TSTP Solution File: LCL518+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL518+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:52:51 EDT 2022
% Result : Theorem 108.06s 108.25s
% Output : CNFRefutation 108.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 149
% Syntax : Number of formulae : 808 ( 404 unt; 0 def)
% Number of atoms : 1390 ( 910 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 1145 ( 563 ~; 550 |; 13 &)
% ( 12 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 15 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-2 aty)
% Number of variables : 1487 ( 31 sgn 62 !; 11 ?)
% 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(kn1,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ) ).
fof(kn2,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ) ).
fof(kn3,axiom,
( kn3
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ) ).
fof(r1,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ) ).
fof(op_and,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ).
fof(rosser_op_or,axiom,
op_or ).
fof(rosser_op_implies_and,axiom,
op_implies_and ).
fof(rosser_op_equiv,axiom,
op_equiv ).
fof(rosser_modus_ponens,axiom,
modus_ponens ).
fof(rosser_kn1,axiom,
kn1 ).
fof(rosser_kn2,axiom,
kn2 ).
fof(rosser_kn3,axiom,
kn3 ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents ).
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_r1,conjecture,
r1 ).
fof(subgoal_0,plain,
r1,
inference(strip,[],[principia_r1]) ).
fof(negate_0_0,plain,
~ r1,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ r1
<=> ? [P] : ~ is_a_theorem(implies(or(P,P),P)) ),
inference(canonicalize,[],[r1]) ).
fof(normalize_0_1,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_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6))
| r1 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ r1,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ kn2
<=> ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P)) ),
inference(canonicalize,[],[kn2]) ).
fof(normalize_0_5,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_P_1,skolemFOFtoCNF_Q),skolemFOFtoCNF_P_1))
| kn2 )
& ( ~ kn2
| is_a_theorem(implies(and(P,Q),P)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [P,Q] :
( ~ kn2
| is_a_theorem(implies(and(P,Q),P)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
kn2,
inference(canonicalize,[],[rosser_kn2]) ).
fof(normalize_0_8,plain,
( ~ op_and
| ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[op_and]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
op_and,
inference(canonicalize,[],[principia_op_and]) ).
fof(normalize_0_11,plain,
( ~ op_implies_or
| ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[op_implies_or]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
op_implies_or,
inference(canonicalize,[],[principia_op_implies_or]) ).
fof(normalize_0_14,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
op_or,
inference(canonicalize,[],[rosser_op_or]) ).
fof(normalize_0_17,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
op_implies_and,
inference(canonicalize,[],[rosser_op_implies_and]) ).
fof(normalize_0_20,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_21,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_20]) ).
fof(normalize_0_22,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
modus_ponens,
inference(canonicalize,[],[rosser_modus_ponens]) ).
fof(normalize_0_24,plain,
( ~ kn1
<=> ? [P] : ~ is_a_theorem(implies(P,and(P,P))) ),
inference(canonicalize,[],[kn1]) ).
fof(normalize_0_25,plain,
! [P] :
( ( ~ is_a_theorem(implies(skolemFOFtoCNF_P,and(skolemFOFtoCNF_P,skolemFOFtoCNF_P)))
| kn1 )
& ( ~ kn1
| is_a_theorem(implies(P,and(P,P))) ) ),
inference(clausify,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [P] :
( ~ kn1
| is_a_theorem(implies(P,and(P,P))) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
kn1,
inference(canonicalize,[],[rosser_kn1]) ).
fof(normalize_0_28,plain,
( ~ kn3
<=> ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
inference(canonicalize,[],[kn3]) ).
fof(normalize_0_29,plain,
! [P,Q,R] :
( ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_P_2,skolemFOFtoCNF_Q_1),implies(not(and(skolemFOFtoCNF_Q_1,skolemFOFtoCNF_R)),not(and(skolemFOFtoCNF_R,skolemFOFtoCNF_P_2)))))
| kn3 )
& ( ~ kn3
| is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ) ),
inference(clausify,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [P,Q,R] :
( ~ kn3
| is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
inference(conjunct,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
kn3,
inference(canonicalize,[],[rosser_kn3]) ).
fof(normalize_0_32,plain,
( ~ substitution_of_equivalents
<=> ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_33,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_32]) ).
fof(normalize_0_34,plain,
! [X,Y] :
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(conjunct,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
substitution_of_equivalents,
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_36,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_37,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
op_equiv,
inference(canonicalize,[],[principia_op_equiv]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6))
| r1 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ r1,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6)),
inference(resolve,[$cnf( r1 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ kn2
| is_a_theorem(implies(and(P,Q),P)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
kn2,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(and(P,Q),P)),
inference(resolve,[$cnf( kn2 )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(and(not(not(X_33)),Q),not(not(X_33)))),
inference(subst,[],[refute_0_5:[bind(P,$fot(not(not(X_33))))]]) ).
cnf(refute_0_7,plain,
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
op_and,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
and(X,Y) = not(or(not(X),not(Y))),
inference(resolve,[$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_12]) ).
cnf(refute_0_11,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_13]) ).
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( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[refute_0_9,refute_0_24]) ).
cnf(refute_0_26,plain,
and(not(X_7),Y) = not(implies(not(X_7),not(Y))),
inference(subst,[],[refute_0_25:[bind(X,$fot(not(X_7)))]]) ).
cnf(refute_0_27,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_28,plain,
op_or,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_29,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_28,refute_0_27]) ).
cnf(refute_0_30,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_31,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_32,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_31,refute_0_30]) ).
cnf(refute_0_33,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_34,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_34:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_36,plain,
( not(and(not(X),not(Y))) != implies(not(X),Y)
| or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) ),[1],$fot(implies(not(X),Y))]]) ).
cnf(refute_0_37,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_29,refute_0_37]) ).
cnf(refute_0_39,plain,
or(X_7,not(Y)) = implies(not(X_7),not(Y)),
inference(subst,[],[refute_0_38:[bind(X,$fot(X_7)),bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_40,plain,
( or(X_7,not(Y)) != implies(not(X_7),not(Y))
| implies(not(X_7),not(Y)) = or(X_7,not(Y)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X_7,not(Y)))),bind(Y0,$fot(implies(not(X_7),not(Y))))]]) ).
cnf(refute_0_41,plain,
implies(not(X_7),not(Y)) = or(X_7,not(Y)),
inference(resolve,[$cnf( $equal(or(X_7,not(Y)),implies(not(X_7),not(Y))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( and(not(X_7),Y) != not(implies(not(X_7),not(Y)))
| implies(not(X_7),not(Y)) != or(X_7,not(Y))
| and(not(X_7),Y) = not(or(X_7,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(X_7),Y),not(implies(not(X_7),not(Y)))) ),[1,0],$fot(or(X_7,not(Y)))]]) ).
cnf(refute_0_43,plain,
( and(not(X_7),Y) != not(implies(not(X_7),not(Y)))
| and(not(X_7),Y) = not(or(X_7,not(Y))) ),
inference(resolve,[$cnf( $equal(implies(not(X_7),not(Y)),or(X_7,not(Y))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
and(not(X_7),Y) = not(or(X_7,not(Y))),
inference(resolve,[$cnf( $equal(and(not(X_7),Y),not(implies(not(X_7),not(Y)))) )],[refute_0_26,refute_0_43]) ).
cnf(refute_0_45,plain,
and(not(not(X_12)),Y) = not(or(not(X_12),not(Y))),
inference(subst,[],[refute_0_44:[bind(X_7,$fot(not(X_12)))]]) ).
cnf(refute_0_46,plain,
implies(X_12,not(Y)) = or(not(X_12),not(Y)),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_12)),bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_47,plain,
( implies(X_12,not(Y)) != or(not(X_12),not(Y))
| or(not(X_12),not(Y)) = implies(X_12,not(Y)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X_12,not(Y)))),bind(Y0,$fot(or(not(X_12),not(Y))))]]) ).
cnf(refute_0_48,plain,
or(not(X_12),not(Y)) = implies(X_12,not(Y)),
inference(resolve,[$cnf( $equal(implies(X_12,not(Y)),or(not(X_12),not(Y))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( and(not(not(X_12)),Y) != not(or(not(X_12),not(Y)))
| or(not(X_12),not(Y)) != implies(X_12,not(Y))
| and(not(not(X_12)),Y) = not(implies(X_12,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X_12)),Y),not(or(not(X_12),not(Y)))) ),[1,0],$fot(implies(X_12,not(Y)))]]) ).
cnf(refute_0_50,plain,
( and(not(not(X_12)),Y) != not(or(not(X_12),not(Y)))
| and(not(not(X_12)),Y) = not(implies(X_12,not(Y))) ),
inference(resolve,[$cnf( $equal(or(not(X_12),not(Y)),implies(X_12,not(Y))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
and(not(not(X_12)),Y) = not(implies(X_12,not(Y))),
inference(resolve,[$cnf( $equal(and(not(not(X_12)),Y),not(or(not(X_12),not(Y)))) )],[refute_0_45,refute_0_50]) ).
cnf(refute_0_52,plain,
( and(X,Y) != not(implies(X,not(Y)))
| not(implies(X,not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(implies(X,not(Y)))))]]) ).
cnf(refute_0_53,plain,
not(implies(X,not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(implies(X,not(Y)))) )],[refute_0_25,refute_0_52]) ).
cnf(refute_0_54,plain,
not(implies(X_12,not(Y))) = and(X_12,Y),
inference(subst,[],[refute_0_53:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_55,plain,
( and(not(not(X_12)),Y) != not(implies(X_12,not(Y)))
| not(implies(X_12,not(Y))) != and(X_12,Y)
| and(not(not(X_12)),Y) = and(X_12,Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(not(not(X_12)),Y),and(X_12,Y)) ),[0],$fot(not(implies(X_12,not(Y))))]]) ).
