39),or(not(X),X_40)))) )],[refute_0_245,refute_0_250]) ).
cnf(refute_0_252,plain,
or(not(X),X_39) = implies(X,X_39),
inference(subst,[],[refute_0_17:[bind(Y,$fot(X_39))]]) ).
cnf(refute_0_253,plain,
implies(or(not(X),X_39),implies(X,X_40)) = implies(or(not(X),X_39),implies(X,X_40)),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_39),implies(X,X_40)))]]) ).
cnf(refute_0_254,plain,
( implies(or(not(X),X_39),implies(X,X_40)) != implies(or(not(X),X_39),implies(X,X_40))
| or(not(X),X_39) != implies(X,X_39)
| implies(or(not(X),X_39),implies(X,X_40)) = implies(implies(X,X_39),implies(X,X_40)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_39),implies(X,X_40)),implies(or(not(X),X_39),implies(X,X_40))) ),[1,0],$fot(implies(X,X_39))]]) ).
cnf(refute_0_255,plain,
( or(not(X),X_39) != implies(X,X_39)
| implies(or(not(X),X_39),implies(X,X_40)) = implies(implies(X,X_39),implies(X,X_40)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_39),implies(X,X_40)),implies(or(not(X),X_39),implies(X,X_40))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
implies(or(not(X),X_39),implies(X,X_40)) = implies(implies(X,X_39),implies(X,X_40)),
inference(resolve,[$cnf( $equal(or(not(X),X_39),implies(X,X_39)) )],[refute_0_252,refute_0_255]) ).
cnf(refute_0_257,plain,
implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40))) = implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40))),
introduced(tautology,[refl,[$fot(implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40))))]]) ).
cnf(refute_0_258,plain,
( implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40))) != implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40)))
| implies(or(not(X),X_39),implies(X,X_40)) != implies(implies(X,X_39),implies(X,X_40))
| implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40))) = implies(implies(X_39,X_40),implies(implies(X,X_39),implies(X,X_40))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40))),implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40)))) ),[1,1],$fot(implies(implies(X,X_39),implies(X,X_40)))]]) ).
cnf(refute_0_259,plain,
( implies(or(not(X),X_39),implies(X,X_40)) != implies(implies(X,X_39),implies(X,X_40))
| implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40))) = implies(implies(X_39,X_40),implies(implies(X,X_39),implies(X,X_40))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40))),implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40)))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40))) = implies(implies(X_39,X_40),implies(implies(X,X_39),implies(X,X_40))),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_39),implies(X,X_40)),implies(implies(X,X_39),implies(X,X_40))) )],[refute_0_256,refute_0_259]) ).
cnf(refute_0_261,plain,
( implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40))) != implies(implies(X_39,X_40),implies(implies(X,X_39),implies(X,X_40)))
| ~ is_a_theorem(implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40))))
| is_a_theorem(implies(implies(X_39,X_40),implies(implies(X,X_39),implies(X,X_40)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40)))) ),[0],$fot(implies(implies(X_39,X_40),implies(implies(X,X_39),implies(X,X_40))))]]) ).
cnf(refute_0_262,plain,
( ~ is_a_theorem(implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40))))
| is_a_theorem(implies(implies(X_39,X_40),implies(implies(X,X_39),implies(X,X_40)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40))),implies(implies(X_39,X_40),implies(implies(X,X_39),implies(X,X_40)))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
is_a_theorem(implies(implies(X_39,X_40),implies(implies(X,X_39),implies(X,X_40)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_39,X_40),implies(or(not(X),X_39),implies(X,X_40)))) )],[refute_0_251,refute_0_262]) ).
cnf(refute_0_264,plain,
( ~ is_a_theorem(implies(X_39,X_40))
| ~ is_a_theorem(implies(implies(X_39,X_40),implies(implies(X,X_39),implies(X,X_40))))
| is_a_theorem(implies(implies(X,X_39),implies(X,X_40))) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(implies(X_39,X_40))),bind(Y,$fot(implies(implies(X,X_39),implies(X,X_40))))]]) ).
cnf(refute_0_265,plain,
( ~ is_a_theorem(implies(X_39,X_40))
| is_a_theorem(implies(implies(X,X_39),implies(X,X_40))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_39,X_40),implies(implies(X,X_39),implies(X,X_40)))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
( ~ is_a_theorem(implies(X_1435,and(X_1435,X_1435)))
| is_a_theorem(implies(implies(X_1434,X_1435),implies(X_1434,and(X_1435,X_1435)))) ),
inference(subst,[],[refute_0_265:[bind(X,$fot(X_1434)),bind(X_39,$fot(X_1435)),bind(X_40,$fot(and(X_1435,X_1435)))]]) ).
cnf(refute_0_267,plain,
is_a_theorem(implies(implies(X_1434,X_1435),implies(X_1434,and(X_1435,X_1435)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1435,and(X_1435,X_1435))) )],[refute_0_241,refute_0_266]) ).
cnf(refute_0_268,plain,
is_a_theorem(implies(implies(X_1439,X_1440),implies(X_1439,and(X_1440,X_1440)))),
inference(subst,[],[refute_0_267:[bind(X_1434,$fot(X_1439)),bind(X_1435,$fot(X_1440))]]) ).
cnf(refute_0_269,plain,
( ~ is_a_theorem(implies(X_1439,X_1440))
| is_a_theorem(implies(X_1439,and(X_1440,X_1440))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1439,X_1440),implies(X_1439,and(X_1440,X_1440)))) )],[refute_0_268,refute_0_223]) ).
cnf(refute_0_270,plain,
( ~ is_a_theorem(implies(or(X_9739,X_9739),X_9739))
| is_a_theorem(implies(or(X_9739,X_9739),and(X_9739,X_9739))) ),
inference(subst,[],[refute_0_269:[bind(X_1439,$fot(or(X_9739,X_9739))),bind(X_1440,$fot(X_9739))]]) ).
cnf(refute_0_271,plain,
is_a_theorem(implies(or(X_9739,X_9739),and(X_9739,X_9739))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_9739,X_9739),X_9739)) )],[refute_0_222,refute_0_270]) ).
cnf(refute_0_272,plain,
is_a_theorem(implies(or(X_9740,X_9740),and(X_9740,X_9740))),
inference(subst,[],[refute_0_271:[bind(X_9739,$fot(X_9740))]]) ).
cnf(refute_0_273,plain,
is_a_theorem(or(P,implies(or(X_9740,X_9740),and(X_9740,X_9740)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_9740,X_9740),and(X_9740,X_9740))) )],[refute_0_272,refute_0_221]) ).
cnf(refute_0_274,plain,
is_a_theorem(or(X_9782,implies(or(X_9783,X_9783),and(X_9783,X_9783)))),
inference(subst,[],[refute_0_273:[bind(P,$fot(X_9782)),bind(X_9740,$fot(X_9783))]]) ).
cnf(refute_0_275,plain,
is_a_theorem(or(implies(or(X_9783,X_9783),and(X_9783,X_9783)),X_9782)),
inference(resolve,[$cnf( is_a_theorem(or(X_9782,implies(or(X_9783,X_9783),and(X_9783,X_9783)))) )],[refute_0_274,refute_0_217]) ).
cnf(refute_0_276,plain,
is_a_theorem(or(implies(or(not(X),not(X)),and(not(X),not(X))),X_9827)),
inference(subst,[],[refute_0_275:[bind(X_9782,$fot(X_9827)),bind(X_9783,$fot(not(X)))]]) ).
cnf(refute_0_277,plain,
( implies(X,not(X)) != or(not(X),not(X))
| or(not(X),not(X)) = implies(X,not(X)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,not(X)))),bind(Y0,$fot(or(not(X),not(X))))]]) ).
cnf(refute_0_278,plain,
or(not(X),not(X)) = implies(X,not(X)),
inference(resolve,[$cnf( $equal(implies(X,not(X)),or(not(X),not(X))) )],[refute_0_196,refute_0_277]) ).
cnf(refute_0_279,plain,
( or(not(X),not(X)) != implies(X,not(X))
| ~ is_a_theorem(or(implies(or(not(X),not(X)),and(not(X),not(X))),X_9827))
| is_a_theorem(or(implies(implies(X,not(X)),and(not(X),not(X))),X_9827)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(or(not(X),not(X)),and(not(X),not(X))),X_9827)) ),[0,0,0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_280,plain,
( ~ is_a_theorem(or(implies(or(not(X),not(X)),and(not(X),not(X))),X_9827))
| is_a_theorem(or(implies(implies(X,not(X)),and(not(X),not(X))),X_9827)) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
is_a_theorem(or(implies(implies(X,not(X)),and(not(X),not(X))),X_9827)),
inference(resolve,[$cnf( is_a_theorem(or(implies(or(not(X),not(X)),and(not(X),not(X))),X_9827)) )],[refute_0_276,refute_0_280]) ).
cnf(refute_0_282,plain,
( and(X,Y) != not(implies(X,not(Y)))
| not(implies(X,not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(implies(X,not(Y)))))]]) ).
cnf(refute_0_283,plain,
not(implies(X,not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(implies(X,not(Y)))) )],[refute_0_25,refute_0_282]) ).
cnf(refute_0_284,plain,
not(implies(X,not(X))) = and(X,X),
inference(subst,[],[refute_0_283:[bind(Y,$fot(X))]]) ).
cnf(refute_0_285,plain,
not(not(implies(X,not(X)))) = not(not(implies(X,not(X)))),
introduced(tautology,[refl,[$fot(not(not(implies(X,not(X)))))]]) ).
cnf(refute_0_286,plain,
( not(implies(X,not(X))) != and(X,X)
| not(not(implies(X,not(X)))) != not(not(implies(X,not(X))))
| not(not(implies(X,not(X)))) = not(and(X,X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(X,not(X)))),not(not(implies(X,not(X))))) ),[1,0],$fot(and(X,X))]]) ).
cnf(refute_0_287,plain,
( not(implies(X,not(X))) != and(X,X)
| not(not(implies(X,not(X)))) = not(and(X,X)) ),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(X)))),not(not(implies(X,not(X))))) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
not(not(implies(X,not(X)))) = not(and(X,X)),
inference(resolve,[$cnf( $equal(not(implies(X,not(X))),and(X,X)) )],[refute_0_284,refute_0_287]) ).
cnf(refute_0_289,plain,
and(not(not(implies(X,not(X)))),or(X,X)) = and(not(not(implies(X,not(X)))),or(X,X)),
introduced(tautology,[refl,[$fot(and(not(not(implies(X,not(X)))),or(X,X)))]]) ).
cnf(refute_0_290,plain,
( and(not(not(implies(X,not(X)))),or(X,X)) != and(not(not(implies(X,not(X)))),or(X,X))
| not(not(implies(X,not(X)))) != not(and(X,X))
| and(not(not(implies(X,not(X)))),or(X,X)) = and(not(and(X,X)),or(X,X)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(implies(X,not(X)))),or(X,X)),and(not(not(implies(X,not(X)))),or(X,X))) ),[1,0],$fot(not(and(X,X)))]]) ).
cnf(refute_0_291,plain,
( not(not(implies(X,not(X)))) != not(and(X,X))
| and(not(not(implies(X,not(X)))),or(X,X)) = and(not(and(X,X)),or(X,X)) ),
inference(resolve,[$cnf( $equal(and(not(not(implies(X,not(X)))),or(X,X)),and(not(not(implies(X,not(X)))),or(X,X))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
and(not(not(implies(X,not(X)))),or(X,X)) = and(not(and(X,X)),or(X,X)),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(X)))),not(and(X,X))) )],[refute_0_288,refute_0_291]) ).
cnf(refute_0_293,plain,
implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827) = implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827),
introduced(tautology,[refl,[$fot(implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827))]]) ).
cnf(refute_0_294,plain,
( and(not(not(implies(X,not(X)))),or(X,X)) != and(not(and(X,X)),or(X,X))
| implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827) != implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827)
| implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827) = implies(and(not(and(X,X)),or(X,X)),X_9827) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827),implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827)) ),[1,0],$fot(and(not(and(X,X)),or(X,X)))]]) ).
cnf(refute_0_295,plain,
( and(not(not(implies(X,not(X)))),or(X,X)) != and(not(and(X,X)),or(X,X))
| implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827) = implies(and(not(and(X,X)),or(X,X)),X_9827) ),
inference(resolve,[$cnf( $equal(implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827),implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827)) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827) = implies(and(not(and(X,X)),or(X,X)),X_9827),
inference(resolve,[$cnf( $equal(and(not(not(implies(X,not(X)))),or(X,X)),and(not(and(X,X)),or(X,X))) )],[refute_0_292,refute_0_295]) ).
cnf(refute_0_297,plain,
implies(and(not(not(X_83)),or(X_84,X_85)),Y) = or(not(and(not(not(X_83)),or(X_84,X_85))),Y),
inference(subst,[],[refute_0_12:[bind(X,$fot(and(not(not(X_83)),or(X_84,X_85))))]]) ).
cnf(refute_0_298,plain,
implies(X,and(not(X_32),not(X_33))) = or(not(X),and(not(X_32),not(X_33))),
inference(subst,[],[refute_0_12:[bind(Y,$fot(and(not(X_32),not(X_33))))]]) ).
cnf(refute_0_299,plain,
or(X,and(not(X_1),not(X_2))) = not(and(not(X),not(and(not(X_1),not(X_2))))),
inference(subst,[],[refute_0_5:[bind(Y,$fot(and(not(X_1),not(X_2))))]]) ).
cnf(refute_0_300,plain,
or(X_1,X_2) = not(and(not(X_1),not(X_2))),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_1)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_301,plain,
( or(X_1,X_2) != not(and(not(X_1),not(X_2)))
| not(and(not(X_1),not(X_2))) = or(X_1,X_2) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X_1,X_2))),bind(Y0,$fot(not(and(not(X_1),not(X_2)))))]]) ).
cnf(refute_0_302,plain,
not(and(not(X_1),not(X_2))) = or(X_1,X_2),
inference(resolve,[$cnf( $equal(or(X_1,X_2),not(and(not(X_1),not(X_2)))) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
( not(and(not(X_1),not(X_2))) != or(X_1,X_2)
| or(X,and(not(X_1),not(X_2))) != not(and(not(X),not(and(not(X_1),not(X_2)))))
| or(X,and(not(X_1),not(X_2))) = not(and(not(X),or(X_1,X_2))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,and(not(X_1),not(X_2))),not(and(not(X),not(and(not(X_1),not(X_2)))))) ),[1,0,1],$fot(or(X_1,X_2))]]) ).
cnf(refute_0_304,plain,
( or(X,and(not(X_1),not(X_2))) != not(and(not(X),not(and(not(X_1),not(X_2)))))
| or(X,and(not(X_1),not(X_2))) = not(and(not(X),or(X_1,X_2))) ),
inference(resolve,[$cnf( $equal(not(and(not(X_1),not(X_2))),or(X_1,X_2)) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
or(X,and(not(X_1),not(X_2))) = not(and(not(X),or(X_1,X_2))),
inference(resolve,[$cnf( $equal(or(X,and(not(X_1),not(X_2))),not(and(not(X),not(and(not(X_1),not(X_2)))))) )],[refute_0_299,refute_0_304]) ).
cnf(refute_0_306,plain,
or(not(X),and(not(X_32),not(X_33))) = not(and(not(not(X)),or(X_32,X_33))),
inference(subst,[],[refute_0_305:[bind(X,$fot(not(X))),bind(X_1,$fot(X_32)),bind(X_2,$fot(X_33))]]) ).
cnf(refute_0_307,plain,
( implies(X,and(not(X_32),not(X_33))) != or(not(X),and(not(X_32),not(X_33)))
| or(not(X),and(not(X_32),not(X_33))) != not(and(not(not(X)),or(X_32,X_33)))
| implies(X,and(not(X_32),not(X_33))) = not(and(not(not(X)),or(X_32,X_33))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,and(not(X_32),not(X_33))),not(and(not(not(X)),or(X_32,X_33)))) ),[0],$fot(or(not(X),and(not(X_32),not(X_33))))]]) ).
cnf(refute_0_308,plain,
( implies(X,and(not(X_32),not(X_33))) != or(not(X),and(not(X_32),not(X_33)))
| implies(X,and(not(X_32),not(X_33))) = not(and(not(not(X)),or(X_32,X_33))) ),
inference(resolve,[$cnf( $equal(or(not(X),and(not(X_32),not(X_33))),not(and(not(not(X)),or(X_32,X_33)))) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
implies(X,and(not(X_32),not(X_33))) = not(and(not(not(X)),or(X_32,X_33))),
inference(resolve,[$cnf( $equal(implies(X,and(not(X_32),not(X_33))),or(not(X),and(not(X_32),not(X_33)))) )],[refute_0_298,refute_0_308]) ).
cnf(refute_0_310,plain,
implies(X_83,and(not(X_84),not(X_85))) = not(and(not(not(X_83)),or(X_84,X_85))),
inference(subst,[],[refute_0_309:[bind(X,$fot(X_83)),bind(X_32,$fot(X_84)),bind(X_33,$fot(X_85))]]) ).
cnf(refute_0_311,plain,
( implies(X_83,and(not(X_84),not(X_85))) != not(and(not(not(X_83)),or(X_84,X_85)))
| not(and(not(not(X_83)),or(X_84,X_85))) = implies(X_83,and(not(X_84),not(X_85))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X_83,and(not(X_84),not(X_85))))),bind(Y0,$fot(not(and(not(not(X_83)),or(X_84,X_85)))))]]) ).
cnf(refute_0_312,plain,
not(and(not(not(X_83)),or(X_84,X_85))) = implies(X_83,and(not(X_84),not(X_85))),
inference(resolve,[$cnf( $equal(implies(X_83,and(not(X_84),not(X_85))),not(and(not(not(X_83)),or(X_84,X_85)))) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
( implies(and(not(not(X_83)),or(X_84,X_85)),Y) != or(not(and(not(not(X_83)),or(X_84,X_85))),Y)
| not(and(not(not(X_83)),or(X_84,X_85))) != implies(X_83,and(not(X_84),not(X_85)))
| implies(and(not(not(X_83)),or(X_84,X_85)),Y) = or(implies(X_83,and(not(X_84),not(X_85))),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(not(not(X_83)),or(X_84,X_85)),Y),or(not(and(not(not(X_83)),or(X_84,X_85))),Y)) ),[1,0],$fot(implies(X_83,and(not(X_84),not(X_85))))]]) ).
cnf(refute_0_314,plain,
( implies(and(not(not(X_83)),or(X_84,X_85)),Y) != or(not(and(not(not(X_83)),or(X_84,X_85))),Y)
| implies(and(not(not(X_83)),or(X_84,X_85)),Y) = or(implies(X_83,and(not(X_84),not(X_85))),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(not(X_83)),or(X_84,X_85))),implies(X_83,and(not(X_84),not(X_85)))) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
implies(and(not(not(X_83)),or(X_84,X_85)),Y) = or(implies(X_83,and(not(X_84),not(X_85))),Y),
inference(resolve,[$cnf( $equal(implies(and(not(not(X_83)),or(X_84,X_85)),Y),or(not(and(not(not(X_83)),or(X_84,X_85))),Y)) )],[refute_0_297,refute_0_314]) ).
cnf(refute_0_316,plain,
( implies(and(not(not(X_83)),or(X_84,X_85)),Y) != or(implies(X_83,and(not(X_84),not(X_85))),Y)
| or(implies(X_83,and(not(X_84),not(X_85))),Y) = implies(and(not(not(X_83)),or(X_84,X_85)),Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(and(not(not(X_83)),or(X_84,X_85)),Y))),bind(Y0,$fot(or(implies(X_83,and(not(X_84),not(X_85))),Y)))]]) ).
cnf(refute_0_317,plain,
or(implies(X_83,and(not(X_84),not(X_85))),Y) = implies(and(not(not(X_83)),or(X_84,X_85)),Y),
inference(resolve,[$cnf( $equal(implies(and(not(not(X_83)),or(X_84,X_85)),Y),or(implies(X_83,and(not(X_84),not(X_85))),Y)) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
or(implies(implies(X,not(X)),and(not(X),not(X))),X_9827) = implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827),
inference(subst,[],[refute_0_317:[bind(Y,$fot(X_9827)),bind(X_83,$fot(implies(X,not(X)))),bind(X_84,$fot(X)),bind(X_85,$fot(X))]]) ).
cnf(refute_0_319,plain,
( implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827) != implies(and(not(and(X,X)),or(X,X)),X_9827)
| or(implies(implies(X,not(X)),and(not(X),not(X))),X_9827) != implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827)
| or(implies(implies(X,not(X)),and(not(X),not(X))),X_9827) = implies(and(not(and(X,X)),or(X,X)),X_9827) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(or(implies(implies(X,not(X)),and(not(X),not(X))),X_9827))),bind(Y0,$fot(implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827))),bind(Z,$fot(implies(and(not(and(X,X)),or(X,X)),X_9827)))]]) ).
cnf(refute_0_320,plain,
( implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827) != implies(and(not(and(X,X)),or(X,X)),X_9827)
| or(implies(implies(X,not(X)),and(not(X),not(X))),X_9827) = implies(and(not(and(X,X)),or(X,X)),X_9827) ),
inference(resolve,[$cnf( $equal(or(implies(implies(X,not(X)),and(not(X),not(X))),X_9827),implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827)) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
or(implies(implies(X,not(X)),and(not(X),not(X))),X_9827) = implies(and(not(and(X,X)),or(X,X)),X_9827),
inference(resolve,[$cnf( $equal(implies(and(not(not(implies(X,not(X)))),or(X,X)),X_9827),implies(and(not(and(X,X)),or(X,X)),X_9827)) )],[refute_0_296,refute_0_320]) ).
cnf(refute_0_322,plain,
( or(implies(implies(X,not(X)),and(not(X),not(X))),X_9827) != implies(and(not(and(X,X)),or(X,X)),X_9827)
| ~ is_a_theorem(or(implies(implies(X,not(X)),and(not(X),not(X))),X_9827))
| is_a_theorem(implies(and(not(and(X,X)),or(X,X)),X_9827)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(implies(X,not(X)),and(not(X),not(X))),X_9827)) ),[0],$fot(implies(and(not(and(X,X)),or(X,X)),X_9827))]]) ).
cnf(refute_0_323,plain,
( ~ is_a_theorem(or(implies(implies(X,not(X)),and(not(X),not(X))),X_9827))
| is_a_theorem(implies(and(not(and(X,X)),or(X,X)),X_9827)) ),
inference(resolve,[$cnf( $equal(or(implies(implies(X,not(X)),and(not(X),not(X))),X_9827),implies(and(not(and(X,X)),or(X,X)),X_9827)) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
is_a_theorem(implies(and(not(and(X,X)),or(X,X)),X_9827)),
inference(resolve,[$cnf( is_a_theorem(or(implies(implies(X,not(X)),and(not(X),not(X))),X_9827)) )],[refute_0_281,refute_0_323]) ).
cnf(refute_0_325,plain,
is_a_theorem(implies(and(not(and(X,X)),or(X,X)),X_10144)),
inference(subst,[],[refute_0_324:[bind(X_9827,$fot(X_10144))]]) ).
cnf(refute_0_326,plain,
( ~ is_a_theorem(implies(Q,R))
| ~ is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| is_a_theorem(implies(or(P,Q),or(P,R))) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(implies(Q,R))),bind(Y,$fot(implies(or(P,Q),or(P,R))))]]) ).
cnf(refute_0_327,plain,
( ~ is_a_theorem(implies(Q,R))
| is_a_theorem(implies(or(P,Q),or(P,R))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )],[refute_0_244,refute_0_326]) ).
cnf(refute_0_328,plain,
( ~ is_a_theorem(implies(and(not(and(X,X)),or(X,X)),X_10144))
| is_a_theorem(implies(or(X_10142,and(not(and(X,X)),or(X,X))),or(X_10142,X_10144))) ),
inference(subst,[],[refute_0_327:[bind(P,$fot(X_10142)),bind(Q,$fot(and(not(and(X,X)),or(X,X)))),bind(R,$fot(X_10144))]]) ).
cnf(refute_0_329,plain,
is_a_theorem(implies(or(X_10142,and(not(and(X,X)),or(X,X))),or(X_10142,X_10144))),
inference(resolve,[$cnf( is_a_theorem(implies(and(not(and(X,X)),or(X,X)),X_10144)) )],[refute_0_325,refute_0_328]) ).
cnf(refute_0_330,plain,
is_a_theorem(implies(or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),and(not(and(X_10773,X_10773)),or(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))),
inference(subst,[],[refute_0_329:[bind(X,$fot(X_10773)),bind(X_10142,$fot(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)))),bind(X_10144,$fot(X_10775))]]) ).
cnf(refute_0_331,plain,
implies(or(and(not(X_127),X_128),and(not(X_128),X_127)),Y) = or(not(or(and(not(X_127),X_128),and(not(X_128),X_127))),Y),
inference(subst,[],[refute_0_12:[bind(X,$fot(or(and(not(X_127),X_128),and(not(X_128),X_127))))]]) ).
cnf(refute_0_332,plain,
equiv(not(X_70),Y) = and(implies(not(X_70),Y),implies(Y,not(X_70))),
inference(subst,[],[refute_0_172:[bind(X,$fot(not(X_70)))]]) ).
cnf(refute_0_333,plain,
and(X,implies(X_10,not(X_11))) = not(implies(X,not(implies(X_10,not(X_11))))),
inference(subst,[],[refute_0_25:[bind(Y,$fot(implies(X_10,not(X_11))))]]) ).
cnf(refute_0_334,plain,
( and(X,implies(X_10,not(X_11))) != not(implies(X,not(implies(X_10,not(X_11)))))
| not(implies(X_10,not(X_11))) != and(X_10,X_11)
| and(X,implies(X_10,not(X_11))) = not(implies(X,and(X_10,X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,implies(X_10,not(X_11))),not(implies(X,not(implies(X_10,not(X_11)))))) ),[1,0,1],$fot(and(X_10,X_11))]]) ).
cnf(refute_0_335,plain,
( and(X,implies(X_10,not(X_11))) != not(implies(X,not(implies(X_10,not(X_11)))))
| and(X,implies(X_10,not(X_11))) = not(implies(X,and(X_10,X_11))) ),
inference(resolve,[$cnf( $equal(not(implies(X_10,not(X_11))),and(X_10,X_11)) )],[refute_0_28,refute_0_334]) ).
cnf(refute_0_336,plain,
and(X,implies(X_10,not(X_11))) = not(implies(X,and(X_10,X_11))),
inference(resolve,[$cnf( $equal(and(X,implies(X_10,not(X_11))),not(implies(X,not(implies(X_10,not(X_11)))))) )],[refute_0_333,refute_0_335]) ).
cnf(refute_0_337,plain,
and(implies(not(X_70),Y),implies(Y,not(X_70))) = not(implies(implies(not(X_70),Y),and(Y,X_70))),
inference(subst,[],[refute_0_336:[bind(X,$fot(implies(not(X_70),Y))),bind(X_10,$fot(Y)),bind(X_11,$fot(X_70))]]) ).
cnf(refute_0_338,plain,
( and(implies(not(X_70),Y),implies(Y,not(X_70))) != not(implies(implies(not(X_70),Y),and(Y,X_70)))
| equiv(not(X_70),Y) != and(implies(not(X_70),Y),implies(Y,not(X_70)))
| equiv(not(X_70),Y) = not(implies(implies(not(X_70),Y),and(Y,X_70))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X_70),Y),and(implies(not(X_70),Y),implies(Y,not(X_70)))) ),[1],$fot(not(implies(implies(not(X_70),Y),and(Y,X_70))))]]) ).
cnf(refute_0_339,plain,
( equiv(not(X_70),Y) != and(implies(not(X_70),Y),implies(Y,not(X_70)))
| equiv(not(X_70),Y) = not(implies(implies(not(X_70),Y),and(Y,X_70))) ),
inference(resolve,[$cnf( $equal(and(implies(not(X_70),Y),implies(Y,not(X_70))),not(implies(implies(not(X_70),Y),and(Y,X_70)))) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
equiv(not(X_70),Y) = not(implies(implies(not(X_70),Y),and(Y,X_70))),
inference(resolve,[$cnf( $equal(equiv(not(X_70),Y),and(implies(not(X_70),Y),implies(Y,not(X_70)))) )],[refute_0_332,refute_0_339]) ).
cnf(refute_0_341,plain,
equiv(not(X_107),not(X_11)) = not(implies(implies(not(X_107),not(X_11)),and(not(X_11),X_107))),
inference(subst,[],[refute_0_340:[bind(Y,$fot(not(X_11))),bind(X_70,$fot(X_107))]]) ).
cnf(refute_0_342,plain,
implies(implies(not(X_107),not(X_11)),and(not(X_11),X_107)) = or(and(not(X_107),X_11),and(not(X_11),X_107)),
inference(subst,[],[refute_0_164:[bind(Y,$fot(and(not(X_11),X_107))),bind(X_10,$fot(not(X_107)))]]) ).
cnf(refute_0_343,plain,
( equiv(not(X_107),not(X_11)) != not(implies(implies(not(X_107),not(X_11)),and(not(X_11),X_107)))
| implies(implies(not(X_107),not(X_11)),and(not(X_11),X_107)) != or(and(not(X_107),X_11),and(not(X_11),X_107))
| equiv(not(X_107),not(X_11)) = not(or(and(not(X_107),X_11),and(not(X_11),X_107))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X_107),not(X_11)),not(implies(implies(not(X_107),not(X_11)),and(not(X_11),X_107)))) ),[1,0],$fot(or(and(not(X_107),X_11),and(not(X_11),X_107)))]]) ).
cnf(refute_0_344,plain,
( equiv(not(X_107),not(X_11)) != not(implies(implies(not(X_107),not(X_11)),and(not(X_11),X_107)))
| equiv(not(X_107),not(X_11)) = not(or(and(not(X_107),X_11),and(not(X_11),X_107))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_107),not(X_11)),and(not(X_11),X_107)),or(and(not(X_107),X_11),and(not(X_11),X_107))) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
equiv(not(X_107),not(X_11)) = not(or(and(not(X_107),X_11),and(not(X_11),X_107))),
inference(resolve,[$cnf( $equal(equiv(not(X_107),not(X_11)),not(implies(implies(not(X_107),not(X_11)),and(not(X_11),X_107)))) )],[refute_0_341,refute_0_344]) ).
cnf(refute_0_346,plain,
equiv(not(X_127),not(X_128)) = not(or(and(not(X_127),X_128),and(not(X_128),X_127))),
inference(subst,[],[refute_0_345:[bind(X_107,$fot(X_127)),bind(X_11,$fot(X_128))]]) ).
cnf(refute_0_347,plain,
( equiv(not(X_127),not(X_128)) != not(or(and(not(X_127),X_128),and(not(X_128),X_127)))
| not(or(and(not(X_127),X_128),and(not(X_128),X_127))) = equiv(not(X_127),not(X_128)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(not(X_127),not(X_128)))),bind(Y0,$fot(not(or(and(not(X_127),X_128),and(not(X_128),X_127)))))]]) ).
cnf(refute_0_348,plain,
not(or(and(not(X_127),X_128),and(not(X_128),X_127))) = equiv(not(X_127),not(X_128)),
inference(resolve,[$cnf( $equal(equiv(not(X_127),not(X_128)),not(or(and(not(X_127),X_128),and(not(X_128),X_127)))) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
( implies(or(and(not(X_127),X_128),and(not(X_128),X_127)),Y) != or(not(or(and(not(X_127),X_128),and(not(X_128),X_127))),Y)
| not(or(and(not(X_127),X_128),and(not(X_128),X_127))) != equiv(not(X_127),not(X_128))
| implies(or(and(not(X_127),X_128),and(not(X_128),X_127)),Y) = or(equiv(not(X_127),not(X_128)),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(and(not(X_127),X_128),and(not(X_128),X_127)),Y),or(not(or(and(not(X_127),X_128),and(not(X_128),X_127))),Y)) ),[1,0],$fot(equiv(not(X_127),not(X_128)))]]) ).
cnf(refute_0_350,plain,
( implies(or(and(not(X_127),X_128),and(not(X_128),X_127)),Y) != or(not(or(and(not(X_127),X_128),and(not(X_128),X_127))),Y)
| implies(or(and(not(X_127),X_128),and(not(X_128),X_127)),Y) = or(equiv(not(X_127),not(X_128)),Y) ),
inference(resolve,[$cnf( $equal(not(or(and(not(X_127),X_128),and(not(X_128),X_127))),equiv(not(X_127),not(X_128))) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
implies(or(and(not(X_127),X_128),and(not(X_128),X_127)),Y) = or(equiv(not(X_127),not(X_128)),Y),
inference(resolve,[$cnf( $equal(implies(or(and(not(X_127),X_128),and(not(X_128),X_127)),Y),or(not(or(and(not(X_127),X_128),and(not(X_128),X_127))),Y)) )],[refute_0_331,refute_0_350]) ).
cnf(refute_0_352,plain,
implies(or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),and(not(and(X_10773,X_10773)),or(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) = or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)),
inference(subst,[],[refute_0_351:[bind(Y,$fot(or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))),bind(X_127,$fot(or(X_10773,X_10773))),bind(X_128,$fot(and(X_10773,X_10773)))]]) ).
cnf(refute_0_353,plain,
( implies(or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),and(not(and(X_10773,X_10773)),or(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) != or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))
| ~ is_a_theorem(implies(or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),and(not(and(X_10773,X_10773)),or(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)))
| is_a_theorem(or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),and(not(and(X_10773,X_10773)),or(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))) ),[0],$fot(or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)))]]) ).
cnf(refute_0_354,plain,
( ~ is_a_theorem(implies(or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),and(not(and(X_10773,X_10773)),or(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)))
| is_a_theorem(or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))) ),
inference(resolve,[$cnf( $equal(implies(or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),and(not(and(X_10773,X_10773)),or(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)),or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
is_a_theorem(or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))),
inference(resolve,[$cnf( is_a_theorem(implies(or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),and(not(and(X_10773,X_10773)),or(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))) )],[refute_0_330,refute_0_354]) ).
cnf(refute_0_356,plain,
or(and(not(X_1),not(X_2)),Y) = not(and(not(and(not(X_1),not(X_2))),not(Y))),
inference(subst,[],[refute_0_5:[bind(X,$fot(and(not(X_1),not(X_2))))]]) ).
cnf(refute_0_357,plain,
( not(and(not(X_1),not(X_2))) != or(X_1,X_2)
| or(and(not(X_1),not(X_2)),Y) != not(and(not(and(not(X_1),not(X_2))),not(Y)))
| or(and(not(X_1),not(X_2)),Y) = not(and(or(X_1,X_2),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_1),not(X_2)),Y),not(and(not(and(not(X_1),not(X_2))),not(Y)))) ),[1,0,0],$fot(or(X_1,X_2))]]) ).
cnf(refute_0_358,plain,
( or(and(not(X_1),not(X_2)),Y) != not(and(not(and(not(X_1),not(X_2))),not(Y)))
| or(and(not(X_1),not(X_2)),Y) = not(and(or(X_1,X_2),not(Y))) ),
inference(resolve,[$cnf( $equal(not(and(not(X_1),not(X_2))),or(X_1,X_2)) )],[refute_0_302,refute_0_357]) ).
cnf(refute_0_359,plain,
or(and(not(X_1),not(X_2)),Y) = not(and(or(X_1,X_2),not(Y))),
inference(resolve,[$cnf( $equal(or(and(not(X_1),not(X_2)),Y),not(and(not(and(not(X_1),not(X_2))),not(Y)))) )],[refute_0_356,refute_0_358]) ).
cnf(refute_0_360,plain,
or(and(not(X_10773),not(not(X_10773))),X_10775) = not(and(or(X_10773,not(X_10773)),not(X_10775))),
inference(subst,[],[refute_0_359:[bind(Y,$fot(X_10775)),bind(X_1,$fot(X_10773)),bind(X_2,$fot(not(X_10773)))]]) ).
cnf(refute_0_361,plain,
and(Y,Y) = not(implies(Y,not(Y))),
inference(subst,[],[refute_0_25:[bind(X,$fot(Y))]]) ).
cnf(refute_0_362,plain,
implies(Y,not(Y)) = not(Y),
inference(subst,[],[refute_0_200:[bind(X,$fot(Y))]]) ).
cnf(refute_0_363,plain,
( and(Y,Y) != not(implies(Y,not(Y)))
| implies(Y,not(Y)) != not(Y)
| and(Y,Y) = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and(Y,Y),not(implies(Y,not(Y)))) ),[1,0],$fot(not(Y))]]) ).
cnf(refute_0_364,plain,
( and(Y,Y) != not(implies(Y,not(Y)))
| and(Y,Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(implies(Y,not(Y)),not(Y)) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
and(Y,Y) = not(not(Y)),
inference(resolve,[$cnf( $equal(and(Y,Y),not(implies(Y,not(Y)))) )],[refute_0_361,refute_0_364]) ).
cnf(refute_0_366,plain,
and(X_10773,X_10773) = not(not(X_10773)),
inference(subst,[],[refute_0_365:[bind(Y,$fot(X_10773))]]) ).
cnf(refute_0_367,plain,
and(not(X_10773),and(X_10773,X_10773)) = and(not(X_10773),and(X_10773,X_10773)),
introduced(tautology,[refl,[$fot(and(not(X_10773),and(X_10773,X_10773)))]]) ).
cnf(refute_0_368,plain,
( and(X_10773,X_10773) != not(not(X_10773))
| and(not(X_10773),and(X_10773,X_10773)) != and(not(X_10773),and(X_10773,X_10773))
| and(not(X_10773),and(X_10773,X_10773)) = and(not(X_10773),not(not(X_10773))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(X_10773),and(X_10773,X_10773)),and(not(X_10773),and(X_10773,X_10773))) ),[1,1],$fot(not(not(X_10773)))]]) ).
cnf(refute_0_369,plain,
( and(X_10773,X_10773) != not(not(X_10773))
| and(not(X_10773),and(X_10773,X_10773)) = and(not(X_10773),not(not(X_10773))) ),
inference(resolve,[$cnf( $equal(and(not(X_10773),and(X_10773,X_10773)),and(not(X_10773),and(X_10773,X_10773))) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
and(not(X_10773),and(X_10773,X_10773)) = and(not(X_10773),not(not(X_10773))),
inference(resolve,[$cnf( $equal(and(X_10773,X_10773),not(not(X_10773))) )],[refute_0_366,refute_0_369]) ).
cnf(refute_0_371,plain,
or(X_10773,X_10773) = X_10773,
inference(subst,[],[refute_0_190:[bind(X_27414,$fot(X_10773))]]) ).
cnf(refute_0_372,plain,
not(or(X_10773,X_10773)) = not(or(X_10773,X_10773)),
introduced(tautology,[refl,[$fot(not(or(X_10773,X_10773)))]]) ).
cnf(refute_0_373,plain,
( not(or(X_10773,X_10773)) != not(or(X_10773,X_10773))
| or(X_10773,X_10773) != X_10773
| not(or(X_10773,X_10773)) = not(X_10773) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(X_10773,X_10773)),not(or(X_10773,X_10773))) ),[1,0],$fot(X_10773)]]) ).
cnf(refute_0_374,plain,
( or(X_10773,X_10773) != X_10773
| not(or(X_10773,X_10773)) = not(X_10773) ),
inference(resolve,[$cnf( $equal(not(or(X_10773,X_10773)),not(or(X_10773,X_10773))) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
not(or(X_10773,X_10773)) = not(X_10773),
inference(resolve,[$cnf( $equal(or(X_10773,X_10773),X_10773) )],[refute_0_371,refute_0_374]) ).
cnf(refute_0_376,plain,
and(not(or(X_10773,X_10773)),and(X_10773,X_10773)) = and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),
introduced(tautology,[refl,[$fot(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)))]]) ).
cnf(refute_0_377,plain,
( and(not(or(X_10773,X_10773)),and(X_10773,X_10773)) != and(not(or(X_10773,X_10773)),and(X_10773,X_10773))
| not(or(X_10773,X_10773)) != not(X_10773)
| and(not(or(X_10773,X_10773)),and(X_10773,X_10773)) = and(not(X_10773),and(X_10773,X_10773)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),and(not(or(X_10773,X_10773)),and(X_10773,X_10773))) ),[1,0],$fot(not(X_10773))]]) ).
cnf(refute_0_378,plain,
( not(or(X_10773,X_10773)) != not(X_10773)
| and(not(or(X_10773,X_10773)),and(X_10773,X_10773)) = and(not(X_10773),and(X_10773,X_10773)) ),
inference(resolve,[$cnf( $equal(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),and(not(or(X_10773,X_10773)),and(X_10773,X_10773))) )],[refute_0_376,refute_0_377]) ).
cnf(refute_0_379,plain,
and(not(or(X_10773,X_10773)),and(X_10773,X_10773)) = and(not(X_10773),and(X_10773,X_10773)),
inference(resolve,[$cnf( $equal(not(or(X_10773,X_10773)),not(X_10773)) )],[refute_0_375,refute_0_378]) ).
cnf(refute_0_380,plain,
( and(not(X_10773),and(X_10773,X_10773)) != and(not(X_10773),not(not(X_10773)))
| and(not(or(X_10773,X_10773)),and(X_10773,X_10773)) != and(not(X_10773),and(X_10773,X_10773))
| and(not(or(X_10773,X_10773)),and(X_10773,X_10773)) = and(not(X_10773),not(not(X_10773))) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)))),bind(Y0,$fot(and(not(X_10773),and(X_10773,X_10773)))),bind(Z,$fot(and(not(X_10773),not(not(X_10773)))))]]) ).
cnf(refute_0_381,plain,
( and(not(X_10773),and(X_10773,X_10773)) != and(not(X_10773),not(not(X_10773)))
| and(not(or(X_10773,X_10773)),and(X_10773,X_10773)) = and(not(X_10773),not(not(X_10773))) ),
inference(resolve,[$cnf( $equal(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),and(not(X_10773),and(X_10773,X_10773))) )],[refute_0_379,refute_0_380]) ).
cnf(refute_0_382,plain,
and(not(or(X_10773,X_10773)),and(X_10773,X_10773)) = and(not(X_10773),not(not(X_10773))),
inference(resolve,[$cnf( $equal(and(not(X_10773),and(X_10773,X_10773)),and(not(X_10773),not(not(X_10773)))) )],[refute_0_370,refute_0_381]) ).
cnf(refute_0_383,plain,
or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775) = or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775),
introduced(tautology,[refl,[$fot(or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))]]) ).
cnf(refute_0_384,plain,
( and(not(or(X_10773,X_10773)),and(X_10773,X_10773)) != and(not(X_10773),not(not(X_10773)))
| or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775) != or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)
| or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775) = or(and(not(X_10773),not(not(X_10773))),X_10775) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) ),[1,0],$fot(and(not(X_10773),not(not(X_10773))))]]) ).
cnf(refute_0_385,plain,
( and(not(or(X_10773,X_10773)),and(X_10773,X_10773)) != and(not(X_10773),not(not(X_10773)))
| or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775) = or(and(not(X_10773),not(not(X_10773))),X_10775) ),
inference(resolve,[$cnf( $equal(or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) )],[refute_0_383,refute_0_384]) ).
cnf(refute_0_386,plain,
or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775) = or(and(not(X_10773),not(not(X_10773))),X_10775),
inference(resolve,[$cnf( $equal(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),and(not(X_10773),not(not(X_10773)))) )],[refute_0_382,refute_0_385]) ).
cnf(refute_0_387,plain,
( or(and(not(X_10773),not(not(X_10773))),X_10775) != not(and(or(X_10773,not(X_10773)),not(X_10775)))
| or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775) != or(and(not(X_10773),not(not(X_10773))),X_10775)
| or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775) = not(and(or(X_10773,not(X_10773)),not(X_10775))) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))),bind(Y0,$fot(or(and(not(X_10773),not(not(X_10773))),X_10775))),bind(Z,$fot(not(and(or(X_10773,not(X_10773)),not(X_10775)))))]]) ).
cnf(refute_0_388,plain,
( or(and(not(X_10773),not(not(X_10773))),X_10775) != not(and(or(X_10773,not(X_10773)),not(X_10775)))
| or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775) = not(and(or(X_10773,not(X_10773)),not(X_10775))) ),
inference(resolve,[$cnf( $equal(or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775),or(and(not(X_10773),not(not(X_10773))),X_10775)) )],[refute_0_386,refute_0_387]) ).
cnf(refute_0_389,plain,
or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775) = not(and(or(X_10773,not(X_10773)),not(X_10775))),
inference(resolve,[$cnf( $equal(or(and(not(X_10773),not(not(X_10773))),X_10775),not(and(or(X_10773,not(X_10773)),not(X_10775)))) )],[refute_0_360,refute_0_388]) ).