cnf(refute_0_56,plain,
( and(not(not(X_12)),Y) != not(implies(X_12,not(Y)))
| and(not(not(X_12)),Y) = and(X_12,Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_12,not(Y))),and(X_12,Y)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
and(not(not(X_12)),Y) = and(X_12,Y),
inference(resolve,[$cnf( $equal(and(not(not(X_12)),Y),not(implies(X_12,not(Y)))) )],[refute_0_51,refute_0_56]) ).
cnf(refute_0_58,plain,
and(not(not(X_33)),Q) = and(X_33,Q),
inference(subst,[],[refute_0_57:[bind(Y,$fot(Q)),bind(X_12,$fot(X_33))]]) ).
cnf(refute_0_59,plain,
( and(not(not(X_33)),Q) != and(X_33,Q)
| ~ is_a_theorem(implies(and(not(not(X_33)),Q),not(not(X_33))))
| is_a_theorem(implies(and(X_33,Q),not(not(X_33)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(not(not(X_33)),Q),not(not(X_33)))) ),[0,0],$fot(and(X_33,Q))]]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(implies(and(not(not(X_33)),Q),not(not(X_33))))
| is_a_theorem(implies(and(X_33,Q),not(not(X_33)))) ),
inference(resolve,[$cnf( $equal(and(not(not(X_33)),Q),and(X_33,Q)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(and(X_33,Q),not(not(X_33)))),
inference(resolve,[$cnf( is_a_theorem(implies(and(not(not(X_33)),Q),not(not(X_33)))) )],[refute_0_6,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_63,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_64,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_63,refute_0_62]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(and(X_33,Q))
| ~ is_a_theorem(implies(and(X_33,Q),not(not(X_33))))
| is_a_theorem(not(not(X_33))) ),
inference(subst,[],[refute_0_64:[bind(X,$fot(and(X_33,Q))),bind(Y,$fot(not(not(X_33))))]]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(and(X_33,Q))
| is_a_theorem(not(not(X_33))) ),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_33,Q),not(not(X_33)))) )],[refute_0_61,refute_0_65]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(and(or(or(X_316,X_317),not(X_316)),or(or(X_316,X_317),not(X_316))))
| is_a_theorem(not(not(or(or(X_316,X_317),not(X_316))))) ),
inference(subst,[],[refute_0_66:[bind(Q,$fot(or(or(X_316,X_317),not(X_316)))),bind(X_33,$fot(or(or(X_316,X_317),not(X_316))))]]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(and(P,not(X_88)),P)),
inference(subst,[],[refute_0_5:[bind(Q,$fot(not(X_88)))]]) ).
cnf(refute_0_69,plain,
implies(and(X,not(Y)),X_13) = or(not(and(X,not(Y))),X_13),
inference(subst,[],[refute_0_12:[bind(X,$fot(and(X,not(Y)))),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_70,plain,
( implies(and(X,not(Y)),X_13) != or(not(and(X,not(Y))),X_13)
| not(and(X,not(Y))) != implies(X,Y)
| implies(and(X,not(Y)),X_13) = or(implies(X,Y),X_13) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(X,not(Y)),X_13),or(not(and(X,not(Y))),X_13)) ),[1,0],$fot(implies(X,Y))]]) ).
cnf(refute_0_71,plain,
( implies(and(X,not(Y)),X_13) != or(not(and(X,not(Y))),X_13)
| implies(and(X,not(Y)),X_13) = or(implies(X,Y),X_13) ),
inference(resolve,[$cnf( $equal(not(and(X,not(Y))),implies(X,Y)) )],[refute_0_34,refute_0_70]) ).
cnf(refute_0_72,plain,
implies(and(X,not(Y)),X_13) = or(implies(X,Y),X_13),
inference(resolve,[$cnf( $equal(implies(and(X,not(Y)),X_13),or(not(and(X,not(Y))),X_13)) )],[refute_0_69,refute_0_71]) ).
cnf(refute_0_73,plain,
implies(and(P,not(X_88)),P) = or(implies(P,X_88),P),
inference(subst,[],[refute_0_72:[bind(X,$fot(P)),bind(Y,$fot(X_88)),bind(X_13,$fot(P))]]) ).
cnf(refute_0_74,plain,
( implies(and(P,not(X_88)),P) != or(implies(P,X_88),P)
| ~ is_a_theorem(implies(and(P,not(X_88)),P))
| is_a_theorem(or(implies(P,X_88),P)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(P,not(X_88)),P)) ),[0],$fot(or(implies(P,X_88),P))]]) ).
cnf(refute_0_75,plain,
( ~ is_a_theorem(implies(and(P,not(X_88)),P))
| is_a_theorem(or(implies(P,X_88),P)) ),
inference(resolve,[$cnf( $equal(implies(and(P,not(X_88)),P),or(implies(P,X_88),P)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
is_a_theorem(or(implies(P,X_88),P)),
inference(resolve,[$cnf( is_a_theorem(implies(and(P,not(X_88)),P)) )],[refute_0_68,refute_0_75]) ).
cnf(refute_0_77,plain,
is_a_theorem(or(implies(not(X),X_91),not(X))),
inference(subst,[],[refute_0_76:[bind(P,$fot(not(X))),bind(X_88,$fot(X_91))]]) ).
cnf(refute_0_78,plain,
or(X,X_91) = implies(not(X),X_91),
inference(subst,[],[refute_0_38:[bind(Y,$fot(X_91))]]) ).
cnf(refute_0_79,plain,
( or(X,X_91) != implies(not(X),X_91)
| implies(not(X),X_91) = or(X,X_91) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_91))),bind(Y0,$fot(implies(not(X),X_91)))]]) ).
cnf(refute_0_80,plain,
implies(not(X),X_91) = or(X,X_91),
inference(resolve,[$cnf( $equal(or(X,X_91),implies(not(X),X_91)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
( implies(not(X),X_91) != or(X,X_91)
| ~ is_a_theorem(or(implies(not(X),X_91),not(X)))
| is_a_theorem(or(or(X,X_91),not(X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(not(X),X_91),not(X))) ),[0,0],$fot(or(X,X_91))]]) ).
cnf(refute_0_82,plain,
( ~ is_a_theorem(or(implies(not(X),X_91),not(X)))
| is_a_theorem(or(or(X,X_91),not(X))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_91),or(X,X_91)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
is_a_theorem(or(or(X,X_91),not(X))),
inference(resolve,[$cnf( is_a_theorem(or(implies(not(X),X_91),not(X))) )],[refute_0_77,refute_0_82]) ).
cnf(refute_0_84,plain,
( ~ kn1
| is_a_theorem(implies(P,and(P,P))) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_85,plain,
kn1,
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_86,plain,
is_a_theorem(implies(P,and(P,P))),
inference(resolve,[$cnf( kn1 )],[refute_0_85,refute_0_84]) ).
cnf(refute_0_87,plain,
is_a_theorem(implies(X_295,and(X_295,X_295))),
inference(subst,[],[refute_0_86:[bind(P,$fot(X_295))]]) ).
cnf(refute_0_88,plain,
( ~ is_a_theorem(X_295)
| ~ is_a_theorem(implies(X_295,and(X_295,X_295)))
| is_a_theorem(and(X_295,X_295)) ),
inference(subst,[],[refute_0_64:[bind(X,$fot(X_295)),bind(Y,$fot(and(X_295,X_295)))]]) ).
cnf(refute_0_89,plain,
( ~ is_a_theorem(X_295)
| is_a_theorem(and(X_295,X_295)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_295,and(X_295,X_295))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( ~ is_a_theorem(or(or(X,X_91),not(X)))
| is_a_theorem(and(or(or(X,X_91),not(X)),or(or(X,X_91),not(X)))) ),
inference(subst,[],[refute_0_89:[bind(X_295,$fot(or(or(X,X_91),not(X))))]]) ).
cnf(refute_0_91,plain,
is_a_theorem(and(or(or(X,X_91),not(X)),or(or(X,X_91),not(X)))),
inference(resolve,[$cnf( is_a_theorem(or(or(X,X_91),not(X))) )],[refute_0_83,refute_0_90]) ).
cnf(refute_0_92,plain,
is_a_theorem(and(or(or(X_316,X_317),not(X_316)),or(or(X_316,X_317),not(X_316)))),
inference(subst,[],[refute_0_91:[bind(X,$fot(X_316)),bind(X_91,$fot(X_317))]]) ).
cnf(refute_0_93,plain,
is_a_theorem(not(not(or(or(X_316,X_317),not(X_316))))),
inference(resolve,[$cnf( is_a_theorem(and(or(or(X_316,X_317),not(X_316)),or(or(X_316,X_317),not(X_316)))) )],[refute_0_92,refute_0_67]) ).
cnf(refute_0_94,plain,
( and(not(X_7),Y) != not(or(X_7,not(Y)))
| not(or(X_7,not(Y))) = and(not(X_7),Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(not(X_7),Y))),bind(Y0,$fot(not(or(X_7,not(Y)))))]]) ).
cnf(refute_0_95,plain,
not(or(X_7,not(Y))) = and(not(X_7),Y),
inference(resolve,[$cnf( $equal(and(not(X_7),Y),not(or(X_7,not(Y)))) )],[refute_0_44,refute_0_94]) ).
cnf(refute_0_96,plain,
not(or(or(X_316,X_317),not(X_316))) = and(not(or(X_316,X_317)),X_316),
inference(subst,[],[refute_0_95:[bind(Y,$fot(X_316)),bind(X_7,$fot(or(X_316,X_317)))]]) ).
cnf(refute_0_97,plain,
not(not(or(or(X_316,X_317),not(X_316)))) = not(not(or(or(X_316,X_317),not(X_316)))),
introduced(tautology,[refl,[$fot(not(not(or(or(X_316,X_317),not(X_316)))))]]) ).
cnf(refute_0_98,plain,
( not(not(or(or(X_316,X_317),not(X_316)))) != not(not(or(or(X_316,X_317),not(X_316))))
| not(or(or(X_316,X_317),not(X_316))) != and(not(or(X_316,X_317)),X_316)
| not(not(or(or(X_316,X_317),not(X_316)))) = not(and(not(or(X_316,X_317)),X_316)) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(or(or(X_316,X_317),not(X_316)))),not(not(or(or(X_316,X_317),not(X_316))))) ),[1,0],$fot(and(not(or(X_316,X_317)),X_316))]]) ).
cnf(refute_0_99,plain,
( not(or(or(X_316,X_317),not(X_316))) != and(not(or(X_316,X_317)),X_316)
| not(not(or(or(X_316,X_317),not(X_316)))) = not(and(not(or(X_316,X_317)),X_316)) ),
inference(resolve,[$cnf( $equal(not(not(or(or(X_316,X_317),not(X_316)))),not(not(or(or(X_316,X_317),not(X_316))))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
not(not(or(or(X_316,X_317),not(X_316)))) = not(and(not(or(X_316,X_317)),X_316)),
inference(resolve,[$cnf( $equal(not(or(or(X_316,X_317),not(X_316))),and(not(or(X_316,X_317)),X_316)) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
( not(not(or(or(X_316,X_317),not(X_316)))) != not(and(not(or(X_316,X_317)),X_316))
| ~ is_a_theorem(not(not(or(or(X_316,X_317),not(X_316)))))
| is_a_theorem(not(and(not(or(X_316,X_317)),X_316))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(not(or(or(X_316,X_317),not(X_316))))) ),[0],$fot(not(and(not(or(X_316,X_317)),X_316)))]]) ).
cnf(refute_0_102,plain,
( ~ is_a_theorem(not(not(or(or(X_316,X_317),not(X_316)))))
| is_a_theorem(not(and(not(or(X_316,X_317)),X_316))) ),
inference(resolve,[$cnf( $equal(not(not(or(or(X_316,X_317),not(X_316)))),not(and(not(or(X_316,X_317)),X_316))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
is_a_theorem(not(and(not(or(X_316,X_317)),X_316))),
inference(resolve,[$cnf( is_a_theorem(not(not(or(or(X_316,X_317),not(X_316))))) )],[refute_0_93,refute_0_102]) ).
cnf(refute_0_104,plain,
is_a_theorem(not(and(not(or(X_318,not(Y))),X_318))),
inference(subst,[],[refute_0_103:[bind(X_316,$fot(X_318)),bind(X_317,$fot(not(Y)))]]) ).
cnf(refute_0_105,plain,
and(not(X_318),Y) = not(or(X_318,not(Y))),
inference(subst,[],[refute_0_44:[bind(X_7,$fot(X_318))]]) ).
cnf(refute_0_106,plain,
( and(not(X_318),Y) != not(or(X_318,not(Y)))
| not(or(X_318,not(Y))) = and(not(X_318),Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(not(X_318),Y))),bind(Y0,$fot(not(or(X_318,not(Y)))))]]) ).
cnf(refute_0_107,plain,
not(or(X_318,not(Y))) = and(not(X_318),Y),
inference(resolve,[$cnf( $equal(and(not(X_318),Y),not(or(X_318,not(Y)))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
( not(or(X_318,not(Y))) != and(not(X_318),Y)
| ~ is_a_theorem(not(and(not(or(X_318,not(Y))),X_318)))
| is_a_theorem(not(and(and(not(X_318),Y),X_318))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(not(or(X_318,not(Y))),X_318))) ),[0,0,0],$fot(and(not(X_318),Y))]]) ).
cnf(refute_0_109,plain,
( ~ is_a_theorem(not(and(not(or(X_318,not(Y))),X_318)))
| is_a_theorem(not(and(and(not(X_318),Y),X_318))) ),
inference(resolve,[$cnf( $equal(not(or(X_318,not(Y))),and(not(X_318),Y)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
is_a_theorem(not(and(and(not(X_318),Y),X_318))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(or(X_318,not(Y))),X_318))) )],[refute_0_104,refute_0_109]) ).
cnf(refute_0_111,plain,
is_a_theorem(not(and(and(not(X_5448),not(X_5448)),X_5448))),
inference(subst,[],[refute_0_110:[bind(Y,$fot(not(X_5448))),bind(X_318,$fot(X_5448))]]) ).
cnf(refute_0_112,plain,
is_a_theorem(implies(and(X_296,Q),X_296)),
inference(subst,[],[refute_0_5:[bind(P,$fot(X_296))]]) ).
cnf(refute_0_113,plain,
( ~ is_a_theorem(and(X_296,Q))
| ~ is_a_theorem(implies(and(X_296,Q),X_296))
| is_a_theorem(X_296) ),
inference(subst,[],[refute_0_64:[bind(X,$fot(and(X_296,Q))),bind(Y,$fot(X_296))]]) ).
cnf(refute_0_114,plain,
( ~ is_a_theorem(and(X_296,Q))
| is_a_theorem(X_296) ),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_296,Q),X_296)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
( ~ is_a_theorem(and(or(X_415,not(or(X_415,X_415))),or(X_415,not(or(X_415,X_415)))))
| is_a_theorem(or(X_415,not(or(X_415,X_415)))) ),
inference(subst,[],[refute_0_114:[bind(Q,$fot(or(X_415,not(or(X_415,X_415))))),bind(X_296,$fot(or(X_415,not(or(X_415,X_415)))))]]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(X_413,and(X_413,X_413))),
inference(subst,[],[refute_0_86:[bind(P,$fot(X_413))]]) ).
cnf(refute_0_117,plain,
is_a_theorem(implies(implies(X_27,not(X_28)),and(implies(X_27,not(X_28)),implies(X_27,not(X_28))))),
inference(subst,[],[refute_0_86:[bind(P,$fot(implies(X_27,not(X_28))))]]) ).
cnf(refute_0_118,plain,
and(X,implies(X_1,not(X_2))) = not(implies(X,not(implies(X_1,not(X_2))))),
inference(subst,[],[refute_0_25:[bind(Y,$fot(implies(X_1,not(X_2))))]]) ).
cnf(refute_0_119,plain,
and(X_1,X_2) = not(implies(X_1,not(X_2))),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_1)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_120,plain,
( and(X_1,X_2) != not(implies(X_1,not(X_2)))
| not(implies(X_1,not(X_2))) = and(X_1,X_2) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(X_1,X_2))),bind(Y0,$fot(not(implies(X_1,not(X_2)))))]]) ).
cnf(refute_0_121,plain,
not(implies(X_1,not(X_2))) = and(X_1,X_2),
inference(resolve,[$cnf( $equal(and(X_1,X_2),not(implies(X_1,not(X_2)))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
( and(X,implies(X_1,not(X_2))) != not(implies(X,not(implies(X_1,not(X_2)))))
| not(implies(X_1,not(X_2))) != and(X_1,X_2)
| and(X,implies(X_1,not(X_2))) = not(implies(X,and(X_1,X_2))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,implies(X_1,not(X_2))),not(implies(X,not(implies(X_1,not(X_2)))))) ),[1,0,1],$fot(and(X_1,X_2))]]) ).
cnf(refute_0_123,plain,
( and(X,implies(X_1,not(X_2))) != not(implies(X,not(implies(X_1,not(X_2)))))
| and(X,implies(X_1,not(X_2))) = not(implies(X,and(X_1,X_2))) ),
inference(resolve,[$cnf( $equal(not(implies(X_1,not(X_2))),and(X_1,X_2)) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
and(X,implies(X_1,not(X_2))) = not(implies(X,and(X_1,X_2))),
inference(resolve,[$cnf( $equal(and(X,implies(X_1,not(X_2))),not(implies(X,not(implies(X_1,not(X_2)))))) )],[refute_0_118,refute_0_123]) ).
cnf(refute_0_125,plain,
and(implies(X_27,not(X_28)),implies(X_27,not(X_28))) = not(implies(implies(X_27,not(X_28)),and(X_27,X_28))),
inference(subst,[],[refute_0_124:[bind(X,$fot(implies(X_27,not(X_28)))),bind(X_1,$fot(X_27)),bind(X_2,$fot(X_28))]]) ).
cnf(refute_0_126,plain,
( and(implies(X_27,not(X_28)),implies(X_27,not(X_28))) != not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))
| ~ is_a_theorem(implies(implies(X_27,not(X_28)),and(implies(X_27,not(X_28)),implies(X_27,not(X_28)))))
| is_a_theorem(implies(implies(X_27,not(X_28)),not(implies(implies(X_27,not(X_28)),and(X_27,X_28))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_27,not(X_28)),and(implies(X_27,not(X_28)),implies(X_27,not(X_28))))) ),[0,1],$fot(not(implies(implies(X_27,not(X_28)),and(X_27,X_28))))]]) ).
cnf(refute_0_127,plain,
( ~ is_a_theorem(implies(implies(X_27,not(X_28)),and(implies(X_27,not(X_28)),implies(X_27,not(X_28)))))
| is_a_theorem(implies(implies(X_27,not(X_28)),not(implies(implies(X_27,not(X_28)),and(X_27,X_28))))) ),
inference(resolve,[$cnf( $equal(and(implies(X_27,not(X_28)),implies(X_27,not(X_28))),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
is_a_theorem(implies(implies(X_27,not(X_28)),not(implies(implies(X_27,not(X_28)),and(X_27,X_28))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_27,not(X_28)),and(implies(X_27,not(X_28)),implies(X_27,not(X_28))))) )],[refute_0_117,refute_0_127]) ).