cnf(refute_0_390,plain,
or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) = or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)),
introduced(tautology,[refl,[$fot(or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)))]]) ).
cnf(refute_0_391,plain,
( or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775) != not(and(or(X_10773,not(X_10773)),not(X_10775)))
| or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) != or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))
| or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) = or(equiv(not(X_10773),not(not(not(X_10773)))),not(and(or(X_10773,not(X_10773)),not(X_10775)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)),or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))) ),[1,1],$fot(not(and(or(X_10773,not(X_10773)),not(X_10775))))]]) ).
cnf(refute_0_392,plain,
( or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775) != not(and(or(X_10773,not(X_10773)),not(X_10775)))
| or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) = or(equiv(not(X_10773),not(not(not(X_10773)))),not(and(or(X_10773,not(X_10773)),not(X_10775)))) ),
inference(resolve,[$cnf( $equal(or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)),or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))) )],[refute_0_390,refute_0_391]) ).
cnf(refute_0_393,plain,
or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) = or(equiv(not(X_10773),not(not(not(X_10773)))),not(and(or(X_10773,not(X_10773)),not(X_10775)))),
inference(resolve,[$cnf( $equal(or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775),not(and(or(X_10773,not(X_10773)),not(X_10775)))) )],[refute_0_389,refute_0_392]) ).
cnf(refute_0_394,plain,
not(and(X_10773,X_10773)) = not(and(X_10773,X_10773)),
introduced(tautology,[refl,[$fot(not(and(X_10773,X_10773)))]]) ).
cnf(refute_0_395,plain,
( and(X_10773,X_10773) != not(not(X_10773))
| not(and(X_10773,X_10773)) != not(and(X_10773,X_10773))
| not(and(X_10773,X_10773)) = not(not(not(X_10773))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(X_10773,X_10773)),not(and(X_10773,X_10773))) ),[1,0],$fot(not(not(X_10773)))]]) ).
cnf(refute_0_396,plain,
( and(X_10773,X_10773) != not(not(X_10773))
| not(and(X_10773,X_10773)) = not(not(not(X_10773))) ),
inference(resolve,[$cnf( $equal(not(and(X_10773,X_10773)),not(and(X_10773,X_10773))) )],[refute_0_394,refute_0_395]) ).
cnf(refute_0_397,plain,
not(and(X_10773,X_10773)) = not(not(not(X_10773))),
inference(resolve,[$cnf( $equal(and(X_10773,X_10773),not(not(X_10773))) )],[refute_0_366,refute_0_396]) ).
cnf(refute_0_398,plain,
equiv(not(X_10773),not(and(X_10773,X_10773))) = equiv(not(X_10773),not(and(X_10773,X_10773))),
introduced(tautology,[refl,[$fot(equiv(not(X_10773),not(and(X_10773,X_10773))))]]) ).
cnf(refute_0_399,plain,
( equiv(not(X_10773),not(and(X_10773,X_10773))) != equiv(not(X_10773),not(and(X_10773,X_10773)))
| not(and(X_10773,X_10773)) != not(not(not(X_10773)))
| equiv(not(X_10773),not(and(X_10773,X_10773))) = equiv(not(X_10773),not(not(not(X_10773)))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X_10773),not(and(X_10773,X_10773))),equiv(not(X_10773),not(and(X_10773,X_10773)))) ),[1,1],$fot(not(not(not(X_10773))))]]) ).
cnf(refute_0_400,plain,
( not(and(X_10773,X_10773)) != not(not(not(X_10773)))
| equiv(not(X_10773),not(and(X_10773,X_10773))) = equiv(not(X_10773),not(not(not(X_10773)))) ),
inference(resolve,[$cnf( $equal(equiv(not(X_10773),not(and(X_10773,X_10773))),equiv(not(X_10773),not(and(X_10773,X_10773)))) )],[refute_0_398,refute_0_399]) ).
cnf(refute_0_401,plain,
equiv(not(X_10773),not(and(X_10773,X_10773))) = equiv(not(X_10773),not(not(not(X_10773)))),
inference(resolve,[$cnf( $equal(not(and(X_10773,X_10773)),not(not(not(X_10773)))) )],[refute_0_397,refute_0_400]) ).
cnf(refute_0_402,plain,
equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))) = equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),
introduced(tautology,[refl,[$fot(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))))]]) ).
cnf(refute_0_403,plain,
( equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))) != equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773)))
| not(or(X_10773,X_10773)) != not(X_10773)
| equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))) = equiv(not(X_10773),not(and(X_10773,X_10773))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773)))) ),[1,0],$fot(not(X_10773))]]) ).
cnf(refute_0_404,plain,
( not(or(X_10773,X_10773)) != not(X_10773)
| equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))) = equiv(not(X_10773),not(and(X_10773,X_10773))) ),
inference(resolve,[$cnf( $equal(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773)))) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))) = equiv(not(X_10773),not(and(X_10773,X_10773))),
inference(resolve,[$cnf( $equal(not(or(X_10773,X_10773)),not(X_10773)) )],[refute_0_375,refute_0_404]) ).
cnf(refute_0_406,plain,
( equiv(not(X_10773),not(and(X_10773,X_10773))) != equiv(not(X_10773),not(not(not(X_10773))))
| equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))) != equiv(not(X_10773),not(and(X_10773,X_10773)))
| equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))) = equiv(not(X_10773),not(not(not(X_10773)))) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))))),bind(Y0,$fot(equiv(not(X_10773),not(and(X_10773,X_10773))))),bind(Z,$fot(equiv(not(X_10773),not(not(not(X_10773))))))]]) ).
cnf(refute_0_407,plain,
( equiv(not(X_10773),not(and(X_10773,X_10773))) != equiv(not(X_10773),not(not(not(X_10773))))
| equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))) = equiv(not(X_10773),not(not(not(X_10773)))) ),
inference(resolve,[$cnf( $equal(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),equiv(not(X_10773),not(and(X_10773,X_10773)))) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))) = equiv(not(X_10773),not(not(not(X_10773)))),
inference(resolve,[$cnf( $equal(equiv(not(X_10773),not(and(X_10773,X_10773))),equiv(not(X_10773),not(not(not(X_10773))))) )],[refute_0_401,refute_0_407]) ).
cnf(refute_0_409,plain,
or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) = or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)),
introduced(tautology,[refl,[$fot(or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)))]]) ).
cnf(refute_0_410,plain,
( equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))) != equiv(not(X_10773),not(not(not(X_10773))))
| or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) != or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))
| or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) = or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) ),
introduced(tautology,[equality,[$cnf( $equal(or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)),or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))) ),[1,0],$fot(equiv(not(X_10773),not(not(not(X_10773)))))]]) ).
cnf(refute_0_411,plain,
( equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))) != equiv(not(X_10773),not(not(not(X_10773))))
| or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) = or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) ),
inference(resolve,[$cnf( $equal(or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)),or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) = or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)),
inference(resolve,[$cnf( $equal(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),equiv(not(X_10773),not(not(not(X_10773))))) )],[refute_0_408,refute_0_411]) ).
cnf(refute_0_413,plain,
( or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) != or(equiv(not(X_10773),not(not(not(X_10773)))),not(and(or(X_10773,not(X_10773)),not(X_10775))))
| or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) != or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))
| or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) = or(equiv(not(X_10773),not(not(not(X_10773)))),not(and(or(X_10773,not(X_10773)),not(X_10775)))) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)))),bind(Y0,$fot(or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)))),bind(Z,$fot(or(equiv(not(X_10773),not(not(not(X_10773)))),not(and(or(X_10773,not(X_10773)),not(X_10775))))))]]) ).
cnf(refute_0_414,plain,
( or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) != or(equiv(not(X_10773),not(not(not(X_10773)))),not(and(or(X_10773,not(X_10773)),not(X_10775))))
| or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) = or(equiv(not(X_10773),not(not(not(X_10773)))),not(and(or(X_10773,not(X_10773)),not(X_10775)))) ),
inference(resolve,[$cnf( $equal(or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)),or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))) )],[refute_0_412,refute_0_413]) ).
cnf(refute_0_415,plain,
or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) = or(equiv(not(X_10773),not(not(not(X_10773)))),not(and(or(X_10773,not(X_10773)),not(X_10775)))),
inference(resolve,[$cnf( $equal(or(equiv(not(X_10773),not(not(not(X_10773)))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)),or(equiv(not(X_10773),not(not(not(X_10773)))),not(and(or(X_10773,not(X_10773)),not(X_10775))))) )],[refute_0_393,refute_0_414]) ).
cnf(refute_0_416,plain,
( or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)) != or(equiv(not(X_10773),not(not(not(X_10773)))),not(and(or(X_10773,not(X_10773)),not(X_10775))))
| ~ is_a_theorem(or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)))
| is_a_theorem(or(equiv(not(X_10773),not(not(not(X_10773)))),not(and(or(X_10773,not(X_10773)),not(X_10775))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))) ),[0],$fot(or(equiv(not(X_10773),not(not(not(X_10773)))),not(and(or(X_10773,not(X_10773)),not(X_10775)))))]]) ).
cnf(refute_0_417,plain,
( ~ is_a_theorem(or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)))
| is_a_theorem(or(equiv(not(X_10773),not(not(not(X_10773)))),not(and(or(X_10773,not(X_10773)),not(X_10775))))) ),
inference(resolve,[$cnf( $equal(or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775)),or(equiv(not(X_10773),not(not(not(X_10773)))),not(and(or(X_10773,not(X_10773)),not(X_10775))))) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
is_a_theorem(or(equiv(not(X_10773),not(not(not(X_10773)))),not(and(or(X_10773,not(X_10773)),not(X_10775))))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(not(or(X_10773,X_10773)),not(and(X_10773,X_10773))),or(and(not(or(X_10773,X_10773)),and(X_10773,X_10773)),X_10775))) )],[refute_0_355,refute_0_417]) ).
cnf(refute_0_419,plain,
is_a_theorem(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),not(not(not(not(Y))))),not(X_31771))))),
inference(subst,[],[refute_0_418:[bind(X_10773,$fot(not(not(not(Y))))),bind(X_10775,$fot(X_31771))]]) ).
cnf(refute_0_420,plain,
or(Y,Y) = not(and(not(Y),not(Y))),
inference(subst,[],[refute_0_5:[bind(X,$fot(Y))]]) ).
cnf(refute_0_421,plain,
and(not(Y),not(Y)) = not(not(not(Y))),
inference(subst,[],[refute_0_365:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_422,plain,
( and(not(Y),not(Y)) != not(not(not(Y)))
| or(Y,Y) != not(and(not(Y),not(Y)))
| or(Y,Y) = not(not(not(not(Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(Y,Y),not(and(not(Y),not(Y)))) ),[1,0],$fot(not(not(not(Y))))]]) ).
cnf(refute_0_423,plain,
( or(Y,Y) != not(and(not(Y),not(Y)))
| or(Y,Y) = not(not(not(not(Y)))) ),
inference(resolve,[$cnf( $equal(and(not(Y),not(Y)),not(not(not(Y)))) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
or(Y,Y) = not(not(not(not(Y)))),
inference(resolve,[$cnf( $equal(or(Y,Y),not(and(not(Y),not(Y)))) )],[refute_0_420,refute_0_423]) ).
cnf(refute_0_425,plain,
or(Y,Y) = Y,
inference(subst,[],[refute_0_190:[bind(X_27414,$fot(Y))]]) ).
cnf(refute_0_426,plain,
( or(Y,Y) != Y
| or(Y,Y) != not(not(not(not(Y))))
| Y = not(not(not(not(Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(Y,Y),not(not(not(not(Y))))) ),[0],$fot(Y)]]) ).
cnf(refute_0_427,plain,
( or(Y,Y) != not(not(not(not(Y))))
| Y = not(not(not(not(Y)))) ),
inference(resolve,[$cnf( $equal(or(Y,Y),Y) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
Y = not(not(not(not(Y)))),
inference(resolve,[$cnf( $equal(or(Y,Y),not(not(not(not(Y))))) )],[refute_0_424,refute_0_427]) ).
cnf(refute_0_429,plain,
( Y != not(not(not(not(Y))))
| not(not(not(not(Y)))) = Y ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(Y)),bind(Y0,$fot(not(not(not(not(Y))))))]]) ).
cnf(refute_0_430,plain,
not(not(not(not(Y)))) = Y,
inference(resolve,[$cnf( $equal(Y,not(not(not(not(Y))))) )],[refute_0_428,refute_0_429]) ).
cnf(refute_0_431,plain,
( not(not(not(not(Y)))) != Y
| ~ is_a_theorem(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),not(not(not(not(Y))))),not(X_31771)))))
| is_a_theorem(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),not(not(not(not(Y))))),not(X_31771))))) ),[0,1,0,0,1],$fot(Y)]]) ).
cnf(refute_0_432,plain,
( ~ is_a_theorem(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),not(not(not(not(Y))))),not(X_31771)))))
| is_a_theorem(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771))))) ),
inference(resolve,[$cnf( $equal(not(not(not(not(Y)))),Y) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
is_a_theorem(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771))))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),not(not(not(not(Y))))),not(X_31771))))) )],[refute_0_419,refute_0_432]) ).
cnf(refute_0_434,plain,
not(and(not(and(Y,not(Y))),not(X_31771))) = or(and(Y,not(Y)),X_31771),
inference(subst,[],[refute_0_36:[bind(X,$fot(and(Y,not(Y)))),bind(Y,$fot(X_31771))]]) ).
cnf(refute_0_435,plain,
or(and(not(X_2),not(X_2)),Y) = not(and(or(X_2,X_2),not(Y))),
inference(subst,[],[refute_0_359:[bind(X_1,$fot(X_2))]]) ).
cnf(refute_0_436,plain,
and(not(X_2),not(X_2)) = not(not(not(X_2))),
inference(subst,[],[refute_0_365:[bind(Y,$fot(not(X_2)))]]) ).
cnf(refute_0_437,plain,
( and(not(X_2),not(X_2)) != not(not(not(X_2)))
| or(and(not(X_2),not(X_2)),Y) != not(and(or(X_2,X_2),not(Y)))
| or(not(not(not(X_2))),Y) = not(and(or(X_2,X_2),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_2),not(X_2)),Y),not(and(or(X_2,X_2),not(Y)))) ),[0,0],$fot(not(not(not(X_2))))]]) ).
cnf(refute_0_438,plain,
( or(and(not(X_2),not(X_2)),Y) != not(and(or(X_2,X_2),not(Y)))
| or(not(not(not(X_2))),Y) = not(and(or(X_2,X_2),not(Y))) ),
inference(resolve,[$cnf( $equal(and(not(X_2),not(X_2)),not(not(not(X_2)))) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
or(not(not(not(X_2))),Y) = not(and(or(X_2,X_2),not(Y))),
inference(resolve,[$cnf( $equal(or(and(not(X_2),not(X_2)),Y),not(and(or(X_2,X_2),not(Y)))) )],[refute_0_435,refute_0_438]) ).
cnf(refute_0_440,plain,
or(not(not(not(X_2))),Y) = implies(not(not(X_2)),Y),
inference(subst,[],[refute_0_17:[bind(X,$fot(not(not(X_2))))]]) ).
cnf(refute_0_441,plain,
( or(not(not(not(X_2))),Y) != implies(not(not(X_2)),Y)
| or(not(not(not(X_2))),Y) != not(and(or(X_2,X_2),not(Y)))
| implies(not(not(X_2)),Y) = not(and(or(X_2,X_2),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(not(not(X_2))),Y),not(and(or(X_2,X_2),not(Y)))) ),[0],$fot(implies(not(not(X_2)),Y))]]) ).
cnf(refute_0_442,plain,
( or(not(not(not(X_2))),Y) != not(and(or(X_2,X_2),not(Y)))
| implies(not(not(X_2)),Y) = not(and(or(X_2,X_2),not(Y))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(X_2))),Y),implies(not(not(X_2)),Y)) )],[refute_0_440,refute_0_441]) ).
cnf(refute_0_443,plain,
or(X_2,X_2) = X_2,
inference(subst,[],[refute_0_190:[bind(X_27414,$fot(X_2))]]) ).
cnf(refute_0_444,plain,
and(or(X_2,X_2),not(Y)) = and(or(X_2,X_2),not(Y)),
introduced(tautology,[refl,[$fot(and(or(X_2,X_2),not(Y)))]]) ).
cnf(refute_0_445,plain,
( and(or(X_2,X_2),not(Y)) != and(or(X_2,X_2),not(Y))
| or(X_2,X_2) != X_2
| and(or(X_2,X_2),not(Y)) = and(X_2,not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(X_2,X_2),not(Y)),and(or(X_2,X_2),not(Y))) ),[1,0],$fot(X_2)]]) ).
cnf(refute_0_446,plain,
( or(X_2,X_2) != X_2
| and(or(X_2,X_2),not(Y)) = and(X_2,not(Y)) ),
inference(resolve,[$cnf( $equal(and(or(X_2,X_2),not(Y)),and(or(X_2,X_2),not(Y))) )],[refute_0_444,refute_0_445]) ).
cnf(refute_0_447,plain,
and(or(X_2,X_2),not(Y)) = and(X_2,not(Y)),
inference(resolve,[$cnf( $equal(or(X_2,X_2),X_2) )],[refute_0_443,refute_0_446]) ).
cnf(refute_0_448,plain,
not(and(or(X_2,X_2),not(Y))) = not(and(or(X_2,X_2),not(Y))),
introduced(tautology,[refl,[$fot(not(and(or(X_2,X_2),not(Y))))]]) ).
cnf(refute_0_449,plain,
( and(or(X_2,X_2),not(Y)) != and(X_2,not(Y))
| not(and(or(X_2,X_2),not(Y))) != not(and(or(X_2,X_2),not(Y)))
| not(and(or(X_2,X_2),not(Y))) = not(and(X_2,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(or(X_2,X_2),not(Y))),not(and(or(X_2,X_2),not(Y)))) ),[1,0],$fot(and(X_2,not(Y)))]]) ).
cnf(refute_0_450,plain,
( and(or(X_2,X_2),not(Y)) != and(X_2,not(Y))
| not(and(or(X_2,X_2),not(Y))) = not(and(X_2,not(Y))) ),
inference(resolve,[$cnf( $equal(not(and(or(X_2,X_2),not(Y))),not(and(or(X_2,X_2),not(Y)))) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
not(and(or(X_2,X_2),not(Y))) = not(and(X_2,not(Y))),
inference(resolve,[$cnf( $equal(and(or(X_2,X_2),not(Y)),and(X_2,not(Y))) )],[refute_0_447,refute_0_450]) ).
cnf(refute_0_452,plain,
( implies(not(not(X_2)),Y) != not(and(or(X_2,X_2),not(Y)))
| not(and(or(X_2,X_2),not(Y))) != not(and(X_2,not(Y)))
| implies(not(not(X_2)),Y) = not(and(X_2,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(not(X_2)),Y),not(and(X_2,not(Y)))) ),[0],$fot(not(and(or(X_2,X_2),not(Y))))]]) ).
cnf(refute_0_453,plain,
( implies(not(not(X_2)),Y) != not(and(or(X_2,X_2),not(Y)))
| implies(not(not(X_2)),Y) = not(and(X_2,not(Y))) ),
inference(resolve,[$cnf( $equal(not(and(or(X_2,X_2),not(Y))),not(and(X_2,not(Y)))) )],[refute_0_451,refute_0_452]) ).
cnf(refute_0_454,plain,
( or(not(not(not(X_2))),Y) != not(and(or(X_2,X_2),not(Y)))
| implies(not(not(X_2)),Y) = not(and(X_2,not(Y))) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_2)),Y),not(and(or(X_2,X_2),not(Y)))) )],[refute_0_442,refute_0_453]) ).
cnf(refute_0_455,plain,
implies(not(not(X_2)),Y) = not(and(X_2,not(Y))),
inference(resolve,[$cnf( $equal(or(not(not(not(X_2))),Y),not(and(or(X_2,X_2),not(Y)))) )],[refute_0_439,refute_0_454]) ).
cnf(refute_0_456,plain,
implies(not(not(Y)),Y) = not(and(Y,not(Y))),
inference(subst,[],[refute_0_455:[bind(X_2,$fot(Y))]]) ).
cnf(refute_0_457,plain,
or(not(not(not(Y))),Y) = implies(not(not(Y)),Y),
inference(subst,[],[refute_0_17:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_458,plain,
( implies(not(not(Y)),Y) != not(and(Y,not(Y)))
| or(not(not(not(Y))),Y) != implies(not(not(Y)),Y)
| or(not(not(not(Y))),Y) = not(and(Y,not(Y))) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(or(not(not(not(Y))),Y))),bind(Y0,$fot(implies(not(not(Y)),Y))),bind(Z,$fot(not(and(Y,not(Y)))))]]) ).
cnf(refute_0_459,plain,
( implies(not(not(Y)),Y) != not(and(Y,not(Y)))
| or(not(not(not(Y))),Y) = not(and(Y,not(Y))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(Y))),Y),implies(not(not(Y)),Y)) )],[refute_0_457,refute_0_458]) ).
cnf(refute_0_460,plain,
or(not(not(not(Y))),Y) = not(and(Y,not(Y))),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),Y),not(and(Y,not(Y)))) )],[refute_0_456,refute_0_459]) ).
cnf(refute_0_461,plain,
and(or(not(not(not(Y))),Y),not(X_31771)) = and(or(not(not(not(Y))),Y),not(X_31771)),
introduced(tautology,[refl,[$fot(and(or(not(not(not(Y))),Y),not(X_31771)))]]) ).
cnf(refute_0_462,plain,
( and(or(not(not(not(Y))),Y),not(X_31771)) != and(or(not(not(not(Y))),Y),not(X_31771))
| or(not(not(not(Y))),Y) != not(and(Y,not(Y)))
| and(or(not(not(not(Y))),Y),not(X_31771)) = and(not(and(Y,not(Y))),not(X_31771)) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(not(not(not(Y))),Y),not(X_31771)),and(or(not(not(not(Y))),Y),not(X_31771))) ),[1,0],$fot(not(and(Y,not(Y))))]]) ).
cnf(refute_0_463,plain,
( or(not(not(not(Y))),Y) != not(and(Y,not(Y)))
| and(or(not(not(not(Y))),Y),not(X_31771)) = and(not(and(Y,not(Y))),not(X_31771)) ),
inference(resolve,[$cnf( $equal(and(or(not(not(not(Y))),Y),not(X_31771)),and(or(not(not(not(Y))),Y),not(X_31771))) )],[refute_0_461,refute_0_462]) ).
cnf(refute_0_464,plain,
and(or(not(not(not(Y))),Y),not(X_31771)) = and(not(and(Y,not(Y))),not(X_31771)),
inference(resolve,[$cnf( $equal(or(not(not(not(Y))),Y),not(and(Y,not(Y)))) )],[refute_0_460,refute_0_463]) ).
cnf(refute_0_465,plain,
not(and(or(not(not(not(Y))),Y),not(X_31771))) = not(and(or(not(not(not(Y))),Y),not(X_31771))),
introduced(tautology,[refl,[$fot(not(and(or(not(not(not(Y))),Y),not(X_31771))))]]) ).
cnf(refute_0_466,plain,
( and(or(not(not(not(Y))),Y),not(X_31771)) != and(not(and(Y,not(Y))),not(X_31771))
| not(and(or(not(not(not(Y))),Y),not(X_31771))) != not(and(or(not(not(not(Y))),Y),not(X_31771)))
| not(and(or(not(not(not(Y))),Y),not(X_31771))) = not(and(not(and(Y,not(Y))),not(X_31771))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(or(not(not(not(Y))),Y),not(X_31771))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) ),[1,0],$fot(and(not(and(Y,not(Y))),not(X_31771)))]]) ).
cnf(refute_0_467,plain,
( and(or(not(not(not(Y))),Y),not(X_31771)) != and(not(and(Y,not(Y))),not(X_31771))
| not(and(or(not(not(not(Y))),Y),not(X_31771))) = not(and(not(and(Y,not(Y))),not(X_31771))) ),
inference(resolve,[$cnf( $equal(not(and(or(not(not(not(Y))),Y),not(X_31771))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
not(and(or(not(not(not(Y))),Y),not(X_31771))) = not(and(not(and(Y,not(Y))),not(X_31771))),
inference(resolve,[$cnf( $equal(and(or(not(not(not(Y))),Y),not(X_31771)),and(not(and(Y,not(Y))),not(X_31771))) )],[refute_0_464,refute_0_467]) ).
cnf(refute_0_469,plain,
( not(and(not(and(Y,not(Y))),not(X_31771))) != or(and(Y,not(Y)),X_31771)
| not(and(or(not(not(not(Y))),Y),not(X_31771))) != not(and(not(and(Y,not(Y))),not(X_31771)))
| not(and(or(not(not(not(Y))),Y),not(X_31771))) = or(and(Y,not(Y)),X_31771) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(not(and(or(not(not(not(Y))),Y),not(X_31771))))),bind(Y0,$fot(not(and(not(and(Y,not(Y))),not(X_31771))))),bind(Z,$fot(or(and(Y,not(Y)),X_31771)))]]) ).
cnf(refute_0_470,plain,
( not(and(not(and(Y,not(Y))),not(X_31771))) != or(and(Y,not(Y)),X_31771)
| not(and(or(not(not(not(Y))),Y),not(X_31771))) = or(and(Y,not(Y)),X_31771) ),
inference(resolve,[$cnf( $equal(not(and(or(not(not(not(Y))),Y),not(X_31771))),not(and(not(and(Y,not(Y))),not(X_31771)))) )],[refute_0_468,refute_0_469]) ).
cnf(refute_0_471,plain,
not(and(or(not(not(not(Y))),Y),not(X_31771))) = or(and(Y,not(Y)),X_31771),
inference(resolve,[$cnf( $equal(not(and(not(and(Y,not(Y))),not(X_31771))),or(and(Y,not(Y)),X_31771)) )],[refute_0_434,refute_0_470]) ).
cnf(refute_0_472,plain,
or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) = or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771)))),
introduced(tautology,[refl,[$fot(or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771)))))]]) ).
cnf(refute_0_473,plain,
( not(and(or(not(not(not(Y))),Y),not(X_31771))) != or(and(Y,not(Y)),X_31771)
| or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) != or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771))))
| or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) = or(equiv(Y,not(not(Y))),or(and(Y,not(Y)),X_31771)) ),
introduced(tautology,[equality,[$cnf( $equal(or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771)))),or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771))))) ),[1,1],$fot(or(and(Y,not(Y)),X_31771))]]) ).
cnf(refute_0_474,plain,
( not(and(or(not(not(not(Y))),Y),not(X_31771))) != or(and(Y,not(Y)),X_31771)
| or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) = or(equiv(Y,not(not(Y))),or(and(Y,not(Y)),X_31771)) ),
inference(resolve,[$cnf( $equal(or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771)))),or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771))))) )],[refute_0_472,refute_0_473]) ).
cnf(refute_0_475,plain,
or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) = or(equiv(Y,not(not(Y))),or(and(Y,not(Y)),X_31771)),
inference(resolve,[$cnf( $equal(not(and(or(not(not(not(Y))),Y),not(X_31771))),or(and(Y,not(Y)),X_31771)) )],[refute_0_471,refute_0_474]) ).
cnf(refute_0_476,plain,
equiv(not(not(X_2)),not(X_128)) = not(or(and(not(not(X_2)),X_128),and(not(X_128),not(X_2)))),
inference(subst,[],[refute_0_345:[bind(X_107,$fot(not(X_2))),bind(X_11,$fot(X_128))]]) ).
cnf(refute_0_477,plain,
or(and(not(not(X_2)),X_128),and(not(X_128),not(X_2))) = not(and(not(and(not(not(X_2)),X_128)),or(X_128,X_2))),
inference(subst,[],[refute_0_305:[bind(X,$fot(and(not(not(X_2)),X_128))),bind(X_1,$fot(X_128))]]) ).
cnf(refute_0_478,plain,
( equiv(not(not(X_2)),not(X_128)) != not(or(and(not(not(X_2)),X_128),and(not(X_128),not(X_2))))
| or(and(not(not(X_2)),X_128),and(not(X_128),not(X_2))) != not(and(not(and(not(not(X_2)),X_128)),or(X_128,X_2)))
| equiv(not(not(X_2)),not(X_128)) = not(not(and(not(and(not(not(X_2)),X_128)),or(X_128,X_2)))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(not(X_2)),not(X_128)),not(or(and(not(not(X_2)),X_128),and(not(X_128),not(X_2))))) ),[1,0],$fot(not(and(not(and(not(not(X_2)),X_128)),or(X_128,X_2))))]]) ).
cnf(refute_0_479,plain,
( equiv(not(not(X_2)),not(X_128)) != not(or(and(not(not(X_2)),X_128),and(not(X_128),not(X_2))))
| equiv(not(not(X_2)),not(X_128)) = not(not(and(not(and(not(not(X_2)),X_128)),or(X_128,X_2)))) ),
inference(resolve,[$cnf( $equal(or(and(not(not(X_2)),X_128),and(not(X_128),not(X_2))),not(and(not(and(not(not(X_2)),X_128)),or(X_128,X_2)))) )],[refute_0_477,refute_0_478]) ).
cnf(refute_0_480,plain,
equiv(not(not(X_2)),not(X_128)) = not(not(and(not(and(not(not(X_2)),X_128)),or(X_128,X_2)))),
inference(resolve,[$cnf( $equal(equiv(not(not(X_2)),not(X_128)),not(or(and(not(not(X_2)),X_128),and(not(X_128),not(X_2))))) )],[refute_0_476,refute_0_479]) ).
cnf(refute_0_481,plain,
equiv(not(not(X_765)),not(not(X))) = not(not(and(not(and(not(not(X_765)),not(X))),or(not(X),X_765)))),
inference(subst,[],[refute_0_480:[bind(X_128,$fot(not(X))),bind(X_2,$fot(X_765))]]) ).
cnf(refute_0_482,plain,
implies(X,X_765) = or(not(X),X_765),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_765))]]) ).
cnf(refute_0_483,plain,
( implies(X,X_765) != or(not(X),X_765)
| or(not(X),X_765) = implies(X,X_765) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_765))),bind(Y0,$fot(or(not(X),X_765)))]]) ).
cnf(refute_0_484,plain,
or(not(X),X_765) = implies(X,X_765),
inference(resolve,[$cnf( $equal(implies(X,X_765),or(not(X),X_765)) )],[refute_0_482,refute_0_483]) ).
cnf(refute_0_485,plain,
( equiv(not(not(X_765)),not(not(X))) != not(not(and(not(and(not(not(X_765)),not(X))),or(not(X),X_765))))
| or(not(X),X_765) != implies(X,X_765)
| equiv(not(not(X_765)),not(not(X))) = not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(not(X_765)),not(not(X))),not(not(and(not(and(not(not(X_765)),not(X))),or(not(X),X_765))))) ),[1,0,0,1],$fot(implies(X,X_765))]]) ).
cnf(refute_0_486,plain,
( equiv(not(not(X_765)),not(not(X))) != not(not(and(not(and(not(not(X_765)),not(X))),or(not(X),X_765))))
| equiv(not(not(X_765)),not(not(X))) = not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_765),implies(X,X_765)) )],[refute_0_484,refute_0_485]) ).
cnf(refute_0_487,plain,
equiv(not(not(X_765)),not(not(X))) = not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))),
inference(resolve,[$cnf( $equal(equiv(not(not(X_765)),not(not(X))),not(not(and(not(and(not(not(X_765)),not(X))),or(not(X),X_765))))) )],[refute_0_481,refute_0_486]) ).
cnf(refute_0_488,plain,
( equiv(X,Y) != and(implies(X,Y),implies(Y,X))
| and(implies(X,Y),implies(Y,X)) = equiv(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(X,Y))),bind(Y0,$fot(and(implies(X,Y),implies(Y,X))))]]) ).
cnf(refute_0_489,plain,
and(implies(X,Y),implies(Y,X)) = equiv(X,Y),
inference(resolve,[$cnf( $equal(equiv(X,Y),and(implies(X,Y),implies(Y,X))) )],[refute_0_172,refute_0_488]) ).
cnf(refute_0_490,plain,
and(implies(X_765,X),implies(X,X_765)) = equiv(X_765,X),
inference(subst,[],[refute_0_489:[bind(X,$fot(X_765)),bind(Y,$fot(X))]]) ).
cnf(refute_0_491,plain,
or(not(X_765),X) = implies(X_765,X),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_765)),bind(Y,$fot(X))]]) ).
cnf(refute_0_492,plain,
not(and(not(not(X_765)),not(X))) = or(not(X_765),X),
inference(subst,[],[refute_0_36:[bind(X,$fot(not(X_765))),bind(Y,$fot(X))]]) ).
cnf(refute_0_493,plain,
( not(and(not(not(X_765)),not(X))) != or(not(X_765),X)
| or(not(X_765),X) != implies(X_765,X)
| not(and(not(not(X_765)),not(X))) = implies(X_765,X) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(not(and(not(not(X_765)),not(X))))),bind(Y0,$fot(or(not(X_765),X))),bind(Z,$fot(implies(X_765,X)))]]) ).
cnf(refute_0_494,plain,
( or(not(X_765),X) != implies(X_765,X)
| not(and(not(not(X_765)),not(X))) = implies(X_765,X) ),
inference(resolve,[$cnf( $equal(not(and(not(not(X_765)),not(X))),or(not(X_765),X)) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
not(and(not(not(X_765)),not(X))) = implies(X_765,X),
inference(resolve,[$cnf( $equal(or(not(X_765),X),implies(X_765,X)) )],[refute_0_491,refute_0_494]) ).
cnf(refute_0_496,plain,
and(not(and(not(not(X_765)),not(X))),implies(X,X_765)) = and(not(and(not(not(X_765)),not(X))),implies(X,X_765)),
introduced(tautology,[refl,[$fot(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))]]) ).
cnf(refute_0_497,plain,
( and(not(and(not(not(X_765)),not(X))),implies(X,X_765)) != and(not(and(not(not(X_765)),not(X))),implies(X,X_765))
| not(and(not(not(X_765)),not(X))) != implies(X_765,X)
| and(not(and(not(not(X_765)),not(X))),implies(X,X_765)) = and(implies(X_765,X),implies(X,X_765)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)),and(not(and(not(not(X_765)),not(X))),implies(X,X_765))) ),[1,0],$fot(implies(X_765,X))]]) ).
cnf(refute_0_498,plain,
( not(and(not(not(X_765)),not(X))) != implies(X_765,X)
| and(not(and(not(not(X_765)),not(X))),implies(X,X_765)) = and(implies(X_765,X),implies(X,X_765)) ),
inference(resolve,[$cnf( $equal(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)),and(not(and(not(not(X_765)),not(X))),implies(X,X_765))) )],[refute_0_496,refute_0_497]) ).
cnf(refute_0_499,plain,
and(not(and(not(not(X_765)),not(X))),implies(X,X_765)) = and(implies(X_765,X),implies(X,X_765)),
inference(resolve,[$cnf( $equal(not(and(not(not(X_765)),not(X))),implies(X_765,X)) )],[refute_0_495,refute_0_498]) ).
cnf(refute_0_500,plain,
( and(implies(X_765,X),implies(X,X_765)) != equiv(X_765,X)
| and(not(and(not(not(X_765)),not(X))),implies(X,X_765)) != and(implies(X_765,X),implies(X,X_765))
| and(not(and(not(not(X_765)),not(X))),implies(X,X_765)) = equiv(X_765,X) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))),bind(Y0,$fot(and(implies(X_765,X),implies(X,X_765)))),bind(Z,$fot(equiv(X_765,X)))]]) ).
cnf(refute_0_501,plain,
( and(implies(X_765,X),implies(X,X_765)) != equiv(X_765,X)
| and(not(and(not(not(X_765)),not(X))),implies(X,X_765)) = equiv(X_765,X) ),
inference(resolve,[$cnf( $equal(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)),and(implies(X_765,X),implies(X,X_765))) )],[refute_0_499,refute_0_500]) ).
cnf(refute_0_502,plain,
and(not(and(not(not(X_765)),not(X))),implies(X,X_765)) = equiv(X_765,X),
inference(resolve,[$cnf( $equal(and(implies(X_765,X),implies(X,X_765)),equiv(X_765,X)) )],[refute_0_490,refute_0_501]) ).
cnf(refute_0_503,plain,
not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))) = not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))),
introduced(tautology,[refl,[$fot(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))))]]) ).
cnf(refute_0_504,plain,
( and(not(and(not(not(X_765)),not(X))),implies(X,X_765)) != equiv(X_765,X)
| not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))) != not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))
| not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))) = not(equiv(X_765,X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))),not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))) ),[1,0],$fot(equiv(X_765,X))]]) ).
cnf(refute_0_505,plain,
( and(not(and(not(not(X_765)),not(X))),implies(X,X_765)) != equiv(X_765,X)
| not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))) = not(equiv(X_765,X)) ),
inference(resolve,[$cnf( $equal(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))),not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))) )],[refute_0_503,refute_0_504]) ).
cnf(refute_0_506,plain,
not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))) = not(equiv(X_765,X)),
inference(resolve,[$cnf( $equal(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)),equiv(X_765,X)) )],[refute_0_502,refute_0_505]) ).
cnf(refute_0_507,plain,
not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))) = not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))),
introduced(tautology,[refl,[$fot(not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))))]]) ).
cnf(refute_0_508,plain,
( not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))) != not(equiv(X_765,X))
| not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))) != not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))))
| not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))) = not(not(equiv(X_765,X))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))),not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))))) ),[1,0],$fot(not(equiv(X_765,X)))]]) ).
cnf(refute_0_509,plain,
( not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))) != not(equiv(X_765,X))
| not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))) = not(not(equiv(X_765,X))) ),
inference(resolve,[$cnf( $equal(not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))),not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))))) )],[refute_0_507,refute_0_508]) ).
cnf(refute_0_510,plain,
not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))) = not(not(equiv(X_765,X))),
inference(resolve,[$cnf( $equal(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))),not(equiv(X_765,X))) )],[refute_0_506,refute_0_509]) ).
cnf(refute_0_511,plain,
( equiv(not(not(X_765)),not(not(X))) != not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))))
| not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))) != not(not(equiv(X_765,X)))
| equiv(not(not(X_765)),not(not(X))) = not(not(equiv(X_765,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(equiv(not(not(X_765)),not(not(X))),not(not(equiv(X_765,X)))) ),[0],$fot(not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))))]]) ).
cnf(refute_0_512,plain,
( equiv(not(not(X_765)),not(not(X))) != not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))))
| equiv(not(not(X_765)),not(not(X))) = not(not(equiv(X_765,X))) ),
inference(resolve,[$cnf( $equal(not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765)))),not(not(equiv(X_765,X)))) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
equiv(not(not(X_765)),not(not(X))) = not(not(equiv(X_765,X))),
inference(resolve,[$cnf( $equal(equiv(not(not(X_765)),not(not(X))),not(not(and(not(and(not(not(X_765)),not(X))),implies(X,X_765))))) )],[refute_0_487,refute_0_512]) ).
cnf(refute_0_514,plain,
equiv(not(not(not(not(X_27437)))),not(not(X))) = not(not(equiv(not(not(X_27437)),X))),
inference(subst,[],[refute_0_513:[bind(X_765,$fot(not(not(X_27437))))]]) ).
cnf(refute_0_515,plain,
X_27437 = not(not(not(not(X_27437)))),
inference(subst,[],[refute_0_428:[bind(Y,$fot(X_27437))]]) ).
cnf(refute_0_516,plain,
( X_27437 != not(not(not(not(X_27437))))
| not(not(not(not(X_27437)))) = X_27437 ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(X_27437)),bind(Y0,$fot(not(not(not(not(X_27437))))))]]) ).
cnf(refute_0_517,plain,
not(not(not(not(X_27437)))) = X_27437,
inference(resolve,[$cnf( $equal(X_27437,not(not(not(not(X_27437))))) )],[refute_0_515,refute_0_516]) ).
cnf(refute_0_518,plain,
( equiv(not(not(not(not(X_27437)))),not(not(X))) != not(not(equiv(not(not(X_27437)),X)))
| not(not(not(not(X_27437)))) != X_27437
| equiv(X_27437,not(not(X))) = not(not(equiv(not(not(X_27437)),X))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(not(not(not(X_27437)))),not(not(X))),not(not(equiv(not(not(X_27437)),X)))) ),[0,0],$fot(X_27437)]]) ).
cnf(refute_0_519,plain,
( equiv(not(not(not(not(X_27437)))),not(not(X))) != not(not(equiv(not(not(X_27437)),X)))
| equiv(X_27437,not(not(X))) = not(not(equiv(not(not(X_27437)),X))) ),
inference(resolve,[$cnf( $equal(not(not(not(not(X_27437)))),X_27437) )],[refute_0_517,refute_0_518]) ).
cnf(refute_0_520,plain,
equiv(X_27437,not(not(X))) = not(not(equiv(not(not(X_27437)),X))),
inference(resolve,[$cnf( $equal(equiv(not(not(not(not(X_27437)))),not(not(X))),not(not(equiv(not(not(X_27437)),X)))) )],[refute_0_514,refute_0_519]) ).
cnf(refute_0_521,plain,
( equiv(X_27437,not(not(X))) != not(not(equiv(not(not(X_27437)),X)))
| not(not(equiv(not(not(X_27437)),X))) = equiv(X_27437,not(not(X))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(X_27437,not(not(X))))),bind(Y0,$fot(not(not(equiv(not(not(X_27437)),X)))))]]) ).
cnf(refute_0_522,plain,
not(not(equiv(not(not(X_27437)),X))) = equiv(X_27437,not(not(X))),
inference(resolve,[$cnf( $equal(equiv(X_27437,not(not(X))),not(not(equiv(not(not(X_27437)),X)))) )],[refute_0_520,refute_0_521]) ).
cnf(refute_0_523,plain,
not(not(equiv(not(not(Y)),Y))) = equiv(Y,not(not(Y))),
inference(subst,[],[refute_0_522:[bind(X,$fot(Y)),bind(X_27437,$fot(Y))]]) ).
cnf(refute_0_524,plain,
equiv(not(not(not(not(Y)))),not(not(Y))) = not(not(equiv(not(not(Y)),Y))),
inference(subst,[],[refute_0_513:[bind(X,$fot(Y)),bind(X_765,$fot(not(not(Y))))]]) ).
cnf(refute_0_525,plain,
( equiv(not(not(not(not(Y)))),not(not(Y))) != not(not(equiv(not(not(Y)),Y)))
| not(not(equiv(not(not(Y)),Y))) != equiv(Y,not(not(Y)))
| equiv(not(not(not(not(Y)))),not(not(Y))) = equiv(Y,not(not(Y))) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(equiv(not(not(not(not(Y)))),not(not(Y))))),bind(Y0,$fot(not(not(equiv(not(not(Y)),Y))))),bind(Z,$fot(equiv(Y,not(not(Y)))))]]) ).
cnf(refute_0_526,plain,
( not(not(equiv(not(not(Y)),Y))) != equiv(Y,not(not(Y)))
| equiv(not(not(not(not(Y)))),not(not(Y))) = equiv(Y,not(not(Y))) ),
inference(resolve,[$cnf( $equal(equiv(not(not(not(not(Y)))),not(not(Y))),not(not(equiv(not(not(Y)),Y)))) )],[refute_0_524,refute_0_525]) ).
cnf(refute_0_527,plain,
equiv(not(not(not(not(Y)))),not(not(Y))) = equiv(Y,not(not(Y))),
inference(resolve,[$cnf( $equal(not(not(equiv(not(not(Y)),Y))),equiv(Y,not(not(Y)))) )],[refute_0_523,refute_0_526]) ).
cnf(refute_0_528,plain,
equiv(not(not(X_765)),not(not(not(not(X_27437))))) = not(not(equiv(X_765,not(not(X_27437))))),
inference(subst,[],[refute_0_513:[bind(X,$fot(not(not(X_27437))))]]) ).
cnf(refute_0_529,plain,
( equiv(not(not(X_765)),not(not(not(not(X_27437))))) != not(not(equiv(X_765,not(not(X_27437)))))
| not(not(not(not(X_27437)))) != X_27437
| equiv(not(not(X_765)),X_27437) = not(not(equiv(X_765,not(not(X_27437))))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(not(X_765)),not(not(not(not(X_27437))))),not(not(equiv(X_765,not(not(X_27437)))))) ),[0,1],$fot(X_27437)]]) ).
cnf(refute_0_530,plain,
( equiv(not(not(X_765)),not(not(not(not(X_27437))))) != not(not(equiv(X_765,not(not(X_27437)))))
| equiv(not(not(X_765)),X_27437) = not(not(equiv(X_765,not(not(X_27437))))) ),
inference(resolve,[$cnf( $equal(not(not(not(not(X_27437)))),X_27437) )],[refute_0_517,refute_0_529]) ).