cnf(refute_0_129,plain,
implies(implies(X,not(Y)),X_13) = or(not(implies(X,not(Y))),X_13),
inference(subst,[],[refute_0_12:[bind(X,$fot(implies(X,not(Y)))),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_130,plain,
( implies(implies(X,not(Y)),X_13) != or(not(implies(X,not(Y))),X_13)
| not(implies(X,not(Y))) != and(X,Y)
| implies(implies(X,not(Y)),X_13) = or(and(X,Y),X_13) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(Y)),X_13),or(not(implies(X,not(Y))),X_13)) ),[1,0],$fot(and(X,Y))]]) ).
cnf(refute_0_131,plain,
( implies(implies(X,not(Y)),X_13) != or(not(implies(X,not(Y))),X_13)
| implies(implies(X,not(Y)),X_13) = or(and(X,Y),X_13) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_53,refute_0_130]) ).
cnf(refute_0_132,plain,
implies(implies(X,not(Y)),X_13) = or(and(X,Y),X_13),
inference(resolve,[$cnf( $equal(implies(implies(X,not(Y)),X_13),or(not(implies(X,not(Y))),X_13)) )],[refute_0_129,refute_0_131]) ).
cnf(refute_0_133,plain,
implies(implies(X_27,not(X_28)),and(X_27,X_28)) = or(and(X_27,X_28),and(X_27,X_28)),
inference(subst,[],[refute_0_132:[bind(X,$fot(X_27)),bind(Y,$fot(X_28)),bind(X_13,$fot(and(X_27,X_28)))]]) ).
cnf(refute_0_134,plain,
not(implies(implies(X_27,not(X_28)),and(X_27,X_28))) = not(implies(implies(X_27,not(X_28)),and(X_27,X_28))),
introduced(tautology,[refl,[$fot(not(implies(implies(X_27,not(X_28)),and(X_27,X_28))))]]) ).
cnf(refute_0_135,plain,
( implies(implies(X_27,not(X_28)),and(X_27,X_28)) != or(and(X_27,X_28),and(X_27,X_28))
| not(implies(implies(X_27,not(X_28)),and(X_27,X_28))) != not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))
| not(implies(implies(X_27,not(X_28)),and(X_27,X_28))) = not(or(and(X_27,X_28),and(X_27,X_28))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(implies(X_27,not(X_28)),and(X_27,X_28))),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))) ),[1,0],$fot(or(and(X_27,X_28),and(X_27,X_28)))]]) ).
cnf(refute_0_136,plain,
( implies(implies(X_27,not(X_28)),and(X_27,X_28)) != or(and(X_27,X_28),and(X_27,X_28))
| not(implies(implies(X_27,not(X_28)),and(X_27,X_28))) = not(or(and(X_27,X_28),and(X_27,X_28))) ),
inference(resolve,[$cnf( $equal(not(implies(implies(X_27,not(X_28)),and(X_27,X_28))),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
not(implies(implies(X_27,not(X_28)),and(X_27,X_28))) = not(or(and(X_27,X_28),and(X_27,X_28))),
inference(resolve,[$cnf( $equal(implies(implies(X_27,not(X_28)),and(X_27,X_28)),or(and(X_27,X_28),and(X_27,X_28))) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))) = or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))),
introduced(tautology,[refl,[$fot(or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))))]]) ).
cnf(refute_0_139,plain,
( not(implies(implies(X_27,not(X_28)),and(X_27,X_28))) != not(or(and(X_27,X_28),and(X_27,X_28)))
| or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))) != or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28))))
| or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))) = or(and(X_27,X_28),not(or(and(X_27,X_28),and(X_27,X_28)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))),or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28))))) ),[1,1],$fot(not(or(and(X_27,X_28),and(X_27,X_28))))]]) ).
cnf(refute_0_140,plain,
( not(implies(implies(X_27,not(X_28)),and(X_27,X_28))) != not(or(and(X_27,X_28),and(X_27,X_28)))
| or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))) = or(and(X_27,X_28),not(or(and(X_27,X_28),and(X_27,X_28)))) ),
inference(resolve,[$cnf( $equal(or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))),or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28))))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))) = or(and(X_27,X_28),not(or(and(X_27,X_28),and(X_27,X_28)))),
inference(resolve,[$cnf( $equal(not(implies(implies(X_27,not(X_28)),and(X_27,X_28))),not(or(and(X_27,X_28),and(X_27,X_28)))) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
implies(implies(X_27,not(X_28)),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))) = or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))),
inference(subst,[],[refute_0_132:[bind(X,$fot(X_27)),bind(Y,$fot(X_28)),bind(X_13,$fot(not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))))]]) ).
cnf(refute_0_143,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_144,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_15,refute_0_143]) ).
cnf(refute_0_145,plain,
( implies(implies(X_27,not(X_28)),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))) != or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28))))
| or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))) != or(and(X_27,X_28),not(or(and(X_27,X_28),and(X_27,X_28))))
| implies(implies(X_27,not(X_28)),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))) = or(and(X_27,X_28),not(or(and(X_27,X_28),and(X_27,X_28)))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(implies(implies(X_27,not(X_28)),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))))),bind(Y0,$fot(or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))))),bind(Z,$fot(or(and(X_27,X_28),not(or(and(X_27,X_28),and(X_27,X_28))))))]]) ).
cnf(refute_0_146,plain,
( or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))) != or(and(X_27,X_28),not(or(and(X_27,X_28),and(X_27,X_28))))
| implies(implies(X_27,not(X_28)),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))) = or(and(X_27,X_28),not(or(and(X_27,X_28),and(X_27,X_28)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_27,not(X_28)),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))),or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28))))) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
implies(implies(X_27,not(X_28)),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))) = or(and(X_27,X_28),not(or(and(X_27,X_28),and(X_27,X_28)))),
inference(resolve,[$cnf( $equal(or(and(X_27,X_28),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))),or(and(X_27,X_28),not(or(and(X_27,X_28),and(X_27,X_28))))) )],[refute_0_141,refute_0_146]) ).
cnf(refute_0_148,plain,
( implies(implies(X_27,not(X_28)),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))) != or(and(X_27,X_28),not(or(and(X_27,X_28),and(X_27,X_28))))
| ~ is_a_theorem(implies(implies(X_27,not(X_28)),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))))
| is_a_theorem(or(and(X_27,X_28),not(or(and(X_27,X_28),and(X_27,X_28))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_27,not(X_28)),not(implies(implies(X_27,not(X_28)),and(X_27,X_28))))) ),[0],$fot(or(and(X_27,X_28),not(or(and(X_27,X_28),and(X_27,X_28)))))]]) ).
cnf(refute_0_149,plain,
( ~ is_a_theorem(implies(implies(X_27,not(X_28)),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))))
| is_a_theorem(or(and(X_27,X_28),not(or(and(X_27,X_28),and(X_27,X_28))))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_27,not(X_28)),not(implies(implies(X_27,not(X_28)),and(X_27,X_28)))),or(and(X_27,X_28),not(or(and(X_27,X_28),and(X_27,X_28))))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
is_a_theorem(or(and(X_27,X_28),not(or(and(X_27,X_28),and(X_27,X_28))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_27,not(X_28)),not(implies(implies(X_27,not(X_28)),and(X_27,X_28))))) )],[refute_0_128,refute_0_149]) ).
cnf(refute_0_151,plain,
is_a_theorem(or(and(X_174,not(Y)),not(or(and(X_174,not(Y)),and(X_174,not(Y)))))),
inference(subst,[],[refute_0_150:[bind(X_27,$fot(X_174)),bind(X_28,$fot(not(Y)))]]) ).
cnf(refute_0_152,plain,
or(and(X,not(Y)),X_8) = implies(not(and(X,not(Y))),X_8),
inference(subst,[],[refute_0_38:[bind(X,$fot(and(X,not(Y)))),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_153,plain,
( not(and(X,not(Y))) != implies(X,Y)
| or(and(X,not(Y)),X_8) != implies(not(and(X,not(Y))),X_8)
| or(and(X,not(Y)),X_8) = implies(implies(X,Y),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X,not(Y)),X_8),implies(not(and(X,not(Y))),X_8)) ),[1,0],$fot(implies(X,Y))]]) ).
cnf(refute_0_154,plain,
( or(and(X,not(Y)),X_8) != implies(not(and(X,not(Y))),X_8)
| or(and(X,not(Y)),X_8) = implies(implies(X,Y),X_8) ),
inference(resolve,[$cnf( $equal(not(and(X,not(Y))),implies(X,Y)) )],[refute_0_34,refute_0_153]) ).
cnf(refute_0_155,plain,
or(and(X,not(Y)),X_8) = implies(implies(X,Y),X_8),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),X_8),implies(not(and(X,not(Y))),X_8)) )],[refute_0_152,refute_0_154]) ).
cnf(refute_0_156,plain,
or(and(X_174,not(Y)),and(X_174,not(Y))) = implies(implies(X_174,Y),and(X_174,not(Y))),
inference(subst,[],[refute_0_155:[bind(X,$fot(X_174)),bind(X_8,$fot(and(X_174,not(Y))))]]) ).