cnf(refute_0_531,plain,
equiv(not(not(X_765)),X_27437) = not(not(equiv(X_765,not(not(X_27437))))),
inference(resolve,[$cnf( $equal(equiv(not(not(X_765)),not(not(not(not(X_27437))))),not(not(equiv(X_765,not(not(X_27437)))))) )],[refute_0_528,refute_0_530]) ).
cnf(refute_0_532,plain,
( equiv(not(not(X_765)),X_27437) != not(not(equiv(X_765,not(not(X_27437)))))
| not(not(equiv(X_765,not(not(X_27437))))) = equiv(not(not(X_765)),X_27437) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(not(not(X_765)),X_27437))),bind(Y0,$fot(not(not(equiv(X_765,not(not(X_27437)))))))]]) ).
cnf(refute_0_533,plain,
not(not(equiv(X_765,not(not(X_27437))))) = equiv(not(not(X_765)),X_27437),
inference(resolve,[$cnf( $equal(equiv(not(not(X_765)),X_27437),not(not(equiv(X_765,not(not(X_27437)))))) )],[refute_0_531,refute_0_532]) ).
cnf(refute_0_534,plain,
not(not(equiv(not(not(Y)),not(not(not(not(Y))))))) = equiv(not(not(not(not(Y)))),not(not(Y))),
inference(subst,[],[refute_0_533:[bind(X_27437,$fot(not(not(Y)))),bind(X_765,$fot(not(not(Y))))]]) ).
cnf(refute_0_535,plain,
( equiv(not(not(not(not(Y)))),not(not(Y))) != equiv(Y,not(not(Y)))
| not(not(equiv(not(not(Y)),not(not(not(not(Y))))))) != equiv(not(not(not(not(Y)))),not(not(Y)))
| not(not(equiv(not(not(Y)),not(not(not(not(Y))))))) = equiv(Y,not(not(Y))) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(not(not(equiv(not(not(Y)),not(not(not(not(Y))))))))),bind(Y0,$fot(equiv(not(not(not(not(Y)))),not(not(Y))))),bind(Z,$fot(equiv(Y,not(not(Y)))))]]) ).
cnf(refute_0_536,plain,
( equiv(not(not(not(not(Y)))),not(not(Y))) != equiv(Y,not(not(Y)))
| not(not(equiv(not(not(Y)),not(not(not(not(Y))))))) = equiv(Y,not(not(Y))) ),
inference(resolve,[$cnf( $equal(not(not(equiv(not(not(Y)),not(not(not(not(Y))))))),equiv(not(not(not(not(Y)))),not(not(Y)))) )],[refute_0_534,refute_0_535]) ).
cnf(refute_0_537,plain,
not(not(equiv(not(not(Y)),not(not(not(not(Y))))))) = equiv(Y,not(not(Y))),
inference(resolve,[$cnf( $equal(equiv(not(not(not(not(Y)))),not(not(Y))),equiv(Y,not(not(Y)))) )],[refute_0_527,refute_0_536]) ).
cnf(refute_0_538,plain,
equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))) = not(not(equiv(not(not(Y)),not(not(not(not(Y))))))),
inference(subst,[],[refute_0_513:[bind(X,$fot(not(not(not(not(Y)))))),bind(X_765,$fot(not(not(Y))))]]) ).
cnf(refute_0_539,plain,
( equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))) != not(not(equiv(not(not(Y)),not(not(not(not(Y)))))))
| not(not(equiv(not(not(Y)),not(not(not(not(Y))))))) != equiv(Y,not(not(Y)))
| equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))) = equiv(Y,not(not(Y))) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))))),bind(Y0,$fot(not(not(equiv(not(not(Y)),not(not(not(not(Y))))))))),bind(Z,$fot(equiv(Y,not(not(Y)))))]]) ).
cnf(refute_0_540,plain,
( not(not(equiv(not(not(Y)),not(not(not(not(Y))))))) != equiv(Y,not(not(Y)))
| equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))) = equiv(Y,not(not(Y))) ),
inference(resolve,[$cnf( $equal(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(not(equiv(not(not(Y)),not(not(not(not(Y)))))))) )],[refute_0_538,refute_0_539]) ).
cnf(refute_0_541,plain,
equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))) = equiv(Y,not(not(Y))),
inference(resolve,[$cnf( $equal(not(not(equiv(not(not(Y)),not(not(not(not(Y))))))),equiv(Y,not(not(Y)))) )],[refute_0_537,refute_0_540]) ).
cnf(refute_0_542,plain,
or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) = or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))),
introduced(tautology,[refl,[$fot(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))))]]) ).
cnf(refute_0_543,plain,
( equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))) != equiv(Y,not(not(Y)))
| or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) != or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771))))
| or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) = or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))),or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771))))) ),[1,0],$fot(equiv(Y,not(not(Y))))]]) ).
cnf(refute_0_544,plain,
( equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))) != equiv(Y,not(not(Y)))
| or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) = or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) ),
inference(resolve,[$cnf( $equal(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))),or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771))))) )],[refute_0_542,refute_0_543]) ).
cnf(refute_0_545,plain,
or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) = or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771)))),
inference(resolve,[$cnf( $equal(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),equiv(Y,not(not(Y)))) )],[refute_0_541,refute_0_544]) ).
cnf(refute_0_546,plain,
( or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) != or(equiv(Y,not(not(Y))),or(and(Y,not(Y)),X_31771))
| or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) != or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771))))
| or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) = or(equiv(Y,not(not(Y))),or(and(Y,not(Y)),X_31771)) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))))),bind(Y0,$fot(or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771)))))),bind(Z,$fot(or(equiv(Y,not(not(Y))),or(and(Y,not(Y)),X_31771))))]]) ).
cnf(refute_0_547,plain,
( or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) != or(equiv(Y,not(not(Y))),or(and(Y,not(Y)),X_31771))
| or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) = or(equiv(Y,not(not(Y))),or(and(Y,not(Y)),X_31771)) ),
inference(resolve,[$cnf( $equal(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))),or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771))))) )],[refute_0_545,refute_0_546]) ).
cnf(refute_0_548,plain,
or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) = or(equiv(Y,not(not(Y))),or(and(Y,not(Y)),X_31771)),
inference(resolve,[$cnf( $equal(or(equiv(Y,not(not(Y))),not(and(or(not(not(not(Y))),Y),not(X_31771)))),or(equiv(Y,not(not(Y))),or(and(Y,not(Y)),X_31771))) )],[refute_0_475,refute_0_547]) ).
cnf(refute_0_549,plain,
( or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))) != or(equiv(Y,not(not(Y))),or(and(Y,not(Y)),X_31771))
| ~ is_a_theorem(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))))
| is_a_theorem(or(equiv(Y,not(not(Y))),or(and(Y,not(Y)),X_31771))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771))))) ),[0],$fot(or(equiv(Y,not(not(Y))),or(and(Y,not(Y)),X_31771)))]]) ).
cnf(refute_0_550,plain,
( ~ is_a_theorem(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))))
| is_a_theorem(or(equiv(Y,not(not(Y))),or(and(Y,not(Y)),X_31771))) ),
inference(resolve,[$cnf( $equal(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771)))),or(equiv(Y,not(not(Y))),or(and(Y,not(Y)),X_31771))) )],[refute_0_548,refute_0_549]) ).
cnf(refute_0_551,plain,
is_a_theorem(or(equiv(Y,not(not(Y))),or(and(Y,not(Y)),X_31771))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(not(not(not(not(Y)))),not(not(not(not(not(not(Y))))))),not(and(or(not(not(not(Y))),Y),not(X_31771))))) )],[refute_0_433,refute_0_550]) ).
cnf(refute_0_552,plain,
is_a_theorem(or(equiv(X_31772,not(not(X_31772))),or(and(X_31772,not(X_31772)),and(X_31772,not(X_31772))))),
inference(subst,[],[refute_0_551:[bind(Y,$fot(X_31772)),bind(X_31771,$fot(and(X_31772,not(X_31772))))]]) ).
cnf(refute_0_553,plain,
or(and(X_31772,not(X_31772)),and(X_31772,not(X_31772))) = and(X_31772,not(X_31772)),
inference(subst,[],[refute_0_190:[bind(X_27414,$fot(and(X_31772,not(X_31772))))]]) ).
cnf(refute_0_554,plain,
( or(and(X_31772,not(X_31772)),and(X_31772,not(X_31772))) != and(X_31772,not(X_31772))
| ~ is_a_theorem(or(equiv(X_31772,not(not(X_31772))),or(and(X_31772,not(X_31772)),and(X_31772,not(X_31772)))))
| is_a_theorem(or(equiv(X_31772,not(not(X_31772))),and(X_31772,not(X_31772)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(equiv(X_31772,not(not(X_31772))),or(and(X_31772,not(X_31772)),and(X_31772,not(X_31772))))) ),[0,1],$fot(and(X_31772,not(X_31772)))]]) ).
cnf(refute_0_555,plain,
( ~ is_a_theorem(or(equiv(X_31772,not(not(X_31772))),or(and(X_31772,not(X_31772)),and(X_31772,not(X_31772)))))
| is_a_theorem(or(equiv(X_31772,not(not(X_31772))),and(X_31772,not(X_31772)))) ),
inference(resolve,[$cnf( $equal(or(and(X_31772,not(X_31772)),and(X_31772,not(X_31772))),and(X_31772,not(X_31772))) )],[refute_0_553,refute_0_554]) ).
cnf(refute_0_556,plain,
is_a_theorem(or(equiv(X_31772,not(not(X_31772))),and(X_31772,not(X_31772)))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(X_31772,not(not(X_31772))),or(and(X_31772,not(X_31772)),and(X_31772,not(X_31772))))) )],[refute_0_552,refute_0_555]) ).
cnf(refute_0_557,plain,
is_a_theorem(or(equiv(X_31774,not(not(X_31774))),and(X_31774,not(X_31774)))),
inference(subst,[],[refute_0_556:[bind(X_31772,$fot(X_31774))]]) ).
cnf(refute_0_558,plain,
is_a_theorem(or(and(X_31774,not(X_31774)),equiv(X_31774,not(not(X_31774))))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(X_31774,not(not(X_31774))),and(X_31774,not(X_31774)))) )],[refute_0_557,refute_0_216]) ).
cnf(refute_0_559,plain,
is_a_theorem(or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),not(not(not(not(Y))))))),
inference(subst,[],[refute_0_558:[bind(X_31774,$fot(not(not(Y))))]]) ).
cnf(refute_0_560,plain,
( not(not(not(not(Y)))) != Y
| ~ is_a_theorem(or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),not(not(not(not(Y)))))))
| is_a_theorem(or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),not(not(not(not(Y))))))) ),[0,1,1],$fot(Y)]]) ).
cnf(refute_0_561,plain,
( ~ is_a_theorem(or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),not(not(not(not(Y)))))))
| is_a_theorem(or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),Y))) ),
inference(resolve,[$cnf( $equal(not(not(not(not(Y)))),Y) )],[refute_0_430,refute_0_560]) ).
cnf(refute_0_562,plain,
is_a_theorem(or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),Y))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),not(not(not(not(Y))))))) )],[refute_0_559,refute_0_561]) ).
cnf(refute_0_563,plain,
or(and(and(X_47,X_48),not(X_46)),Y) = not(and(not(and(and(X_47,X_48),not(X_46))),not(Y))),
inference(subst,[],[refute_0_5:[bind(X,$fot(and(and(X_47,X_48),not(X_46))))]]) ).
cnf(refute_0_564,plain,
or(implies(X_47,not(X_48)),X_46) = not(and(and(X_47,X_48),not(X_46))),
inference(subst,[],[refute_0_31:[bind(Y,$fot(X_46)),bind(X_10,$fot(X_47)),bind(X_11,$fot(X_48))]]) ).
cnf(refute_0_565,plain,
( or(implies(X_47,not(X_48)),X_46) != not(and(and(X_47,X_48),not(X_46)))
| not(and(and(X_47,X_48),not(X_46))) = or(implies(X_47,not(X_48)),X_46) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(implies(X_47,not(X_48)),X_46))),bind(Y0,$fot(not(and(and(X_47,X_48),not(X_46)))))]]) ).
cnf(refute_0_566,plain,
not(and(and(X_47,X_48),not(X_46))) = or(implies(X_47,not(X_48)),X_46),
inference(resolve,[$cnf( $equal(or(implies(X_47,not(X_48)),X_46),not(and(and(X_47,X_48),not(X_46)))) )],[refute_0_564,refute_0_565]) ).
cnf(refute_0_567,plain,
( not(and(and(X_47,X_48),not(X_46))) != or(implies(X_47,not(X_48)),X_46)
| or(and(and(X_47,X_48),not(X_46)),Y) != not(and(not(and(and(X_47,X_48),not(X_46))),not(Y)))
| or(and(and(X_47,X_48),not(X_46)),Y) = not(and(or(implies(X_47,not(X_48)),X_46),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(and(X_47,X_48),not(X_46)),Y),not(and(not(and(and(X_47,X_48),not(X_46))),not(Y)))) ),[1,0,0],$fot(or(implies(X_47,not(X_48)),X_46))]]) ).
cnf(refute_0_568,plain,
( or(and(and(X_47,X_48),not(X_46)),Y) != not(and(not(and(and(X_47,X_48),not(X_46))),not(Y)))
| or(and(and(X_47,X_48),not(X_46)),Y) = not(and(or(implies(X_47,not(X_48)),X_46),not(Y))) ),
inference(resolve,[$cnf( $equal(not(and(and(X_47,X_48),not(X_46))),or(implies(X_47,not(X_48)),X_46)) )],[refute_0_566,refute_0_567]) ).
cnf(refute_0_569,plain,
or(and(and(X_47,X_48),not(X_46)),Y) = not(and(or(implies(X_47,not(X_48)),X_46),not(Y))),
inference(resolve,[$cnf( $equal(or(and(and(X_47,X_48),not(X_46)),Y),not(and(not(and(and(X_47,X_48),not(X_46))),not(Y)))) )],[refute_0_563,refute_0_568]) ).
cnf(refute_0_570,plain,
or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) = not(and(or(implies(X_28779,not(X_28780)),implies(X_28779,not(X_28780))),not(X_28777))),
inference(subst,[],[refute_0_569:[bind(Y,$fot(X_28777)),bind(X_46,$fot(implies(X_28779,not(X_28780)))),bind(X_47,$fot(X_28779)),bind(X_48,$fot(X_28780))]]) ).
cnf(refute_0_571,plain,
or(implies(X_28779,not(X_28780)),implies(X_28779,not(X_28780))) = implies(X_28779,not(X_28780)),
inference(subst,[],[refute_0_190:[bind(X_27414,$fot(implies(X_28779,not(X_28780))))]]) ).
cnf(refute_0_572,plain,
( or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) != not(and(or(implies(X_28779,not(X_28780)),implies(X_28779,not(X_28780))),not(X_28777)))
| or(implies(X_28779,not(X_28780)),implies(X_28779,not(X_28780))) != implies(X_28779,not(X_28780))
| or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) = not(and(implies(X_28779,not(X_28780)),not(X_28777))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777),not(and(or(implies(X_28779,not(X_28780)),implies(X_28779,not(X_28780))),not(X_28777)))) ),[1,0,0],$fot(implies(X_28779,not(X_28780)))]]) ).
cnf(refute_0_573,plain,
( or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) != not(and(or(implies(X_28779,not(X_28780)),implies(X_28779,not(X_28780))),not(X_28777)))
| or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) = not(and(implies(X_28779,not(X_28780)),not(X_28777))) ),
inference(resolve,[$cnf( $equal(or(implies(X_28779,not(X_28780)),implies(X_28779,not(X_28780))),implies(X_28779,not(X_28780))) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) = not(and(implies(X_28779,not(X_28780)),not(X_28777))),
inference(resolve,[$cnf( $equal(or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777),not(and(or(implies(X_28779,not(X_28780)),implies(X_28779,not(X_28780))),not(X_28777)))) )],[refute_0_570,refute_0_573]) ).
cnf(refute_0_575,plain,
or(not(not(and(X_28779,X_28780))),X_28777) = implies(not(and(X_28779,X_28780)),X_28777),
inference(subst,[],[refute_0_17:[bind(X,$fot(not(and(X_28779,X_28780)))),bind(Y,$fot(X_28777))]]) ).
cnf(refute_0_576,plain,
and(and(X_28779,X_28780),and(X_28779,X_28780)) = not(not(and(X_28779,X_28780))),
inference(subst,[],[refute_0_365:[bind(Y,$fot(and(X_28779,X_28780)))]]) ).
cnf(refute_0_577,plain,
not(implies(X_28779,not(X_28780))) = and(X_28779,X_28780),
inference(subst,[],[refute_0_283:[bind(X,$fot(X_28779)),bind(Y,$fot(X_28780))]]) ).
cnf(refute_0_578,plain,
and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))) = and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),
introduced(tautology,[refl,[$fot(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))))]]) ).
cnf(refute_0_579,plain,
( and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))) != and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780))))
| not(implies(X_28779,not(X_28780))) != and(X_28779,X_28780)
| and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))) = and(and(X_28779,X_28780),and(X_28779,X_28780)) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780))))) ),[1,1],$fot(and(X_28779,X_28780))]]) ).
cnf(refute_0_580,plain,
( not(implies(X_28779,not(X_28780))) != and(X_28779,X_28780)
| and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))) = and(and(X_28779,X_28780),and(X_28779,X_28780)) ),
inference(resolve,[$cnf( $equal(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780))))) )],[refute_0_578,refute_0_579]) ).
cnf(refute_0_581,plain,
and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))) = and(and(X_28779,X_28780),and(X_28779,X_28780)),
inference(resolve,[$cnf( $equal(not(implies(X_28779,not(X_28780))),and(X_28779,X_28780)) )],[refute_0_577,refute_0_580]) ).
cnf(refute_0_582,plain,
( and(and(X_28779,X_28780),and(X_28779,X_28780)) != not(not(and(X_28779,X_28780)))
| and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))) != and(and(X_28779,X_28780),and(X_28779,X_28780))
| and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))) = not(not(and(X_28779,X_28780))) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))))),bind(Y0,$fot(and(and(X_28779,X_28780),and(X_28779,X_28780)))),bind(Z,$fot(not(not(and(X_28779,X_28780)))))]]) ).
cnf(refute_0_583,plain,
( and(and(X_28779,X_28780),and(X_28779,X_28780)) != not(not(and(X_28779,X_28780)))
| and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))) = not(not(and(X_28779,X_28780))) ),
inference(resolve,[$cnf( $equal(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),and(and(X_28779,X_28780),and(X_28779,X_28780))) )],[refute_0_581,refute_0_582]) ).
cnf(refute_0_584,plain,
and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))) = not(not(and(X_28779,X_28780))),
inference(resolve,[$cnf( $equal(and(and(X_28779,X_28780),and(X_28779,X_28780)),not(not(and(X_28779,X_28780)))) )],[refute_0_576,refute_0_583]) ).
cnf(refute_0_585,plain,
or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) = or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777),
introduced(tautology,[refl,[$fot(or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777))]]) ).
cnf(refute_0_586,plain,
( and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))) != not(not(and(X_28779,X_28780)))
| or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) != or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777)
| or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) = or(not(not(and(X_28779,X_28780))),X_28777) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777),or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777)) ),[1,0],$fot(not(not(and(X_28779,X_28780))))]]) ).
cnf(refute_0_587,plain,
( and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))) != not(not(and(X_28779,X_28780)))
| or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) = or(not(not(and(X_28779,X_28780))),X_28777) ),
inference(resolve,[$cnf( $equal(or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777),or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777)) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) = or(not(not(and(X_28779,X_28780))),X_28777),
inference(resolve,[$cnf( $equal(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),not(not(and(X_28779,X_28780)))) )],[refute_0_584,refute_0_587]) ).
cnf(refute_0_589,plain,
( or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) != or(not(not(and(X_28779,X_28780))),X_28777)
| or(not(not(and(X_28779,X_28780))),X_28777) != implies(not(and(X_28779,X_28780)),X_28777)
| or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) = implies(not(and(X_28779,X_28780)),X_28777) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777))),bind(Y0,$fot(or(not(not(and(X_28779,X_28780))),X_28777))),bind(Z,$fot(implies(not(and(X_28779,X_28780)),X_28777)))]]) ).
cnf(refute_0_590,plain,
( or(not(not(and(X_28779,X_28780))),X_28777) != implies(not(and(X_28779,X_28780)),X_28777)
| or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) = implies(not(and(X_28779,X_28780)),X_28777) ),
inference(resolve,[$cnf( $equal(or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777),or(not(not(and(X_28779,X_28780))),X_28777)) )],[refute_0_588,refute_0_589]) ).
cnf(refute_0_591,plain,
or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) = implies(not(and(X_28779,X_28780)),X_28777),
inference(resolve,[$cnf( $equal(or(not(not(and(X_28779,X_28780))),X_28777),implies(not(and(X_28779,X_28780)),X_28777)) )],[refute_0_575,refute_0_590]) ).
cnf(refute_0_592,plain,
( or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) != implies(not(and(X_28779,X_28780)),X_28777)
| or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) != not(and(implies(X_28779,not(X_28780)),not(X_28777)))
| implies(not(and(X_28779,X_28780)),X_28777) = not(and(implies(X_28779,not(X_28780)),not(X_28777))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777),not(and(implies(X_28779,not(X_28780)),not(X_28777)))) ),[0],$fot(implies(not(and(X_28779,X_28780)),X_28777))]]) ).
cnf(refute_0_593,plain,
( or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777) != not(and(implies(X_28779,not(X_28780)),not(X_28777)))
| implies(not(and(X_28779,X_28780)),X_28777) = not(and(implies(X_28779,not(X_28780)),not(X_28777))) ),
inference(resolve,[$cnf( $equal(or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777),implies(not(and(X_28779,X_28780)),X_28777)) )],[refute_0_591,refute_0_592]) ).
cnf(refute_0_594,plain,
implies(not(and(X_28779,X_28780)),X_28777) = not(and(implies(X_28779,not(X_28780)),not(X_28777))),
inference(resolve,[$cnf( $equal(or(and(and(X_28779,X_28780),not(implies(X_28779,not(X_28780)))),X_28777),not(and(implies(X_28779,not(X_28780)),not(X_28777)))) )],[refute_0_574,refute_0_593]) ).
cnf(refute_0_595,plain,
( implies(not(and(X_28779,X_28780)),X_28777) != not(and(implies(X_28779,not(X_28780)),not(X_28777)))
| not(and(implies(X_28779,not(X_28780)),not(X_28777))) = implies(not(and(X_28779,X_28780)),X_28777) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(not(and(X_28779,X_28780)),X_28777))),bind(Y0,$fot(not(and(implies(X_28779,not(X_28780)),not(X_28777)))))]]) ).
cnf(refute_0_596,plain,
not(and(implies(X_28779,not(X_28780)),not(X_28777))) = implies(not(and(X_28779,X_28780)),X_28777),
inference(resolve,[$cnf( $equal(implies(not(and(X_28779,X_28780)),X_28777),not(and(implies(X_28779,not(X_28780)),not(X_28777)))) )],[refute_0_594,refute_0_595]) ).
cnf(refute_0_597,plain,
not(and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y)))) = implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y)),
inference(subst,[],[refute_0_596:[bind(X_28777,$fot(equiv(not(not(Y)),Y))),bind(X_28779,$fot(Y)),bind(X_28780,$fot(not(Y)))]]) ).
cnf(refute_0_598,plain,
or(not(Y),not(not(Y))) = implies(Y,not(not(Y))),
inference(subst,[],[refute_0_17:[bind(X,$fot(Y)),bind(Y,$fot(not(not(Y))))]]) ).
cnf(refute_0_599,plain,
and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))) = and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))),
introduced(tautology,[refl,[$fot(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))))]]) ).
cnf(refute_0_600,plain,
( and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))) != and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))
| or(not(Y),not(not(Y))) != implies(Y,not(not(Y)))
| and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))) = and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))),and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))) ),[1,0],$fot(implies(Y,not(not(Y))))]]) ).
cnf(refute_0_601,plain,
( or(not(Y),not(not(Y))) != implies(Y,not(not(Y)))
| and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))) = and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y))) ),
inference(resolve,[$cnf( $equal(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))),and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))) )],[refute_0_599,refute_0_600]) ).
cnf(refute_0_602,plain,
and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))) = and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y))),
inference(resolve,[$cnf( $equal(or(not(Y),not(not(Y))),implies(Y,not(not(Y)))) )],[refute_0_598,refute_0_601]) ).
cnf(refute_0_603,plain,
not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))) = not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))),
introduced(tautology,[refl,[$fot(not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))))]]) ).
cnf(refute_0_604,plain,
( and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))) != and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y)))
| not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))) != not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))))
| not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))) = not(and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))),not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))))) ),[1,0],$fot(and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y))))]]) ).
cnf(refute_0_605,plain,
( and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))) != and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y)))
| not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))) = not(and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y)))) ),
inference(resolve,[$cnf( $equal(not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))),not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))))) )],[refute_0_603,refute_0_604]) ).
cnf(refute_0_606,plain,
not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))) = not(and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y)))),
inference(resolve,[$cnf( $equal(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))),and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y)))) )],[refute_0_602,refute_0_605]) ).
cnf(refute_0_607,plain,
( not(and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y)))) != implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y))
| not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))) != not(and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y))))
| not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))) = implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y)) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))))),bind(Y0,$fot(not(and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y)))))),bind(Z,$fot(implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y))))]]) ).
cnf(refute_0_608,plain,
( not(and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y)))) != implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y))
| not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))) = implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y)) ),
inference(resolve,[$cnf( $equal(not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))),not(and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y))))) )],[refute_0_606,refute_0_607]) ).
cnf(refute_0_609,plain,
not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))) = implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y)),
inference(resolve,[$cnf( $equal(not(and(implies(Y,not(not(Y))),not(equiv(not(not(Y)),Y)))),implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y))) )],[refute_0_597,refute_0_608]) ).
cnf(refute_0_610,plain,
or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),Y)) = not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))),
inference(subst,[],[refute_0_359:[bind(Y,$fot(equiv(not(not(Y)),Y))),bind(X_1,$fot(not(Y))),bind(X_2,$fot(not(not(Y))))]]) ).
cnf(refute_0_611,plain,
( not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))) != implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y))
| or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),Y)) != not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))))
| or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),Y)) = implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y)) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),Y)))),bind(Y0,$fot(not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))))),bind(Z,$fot(implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y))))]]) ).
cnf(refute_0_612,plain,
( not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))) != implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y))
| or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),Y)) = implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y)) ),
inference(resolve,[$cnf( $equal(or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),Y)),not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y))))) )],[refute_0_610,refute_0_611]) ).
cnf(refute_0_613,plain,
or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),Y)) = implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y)),
inference(resolve,[$cnf( $equal(not(and(or(not(Y),not(not(Y))),not(equiv(not(not(Y)),Y)))),implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y))) )],[refute_0_609,refute_0_612]) ).
cnf(refute_0_614,plain,
( or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),Y)) != implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y))
| ~ is_a_theorem(or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),Y)))
| is_a_theorem(implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),Y))) ),[0],$fot(implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y)))]]) ).
cnf(refute_0_615,plain,
( ~ is_a_theorem(or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),Y)))
| is_a_theorem(implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y))) ),
inference(resolve,[$cnf( $equal(or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),Y)),implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y))) )],[refute_0_613,refute_0_614]) ).
cnf(refute_0_616,plain,
is_a_theorem(implies(not(and(Y,not(Y))),equiv(not(not(Y)),Y))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(not(Y)),not(not(not(Y)))),equiv(not(not(Y)),Y))) )],[refute_0_562,refute_0_615]) ).
cnf(refute_0_617,plain,
is_a_theorem(implies(not(and(X_31802,not(X_31802))),equiv(not(not(X_31802)),X_31802))),
inference(subst,[],[refute_0_616:[bind(Y,$fot(X_31802))]]) ).
cnf(refute_0_618,plain,
( ~ is_a_theorem(not(and(X_31802,not(X_31802))))
| is_a_theorem(equiv(not(not(X_31802)),X_31802)) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(and(X_31802,not(X_31802))),equiv(not(not(X_31802)),X_31802))) )],[refute_0_617,refute_0_215]) ).
cnf(refute_0_619,plain,
( ~ is_a_theorem(or(not(X),not(X)))
| is_a_theorem(not(X)) ),
inference(subst,[],[refute_0_69:[bind(X_171,$fot(not(X)))]]) ).
cnf(refute_0_620,plain,
( or(not(X),not(X)) != implies(X,not(X))
| ~ is_a_theorem(implies(X,not(X)))
| is_a_theorem(or(not(X),not(X))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(or(not(X),not(X))) ),[0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_621,plain,
( ~ is_a_theorem(implies(X,not(X)))
| is_a_theorem(or(not(X),not(X))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_278,refute_0_620]) ).
cnf(refute_0_622,plain,
( ~ is_a_theorem(implies(X,not(X)))
| is_a_theorem(not(X)) ),
inference(resolve,[$cnf( is_a_theorem(or(not(X),not(X))) )],[refute_0_621,refute_0_619]) ).
cnf(refute_0_623,plain,
( ~ is_a_theorem(implies(and(X_9538,not(X_9538)),not(and(X_9538,not(X_9538)))))
| is_a_theorem(not(and(X_9538,not(X_9538)))) ),
inference(subst,[],[refute_0_622:[bind(X,$fot(and(X_9538,not(X_9538))))]]) ).
cnf(refute_0_624,plain,
is_a_theorem(implies(or(X_15,not(X)),or(not(X),X_15))),
inference(subst,[],[refute_0_59:[bind(P,$fot(X_15)),bind(Q,$fot(not(X)))]]) ).
cnf(refute_0_625,plain,
implies(X,X_15) = or(not(X),X_15),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_15))]]) ).
cnf(refute_0_626,plain,
( implies(X,X_15) != or(not(X),X_15)
| or(not(X),X_15) = implies(X,X_15) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_15))),bind(Y0,$fot(or(not(X),X_15)))]]) ).
cnf(refute_0_627,plain,
or(not(X),X_15) = implies(X,X_15),
inference(resolve,[$cnf( $equal(implies(X,X_15),or(not(X),X_15)) )],[refute_0_625,refute_0_626]) ).
cnf(refute_0_628,plain,
( or(not(X),X_15) != implies(X,X_15)
| ~ is_a_theorem(implies(or(X_15,not(X)),or(not(X),X_15)))
| is_a_theorem(implies(or(X_15,not(X)),implies(X,X_15))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_15,not(X)),or(not(X),X_15))) ),[0,1],$fot(implies(X,X_15))]]) ).
cnf(refute_0_629,plain,
( ~ is_a_theorem(implies(or(X_15,not(X)),or(not(X),X_15)))
| is_a_theorem(implies(or(X_15,not(X)),implies(X,X_15))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_15),implies(X,X_15)) )],[refute_0_627,refute_0_628]) ).
cnf(refute_0_630,plain,
is_a_theorem(implies(or(X_15,not(X)),implies(X,X_15))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_15,not(X)),or(not(X),X_15))) )],[refute_0_624,refute_0_629]) ).
cnf(refute_0_631,plain,
( ~ is_a_theorem(implies(or(X_15,not(X)),implies(X,X_15)))
| ~ is_a_theorem(or(X_15,not(X)))
| is_a_theorem(implies(X,X_15)) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(or(X_15,not(X)))),bind(Y,$fot(implies(X,X_15)))]]) ).
cnf(refute_0_632,plain,
( ~ is_a_theorem(or(X_15,not(X)))
| is_a_theorem(implies(X,X_15)) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_15,not(X)),implies(X,X_15))) )],[refute_0_630,refute_0_631]) ).
cnf(refute_0_633,plain,
( ~ is_a_theorem(or(not(X),not(X_225)))
| is_a_theorem(implies(X_225,not(X))) ),
inference(subst,[],[refute_0_632:[bind(X,$fot(X_225)),bind(X_15,$fot(not(X)))]]) ).
cnf(refute_0_634,plain,
implies(X,not(X_225)) = or(not(X),not(X_225)),
inference(subst,[],[refute_0_12:[bind(Y,$fot(not(X_225)))]]) ).
cnf(refute_0_635,plain,
( implies(X,not(X_225)) != or(not(X),not(X_225))
| or(not(X),not(X_225)) = implies(X,not(X_225)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,not(X_225)))),bind(Y0,$fot(or(not(X),not(X_225))))]]) ).
cnf(refute_0_636,plain,
or(not(X),not(X_225)) = implies(X,not(X_225)),
inference(resolve,[$cnf( $equal(implies(X,not(X_225)),or(not(X),not(X_225))) )],[refute_0_634,refute_0_635]) ).
cnf(refute_0_637,plain,
( or(not(X),not(X_225)) != implies(X,not(X_225))
| ~ is_a_theorem(implies(X,not(X_225)))
| is_a_theorem(or(not(X),not(X_225))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(or(not(X),not(X_225))) ),[0],$fot(implies(X,not(X_225)))]]) ).
cnf(refute_0_638,plain,
( ~ is_a_theorem(implies(X,not(X_225)))
| is_a_theorem(or(not(X),not(X_225))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_225)),implies(X,not(X_225))) )],[refute_0_636,refute_0_637]) ).
cnf(refute_0_639,plain,
( ~ is_a_theorem(implies(X,not(X_225)))
| is_a_theorem(implies(X_225,not(X))) ),
inference(resolve,[$cnf( is_a_theorem(or(not(X),not(X_225))) )],[refute_0_638,refute_0_633]) ).
cnf(refute_0_640,plain,
( ~ is_a_theorem(implies(not(X_225),not(X_225)))
| is_a_theorem(implies(X_225,not(not(X_225)))) ),
inference(subst,[],[refute_0_639:[bind(X,$fot(not(X_225)))]]) ).
cnf(refute_0_641,plain,
is_a_theorem(implies(not(X_225),not(X_225))),
inference(subst,[],[refute_0_139:[bind(X_2830,$fot(not(X_225)))]]) ).
cnf(refute_0_642,plain,
is_a_theorem(implies(X_225,not(not(X_225)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_225),not(X_225))) )],[refute_0_641,refute_0_640]) ).
cnf(refute_0_643,plain,
( ~ is_a_theorem(X_3627)
| ~ is_a_theorem(implies(X_3627,implies(X_3628,not(not(X_3627)))))
| is_a_theorem(implies(X_3628,not(not(X_3627)))) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(X_3627)),bind(Y,$fot(implies(X_3628,not(not(X_3627)))))]]) ).
cnf(refute_0_644,plain,
is_a_theorem(implies(X_170,implies(X_5,X_170))),
inference(subst,[],[refute_0_81:[bind(Q,$fot(X_170))]]) ).
cnf(refute_0_645,plain,
( ~ is_a_theorem(X_170)
| ~ is_a_theorem(implies(X_170,implies(X_5,X_170)))
| is_a_theorem(implies(X_5,X_170)) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(X_170)),bind(Y,$fot(implies(X_5,X_170)))]]) ).
cnf(refute_0_646,plain,
( ~ is_a_theorem(X_170)
| is_a_theorem(implies(X_5,X_170)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_170,implies(X_5,X_170))) )],[refute_0_644,refute_0_645]) ).
cnf(refute_0_647,plain,
( ~ is_a_theorem(or(X_2834,not(X_2834)))
| is_a_theorem(implies(X_5,or(X_2834,not(X_2834)))) ),
inference(subst,[],[refute_0_646:[bind(X_170,$fot(or(X_2834,not(X_2834))))]]) ).
cnf(refute_0_648,plain,
is_a_theorem(implies(or(not(X),X_16),or(X_16,not(X)))),
inference(subst,[],[refute_0_59:[bind(P,$fot(not(X))),bind(Q,$fot(X_16))]]) ).
cnf(refute_0_649,plain,
implies(X,X_16) = or(not(X),X_16),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_16))]]) ).
cnf(refute_0_650,plain,
( implies(X,X_16) != or(not(X),X_16)
| or(not(X),X_16) = implies(X,X_16) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_16))),bind(Y0,$fot(or(not(X),X_16)))]]) ).
cnf(refute_0_651,plain,
or(not(X),X_16) = implies(X,X_16),
inference(resolve,[$cnf( $equal(implies(X,X_16),or(not(X),X_16)) )],[refute_0_649,refute_0_650]) ).
cnf(refute_0_652,plain,
( or(not(X),X_16) != implies(X,X_16)
| ~ is_a_theorem(implies(or(not(X),X_16),or(X_16,not(X))))
| is_a_theorem(implies(implies(X,X_16),or(X_16,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),X_16),or(X_16,not(X)))) ),[0,0],$fot(implies(X,X_16))]]) ).
cnf(refute_0_653,plain,
( ~ is_a_theorem(implies(or(not(X),X_16),or(X_16,not(X))))
| is_a_theorem(implies(implies(X,X_16),or(X_16,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_16),implies(X,X_16)) )],[refute_0_651,refute_0_652]) ).
cnf(refute_0_654,plain,
is_a_theorem(implies(implies(X,X_16),or(X_16,not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),X_16),or(X_16,not(X)))) )],[refute_0_648,refute_0_653]) ).
cnf(refute_0_655,plain,
( ~ is_a_theorem(implies(X,X_16))
| ~ is_a_theorem(implies(implies(X,X_16),or(X_16,not(X))))
| is_a_theorem(or(X_16,not(X))) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(implies(X,X_16))),bind(Y,$fot(or(X_16,not(X))))]]) ).
cnf(refute_0_656,plain,
( ~ is_a_theorem(implies(X,X_16))
| is_a_theorem(or(X_16,not(X))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,X_16),or(X_16,not(X)))) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
( ~ is_a_theorem(implies(X_2832,X_2832))
| is_a_theorem(or(X_2832,not(X_2832))) ),
inference(subst,[],[refute_0_656:[bind(X,$fot(X_2832)),bind(X_16,$fot(X_2832))]]) ).
cnf(refute_0_658,plain,
is_a_theorem(implies(X_2832,X_2832)),
inference(subst,[],[refute_0_139:[bind(X_2830,$fot(X_2832))]]) ).
cnf(refute_0_659,plain,
is_a_theorem(or(X_2832,not(X_2832))),
inference(resolve,[$cnf( is_a_theorem(implies(X_2832,X_2832)) )],[refute_0_658,refute_0_657]) ).
cnf(refute_0_660,plain,
is_a_theorem(or(X_2834,not(X_2834))),
inference(subst,[],[refute_0_659:[bind(X_2832,$fot(X_2834))]]) ).
cnf(refute_0_661,plain,
is_a_theorem(implies(X_5,or(X_2834,not(X_2834)))),
inference(resolve,[$cnf( is_a_theorem(or(X_2834,not(X_2834))) )],[refute_0_660,refute_0_647]) ).
cnf(refute_0_662,plain,
is_a_theorem(implies(X_3611,or(X_3612,not(X_3612)))),
inference(subst,[],[refute_0_661:[bind(X_2834,$fot(X_3612)),bind(X_5,$fot(X_3611))]]) ).
cnf(refute_0_663,plain,
( ~ is_a_theorem(implies(X_3611,or(X_3612,not(X_3612))))
| is_a_theorem(or(X_3612,implies(X_3611,not(X_3612)))) ),
inference(subst,[],[refute_0_142:[bind(X,$fot(X_3611)),bind(X_72,$fot(X_3612)),bind(X_73,$fot(not(X_3612)))]]) ).
cnf(refute_0_664,plain,
is_a_theorem(or(X_3612,implies(X_3611,not(X_3612)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_3611,or(X_3612,not(X_3612)))) )],[refute_0_662,refute_0_663]) ).
cnf(refute_0_665,plain,
is_a_theorem(or(not(X),implies(X_3620,not(not(X))))),
inference(subst,[],[refute_0_664:[bind(X_3611,$fot(X_3620)),bind(X_3612,$fot(not(X)))]]) ).
cnf(refute_0_666,plain,
implies(X,implies(X_3620,not(not(X)))) = or(not(X),implies(X_3620,not(not(X)))),
inference(subst,[],[refute_0_12:[bind(Y,$fot(implies(X_3620,not(not(X)))))]]) ).
cnf(refute_0_667,plain,
( implies(X,implies(X_3620,not(not(X)))) != or(not(X),implies(X_3620,not(not(X))))
| or(not(X),implies(X_3620,not(not(X)))) = implies(X,implies(X_3620,not(not(X)))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,implies(X_3620,not(not(X)))))),bind(Y0,$fot(or(not(X),implies(X_3620,not(not(X))))))]]) ).
cnf(refute_0_668,plain,
or(not(X),implies(X_3620,not(not(X)))) = implies(X,implies(X_3620,not(not(X)))),
inference(resolve,[$cnf( $equal(implies(X,implies(X_3620,not(not(X)))),or(not(X),implies(X_3620,not(not(X))))) )],[refute_0_666,refute_0_667]) ).
cnf(refute_0_669,plain,
( or(not(X),implies(X_3620,not(not(X)))) != implies(X,implies(X_3620,not(not(X))))
| ~ is_a_theorem(or(not(X),implies(X_3620,not(not(X)))))
| is_a_theorem(implies(X,implies(X_3620,not(not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X),implies(X_3620,not(not(X))))) ),[0],$fot(implies(X,implies(X_3620,not(not(X)))))]]) ).
cnf(refute_0_670,plain,
( ~ is_a_theorem(or(not(X),implies(X_3620,not(not(X)))))
| is_a_theorem(implies(X,implies(X_3620,not(not(X))))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_3620,not(not(X)))),implies(X,implies(X_3620,not(not(X))))) )],[refute_0_668,refute_0_669]) ).
cnf(refute_0_671,plain,
is_a_theorem(implies(X,implies(X_3620,not(not(X))))),
inference(resolve,[$cnf( is_a_theorem(or(not(X),implies(X_3620,not(not(X))))) )],[refute_0_665,refute_0_670]) ).
cnf(refute_0_672,plain,
is_a_theorem(implies(X_3627,implies(X_3628,not(not(X_3627))))),
inference(subst,[],[refute_0_671:[bind(X,$fot(X_3627)),bind(X_3620,$fot(X_3628))]]) ).
cnf(refute_0_673,plain,
( ~ is_a_theorem(X_3627)
| is_a_theorem(implies(X_3628,not(not(X_3627)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_3627,implies(X_3628,not(not(X_3627))))) )],[refute_0_672,refute_0_643]) ).
cnf(refute_0_674,plain,
( ~ is_a_theorem(implies(X_225,not(not(X_225))))
| is_a_theorem(implies(X_9509,not(not(implies(X_225,not(not(X_225))))))) ),
inference(subst,[],[refute_0_673:[bind(X_3627,$fot(implies(X_225,not(not(X_225))))),bind(X_3628,$fot(X_9509))]]) ).
cnf(refute_0_675,plain,
is_a_theorem(implies(X_9509,not(not(implies(X_225,not(not(X_225))))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_225,not(not(X_225)))) )],[refute_0_642,refute_0_674]) ).
cnf(refute_0_676,plain,
not(implies(X_225,not(not(X_225)))) = and(X_225,not(X_225)),
inference(subst,[],[refute_0_283:[bind(X,$fot(X_225)),bind(Y,$fot(not(X_225)))]]) ).
cnf(refute_0_677,plain,
not(not(implies(X_225,not(not(X_225))))) = not(not(implies(X_225,not(not(X_225))))),
introduced(tautology,[refl,[$fot(not(not(implies(X_225,not(not(X_225))))))]]) ).
cnf(refute_0_678,plain,
( not(implies(X_225,not(not(X_225)))) != and(X_225,not(X_225))
| not(not(implies(X_225,not(not(X_225))))) != not(not(implies(X_225,not(not(X_225)))))
| not(not(implies(X_225,not(not(X_225))))) = not(and(X_225,not(X_225))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(X_225,not(not(X_225))))),not(not(implies(X_225,not(not(X_225)))))) ),[1,0],$fot(and(X_225,not(X_225)))]]) ).
cnf(refute_0_679,plain,
( not(implies(X_225,not(not(X_225)))) != and(X_225,not(X_225))
| not(not(implies(X_225,not(not(X_225))))) = not(and(X_225,not(X_225))) ),
inference(resolve,[$cnf( $equal(not(not(implies(X_225,not(not(X_225))))),not(not(implies(X_225,not(not(X_225)))))) )],[refute_0_677,refute_0_678]) ).
cnf(refute_0_680,plain,
not(not(implies(X_225,not(not(X_225))))) = not(and(X_225,not(X_225))),
inference(resolve,[$cnf( $equal(not(implies(X_225,not(not(X_225)))),and(X_225,not(X_225))) )],[refute_0_676,refute_0_679]) ).
cnf(refute_0_681,plain,
implies(X_9509,not(not(implies(X_225,not(not(X_225)))))) = implies(X_9509,not(not(implies(X_225,not(not(X_225)))))),
introduced(tautology,[refl,[$fot(implies(X_9509,not(not(implies(X_225,not(not(X_225)))))))]]) ).