cnf(refute_0_157,plain,
( or(and(X_174,not(Y)),and(X_174,not(Y))) != implies(implies(X_174,Y),and(X_174,not(Y)))
| ~ is_a_theorem(or(and(X_174,not(Y)),not(or(and(X_174,not(Y)),and(X_174,not(Y))))))
| is_a_theorem(or(and(X_174,not(Y)),not(implies(implies(X_174,Y),and(X_174,not(Y)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_174,not(Y)),not(or(and(X_174,not(Y)),and(X_174,not(Y)))))) ),[0,1,0],$fot(implies(implies(X_174,Y),and(X_174,not(Y))))]]) ).
cnf(refute_0_158,plain,
( ~ is_a_theorem(or(and(X_174,not(Y)),not(or(and(X_174,not(Y)),and(X_174,not(Y))))))
| is_a_theorem(or(and(X_174,not(Y)),not(implies(implies(X_174,Y),and(X_174,not(Y)))))) ),
inference(resolve,[$cnf( $equal(or(and(X_174,not(Y)),and(X_174,not(Y))),implies(implies(X_174,Y),and(X_174,not(Y)))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
is_a_theorem(or(and(X_174,not(Y)),not(implies(implies(X_174,Y),and(X_174,not(Y)))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_174,not(Y)),not(or(and(X_174,not(Y)),and(X_174,not(Y)))))) )],[refute_0_151,refute_0_158]) ).
cnf(refute_0_160,plain,
implies(X,and(X_5,not(X_6))) = not(and(X,not(and(X_5,not(X_6))))),
inference(subst,[],[refute_0_32:[bind(Y,$fot(and(X_5,not(X_6))))]]) ).
cnf(refute_0_161,plain,
implies(X_5,X_6) = not(and(X_5,not(X_6))),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_5)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_162,plain,
( implies(X_5,X_6) != not(and(X_5,not(X_6)))
| not(and(X_5,not(X_6))) = implies(X_5,X_6) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X_5,X_6))),bind(Y0,$fot(not(and(X_5,not(X_6)))))]]) ).
cnf(refute_0_163,plain,
not(and(X_5,not(X_6))) = implies(X_5,X_6),
inference(resolve,[$cnf( $equal(implies(X_5,X_6),not(and(X_5,not(X_6)))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
( implies(X,and(X_5,not(X_6))) != not(and(X,not(and(X_5,not(X_6)))))
| not(and(X_5,not(X_6))) != implies(X_5,X_6)
| implies(X,and(X_5,not(X_6))) = not(and(X,implies(X_5,X_6))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,and(X_5,not(X_6))),not(and(X,not(and(X_5,not(X_6)))))) ),[1,0,1],$fot(implies(X_5,X_6))]]) ).
cnf(refute_0_165,plain,
( implies(X,and(X_5,not(X_6))) != not(and(X,not(and(X_5,not(X_6)))))
| implies(X,and(X_5,not(X_6))) = not(and(X,implies(X_5,X_6))) ),
inference(resolve,[$cnf( $equal(not(and(X_5,not(X_6))),implies(X_5,X_6)) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
implies(X,and(X_5,not(X_6))) = not(and(X,implies(X_5,X_6))),
inference(resolve,[$cnf( $equal(implies(X,and(X_5,not(X_6))),not(and(X,not(and(X_5,not(X_6)))))) )],[refute_0_160,refute_0_165]) ).
cnf(refute_0_167,plain,
implies(implies(X_174,Y),and(X_174,not(Y))) = not(and(implies(X_174,Y),implies(X_174,Y))),
inference(subst,[],[refute_0_166:[bind(X,$fot(implies(X_174,Y))),bind(X_5,$fot(X_174)),bind(X_6,$fot(Y))]]) ).
cnf(refute_0_168,plain,
not(implies(implies(X_174,Y),and(X_174,not(Y)))) = not(implies(implies(X_174,Y),and(X_174,not(Y)))),
introduced(tautology,[refl,[$fot(not(implies(implies(X_174,Y),and(X_174,not(Y)))))]]) ).
cnf(refute_0_169,plain,
( implies(implies(X_174,Y),and(X_174,not(Y))) != not(and(implies(X_174,Y),implies(X_174,Y)))
| not(implies(implies(X_174,Y),and(X_174,not(Y)))) != not(implies(implies(X_174,Y),and(X_174,not(Y))))
| not(implies(implies(X_174,Y),and(X_174,not(Y)))) = not(not(and(implies(X_174,Y),implies(X_174,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(implies(X_174,Y),and(X_174,not(Y)))),not(implies(implies(X_174,Y),and(X_174,not(Y))))) ),[1,0],$fot(not(and(implies(X_174,Y),implies(X_174,Y))))]]) ).
cnf(refute_0_170,plain,
( implies(implies(X_174,Y),and(X_174,not(Y))) != not(and(implies(X_174,Y),implies(X_174,Y)))
| not(implies(implies(X_174,Y),and(X_174,not(Y)))) = not(not(and(implies(X_174,Y),implies(X_174,Y)))) ),
inference(resolve,[$cnf( $equal(not(implies(implies(X_174,Y),and(X_174,not(Y)))),not(implies(implies(X_174,Y),and(X_174,not(Y))))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
not(implies(implies(X_174,Y),and(X_174,not(Y)))) = not(not(and(implies(X_174,Y),implies(X_174,Y)))),
inference(resolve,[$cnf( $equal(implies(implies(X_174,Y),and(X_174,not(Y))),not(and(implies(X_174,Y),implies(X_174,Y)))) )],[refute_0_167,refute_0_170]) ).
cnf(refute_0_172,plain,
implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y))))) = implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y))))),
introduced(tautology,[refl,[$fot(implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y))))))]]) ).
cnf(refute_0_173,plain,
( implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y))))) != implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y)))))
| not(implies(implies(X_174,Y),and(X_174,not(Y)))) != not(not(and(implies(X_174,Y),implies(X_174,Y))))
| implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y))))) = implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y))))),implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y)))))) ),[1,1],$fot(not(not(and(implies(X_174,Y),implies(X_174,Y)))))]]) ).
cnf(refute_0_174,plain,
( not(implies(implies(X_174,Y),and(X_174,not(Y)))) != not(not(and(implies(X_174,Y),implies(X_174,Y))))
| implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y))))) = implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y))))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y))))),implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y)))))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y))))) = implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y))))),
inference(resolve,[$cnf( $equal(not(implies(implies(X_174,Y),and(X_174,not(Y)))),not(not(and(implies(X_174,Y),implies(X_174,Y))))) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
or(and(X_174,not(Y)),not(implies(implies(X_174,Y),and(X_174,not(Y))))) = implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y))))),
inference(subst,[],[refute_0_155:[bind(X,$fot(X_174)),bind(X_8,$fot(not(implies(implies(X_174,Y),and(X_174,not(Y))))))]]) ).
cnf(refute_0_177,plain,
( implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y))))) != implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y)))))
| or(and(X_174,not(Y)),not(implies(implies(X_174,Y),and(X_174,not(Y))))) != implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y)))))
| or(and(X_174,not(Y)),not(implies(implies(X_174,Y),and(X_174,not(Y))))) = implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y))))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(or(and(X_174,not(Y)),not(implies(implies(X_174,Y),and(X_174,not(Y))))))),bind(Y0,$fot(implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y))))))),bind(Z,$fot(implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y)))))))]]) ).
cnf(refute_0_178,plain,
( implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y))))) != implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y)))))
| or(and(X_174,not(Y)),not(implies(implies(X_174,Y),and(X_174,not(Y))))) = implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y))))) ),
inference(resolve,[$cnf( $equal(or(and(X_174,not(Y)),not(implies(implies(X_174,Y),and(X_174,not(Y))))),implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y)))))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
or(and(X_174,not(Y)),not(implies(implies(X_174,Y),and(X_174,not(Y))))) = implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y))))),
inference(resolve,[$cnf( $equal(implies(implies(X_174,Y),not(implies(implies(X_174,Y),and(X_174,not(Y))))),implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y)))))) )],[refute_0_175,refute_0_178]) ).
cnf(refute_0_180,plain,
( or(and(X_174,not(Y)),not(implies(implies(X_174,Y),and(X_174,not(Y))))) != implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y)))))
| ~ is_a_theorem(or(and(X_174,not(Y)),not(implies(implies(X_174,Y),and(X_174,not(Y))))))
| is_a_theorem(implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_174,not(Y)),not(implies(implies(X_174,Y),and(X_174,not(Y)))))) ),[0],$fot(implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y))))))]]) ).
cnf(refute_0_181,plain,
( ~ is_a_theorem(or(and(X_174,not(Y)),not(implies(implies(X_174,Y),and(X_174,not(Y))))))
| is_a_theorem(implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y)))))) ),
inference(resolve,[$cnf( $equal(or(and(X_174,not(Y)),not(implies(implies(X_174,Y),and(X_174,not(Y))))),implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y)))))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
is_a_theorem(implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y)))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_174,not(Y)),not(implies(implies(X_174,Y),and(X_174,not(Y)))))) )],[refute_0_159,refute_0_181]) ).
cnf(refute_0_183,plain,
( ~ is_a_theorem(implies(X_174,Y))
| ~ is_a_theorem(implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y))))))
| is_a_theorem(not(not(and(implies(X_174,Y),implies(X_174,Y))))) ),
inference(subst,[],[refute_0_64:[bind(X,$fot(implies(X_174,Y))),bind(Y,$fot(not(not(and(implies(X_174,Y),implies(X_174,Y))))))]]) ).