cnf(refute_0_682,plain,
( implies(X_9509,not(not(implies(X_225,not(not(X_225)))))) != implies(X_9509,not(not(implies(X_225,not(not(X_225))))))
| not(not(implies(X_225,not(not(X_225))))) != not(and(X_225,not(X_225)))
| implies(X_9509,not(not(implies(X_225,not(not(X_225)))))) = implies(X_9509,not(and(X_225,not(X_225)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_9509,not(not(implies(X_225,not(not(X_225)))))),implies(X_9509,not(not(implies(X_225,not(not(X_225))))))) ),[1,1],$fot(not(and(X_225,not(X_225))))]]) ).
cnf(refute_0_683,plain,
( not(not(implies(X_225,not(not(X_225))))) != not(and(X_225,not(X_225)))
| implies(X_9509,not(not(implies(X_225,not(not(X_225)))))) = implies(X_9509,not(and(X_225,not(X_225)))) ),
inference(resolve,[$cnf( $equal(implies(X_9509,not(not(implies(X_225,not(not(X_225)))))),implies(X_9509,not(not(implies(X_225,not(not(X_225))))))) )],[refute_0_681,refute_0_682]) ).
cnf(refute_0_684,plain,
implies(X_9509,not(not(implies(X_225,not(not(X_225)))))) = implies(X_9509,not(and(X_225,not(X_225)))),
inference(resolve,[$cnf( $equal(not(not(implies(X_225,not(not(X_225))))),not(and(X_225,not(X_225)))) )],[refute_0_680,refute_0_683]) ).
cnf(refute_0_685,plain,
( implies(X_9509,not(not(implies(X_225,not(not(X_225)))))) != implies(X_9509,not(and(X_225,not(X_225))))
| ~ is_a_theorem(implies(X_9509,not(not(implies(X_225,not(not(X_225)))))))
| is_a_theorem(implies(X_9509,not(and(X_225,not(X_225))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_9509,not(not(implies(X_225,not(not(X_225))))))) ),[0],$fot(implies(X_9509,not(and(X_225,not(X_225)))))]]) ).
cnf(refute_0_686,plain,
( ~ is_a_theorem(implies(X_9509,not(not(implies(X_225,not(not(X_225)))))))
| is_a_theorem(implies(X_9509,not(and(X_225,not(X_225))))) ),
inference(resolve,[$cnf( $equal(implies(X_9509,not(not(implies(X_225,not(not(X_225)))))),implies(X_9509,not(and(X_225,not(X_225))))) )],[refute_0_684,refute_0_685]) ).
cnf(refute_0_687,plain,
is_a_theorem(implies(X_9509,not(and(X_225,not(X_225))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_9509,not(not(implies(X_225,not(not(X_225))))))) )],[refute_0_675,refute_0_686]) ).
cnf(refute_0_688,plain,
is_a_theorem(implies(and(X_9538,not(X_9538)),not(and(X_9538,not(X_9538))))),
inference(subst,[],[refute_0_687:[bind(X_225,$fot(X_9538)),bind(X_9509,$fot(and(X_9538,not(X_9538))))]]) ).
cnf(refute_0_689,plain,
is_a_theorem(not(and(X_9538,not(X_9538)))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_9538,not(X_9538)),not(and(X_9538,not(X_9538))))) )],[refute_0_688,refute_0_623]) ).
cnf(refute_0_690,plain,
is_a_theorem(not(and(X_31802,not(X_31802)))),
inference(subst,[],[refute_0_689:[bind(X_9538,$fot(X_31802))]]) ).
cnf(refute_0_691,plain,
is_a_theorem(equiv(not(not(X_31802)),X_31802)),
inference(resolve,[$cnf( is_a_theorem(not(and(X_31802,not(X_31802)))) )],[refute_0_690,refute_0_618]) ).
cnf(refute_0_692,plain,
is_a_theorem(equiv(not(not(X_31803)),X_31803)),
inference(subst,[],[refute_0_691:[bind(X_31802,$fot(X_31803))]]) ).
cnf(refute_0_693,plain,
not(not(X_31803)) = X_31803,
inference(resolve,[$cnf( is_a_theorem(equiv(not(not(X_31803)),X_31803)) )],[refute_0_692,refute_0_214]) ).
cnf(refute_0_694,plain,
not(not(Y)) = Y,
inference(subst,[],[refute_0_693:[bind(X_31803,$fot(Y))]]) ).
cnf(refute_0_695,plain,
or(X_94,not(not(Y))) = or(X_94,not(not(Y))),
introduced(tautology,[refl,[$fot(or(X_94,not(not(Y))))]]) ).
cnf(refute_0_696,plain,
( not(not(Y)) != Y
| or(X_94,not(not(Y))) != or(X_94,not(not(Y)))
| or(X_94,not(not(Y))) = or(X_94,Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_94,not(not(Y))),or(X_94,not(not(Y)))) ),[1,1],$fot(Y)]]) ).
cnf(refute_0_697,plain,
( not(not(Y)) != Y
| or(X_94,not(not(Y))) = or(X_94,Y) ),
inference(resolve,[$cnf( $equal(or(X_94,not(not(Y))),or(X_94,not(not(Y)))) )],[refute_0_695,refute_0_696]) ).
cnf(refute_0_698,plain,
or(X_94,not(not(Y))) = or(X_94,Y),
inference(resolve,[$cnf( $equal(not(not(Y)),Y) )],[refute_0_694,refute_0_697]) ).
cnf(refute_0_699,plain,
not(not(or(X_94,not(not(Y))))) = or(X_94,not(not(Y))),
inference(subst,[],[refute_0_693:[bind(X_31803,$fot(or(X_94,not(not(Y)))))]]) ).
cnf(refute_0_700,plain,
( not(not(or(X_94,not(not(Y))))) != or(X_94,not(not(Y)))
| or(X_94,not(not(Y))) != or(X_94,Y)
| not(not(or(X_94,not(not(Y))))) = or(X_94,Y) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(not(not(or(X_94,not(not(Y))))))),bind(Y0,$fot(or(X_94,not(not(Y))))),bind(Z,$fot(or(X_94,Y)))]]) ).
cnf(refute_0_701,plain,
( or(X_94,not(not(Y))) != or(X_94,Y)
| not(not(or(X_94,not(not(Y))))) = or(X_94,Y) ),
inference(resolve,[$cnf( $equal(not(not(or(X_94,not(not(Y))))),or(X_94,not(not(Y)))) )],[refute_0_699,refute_0_700]) ).
cnf(refute_0_702,plain,
not(not(or(X_94,not(not(Y))))) = or(X_94,Y),
inference(resolve,[$cnf( $equal(or(X_94,not(not(Y))),or(X_94,Y)) )],[refute_0_698,refute_0_701]) ).
cnf(refute_0_703,plain,
( implies(not(X_94),Y) != not(not(or(X_94,not(not(Y)))))
| not(not(or(X_94,not(not(Y))))) != or(X_94,Y)
| implies(not(X_94),Y) = or(X_94,Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(X_94),Y),or(X_94,Y)) ),[0],$fot(not(not(or(X_94,not(not(Y))))))]]) ).
cnf(refute_0_704,plain,
( implies(not(X_94),Y) != not(not(or(X_94,not(not(Y)))))
| implies(not(X_94),Y) = or(X_94,Y) ),
inference(resolve,[$cnf( $equal(not(not(or(X_94,not(not(Y))))),or(X_94,Y)) )],[refute_0_702,refute_0_703]) ).
cnf(refute_0_705,plain,
implies(not(X_94),Y) = or(X_94,Y),
inference(resolve,[$cnf( $equal(implies(not(X_94),Y),not(not(or(X_94,not(not(Y)))))) )],[refute_0_213,refute_0_704]) ).
cnf(refute_0_706,plain,
implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3) = or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3),
inference(subst,[],[refute_0_705:[bind(Y,$fot(skolemFOFtoCNF_Q_3)),bind(X_94,$fot(skolemFOFtoCNF_P_4))]]) ).
cnf(refute_0_707,plain,
implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)) = implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)),
introduced(tautology,[refl,[$fot(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)))]]) ).
cnf(refute_0_708,plain,
( implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3) != or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)
| implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)) != implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3))
| implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)) = implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)),implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3))) ),[1,1],$fot(or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_709,plain,
( implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3) != or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)
| implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)) = implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)) ),
inference(resolve,[$cnf( $equal(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)),implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3))) )],[refute_0_707,refute_0_708]) ).
cnf(refute_0_710,plain,
implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)) = implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)),
inference(resolve,[$cnf( $equal(implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3),or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)) )],[refute_0_706,refute_0_709]) ).
cnf(refute_0_711,plain,
( implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)) != implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3))
| ~ is_a_theorem(implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)))
| is_a_theorem(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3))) ),[0],$fot(implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)))]]) ).
cnf(refute_0_712,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)))
| is_a_theorem(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3))) ),
inference(resolve,[$cnf( $equal(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)),implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3))) )],[refute_0_710,refute_0_711]) ).
cnf(refute_0_713,plain,
~ is_a_theorem(implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3))),
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3))) )],[refute_0_712,refute_0_2]) ).
cnf(refute_0_714,plain,
( ~ is_a_theorem(or(implies(not(equiv(X_5092,X_5092)),X_5091),implies(not(equiv(X_5092,X_5092)),X_5091)))
| is_a_theorem(implies(not(equiv(X_5092,X_5092)),X_5091)) ),
inference(subst,[],[refute_0_69:[bind(X_171,$fot(implies(not(equiv(X_5092,X_5092)),X_5091)))]]) ).
cnf(refute_0_715,plain,
( ~ is_a_theorem(or(X_2845,equiv(X_2846,X_2846)))
| is_a_theorem(or(equiv(X_2846,X_2846),X_2845)) ),
inference(subst,[],[refute_0_61:[bind(P,$fot(X_2845)),bind(Q,$fot(equiv(X_2846,X_2846)))]]) ).
cnf(refute_0_716,plain,
( ~ is_a_theorem(equiv(X_2833,X_2833))
| is_a_theorem(or(P,equiv(X_2833,X_2833))) ),
inference(subst,[],[refute_0_220:[bind(X_170,$fot(equiv(X_2833,X_2833)))]]) ).
cnf(refute_0_717,plain,
( ~ is_a_theorem(X_176)
| ~ is_a_theorem(implies(X_176,and(X_176,X_176)))
| is_a_theorem(and(X_176,X_176)) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(X_176)),bind(Y,$fot(and(X_176,X_176)))]]) ).
cnf(refute_0_718,plain,
is_a_theorem(implies(X_176,and(X_176,X_176))),
inference(subst,[],[refute_0_240:[bind(X_5,$fot(X_176))]]) ).
cnf(refute_0_719,plain,
( ~ is_a_theorem(X_176)
| is_a_theorem(and(X_176,X_176)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_176,and(X_176,X_176))) )],[refute_0_718,refute_0_717]) ).
cnf(refute_0_720,plain,
( ~ is_a_theorem(implies(X_2832,X_2832))
| is_a_theorem(and(implies(X_2832,X_2832),implies(X_2832,X_2832))) ),
inference(subst,[],[refute_0_719:[bind(X_176,$fot(implies(X_2832,X_2832)))]]) ).
cnf(refute_0_721,plain,
is_a_theorem(and(implies(X_2832,X_2832),implies(X_2832,X_2832))),
inference(resolve,[$cnf( is_a_theorem(implies(X_2832,X_2832)) )],[refute_0_658,refute_0_720]) ).
cnf(refute_0_722,plain,
and(implies(X_2832,X_2832),implies(X_2832,X_2832)) = equiv(X_2832,X_2832),
inference(subst,[],[refute_0_489:[bind(X,$fot(X_2832)),bind(Y,$fot(X_2832))]]) ).
cnf(refute_0_723,plain,
( and(implies(X_2832,X_2832),implies(X_2832,X_2832)) != equiv(X_2832,X_2832)
| ~ is_a_theorem(and(implies(X_2832,X_2832),implies(X_2832,X_2832)))
| is_a_theorem(equiv(X_2832,X_2832)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(and(implies(X_2832,X_2832),implies(X_2832,X_2832))) ),[0],$fot(equiv(X_2832,X_2832))]]) ).
cnf(refute_0_724,plain,
( ~ is_a_theorem(and(implies(X_2832,X_2832),implies(X_2832,X_2832)))
| is_a_theorem(equiv(X_2832,X_2832)) ),
inference(resolve,[$cnf( $equal(and(implies(X_2832,X_2832),implies(X_2832,X_2832)),equiv(X_2832,X_2832)) )],[refute_0_722,refute_0_723]) ).
cnf(refute_0_725,plain,
is_a_theorem(equiv(X_2832,X_2832)),
inference(resolve,[$cnf( is_a_theorem(and(implies(X_2832,X_2832),implies(X_2832,X_2832))) )],[refute_0_721,refute_0_724]) ).
cnf(refute_0_726,plain,
is_a_theorem(equiv(X_2833,X_2833)),
inference(subst,[],[refute_0_725:[bind(X_2832,$fot(X_2833))]]) ).
cnf(refute_0_727,plain,
is_a_theorem(or(P,equiv(X_2833,X_2833))),
inference(resolve,[$cnf( is_a_theorem(equiv(X_2833,X_2833)) )],[refute_0_726,refute_0_716]) ).
cnf(refute_0_728,plain,
is_a_theorem(or(X_2845,equiv(X_2846,X_2846))),
inference(subst,[],[refute_0_727:[bind(P,$fot(X_2845)),bind(X_2833,$fot(X_2846))]]) ).
cnf(refute_0_729,plain,
is_a_theorem(or(equiv(X_2846,X_2846),X_2845)),
inference(resolve,[$cnf( is_a_theorem(or(X_2845,equiv(X_2846,X_2846))) )],[refute_0_728,refute_0_715]) ).
cnf(refute_0_730,plain,
is_a_theorem(or(equiv(X_2846,X_2846),or(X_5022,X_5023))),
inference(subst,[],[refute_0_729:[bind(X_2845,$fot(or(X_5022,X_5023)))]]) ).
cnf(refute_0_731,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_55:[bind(X,$fot(or(P,or(Q,R)))),bind(Y,$fot(or(Q,or(P,R))))]]) ).
cnf(refute_0_732,plain,
( ~ is_a_theorem(or(P,or(Q,R)))
| is_a_theorem(or(Q,or(P,R))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) )],[refute_0_85,refute_0_731]) ).
cnf(refute_0_733,plain,
( ~ is_a_theorem(or(equiv(X_2846,X_2846),or(X_5022,X_5023)))
| is_a_theorem(or(X_5022,or(equiv(X_2846,X_2846),X_5023))) ),
inference(subst,[],[refute_0_732:[bind(P,$fot(equiv(X_2846,X_2846))),bind(Q,$fot(X_5022)),bind(R,$fot(X_5023))]]) ).
cnf(refute_0_734,plain,
is_a_theorem(or(X_5022,or(equiv(X_2846,X_2846),X_5023))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(X_2846,X_2846),or(X_5022,X_5023))) )],[refute_0_730,refute_0_733]) ).
cnf(refute_0_735,plain,
is_a_theorem(or(X_5088,or(equiv(not(not(X_765)),not(not(X_765))),X_5089))),
inference(subst,[],[refute_0_734:[bind(X_2846,$fot(not(not(X_765)))),bind(X_5022,$fot(X_5088)),bind(X_5023,$fot(X_5089))]]) ).
cnf(refute_0_736,plain,
equiv(not(not(X_765)),not(not(X_765))) = not(not(equiv(X_765,X_765))),
inference(subst,[],[refute_0_513:[bind(X,$fot(X_765))]]) ).
cnf(refute_0_737,plain,
( equiv(not(not(X_765)),not(not(X_765))) != not(not(equiv(X_765,X_765)))
| ~ is_a_theorem(or(X_5088,or(equiv(not(not(X_765)),not(not(X_765))),X_5089)))
| is_a_theorem(or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_5088,or(equiv(not(not(X_765)),not(not(X_765))),X_5089))) ),[0,1,0],$fot(not(not(equiv(X_765,X_765))))]]) ).
cnf(refute_0_738,plain,
( ~ is_a_theorem(or(X_5088,or(equiv(not(not(X_765)),not(not(X_765))),X_5089)))
| is_a_theorem(or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089))) ),
inference(resolve,[$cnf( $equal(equiv(not(not(X_765)),not(not(X_765))),not(not(equiv(X_765,X_765)))) )],[refute_0_736,refute_0_737]) ).
cnf(refute_0_739,plain,
is_a_theorem(or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089))),
inference(resolve,[$cnf( is_a_theorem(or(X_5088,or(equiv(not(not(X_765)),not(not(X_765))),X_5089))) )],[refute_0_735,refute_0_738]) ).
cnf(refute_0_740,plain,
or(not(not(equiv(X_765,X_765))),X_5089) = implies(not(equiv(X_765,X_765)),X_5089),
inference(subst,[],[refute_0_17:[bind(X,$fot(not(equiv(X_765,X_765)))),bind(Y,$fot(X_5089))]]) ).
cnf(refute_0_741,plain,
or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089)) = or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089)),
introduced(tautology,[refl,[$fot(or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089)))]]) ).
cnf(refute_0_742,plain,
( or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089)) != or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089))
| or(not(not(equiv(X_765,X_765))),X_5089) != implies(not(equiv(X_765,X_765)),X_5089)
| or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089)) = or(X_5088,implies(not(equiv(X_765,X_765)),X_5089)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089)),or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089))) ),[1,1],$fot(implies(not(equiv(X_765,X_765)),X_5089))]]) ).
cnf(refute_0_743,plain,
( or(not(not(equiv(X_765,X_765))),X_5089) != implies(not(equiv(X_765,X_765)),X_5089)
| or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089)) = or(X_5088,implies(not(equiv(X_765,X_765)),X_5089)) ),
inference(resolve,[$cnf( $equal(or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089)),or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089))) )],[refute_0_741,refute_0_742]) ).
cnf(refute_0_744,plain,
or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089)) = or(X_5088,implies(not(equiv(X_765,X_765)),X_5089)),
inference(resolve,[$cnf( $equal(or(not(not(equiv(X_765,X_765))),X_5089),implies(not(equiv(X_765,X_765)),X_5089)) )],[refute_0_740,refute_0_743]) ).
cnf(refute_0_745,plain,
( or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089)) != or(X_5088,implies(not(equiv(X_765,X_765)),X_5089))
| ~ is_a_theorem(or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089)))
| is_a_theorem(or(X_5088,implies(not(equiv(X_765,X_765)),X_5089))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089))) ),[0],$fot(or(X_5088,implies(not(equiv(X_765,X_765)),X_5089)))]]) ).
cnf(refute_0_746,plain,
( ~ is_a_theorem(or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089)))
| is_a_theorem(or(X_5088,implies(not(equiv(X_765,X_765)),X_5089))) ),
inference(resolve,[$cnf( $equal(or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089)),or(X_5088,implies(not(equiv(X_765,X_765)),X_5089))) )],[refute_0_744,refute_0_745]) ).
cnf(refute_0_747,plain,
is_a_theorem(or(X_5088,implies(not(equiv(X_765,X_765)),X_5089))),
inference(resolve,[$cnf( is_a_theorem(or(X_5088,or(not(not(equiv(X_765,X_765))),X_5089))) )],[refute_0_739,refute_0_746]) ).
cnf(refute_0_748,plain,
is_a_theorem(or(implies(not(equiv(X_5092,X_5092)),X_5091),implies(not(equiv(X_5092,X_5092)),X_5091))),
inference(subst,[],[refute_0_747:[bind(X_5088,$fot(implies(not(equiv(X_5092,X_5092)),X_5091))),bind(X_5089,$fot(X_5091)),bind(X_765,$fot(X_5092))]]) ).
cnf(refute_0_749,plain,
is_a_theorem(implies(not(equiv(X_5092,X_5092)),X_5091)),
inference(resolve,[$cnf( is_a_theorem(or(implies(not(equiv(X_5092,X_5092)),X_5091),implies(not(equiv(X_5092,X_5092)),X_5091))) )],[refute_0_748,refute_0_714]) ).
cnf(refute_0_750,plain,
is_a_theorem(implies(not(equiv(X_5092,X_5092)),X_10144)),
inference(subst,[],[refute_0_749:[bind(X_5091,$fot(X_10144))]]) ).
cnf(refute_0_751,plain,
( ~ is_a_theorem(implies(not(equiv(X_5092,X_5092)),X_10144))
| is_a_theorem(implies(or(X_10142,not(equiv(X_5092,X_5092))),or(X_10142,X_10144))) ),
inference(subst,[],[refute_0_327:[bind(P,$fot(X_10142)),bind(Q,$fot(not(equiv(X_5092,X_5092)))),bind(R,$fot(X_10144))]]) ).
cnf(refute_0_752,plain,
is_a_theorem(implies(or(X_10142,not(equiv(X_5092,X_5092))),or(X_10142,X_10144))),
inference(resolve,[$cnf( is_a_theorem(implies(not(equiv(X_5092,X_5092)),X_10144)) )],[refute_0_750,refute_0_751]) ).
cnf(refute_0_753,plain,
is_a_theorem(implies(or(X_5092,not(equiv(X_5092,X_5092))),or(X_5092,X_10144))),
inference(subst,[],[refute_0_752:[bind(X_10142,$fot(X_5092))]]) ).
cnf(refute_0_754,plain,
( ~ is_a_theorem(equiv(or(X_35672,not(equiv(X_35672,X_35672))),X_35672))
| or(X_35672,not(equiv(X_35672,X_35672))) = X_35672 ),
inference(subst,[],[refute_0_51:[bind(X,$fot(or(X_35672,not(equiv(X_35672,X_35672))))),bind(Y,$fot(X_35672))]]) ).
cnf(refute_0_755,plain,
( ~ is_a_theorem(implies(implies(or(X_35671,not(equiv(X_35671,X_35671))),X_35671),equiv(or(X_35671,not(equiv(X_35671,X_35671))),X_35671)))
| ~ is_a_theorem(implies(or(X_35671,not(equiv(X_35671,X_35671))),X_35671))
| is_a_theorem(equiv(or(X_35671,not(equiv(X_35671,X_35671))),X_35671)) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(implies(or(X_35671,not(equiv(X_35671,X_35671))),X_35671))),bind(Y,$fot(equiv(or(X_35671,not(equiv(X_35671,X_35671))),X_35671)))]]) ).
cnf(refute_0_756,plain,
( ~ is_a_theorem(or(X_802,implies(implies(X_800,X_801),or(X_801,not(X_800)))))
| is_a_theorem(or(implies(implies(X_800,X_801),or(X_801,not(X_800))),X_802)) ),
inference(subst,[],[refute_0_61:[bind(P,$fot(X_802)),bind(Q,$fot(implies(implies(X_800,X_801),or(X_801,not(X_800)))))]]) ).
cnf(refute_0_757,plain,
( ~ is_a_theorem(implies(implies(X,X_16),or(X_16,not(X))))
| is_a_theorem(or(X_192,implies(implies(X,X_16),or(X_16,not(X))))) ),
inference(subst,[],[refute_0_220:[bind(P,$fot(X_192)),bind(X_170,$fot(implies(implies(X,X_16),or(X_16,not(X)))))]]) ).
cnf(refute_0_758,plain,
is_a_theorem(or(X_192,implies(implies(X,X_16),or(X_16,not(X))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,X_16),or(X_16,not(X)))) )],[refute_0_654,refute_0_757]) ).
cnf(refute_0_759,plain,
is_a_theorem(or(X_802,implies(implies(X_800,X_801),or(X_801,not(X_800))))),
inference(subst,[],[refute_0_758:[bind(X,$fot(X_800)),bind(X_16,$fot(X_801)),bind(X_192,$fot(X_802))]]) ).
cnf(refute_0_760,plain,
is_a_theorem(or(implies(implies(X_800,X_801),or(X_801,not(X_800))),X_802)),
inference(resolve,[$cnf( is_a_theorem(or(X_802,implies(implies(X_800,X_801),or(X_801,not(X_800))))) )],[refute_0_759,refute_0_756]) ).
cnf(refute_0_761,plain,
is_a_theorem(or(implies(implies(X_1044,not(X)),or(not(X),not(X_1044))),X_1046)),
inference(subst,[],[refute_0_760:[bind(X_800,$fot(X_1044)),bind(X_801,$fot(not(X))),bind(X_802,$fot(X_1046))]]) ).
cnf(refute_0_762,plain,
implies(X,not(X_1044)) = or(not(X),not(X_1044)),
inference(subst,[],[refute_0_12:[bind(Y,$fot(not(X_1044)))]]) ).
cnf(refute_0_763,plain,
( implies(X,not(X_1044)) != or(not(X),not(X_1044))
| or(not(X),not(X_1044)) = implies(X,not(X_1044)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,not(X_1044)))),bind(Y0,$fot(or(not(X),not(X_1044))))]]) ).
cnf(refute_0_764,plain,
or(not(X),not(X_1044)) = implies(X,not(X_1044)),
inference(resolve,[$cnf( $equal(implies(X,not(X_1044)),or(not(X),not(X_1044))) )],[refute_0_762,refute_0_763]) ).
cnf(refute_0_765,plain,
( or(not(X),not(X_1044)) != implies(X,not(X_1044))
| ~ is_a_theorem(or(implies(implies(X_1044,not(X)),or(not(X),not(X_1044))),X_1046))
| is_a_theorem(or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(implies(X_1044,not(X)),or(not(X),not(X_1044))),X_1046)) ),[0,0,1],$fot(implies(X,not(X_1044)))]]) ).
cnf(refute_0_766,plain,
( ~ is_a_theorem(or(implies(implies(X_1044,not(X)),or(not(X),not(X_1044))),X_1046))
| is_a_theorem(or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046)) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_1044)),implies(X,not(X_1044))) )],[refute_0_764,refute_0_765]) ).
cnf(refute_0_767,plain,
is_a_theorem(or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046)),
inference(resolve,[$cnf( is_a_theorem(or(implies(implies(X_1044,not(X)),or(not(X),not(X_1044))),X_1046)) )],[refute_0_761,refute_0_766]) ).
cnf(refute_0_768,plain,
implies(and(not(X_43),not(implies(X,not(Y)))),X_45) = or(or(X_43,implies(X,not(Y))),X_45),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_43)),bind(Y,$fot(implies(X,not(Y)))),bind(X_6,$fot(X_45))]]) ).
cnf(refute_0_769,plain,
( implies(and(not(X_43),not(implies(X,not(Y)))),X_45) != or(or(X_43,implies(X,not(Y))),X_45)
| not(implies(X,not(Y))) != and(X,Y)
| implies(and(not(X_43),and(X,Y)),X_45) = or(or(X_43,implies(X,not(Y))),X_45) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(not(X_43),not(implies(X,not(Y)))),X_45),or(or(X_43,implies(X,not(Y))),X_45)) ),[0,0,1],$fot(and(X,Y))]]) ).
cnf(refute_0_770,plain,
( implies(and(not(X_43),not(implies(X,not(Y)))),X_45) != or(or(X_43,implies(X,not(Y))),X_45)
| implies(and(not(X_43),and(X,Y)),X_45) = or(or(X_43,implies(X,not(Y))),X_45) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_283,refute_0_769]) ).
cnf(refute_0_771,plain,
implies(and(not(X_43),and(X,Y)),X_45) = or(or(X_43,implies(X,not(Y))),X_45),
inference(resolve,[$cnf( $equal(implies(and(not(X_43),not(implies(X,not(Y)))),X_45),or(or(X_43,implies(X,not(Y))),X_45)) )],[refute_0_768,refute_0_770]) ).
cnf(refute_0_772,plain,
( implies(and(not(X_43),and(X,Y)),X_45) != or(or(X_43,implies(X,not(Y))),X_45)
| or(or(X_43,implies(X,not(Y))),X_45) = implies(and(not(X_43),and(X,Y)),X_45) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(and(not(X_43),and(X,Y)),X_45))),bind(Y0,$fot(or(or(X_43,implies(X,not(Y))),X_45)))]]) ).
cnf(refute_0_773,plain,
or(or(X_43,implies(X,not(Y))),X_45) = implies(and(not(X_43),and(X,Y)),X_45),
inference(resolve,[$cnf( $equal(implies(and(not(X_43),and(X,Y)),X_45),or(or(X_43,implies(X,not(Y))),X_45)) )],[refute_0_771,refute_0_772]) ).
cnf(refute_0_774,plain,
or(or(and(X_1044,X),implies(X,not(X_1044))),X_1046) = implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1046),
inference(subst,[],[refute_0_773:[bind(Y,$fot(X_1044)),bind(X_43,$fot(and(X_1044,X))),bind(X_45,$fot(X_1046))]]) ).
cnf(refute_0_775,plain,
implies(implies(X_1044,not(X)),implies(X,not(X_1044))) = or(and(X_1044,X),implies(X,not(X_1044))),
inference(subst,[],[refute_0_164:[bind(Y,$fot(implies(X,not(X_1044)))),bind(X_10,$fot(X_1044)),bind(X_11,$fot(X))]]) ).
cnf(refute_0_776,plain,
or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046) = or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046),
introduced(tautology,[refl,[$fot(or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046))]]) ).
cnf(refute_0_777,plain,
( implies(implies(X_1044,not(X)),implies(X,not(X_1044))) != or(and(X_1044,X),implies(X,not(X_1044)))
| or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046) != or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046)
| or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046) = or(or(and(X_1044,X),implies(X,not(X_1044))),X_1046) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046),or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046)) ),[1,0],$fot(or(and(X_1044,X),implies(X,not(X_1044))))]]) ).
cnf(refute_0_778,plain,
( implies(implies(X_1044,not(X)),implies(X,not(X_1044))) != or(and(X_1044,X),implies(X,not(X_1044)))
| or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046) = or(or(and(X_1044,X),implies(X,not(X_1044))),X_1046) ),
inference(resolve,[$cnf( $equal(or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046),or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046)) )],[refute_0_776,refute_0_777]) ).
cnf(refute_0_779,plain,
or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046) = or(or(and(X_1044,X),implies(X,not(X_1044))),X_1046),
inference(resolve,[$cnf( $equal(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),or(and(X_1044,X),implies(X,not(X_1044)))) )],[refute_0_775,refute_0_778]) ).
cnf(refute_0_780,plain,
( or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046) != or(or(and(X_1044,X),implies(X,not(X_1044))),X_1046)
| or(or(and(X_1044,X),implies(X,not(X_1044))),X_1046) != implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1046)
| or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046) = implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1046) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046))),bind(Y0,$fot(or(or(and(X_1044,X),implies(X,not(X_1044))),X_1046))),bind(Z,$fot(implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1046)))]]) ).
cnf(refute_0_781,plain,
( or(or(and(X_1044,X),implies(X,not(X_1044))),X_1046) != implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1046)
| or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046) = implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1046) ),
inference(resolve,[$cnf( $equal(or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046),or(or(and(X_1044,X),implies(X,not(X_1044))),X_1046)) )],[refute_0_779,refute_0_780]) ).
cnf(refute_0_782,plain,
or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046) = implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1046),
inference(resolve,[$cnf( $equal(or(or(and(X_1044,X),implies(X,not(X_1044))),X_1046),implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1046)) )],[refute_0_774,refute_0_781]) ).
cnf(refute_0_783,plain,
( or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046) != implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1046)
| ~ is_a_theorem(or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046))
| is_a_theorem(implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1046)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046)) ),[0],$fot(implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1046))]]) ).
cnf(refute_0_784,plain,
( ~ is_a_theorem(or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046))
| is_a_theorem(implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1046)) ),
inference(resolve,[$cnf( $equal(or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046),implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1046)) )],[refute_0_782,refute_0_783]) ).
cnf(refute_0_785,plain,
is_a_theorem(implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1046)),
inference(resolve,[$cnf( is_a_theorem(or(implies(implies(X_1044,not(X)),implies(X,not(X_1044))),X_1046)) )],[refute_0_767,refute_0_784]) ).
cnf(refute_0_786,plain,
is_a_theorem(implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1436)),
inference(subst,[],[refute_0_785:[bind(X_1046,$fot(X_1436))]]) ).
cnf(refute_0_787,plain,
( ~ is_a_theorem(implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1436))
| is_a_theorem(implies(implies(X_1434,and(not(and(X_1044,X)),and(X,X_1044))),implies(X_1434,X_1436))) ),
inference(subst,[],[refute_0_265:[bind(X,$fot(X_1434)),bind(X_39,$fot(and(not(and(X_1044,X)),and(X,X_1044)))),bind(X_40,$fot(X_1436))]]) ).
cnf(refute_0_788,plain,
is_a_theorem(implies(implies(X_1434,and(not(and(X_1044,X)),and(X,X_1044))),implies(X_1434,X_1436))),
inference(resolve,[$cnf( is_a_theorem(implies(and(not(and(X_1044,X)),and(X,X_1044)),X_1436)) )],[refute_0_786,refute_0_787]) ).
cnf(refute_0_789,plain,
is_a_theorem(implies(implies(X_1479,and(not(and(not(X),not(Y))),and(not(Y),not(X)))),implies(X_1479,X_1480))),
inference(subst,[],[refute_0_788:[bind(X,$fot(not(Y))),bind(X_1044,$fot(not(X))),bind(X_1434,$fot(X_1479)),bind(X_1436,$fot(X_1480))]]) ).
cnf(refute_0_790,plain,
( not(and(not(X),not(Y))) != or(X,Y)
| ~ is_a_theorem(implies(implies(X_1479,and(not(and(not(X),not(Y))),and(not(Y),not(X)))),implies(X_1479,X_1480)))
| is_a_theorem(implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_1479,and(not(and(not(X),not(Y))),and(not(Y),not(X)))),implies(X_1479,X_1480))) ),[0,0,1,0],$fot(or(X,Y))]]) ).
cnf(refute_0_791,plain,
( ~ is_a_theorem(implies(implies(X_1479,and(not(and(not(X),not(Y))),and(not(Y),not(X)))),implies(X_1479,X_1480)))
| is_a_theorem(implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480))) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),or(X,Y)) )],[refute_0_36,refute_0_790]) ).
cnf(refute_0_792,plain,
is_a_theorem(implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1479,and(not(and(not(X),not(Y))),and(not(Y),not(X)))),implies(X_1479,X_1480))) )],[refute_0_789,refute_0_791]) ).
cnf(refute_0_793,plain,
implies(implies(X_1479,not(implies(or(X,Y),or(Y,X)))),implies(X_1479,X_1480)) = or(and(X_1479,implies(or(X,Y),or(Y,X))),implies(X_1479,X_1480)),
inference(subst,[],[refute_0_164:[bind(Y,$fot(implies(X_1479,X_1480))),bind(X_10,$fot(X_1479)),bind(X_11,$fot(implies(or(X,Y),or(Y,X))))]]) ).
cnf(refute_0_794,plain,
and(X_10,and(not(X),not(Y))) = not(implies(X_10,not(and(not(X),not(Y))))),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_10)),bind(Y,$fot(and(not(X),not(Y))))]]) ).
cnf(refute_0_795,plain,
( and(X_10,and(not(X),not(Y))) != not(implies(X_10,not(and(not(X),not(Y)))))
| not(and(not(X),not(Y))) != or(X,Y)
| and(X_10,and(not(X),not(Y))) = not(implies(X_10,or(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_10,and(not(X),not(Y))),not(implies(X_10,not(and(not(X),not(Y)))))) ),[1,0,1],$fot(or(X,Y))]]) ).
cnf(refute_0_796,plain,
( and(X_10,and(not(X),not(Y))) != not(implies(X_10,not(and(not(X),not(Y)))))
| and(X_10,and(not(X),not(Y))) = not(implies(X_10,or(X,Y))) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),or(X,Y)) )],[refute_0_36,refute_0_795]) ).
cnf(refute_0_797,plain,
and(X_10,and(not(X),not(Y))) = not(implies(X_10,or(X,Y))),
inference(resolve,[$cnf( $equal(and(X_10,and(not(X),not(Y))),not(implies(X_10,not(and(not(X),not(Y)))))) )],[refute_0_794,refute_0_796]) ).
cnf(refute_0_798,plain,
and(or(X,Y),and(not(Y),not(X))) = not(implies(or(X,Y),or(Y,X))),
inference(subst,[],[refute_0_797:[bind(X,$fot(Y)),bind(Y,$fot(X)),bind(X_10,$fot(or(X,Y)))]]) ).
cnf(refute_0_799,plain,
implies(X_1479,and(or(X,Y),and(not(Y),not(X)))) = implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),
introduced(tautology,[refl,[$fot(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))))]]) ).
cnf(refute_0_800,plain,
( and(or(X,Y),and(not(Y),not(X))) != not(implies(or(X,Y),or(Y,X)))
| implies(X_1479,and(or(X,Y),and(not(Y),not(X)))) != implies(X_1479,and(or(X,Y),and(not(Y),not(X))))
| implies(X_1479,and(or(X,Y),and(not(Y),not(X)))) = implies(X_1479,not(implies(or(X,Y),or(Y,X)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,and(or(X,Y),and(not(Y),not(X))))) ),[1,1],$fot(not(implies(or(X,Y),or(Y,X))))]]) ).
cnf(refute_0_801,plain,
( and(or(X,Y),and(not(Y),not(X))) != not(implies(or(X,Y),or(Y,X)))
| implies(X_1479,and(or(X,Y),and(not(Y),not(X)))) = implies(X_1479,not(implies(or(X,Y),or(Y,X)))) ),
inference(resolve,[$cnf( $equal(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,and(or(X,Y),and(not(Y),not(X))))) )],[refute_0_799,refute_0_800]) ).
cnf(refute_0_802,plain,
implies(X_1479,and(or(X,Y),and(not(Y),not(X)))) = implies(X_1479,not(implies(or(X,Y),or(Y,X)))),
inference(resolve,[$cnf( $equal(and(or(X,Y),and(not(Y),not(X))),not(implies(or(X,Y),or(Y,X)))) )],[refute_0_798,refute_0_801]) ).
cnf(refute_0_803,plain,
implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)) = implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)),
introduced(tautology,[refl,[$fot(implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)))]]) ).
cnf(refute_0_804,plain,
( implies(X_1479,and(or(X,Y),and(not(Y),not(X)))) != implies(X_1479,not(implies(or(X,Y),or(Y,X))))
| implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)) != implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480))
| implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)) = implies(implies(X_1479,not(implies(or(X,Y),or(Y,X)))),implies(X_1479,X_1480)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)),implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480))) ),[1,0],$fot(implies(X_1479,not(implies(or(X,Y),or(Y,X)))))]]) ).
cnf(refute_0_805,plain,
( implies(X_1479,and(or(X,Y),and(not(Y),not(X)))) != implies(X_1479,not(implies(or(X,Y),or(Y,X))))
| implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)) = implies(implies(X_1479,not(implies(or(X,Y),or(Y,X)))),implies(X_1479,X_1480)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)),implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480))) )],[refute_0_803,refute_0_804]) ).
cnf(refute_0_806,plain,
implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)) = implies(implies(X_1479,not(implies(or(X,Y),or(Y,X)))),implies(X_1479,X_1480)),
inference(resolve,[$cnf( $equal(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,not(implies(or(X,Y),or(Y,X))))) )],[refute_0_802,refute_0_805]) ).
cnf(refute_0_807,plain,
( implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)) != implies(implies(X_1479,not(implies(or(X,Y),or(Y,X)))),implies(X_1479,X_1480))
| implies(implies(X_1479,not(implies(or(X,Y),or(Y,X)))),implies(X_1479,X_1480)) != or(and(X_1479,implies(or(X,Y),or(Y,X))),implies(X_1479,X_1480))
| implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)) = or(and(X_1479,implies(or(X,Y),or(Y,X))),implies(X_1479,X_1480)) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)))),bind(Y0,$fot(implies(implies(X_1479,not(implies(or(X,Y),or(Y,X)))),implies(X_1479,X_1480)))),bind(Z,$fot(or(and(X_1479,implies(or(X,Y),or(Y,X))),implies(X_1479,X_1480))))]]) ).
cnf(refute_0_808,plain,
( implies(implies(X_1479,not(implies(or(X,Y),or(Y,X)))),implies(X_1479,X_1480)) != or(and(X_1479,implies(or(X,Y),or(Y,X))),implies(X_1479,X_1480))
| implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)) = or(and(X_1479,implies(or(X,Y),or(Y,X))),implies(X_1479,X_1480)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)),implies(implies(X_1479,not(implies(or(X,Y),or(Y,X)))),implies(X_1479,X_1480))) )],[refute_0_806,refute_0_807]) ).
cnf(refute_0_809,plain,
implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)) = or(and(X_1479,implies(or(X,Y),or(Y,X))),implies(X_1479,X_1480)),
inference(resolve,[$cnf( $equal(implies(implies(X_1479,not(implies(or(X,Y),or(Y,X)))),implies(X_1479,X_1480)),or(and(X_1479,implies(or(X,Y),or(Y,X))),implies(X_1479,X_1480))) )],[refute_0_793,refute_0_808]) ).
cnf(refute_0_810,plain,
( implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)) != or(and(X_1479,implies(or(X,Y),or(Y,X))),implies(X_1479,X_1480))
| ~ is_a_theorem(implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)))
| is_a_theorem(or(and(X_1479,implies(or(X,Y),or(Y,X))),implies(X_1479,X_1480))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480))) ),[0],$fot(or(and(X_1479,implies(or(X,Y),or(Y,X))),implies(X_1479,X_1480)))]]) ).
cnf(refute_0_811,plain,
( ~ is_a_theorem(implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)))
| is_a_theorem(or(and(X_1479,implies(or(X,Y),or(Y,X))),implies(X_1479,X_1480))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480)),or(and(X_1479,implies(or(X,Y),or(Y,X))),implies(X_1479,X_1480))) )],[refute_0_809,refute_0_810]) ).
cnf(refute_0_812,plain,
is_a_theorem(or(and(X_1479,implies(or(X,Y),or(Y,X))),implies(X_1479,X_1480))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1479,and(or(X,Y),and(not(Y),not(X)))),implies(X_1479,X_1480))) )],[refute_0_792,refute_0_811]) ).
cnf(refute_0_813,plain,
is_a_theorem(or(and(X_4148,implies(or(X,Y),or(Y,X))),implies(X_4148,X_4150))),
inference(subst,[],[refute_0_812:[bind(X_1479,$fot(X_4148)),bind(X_1480,$fot(X_4150))]]) ).
cnf(refute_0_814,plain,
is_a_theorem(implies(or(X_71,or(not(X),X_73)),or(not(X),or(X_71,X_73)))),
inference(subst,[],[refute_0_85:[bind(P,$fot(X_71)),bind(Q,$fot(not(X))),bind(R,$fot(X_73))]]) ).
cnf(refute_0_815,plain,
implies(X,or(X_71,X_73)) = or(not(X),or(X_71,X_73)),
inference(subst,[],[refute_0_12:[bind(Y,$fot(or(X_71,X_73)))]]) ).
cnf(refute_0_816,plain,
( implies(X,or(X_71,X_73)) != or(not(X),or(X_71,X_73))
| or(not(X),or(X_71,X_73)) = implies(X,or(X_71,X_73)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,or(X_71,X_73)))),bind(Y0,$fot(or(not(X),or(X_71,X_73))))]]) ).
cnf(refute_0_817,plain,
or(not(X),or(X_71,X_73)) = implies(X,or(X_71,X_73)),
inference(resolve,[$cnf( $equal(implies(X,or(X_71,X_73)),or(not(X),or(X_71,X_73))) )],[refute_0_815,refute_0_816]) ).
cnf(refute_0_818,plain,
( or(not(X),or(X_71,X_73)) != implies(X,or(X_71,X_73))
| ~ is_a_theorem(implies(or(X_71,or(not(X),X_73)),or(not(X),or(X_71,X_73))))
| is_a_theorem(implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_71,or(not(X),X_73)),or(not(X),or(X_71,X_73)))) ),[0,1],$fot(implies(X,or(X_71,X_73)))]]) ).
cnf(refute_0_819,plain,
( ~ is_a_theorem(implies(or(X_71,or(not(X),X_73)),or(not(X),or(X_71,X_73))))
| is_a_theorem(implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_71,X_73)),implies(X,or(X_71,X_73))) )],[refute_0_817,refute_0_818]) ).
cnf(refute_0_820,plain,
is_a_theorem(implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_71,or(not(X),X_73)),or(not(X),or(X_71,X_73)))) )],[refute_0_814,refute_0_819]) ).
cnf(refute_0_821,plain,
or(X_71,or(not(X),X_73)) = or(X_71,or(not(X),X_73)),
introduced(tautology,[refl,[$fot(or(X_71,or(not(X),X_73)))]]) ).