cnf(refute_0_184,plain,
( ~ is_a_theorem(implies(X_174,Y))
| is_a_theorem(not(not(and(implies(X_174,Y),implies(X_174,Y))))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_174,Y),not(not(and(implies(X_174,Y),implies(X_174,Y)))))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
( ~ is_a_theorem(implies(X_413,and(X_413,X_413)))
| is_a_theorem(not(not(and(implies(X_413,and(X_413,X_413)),implies(X_413,and(X_413,X_413)))))) ),
inference(subst,[],[refute_0_184:[bind(Y,$fot(and(X_413,X_413))),bind(X_174,$fot(X_413))]]) ).
cnf(refute_0_186,plain,
is_a_theorem(not(not(and(implies(X_413,and(X_413,X_413)),implies(X_413,and(X_413,X_413)))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_413,and(X_413,X_413))) )],[refute_0_116,refute_0_185]) ).
cnf(refute_0_187,plain,
is_a_theorem(not(not(and(implies(not(X),and(not(X),not(X))),implies(not(X),and(not(X),not(X))))))),
inference(subst,[],[refute_0_186:[bind(X_413,$fot(not(X)))]]) ).
cnf(refute_0_188,plain,
or(X,and(not(X),not(X))) = implies(not(X),and(not(X),not(X))),
inference(subst,[],[refute_0_38:[bind(Y,$fot(and(not(X),not(X))))]]) ).
cnf(refute_0_189,plain,
( or(X,and(not(X),not(X))) != implies(not(X),and(not(X),not(X)))
| implies(not(X),and(not(X),not(X))) = or(X,and(not(X),not(X))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,and(not(X),not(X))))),bind(Y0,$fot(implies(not(X),and(not(X),not(X)))))]]) ).
cnf(refute_0_190,plain,
implies(not(X),and(not(X),not(X))) = or(X,and(not(X),not(X))),
inference(resolve,[$cnf( $equal(or(X,and(not(X),not(X))),implies(not(X),and(not(X),not(X)))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
( implies(not(X),and(not(X),not(X))) != or(X,and(not(X),not(X)))
| ~ is_a_theorem(not(not(and(implies(not(X),and(not(X),not(X))),implies(not(X),and(not(X),not(X)))))))
| is_a_theorem(not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(not(and(implies(not(X),and(not(X),not(X))),implies(not(X),and(not(X),not(X))))))) ),[0,0,0,1],$fot(or(X,and(not(X),not(X))))]]) ).
cnf(refute_0_192,plain,
( ~ is_a_theorem(not(not(and(implies(not(X),and(not(X),not(X))),implies(not(X),and(not(X),not(X)))))))
| is_a_theorem(not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
is_a_theorem(not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))))),
inference(resolve,[$cnf( is_a_theorem(not(not(and(implies(not(X),and(not(X),not(X))),implies(not(X),and(not(X),not(X))))))) )],[refute_0_187,refute_0_192]) ).
cnf(refute_0_194,plain,
and(X,or(X_11,not(X_10))) = not(implies(X,not(or(X_11,not(X_10))))),
inference(subst,[],[refute_0_25:[bind(Y,$fot(or(X_11,not(X_10))))]]) ).
cnf(refute_0_195,plain,
and(not(X_11),X_10) = not(or(X_11,not(X_10))),
inference(subst,[],[refute_0_44:[bind(Y,$fot(X_10)),bind(X_7,$fot(X_11))]]) ).
cnf(refute_0_196,plain,
( and(not(X_11),X_10) != not(or(X_11,not(X_10)))
| not(or(X_11,not(X_10))) = and(not(X_11),X_10) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(not(X_11),X_10))),bind(Y0,$fot(not(or(X_11,not(X_10)))))]]) ).
cnf(refute_0_197,plain,
not(or(X_11,not(X_10))) = and(not(X_11),X_10),
inference(resolve,[$cnf( $equal(and(not(X_11),X_10),not(or(X_11,not(X_10)))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
( and(X,or(X_11,not(X_10))) != not(implies(X,not(or(X_11,not(X_10)))))
| not(or(X_11,not(X_10))) != and(not(X_11),X_10)
| and(X,or(X_11,not(X_10))) = not(implies(X,and(not(X_11),X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,or(X_11,not(X_10))),not(implies(X,not(or(X_11,not(X_10)))))) ),[1,0,1],$fot(and(not(X_11),X_10))]]) ).
cnf(refute_0_199,plain,
( and(X,or(X_11,not(X_10))) != not(implies(X,not(or(X_11,not(X_10)))))
| and(X,or(X_11,not(X_10))) = not(implies(X,and(not(X_11),X_10))) ),
inference(resolve,[$cnf( $equal(not(or(X_11,not(X_10))),and(not(X_11),X_10)) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
and(X,or(X_11,not(X_10))) = not(implies(X,and(not(X_11),X_10))),
inference(resolve,[$cnf( $equal(and(X,or(X_11,not(X_10))),not(implies(X,not(or(X_11,not(X_10)))))) )],[refute_0_194,refute_0_199]) ).
cnf(refute_0_201,plain,
( and(X,or(X_11,not(X_10))) != not(implies(X,and(not(X_11),X_10)))
| not(implies(X,and(not(X_11),X_10))) = and(X,or(X_11,not(X_10))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(X,or(X_11,not(X_10))))),bind(Y0,$fot(not(implies(X,and(not(X_11),X_10)))))]]) ).
cnf(refute_0_202,plain,
not(implies(X,and(not(X_11),X_10))) = and(X,or(X_11,not(X_10))),
inference(resolve,[$cnf( $equal(and(X,or(X_11,not(X_10))),not(implies(X,and(not(X_11),X_10)))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
not(implies(or(X,not(or(X,X))),and(not(X),or(X,X)))) = and(or(X,not(or(X,X))),or(X,not(or(X,X)))),
inference(subst,[],[refute_0_202:[bind(X,$fot(or(X,not(or(X,X))))),bind(X_10,$fot(or(X,X))),bind(X_11,$fot(X))]]) ).
cnf(refute_0_204,plain,
implies(or(X_7,not(Y)),X_13) = or(not(or(X_7,not(Y))),X_13),
inference(subst,[],[refute_0_12:[bind(X,$fot(or(X_7,not(Y)))),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_205,plain,
( implies(or(X_7,not(Y)),X_13) != or(not(or(X_7,not(Y))),X_13)
| not(or(X_7,not(Y))) != and(not(X_7),Y)
| implies(or(X_7,not(Y)),X_13) = or(and(not(X_7),Y),X_13) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_7,not(Y)),X_13),or(not(or(X_7,not(Y))),X_13)) ),[1,0],$fot(and(not(X_7),Y))]]) ).
cnf(refute_0_206,plain,
( implies(or(X_7,not(Y)),X_13) != or(not(or(X_7,not(Y))),X_13)
| implies(or(X_7,not(Y)),X_13) = or(and(not(X_7),Y),X_13) ),
inference(resolve,[$cnf( $equal(not(or(X_7,not(Y))),and(not(X_7),Y)) )],[refute_0_95,refute_0_205]) ).
cnf(refute_0_207,plain,
implies(or(X_7,not(Y)),X_13) = or(and(not(X_7),Y),X_13),
inference(resolve,[$cnf( $equal(implies(or(X_7,not(Y)),X_13),or(not(or(X_7,not(Y))),X_13)) )],[refute_0_204,refute_0_206]) ).
cnf(refute_0_208,plain,
( implies(or(X_7,not(Y)),X_13) != or(and(not(X_7),Y),X_13)
| or(and(not(X_7),Y),X_13) = implies(or(X_7,not(Y)),X_13) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(or(X_7,not(Y)),X_13))),bind(Y0,$fot(or(and(not(X_7),Y),X_13)))]]) ).
cnf(refute_0_209,plain,
or(and(not(X_7),Y),X_13) = implies(or(X_7,not(Y)),X_13),
inference(resolve,[$cnf( $equal(implies(or(X_7,not(Y)),X_13),or(and(not(X_7),Y),X_13)) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
or(and(not(X),or(X,X)),and(not(X),or(X,X))) = implies(or(X,not(or(X,X))),and(not(X),or(X,X))),
inference(subst,[],[refute_0_209:[bind(Y,$fot(or(X,X))),bind(X_13,$fot(and(not(X),or(X,X)))),bind(X_7,$fot(X))]]) ).
cnf(refute_0_211,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_212,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[refute_0_38,refute_0_211]) ).
cnf(refute_0_213,plain,
implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))) = or(and(not(X),or(X,X)),and(not(X),or(X,X))),
inference(subst,[],[refute_0_212:[bind(X,$fot(and(not(X),or(X,X)))),bind(Y,$fot(and(not(X),or(X,X))))]]) ).
cnf(refute_0_214,plain,
( implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))) != or(and(not(X),or(X,X)),and(not(X),or(X,X)))
| or(and(not(X),or(X,X)),and(not(X),or(X,X))) != implies(or(X,not(or(X,X))),and(not(X),or(X,X)))
| implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))) = implies(or(X,not(or(X,X))),and(not(X),or(X,X))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))))),bind(Y0,$fot(or(and(not(X),or(X,X)),and(not(X),or(X,X))))),bind(Z,$fot(implies(or(X,not(or(X,X))),and(not(X),or(X,X)))))]]) ).
cnf(refute_0_215,plain,
( or(and(not(X),or(X,X)),and(not(X),or(X,X))) != implies(or(X,not(or(X,X))),and(not(X),or(X,X)))
| implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))) = implies(or(X,not(or(X,X))),and(not(X),or(X,X))) ),
inference(resolve,[$cnf( $equal(implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))),or(and(not(X),or(X,X)),and(not(X),or(X,X)))) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))) = implies(or(X,not(or(X,X))),and(not(X),or(X,X))),
inference(resolve,[$cnf( $equal(or(and(not(X),or(X,X)),and(not(X),or(X,X))),implies(or(X,not(or(X,X))),and(not(X),or(X,X)))) )],[refute_0_210,refute_0_215]) ).
cnf(refute_0_217,plain,
implies(not(X),X) = or(X,X),
inference(subst,[],[refute_0_212:[bind(Y,$fot(X))]]) ).
cnf(refute_0_218,plain,
and(not(X),implies(not(X),X)) = and(not(X),implies(not(X),X)),
introduced(tautology,[refl,[$fot(and(not(X),implies(not(X),X)))]]) ).
cnf(refute_0_219,plain,
( and(not(X),implies(not(X),X)) != and(not(X),implies(not(X),X))
| implies(not(X),X) != or(X,X)
| and(not(X),implies(not(X),X)) = and(not(X),or(X,X)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(X),implies(not(X),X)),and(not(X),implies(not(X),X))) ),[1,1],$fot(or(X,X))]]) ).
cnf(refute_0_220,plain,
( implies(not(X),X) != or(X,X)
| and(not(X),implies(not(X),X)) = and(not(X),or(X,X)) ),
inference(resolve,[$cnf( $equal(and(not(X),implies(not(X),X)),and(not(X),implies(not(X),X))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
and(not(X),implies(not(X),X)) = and(not(X),or(X,X)),
inference(resolve,[$cnf( $equal(implies(not(X),X),or(X,X)) )],[refute_0_217,refute_0_220]) ).
cnf(refute_0_222,plain,
implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X))) = implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X))),
introduced(tautology,[refl,[$fot(implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X))))]]) ).
cnf(refute_0_223,plain,
( and(not(X),implies(not(X),X)) != and(not(X),or(X,X))
| implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X))) != implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X)))
| implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X))) = implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X))),implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X)))) ),[1,1],$fot(and(not(X),or(X,X)))]]) ).
cnf(refute_0_224,plain,
( and(not(X),implies(not(X),X)) != and(not(X),or(X,X))
| implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X))) = implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))) ),
inference(resolve,[$cnf( $equal(implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X))),implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X)))) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X))) = implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))),
inference(resolve,[$cnf( $equal(and(not(X),implies(not(X),X)),and(not(X),or(X,X))) )],[refute_0_221,refute_0_224]) ).
cnf(refute_0_226,plain,
or(X,and(X_47,not(X_48))) = implies(not(X),and(X_47,not(X_48))),
inference(subst,[],[refute_0_38:[bind(Y,$fot(and(X_47,not(X_48))))]]) ).
cnf(refute_0_227,plain,
implies(not(X),and(X_47,not(X_48))) = not(and(not(X),implies(X_47,X_48))),
inference(subst,[],[refute_0_166:[bind(X,$fot(not(X))),bind(X_5,$fot(X_47)),bind(X_6,$fot(X_48))]]) ).
cnf(refute_0_228,plain,
( implies(not(X),and(X_47,not(X_48))) != not(and(not(X),implies(X_47,X_48)))
| or(X,and(X_47,not(X_48))) != implies(not(X),and(X_47,not(X_48)))
| or(X,and(X_47,not(X_48))) = not(and(not(X),implies(X_47,X_48))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,and(X_47,not(X_48))),implies(not(X),and(X_47,not(X_48)))) ),[1],$fot(not(and(not(X),implies(X_47,X_48))))]]) ).
cnf(refute_0_229,plain,
( or(X,and(X_47,not(X_48))) != implies(not(X),and(X_47,not(X_48)))
| or(X,and(X_47,not(X_48))) = not(and(not(X),implies(X_47,X_48))) ),
inference(resolve,[$cnf( $equal(implies(not(X),and(X_47,not(X_48))),not(and(not(X),implies(X_47,X_48)))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
or(X,and(X_47,not(X_48))) = not(and(not(X),implies(X_47,X_48))),
inference(resolve,[$cnf( $equal(or(X,and(X_47,not(X_48))),implies(not(X),and(X_47,not(X_48)))) )],[refute_0_226,refute_0_229]) ).
cnf(refute_0_231,plain,
or(X_143,and(not(X),not(X_145))) = not(and(not(X_143),implies(not(X),X_145))),
inference(subst,[],[refute_0_230:[bind(X,$fot(X_143)),bind(X_47,$fot(not(X))),bind(X_48,$fot(X_145))]]) ).
cnf(refute_0_232,plain,
or(X,X_145) = implies(not(X),X_145),
inference(subst,[],[refute_0_38:[bind(Y,$fot(X_145))]]) ).
cnf(refute_0_233,plain,
( or(X,X_145) != implies(not(X),X_145)
| implies(not(X),X_145) = or(X,X_145) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_145))),bind(Y0,$fot(implies(not(X),X_145)))]]) ).
cnf(refute_0_234,plain,
implies(not(X),X_145) = or(X,X_145),
inference(resolve,[$cnf( $equal(or(X,X_145),implies(not(X),X_145)) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
( implies(not(X),X_145) != or(X,X_145)
| or(X_143,and(not(X),not(X_145))) != not(and(not(X_143),implies(not(X),X_145)))
| or(X_143,and(not(X),not(X_145))) = not(and(not(X_143),or(X,X_145))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_143,and(not(X),not(X_145))),not(and(not(X_143),implies(not(X),X_145)))) ),[1,0,1],$fot(or(X,X_145))]]) ).
cnf(refute_0_236,plain,
( or(X_143,and(not(X),not(X_145))) != not(and(not(X_143),implies(not(X),X_145)))
| or(X_143,and(not(X),not(X_145))) = not(and(not(X_143),or(X,X_145))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_145),or(X,X_145)) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
or(X_143,and(not(X),not(X_145))) = not(and(not(X_143),or(X,X_145))),
inference(resolve,[$cnf( $equal(or(X_143,and(not(X),not(X_145))),not(and(not(X_143),implies(not(X),X_145)))) )],[refute_0_231,refute_0_236]) ).
cnf(refute_0_238,plain,
or(X,and(not(X),not(X))) = not(and(not(X),or(X,X))),
inference(subst,[],[refute_0_237:[bind(X_143,$fot(X)),bind(X_145,$fot(X))]]) ).
cnf(refute_0_239,plain,
( or(X,and(X_47,not(X_48))) != not(and(not(X),implies(X_47,X_48)))
| not(and(not(X),implies(X_47,X_48))) = or(X,and(X_47,not(X_48))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,and(X_47,not(X_48))))),bind(Y0,$fot(not(and(not(X),implies(X_47,X_48)))))]]) ).
cnf(refute_0_240,plain,
not(and(not(X),implies(X_47,X_48))) = or(X,and(X_47,not(X_48))),
inference(resolve,[$cnf( $equal(or(X,and(X_47,not(X_48))),not(and(not(X),implies(X_47,X_48)))) )],[refute_0_230,refute_0_239]) ).
cnf(refute_0_241,plain,
not(and(not(X),implies(not(X),X))) = or(X,and(not(X),not(X))),
inference(subst,[],[refute_0_240:[bind(X_47,$fot(not(X))),bind(X_48,$fot(X))]]) ).
cnf(refute_0_242,plain,
( not(and(not(X),implies(not(X),X))) != or(X,and(not(X),not(X)))
| or(X,and(not(X),not(X))) != not(and(not(X),or(X,X)))
| not(and(not(X),implies(not(X),X))) = not(and(not(X),or(X,X))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(not(and(not(X),implies(not(X),X))))),bind(Y0,$fot(or(X,and(not(X),not(X))))),bind(Z,$fot(not(and(not(X),or(X,X)))))]]) ).
cnf(refute_0_243,plain,
( or(X,and(not(X),not(X))) != not(and(not(X),or(X,X)))
| not(and(not(X),implies(not(X),X))) = not(and(not(X),or(X,X))) ),
inference(resolve,[$cnf( $equal(not(and(not(X),implies(not(X),X))),or(X,and(not(X),not(X)))) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
not(and(not(X),implies(not(X),X))) = not(and(not(X),or(X,X))),
inference(resolve,[$cnf( $equal(or(X,and(not(X),not(X))),not(and(not(X),or(X,X)))) )],[refute_0_238,refute_0_243]) ).
cnf(refute_0_245,plain,
implies(not(X),and(not(X),not(X))) = not(and(not(X),implies(not(X),X))),
inference(subst,[],[refute_0_166:[bind(X,$fot(not(X))),bind(X_5,$fot(not(X))),bind(X_6,$fot(X))]]) ).
cnf(refute_0_246,plain,
( implies(not(X),and(not(X),not(X))) != not(and(not(X),implies(not(X),X)))
| not(and(not(X),implies(not(X),X))) != not(and(not(X),or(X,X)))
| implies(not(X),and(not(X),not(X))) = not(and(not(X),or(X,X))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(implies(not(X),and(not(X),not(X))))),bind(Y0,$fot(not(and(not(X),implies(not(X),X))))),bind(Z,$fot(not(and(not(X),or(X,X)))))]]) ).
cnf(refute_0_247,plain,
( not(and(not(X),implies(not(X),X))) != not(and(not(X),or(X,X)))
| implies(not(X),and(not(X),not(X))) = not(and(not(X),or(X,X))) ),
inference(resolve,[$cnf( $equal(implies(not(X),and(not(X),not(X))),not(and(not(X),implies(not(X),X)))) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
implies(not(X),and(not(X),not(X))) = not(and(not(X),or(X,X))),
inference(resolve,[$cnf( $equal(not(and(not(X),implies(not(X),X))),not(and(not(X),or(X,X)))) )],[refute_0_244,refute_0_247]) ).