cnf(refute_0_822,plain,
( or(X_71,or(not(X),X_73)) != or(X_71,or(not(X),X_73))
| or(not(X),X_73) != implies(X,X_73)
| or(X_71,or(not(X),X_73)) = or(X_71,implies(X,X_73)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_71,or(not(X),X_73)),or(X_71,or(not(X),X_73))) ),[1,1],$fot(implies(X,X_73))]]) ).
cnf(refute_0_823,plain,
( or(not(X),X_73) != implies(X,X_73)
| or(X_71,or(not(X),X_73)) = or(X_71,implies(X,X_73)) ),
inference(resolve,[$cnf( $equal(or(X_71,or(not(X),X_73)),or(X_71,or(not(X),X_73))) )],[refute_0_821,refute_0_822]) ).
cnf(refute_0_824,plain,
or(X_71,or(not(X),X_73)) = or(X_71,implies(X,X_73)),
inference(resolve,[$cnf( $equal(or(not(X),X_73),implies(X,X_73)) )],[refute_0_89,refute_0_823]) ).
cnf(refute_0_825,plain,
implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73))) = implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73))),
introduced(tautology,[refl,[$fot(implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73))))]]) ).
cnf(refute_0_826,plain,
( implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73))) != implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73)))
| or(X_71,or(not(X),X_73)) != or(X_71,implies(X,X_73))
| implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73))) = implies(or(X_71,implies(X,X_73)),implies(X,or(X_71,X_73))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73))),implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73)))) ),[1,0],$fot(or(X_71,implies(X,X_73)))]]) ).
cnf(refute_0_827,plain,
( or(X_71,or(not(X),X_73)) != or(X_71,implies(X,X_73))
| implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73))) = implies(or(X_71,implies(X,X_73)),implies(X,or(X_71,X_73))) ),
inference(resolve,[$cnf( $equal(implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73))),implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73)))) )],[refute_0_825,refute_0_826]) ).
cnf(refute_0_828,plain,
implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73))) = implies(or(X_71,implies(X,X_73)),implies(X,or(X_71,X_73))),
inference(resolve,[$cnf( $equal(or(X_71,or(not(X),X_73)),or(X_71,implies(X,X_73))) )],[refute_0_824,refute_0_827]) ).
cnf(refute_0_829,plain,
( implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73))) != implies(or(X_71,implies(X,X_73)),implies(X,or(X_71,X_73)))
| ~ is_a_theorem(implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73))))
| is_a_theorem(implies(or(X_71,implies(X,X_73)),implies(X,or(X_71,X_73)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73)))) ),[0],$fot(implies(or(X_71,implies(X,X_73)),implies(X,or(X_71,X_73))))]]) ).
cnf(refute_0_830,plain,
( ~ is_a_theorem(implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73))))
| is_a_theorem(implies(or(X_71,implies(X,X_73)),implies(X,or(X_71,X_73)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73))),implies(or(X_71,implies(X,X_73)),implies(X,or(X_71,X_73)))) )],[refute_0_828,refute_0_829]) ).
cnf(refute_0_831,plain,
is_a_theorem(implies(or(X_71,implies(X,X_73)),implies(X,or(X_71,X_73)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_71,or(not(X),X_73)),implies(X,or(X_71,X_73)))) )],[refute_0_820,refute_0_830]) ).
cnf(refute_0_832,plain,
( ~ is_a_theorem(implies(or(X_71,implies(X,X_73)),implies(X,or(X_71,X_73))))
| ~ is_a_theorem(or(X_71,implies(X,X_73)))
| is_a_theorem(implies(X,or(X_71,X_73))) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(or(X_71,implies(X,X_73)))),bind(Y,$fot(implies(X,or(X_71,X_73))))]]) ).
cnf(refute_0_833,plain,
( ~ is_a_theorem(or(X_71,implies(X,X_73)))
| is_a_theorem(implies(X,or(X_71,X_73))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_71,implies(X,X_73)),implies(X,or(X_71,X_73)))) )],[refute_0_831,refute_0_832]) ).
cnf(refute_0_834,plain,
( ~ is_a_theorem(or(and(X_4148,implies(or(X,Y),or(Y,X))),implies(X_4148,X_4150)))
| is_a_theorem(implies(X_4148,or(and(X_4148,implies(or(X,Y),or(Y,X))),X_4150))) ),
inference(subst,[],[refute_0_833:[bind(X,$fot(X_4148)),bind(X_71,$fot(and(X_4148,implies(or(X,Y),or(Y,X))))),bind(X_73,$fot(X_4150))]]) ).
cnf(refute_0_835,plain,
is_a_theorem(implies(X_4148,or(and(X_4148,implies(or(X,Y),or(Y,X))),X_4150))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_4148,implies(or(X,Y),or(Y,X))),implies(X_4148,X_4150))) )],[refute_0_813,refute_0_834]) ).
cnf(refute_0_836,plain,
is_a_theorem(implies(X_35605,or(and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603))),and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603)))))),
inference(subst,[],[refute_0_835:[bind(X,$fot(X_35603)),bind(Y,$fot(X_35604)),bind(X_4148,$fot(X_35605)),bind(X_4150,$fot(and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603)))))]]) ).
cnf(refute_0_837,plain,
or(and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603))),and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603)))) = and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603))),
inference(subst,[],[refute_0_190:[bind(X_27414,$fot(and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603)))))]]) ).
cnf(refute_0_838,plain,
( or(and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603))),and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603)))) != and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603)))
| ~ is_a_theorem(implies(X_35605,or(and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603))),and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603))))))
| is_a_theorem(implies(X_35605,and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_35605,or(and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603))),and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603)))))) ),[0,1],$fot(and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603))))]]) ).
cnf(refute_0_839,plain,
( ~ is_a_theorem(implies(X_35605,or(and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603))),and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603))))))
| is_a_theorem(implies(X_35605,and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603))))) ),
inference(resolve,[$cnf( $equal(or(and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603))),and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603)))),and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603)))) )],[refute_0_837,refute_0_838]) ).
cnf(refute_0_840,plain,
is_a_theorem(implies(X_35605,and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_35605,or(and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603))),and(X_35605,implies(or(X_35603,X_35604),or(X_35604,X_35603)))))) )],[refute_0_836,refute_0_839]) ).
cnf(refute_0_841,plain,
is_a_theorem(implies(X_35609,and(X_35609,implies(or(not(X),X_35608),or(X_35608,not(X)))))),
inference(subst,[],[refute_0_840:[bind(X_35603,$fot(not(X))),bind(X_35604,$fot(X_35608)),bind(X_35605,$fot(X_35609))]]) ).
cnf(refute_0_842,plain,
implies(X,X_35608) = or(not(X),X_35608),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_35608))]]) ).
cnf(refute_0_843,plain,
( implies(X,X_35608) != or(not(X),X_35608)
| or(not(X),X_35608) = implies(X,X_35608) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_35608))),bind(Y0,$fot(or(not(X),X_35608)))]]) ).
cnf(refute_0_844,plain,
or(not(X),X_35608) = implies(X,X_35608),
inference(resolve,[$cnf( $equal(implies(X,X_35608),or(not(X),X_35608)) )],[refute_0_842,refute_0_843]) ).
cnf(refute_0_845,plain,
( or(not(X),X_35608) != implies(X,X_35608)
| ~ is_a_theorem(implies(X_35609,and(X_35609,implies(or(not(X),X_35608),or(X_35608,not(X))))))
| is_a_theorem(implies(X_35609,and(X_35609,implies(implies(X,X_35608),or(X_35608,not(X)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_35609,and(X_35609,implies(or(not(X),X_35608),or(X_35608,not(X)))))) ),[0,1,1,0],$fot(implies(X,X_35608))]]) ).
cnf(refute_0_846,plain,
( ~ is_a_theorem(implies(X_35609,and(X_35609,implies(or(not(X),X_35608),or(X_35608,not(X))))))
| is_a_theorem(implies(X_35609,and(X_35609,implies(implies(X,X_35608),or(X_35608,not(X)))))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_35608),implies(X,X_35608)) )],[refute_0_844,refute_0_845]) ).
cnf(refute_0_847,plain,
is_a_theorem(implies(X_35609,and(X_35609,implies(implies(X,X_35608),or(X_35608,not(X)))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_35609,and(X_35609,implies(or(not(X),X_35608),or(X_35608,not(X)))))) )],[refute_0_841,refute_0_846]) ).
cnf(refute_0_848,plain,
is_a_theorem(implies(X_35660,and(X_35660,implies(implies(equiv(X_35659,X_35659),X_35659),or(X_35659,not(equiv(X_35659,X_35659))))))),
inference(subst,[],[refute_0_847:[bind(X,$fot(equiv(X_35659,X_35659))),bind(X_35608,$fot(X_35659)),bind(X_35609,$fot(X_35660))]]) ).
cnf(refute_0_849,plain,
( ~ is_a_theorem(equiv(X_33610,implies(or(X_33610,not(X_33610)),X_33610)))
| X_33610 = implies(or(X_33610,not(X_33610)),X_33610) ),
inference(subst,[],[refute_0_51:[bind(X,$fot(X_33610)),bind(Y,$fot(implies(or(X_33610,not(X_33610)),X_33610)))]]) ).
cnf(refute_0_850,plain,
( ~ is_a_theorem(implies(implies(implies(or(X_33609,not(X_33609)),X_33609),X_33609),equiv(X_33609,implies(or(X_33609,not(X_33609)),X_33609))))
| ~ is_a_theorem(implies(implies(or(X_33609,not(X_33609)),X_33609),X_33609))
| is_a_theorem(equiv(X_33609,implies(or(X_33609,not(X_33609)),X_33609))) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(implies(implies(or(X_33609,not(X_33609)),X_33609),X_33609))),bind(Y,$fot(equiv(X_33609,implies(or(X_33609,not(X_33609)),X_33609))))]]) ).
cnf(refute_0_851,plain,
( ~ is_a_theorem(implies(implies(implies(X_33138,or(and(not(X_33138),X_33138),X_33138)),X_33139),X_33139))
| is_a_theorem(or(X_33139,not(implies(implies(X_33138,or(and(not(X_33138),X_33138),X_33138)),X_33139)))) ),
inference(subst,[],[refute_0_656:[bind(X,$fot(implies(implies(X_33138,or(and(not(X_33138),X_33138),X_33138)),X_33139))),bind(X_16,$fot(X_33139))]]) ).
cnf(refute_0_852,plain,
( ~ is_a_theorem(implies(or(X_32642,X_32641),or(and(not(X_32641),X_32642),X_32641)))
| is_a_theorem(implies(implies(implies(or(X_32642,X_32641),or(and(not(X_32641),X_32642),X_32641)),X_3654),X_3654)) ),
inference(subst,[],[refute_0_157:[bind(X_3653,$fot(implies(or(X_32642,X_32641),or(and(not(X_32641),X_32642),X_32641))))]]) ).
cnf(refute_0_853,plain,
is_a_theorem(implies(implies(X_104,not(X_11)),implies(implies(X_103,X_104),implies(X_103,not(X_11))))),
inference(subst,[],[refute_0_263:[bind(X,$fot(X_103)),bind(X_39,$fot(X_104)),bind(X_40,$fot(not(X_11)))]]) ).
cnf(refute_0_854,plain,
implies(implies(X_104,not(X_11)),implies(implies(X_103,X_104),implies(X_103,not(X_11)))) = or(and(X_104,X_11),implies(implies(X_103,X_104),implies(X_103,not(X_11)))),
inference(subst,[],[refute_0_164:[bind(Y,$fot(implies(implies(X_103,X_104),implies(X_103,not(X_11))))),bind(X_10,$fot(X_104))]]) ).
cnf(refute_0_855,plain,
( implies(implies(X_104,not(X_11)),implies(implies(X_103,X_104),implies(X_103,not(X_11)))) != or(and(X_104,X_11),implies(implies(X_103,X_104),implies(X_103,not(X_11))))
| ~ is_a_theorem(implies(implies(X_104,not(X_11)),implies(implies(X_103,X_104),implies(X_103,not(X_11)))))
| is_a_theorem(or(and(X_104,X_11),implies(implies(X_103,X_104),implies(X_103,not(X_11))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_104,not(X_11)),implies(implies(X_103,X_104),implies(X_103,not(X_11))))) ),[0],$fot(or(and(X_104,X_11),implies(implies(X_103,X_104),implies(X_103,not(X_11)))))]]) ).
cnf(refute_0_856,plain,
( ~ is_a_theorem(implies(implies(X_104,not(X_11)),implies(implies(X_103,X_104),implies(X_103,not(X_11)))))
| is_a_theorem(or(and(X_104,X_11),implies(implies(X_103,X_104),implies(X_103,not(X_11))))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_104,not(X_11)),implies(implies(X_103,X_104),implies(X_103,not(X_11)))),or(and(X_104,X_11),implies(implies(X_103,X_104),implies(X_103,not(X_11))))) )],[refute_0_854,refute_0_855]) ).
cnf(refute_0_857,plain,
is_a_theorem(or(and(X_104,X_11),implies(implies(X_103,X_104),implies(X_103,not(X_11))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_104,not(X_11)),implies(implies(X_103,X_104),implies(X_103,not(X_11))))) )],[refute_0_853,refute_0_856]) ).
cnf(refute_0_858,plain,
is_a_theorem(or(and(and(not(X_43),not(X_44)),X_144),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))),
inference(subst,[],[refute_0_857:[bind(X_103,$fot(X_142)),bind(X_104,$fot(and(not(X_43),not(X_44)))),bind(X_11,$fot(X_144))]]) ).
cnf(refute_0_859,plain,
and(and(not(X_43),not(X_44)),X_144) = not(or(or(X_43,X_44),not(X_144))),
inference(subst,[],[refute_0_43:[bind(Y,$fot(X_144))]]) ).
cnf(refute_0_860,plain,
( and(and(not(X_43),not(X_44)),X_144) != not(or(or(X_43,X_44),not(X_144)))
| ~ is_a_theorem(or(and(and(not(X_43),not(X_44)),X_144),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))))
| is_a_theorem(or(not(or(or(X_43,X_44),not(X_144))),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(and(not(X_43),not(X_44)),X_144),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))) ),[0,0],$fot(not(or(or(X_43,X_44),not(X_144))))]]) ).
cnf(refute_0_861,plain,
( ~ is_a_theorem(or(and(and(not(X_43),not(X_44)),X_144),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))))
| is_a_theorem(or(not(or(or(X_43,X_44),not(X_144))),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))) ),
inference(resolve,[$cnf( $equal(and(and(not(X_43),not(X_44)),X_144),not(or(or(X_43,X_44),not(X_144)))) )],[refute_0_859,refute_0_860]) ).
cnf(refute_0_862,plain,
is_a_theorem(or(not(or(or(X_43,X_44),not(X_144))),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))),
inference(resolve,[$cnf( is_a_theorem(or(and(and(not(X_43),not(X_44)),X_144),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))) )],[refute_0_858,refute_0_861]) ).
cnf(refute_0_863,plain,
or(not(or(or(X_43,X_44),not(X_144))),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))) = implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))),
inference(subst,[],[refute_0_17:[bind(X,$fot(or(or(X_43,X_44),not(X_144)))),bind(Y,$fot(implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))))]]) ).
cnf(refute_0_864,plain,
( or(not(or(or(X_43,X_44),not(X_144))),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))) != implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))
| ~ is_a_theorem(or(not(or(or(X_43,X_44),not(X_144))),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))))
| is_a_theorem(implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(or(or(X_43,X_44),not(X_144))),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))) ),[0],$fot(implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))))]]) ).
cnf(refute_0_865,plain,
( ~ is_a_theorem(or(not(or(or(X_43,X_44),not(X_144))),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))))
| is_a_theorem(implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))) ),
inference(resolve,[$cnf( $equal(or(not(or(or(X_43,X_44),not(X_144))),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))),implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))) )],[refute_0_863,refute_0_864]) ).
cnf(refute_0_866,plain,
is_a_theorem(implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))),
inference(resolve,[$cnf( is_a_theorem(or(not(or(or(X_43,X_44),not(X_144))),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))) )],[refute_0_862,refute_0_865]) ).
cnf(refute_0_867,plain,
implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144))) = or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144))),
inference(subst,[],[refute_0_705:[bind(Y,$fot(not(and(X_142,X_144)))),bind(X_94,$fot(and(X_142,or(X_43,X_44))))]]) ).
cnf(refute_0_868,plain,
or(implies(X_47,not(X_48)),implies(X,not(Y))) = not(and(and(X_47,X_48),not(implies(X,not(Y))))),
inference(subst,[],[refute_0_31:[bind(Y,$fot(implies(X,not(Y)))),bind(X_10,$fot(X_47)),bind(X_11,$fot(X_48))]]) ).
cnf(refute_0_869,plain,
( not(implies(X,not(Y))) != and(X,Y)
| or(implies(X_47,not(X_48)),implies(X,not(Y))) != not(and(and(X_47,X_48),not(implies(X,not(Y)))))
| or(implies(X_47,not(X_48)),implies(X,not(Y))) = not(and(and(X_47,X_48),and(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(X_47,not(X_48)),implies(X,not(Y))),not(and(and(X_47,X_48),not(implies(X,not(Y)))))) ),[1,0,1],$fot(and(X,Y))]]) ).
cnf(refute_0_870,plain,
( or(implies(X_47,not(X_48)),implies(X,not(Y))) != not(and(and(X_47,X_48),not(implies(X,not(Y)))))
| or(implies(X_47,not(X_48)),implies(X,not(Y))) = not(and(and(X_47,X_48),and(X,Y))) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_283,refute_0_869]) ).
cnf(refute_0_871,plain,
or(implies(X_47,not(X_48)),implies(X,not(Y))) = not(and(and(X_47,X_48),and(X,Y))),
inference(resolve,[$cnf( $equal(or(implies(X_47,not(X_48)),implies(X,not(Y))),not(and(and(X_47,X_48),not(implies(X,not(Y)))))) )],[refute_0_868,refute_0_870]) ).
cnf(refute_0_872,plain,
or(implies(X,not(Y)),implies(X,not(Y))) = not(and(and(X,Y),and(X,Y))),
inference(subst,[],[refute_0_871:[bind(X_47,$fot(X)),bind(X_48,$fot(Y))]]) ).
cnf(refute_0_873,plain,
or(implies(X,not(Y)),implies(X,not(Y))) = implies(X,not(Y)),
inference(subst,[],[refute_0_190:[bind(X_27414,$fot(implies(X,not(Y))))]]) ).
cnf(refute_0_874,plain,
( or(implies(X,not(Y)),implies(X,not(Y))) != implies(X,not(Y))
| or(implies(X,not(Y)),implies(X,not(Y))) != not(and(and(X,Y),and(X,Y)))
| implies(X,not(Y)) = not(and(and(X,Y),and(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(X,not(Y)),implies(X,not(Y))),not(and(and(X,Y),and(X,Y)))) ),[0],$fot(implies(X,not(Y)))]]) ).
cnf(refute_0_875,plain,
( or(implies(X,not(Y)),implies(X,not(Y))) != not(and(and(X,Y),and(X,Y)))
| implies(X,not(Y)) = not(and(and(X,Y),and(X,Y))) ),
inference(resolve,[$cnf( $equal(or(implies(X,not(Y)),implies(X,not(Y))),implies(X,not(Y))) )],[refute_0_873,refute_0_874]) ).
cnf(refute_0_876,plain,
implies(X,not(Y)) = not(and(and(X,Y),and(X,Y))),
inference(resolve,[$cnf( $equal(or(implies(X,not(Y)),implies(X,not(Y))),not(and(and(X,Y),and(X,Y)))) )],[refute_0_872,refute_0_875]) ).
cnf(refute_0_877,plain,
and(and(X,Y),and(X,Y)) = not(not(and(X,Y))),
inference(subst,[],[refute_0_365:[bind(Y,$fot(and(X,Y)))]]) ).
cnf(refute_0_878,plain,
not(and(and(X,Y),and(X,Y))) = not(and(and(X,Y),and(X,Y))),
introduced(tautology,[refl,[$fot(not(and(and(X,Y),and(X,Y))))]]) ).
cnf(refute_0_879,plain,
( and(and(X,Y),and(X,Y)) != not(not(and(X,Y)))
| not(and(and(X,Y),and(X,Y))) != not(and(and(X,Y),and(X,Y)))
| not(and(and(X,Y),and(X,Y))) = not(not(not(and(X,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(and(X,Y),and(X,Y))),not(and(and(X,Y),and(X,Y)))) ),[1,0],$fot(not(not(and(X,Y))))]]) ).
cnf(refute_0_880,plain,
( and(and(X,Y),and(X,Y)) != not(not(and(X,Y)))
| not(and(and(X,Y),and(X,Y))) = not(not(not(and(X,Y)))) ),
inference(resolve,[$cnf( $equal(not(and(and(X,Y),and(X,Y))),not(and(and(X,Y),and(X,Y)))) )],[refute_0_878,refute_0_879]) ).
cnf(refute_0_881,plain,
not(and(and(X,Y),and(X,Y))) = not(not(not(and(X,Y)))),
inference(resolve,[$cnf( $equal(and(and(X,Y),and(X,Y)),not(not(and(X,Y)))) )],[refute_0_877,refute_0_880]) ).
cnf(refute_0_882,plain,
( implies(X,not(Y)) != not(and(and(X,Y),and(X,Y)))
| not(and(and(X,Y),and(X,Y))) != not(not(not(and(X,Y))))
| implies(X,not(Y)) = not(not(not(and(X,Y)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,not(Y)),not(not(not(and(X,Y))))) ),[0],$fot(not(and(and(X,Y),and(X,Y))))]]) ).
cnf(refute_0_883,plain,
( implies(X,not(Y)) != not(and(and(X,Y),and(X,Y)))
| implies(X,not(Y)) = not(not(not(and(X,Y)))) ),
inference(resolve,[$cnf( $equal(not(and(and(X,Y),and(X,Y))),not(not(not(and(X,Y))))) )],[refute_0_881,refute_0_882]) ).
cnf(refute_0_884,plain,
implies(X,not(Y)) = not(not(not(and(X,Y)))),
inference(resolve,[$cnf( $equal(implies(X,not(Y)),not(and(and(X,Y),and(X,Y)))) )],[refute_0_876,refute_0_883]) ).
cnf(refute_0_885,plain,
not(not(not(and(X,Y)))) = not(and(X,Y)),
inference(subst,[],[refute_0_693:[bind(X_31803,$fot(not(and(X,Y))))]]) ).
cnf(refute_0_886,plain,
( implies(X,not(Y)) != not(not(not(and(X,Y))))
| not(not(not(and(X,Y)))) != not(and(X,Y))
| implies(X,not(Y)) = not(and(X,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,not(Y)),not(and(X,Y))) ),[0],$fot(not(not(not(and(X,Y)))))]]) ).
cnf(refute_0_887,plain,
( implies(X,not(Y)) != not(not(not(and(X,Y))))
| implies(X,not(Y)) = not(and(X,Y)) ),
inference(resolve,[$cnf( $equal(not(not(not(and(X,Y)))),not(and(X,Y))) )],[refute_0_885,refute_0_886]) ).
cnf(refute_0_888,plain,
implies(X,not(Y)) = not(and(X,Y)),
inference(resolve,[$cnf( $equal(implies(X,not(Y)),not(not(not(and(X,Y))))) )],[refute_0_884,refute_0_887]) ).
cnf(refute_0_889,plain,
implies(X_142,not(X_144)) = not(and(X_142,X_144)),
inference(subst,[],[refute_0_888:[bind(X,$fot(X_142)),bind(Y,$fot(X_144))]]) ).
cnf(refute_0_890,plain,
implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144))) = implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144))),
introduced(tautology,[refl,[$fot(implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144))))]]) ).
cnf(refute_0_891,plain,
( implies(X_142,not(X_144)) != not(and(X_142,X_144))
| implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144))) != implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144)))
| implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144))) = implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144))),implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144)))) ),[1,1],$fot(not(and(X_142,X_144)))]]) ).
cnf(refute_0_892,plain,
( implies(X_142,not(X_144)) != not(and(X_142,X_144))
| implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144))) = implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144))) ),
inference(resolve,[$cnf( $equal(implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144))),implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144)))) )],[refute_0_890,refute_0_891]) ).
cnf(refute_0_893,plain,
implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144))) = implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144))),
inference(resolve,[$cnf( $equal(implies(X_142,not(X_144)),not(and(X_142,X_144))) )],[refute_0_889,refute_0_892]) ).
cnf(refute_0_894,plain,
implies(X_142,not(or(X_43,X_44))) = not(and(X_142,or(X_43,X_44))),
inference(subst,[],[refute_0_888:[bind(X,$fot(X_142)),bind(Y,$fot(or(X_43,X_44)))]]) ).
cnf(refute_0_895,plain,
implies(not(X_43),X_44) = or(X_43,X_44),
inference(subst,[],[refute_0_705:[bind(Y,$fot(X_44)),bind(X_94,$fot(X_43))]]) ).
cnf(refute_0_896,plain,
not(implies(not(X_43),X_44)) = not(implies(not(X_43),X_44)),
introduced(tautology,[refl,[$fot(not(implies(not(X_43),X_44)))]]) ).
cnf(refute_0_897,plain,
( implies(not(X_43),X_44) != or(X_43,X_44)
| not(implies(not(X_43),X_44)) != not(implies(not(X_43),X_44))
| not(implies(not(X_43),X_44)) = not(or(X_43,X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(X_43),X_44)),not(implies(not(X_43),X_44))) ),[1,0],$fot(or(X_43,X_44))]]) ).
cnf(refute_0_898,plain,
( implies(not(X_43),X_44) != or(X_43,X_44)
| not(implies(not(X_43),X_44)) = not(or(X_43,X_44)) ),
inference(resolve,[$cnf( $equal(not(implies(not(X_43),X_44)),not(implies(not(X_43),X_44))) )],[refute_0_896,refute_0_897]) ).
cnf(refute_0_899,plain,
not(implies(not(X_43),X_44)) = not(or(X_43,X_44)),
inference(resolve,[$cnf( $equal(implies(not(X_43),X_44),or(X_43,X_44)) )],[refute_0_895,refute_0_898]) ).
cnf(refute_0_900,plain,
and(X_10,and(not(Y),not(Y))) = not(implies(X_10,or(Y,Y))),
inference(subst,[],[refute_0_797:[bind(X,$fot(Y))]]) ).
cnf(refute_0_901,plain,
( and(X_10,and(not(Y),not(Y))) != not(implies(X_10,or(Y,Y)))
| and(not(Y),not(Y)) != not(not(not(Y)))
| and(X_10,not(not(not(Y)))) = not(implies(X_10,or(Y,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_10,and(not(Y),not(Y))),not(implies(X_10,or(Y,Y)))) ),[0,1],$fot(not(not(not(Y))))]]) ).
cnf(refute_0_902,plain,
( and(X_10,and(not(Y),not(Y))) != not(implies(X_10,or(Y,Y)))
| and(X_10,not(not(not(Y)))) = not(implies(X_10,or(Y,Y))) ),
inference(resolve,[$cnf( $equal(and(not(Y),not(Y)),not(not(not(Y)))) )],[refute_0_421,refute_0_901]) ).
cnf(refute_0_903,plain,
and(X_10,not(not(not(Y)))) = not(implies(X_10,or(Y,Y))),
inference(resolve,[$cnf( $equal(and(X_10,and(not(Y),not(Y))),not(implies(X_10,or(Y,Y)))) )],[refute_0_900,refute_0_902]) ).
cnf(refute_0_904,plain,
implies(X_10,or(Y,Y)) = implies(X_10,or(Y,Y)),
introduced(tautology,[refl,[$fot(implies(X_10,or(Y,Y)))]]) ).
cnf(refute_0_905,plain,
( implies(X_10,or(Y,Y)) != implies(X_10,or(Y,Y))
| or(Y,Y) != Y
| implies(X_10,or(Y,Y)) = implies(X_10,Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_10,or(Y,Y)),implies(X_10,or(Y,Y))) ),[1,1],$fot(Y)]]) ).
cnf(refute_0_906,plain,
( or(Y,Y) != Y
| implies(X_10,or(Y,Y)) = implies(X_10,Y) ),
inference(resolve,[$cnf( $equal(implies(X_10,or(Y,Y)),implies(X_10,or(Y,Y))) )],[refute_0_904,refute_0_905]) ).
cnf(refute_0_907,plain,
implies(X_10,or(Y,Y)) = implies(X_10,Y),
inference(resolve,[$cnf( $equal(or(Y,Y),Y) )],[refute_0_425,refute_0_906]) ).
cnf(refute_0_908,plain,
not(implies(X_10,or(Y,Y))) = not(implies(X_10,or(Y,Y))),
introduced(tautology,[refl,[$fot(not(implies(X_10,or(Y,Y))))]]) ).
cnf(refute_0_909,plain,
( implies(X_10,or(Y,Y)) != implies(X_10,Y)
| not(implies(X_10,or(Y,Y))) != not(implies(X_10,or(Y,Y)))
| not(implies(X_10,or(Y,Y))) = not(implies(X_10,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_10,or(Y,Y))),not(implies(X_10,or(Y,Y)))) ),[1,0],$fot(implies(X_10,Y))]]) ).
cnf(refute_0_910,plain,
( implies(X_10,or(Y,Y)) != implies(X_10,Y)
| not(implies(X_10,or(Y,Y))) = not(implies(X_10,Y)) ),
inference(resolve,[$cnf( $equal(not(implies(X_10,or(Y,Y))),not(implies(X_10,or(Y,Y)))) )],[refute_0_908,refute_0_909]) ).
cnf(refute_0_911,plain,
not(implies(X_10,or(Y,Y))) = not(implies(X_10,Y)),
inference(resolve,[$cnf( $equal(implies(X_10,or(Y,Y)),implies(X_10,Y)) )],[refute_0_907,refute_0_910]) ).
cnf(refute_0_912,plain,
( and(X_10,not(not(not(Y)))) != not(implies(X_10,or(Y,Y)))
| not(implies(X_10,or(Y,Y))) != not(implies(X_10,Y))
| and(X_10,not(not(not(Y)))) = not(implies(X_10,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_10,not(not(not(Y)))),not(implies(X_10,Y))) ),[0],$fot(not(implies(X_10,or(Y,Y))))]]) ).
cnf(refute_0_913,plain,
( and(X_10,not(not(not(Y)))) != not(implies(X_10,or(Y,Y)))
| and(X_10,not(not(not(Y)))) = not(implies(X_10,Y)) ),
inference(resolve,[$cnf( $equal(not(implies(X_10,or(Y,Y))),not(implies(X_10,Y))) )],[refute_0_911,refute_0_912]) ).
cnf(refute_0_914,plain,
and(X_10,not(not(not(Y)))) = not(implies(X_10,Y)),
inference(resolve,[$cnf( $equal(and(X_10,not(not(not(Y)))),not(implies(X_10,or(Y,Y)))) )],[refute_0_903,refute_0_913]) ).
cnf(refute_0_915,plain,
not(not(not(Y))) = not(Y),
inference(subst,[],[refute_0_693:[bind(X_31803,$fot(not(Y)))]]) ).
cnf(refute_0_916,plain,
and(X_10,not(not(not(Y)))) = and(X_10,not(not(not(Y)))),
introduced(tautology,[refl,[$fot(and(X_10,not(not(not(Y)))))]]) ).
cnf(refute_0_917,plain,
( and(X_10,not(not(not(Y)))) != and(X_10,not(not(not(Y))))
| not(not(not(Y))) != not(Y)
| and(X_10,not(not(not(Y)))) = and(X_10,not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_10,not(not(not(Y)))),and(X_10,not(not(not(Y))))) ),[1,1],$fot(not(Y))]]) ).
cnf(refute_0_918,plain,
( not(not(not(Y))) != not(Y)
| and(X_10,not(not(not(Y)))) = and(X_10,not(Y)) ),
inference(resolve,[$cnf( $equal(and(X_10,not(not(not(Y)))),and(X_10,not(not(not(Y))))) )],[refute_0_916,refute_0_917]) ).
cnf(refute_0_919,plain,
and(X_10,not(not(not(Y)))) = and(X_10,not(Y)),
inference(resolve,[$cnf( $equal(not(not(not(Y))),not(Y)) )],[refute_0_915,refute_0_918]) ).
cnf(refute_0_920,plain,
( and(X_10,not(not(not(Y)))) != and(X_10,not(Y))
| and(X_10,not(not(not(Y)))) != not(implies(X_10,Y))
| and(X_10,not(Y)) = not(implies(X_10,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_10,not(not(not(Y)))),not(implies(X_10,Y))) ),[0],$fot(and(X_10,not(Y)))]]) ).
cnf(refute_0_921,plain,
( and(X_10,not(not(not(Y)))) != not(implies(X_10,Y))
| and(X_10,not(Y)) = not(implies(X_10,Y)) ),
inference(resolve,[$cnf( $equal(and(X_10,not(not(not(Y)))),and(X_10,not(Y))) )],[refute_0_919,refute_0_920]) ).
cnf(refute_0_922,plain,
and(X_10,not(Y)) = not(implies(X_10,Y)),
inference(resolve,[$cnf( $equal(and(X_10,not(not(not(Y)))),not(implies(X_10,Y))) )],[refute_0_914,refute_0_921]) ).
cnf(refute_0_923,plain,
and(not(X_43),not(X_44)) = not(implies(not(X_43),X_44)),
inference(subst,[],[refute_0_922:[bind(Y,$fot(X_44)),bind(X_10,$fot(not(X_43)))]]) ).
cnf(refute_0_924,plain,
( and(not(X_43),not(X_44)) != not(implies(not(X_43),X_44))
| not(implies(not(X_43),X_44)) != not(or(X_43,X_44))
| and(not(X_43),not(X_44)) = not(or(X_43,X_44)) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(and(not(X_43),not(X_44)))),bind(Y0,$fot(not(implies(not(X_43),X_44)))),bind(Z,$fot(not(or(X_43,X_44))))]]) ).
cnf(refute_0_925,plain,
( not(implies(not(X_43),X_44)) != not(or(X_43,X_44))
| and(not(X_43),not(X_44)) = not(or(X_43,X_44)) ),
inference(resolve,[$cnf( $equal(and(not(X_43),not(X_44)),not(implies(not(X_43),X_44))) )],[refute_0_923,refute_0_924]) ).
cnf(refute_0_926,plain,
and(not(X_43),not(X_44)) = not(or(X_43,X_44)),
inference(resolve,[$cnf( $equal(not(implies(not(X_43),X_44)),not(or(X_43,X_44))) )],[refute_0_899,refute_0_925]) ).
cnf(refute_0_927,plain,
implies(X_142,and(not(X_43),not(X_44))) = implies(X_142,and(not(X_43),not(X_44))),
introduced(tautology,[refl,[$fot(implies(X_142,and(not(X_43),not(X_44))))]]) ).
cnf(refute_0_928,plain,
( and(not(X_43),not(X_44)) != not(or(X_43,X_44))
| implies(X_142,and(not(X_43),not(X_44))) != implies(X_142,and(not(X_43),not(X_44)))
| implies(X_142,and(not(X_43),not(X_44))) = implies(X_142,not(or(X_43,X_44))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,and(not(X_43),not(X_44)))) ),[1,1],$fot(not(or(X_43,X_44)))]]) ).
cnf(refute_0_929,plain,
( and(not(X_43),not(X_44)) != not(or(X_43,X_44))
| implies(X_142,and(not(X_43),not(X_44))) = implies(X_142,not(or(X_43,X_44))) ),
inference(resolve,[$cnf( $equal(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,and(not(X_43),not(X_44)))) )],[refute_0_927,refute_0_928]) ).
cnf(refute_0_930,plain,
implies(X_142,and(not(X_43),not(X_44))) = implies(X_142,not(or(X_43,X_44))),
inference(resolve,[$cnf( $equal(and(not(X_43),not(X_44)),not(or(X_43,X_44))) )],[refute_0_926,refute_0_929]) ).
cnf(refute_0_931,plain,
( implies(X_142,and(not(X_43),not(X_44))) != implies(X_142,not(or(X_43,X_44)))
| implies(X_142,not(or(X_43,X_44))) != not(and(X_142,or(X_43,X_44)))
| implies(X_142,and(not(X_43),not(X_44))) = not(and(X_142,or(X_43,X_44))) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(implies(X_142,and(not(X_43),not(X_44))))),bind(Y0,$fot(implies(X_142,not(or(X_43,X_44))))),bind(Z,$fot(not(and(X_142,or(X_43,X_44)))))]]) ).
cnf(refute_0_932,plain,
( implies(X_142,not(or(X_43,X_44))) != not(and(X_142,or(X_43,X_44)))
| implies(X_142,and(not(X_43),not(X_44))) = not(and(X_142,or(X_43,X_44))) ),
inference(resolve,[$cnf( $equal(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(or(X_43,X_44)))) )],[refute_0_930,refute_0_931]) ).
cnf(refute_0_933,plain,
implies(X_142,and(not(X_43),not(X_44))) = not(and(X_142,or(X_43,X_44))),
inference(resolve,[$cnf( $equal(implies(X_142,not(or(X_43,X_44))),not(and(X_142,or(X_43,X_44)))) )],[refute_0_894,refute_0_932]) ).
cnf(refute_0_934,plain,
implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))) = implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))),
introduced(tautology,[refl,[$fot(implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))]]) ).
cnf(refute_0_935,plain,
( implies(X_142,and(not(X_43),not(X_44))) != not(and(X_142,or(X_43,X_44)))
| implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))) != implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))
| implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))) = implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))) ),[1,0],$fot(not(and(X_142,or(X_43,X_44))))]]) ).
cnf(refute_0_936,plain,
( implies(X_142,and(not(X_43),not(X_44))) != not(and(X_142,or(X_43,X_44)))
| implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))) = implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))) )],[refute_0_934,refute_0_935]) ).
cnf(refute_0_937,plain,
implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))) = implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144))),
inference(resolve,[$cnf( $equal(implies(X_142,and(not(X_43),not(X_44))),not(and(X_142,or(X_43,X_44)))) )],[refute_0_933,refute_0_936]) ).
cnf(refute_0_938,plain,
( implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))) != implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144)))
| implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144))) != implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144)))
| implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))) = implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144))) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))),bind(Y0,$fot(implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144))))),bind(Z,$fot(implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144)))))]]) ).
cnf(refute_0_939,plain,
( implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144))) != implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144)))
| implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))) = implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))),implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144)))) )],[refute_0_937,refute_0_938]) ).
cnf(refute_0_940,plain,
implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))) = implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144))),
inference(resolve,[$cnf( $equal(implies(not(and(X_142,or(X_43,X_44))),implies(X_142,not(X_144))),implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144)))) )],[refute_0_893,refute_0_939]) ).
cnf(refute_0_941,plain,
( implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))) != implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144)))
| implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144))) != or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144)))
| implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))) = or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144))) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))),bind(Y0,$fot(implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144))))),bind(Z,$fot(or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144)))))]]) ).
cnf(refute_0_942,plain,
( implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144))) != or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144)))
| implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))) = or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))),implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144)))) )],[refute_0_940,refute_0_941]) ).
cnf(refute_0_943,plain,
implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))) = or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144))),
inference(resolve,[$cnf( $equal(implies(not(and(X_142,or(X_43,X_44))),not(and(X_142,X_144))),or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144)))) )],[refute_0_867,refute_0_942]) ).
cnf(refute_0_944,plain,
implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))) = implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))),
introduced(tautology,[refl,[$fot(implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))))]]) ).
cnf(refute_0_945,plain,
( implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))) != or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144)))
| implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))) != implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))
| implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))) = implies(or(or(X_43,X_44),not(X_144)),or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))),implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))) ),[1,1],$fot(or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144))))]]) ).
cnf(refute_0_946,plain,
( implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))) != or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144)))
| implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))) = implies(or(or(X_43,X_44),not(X_144)),or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144)))) ),
inference(resolve,[$cnf( $equal(implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))),implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))) )],[refute_0_944,refute_0_945]) ).
cnf(refute_0_947,plain,
implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))) = implies(or(or(X_43,X_44),not(X_144)),or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144)))),
inference(resolve,[$cnf( $equal(implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))),or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144)))) )],[refute_0_943,refute_0_946]) ).
cnf(refute_0_948,plain,
( implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))) != implies(or(or(X_43,X_44),not(X_144)),or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144))))
| ~ is_a_theorem(implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))))
| is_a_theorem(implies(or(or(X_43,X_44),not(X_144)),or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))) ),[0],$fot(implies(or(or(X_43,X_44),not(X_144)),or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144)))))]]) ).
cnf(refute_0_949,plain,
( ~ is_a_theorem(implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))))
| is_a_theorem(implies(or(or(X_43,X_44),not(X_144)),or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144))))) ),
inference(resolve,[$cnf( $equal(implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144)))),implies(or(or(X_43,X_44),not(X_144)),or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144))))) )],[refute_0_947,refute_0_948]) ).
cnf(refute_0_950,plain,
is_a_theorem(implies(or(or(X_43,X_44),not(X_144)),or(and(X_142,or(X_43,X_44)),not(and(X_142,X_144))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(or(X_43,X_44),not(X_144)),implies(implies(X_142,and(not(X_43),not(X_44))),implies(X_142,not(X_144))))) )],[refute_0_866,refute_0_949]) ).
cnf(refute_0_951,plain,
is_a_theorem(implies(or(or(X_32626,X_32627),not(X_32625)),or(and(X_32625,or(X_32626,X_32627)),not(and(X_32625,X_32625))))),
inference(subst,[],[refute_0_950:[bind(X_142,$fot(X_32625)),bind(X_144,$fot(X_32625)),bind(X_43,$fot(X_32626)),bind(X_44,$fot(X_32627))]]) ).
cnf(refute_0_952,plain,
( and(Y,Y) != not(not(Y))
| not(not(Y)) != Y
| and(Y,Y) = Y ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(Y,Y),Y) ),[0],$fot(not(not(Y)))]]) ).
cnf(refute_0_953,plain,
( and(Y,Y) != not(not(Y))
| and(Y,Y) = Y ),
inference(resolve,[$cnf( $equal(not(not(Y)),Y) )],[refute_0_694,refute_0_952]) ).
cnf(refute_0_954,plain,
and(Y,Y) = Y,
inference(resolve,[$cnf( $equal(and(Y,Y),not(not(Y))) )],[refute_0_365,refute_0_953]) ).
cnf(refute_0_955,plain,
and(X_32625,X_32625) = X_32625,
inference(subst,[],[refute_0_954:[bind(Y,$fot(X_32625))]]) ).
cnf(refute_0_956,plain,
( and(X_32625,X_32625) != X_32625
| ~ is_a_theorem(implies(or(or(X_32626,X_32627),not(X_32625)),or(and(X_32625,or(X_32626,X_32627)),not(and(X_32625,X_32625)))))
| is_a_theorem(implies(or(or(X_32626,X_32627),not(X_32625)),or(and(X_32625,or(X_32626,X_32627)),not(X_32625)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(or(X_32626,X_32627),not(X_32625)),or(and(X_32625,or(X_32626,X_32627)),not(and(X_32625,X_32625))))) ),[0,1,1,0],$fot(X_32625)]]) ).
cnf(refute_0_957,plain,
( ~ is_a_theorem(implies(or(or(X_32626,X_32627),not(X_32625)),or(and(X_32625,or(X_32626,X_32627)),not(and(X_32625,X_32625)))))
| is_a_theorem(implies(or(or(X_32626,X_32627),not(X_32625)),or(and(X_32625,or(X_32626,X_32627)),not(X_32625)))) ),
inference(resolve,[$cnf( $equal(and(X_32625,X_32625),X_32625) )],[refute_0_955,refute_0_956]) ).
cnf(refute_0_958,plain,
is_a_theorem(implies(or(or(X_32626,X_32627),not(X_32625)),or(and(X_32625,or(X_32626,X_32627)),not(X_32625)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(or(X_32626,X_32627),not(X_32625)),or(and(X_32625,or(X_32626,X_32627)),not(and(X_32625,X_32625))))) )],[refute_0_951,refute_0_957]) ).
cnf(refute_0_959,plain,
is_a_theorem(implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,or(X_32638,X_32638)),not(X_32636)))),
inference(subst,[],[refute_0_958:[bind(X_32625,$fot(X_32636)),bind(X_32626,$fot(X_32638)),bind(X_32627,$fot(X_32638))]]) ).
cnf(refute_0_960,plain,
or(X_32638,X_32638) = X_32638,
inference(subst,[],[refute_0_190:[bind(X_27414,$fot(X_32638))]]) ).
cnf(refute_0_961,plain,
( or(X_32638,X_32638) != X_32638
| ~ is_a_theorem(implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,or(X_32638,X_32638)),not(X_32636))))
| is_a_theorem(implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,or(X_32638,X_32638)),not(X_32636)))) ),[0,1,0,1],$fot(X_32638)]]) ).
cnf(refute_0_962,plain,
( ~ is_a_theorem(implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,or(X_32638,X_32638)),not(X_32636))))
| is_a_theorem(implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636)))) ),
inference(resolve,[$cnf( $equal(or(X_32638,X_32638),X_32638) )],[refute_0_960,refute_0_961]) ).
cnf(refute_0_963,plain,
is_a_theorem(implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,or(X_32638,X_32638)),not(X_32636)))) )],[refute_0_959,refute_0_962]) ).
cnf(refute_0_964,plain,
or(or(X_32638,X_32638),not(X_32636)) = or(or(X_32638,X_32638),not(X_32636)),
introduced(tautology,[refl,[$fot(or(or(X_32638,X_32638),not(X_32636)))]]) ).
cnf(refute_0_965,plain,
( or(X_32638,X_32638) != X_32638
| or(or(X_32638,X_32638),not(X_32636)) != or(or(X_32638,X_32638),not(X_32636))
| or(or(X_32638,X_32638),not(X_32636)) = or(X_32638,not(X_32636)) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(X_32638,X_32638),not(X_32636)),or(or(X_32638,X_32638),not(X_32636))) ),[1,0],$fot(X_32638)]]) ).
cnf(refute_0_966,plain,
( or(X_32638,X_32638) != X_32638
| or(or(X_32638,X_32638),not(X_32636)) = or(X_32638,not(X_32636)) ),
inference(resolve,[$cnf( $equal(or(or(X_32638,X_32638),not(X_32636)),or(or(X_32638,X_32638),not(X_32636))) )],[refute_0_964,refute_0_965]) ).
cnf(refute_0_967,plain,
or(or(X_32638,X_32638),not(X_32636)) = or(X_32638,not(X_32636)),
inference(resolve,[$cnf( $equal(or(X_32638,X_32638),X_32638) )],[refute_0_960,refute_0_966]) ).
cnf(refute_0_968,plain,
implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636))) = implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636))),
introduced(tautology,[refl,[$fot(implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636))))]]) ).
cnf(refute_0_969,plain,
( implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636))) != implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636)))
| or(or(X_32638,X_32638),not(X_32636)) != or(X_32638,not(X_32636))
| implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636))) = implies(or(X_32638,not(X_32636)),or(and(X_32636,X_32638),not(X_32636))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636))),implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636)))) ),[1,0],$fot(or(X_32638,not(X_32636)))]]) ).
cnf(refute_0_970,plain,
( or(or(X_32638,X_32638),not(X_32636)) != or(X_32638,not(X_32636))
| implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636))) = implies(or(X_32638,not(X_32636)),or(and(X_32636,X_32638),not(X_32636))) ),
inference(resolve,[$cnf( $equal(implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636))),implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636)))) )],[refute_0_968,refute_0_969]) ).
cnf(refute_0_971,plain,
implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636))) = implies(or(X_32638,not(X_32636)),or(and(X_32636,X_32638),not(X_32636))),
inference(resolve,[$cnf( $equal(or(or(X_32638,X_32638),not(X_32636)),or(X_32638,not(X_32636))) )],[refute_0_967,refute_0_970]) ).
cnf(refute_0_972,plain,
( implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636))) != implies(or(X_32638,not(X_32636)),or(and(X_32636,X_32638),not(X_32636)))
| ~ is_a_theorem(implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636))))
| is_a_theorem(implies(or(X_32638,not(X_32636)),or(and(X_32636,X_32638),not(X_32636)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636)))) ),[0],$fot(implies(or(X_32638,not(X_32636)),or(and(X_32636,X_32638),not(X_32636))))]]) ).
cnf(refute_0_973,plain,
( ~ is_a_theorem(implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636))))
| is_a_theorem(implies(or(X_32638,not(X_32636)),or(and(X_32636,X_32638),not(X_32636)))) ),
inference(resolve,[$cnf( $equal(implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636))),implies(or(X_32638,not(X_32636)),or(and(X_32636,X_32638),not(X_32636)))) )],[refute_0_971,refute_0_972]) ).
cnf(refute_0_974,plain,
is_a_theorem(implies(or(X_32638,not(X_32636)),or(and(X_32636,X_32638),not(X_32636)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(or(X_32638,X_32638),not(X_32636)),or(and(X_32636,X_32638),not(X_32636)))) )],[refute_0_963,refute_0_973]) ).
cnf(refute_0_975,plain,
is_a_theorem(implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),not(not(X_31803))))),
inference(subst,[],[refute_0_974:[bind(X_32636,$fot(not(X_31803))),bind(X_32638,$fot(X_32640))]]) ).
cnf(refute_0_976,plain,
( not(not(X_31803)) != X_31803
| ~ is_a_theorem(implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),not(not(X_31803)))))
| is_a_theorem(implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),not(not(X_31803))))) ),[0,1,1],$fot(X_31803)]]) ).
cnf(refute_0_977,plain,
( ~ is_a_theorem(implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),not(not(X_31803)))))
| is_a_theorem(implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803))) ),
inference(resolve,[$cnf( $equal(not(not(X_31803)),X_31803) )],[refute_0_693,refute_0_976]) ).
cnf(refute_0_978,plain,
is_a_theorem(implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),not(not(X_31803))))) )],[refute_0_975,refute_0_977]) ).
cnf(refute_0_979,plain,
or(X_32640,not(not(X_31803))) = or(X_32640,not(not(X_31803))),
introduced(tautology,[refl,[$fot(or(X_32640,not(not(X_31803))))]]) ).
cnf(refute_0_980,plain,
( not(not(X_31803)) != X_31803
| or(X_32640,not(not(X_31803))) != or(X_32640,not(not(X_31803)))
| or(X_32640,not(not(X_31803))) = or(X_32640,X_31803) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_32640,not(not(X_31803))),or(X_32640,not(not(X_31803)))) ),[1,1],$fot(X_31803)]]) ).
cnf(refute_0_981,plain,
( not(not(X_31803)) != X_31803
| or(X_32640,not(not(X_31803))) = or(X_32640,X_31803) ),
inference(resolve,[$cnf( $equal(or(X_32640,not(not(X_31803))),or(X_32640,not(not(X_31803)))) )],[refute_0_979,refute_0_980]) ).
cnf(refute_0_982,plain,
or(X_32640,not(not(X_31803))) = or(X_32640,X_31803),
inference(resolve,[$cnf( $equal(not(not(X_31803)),X_31803) )],[refute_0_693,refute_0_981]) ).
cnf(refute_0_983,plain,
implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803)) = implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803)),
introduced(tautology,[refl,[$fot(implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803)))]]) ).
cnf(refute_0_984,plain,
( implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803)) != implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803))
| or(X_32640,not(not(X_31803))) != or(X_32640,X_31803)
| implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803)) = implies(or(X_32640,X_31803),or(and(not(X_31803),X_32640),X_31803)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803)),implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803))) ),[1,0],$fot(or(X_32640,X_31803))]]) ).
cnf(refute_0_985,plain,
( or(X_32640,not(not(X_31803))) != or(X_32640,X_31803)
| implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803)) = implies(or(X_32640,X_31803),or(and(not(X_31803),X_32640),X_31803)) ),
inference(resolve,[$cnf( $equal(implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803)),implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803))) )],[refute_0_983,refute_0_984]) ).
cnf(refute_0_986,plain,
implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803)) = implies(or(X_32640,X_31803),or(and(not(X_31803),X_32640),X_31803)),
inference(resolve,[$cnf( $equal(or(X_32640,not(not(X_31803))),or(X_32640,X_31803)) )],[refute_0_982,refute_0_985]) ).
cnf(refute_0_987,plain,
( implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803)) != implies(or(X_32640,X_31803),or(and(not(X_31803),X_32640),X_31803))
| ~ is_a_theorem(implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803)))
| is_a_theorem(implies(or(X_32640,X_31803),or(and(not(X_31803),X_32640),X_31803))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803))) ),[0],$fot(implies(or(X_32640,X_31803),or(and(not(X_31803),X_32640),X_31803)))]]) ).
cnf(refute_0_988,plain,
( ~ is_a_theorem(implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803)))
| is_a_theorem(implies(or(X_32640,X_31803),or(and(not(X_31803),X_32640),X_31803))) ),
inference(resolve,[$cnf( $equal(implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803)),implies(or(X_32640,X_31803),or(and(not(X_31803),X_32640),X_31803))) )],[refute_0_986,refute_0_987]) ).
cnf(refute_0_989,plain,
is_a_theorem(implies(or(X_32640,X_31803),or(and(not(X_31803),X_32640),X_31803))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_32640,not(not(X_31803))),or(and(not(X_31803),X_32640),X_31803))) )],[refute_0_978,refute_0_988]) ).
cnf(refute_0_990,plain,
is_a_theorem(implies(or(X_32642,X_32641),or(and(not(X_32641),X_32642),X_32641))),
inference(subst,[],[refute_0_989:[bind(X_31803,$fot(X_32641)),bind(X_32640,$fot(X_32642))]]) ).
cnf(refute_0_991,plain,
is_a_theorem(implies(implies(implies(or(X_32642,X_32641),or(and(not(X_32641),X_32642),X_32641)),X_3654),X_3654)),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_32642,X_32641),or(and(not(X_32641),X_32642),X_32641))) )],[refute_0_990,refute_0_852]) ).
cnf(refute_0_992,plain,
is_a_theorem(implies(implies(implies(or(X_32655,X_32655),or(and(not(X_32655),X_32655),X_32655)),X_32657),X_32657)),
inference(subst,[],[refute_0_991:[bind(X_32641,$fot(X_32655)),bind(X_32642,$fot(X_32655)),bind(X_3654,$fot(X_32657))]]) ).
cnf(refute_0_993,plain,
or(X_32655,X_32655) = X_32655,
inference(subst,[],[refute_0_190:[bind(X_27414,$fot(X_32655))]]) ).
cnf(refute_0_994,plain,
( or(X_32655,X_32655) != X_32655
| ~ is_a_theorem(implies(implies(implies(or(X_32655,X_32655),or(and(not(X_32655),X_32655),X_32655)),X_32657),X_32657))
| is_a_theorem(implies(implies(implies(X_32655,or(and(not(X_32655),X_32655),X_32655)),X_32657),X_32657)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(implies(or(X_32655,X_32655),or(and(not(X_32655),X_32655),X_32655)),X_32657),X_32657)) ),[0,0,0,0],$fot(X_32655)]]) ).
cnf(refute_0_995,plain,
( ~ is_a_theorem(implies(implies(implies(or(X_32655,X_32655),or(and(not(X_32655),X_32655),X_32655)),X_32657),X_32657))
| is_a_theorem(implies(implies(implies(X_32655,or(and(not(X_32655),X_32655),X_32655)),X_32657),X_32657)) ),
inference(resolve,[$cnf( $equal(or(X_32655,X_32655),X_32655) )],[refute_0_993,refute_0_994]) ).
cnf(refute_0_996,plain,
is_a_theorem(implies(implies(implies(X_32655,or(and(not(X_32655),X_32655),X_32655)),X_32657),X_32657)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(or(X_32655,X_32655),or(and(not(X_32655),X_32655),X_32655)),X_32657),X_32657)) )],[refute_0_992,refute_0_995]) ).
cnf(refute_0_997,plain,
is_a_theorem(implies(implies(implies(X_33138,or(and(not(X_33138),X_33138),X_33138)),X_33139),X_33139)),
inference(subst,[],[refute_0_996:[bind(X_32655,$fot(X_33138)),bind(X_32657,$fot(X_33139))]]) ).
cnf(refute_0_998,plain,
is_a_theorem(or(X_33139,not(implies(implies(X_33138,or(and(not(X_33138),X_33138),X_33138)),X_33139)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_33138,or(and(not(X_33138),X_33138),X_33138)),X_33139),X_33139)) )],[refute_0_997,refute_0_851]) ).
cnf(refute_0_999,plain,
is_a_theorem(or(not(X),not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))),
inference(subst,[],[refute_0_998:[bind(X_33138,$fot(X_33140)),bind(X_33139,$fot(not(X)))]]) ).
cnf(refute_0_1000,plain,
implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) = or(not(X),not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))),
inference(subst,[],[refute_0_12:[bind(Y,$fot(not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))))]]) ).
cnf(refute_0_1001,plain,
( implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) != or(not(X),not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))
| or(not(X),not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) = implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))))),bind(Y0,$fot(or(not(X),not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))))]]) ).
cnf(refute_0_1002,plain,
or(not(X),not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) = implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))),
inference(resolve,[$cnf( $equal(implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))),or(not(X),not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))) )],[refute_0_1000,refute_0_1001]) ).
cnf(refute_0_1003,plain,
( or(not(X),not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) != implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))
| ~ is_a_theorem(or(not(X),not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))))
| is_a_theorem(implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X),not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))) ),[0],$fot(implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))))]]) ).
cnf(refute_0_1004,plain,
( ~ is_a_theorem(or(not(X),not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))))
| is_a_theorem(implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))),implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))) )],[refute_0_1002,refute_0_1003]) ).
cnf(refute_0_1005,plain,
is_a_theorem(implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))),
inference(resolve,[$cnf( is_a_theorem(or(not(X),not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))) )],[refute_0_999,refute_0_1004]) ).
cnf(refute_0_1006,plain,
not(not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))) = implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)),
inference(subst,[],[refute_0_693:[bind(X_31803,$fot(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))))]]) ).
cnf(refute_0_1007,plain,
and(X,not(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) = not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))),
inference(subst,[],[refute_0_922:[bind(Y,$fot(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))),bind(X_10,$fot(X))]]) ).
cnf(refute_0_1008,plain,
implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)) = not(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)),
inference(subst,[],[refute_0_888:[bind(X,$fot(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)))),bind(Y,$fot(X))]]) ).
cnf(refute_0_1009,plain,
and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))) = and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))),
introduced(tautology,[refl,[$fot(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))]]) ).
cnf(refute_0_1010,plain,
( and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))) != and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))
| implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)) != not(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))
| and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))) = and(X,not(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))),and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) ),[1,1],$fot(not(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))]]) ).
cnf(refute_0_1011,plain,
( implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)) != not(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))
| and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))) = and(X,not(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) ),
inference(resolve,[$cnf( $equal(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))),and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) )],[refute_0_1009,refute_0_1010]) ).
cnf(refute_0_1012,plain,
and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))) = and(X,not(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))),
inference(resolve,[$cnf( $equal(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)),not(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) )],[refute_0_1008,refute_0_1011]) ).
cnf(refute_0_1013,plain,
( and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))) != and(X,not(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))
| and(X,not(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) != not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))
| and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))) = not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))),bind(Y0,$fot(and(X,not(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))))),bind(Z,$fot(not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))))]]) ).
cnf(refute_0_1014,plain,
( and(X,not(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) != not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))
| and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))) = not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) ),
inference(resolve,[$cnf( $equal(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))),and(X,not(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))) )],[refute_0_1012,refute_0_1013]) ).
cnf(refute_0_1015,plain,
and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))) = not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))),
inference(resolve,[$cnf( $equal(and(X,not(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))),not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))) )],[refute_0_1007,refute_0_1014]) ).
cnf(refute_0_1016,plain,
not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) = not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))),
introduced(tautology,[refl,[$fot(not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))))]]) ).
cnf(refute_0_1017,plain,
( and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))) != not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))
| not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) != not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))
| not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) = not(not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))),not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))) ),[1,0],$fot(not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))))]]) ).
cnf(refute_0_1018,plain,
( and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))) != not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))
| not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) = not(not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))) ),
inference(resolve,[$cnf( $equal(not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))),not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))) )],[refute_0_1016,refute_0_1017]) ).
cnf(refute_0_1019,plain,
not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) = not(not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))),
inference(resolve,[$cnf( $equal(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))),not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))) )],[refute_0_1015,refute_0_1018]) ).
cnf(refute_0_1020,plain,
( not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) != not(not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))))
| not(not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))) != implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))
| not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) = implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))))),bind(Y0,$fot(not(not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))))),bind(Z,$fot(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))))]]) ).
cnf(refute_0_1021,plain,
( not(not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))) != implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))
| not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) = implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)) ),
inference(resolve,[$cnf( $equal(not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))),not(not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))))) )],[refute_0_1019,refute_0_1020]) ).
cnf(refute_0_1022,plain,
not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) = implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)),
inference(resolve,[$cnf( $equal(not(not(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))),implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) )],[refute_0_1006,refute_0_1021]) ).
cnf(refute_0_1023,plain,
implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) = not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))),
inference(subst,[],[refute_0_888:[bind(Y,$fot(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))]]) ).
cnf(refute_0_1024,plain,
( implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) != not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))
| not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) != implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))
| implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) = implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))))),bind(Y0,$fot(not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))))),bind(Z,$fot(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))))]]) ).
cnf(refute_0_1025,plain,
( not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) != implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))
| implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) = implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)) ),
inference(resolve,[$cnf( $equal(implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))),not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))) )],[refute_0_1023,refute_0_1024]) ).
cnf(refute_0_1026,plain,
implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) = implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)),
inference(resolve,[$cnf( $equal(not(and(X,implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))),implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) )],[refute_0_1022,refute_0_1025]) ).
cnf(refute_0_1027,plain,
( implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))) != implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))
| ~ is_a_theorem(implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))))
| is_a_theorem(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))) ),[0],$fot(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))]]) ).
cnf(refute_0_1028,plain,
( ~ is_a_theorem(implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))))
| is_a_theorem(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) ),
inference(resolve,[$cnf( $equal(implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X)))),implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) )],[refute_0_1026,refute_0_1027]) ).
cnf(refute_0_1029,plain,
is_a_theorem(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))),
inference(resolve,[$cnf( is_a_theorem(implies(X,not(implies(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),not(X))))) )],[refute_0_1005,refute_0_1028]) ).
cnf(refute_0_1030,plain,
or(and(not(X_49),and(X_50,X_51)),Y) = not(and(not(and(not(X_49),and(X_50,X_51))),not(Y))),
inference(subst,[],[refute_0_5:[bind(X,$fot(and(not(X_49),and(X_50,X_51))))]]) ).
cnf(refute_0_1031,plain,
or(X,implies(X_10,not(X_11))) = not(and(not(X),not(implies(X_10,not(X_11))))),
inference(subst,[],[refute_0_5:[bind(Y,$fot(implies(X_10,not(X_11))))]]) ).
cnf(refute_0_1032,plain,
( not(implies(X_10,not(X_11))) != and(X_10,X_11)
| or(X,implies(X_10,not(X_11))) != not(and(not(X),not(implies(X_10,not(X_11)))))
| or(X,implies(X_10,not(X_11))) = not(and(not(X),and(X_10,X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,implies(X_10,not(X_11))),not(and(not(X),not(implies(X_10,not(X_11)))))) ),[1,0,1],$fot(and(X_10,X_11))]]) ).
cnf(refute_0_1033,plain,
( or(X,implies(X_10,not(X_11))) != not(and(not(X),not(implies(X_10,not(X_11)))))
| or(X,implies(X_10,not(X_11))) = not(and(not(X),and(X_10,X_11))) ),
inference(resolve,[$cnf( $equal(not(implies(X_10,not(X_11))),and(X_10,X_11)) )],[refute_0_28,refute_0_1032]) ).
cnf(refute_0_1034,plain,
or(X,implies(X_10,not(X_11))) = not(and(not(X),and(X_10,X_11))),
inference(resolve,[$cnf( $equal(or(X,implies(X_10,not(X_11))),not(and(not(X),not(implies(X_10,not(X_11)))))) )],[refute_0_1031,refute_0_1033]) ).
cnf(refute_0_1035,plain,
or(X_49,implies(X_50,not(X_51))) = not(and(not(X_49),and(X_50,X_51))),
inference(subst,[],[refute_0_1034:[bind(X,$fot(X_49)),bind(X_10,$fot(X_50)),bind(X_11,$fot(X_51))]]) ).
cnf(refute_0_1036,plain,
( or(X_49,implies(X_50,not(X_51))) != not(and(not(X_49),and(X_50,X_51)))
| not(and(not(X_49),and(X_50,X_51))) = or(X_49,implies(X_50,not(X_51))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X_49,implies(X_50,not(X_51))))),bind(Y0,$fot(not(and(not(X_49),and(X_50,X_51)))))]]) ).
cnf(refute_0_1037,plain,
not(and(not(X_49),and(X_50,X_51))) = or(X_49,implies(X_50,not(X_51))),
inference(resolve,[$cnf( $equal(or(X_49,implies(X_50,not(X_51))),not(and(not(X_49),and(X_50,X_51)))) )],[refute_0_1035,refute_0_1036]) ).
cnf(refute_0_1038,plain,
( not(and(not(X_49),and(X_50,X_51))) != or(X_49,implies(X_50,not(X_51)))
| or(and(not(X_49),and(X_50,X_51)),Y) != not(and(not(and(not(X_49),and(X_50,X_51))),not(Y)))
| or(and(not(X_49),and(X_50,X_51)),Y) = not(and(or(X_49,implies(X_50,not(X_51))),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_49),and(X_50,X_51)),Y),not(and(not(and(not(X_49),and(X_50,X_51))),not(Y)))) ),[1,0,0],$fot(or(X_49,implies(X_50,not(X_51))))]]) ).
cnf(refute_0_1039,plain,
( or(and(not(X_49),and(X_50,X_51)),Y) != not(and(not(and(not(X_49),and(X_50,X_51))),not(Y)))
| or(and(not(X_49),and(X_50,X_51)),Y) = not(and(or(X_49,implies(X_50,not(X_51))),not(Y))) ),
inference(resolve,[$cnf( $equal(not(and(not(X_49),and(X_50,X_51))),or(X_49,implies(X_50,not(X_51)))) )],[refute_0_1037,refute_0_1038]) ).
cnf(refute_0_1040,plain,
or(and(not(X_49),and(X_50,X_51)),Y) = not(and(or(X_49,implies(X_50,not(X_51))),not(Y))),
inference(resolve,[$cnf( $equal(or(and(not(X_49),and(X_50,X_51)),Y),not(and(not(and(not(X_49),and(X_50,X_51))),not(Y)))) )],[refute_0_1030,refute_0_1039]) ).
cnf(refute_0_1041,plain,
or(not(or(X_1,X_2)),Y) = implies(or(X_1,X_2),Y),
inference(subst,[],[refute_0_17:[bind(X,$fot(or(X_1,X_2)))]]) ).
cnf(refute_0_1042,plain,
or(and(not(X_1),not(X_2)),and(not(X_1),not(X_2))) = not(and(or(X_1,X_2),not(and(not(X_1),not(X_2))))),
inference(subst,[],[refute_0_359:[bind(Y,$fot(and(not(X_1),not(X_2))))]]) ).
cnf(refute_0_1043,plain,
or(and(not(X_1),not(X_2)),and(not(X_1),not(X_2))) = and(not(X_1),not(X_2)),
inference(subst,[],[refute_0_190:[bind(X_27414,$fot(and(not(X_1),not(X_2))))]]) ).
cnf(refute_0_1044,plain,
( or(and(not(X_1),not(X_2)),and(not(X_1),not(X_2))) != and(not(X_1),not(X_2))
| or(and(not(X_1),not(X_2)),and(not(X_1),not(X_2))) != not(and(or(X_1,X_2),not(and(not(X_1),not(X_2)))))
| and(not(X_1),not(X_2)) = not(and(or(X_1,X_2),not(and(not(X_1),not(X_2))))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_1),not(X_2)),and(not(X_1),not(X_2))),not(and(or(X_1,X_2),not(and(not(X_1),not(X_2)))))) ),[0],$fot(and(not(X_1),not(X_2)))]]) ).
cnf(refute_0_1045,plain,
( or(and(not(X_1),not(X_2)),and(not(X_1),not(X_2))) != not(and(or(X_1,X_2),not(and(not(X_1),not(X_2)))))
| and(not(X_1),not(X_2)) = not(and(or(X_1,X_2),not(and(not(X_1),not(X_2))))) ),
inference(resolve,[$cnf( $equal(or(and(not(X_1),not(X_2)),and(not(X_1),not(X_2))),and(not(X_1),not(X_2))) )],[refute_0_1043,refute_0_1044]) ).
cnf(refute_0_1046,plain,
and(not(X_1),not(X_2)) = not(and(or(X_1,X_2),not(and(not(X_1),not(X_2))))),
inference(resolve,[$cnf( $equal(or(and(not(X_1),not(X_2)),and(not(X_1),not(X_2))),not(and(or(X_1,X_2),not(and(not(X_1),not(X_2)))))) )],[refute_0_1042,refute_0_1045]) ).
cnf(refute_0_1047,plain,
and(or(X_1,X_2),not(and(not(X_1),not(X_2)))) = and(or(X_1,X_2),not(and(not(X_1),not(X_2)))),
introduced(tautology,[refl,[$fot(and(or(X_1,X_2),not(and(not(X_1),not(X_2)))))]]) ).
cnf(refute_0_1048,plain,
( and(or(X_1,X_2),not(and(not(X_1),not(X_2)))) != and(or(X_1,X_2),not(and(not(X_1),not(X_2))))
| not(and(not(X_1),not(X_2))) != or(X_1,X_2)
| and(or(X_1,X_2),not(and(not(X_1),not(X_2)))) = and(or(X_1,X_2),or(X_1,X_2)) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(X_1,X_2),not(and(not(X_1),not(X_2)))),and(or(X_1,X_2),not(and(not(X_1),not(X_2))))) ),[1,1],$fot(or(X_1,X_2))]]) ).
cnf(refute_0_1049,plain,
( not(and(not(X_1),not(X_2))) != or(X_1,X_2)
| and(or(X_1,X_2),not(and(not(X_1),not(X_2)))) = and(or(X_1,X_2),or(X_1,X_2)) ),
inference(resolve,[$cnf( $equal(and(or(X_1,X_2),not(and(not(X_1),not(X_2)))),and(or(X_1,X_2),not(and(not(X_1),not(X_2))))) )],[refute_0_1047,refute_0_1048]) ).
cnf(refute_0_1050,plain,
and(or(X_1,X_2),not(and(not(X_1),not(X_2)))) = and(or(X_1,X_2),or(X_1,X_2)),
inference(resolve,[$cnf( $equal(not(and(not(X_1),not(X_2))),or(X_1,X_2)) )],[refute_0_302,refute_0_1049]) ).
cnf(refute_0_1051,plain,
not(and(or(X_1,X_2),not(and(not(X_1),not(X_2))))) = not(and(or(X_1,X_2),not(and(not(X_1),not(X_2))))),
introduced(tautology,[refl,[$fot(not(and(or(X_1,X_2),not(and(not(X_1),not(X_2))))))]]) ).
cnf(refute_0_1052,plain,
( and(or(X_1,X_2),not(and(not(X_1),not(X_2)))) != and(or(X_1,X_2),or(X_1,X_2))
| not(and(or(X_1,X_2),not(and(not(X_1),not(X_2))))) != not(and(or(X_1,X_2),not(and(not(X_1),not(X_2)))))
| not(and(or(X_1,X_2),not(and(not(X_1),not(X_2))))) = not(and(or(X_1,X_2),or(X_1,X_2))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(or(X_1,X_2),not(and(not(X_1),not(X_2))))),not(and(or(X_1,X_2),not(and(not(X_1),not(X_2)))))) ),[1,0],$fot(and(or(X_1,X_2),or(X_1,X_2)))]]) ).
cnf(refute_0_1053,plain,
( and(or(X_1,X_2),not(and(not(X_1),not(X_2)))) != and(or(X_1,X_2),or(X_1,X_2))
| not(and(or(X_1,X_2),not(and(not(X_1),not(X_2))))) = not(and(or(X_1,X_2),or(X_1,X_2))) ),
inference(resolve,[$cnf( $equal(not(and(or(X_1,X_2),not(and(not(X_1),not(X_2))))),not(and(or(X_1,X_2),not(and(not(X_1),not(X_2)))))) )],[refute_0_1051,refute_0_1052]) ).
cnf(refute_0_1054,plain,
not(and(or(X_1,X_2),not(and(not(X_1),not(X_2))))) = not(and(or(X_1,X_2),or(X_1,X_2))),
inference(resolve,[$cnf( $equal(and(or(X_1,X_2),not(and(not(X_1),not(X_2)))),and(or(X_1,X_2),or(X_1,X_2))) )],[refute_0_1050,refute_0_1053]) ).
cnf(refute_0_1055,plain,
( and(not(X_1),not(X_2)) != not(and(or(X_1,X_2),not(and(not(X_1),not(X_2)))))
| not(and(or(X_1,X_2),not(and(not(X_1),not(X_2))))) != not(and(or(X_1,X_2),or(X_1,X_2)))
| and(not(X_1),not(X_2)) = not(and(or(X_1,X_2),or(X_1,X_2))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(not(X_1),not(X_2)),not(and(or(X_1,X_2),or(X_1,X_2)))) ),[0],$fot(not(and(or(X_1,X_2),not(and(not(X_1),not(X_2))))))]]) ).
cnf(refute_0_1056,plain,
( and(not(X_1),not(X_2)) != not(and(or(X_1,X_2),not(and(not(X_1),not(X_2)))))
| and(not(X_1),not(X_2)) = not(and(or(X_1,X_2),or(X_1,X_2))) ),
inference(resolve,[$cnf( $equal(not(and(or(X_1,X_2),not(and(not(X_1),not(X_2))))),not(and(or(X_1,X_2),or(X_1,X_2)))) )],[refute_0_1054,refute_0_1055]) ).
cnf(refute_0_1057,plain,
and(not(X_1),not(X_2)) = not(and(or(X_1,X_2),or(X_1,X_2))),
inference(resolve,[$cnf( $equal(and(not(X_1),not(X_2)),not(and(or(X_1,X_2),not(and(not(X_1),not(X_2)))))) )],[refute_0_1046,refute_0_1056]) ).
cnf(refute_0_1058,plain,
and(or(X_1,X_2),or(X_1,X_2)) = not(not(or(X_1,X_2))),
inference(subst,[],[refute_0_365:[bind(Y,$fot(or(X_1,X_2)))]]) ).
cnf(refute_0_1059,plain,
not(and(or(X_1,X_2),or(X_1,X_2))) = not(and(or(X_1,X_2),or(X_1,X_2))),
introduced(tautology,[refl,[$fot(not(and(or(X_1,X_2),or(X_1,X_2))))]]) ).
cnf(refute_0_1060,plain,
( and(or(X_1,X_2),or(X_1,X_2)) != not(not(or(X_1,X_2)))
| not(and(or(X_1,X_2),or(X_1,X_2))) != not(and(or(X_1,X_2),or(X_1,X_2)))
| not(and(or(X_1,X_2),or(X_1,X_2))) = not(not(not(or(X_1,X_2)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(or(X_1,X_2),or(X_1,X_2))),not(and(or(X_1,X_2),or(X_1,X_2)))) ),[1,0],$fot(not(not(or(X_1,X_2))))]]) ).
cnf(refute_0_1061,plain,
( and(or(X_1,X_2),or(X_1,X_2)) != not(not(or(X_1,X_2)))
| not(and(or(X_1,X_2),or(X_1,X_2))) = not(not(not(or(X_1,X_2)))) ),
inference(resolve,[$cnf( $equal(not(and(or(X_1,X_2),or(X_1,X_2))),not(and(or(X_1,X_2),or(X_1,X_2)))) )],[refute_0_1059,refute_0_1060]) ).
cnf(refute_0_1062,plain,
not(and(or(X_1,X_2),or(X_1,X_2))) = not(not(not(or(X_1,X_2)))),
inference(resolve,[$cnf( $equal(and(or(X_1,X_2),or(X_1,X_2)),not(not(or(X_1,X_2)))) )],[refute_0_1058,refute_0_1061]) ).
cnf(refute_0_1063,plain,
( and(not(X_1),not(X_2)) != not(and(or(X_1,X_2),or(X_1,X_2)))
| not(and(or(X_1,X_2),or(X_1,X_2))) != not(not(not(or(X_1,X_2))))
| and(not(X_1),not(X_2)) = not(not(not(or(X_1,X_2)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(not(X_1),not(X_2)),not(not(not(or(X_1,X_2))))) ),[0],$fot(not(and(or(X_1,X_2),or(X_1,X_2))))]]) ).
cnf(refute_0_1064,plain,
( and(not(X_1),not(X_2)) != not(and(or(X_1,X_2),or(X_1,X_2)))
| and(not(X_1),not(X_2)) = not(not(not(or(X_1,X_2)))) ),
inference(resolve,[$cnf( $equal(not(and(or(X_1,X_2),or(X_1,X_2))),not(not(not(or(X_1,X_2))))) )],[refute_0_1062,refute_0_1063]) ).
cnf(refute_0_1065,plain,
and(not(X_1),not(X_2)) = not(not(not(or(X_1,X_2)))),
inference(resolve,[$cnf( $equal(and(not(X_1),not(X_2)),not(and(or(X_1,X_2),or(X_1,X_2)))) )],[refute_0_1057,refute_0_1064]) ).
cnf(refute_0_1066,plain,
not(not(not(or(X_1,X_2)))) = not(or(X_1,X_2)),
inference(subst,[],[refute_0_693:[bind(X_31803,$fot(not(or(X_1,X_2))))]]) ).
cnf(refute_0_1067,plain,
( and(not(X_1),not(X_2)) != not(not(not(or(X_1,X_2))))
| not(not(not(or(X_1,X_2)))) != not(or(X_1,X_2))
| and(not(X_1),not(X_2)) = not(or(X_1,X_2)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(not(X_1),not(X_2)),not(or(X_1,X_2))) ),[0],$fot(not(not(not(or(X_1,X_2)))))]]) ).
cnf(refute_0_1068,plain,
( and(not(X_1),not(X_2)) != not(not(not(or(X_1,X_2))))
| and(not(X_1),not(X_2)) = not(or(X_1,X_2)) ),
inference(resolve,[$cnf( $equal(not(not(not(or(X_1,X_2)))),not(or(X_1,X_2))) )],[refute_0_1066,refute_0_1067]) ).
cnf(refute_0_1069,plain,
and(not(X_1),not(X_2)) = not(or(X_1,X_2)),
inference(resolve,[$cnf( $equal(and(not(X_1),not(X_2)),not(not(not(or(X_1,X_2))))) )],[refute_0_1065,refute_0_1068]) ).
cnf(refute_0_1070,plain,
or(and(not(X_1),not(X_2)),Y) = or(and(not(X_1),not(X_2)),Y),
introduced(tautology,[refl,[$fot(or(and(not(X_1),not(X_2)),Y))]]) ).
cnf(refute_0_1071,plain,
( and(not(X_1),not(X_2)) != not(or(X_1,X_2))
| or(and(not(X_1),not(X_2)),Y) != or(and(not(X_1),not(X_2)),Y)
| or(and(not(X_1),not(X_2)),Y) = or(not(or(X_1,X_2)),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_1),not(X_2)),Y),or(and(not(X_1),not(X_2)),Y)) ),[1,0],$fot(not(or(X_1,X_2)))]]) ).
cnf(refute_0_1072,plain,
( and(not(X_1),not(X_2)) != not(or(X_1,X_2))
| or(and(not(X_1),not(X_2)),Y) = or(not(or(X_1,X_2)),Y) ),
inference(resolve,[$cnf( $equal(or(and(not(X_1),not(X_2)),Y),or(and(not(X_1),not(X_2)),Y)) )],[refute_0_1070,refute_0_1071]) ).
cnf(refute_0_1073,plain,
or(and(not(X_1),not(X_2)),Y) = or(not(or(X_1,X_2)),Y),
inference(resolve,[$cnf( $equal(and(not(X_1),not(X_2)),not(or(X_1,X_2))) )],[refute_0_1069,refute_0_1072]) ).
cnf(refute_0_1074,plain,
( or(and(not(X_1),not(X_2)),Y) != or(not(or(X_1,X_2)),Y)
| or(not(or(X_1,X_2)),Y) != implies(or(X_1,X_2),Y)
| or(and(not(X_1),not(X_2)),Y) = implies(or(X_1,X_2),Y) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(or(and(not(X_1),not(X_2)),Y))),bind(Y0,$fot(or(not(or(X_1,X_2)),Y))),bind(Z,$fot(implies(or(X_1,X_2),Y)))]]) ).
cnf(refute_0_1075,plain,
( or(not(or(X_1,X_2)),Y) != implies(or(X_1,X_2),Y)
| or(and(not(X_1),not(X_2)),Y) = implies(or(X_1,X_2),Y) ),
inference(resolve,[$cnf( $equal(or(and(not(X_1),not(X_2)),Y),or(not(or(X_1,X_2)),Y)) )],[refute_0_1073,refute_0_1074]) ).
cnf(refute_0_1076,plain,
or(and(not(X_1),not(X_2)),Y) = implies(or(X_1,X_2),Y),
inference(resolve,[$cnf( $equal(or(not(or(X_1,X_2)),Y),implies(or(X_1,X_2),Y)) )],[refute_0_1041,refute_0_1075]) ).
cnf(refute_0_1077,plain,
( or(and(not(X_1),not(X_2)),Y) != implies(or(X_1,X_2),Y)
| or(and(not(X_1),not(X_2)),Y) != not(and(or(X_1,X_2),not(Y)))
| implies(or(X_1,X_2),Y) = not(and(or(X_1,X_2),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_1),not(X_2)),Y),not(and(or(X_1,X_2),not(Y)))) ),[0],$fot(implies(or(X_1,X_2),Y))]]) ).
cnf(refute_0_1078,plain,
( or(and(not(X_1),not(X_2)),Y) != not(and(or(X_1,X_2),not(Y)))
| implies(or(X_1,X_2),Y) = not(and(or(X_1,X_2),not(Y))) ),
inference(resolve,[$cnf( $equal(or(and(not(X_1),not(X_2)),Y),implies(or(X_1,X_2),Y)) )],[refute_0_1076,refute_0_1077]) ).
cnf(refute_0_1079,plain,
implies(or(X_1,X_2),Y) = not(and(or(X_1,X_2),not(Y))),
inference(resolve,[$cnf( $equal(or(and(not(X_1),not(X_2)),Y),not(and(or(X_1,X_2),not(Y)))) )],[refute_0_359,refute_0_1078]) ).
cnf(refute_0_1080,plain,
( implies(or(X_1,X_2),Y) != not(and(or(X_1,X_2),not(Y)))
| not(and(or(X_1,X_2),not(Y))) = implies(or(X_1,X_2),Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(or(X_1,X_2),Y))),bind(Y0,$fot(not(and(or(X_1,X_2),not(Y)))))]]) ).
cnf(refute_0_1081,plain,
not(and(or(X_1,X_2),not(Y))) = implies(or(X_1,X_2),Y),
inference(resolve,[$cnf( $equal(implies(or(X_1,X_2),Y),not(and(or(X_1,X_2),not(Y)))) )],[refute_0_1079,refute_0_1080]) ).
cnf(refute_0_1082,plain,
not(and(or(X_49,implies(X_50,not(X_51))),not(Y))) = implies(or(X_49,implies(X_50,not(X_51))),Y),
inference(subst,[],[refute_0_1081:[bind(X_1,$fot(X_49)),bind(X_2,$fot(implies(X_50,not(X_51))))]]) ).
cnf(refute_0_1083,plain,
( not(and(or(X_49,implies(X_50,not(X_51))),not(Y))) != implies(or(X_49,implies(X_50,not(X_51))),Y)
| or(and(not(X_49),and(X_50,X_51)),Y) != not(and(or(X_49,implies(X_50,not(X_51))),not(Y)))
| or(and(not(X_49),and(X_50,X_51)),Y) = implies(or(X_49,implies(X_50,not(X_51))),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_49),and(X_50,X_51)),Y),not(and(or(X_49,implies(X_50,not(X_51))),not(Y)))) ),[1],$fot(implies(or(X_49,implies(X_50,not(X_51))),Y))]]) ).
cnf(refute_0_1084,plain,
( or(and(not(X_49),and(X_50,X_51)),Y) != not(and(or(X_49,implies(X_50,not(X_51))),not(Y)))
| or(and(not(X_49),and(X_50,X_51)),Y) = implies(or(X_49,implies(X_50,not(X_51))),Y) ),
inference(resolve,[$cnf( $equal(not(and(or(X_49,implies(X_50,not(X_51))),not(Y))),implies(or(X_49,implies(X_50,not(X_51))),Y)) )],[refute_0_1082,refute_0_1083]) ).
cnf(refute_0_1085,plain,
or(and(not(X_49),and(X_50,X_51)),Y) = implies(or(X_49,implies(X_50,not(X_51))),Y),
inference(resolve,[$cnf( $equal(or(and(not(X_49),and(X_50,X_51)),Y),not(and(or(X_49,implies(X_50,not(X_51))),not(Y)))) )],[refute_0_1040,refute_0_1084]) ).
cnf(refute_0_1086,plain,
implies(X_50,not(X_51)) = not(and(X_50,X_51)),
inference(subst,[],[refute_0_888:[bind(X,$fot(X_50)),bind(Y,$fot(X_51))]]) ).
cnf(refute_0_1087,plain,
or(X_49,implies(X_50,not(X_51))) = or(X_49,implies(X_50,not(X_51))),
introduced(tautology,[refl,[$fot(or(X_49,implies(X_50,not(X_51))))]]) ).
cnf(refute_0_1088,plain,
( implies(X_50,not(X_51)) != not(and(X_50,X_51))
| or(X_49,implies(X_50,not(X_51))) != or(X_49,implies(X_50,not(X_51)))
| or(X_49,implies(X_50,not(X_51))) = or(X_49,not(and(X_50,X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_49,implies(X_50,not(X_51))),or(X_49,implies(X_50,not(X_51)))) ),[1,1],$fot(not(and(X_50,X_51)))]]) ).
cnf(refute_0_1089,plain,
( implies(X_50,not(X_51)) != not(and(X_50,X_51))
| or(X_49,implies(X_50,not(X_51))) = or(X_49,not(and(X_50,X_51))) ),
inference(resolve,[$cnf( $equal(or(X_49,implies(X_50,not(X_51))),or(X_49,implies(X_50,not(X_51)))) )],[refute_0_1087,refute_0_1088]) ).
cnf(refute_0_1090,plain,
or(X_49,implies(X_50,not(X_51))) = or(X_49,not(and(X_50,X_51))),
inference(resolve,[$cnf( $equal(implies(X_50,not(X_51)),not(and(X_50,X_51))) )],[refute_0_1086,refute_0_1089]) ).
cnf(refute_0_1091,plain,
implies(or(X_49,implies(X_50,not(X_51))),Y) = implies(or(X_49,implies(X_50,not(X_51))),Y),
introduced(tautology,[refl,[$fot(implies(or(X_49,implies(X_50,not(X_51))),Y))]]) ).
cnf(refute_0_1092,plain,
( implies(or(X_49,implies(X_50,not(X_51))),Y) != implies(or(X_49,implies(X_50,not(X_51))),Y)
| or(X_49,implies(X_50,not(X_51))) != or(X_49,not(and(X_50,X_51)))
| implies(or(X_49,implies(X_50,not(X_51))),Y) = implies(or(X_49,not(and(X_50,X_51))),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_49,implies(X_50,not(X_51))),Y),implies(or(X_49,implies(X_50,not(X_51))),Y)) ),[1,0],$fot(or(X_49,not(and(X_50,X_51))))]]) ).
cnf(refute_0_1093,plain,
( or(X_49,implies(X_50,not(X_51))) != or(X_49,not(and(X_50,X_51)))
| implies(or(X_49,implies(X_50,not(X_51))),Y) = implies(or(X_49,not(and(X_50,X_51))),Y) ),
inference(resolve,[$cnf( $equal(implies(or(X_49,implies(X_50,not(X_51))),Y),implies(or(X_49,implies(X_50,not(X_51))),Y)) )],[refute_0_1091,refute_0_1092]) ).
cnf(refute_0_1094,plain,
implies(or(X_49,implies(X_50,not(X_51))),Y) = implies(or(X_49,not(and(X_50,X_51))),Y),
inference(resolve,[$cnf( $equal(or(X_49,implies(X_50,not(X_51))),or(X_49,not(and(X_50,X_51)))) )],[refute_0_1090,refute_0_1093]) ).
cnf(refute_0_1095,plain,
( implies(or(X_49,implies(X_50,not(X_51))),Y) != implies(or(X_49,not(and(X_50,X_51))),Y)
| or(and(not(X_49),and(X_50,X_51)),Y) != implies(or(X_49,implies(X_50,not(X_51))),Y)
| or(and(not(X_49),and(X_50,X_51)),Y) = implies(or(X_49,not(and(X_50,X_51))),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_49),and(X_50,X_51)),Y),implies(or(X_49,implies(X_50,not(X_51))),Y)) ),[1],$fot(implies(or(X_49,not(and(X_50,X_51))),Y))]]) ).
cnf(refute_0_1096,plain,
( or(and(not(X_49),and(X_50,X_51)),Y) != implies(or(X_49,implies(X_50,not(X_51))),Y)
| or(and(not(X_49),and(X_50,X_51)),Y) = implies(or(X_49,not(and(X_50,X_51))),Y) ),
inference(resolve,[$cnf( $equal(implies(or(X_49,implies(X_50,not(X_51))),Y),implies(or(X_49,not(and(X_50,X_51))),Y)) )],[refute_0_1094,refute_0_1095]) ).
cnf(refute_0_1097,plain,
or(and(not(X_49),and(X_50,X_51)),Y) = implies(or(X_49,not(and(X_50,X_51))),Y),
inference(resolve,[$cnf( $equal(or(and(not(X_49),and(X_50,X_51)),Y),implies(or(X_49,implies(X_50,not(X_51))),Y)) )],[refute_0_1085,refute_0_1096]) ).
cnf(refute_0_1098,plain,
or(and(not(X_33558),and(X_33560,X_33560)),X_33557) = implies(or(X_33558,not(and(X_33560,X_33560))),X_33557),
inference(subst,[],[refute_0_1097:[bind(Y,$fot(X_33557)),bind(X_49,$fot(X_33558)),bind(X_50,$fot(X_33560)),bind(X_51,$fot(X_33560))]]) ).
cnf(refute_0_1099,plain,
and(X_33560,X_33560) = X_33560,
inference(subst,[],[refute_0_954:[bind(Y,$fot(X_33560))]]) ).
cnf(refute_0_1100,plain,
( and(X_33560,X_33560) != X_33560
| or(and(not(X_33558),and(X_33560,X_33560)),X_33557) != implies(or(X_33558,not(and(X_33560,X_33560))),X_33557)
| or(and(not(X_33558),X_33560),X_33557) = implies(or(X_33558,not(and(X_33560,X_33560))),X_33557) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_33558),and(X_33560,X_33560)),X_33557),implies(or(X_33558,not(and(X_33560,X_33560))),X_33557)) ),[0,0,1],$fot(X_33560)]]) ).
cnf(refute_0_1101,plain,
( or(and(not(X_33558),and(X_33560,X_33560)),X_33557) != implies(or(X_33558,not(and(X_33560,X_33560))),X_33557)
| or(and(not(X_33558),X_33560),X_33557) = implies(or(X_33558,not(and(X_33560,X_33560))),X_33557) ),
inference(resolve,[$cnf( $equal(and(X_33560,X_33560),X_33560) )],[refute_0_1099,refute_0_1100]) ).
cnf(refute_0_1102,plain,
or(and(not(X_33558),X_33560),X_33557) = implies(or(X_33558,not(and(X_33560,X_33560))),X_33557),
inference(resolve,[$cnf( $equal(or(and(not(X_33558),and(X_33560,X_33560)),X_33557),implies(or(X_33558,not(and(X_33560,X_33560))),X_33557)) )],[refute_0_1098,refute_0_1101]) ).
cnf(refute_0_1103,plain,
not(and(X_33560,X_33560)) = not(and(X_33560,X_33560)),
introduced(tautology,[refl,[$fot(not(and(X_33560,X_33560)))]]) ).
cnf(refute_0_1104,plain,
( and(X_33560,X_33560) != X_33560
| not(and(X_33560,X_33560)) != not(and(X_33560,X_33560))
| not(and(X_33560,X_33560)) = not(X_33560) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(X_33560,X_33560)),not(and(X_33560,X_33560))) ),[1,0],$fot(X_33560)]]) ).
cnf(refute_0_1105,plain,
( and(X_33560,X_33560) != X_33560
| not(and(X_33560,X_33560)) = not(X_33560) ),
inference(resolve,[$cnf( $equal(not(and(X_33560,X_33560)),not(and(X_33560,X_33560))) )],[refute_0_1103,refute_0_1104]) ).
cnf(refute_0_1106,plain,
not(and(X_33560,X_33560)) = not(X_33560),
inference(resolve,[$cnf( $equal(and(X_33560,X_33560),X_33560) )],[refute_0_1099,refute_0_1105]) ).
cnf(refute_0_1107,plain,
or(X_33558,not(and(X_33560,X_33560))) = or(X_33558,not(and(X_33560,X_33560))),
introduced(tautology,[refl,[$fot(or(X_33558,not(and(X_33560,X_33560))))]]) ).
cnf(refute_0_1108,plain,
( not(and(X_33560,X_33560)) != not(X_33560)
| or(X_33558,not(and(X_33560,X_33560))) != or(X_33558,not(and(X_33560,X_33560)))
| or(X_33558,not(and(X_33560,X_33560))) = or(X_33558,not(X_33560)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_33558,not(and(X_33560,X_33560))),or(X_33558,not(and(X_33560,X_33560)))) ),[1,1],$fot(not(X_33560))]]) ).
cnf(refute_0_1109,plain,
( not(and(X_33560,X_33560)) != not(X_33560)
| or(X_33558,not(and(X_33560,X_33560))) = or(X_33558,not(X_33560)) ),
inference(resolve,[$cnf( $equal(or(X_33558,not(and(X_33560,X_33560))),or(X_33558,not(and(X_33560,X_33560)))) )],[refute_0_1107,refute_0_1108]) ).
cnf(refute_0_1110,plain,
or(X_33558,not(and(X_33560,X_33560))) = or(X_33558,not(X_33560)),
inference(resolve,[$cnf( $equal(not(and(X_33560,X_33560)),not(X_33560)) )],[refute_0_1106,refute_0_1109]) ).
cnf(refute_0_1111,plain,
implies(or(X_33558,not(and(X_33560,X_33560))),X_33557) = implies(or(X_33558,not(and(X_33560,X_33560))),X_33557),
introduced(tautology,[refl,[$fot(implies(or(X_33558,not(and(X_33560,X_33560))),X_33557))]]) ).
cnf(refute_0_1112,plain,
( implies(or(X_33558,not(and(X_33560,X_33560))),X_33557) != implies(or(X_33558,not(and(X_33560,X_33560))),X_33557)
| or(X_33558,not(and(X_33560,X_33560))) != or(X_33558,not(X_33560))
| implies(or(X_33558,not(and(X_33560,X_33560))),X_33557) = implies(or(X_33558,not(X_33560)),X_33557) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_33558,not(and(X_33560,X_33560))),X_33557),implies(or(X_33558,not(and(X_33560,X_33560))),X_33557)) ),[1,0],$fot(or(X_33558,not(X_33560)))]]) ).
cnf(refute_0_1113,plain,
( or(X_33558,not(and(X_33560,X_33560))) != or(X_33558,not(X_33560))
| implies(or(X_33558,not(and(X_33560,X_33560))),X_33557) = implies(or(X_33558,not(X_33560)),X_33557) ),
inference(resolve,[$cnf( $equal(implies(or(X_33558,not(and(X_33560,X_33560))),X_33557),implies(or(X_33558,not(and(X_33560,X_33560))),X_33557)) )],[refute_0_1111,refute_0_1112]) ).
cnf(refute_0_1114,plain,
implies(or(X_33558,not(and(X_33560,X_33560))),X_33557) = implies(or(X_33558,not(X_33560)),X_33557),
inference(resolve,[$cnf( $equal(or(X_33558,not(and(X_33560,X_33560))),or(X_33558,not(X_33560))) )],[refute_0_1110,refute_0_1113]) ).
cnf(refute_0_1115,plain,
( implies(or(X_33558,not(and(X_33560,X_33560))),X_33557) != implies(or(X_33558,not(X_33560)),X_33557)
| or(and(not(X_33558),X_33560),X_33557) != implies(or(X_33558,not(and(X_33560,X_33560))),X_33557)
| or(and(not(X_33558),X_33560),X_33557) = implies(or(X_33558,not(X_33560)),X_33557) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_33558),X_33560),X_33557),implies(or(X_33558,not(and(X_33560,X_33560))),X_33557)) ),[1],$fot(implies(or(X_33558,not(X_33560)),X_33557))]]) ).
cnf(refute_0_1116,plain,
( or(and(not(X_33558),X_33560),X_33557) != implies(or(X_33558,not(and(X_33560,X_33560))),X_33557)
| or(and(not(X_33558),X_33560),X_33557) = implies(or(X_33558,not(X_33560)),X_33557) ),
inference(resolve,[$cnf( $equal(implies(or(X_33558,not(and(X_33560,X_33560))),X_33557),implies(or(X_33558,not(X_33560)),X_33557)) )],[refute_0_1114,refute_0_1115]) ).
cnf(refute_0_1117,plain,
or(and(not(X_33558),X_33560),X_33557) = implies(or(X_33558,not(X_33560)),X_33557),
inference(resolve,[$cnf( $equal(or(and(not(X_33558),X_33560),X_33557),implies(or(X_33558,not(and(X_33560,X_33560))),X_33557)) )],[refute_0_1102,refute_0_1116]) ).
cnf(refute_0_1118,plain,
or(and(not(X_33140),X_33140),X_33140) = implies(or(X_33140,not(X_33140)),X_33140),
inference(subst,[],[refute_0_1117:[bind(X_33557,$fot(X_33140)),bind(X_33558,$fot(X_33140)),bind(X_33560,$fot(X_33140))]]) ).
cnf(refute_0_1119,plain,
implies(X_33140,or(and(not(X_33140),X_33140),X_33140)) = implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),
introduced(tautology,[refl,[$fot(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)))]]) ).
cnf(refute_0_1120,plain,
( implies(X_33140,or(and(not(X_33140),X_33140),X_33140)) != implies(X_33140,or(and(not(X_33140),X_33140),X_33140))
| or(and(not(X_33140),X_33140),X_33140) != implies(or(X_33140,not(X_33140)),X_33140)
| implies(X_33140,or(and(not(X_33140),X_33140),X_33140)) = implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),implies(X_33140,or(and(not(X_33140),X_33140),X_33140))) ),[1,1],$fot(implies(or(X_33140,not(X_33140)),X_33140))]]) ).
cnf(refute_0_1121,plain,
( or(and(not(X_33140),X_33140),X_33140) != implies(or(X_33140,not(X_33140)),X_33140)
| implies(X_33140,or(and(not(X_33140),X_33140),X_33140)) = implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)) ),
inference(resolve,[$cnf( $equal(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),implies(X_33140,or(and(not(X_33140),X_33140),X_33140))) )],[refute_0_1119,refute_0_1120]) ).
cnf(refute_0_1122,plain,
implies(X_33140,or(and(not(X_33140),X_33140),X_33140)) = implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),
inference(resolve,[$cnf( $equal(or(and(not(X_33140),X_33140),X_33140),implies(or(X_33140,not(X_33140)),X_33140)) )],[refute_0_1118,refute_0_1121]) ).
cnf(refute_0_1123,plain,
and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X) = and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X),
introduced(tautology,[refl,[$fot(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))]]) ).
cnf(refute_0_1124,plain,
( and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X) != and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)
| implies(X_33140,or(and(not(X_33140),X_33140),X_33140)) != implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140))
| and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X) = and(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),X) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X),and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)) ),[1,0],$fot(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)))]]) ).
cnf(refute_0_1125,plain,
( implies(X_33140,or(and(not(X_33140),X_33140),X_33140)) != implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140))
| and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X) = and(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),X) ),
inference(resolve,[$cnf( $equal(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X),and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)) )],[refute_0_1123,refute_0_1124]) ).
cnf(refute_0_1126,plain,
and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X) = and(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),X),
inference(resolve,[$cnf( $equal(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140))) )],[refute_0_1122,refute_0_1125]) ).
cnf(refute_0_1127,plain,
implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)) = implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)),
introduced(tautology,[refl,[$fot(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))]]) ).
cnf(refute_0_1128,plain,
( and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X) != and(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),X)
| implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)) != implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))
| implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)) = implies(X,and(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)),implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) ),[1,1],$fot(and(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),X))]]) ).
cnf(refute_0_1129,plain,
( and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X) != and(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),X)
| implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)) = implies(X,and(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),X)) ),
inference(resolve,[$cnf( $equal(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)),implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) )],[refute_0_1127,refute_0_1128]) ).
cnf(refute_0_1130,plain,
implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)) = implies(X,and(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),X)),
inference(resolve,[$cnf( $equal(and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X),and(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),X)) )],[refute_0_1126,refute_0_1129]) ).
cnf(refute_0_1131,plain,
( implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)) != implies(X,and(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),X))
| ~ is_a_theorem(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))
| is_a_theorem(implies(X,and(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) ),[0],$fot(implies(X,and(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),X)))]]) ).
cnf(refute_0_1132,plain,
( ~ is_a_theorem(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)))
| is_a_theorem(implies(X,and(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),X))) ),
inference(resolve,[$cnf( $equal(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X)),implies(X,and(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),X))) )],[refute_0_1130,refute_0_1131]) ).
cnf(refute_0_1133,plain,
is_a_theorem(implies(X,and(implies(X_33140,implies(or(X_33140,not(X_33140)),X_33140)),X))),
inference(resolve,[$cnf( is_a_theorem(implies(X,and(implies(X_33140,or(and(not(X_33140),X_33140),X_33140)),X))) )],[refute_0_1029,refute_0_1132]) ).
cnf(refute_0_1134,plain,
is_a_theorem(implies(implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562),and(implies(X_33562,implies(or(X_33562,not(X_33562)),X_33562)),implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562)))),
inference(subst,[],[refute_0_1133:[bind(X,$fot(implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562))),bind(X_33140,$fot(X_33562))]]) ).
cnf(refute_0_1135,plain,
equiv(X_33562,implies(or(X_33562,not(X_33562)),X_33562)) = and(implies(X_33562,implies(or(X_33562,not(X_33562)),X_33562)),implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562)),
inference(subst,[],[refute_0_172:[bind(X,$fot(X_33562)),bind(Y,$fot(implies(or(X_33562,not(X_33562)),X_33562)))]]) ).
cnf(refute_0_1136,plain,
( equiv(X_33562,implies(or(X_33562,not(X_33562)),X_33562)) != and(implies(X_33562,implies(or(X_33562,not(X_33562)),X_33562)),implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562))
| and(implies(X_33562,implies(or(X_33562,not(X_33562)),X_33562)),implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562)) = equiv(X_33562,implies(or(X_33562,not(X_33562)),X_33562)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(X_33562,implies(or(X_33562,not(X_33562)),X_33562)))),bind(Y0,$fot(and(implies(X_33562,implies(or(X_33562,not(X_33562)),X_33562)),implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562))))]]) ).
cnf(refute_0_1137,plain,
and(implies(X_33562,implies(or(X_33562,not(X_33562)),X_33562)),implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562)) = equiv(X_33562,implies(or(X_33562,not(X_33562)),X_33562)),
inference(resolve,[$cnf( $equal(equiv(X_33562,implies(or(X_33562,not(X_33562)),X_33562)),and(implies(X_33562,implies(or(X_33562,not(X_33562)),X_33562)),implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562))) )],[refute_0_1135,refute_0_1136]) ).
cnf(refute_0_1138,plain,
( and(implies(X_33562,implies(or(X_33562,not(X_33562)),X_33562)),implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562)) != equiv(X_33562,implies(or(X_33562,not(X_33562)),X_33562))
| ~ is_a_theorem(implies(implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562),and(implies(X_33562,implies(or(X_33562,not(X_33562)),X_33562)),implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562))))
| is_a_theorem(implies(implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562),equiv(X_33562,implies(or(X_33562,not(X_33562)),X_33562)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562),and(implies(X_33562,implies(or(X_33562,not(X_33562)),X_33562)),implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562)))) ),[0,1],$fot(equiv(X_33562,implies(or(X_33562,not(X_33562)),X_33562)))]]) ).
cnf(refute_0_1139,plain,
( ~ is_a_theorem(implies(implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562),and(implies(X_33562,implies(or(X_33562,not(X_33562)),X_33562)),implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562))))
| is_a_theorem(implies(implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562),equiv(X_33562,implies(or(X_33562,not(X_33562)),X_33562)))) ),
inference(resolve,[$cnf( $equal(and(implies(X_33562,implies(or(X_33562,not(X_33562)),X_33562)),implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562)),equiv(X_33562,implies(or(X_33562,not(X_33562)),X_33562))) )],[refute_0_1137,refute_0_1138]) ).
cnf(refute_0_1140,plain,
is_a_theorem(implies(implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562),equiv(X_33562,implies(or(X_33562,not(X_33562)),X_33562)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562),and(implies(X_33562,implies(or(X_33562,not(X_33562)),X_33562)),implies(implies(or(X_33562,not(X_33562)),X_33562),X_33562)))) )],[refute_0_1134,refute_0_1139]) ).
cnf(refute_0_1141,plain,
is_a_theorem(implies(implies(implies(or(X_33609,not(X_33609)),X_33609),X_33609),equiv(X_33609,implies(or(X_33609,not(X_33609)),X_33609)))),
inference(subst,[],[refute_0_1140:[bind(X_33562,$fot(X_33609))]]) ).
cnf(refute_0_1142,plain,
( ~ is_a_theorem(implies(implies(or(X_33609,not(X_33609)),X_33609),X_33609))
| is_a_theorem(equiv(X_33609,implies(or(X_33609,not(X_33609)),X_33609))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(or(X_33609,not(X_33609)),X_33609),X_33609),equiv(X_33609,implies(or(X_33609,not(X_33609)),X_33609)))) )],[refute_0_1141,refute_0_850]) ).
cnf(refute_0_1143,plain,
( ~ is_a_theorem(not(and(X_9538,not(X_9538))))
| is_a_theorem(implies(implies(not(and(X_9538,not(X_9538))),X_24842),X_24842)) ),
inference(subst,[],[refute_0_157:[bind(X_3653,$fot(not(and(X_9538,not(X_9538))))),bind(X_3654,$fot(X_24842))]]) ).
cnf(refute_0_1144,plain,
is_a_theorem(implies(implies(not(and(X_9538,not(X_9538))),X_24842),X_24842)),
inference(resolve,[$cnf( is_a_theorem(not(and(X_9538,not(X_9538)))) )],[refute_0_689,refute_0_1143]) ).
cnf(refute_0_1145,plain,
is_a_theorem(implies(implies(not(and(not(X),not(not(X)))),X_24893),X_24893)),
inference(subst,[],[refute_0_1144:[bind(X_24842,$fot(X_24893)),bind(X_9538,$fot(not(X)))]]) ).
cnf(refute_0_1146,plain,
or(X,not(X)) = not(and(not(X),not(not(X)))),
inference(subst,[],[refute_0_5:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_1147,plain,
( or(X,not(X)) != not(and(not(X),not(not(X))))
| not(and(not(X),not(not(X)))) = or(X,not(X)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,not(X)))),bind(Y0,$fot(not(and(not(X),not(not(X))))))]]) ).
cnf(refute_0_1148,plain,
not(and(not(X),not(not(X)))) = or(X,not(X)),
inference(resolve,[$cnf( $equal(or(X,not(X)),not(and(not(X),not(not(X))))) )],[refute_0_1146,refute_0_1147]) ).
cnf(refute_0_1149,plain,
( not(and(not(X),not(not(X)))) != or(X,not(X))
| ~ is_a_theorem(implies(implies(not(and(not(X),not(not(X)))),X_24893),X_24893))
| is_a_theorem(implies(implies(or(X,not(X)),X_24893),X_24893)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(and(not(X),not(not(X)))),X_24893),X_24893)) ),[0,0,0],$fot(or(X,not(X)))]]) ).
cnf(refute_0_1150,plain,
( ~ is_a_theorem(implies(implies(not(and(not(X),not(not(X)))),X_24893),X_24893))
| is_a_theorem(implies(implies(or(X,not(X)),X_24893),X_24893)) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(not(X)))),or(X,not(X))) )],[refute_0_1148,refute_0_1149]) ).
cnf(refute_0_1151,plain,
is_a_theorem(implies(implies(or(X,not(X)),X_24893),X_24893)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(and(not(X),not(not(X)))),X_24893),X_24893)) )],[refute_0_1145,refute_0_1150]) ).
cnf(refute_0_1152,plain,
is_a_theorem(implies(implies(or(X_33609,not(X_33609)),X_33609),X_33609)),
inference(subst,[],[refute_0_1151:[bind(X,$fot(X_33609)),bind(X_24893,$fot(X_33609))]]) ).
cnf(refute_0_1153,plain,
is_a_theorem(equiv(X_33609,implies(or(X_33609,not(X_33609)),X_33609))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_33609,not(X_33609)),X_33609),X_33609)) )],[refute_0_1152,refute_0_1142]) ).
cnf(refute_0_1154,plain,
is_a_theorem(equiv(X_33610,implies(or(X_33610,not(X_33610)),X_33610))),
inference(subst,[],[refute_0_1153:[bind(X_33609,$fot(X_33610))]]) ).
cnf(refute_0_1155,plain,
X_33610 = implies(or(X_33610,not(X_33610)),X_33610),
inference(resolve,[$cnf( is_a_theorem(equiv(X_33610,implies(or(X_33610,not(X_33610)),X_33610))) )],[refute_0_1154,refute_0_849]) ).
cnf(refute_0_1156,plain,
( ~ is_a_theorem(equiv(equiv(X_35416,X_35416),or(X_35416,not(X_35416))))
| equiv(X_35416,X_35416) = or(X_35416,not(X_35416)) ),
inference(subst,[],[refute_0_51:[bind(X,$fot(equiv(X_35416,X_35416))),bind(Y,$fot(or(X_35416,not(X_35416))))]]) ).
cnf(refute_0_1157,plain,
( ~ is_a_theorem(implies(implies(or(X_35415,not(X_35415)),equiv(X_35415,X_35415)),equiv(equiv(X_35415,X_35415),or(X_35415,not(X_35415)))))
| ~ is_a_theorem(implies(or(X_35415,not(X_35415)),equiv(X_35415,X_35415)))
| is_a_theorem(equiv(equiv(X_35415,X_35415),or(X_35415,not(X_35415)))) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(implies(or(X_35415,not(X_35415)),equiv(X_35415,X_35415)))),bind(Y,$fot(equiv(equiv(X_35415,X_35415),or(X_35415,not(X_35415)))))]]) ).
cnf(refute_0_1158,plain,
( ~ is_a_theorem(implies(implies(implies(or(X_34375,not(X_34375)),equiv(X_34375,X_34375)),X_34376),X_34376))
| is_a_theorem(or(X_34376,not(implies(implies(or(X_34375,not(X_34375)),equiv(X_34375,X_34375)),X_34376)))) ),
inference(subst,[],[refute_0_656:[bind(X,$fot(implies(implies(or(X_34375,not(X_34375)),equiv(X_34375,X_34375)),X_34376))),bind(X_16,$fot(X_34376))]]) ).
cnf(refute_0_1159,plain,
( ~ is_a_theorem(implies(or(X_33584,not(X_33585)),implies(or(X_33585,X_33584),X_33584)))
| is_a_theorem(implies(implies(implies(or(X_33584,not(X_33585)),implies(or(X_33585,X_33584),X_33584)),X_3654),X_3654)) ),
inference(subst,[],[refute_0_157:[bind(X_3653,$fot(implies(or(X_33584,not(X_33585)),implies(or(X_33585,X_33584),X_33584))))]]) ).
cnf(refute_0_1160,plain,
( ~ is_a_theorem(implies(or(X_32642,X_32641),or(and(not(X_32641),X_32642),X_32641)))
| is_a_theorem(or(and(not(X_32641),X_32642),implies(or(X_32642,X_32641),X_32641))) ),
inference(subst,[],[refute_0_142:[bind(X,$fot(or(X_32642,X_32641))),bind(X_72,$fot(and(not(X_32641),X_32642))),bind(X_73,$fot(X_32641))]]) ).
cnf(refute_0_1161,plain,
is_a_theorem(or(and(not(X_32641),X_32642),implies(or(X_32642,X_32641),X_32641))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_32642,X_32641),or(and(not(X_32641),X_32642),X_32641))) )],[refute_0_990,refute_0_1160]) ).
cnf(refute_0_1162,plain,
or(and(not(X_32641),X_32642),implies(or(X_32642,X_32641),X_32641)) = implies(or(X_32641,not(X_32642)),implies(or(X_32642,X_32641),X_32641)),
inference(subst,[],[refute_0_1117:[bind(X_33557,$fot(implies(or(X_32642,X_32641),X_32641))),bind(X_33558,$fot(X_32641)),bind(X_33560,$fot(X_32642))]]) ).
cnf(refute_0_1163,plain,
( or(and(not(X_32641),X_32642),implies(or(X_32642,X_32641),X_32641)) != implies(or(X_32641,not(X_32642)),implies(or(X_32642,X_32641),X_32641))
| ~ is_a_theorem(or(and(not(X_32641),X_32642),implies(or(X_32642,X_32641),X_32641)))
| is_a_theorem(implies(or(X_32641,not(X_32642)),implies(or(X_32642,X_32641),X_32641))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(X_32641),X_32642),implies(or(X_32642,X_32641),X_32641))) ),[0],$fot(implies(or(X_32641,not(X_32642)),implies(or(X_32642,X_32641),X_32641)))]]) ).
cnf(refute_0_1164,plain,
( ~ is_a_theorem(or(and(not(X_32641),X_32642),implies(or(X_32642,X_32641),X_32641)))
| is_a_theorem(implies(or(X_32641,not(X_32642)),implies(or(X_32642,X_32641),X_32641))) ),
inference(resolve,[$cnf( $equal(or(and(not(X_32641),X_32642),implies(or(X_32642,X_32641),X_32641)),implies(or(X_32641,not(X_32642)),implies(or(X_32642,X_32641),X_32641))) )],[refute_0_1162,refute_0_1163]) ).
cnf(refute_0_1165,plain,
is_a_theorem(implies(or(X_32641,not(X_32642)),implies(or(X_32642,X_32641),X_32641))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(X_32641),X_32642),implies(or(X_32642,X_32641),X_32641))) )],[refute_0_1161,refute_0_1164]) ).
cnf(refute_0_1166,plain,
is_a_theorem(implies(or(X_33584,not(X_33585)),implies(or(X_33585,X_33584),X_33584))),
inference(subst,[],[refute_0_1165:[bind(X_32641,$fot(X_33584)),bind(X_32642,$fot(X_33585))]]) ).
cnf(refute_0_1167,plain,
is_a_theorem(implies(implies(implies(or(X_33584,not(X_33585)),implies(or(X_33585,X_33584),X_33584)),X_3654),X_3654)),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_33584,not(X_33585)),implies(or(X_33585,X_33584),X_33584))) )],[refute_0_1166,refute_0_1159]) ).
cnf(refute_0_1168,plain,
is_a_theorem(implies(implies(implies(or(X_34356,not(X_34356)),implies(or(X_34356,X_34356),X_34356)),X_34358),X_34358)),
inference(subst,[],[refute_0_1167:[bind(X_33584,$fot(X_34356)),bind(X_33585,$fot(X_34356)),bind(X_3654,$fot(X_34358))]]) ).
cnf(refute_0_1169,plain,
or(X_34356,X_34356) = X_34356,
inference(subst,[],[refute_0_190:[bind(X_27414,$fot(X_34356))]]) ).
cnf(refute_0_1170,plain,
( or(X_34356,X_34356) != X_34356
| ~ is_a_theorem(implies(implies(implies(or(X_34356,not(X_34356)),implies(or(X_34356,X_34356),X_34356)),X_34358),X_34358))
| is_a_theorem(implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(implies(or(X_34356,not(X_34356)),implies(or(X_34356,X_34356),X_34356)),X_34358),X_34358)) ),[0,0,0,1,0],$fot(X_34356)]]) ).
cnf(refute_0_1171,plain,
( ~ is_a_theorem(implies(implies(implies(or(X_34356,not(X_34356)),implies(or(X_34356,X_34356),X_34356)),X_34358),X_34358))
| is_a_theorem(implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358)) ),
inference(resolve,[$cnf( $equal(or(X_34356,X_34356),X_34356) )],[refute_0_1169,refute_0_1170]) ).
cnf(refute_0_1172,plain,
is_a_theorem(implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(or(X_34356,not(X_34356)),implies(or(X_34356,X_34356),X_34356)),X_34358),X_34358)) )],[refute_0_1168,refute_0_1171]) ).
cnf(refute_0_1173,plain,
equiv(Y,Y) = and(implies(Y,Y),implies(Y,Y)),
inference(subst,[],[refute_0_172:[bind(X,$fot(Y))]]) ).
cnf(refute_0_1174,plain,
and(implies(Y,Y),implies(Y,Y)) = not(not(implies(Y,Y))),
inference(subst,[],[refute_0_365:[bind(Y,$fot(implies(Y,Y)))]]) ).
cnf(refute_0_1175,plain,
( and(implies(Y,Y),implies(Y,Y)) != not(not(implies(Y,Y)))
| equiv(Y,Y) != and(implies(Y,Y),implies(Y,Y))
| equiv(Y,Y) = not(not(implies(Y,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(Y,Y),and(implies(Y,Y),implies(Y,Y))) ),[1],$fot(not(not(implies(Y,Y))))]]) ).
cnf(refute_0_1176,plain,
( equiv(Y,Y) != and(implies(Y,Y),implies(Y,Y))
| equiv(Y,Y) = not(not(implies(Y,Y))) ),
inference(resolve,[$cnf( $equal(and(implies(Y,Y),implies(Y,Y)),not(not(implies(Y,Y)))) )],[refute_0_1174,refute_0_1175]) ).
cnf(refute_0_1177,plain,
equiv(Y,Y) = not(not(implies(Y,Y))),
inference(resolve,[$cnf( $equal(equiv(Y,Y),and(implies(Y,Y),implies(Y,Y))) )],[refute_0_1173,refute_0_1176]) ).
cnf(refute_0_1178,plain,
not(not(implies(Y,Y))) = implies(Y,Y),
inference(subst,[],[refute_0_693:[bind(X_31803,$fot(implies(Y,Y)))]]) ).
cnf(refute_0_1179,plain,
( equiv(Y,Y) != not(not(implies(Y,Y)))
| not(not(implies(Y,Y))) != implies(Y,Y)
| equiv(Y,Y) = implies(Y,Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(equiv(Y,Y),implies(Y,Y)) ),[0],$fot(not(not(implies(Y,Y))))]]) ).
cnf(refute_0_1180,plain,
( equiv(Y,Y) != not(not(implies(Y,Y)))
| equiv(Y,Y) = implies(Y,Y) ),
inference(resolve,[$cnf( $equal(not(not(implies(Y,Y))),implies(Y,Y)) )],[refute_0_1178,refute_0_1179]) ).
cnf(refute_0_1181,plain,
equiv(Y,Y) = implies(Y,Y),
inference(resolve,[$cnf( $equal(equiv(Y,Y),not(not(implies(Y,Y)))) )],[refute_0_1177,refute_0_1180]) ).
cnf(refute_0_1182,plain,
( equiv(Y,Y) != implies(Y,Y)
| implies(Y,Y) = equiv(Y,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(Y,Y))),bind(Y0,$fot(implies(Y,Y)))]]) ).
cnf(refute_0_1183,plain,
implies(Y,Y) = equiv(Y,Y),
inference(resolve,[$cnf( $equal(equiv(Y,Y),implies(Y,Y)) )],[refute_0_1181,refute_0_1182]) ).
cnf(refute_0_1184,plain,
implies(X_34356,X_34356) = equiv(X_34356,X_34356),
inference(subst,[],[refute_0_1183:[bind(Y,$fot(X_34356))]]) ).
cnf(refute_0_1185,plain,
implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)) = implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),
introduced(tautology,[refl,[$fot(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)))]]) ).
cnf(refute_0_1186,plain,
( implies(X_34356,X_34356) != equiv(X_34356,X_34356)
| implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)) != implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356))
| implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)) = implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356))) ),[1,1],$fot(equiv(X_34356,X_34356))]]) ).
cnf(refute_0_1187,plain,
( implies(X_34356,X_34356) != equiv(X_34356,X_34356)
| implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)) = implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)) ),
inference(resolve,[$cnf( $equal(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356))) )],[refute_0_1185,refute_0_1186]) ).
cnf(refute_0_1188,plain,
implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)) = implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),
inference(resolve,[$cnf( $equal(implies(X_34356,X_34356),equiv(X_34356,X_34356)) )],[refute_0_1184,refute_0_1187]) ).
cnf(refute_0_1189,plain,
implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358) = implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),
introduced(tautology,[refl,[$fot(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358))]]) ).
cnf(refute_0_1190,plain,
( implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358) != implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358)
| implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)) != implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356))
| implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358) = implies(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),X_34358) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358)) ),[1,0],$fot(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)))]]) ).
cnf(refute_0_1191,plain,
( implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)) != implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356))
| implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358) = implies(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),X_34358) ),
inference(resolve,[$cnf( $equal(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358)) )],[refute_0_1189,refute_0_1190]) ).
cnf(refute_0_1192,plain,
implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358) = implies(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),X_34358),
inference(resolve,[$cnf( $equal(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356))) )],[refute_0_1188,refute_0_1191]) ).
cnf(refute_0_1193,plain,
implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358) = implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358),
introduced(tautology,[refl,[$fot(implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358))]]) ).
cnf(refute_0_1194,plain,
( implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358) != implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358)
| implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358) != implies(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),X_34358)
| implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358) = implies(implies(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),X_34358),X_34358) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358),implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358)) ),[1,0],$fot(implies(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),X_34358))]]) ).
cnf(refute_0_1195,plain,
( implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358) != implies(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),X_34358)
| implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358) = implies(implies(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),X_34358),X_34358) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358),implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358)) )],[refute_0_1193,refute_0_1194]) ).
cnf(refute_0_1196,plain,
implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358) = implies(implies(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),X_34358),X_34358),
inference(resolve,[$cnf( $equal(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),implies(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),X_34358)) )],[refute_0_1192,refute_0_1195]) ).
cnf(refute_0_1197,plain,
( implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358) != implies(implies(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),X_34358),X_34358)
| ~ is_a_theorem(implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358))
| is_a_theorem(implies(implies(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),X_34358),X_34358)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358)) ),[0],$fot(implies(implies(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),X_34358),X_34358))]]) ).
cnf(refute_0_1198,plain,
( ~ is_a_theorem(implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358))
| is_a_theorem(implies(implies(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),X_34358),X_34358)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358),implies(implies(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),X_34358),X_34358)) )],[refute_0_1196,refute_0_1197]) ).
cnf(refute_0_1199,plain,
is_a_theorem(implies(implies(implies(or(X_34356,not(X_34356)),equiv(X_34356,X_34356)),X_34358),X_34358)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(or(X_34356,not(X_34356)),implies(X_34356,X_34356)),X_34358),X_34358)) )],[refute_0_1172,refute_0_1198]) ).
cnf(refute_0_1200,plain,
is_a_theorem(implies(implies(implies(or(X_34375,not(X_34375)),equiv(X_34375,X_34375)),X_34376),X_34376)),
inference(subst,[],[refute_0_1199:[bind(X_34356,$fot(X_34375)),bind(X_34358,$fot(X_34376))]]) ).
cnf(refute_0_1201,plain,
is_a_theorem(or(X_34376,not(implies(implies(or(X_34375,not(X_34375)),equiv(X_34375,X_34375)),X_34376)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(or(X_34375,not(X_34375)),equiv(X_34375,X_34375)),X_34376),X_34376)) )],[refute_0_1200,refute_0_1158]) ).
cnf(refute_0_1202,plain,
is_a_theorem(or(not(X),not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))),
inference(subst,[],[refute_0_1201:[bind(X_34375,$fot(X_34379)),bind(X_34376,$fot(not(X)))]]) ).
cnf(refute_0_1203,plain,
implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) = or(not(X),not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))),
inference(subst,[],[refute_0_12:[bind(Y,$fot(not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))))]]) ).
cnf(refute_0_1204,plain,
( implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) != or(not(X),not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))
| or(not(X),not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) = implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))))),bind(Y0,$fot(or(not(X),not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))))]]) ).
cnf(refute_0_1205,plain,
or(not(X),not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) = implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))),
inference(resolve,[$cnf( $equal(implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))),or(not(X),not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))) )],[refute_0_1203,refute_0_1204]) ).
cnf(refute_0_1206,plain,
( or(not(X),not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) != implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))
| ~ is_a_theorem(or(not(X),not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))))
| is_a_theorem(implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X),not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))) ),[0],$fot(implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))))]]) ).
cnf(refute_0_1207,plain,
( ~ is_a_theorem(or(not(X),not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))))
| is_a_theorem(implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))),implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))) )],[refute_0_1205,refute_0_1206]) ).
cnf(refute_0_1208,plain,
is_a_theorem(implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))),
inference(resolve,[$cnf( is_a_theorem(or(not(X),not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))) )],[refute_0_1202,refute_0_1207]) ).
cnf(refute_0_1209,plain,
not(not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))) = implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)),
inference(subst,[],[refute_0_693:[bind(X_31803,$fot(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))))]]) ).
cnf(refute_0_1210,plain,
and(X,not(and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))) = not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))),
inference(subst,[],[refute_0_922:[bind(Y,$fot(and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))),bind(X_10,$fot(X))]]) ).
cnf(refute_0_1211,plain,
implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)) = not(and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)),
inference(subst,[],[refute_0_888:[bind(X,$fot(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)))),bind(Y,$fot(X))]]) ).
cnf(refute_0_1212,plain,
and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))) = and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))),
introduced(tautology,[refl,[$fot(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))]]) ).
cnf(refute_0_1213,plain,
( and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))) != and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))
| implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)) != not(and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))
| and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))) = and(X,not(and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))),and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) ),[1,1],$fot(not(and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))]]) ).
cnf(refute_0_1214,plain,
( implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)) != not(and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))
| and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))) = and(X,not(and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))) ),
inference(resolve,[$cnf( $equal(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))),and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) )],[refute_0_1212,refute_0_1213]) ).
cnf(refute_0_1215,plain,
and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))) = and(X,not(and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))),
inference(resolve,[$cnf( $equal(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)),not(and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))) )],[refute_0_1211,refute_0_1214]) ).
cnf(refute_0_1216,plain,
( and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))) != and(X,not(and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))
| and(X,not(and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))) != not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))
| and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))) = not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))),bind(Y0,$fot(and(X,not(and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))))),bind(Z,$fot(not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))))]]) ).
cnf(refute_0_1217,plain,
( and(X,not(and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))) != not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))
| and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))) = not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))) ),
inference(resolve,[$cnf( $equal(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))),and(X,not(and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))) )],[refute_0_1215,refute_0_1216]) ).
cnf(refute_0_1218,plain,
and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))) = not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))),
inference(resolve,[$cnf( $equal(and(X,not(and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))),not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))) )],[refute_0_1210,refute_0_1217]) ).
cnf(refute_0_1219,plain,
not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) = not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))),
introduced(tautology,[refl,[$fot(not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))))]]) ).
cnf(refute_0_1220,plain,
( and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))) != not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))
| not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) != not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))
| not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) = not(not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))),not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))) ),[1,0],$fot(not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))))]]) ).
cnf(refute_0_1221,plain,
( and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))) != not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))
| not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) = not(not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))) ),
inference(resolve,[$cnf( $equal(not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))),not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))) )],[refute_0_1219,refute_0_1220]) ).
cnf(refute_0_1222,plain,
not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) = not(not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))),
inference(resolve,[$cnf( $equal(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))),not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))) )],[refute_0_1218,refute_0_1221]) ).
cnf(refute_0_1223,plain,
( not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) != not(not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))))
| not(not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))) != implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))
| not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) = implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))))),bind(Y0,$fot(not(not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))))),bind(Z,$fot(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))))]]) ).
cnf(refute_0_1224,plain,
( not(not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))) != implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))
| not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) = implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)) ),
inference(resolve,[$cnf( $equal(not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))),not(not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))))) )],[refute_0_1222,refute_0_1223]) ).
cnf(refute_0_1225,plain,
not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) = implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)),
inference(resolve,[$cnf( $equal(not(not(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))),implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))) )],[refute_0_1209,refute_0_1224]) ).
cnf(refute_0_1226,plain,
implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) = not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))),
inference(subst,[],[refute_0_888:[bind(Y,$fot(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))]]) ).
cnf(refute_0_1227,plain,
( implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) != not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))
| not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) != implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))
| implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) = implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))))),bind(Y0,$fot(not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))))),bind(Z,$fot(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))))]]) ).
cnf(refute_0_1228,plain,
( not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) != implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))
| implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) = implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)) ),
inference(resolve,[$cnf( $equal(implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))),not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))) )],[refute_0_1226,refute_0_1227]) ).
cnf(refute_0_1229,plain,
implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) = implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)),
inference(resolve,[$cnf( $equal(not(and(X,implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))),implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))) )],[refute_0_1225,refute_0_1228]) ).
cnf(refute_0_1230,plain,
( implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))) != implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))
| ~ is_a_theorem(implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))))
| is_a_theorem(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))) ),[0],$fot(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X)))]]) ).
cnf(refute_0_1231,plain,
( ~ is_a_theorem(implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))))
| is_a_theorem(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))) ),
inference(resolve,[$cnf( $equal(implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X)))),implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))) )],[refute_0_1229,refute_0_1230]) ).
cnf(refute_0_1232,plain,
is_a_theorem(implies(X,and(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),X))),
inference(resolve,[$cnf( is_a_theorem(implies(X,not(implies(implies(or(X_34379,not(X_34379)),equiv(X_34379,X_34379)),not(X))))) )],[refute_0_1208,refute_0_1231]) ).
cnf(refute_0_1233,plain,
is_a_theorem(implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),equiv(not(X_11),not(X_11))),X_34381))),
inference(subst,[],[refute_0_1232:[bind(X,$fot(X_34381)),bind(X_34379,$fot(not(X_11)))]]) ).
cnf(refute_0_1234,plain,
equiv(not(X_11),not(X_11)) = not(or(and(not(X_11),X_11),and(not(X_11),X_11))),
inference(subst,[],[refute_0_345:[bind(X_107,$fot(X_11))]]) ).
cnf(refute_0_1235,plain,
or(and(not(X_11),X_11),and(not(X_11),X_11)) = and(not(X_11),X_11),
inference(subst,[],[refute_0_190:[bind(X_27414,$fot(and(not(X_11),X_11)))]]) ).
cnf(refute_0_1236,plain,
( equiv(not(X_11),not(X_11)) != not(or(and(not(X_11),X_11),and(not(X_11),X_11)))
| or(and(not(X_11),X_11),and(not(X_11),X_11)) != and(not(X_11),X_11)
| equiv(not(X_11),not(X_11)) = not(and(not(X_11),X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X_11),not(X_11)),not(or(and(not(X_11),X_11),and(not(X_11),X_11)))) ),[1,0],$fot(and(not(X_11),X_11))]]) ).
cnf(refute_0_1237,plain,
( equiv(not(X_11),not(X_11)) != not(or(and(not(X_11),X_11),and(not(X_11),X_11)))
| equiv(not(X_11),not(X_11)) = not(and(not(X_11),X_11)) ),
inference(resolve,[$cnf( $equal(or(and(not(X_11),X_11),and(not(X_11),X_11)),and(not(X_11),X_11)) )],[refute_0_1235,refute_0_1236]) ).
cnf(refute_0_1238,plain,
equiv(not(X_11),not(X_11)) = not(and(not(X_11),X_11)),
inference(resolve,[$cnf( $equal(equiv(not(X_11),not(X_11)),not(or(and(not(X_11),X_11),and(not(X_11),X_11)))) )],[refute_0_1234,refute_0_1237]) ).
cnf(refute_0_1239,plain,
or(X,and(not(X_2),not(X_2))) = not(and(not(X),or(X_2,X_2))),
inference(subst,[],[refute_0_305:[bind(X_1,$fot(X_2))]]) ).
cnf(refute_0_1240,plain,
( and(not(X_2),not(X_2)) != not(not(not(X_2)))
| or(X,and(not(X_2),not(X_2))) != not(and(not(X),or(X_2,X_2)))
| or(X,not(not(not(X_2)))) = not(and(not(X),or(X_2,X_2))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,and(not(X_2),not(X_2))),not(and(not(X),or(X_2,X_2)))) ),[0,1],$fot(not(not(not(X_2))))]]) ).
cnf(refute_0_1241,plain,
( or(X,and(not(X_2),not(X_2))) != not(and(not(X),or(X_2,X_2)))
| or(X,not(not(not(X_2)))) = not(and(not(X),or(X_2,X_2))) ),
inference(resolve,[$cnf( $equal(and(not(X_2),not(X_2)),not(not(not(X_2)))) )],[refute_0_436,refute_0_1240]) ).
cnf(refute_0_1242,plain,
or(X,not(not(not(X_2)))) = not(and(not(X),or(X_2,X_2))),
inference(resolve,[$cnf( $equal(or(X,and(not(X_2),not(X_2))),not(and(not(X),or(X_2,X_2)))) )],[refute_0_1239,refute_0_1241]) ).
cnf(refute_0_1243,plain,
and(not(X),or(X_2,X_2)) = and(not(X),or(X_2,X_2)),
introduced(tautology,[refl,[$fot(and(not(X),or(X_2,X_2)))]]) ).
cnf(refute_0_1244,plain,
( and(not(X),or(X_2,X_2)) != and(not(X),or(X_2,X_2))
| or(X_2,X_2) != X_2
| and(not(X),or(X_2,X_2)) = and(not(X),X_2) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(X),or(X_2,X_2)),and(not(X),or(X_2,X_2))) ),[1,1],$fot(X_2)]]) ).
cnf(refute_0_1245,plain,
( or(X_2,X_2) != X_2
| and(not(X),or(X_2,X_2)) = and(not(X),X_2) ),
inference(resolve,[$cnf( $equal(and(not(X),or(X_2,X_2)),and(not(X),or(X_2,X_2))) )],[refute_0_1243,refute_0_1244]) ).
cnf(refute_0_1246,plain,
and(not(X),or(X_2,X_2)) = and(not(X),X_2),
inference(resolve,[$cnf( $equal(or(X_2,X_2),X_2) )],[refute_0_443,refute_0_1245]) ).
cnf(refute_0_1247,plain,
not(and(not(X),or(X_2,X_2))) = not(and(not(X),or(X_2,X_2))),
introduced(tautology,[refl,[$fot(not(and(not(X),or(X_2,X_2))))]]) ).
cnf(refute_0_1248,plain,
( and(not(X),or(X_2,X_2)) != and(not(X),X_2)
| not(and(not(X),or(X_2,X_2))) != not(and(not(X),or(X_2,X_2)))
| not(and(not(X),or(X_2,X_2))) = not(and(not(X),X_2)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(not(X),or(X_2,X_2))),not(and(not(X),or(X_2,X_2)))) ),[1,0],$fot(and(not(X),X_2))]]) ).
cnf(refute_0_1249,plain,
( and(not(X),or(X_2,X_2)) != and(not(X),X_2)
| not(and(not(X),or(X_2,X_2))) = not(and(not(X),X_2)) ),
inference(resolve,[$cnf( $equal(not(and(not(X),or(X_2,X_2))),not(and(not(X),or(X_2,X_2)))) )],[refute_0_1247,refute_0_1248]) ).
cnf(refute_0_1250,plain,
not(and(not(X),or(X_2,X_2))) = not(and(not(X),X_2)),
inference(resolve,[$cnf( $equal(and(not(X),or(X_2,X_2)),and(not(X),X_2)) )],[refute_0_1246,refute_0_1249]) ).
cnf(refute_0_1251,plain,
( not(and(not(X),or(X_2,X_2))) != not(and(not(X),X_2))
| or(X,not(not(not(X_2)))) != not(and(not(X),or(X_2,X_2)))
| or(X,not(not(not(X_2)))) = not(and(not(X),X_2)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(not(not(X_2)))),not(and(not(X),or(X_2,X_2)))) ),[1],$fot(not(and(not(X),X_2)))]]) ).
cnf(refute_0_1252,plain,
( or(X,not(not(not(X_2)))) != not(and(not(X),or(X_2,X_2)))
| or(X,not(not(not(X_2)))) = not(and(not(X),X_2)) ),
inference(resolve,[$cnf( $equal(not(and(not(X),or(X_2,X_2))),not(and(not(X),X_2))) )],[refute_0_1250,refute_0_1251]) ).
cnf(refute_0_1253,plain,
or(X,not(not(not(X_2)))) = not(and(not(X),X_2)),
inference(resolve,[$cnf( $equal(or(X,not(not(not(X_2)))),not(and(not(X),or(X_2,X_2)))) )],[refute_0_1242,refute_0_1252]) ).
cnf(refute_0_1254,plain,
not(not(not(X_2))) = not(X_2),
inference(subst,[],[refute_0_693:[bind(X_31803,$fot(not(X_2)))]]) ).
cnf(refute_0_1255,plain,
or(X,not(not(not(X_2)))) = or(X,not(not(not(X_2)))),
introduced(tautology,[refl,[$fot(or(X,not(not(not(X_2)))))]]) ).
cnf(refute_0_1256,plain,
( not(not(not(X_2))) != not(X_2)
| or(X,not(not(not(X_2)))) != or(X,not(not(not(X_2))))
| or(X,not(not(not(X_2)))) = or(X,not(X_2)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(not(not(X_2)))),or(X,not(not(not(X_2))))) ),[1,1],$fot(not(X_2))]]) ).
cnf(refute_0_1257,plain,
( not(not(not(X_2))) != not(X_2)
| or(X,not(not(not(X_2)))) = or(X,not(X_2)) ),
inference(resolve,[$cnf( $equal(or(X,not(not(not(X_2)))),or(X,not(not(not(X_2))))) )],[refute_0_1255,refute_0_1256]) ).
cnf(refute_0_1258,plain,
or(X,not(not(not(X_2)))) = or(X,not(X_2)),
inference(resolve,[$cnf( $equal(not(not(not(X_2))),not(X_2)) )],[refute_0_1254,refute_0_1257]) ).
cnf(refute_0_1259,plain,
( or(X,not(not(not(X_2)))) != not(and(not(X),X_2))
| or(X,not(not(not(X_2)))) != or(X,not(X_2))
| or(X,not(X_2)) = not(and(not(X),X_2)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(not(not(X_2)))),not(and(not(X),X_2))) ),[0],$fot(or(X,not(X_2)))]]) ).
cnf(refute_0_1260,plain,
( or(X,not(not(not(X_2)))) != not(and(not(X),X_2))
| or(X,not(X_2)) = not(and(not(X),X_2)) ),
inference(resolve,[$cnf( $equal(or(X,not(not(not(X_2)))),or(X,not(X_2))) )],[refute_0_1258,refute_0_1259]) ).
cnf(refute_0_1261,plain,
or(X,not(X_2)) = not(and(not(X),X_2)),
inference(resolve,[$cnf( $equal(or(X,not(not(not(X_2)))),not(and(not(X),X_2))) )],[refute_0_1253,refute_0_1260]) ).
cnf(refute_0_1262,plain,
( or(X,not(X_2)) != not(and(not(X),X_2))
| not(and(not(X),X_2)) = or(X,not(X_2)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,not(X_2)))),bind(Y0,$fot(not(and(not(X),X_2))))]]) ).
cnf(refute_0_1263,plain,
not(and(not(X),X_2)) = or(X,not(X_2)),
inference(resolve,[$cnf( $equal(or(X,not(X_2)),not(and(not(X),X_2))) )],[refute_0_1261,refute_0_1262]) ).
cnf(refute_0_1264,plain,
not(and(not(X_11),X_11)) = or(X_11,not(X_11)),
inference(subst,[],[refute_0_1263:[bind(X,$fot(X_11)),bind(X_2,$fot(X_11))]]) ).
cnf(refute_0_1265,plain,
( equiv(not(X_11),not(X_11)) != not(and(not(X_11),X_11))
| not(and(not(X_11),X_11)) != or(X_11,not(X_11))
| equiv(not(X_11),not(X_11)) = or(X_11,not(X_11)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(equiv(not(X_11),not(X_11)),or(X_11,not(X_11))) ),[0],$fot(not(and(not(X_11),X_11)))]]) ).
cnf(refute_0_1266,plain,
( equiv(not(X_11),not(X_11)) != not(and(not(X_11),X_11))
| equiv(not(X_11),not(X_11)) = or(X_11,not(X_11)) ),
inference(resolve,[$cnf( $equal(not(and(not(X_11),X_11)),or(X_11,not(X_11))) )],[refute_0_1264,refute_0_1265]) ).
cnf(refute_0_1267,plain,
equiv(not(X_11),not(X_11)) = or(X_11,not(X_11)),
inference(resolve,[$cnf( $equal(equiv(not(X_11),not(X_11)),not(and(not(X_11),X_11))) )],[refute_0_1238,refute_0_1266]) ).
cnf(refute_0_1268,plain,
( equiv(not(X_11),not(X_11)) != or(X_11,not(X_11))
| ~ is_a_theorem(implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),equiv(not(X_11),not(X_11))),X_34381)))
| is_a_theorem(implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),equiv(not(X_11),not(X_11))),X_34381))) ),[0,1,0,1],$fot(or(X_11,not(X_11)))]]) ).
cnf(refute_0_1269,plain,
( ~ is_a_theorem(implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),equiv(not(X_11),not(X_11))),X_34381)))
| is_a_theorem(implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381))) ),
inference(resolve,[$cnf( $equal(equiv(not(X_11),not(X_11)),or(X_11,not(X_11))) )],[refute_0_1267,refute_0_1268]) ).
cnf(refute_0_1270,plain,
is_a_theorem(implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381))),
inference(resolve,[$cnf( is_a_theorem(implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),equiv(not(X_11),not(X_11))),X_34381))) )],[refute_0_1233,refute_0_1269]) ).
cnf(refute_0_1271,plain,
not(not(equiv(X_11,X_11))) = equiv(X_11,X_11),
inference(subst,[],[refute_0_693:[bind(X_31803,$fot(equiv(X_11,X_11)))]]) ).
cnf(refute_0_1272,plain,
implies(X_11,X_11) = equiv(X_11,X_11),
inference(subst,[],[refute_0_1183:[bind(Y,$fot(X_11))]]) ).
cnf(refute_0_1273,plain,
not(implies(X_11,X_11)) = not(implies(X_11,X_11)),
introduced(tautology,[refl,[$fot(not(implies(X_11,X_11)))]]) ).
cnf(refute_0_1274,plain,
( implies(X_11,X_11) != equiv(X_11,X_11)
| not(implies(X_11,X_11)) != not(implies(X_11,X_11))
| not(implies(X_11,X_11)) = not(equiv(X_11,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_11,X_11)),not(implies(X_11,X_11))) ),[1,0],$fot(equiv(X_11,X_11))]]) ).
cnf(refute_0_1275,plain,
( implies(X_11,X_11) != equiv(X_11,X_11)
| not(implies(X_11,X_11)) = not(equiv(X_11,X_11)) ),
inference(resolve,[$cnf( $equal(not(implies(X_11,X_11)),not(implies(X_11,X_11))) )],[refute_0_1273,refute_0_1274]) ).
cnf(refute_0_1276,plain,
not(implies(X_11,X_11)) = not(equiv(X_11,X_11)),
inference(resolve,[$cnf( $equal(implies(X_11,X_11),equiv(X_11,X_11)) )],[refute_0_1272,refute_0_1275]) ).
cnf(refute_0_1277,plain,
and(X_11,not(X_11)) = not(implies(X_11,X_11)),
inference(subst,[],[refute_0_922:[bind(Y,$fot(X_11)),bind(X_10,$fot(X_11))]]) ).
cnf(refute_0_1278,plain,
( and(X_11,not(X_11)) != not(implies(X_11,X_11))
| not(implies(X_11,X_11)) != not(equiv(X_11,X_11))
| and(X_11,not(X_11)) = not(equiv(X_11,X_11)) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(and(X_11,not(X_11)))),bind(Y0,$fot(not(implies(X_11,X_11)))),bind(Z,$fot(not(equiv(X_11,X_11))))]]) ).
cnf(refute_0_1279,plain,
( not(implies(X_11,X_11)) != not(equiv(X_11,X_11))
| and(X_11,not(X_11)) = not(equiv(X_11,X_11)) ),
inference(resolve,[$cnf( $equal(and(X_11,not(X_11)),not(implies(X_11,X_11))) )],[refute_0_1277,refute_0_1278]) ).
cnf(refute_0_1280,plain,
and(X_11,not(X_11)) = not(equiv(X_11,X_11)),
inference(resolve,[$cnf( $equal(not(implies(X_11,X_11)),not(equiv(X_11,X_11))) )],[refute_0_1276,refute_0_1279]) ).
cnf(refute_0_1281,plain,
not(and(X_11,not(X_11))) = not(and(X_11,not(X_11))),
introduced(tautology,[refl,[$fot(not(and(X_11,not(X_11))))]]) ).
cnf(refute_0_1282,plain,
( and(X_11,not(X_11)) != not(equiv(X_11,X_11))
| not(and(X_11,not(X_11))) != not(and(X_11,not(X_11)))
| not(and(X_11,not(X_11))) = not(not(equiv(X_11,X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(X_11,not(X_11))),not(and(X_11,not(X_11)))) ),[1,0],$fot(not(equiv(X_11,X_11)))]]) ).
cnf(refute_0_1283,plain,
( and(X_11,not(X_11)) != not(equiv(X_11,X_11))
| not(and(X_11,not(X_11))) = not(not(equiv(X_11,X_11))) ),
inference(resolve,[$cnf( $equal(not(and(X_11,not(X_11))),not(and(X_11,not(X_11)))) )],[refute_0_1281,refute_0_1282]) ).
cnf(refute_0_1284,plain,
not(and(X_11,not(X_11))) = not(not(equiv(X_11,X_11))),
inference(resolve,[$cnf( $equal(and(X_11,not(X_11)),not(equiv(X_11,X_11))) )],[refute_0_1280,refute_0_1283]) ).
cnf(refute_0_1285,plain,
( not(and(X_11,not(X_11))) != not(not(equiv(X_11,X_11)))
| not(not(equiv(X_11,X_11))) != equiv(X_11,X_11)
| not(and(X_11,not(X_11))) = equiv(X_11,X_11) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(not(and(X_11,not(X_11))))),bind(Y0,$fot(not(not(equiv(X_11,X_11))))),bind(Z,$fot(equiv(X_11,X_11)))]]) ).
cnf(refute_0_1286,plain,
( not(not(equiv(X_11,X_11))) != equiv(X_11,X_11)
| not(and(X_11,not(X_11))) = equiv(X_11,X_11) ),
inference(resolve,[$cnf( $equal(not(and(X_11,not(X_11))),not(not(equiv(X_11,X_11)))) )],[refute_0_1284,refute_0_1285]) ).
cnf(refute_0_1287,plain,
not(and(X_11,not(X_11))) = equiv(X_11,X_11),
inference(resolve,[$cnf( $equal(not(not(equiv(X_11,X_11))),equiv(X_11,X_11)) )],[refute_0_1271,refute_0_1286]) ).
cnf(refute_0_1288,plain,
implies(X_11,not(not(X_11))) = not(and(X_11,not(X_11))),
inference(subst,[],[refute_0_888:[bind(X,$fot(X_11)),bind(Y,$fot(not(X_11)))]]) ).
cnf(refute_0_1289,plain,
or(not(X_11),not(not(X_11))) = implies(X_11,not(not(X_11))),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_11)),bind(Y,$fot(not(not(X_11))))]]) ).
cnf(refute_0_1290,plain,
( implies(X_11,not(not(X_11))) != not(and(X_11,not(X_11)))
| or(not(X_11),not(not(X_11))) != implies(X_11,not(not(X_11)))
| or(not(X_11),not(not(X_11))) = not(and(X_11,not(X_11))) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(or(not(X_11),not(not(X_11))))),bind(Y0,$fot(implies(X_11,not(not(X_11))))),bind(Z,$fot(not(and(X_11,not(X_11)))))]]) ).
cnf(refute_0_1291,plain,
( implies(X_11,not(not(X_11))) != not(and(X_11,not(X_11)))
| or(not(X_11),not(not(X_11))) = not(and(X_11,not(X_11))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),not(not(X_11))),implies(X_11,not(not(X_11)))) )],[refute_0_1289,refute_0_1290]) ).
cnf(refute_0_1292,plain,
or(not(X_11),not(not(X_11))) = not(and(X_11,not(X_11))),
inference(resolve,[$cnf( $equal(implies(X_11,not(not(X_11))),not(and(X_11,not(X_11)))) )],[refute_0_1288,refute_0_1291]) ).
cnf(refute_0_1293,plain,
( not(and(X_11,not(X_11))) != equiv(X_11,X_11)
| or(not(X_11),not(not(X_11))) != not(and(X_11,not(X_11)))
| or(not(X_11),not(not(X_11))) = equiv(X_11,X_11) ),
inference(subst,[],[refute_0_207:[bind(X0,$fot(or(not(X_11),not(not(X_11))))),bind(Y0,$fot(not(and(X_11,not(X_11))))),bind(Z,$fot(equiv(X_11,X_11)))]]) ).
cnf(refute_0_1294,plain,
( not(and(X_11,not(X_11))) != equiv(X_11,X_11)
| or(not(X_11),not(not(X_11))) = equiv(X_11,X_11) ),
inference(resolve,[$cnf( $equal(or(not(X_11),not(not(X_11))),not(and(X_11,not(X_11)))) )],[refute_0_1292,refute_0_1293]) ).
cnf(refute_0_1295,plain,
or(not(X_11),not(not(X_11))) = equiv(X_11,X_11),
inference(resolve,[$cnf( $equal(not(and(X_11,not(X_11))),equiv(X_11,X_11)) )],[refute_0_1287,refute_0_1294]) ).
cnf(refute_0_1296,plain,
implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))) = implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),
introduced(tautology,[refl,[$fot(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))))]]) ).
cnf(refute_0_1297,plain,
( implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))) != implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11)))
| or(not(X_11),not(not(X_11))) != equiv(X_11,X_11)
| implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))) = implies(equiv(X_11,X_11),or(X_11,not(X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11)))) ),[1,0],$fot(equiv(X_11,X_11))]]) ).
cnf(refute_0_1298,plain,
( or(not(X_11),not(not(X_11))) != equiv(X_11,X_11)
| implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))) = implies(equiv(X_11,X_11),or(X_11,not(X_11))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11)))) )],[refute_0_1296,refute_0_1297]) ).
cnf(refute_0_1299,plain,
implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))) = implies(equiv(X_11,X_11),or(X_11,not(X_11))),
inference(resolve,[$cnf( $equal(or(not(X_11),not(not(X_11))),equiv(X_11,X_11)) )],[refute_0_1295,refute_0_1298]) ).
cnf(refute_0_1300,plain,
and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381) = and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381),
introduced(tautology,[refl,[$fot(and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381))]]) ).
cnf(refute_0_1301,plain,
( and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381) != and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381)
| implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))) != implies(equiv(X_11,X_11),or(X_11,not(X_11)))
| and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381) = and(implies(equiv(X_11,X_11),or(X_11,not(X_11))),X_34381) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381),and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381)) ),[1,0],$fot(implies(equiv(X_11,X_11),or(X_11,not(X_11))))]]) ).
cnf(refute_0_1302,plain,
( implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))) != implies(equiv(X_11,X_11),or(X_11,not(X_11)))
| and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381) = and(implies(equiv(X_11,X_11),or(X_11,not(X_11))),X_34381) ),
inference(resolve,[$cnf( $equal(and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381),and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381)) )],[refute_0_1300,refute_0_1301]) ).
cnf(refute_0_1303,plain,
and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381) = and(implies(equiv(X_11,X_11),or(X_11,not(X_11))),X_34381),
inference(resolve,[$cnf( $equal(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),implies(equiv(X_11,X_11),or(X_11,not(X_11)))) )],[refute_0_1299,refute_0_1302]) ).
cnf(refute_0_1304,plain,
implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381)) = implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381)),
introduced(tautology,[refl,[$fot(implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381)))]]) ).
cnf(refute_0_1305,plain,
( and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381) != and(implies(equiv(X_11,X_11),or(X_11,not(X_11))),X_34381)
| implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381)) != implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381))
| implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381)) = implies(X_34381,and(implies(equiv(X_11,X_11),or(X_11,not(X_11))),X_34381)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381)),implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381))) ),[1,1],$fot(and(implies(equiv(X_11,X_11),or(X_11,not(X_11))),X_34381))]]) ).
cnf(refute_0_1306,plain,
( and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381) != and(implies(equiv(X_11,X_11),or(X_11,not(X_11))),X_34381)
| implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381)) = implies(X_34381,and(implies(equiv(X_11,X_11),or(X_11,not(X_11))),X_34381)) ),
inference(resolve,[$cnf( $equal(implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381)),implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381))) )],[refute_0_1304,refute_0_1305]) ).
cnf(refute_0_1307,plain,
implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381)) = implies(X_34381,and(implies(equiv(X_11,X_11),or(X_11,not(X_11))),X_34381)),
inference(resolve,[$cnf( $equal(and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381),and(implies(equiv(X_11,X_11),or(X_11,not(X_11))),X_34381)) )],[refute_0_1303,refute_0_1306]) ).
cnf(refute_0_1308,plain,
( implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381)) != implies(X_34381,and(implies(equiv(X_11,X_11),or(X_11,not(X_11))),X_34381))
| ~ is_a_theorem(implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381)))
| is_a_theorem(implies(X_34381,and(implies(equiv(X_11,X_11),or(X_11,not(X_11))),X_34381))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381))) ),[0],$fot(implies(X_34381,and(implies(equiv(X_11,X_11),or(X_11,not(X_11))),X_34381)))]]) ).
cnf(refute_0_1309,plain,
( ~ is_a_theorem(implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381)))
| is_a_theorem(implies(X_34381,and(implies(equiv(X_11,X_11),or(X_11,not(X_11))),X_34381))) ),
inference(resolve,[$cnf( $equal(implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381)),implies(X_34381,and(implies(equiv(X_11,X_11),or(X_11,not(X_11))),X_34381))) )],[refute_0_1307,refute_0_1308]) ).
cnf(refute_0_1310,plain,
is_a_theorem(implies(X_34381,and(implies(equiv(X_11,X_11),or(X_11,not(X_11))),X_34381))),
inference(resolve,[$cnf( is_a_theorem(implies(X_34381,and(implies(or(not(X_11),not(not(X_11))),or(X_11,not(X_11))),X_34381))) )],[refute_0_1270,refute_0_1309]) ).
cnf(refute_0_1311,plain,
is_a_theorem(implies(implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555)),and(implies(equiv(X_34555,X_34555),or(X_34555,not(X_34555))),implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555))))),
inference(subst,[],[refute_0_1310:[bind(X_11,$fot(X_34555)),bind(X_34381,$fot(implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555))))]]) ).
cnf(refute_0_1312,plain,
equiv(equiv(X_34555,X_34555),or(X_34555,not(X_34555))) = and(implies(equiv(X_34555,X_34555),or(X_34555,not(X_34555))),implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555))),
inference(subst,[],[refute_0_172:[bind(X,$fot(equiv(X_34555,X_34555))),bind(Y,$fot(or(X_34555,not(X_34555))))]]) ).
cnf(refute_0_1313,plain,
( equiv(equiv(X_34555,X_34555),or(X_34555,not(X_34555))) != and(implies(equiv(X_34555,X_34555),or(X_34555,not(X_34555))),implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555)))
| and(implies(equiv(X_34555,X_34555),or(X_34555,not(X_34555))),implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555))) = equiv(equiv(X_34555,X_34555),or(X_34555,not(X_34555))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(equiv(X_34555,X_34555),or(X_34555,not(X_34555))))),bind(Y0,$fot(and(implies(equiv(X_34555,X_34555),or(X_34555,not(X_34555))),implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555)))))]]) ).
cnf(refute_0_1314,plain,
and(implies(equiv(X_34555,X_34555),or(X_34555,not(X_34555))),implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555))) = equiv(equiv(X_34555,X_34555),or(X_34555,not(X_34555))),
inference(resolve,[$cnf( $equal(equiv(equiv(X_34555,X_34555),or(X_34555,not(X_34555))),and(implies(equiv(X_34555,X_34555),or(X_34555,not(X_34555))),implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555)))) )],[refute_0_1312,refute_0_1313]) ).
cnf(refute_0_1315,plain,
( and(implies(equiv(X_34555,X_34555),or(X_34555,not(X_34555))),implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555))) != equiv(equiv(X_34555,X_34555),or(X_34555,not(X_34555)))
| ~ is_a_theorem(implies(implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555)),and(implies(equiv(X_34555,X_34555),or(X_34555,not(X_34555))),implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555)))))
| is_a_theorem(implies(implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555)),equiv(equiv(X_34555,X_34555),or(X_34555,not(X_34555))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555)),and(implies(equiv(X_34555,X_34555),or(X_34555,not(X_34555))),implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555))))) ),[0,1],$fot(equiv(equiv(X_34555,X_34555),or(X_34555,not(X_34555))))]]) ).
cnf(refute_0_1316,plain,
( ~ is_a_theorem(implies(implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555)),and(implies(equiv(X_34555,X_34555),or(X_34555,not(X_34555))),implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555)))))
| is_a_theorem(implies(implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555)),equiv(equiv(X_34555,X_34555),or(X_34555,not(X_34555))))) ),
inference(resolve,[$cnf( $equal(and(implies(equiv(X_34555,X_34555),or(X_34555,not(X_34555))),implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555))),equiv(equiv(X_34555,X_34555),or(X_34555,not(X_34555)))) )],[refute_0_1314,refute_0_1315]) ).
cnf(refute_0_1317,plain,
is_a_theorem(implies(implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555)),equiv(equiv(X_34555,X_34555),or(X_34555,not(X_34555))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555)),and(implies(equiv(X_34555,X_34555),or(X_34555,not(X_34555))),implies(or(X_34555,not(X_34555)),equiv(X_34555,X_34555))))) )],[refute_0_1311,refute_0_1316]) ).
cnf(refute_0_1318,plain,
is_a_theorem(implies(implies(or(X_35415,not(X_35415)),equiv(X_35415,X_35415)),equiv(equiv(X_35415,X_35415),or(X_35415,not(X_35415))))),
inference(subst,[],[refute_0_1317:[bind(X_34555,$fot(X_35415))]]) ).
cnf(refute_0_1319,plain,
( ~ is_a_theorem(implies(or(X_35415,not(X_35415)),equiv(X_35415,X_35415)))
| is_a_theorem(equiv(equiv(X_35415,X_35415),or(X_35415,not(X_35415)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_35415,not(X_35415)),equiv(X_35415,X_35415)),equiv(equiv(X_35415,X_35415),or(X_35415,not(X_35415))))) )],[refute_0_1318,refute_0_1157]) ).
cnf(refute_0_1320,plain,
( ~ is_a_theorem(equiv(X_2833,X_2833))
| is_a_theorem(implies(X_5,equiv(X_2833,X_2833))) ),
inference(subst,[],[refute_0_646:[bind(X_170,$fot(equiv(X_2833,X_2833)))]]) ).
cnf(refute_0_1321,plain,
is_a_theorem(implies(X_5,equiv(X_2833,X_2833))),
inference(resolve,[$cnf( is_a_theorem(equiv(X_2833,X_2833)) )],[refute_0_726,refute_0_1320]) ).
cnf(refute_0_1322,plain,
is_a_theorem(implies(or(X_35415,not(X_35415)),equiv(X_35415,X_35415))),
inference(subst,[],[refute_0_1321:[bind(X_2833,$fot(X_35415)),bind(X_5,$fot(or(X_35415,not(X_35415))))]]) ).
cnf(refute_0_1323,plain,
is_a_theorem(equiv(equiv(X_35415,X_35415),or(X_35415,not(X_35415)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_35415,not(X_35415)),equiv(X_35415,X_35415))) )],[refute_0_1322,refute_0_1319]) ).
cnf(refute_0_1324,plain,
is_a_theorem(equiv(equiv(X_35416,X_35416),or(X_35416,not(X_35416)))),
inference(subst,[],[refute_0_1323:[bind(X_35415,$fot(X_35416))]]) ).
cnf(refute_0_1325,plain,
equiv(X_35416,X_35416) = or(X_35416,not(X_35416)),
inference(resolve,[$cnf( is_a_theorem(equiv(equiv(X_35416,X_35416),or(X_35416,not(X_35416)))) )],[refute_0_1324,refute_0_1156]) ).
cnf(refute_0_1326,plain,
( equiv(X_35416,X_35416) != or(X_35416,not(X_35416))
| or(X_35416,not(X_35416)) = equiv(X_35416,X_35416) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(X_35416,X_35416))),bind(Y0,$fot(or(X_35416,not(X_35416))))]]) ).
cnf(refute_0_1327,plain,
or(X_35416,not(X_35416)) = equiv(X_35416,X_35416),
inference(resolve,[$cnf( $equal(equiv(X_35416,X_35416),or(X_35416,not(X_35416))) )],[refute_0_1325,refute_0_1326]) ).
cnf(refute_0_1328,plain,
or(X_33610,not(X_33610)) = equiv(X_33610,X_33610),
inference(subst,[],[refute_0_1327:[bind(X_35416,$fot(X_33610))]]) ).
cnf(refute_0_1329,plain,
implies(or(X_33610,not(X_33610)),X_33610) = implies(or(X_33610,not(X_33610)),X_33610),
introduced(tautology,[refl,[$fot(implies(or(X_33610,not(X_33610)),X_33610))]]) ).
cnf(refute_0_1330,plain,
( implies(or(X_33610,not(X_33610)),X_33610) != implies(or(X_33610,not(X_33610)),X_33610)
| or(X_33610,not(X_33610)) != equiv(X_33610,X_33610)
| implies(or(X_33610,not(X_33610)),X_33610) = implies(equiv(X_33610,X_33610),X_33610) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_33610,not(X_33610)),X_33610),implies(or(X_33610,not(X_33610)),X_33610)) ),[1,0],$fot(equiv(X_33610,X_33610))]]) ).
cnf(refute_0_1331,plain,
( or(X_33610,not(X_33610)) != equiv(X_33610,X_33610)
| implies(or(X_33610,not(X_33610)),X_33610) = implies(equiv(X_33610,X_33610),X_33610) ),
inference(resolve,[$cnf( $equal(implies(or(X_33610,not(X_33610)),X_33610),implies(or(X_33610,not(X_33610)),X_33610)) )],[refute_0_1329,refute_0_1330]) ).
cnf(refute_0_1332,plain,
implies(or(X_33610,not(X_33610)),X_33610) = implies(equiv(X_33610,X_33610),X_33610),
inference(resolve,[$cnf( $equal(or(X_33610,not(X_33610)),equiv(X_33610,X_33610)) )],[refute_0_1328,refute_0_1331]) ).
cnf(refute_0_1333,plain,
( X_33610 != implies(or(X_33610,not(X_33610)),X_33610)
| implies(or(X_33610,not(X_33610)),X_33610) != implies(equiv(X_33610,X_33610),X_33610)
| X_33610 = implies(equiv(X_33610,X_33610),X_33610) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_33610,implies(equiv(X_33610,X_33610),X_33610)) ),[0],$fot(implies(or(X_33610,not(X_33610)),X_33610))]]) ).
cnf(refute_0_1334,plain,
( X_33610 != implies(or(X_33610,not(X_33610)),X_33610)
| X_33610 = implies(equiv(X_33610,X_33610),X_33610) ),
inference(resolve,[$cnf( $equal(implies(or(X_33610,not(X_33610)),X_33610),implies(equiv(X_33610,X_33610),X_33610)) )],[refute_0_1332,refute_0_1333]) ).
cnf(refute_0_1335,plain,
X_33610 = implies(equiv(X_33610,X_33610),X_33610),
inference(resolve,[$cnf( $equal(X_33610,implies(or(X_33610,not(X_33610)),X_33610)) )],[refute_0_1155,refute_0_1334]) ).
cnf(refute_0_1336,plain,
X_35659 = implies(equiv(X_35659,X_35659),X_35659),
inference(subst,[],[refute_0_1335:[bind(X_33610,$fot(X_35659))]]) ).
cnf(refute_0_1337,plain,
( X_35659 != implies(equiv(X_35659,X_35659),X_35659)
| implies(equiv(X_35659,X_35659),X_35659) = X_35659 ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(X_35659)),bind(Y0,$fot(implies(equiv(X_35659,X_35659),X_35659)))]]) ).
cnf(refute_0_1338,plain,
implies(equiv(X_35659,X_35659),X_35659) = X_35659,
inference(resolve,[$cnf( $equal(X_35659,implies(equiv(X_35659,X_35659),X_35659)) )],[refute_0_1336,refute_0_1337]) ).
cnf(refute_0_1339,plain,
( implies(equiv(X_35659,X_35659),X_35659) != X_35659
| ~ is_a_theorem(implies(X_35660,and(X_35660,implies(implies(equiv(X_35659,X_35659),X_35659),or(X_35659,not(equiv(X_35659,X_35659)))))))
| is_a_theorem(implies(X_35660,and(X_35660,implies(X_35659,or(X_35659,not(equiv(X_35659,X_35659))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_35660,and(X_35660,implies(implies(equiv(X_35659,X_35659),X_35659),or(X_35659,not(equiv(X_35659,X_35659))))))) ),[0,1,1,0],$fot(X_35659)]]) ).
cnf(refute_0_1340,plain,
( ~ is_a_theorem(implies(X_35660,and(X_35660,implies(implies(equiv(X_35659,X_35659),X_35659),or(X_35659,not(equiv(X_35659,X_35659)))))))
| is_a_theorem(implies(X_35660,and(X_35660,implies(X_35659,or(X_35659,not(equiv(X_35659,X_35659))))))) ),
inference(resolve,[$cnf( $equal(implies(equiv(X_35659,X_35659),X_35659),X_35659) )],[refute_0_1338,refute_0_1339]) ).
cnf(refute_0_1341,plain,
is_a_theorem(implies(X_35660,and(X_35660,implies(X_35659,or(X_35659,not(equiv(X_35659,X_35659))))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_35660,and(X_35660,implies(implies(equiv(X_35659,X_35659),X_35659),or(X_35659,not(equiv(X_35659,X_35659))))))) )],[refute_0_848,refute_0_1340]) ).
cnf(refute_0_1342,plain,
is_a_theorem(implies(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),and(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),implies(X_35661,or(X_35661,not(equiv(X_35661,X_35661))))))),
inference(subst,[],[refute_0_1341:[bind(X_35659,$fot(X_35661)),bind(X_35660,$fot(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661)))]]) ).
cnf(refute_0_1343,plain,
equiv(or(X_35661,not(equiv(X_35661,X_35661))),X_35661) = and(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),implies(X_35661,or(X_35661,not(equiv(X_35661,X_35661))))),
inference(subst,[],[refute_0_172:[bind(X,$fot(or(X_35661,not(equiv(X_35661,X_35661))))),bind(Y,$fot(X_35661))]]) ).
cnf(refute_0_1344,plain,
( equiv(or(X_35661,not(equiv(X_35661,X_35661))),X_35661) != and(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),implies(X_35661,or(X_35661,not(equiv(X_35661,X_35661)))))
| and(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),implies(X_35661,or(X_35661,not(equiv(X_35661,X_35661))))) = equiv(or(X_35661,not(equiv(X_35661,X_35661))),X_35661) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(or(X_35661,not(equiv(X_35661,X_35661))),X_35661))),bind(Y0,$fot(and(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),implies(X_35661,or(X_35661,not(equiv(X_35661,X_35661)))))))]]) ).
cnf(refute_0_1345,plain,
and(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),implies(X_35661,or(X_35661,not(equiv(X_35661,X_35661))))) = equiv(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),
inference(resolve,[$cnf( $equal(equiv(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),and(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),implies(X_35661,or(X_35661,not(equiv(X_35661,X_35661)))))) )],[refute_0_1343,refute_0_1344]) ).
cnf(refute_0_1346,plain,
( and(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),implies(X_35661,or(X_35661,not(equiv(X_35661,X_35661))))) != equiv(or(X_35661,not(equiv(X_35661,X_35661))),X_35661)
| ~ is_a_theorem(implies(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),and(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),implies(X_35661,or(X_35661,not(equiv(X_35661,X_35661)))))))
| is_a_theorem(implies(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),equiv(or(X_35661,not(equiv(X_35661,X_35661))),X_35661))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),and(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),implies(X_35661,or(X_35661,not(equiv(X_35661,X_35661))))))) ),[0,1],$fot(equiv(or(X_35661,not(equiv(X_35661,X_35661))),X_35661))]]) ).
cnf(refute_0_1347,plain,
( ~ is_a_theorem(implies(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),and(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),implies(X_35661,or(X_35661,not(equiv(X_35661,X_35661)))))))
| is_a_theorem(implies(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),equiv(or(X_35661,not(equiv(X_35661,X_35661))),X_35661))) ),
inference(resolve,[$cnf( $equal(and(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),implies(X_35661,or(X_35661,not(equiv(X_35661,X_35661))))),equiv(or(X_35661,not(equiv(X_35661,X_35661))),X_35661)) )],[refute_0_1345,refute_0_1346]) ).
cnf(refute_0_1348,plain,
is_a_theorem(implies(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),equiv(or(X_35661,not(equiv(X_35661,X_35661))),X_35661))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),and(implies(or(X_35661,not(equiv(X_35661,X_35661))),X_35661),implies(X_35661,or(X_35661,not(equiv(X_35661,X_35661))))))) )],[refute_0_1342,refute_0_1347]) ).
cnf(refute_0_1349,plain,
is_a_theorem(implies(implies(or(X_35671,not(equiv(X_35671,X_35671))),X_35671),equiv(or(X_35671,not(equiv(X_35671,X_35671))),X_35671))),
inference(subst,[],[refute_0_1348:[bind(X_35661,$fot(X_35671))]]) ).
cnf(refute_0_1350,plain,
( ~ is_a_theorem(implies(or(X_35671,not(equiv(X_35671,X_35671))),X_35671))
| is_a_theorem(equiv(or(X_35671,not(equiv(X_35671,X_35671))),X_35671)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_35671,not(equiv(X_35671,X_35671))),X_35671),equiv(or(X_35671,not(equiv(X_35671,X_35671))),X_35671))) )],[refute_0_1349,refute_0_755]) ).
cnf(refute_0_1351,plain,
is_a_theorem(implies(or(X_2665,not(X_2663)),implies(X_2663,X_2665))),
inference(subst,[],[refute_0_630:[bind(X,$fot(X_2663)),bind(X_15,$fot(X_2665))]]) ).
cnf(refute_0_1352,plain,
( ~ is_a_theorem(implies(or(X_2665,not(X_2663)),implies(X_2663,X_2665)))
| is_a_theorem(implies(X_2663,implies(or(X_2665,not(X_2663)),X_2665))) ),
inference(subst,[],[refute_0_121:[bind(X,$fot(X_2663)),bind(X_80,$fot(or(X_2665,not(X_2663)))),bind(X_82,$fot(X_2665))]]) ).
cnf(refute_0_1353,plain,
is_a_theorem(implies(X_2663,implies(or(X_2665,not(X_2663)),X_2665))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_2665,not(X_2663)),implies(X_2663,X_2665))) )],[refute_0_1351,refute_0_1352]) ).
cnf(refute_0_1354,plain,
is_a_theorem(implies(equiv(X_24983,X_24983),implies(or(X_2665,not(equiv(X_24983,X_24983))),X_2665))),
inference(subst,[],[refute_0_1353:[bind(X_2663,$fot(equiv(X_24983,X_24983)))]]) ).
cnf(refute_0_1355,plain,
( ~ is_a_theorem(implies(equiv(X_24900,X_24900),X_24899))
| ~ is_a_theorem(implies(implies(equiv(X_24900,X_24900),X_24899),X_24899))
| is_a_theorem(X_24899) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(implies(equiv(X_24900,X_24900),X_24899))),bind(Y,$fot(X_24899))]]) ).
cnf(refute_0_1356,plain,
( ~ is_a_theorem(equiv(X_2832,X_2832))
| is_a_theorem(implies(implies(equiv(X_2832,X_2832),X_24842),X_24842)) ),
inference(subst,[],[refute_0_157:[bind(X_3653,$fot(equiv(X_2832,X_2832))),bind(X_3654,$fot(X_24842))]]) ).
cnf(refute_0_1357,plain,
is_a_theorem(implies(implies(equiv(X_2832,X_2832),X_24842),X_24842)),
inference(resolve,[$cnf( is_a_theorem(equiv(X_2832,X_2832)) )],[refute_0_725,refute_0_1356]) ).
cnf(refute_0_1358,plain,
is_a_theorem(implies(implies(equiv(X_24900,X_24900),X_24899),X_24899)),
inference(subst,[],[refute_0_1357:[bind(X_24842,$fot(X_24899)),bind(X_2832,$fot(X_24900))]]) ).
cnf(refute_0_1359,plain,
( ~ is_a_theorem(implies(equiv(X_24900,X_24900),X_24899))
| is_a_theorem(X_24899) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(equiv(X_24900,X_24900),X_24899),X_24899)) )],[refute_0_1358,refute_0_1355]) ).
cnf(refute_0_1360,plain,
( ~ is_a_theorem(implies(equiv(X_24983,X_24983),implies(or(X_2665,not(equiv(X_24983,X_24983))),X_2665)))
| is_a_theorem(implies(or(X_2665,not(equiv(X_24983,X_24983))),X_2665)) ),
inference(subst,[],[refute_0_1359:[bind(X_24899,$fot(implies(or(X_2665,not(equiv(X_24983,X_24983))),X_2665))),bind(X_24900,$fot(X_24983))]]) ).
cnf(refute_0_1361,plain,
is_a_theorem(implies(or(X_2665,not(equiv(X_24983,X_24983))),X_2665)),
inference(resolve,[$cnf( is_a_theorem(implies(equiv(X_24983,X_24983),implies(or(X_2665,not(equiv(X_24983,X_24983))),X_2665))) )],[refute_0_1354,refute_0_1360]) ).
cnf(refute_0_1362,plain,
is_a_theorem(implies(or(X_35671,not(equiv(X_35671,X_35671))),X_35671)),
inference(subst,[],[refute_0_1361:[bind(X_24983,$fot(X_35671)),bind(X_2665,$fot(X_35671))]]) ).
cnf(refute_0_1363,plain,
is_a_theorem(equiv(or(X_35671,not(equiv(X_35671,X_35671))),X_35671)),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_35671,not(equiv(X_35671,X_35671))),X_35671)) )],[refute_0_1362,refute_0_1350]) ).
cnf(refute_0_1364,plain,
is_a_theorem(equiv(or(X_35672,not(equiv(X_35672,X_35672))),X_35672)),
inference(subst,[],[refute_0_1363:[bind(X_35671,$fot(X_35672))]]) ).
cnf(refute_0_1365,plain,
or(X_35672,not(equiv(X_35672,X_35672))) = X_35672,
inference(resolve,[$cnf( is_a_theorem(equiv(or(X_35672,not(equiv(X_35672,X_35672))),X_35672)) )],[refute_0_1364,refute_0_754]) ).
cnf(refute_0_1366,plain,
or(X_5092,not(equiv(X_5092,X_5092))) = X_5092,
inference(subst,[],[refute_0_1365:[bind(X_35672,$fot(X_5092))]]) ).
cnf(refute_0_1367,plain,
( or(X_5092,not(equiv(X_5092,X_5092))) != X_5092
| ~ is_a_theorem(implies(or(X_5092,not(equiv(X_5092,X_5092))),or(X_5092,X_10144)))
| is_a_theorem(implies(X_5092,or(X_5092,X_10144))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_5092,not(equiv(X_5092,X_5092))),or(X_5092,X_10144))) ),[0,0],$fot(X_5092)]]) ).
cnf(refute_0_1368,plain,
( ~ is_a_theorem(implies(or(X_5092,not(equiv(X_5092,X_5092))),or(X_5092,X_10144)))
| is_a_theorem(implies(X_5092,or(X_5092,X_10144))) ),
inference(resolve,[$cnf( $equal(or(X_5092,not(equiv(X_5092,X_5092))),X_5092) )],[refute_0_1366,refute_0_1367]) ).
cnf(refute_0_1369,plain,
is_a_theorem(implies(X_5092,or(X_5092,X_10144))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_5092,not(equiv(X_5092,X_5092))),or(X_5092,X_10144))) )],[refute_0_753,refute_0_1368]) ).
cnf(refute_0_1370,plain,
is_a_theorem(implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3))),
inference(subst,[],[refute_0_1369:[bind(X_10144,$fot(skolemFOFtoCNF_Q_3)),bind(X_5092,$fot(skolemFOFtoCNF_P_4))]]) ).
cnf(refute_0_1371,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3))) )],[refute_0_1370,refute_0_713]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL497+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 20:17:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 242.92/243.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 242.92/243.05
% 242.92/243.05 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 243.11/243.27
%------------------------------------------------------------------------------