cnf(refute_0_249,plain,
implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))) = implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))),
introduced(tautology,[refl,[$fot(implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))))]]) ).
cnf(refute_0_250,plain,
( implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))) != implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X)))
| implies(not(X),and(not(X),not(X))) != not(and(not(X),or(X,X)))
| implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))) = implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))),implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X)))) ),[1,0],$fot(not(and(not(X),or(X,X))))]]) ).
cnf(refute_0_251,plain,
( implies(not(X),and(not(X),not(X))) != not(and(not(X),or(X,X)))
| implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))) = implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))),implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X)))) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))) = implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X))),
inference(resolve,[$cnf( $equal(implies(not(X),and(not(X),not(X))),not(and(not(X),or(X,X)))) )],[refute_0_248,refute_0_251]) ).
cnf(refute_0_253,plain,
( implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))) != implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X)))
| implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X))) != implies(not(and(not(X),or(X,X))),and(not(X),or(X,X)))
| implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))) = implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))))),bind(Y0,$fot(implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X))))),bind(Z,$fot(implies(not(and(not(X),or(X,X))),and(not(X),or(X,X)))))]]) ).
cnf(refute_0_254,plain,
( implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X))) != implies(not(and(not(X),or(X,X))),and(not(X),or(X,X)))
| implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))) = implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))),implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X)))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))) = implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))),
inference(resolve,[$cnf( $equal(implies(not(and(not(X),or(X,X))),and(not(X),implies(not(X),X))),implies(not(and(not(X),or(X,X))),and(not(X),or(X,X)))) )],[refute_0_225,refute_0_254]) ).
cnf(refute_0_256,plain,
( implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))) != implies(not(and(not(X),or(X,X))),and(not(X),or(X,X)))
| implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))) != implies(or(X,not(or(X,X))),and(not(X),or(X,X)))
| implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))) = implies(or(X,not(or(X,X))),and(not(X),or(X,X))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))))),bind(Y0,$fot(implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))))),bind(Z,$fot(implies(or(X,not(or(X,X))),and(not(X),or(X,X)))))]]) ).
cnf(refute_0_257,plain,
( implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))) != implies(or(X,not(or(X,X))),and(not(X),or(X,X)))
| implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))) = implies(or(X,not(or(X,X))),and(not(X),or(X,X))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))),implies(not(and(not(X),or(X,X))),and(not(X),or(X,X)))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))) = implies(or(X,not(or(X,X))),and(not(X),or(X,X))),
inference(resolve,[$cnf( $equal(implies(not(and(not(X),or(X,X))),and(not(X),or(X,X))),implies(or(X,not(or(X,X))),and(not(X),or(X,X)))) )],[refute_0_216,refute_0_257]) ).
cnf(refute_0_259,plain,
implies(X,and(not(X_143),implies(X_144,X_145))) = not(and(X,not(and(not(X_143),implies(X_144,X_145))))),
inference(subst,[],[refute_0_32:[bind(Y,$fot(and(not(X_143),implies(X_144,X_145))))]]) ).
cnf(refute_0_260,plain,
or(X_143,and(X_144,not(X_145))) = not(and(not(X_143),implies(X_144,X_145))),
inference(subst,[],[refute_0_230:[bind(X,$fot(X_143)),bind(X_47,$fot(X_144)),bind(X_48,$fot(X_145))]]) ).
cnf(refute_0_261,plain,
( or(X_143,and(X_144,not(X_145))) != not(and(not(X_143),implies(X_144,X_145)))
| not(and(not(X_143),implies(X_144,X_145))) = or(X_143,and(X_144,not(X_145))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X_143,and(X_144,not(X_145))))),bind(Y0,$fot(not(and(not(X_143),implies(X_144,X_145)))))]]) ).
cnf(refute_0_262,plain,
not(and(not(X_143),implies(X_144,X_145))) = or(X_143,and(X_144,not(X_145))),
inference(resolve,[$cnf( $equal(or(X_143,and(X_144,not(X_145))),not(and(not(X_143),implies(X_144,X_145)))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
( implies(X,and(not(X_143),implies(X_144,X_145))) != not(and(X,not(and(not(X_143),implies(X_144,X_145)))))
| not(and(not(X_143),implies(X_144,X_145))) != or(X_143,and(X_144,not(X_145)))
| implies(X,and(not(X_143),implies(X_144,X_145))) = not(and(X,or(X_143,and(X_144,not(X_145))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,and(not(X_143),implies(X_144,X_145))),not(and(X,not(and(not(X_143),implies(X_144,X_145)))))) ),[1,0,1],$fot(or(X_143,and(X_144,not(X_145))))]]) ).
cnf(refute_0_264,plain,
( implies(X,and(not(X_143),implies(X_144,X_145))) != not(and(X,not(and(not(X_143),implies(X_144,X_145)))))
| implies(X,and(not(X_143),implies(X_144,X_145))) = not(and(X,or(X_143,and(X_144,not(X_145))))) ),
inference(resolve,[$cnf( $equal(not(and(not(X_143),implies(X_144,X_145))),or(X_143,and(X_144,not(X_145)))) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
implies(X,and(not(X_143),implies(X_144,X_145))) = not(and(X,or(X_143,and(X_144,not(X_145))))),
inference(resolve,[$cnf( $equal(implies(X,and(not(X_143),implies(X_144,X_145))),not(and(X,not(and(not(X_143),implies(X_144,X_145)))))) )],[refute_0_259,refute_0_264]) ).
cnf(refute_0_266,plain,
( implies(X,and(not(X_143),implies(X_144,X_145))) != not(and(X,or(X_143,and(X_144,not(X_145)))))
| not(and(X,or(X_143,and(X_144,not(X_145))))) = implies(X,and(not(X_143),implies(X_144,X_145))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,and(not(X_143),implies(X_144,X_145))))),bind(Y0,$fot(not(and(X,or(X_143,and(X_144,not(X_145)))))))]]) ).
cnf(refute_0_267,plain,
not(and(X,or(X_143,and(X_144,not(X_145))))) = implies(X,and(not(X_143),implies(X_144,X_145))),
inference(resolve,[$cnf( $equal(implies(X,and(not(X_143),implies(X_144,X_145))),not(and(X,or(X_143,and(X_144,not(X_145)))))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))) = implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))),
inference(subst,[],[refute_0_267:[bind(X,$fot(implies(not(X),and(not(X),not(X))))),bind(X_143,$fot(X)),bind(X_144,$fot(not(X))),bind(X_145,$fot(X))]]) ).
cnf(refute_0_269,plain,
( implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))) != implies(or(X,not(or(X,X))),and(not(X),or(X,X)))
| not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))) != implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X)))
| not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))) = implies(or(X,not(or(X,X))),and(not(X),or(X,X))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))))),bind(Y0,$fot(implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))))),bind(Z,$fot(implies(or(X,not(or(X,X))),and(not(X),or(X,X)))))]]) ).
cnf(refute_0_270,plain,
( implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))) != implies(or(X,not(or(X,X))),and(not(X),or(X,X)))
| not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))) = implies(or(X,not(or(X,X))),and(not(X),or(X,X))) ),
inference(resolve,[$cnf( $equal(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))),implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X)))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))) = implies(or(X,not(or(X,X))),and(not(X),or(X,X))),
inference(resolve,[$cnf( $equal(implies(implies(not(X),and(not(X),not(X))),and(not(X),implies(not(X),X))),implies(or(X,not(or(X,X))),and(not(X),or(X,X)))) )],[refute_0_258,refute_0_270]) ).
cnf(refute_0_272,plain,
not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))) = not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))),
introduced(tautology,[refl,[$fot(not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))))]]) ).
cnf(refute_0_273,plain,
( not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))) != implies(or(X,not(or(X,X))),and(not(X),or(X,X)))
| not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))) != not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))))
| not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))) = not(implies(or(X,not(or(X,X))),and(not(X),or(X,X)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))),not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))))) ),[1,0],$fot(implies(or(X,not(or(X,X))),and(not(X),or(X,X))))]]) ).
cnf(refute_0_274,plain,
( not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))) != implies(or(X,not(or(X,X))),and(not(X),or(X,X)))
| not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))) = not(implies(or(X,not(or(X,X))),and(not(X),or(X,X)))) ),
inference(resolve,[$cnf( $equal(not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))),not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))) = not(implies(or(X,not(or(X,X))),and(not(X),or(X,X)))),
inference(resolve,[$cnf( $equal(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))),implies(or(X,not(or(X,X))),and(not(X),or(X,X)))) )],[refute_0_271,refute_0_274]) ).
cnf(refute_0_276,plain,
( not(implies(or(X,not(or(X,X))),and(not(X),or(X,X)))) != and(or(X,not(or(X,X))),or(X,not(or(X,X))))
| not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))) != not(implies(or(X,not(or(X,X))),and(not(X),or(X,X))))
| not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))) = and(or(X,not(or(X,X))),or(X,not(or(X,X)))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))))),bind(Y0,$fot(not(implies(or(X,not(or(X,X))),and(not(X),or(X,X)))))),bind(Z,$fot(and(or(X,not(or(X,X))),or(X,not(or(X,X))))))]]) ).
cnf(refute_0_277,plain,
( not(implies(or(X,not(or(X,X))),and(not(X),or(X,X)))) != and(or(X,not(or(X,X))),or(X,not(or(X,X))))
| not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))) = and(or(X,not(or(X,X))),or(X,not(or(X,X)))) ),
inference(resolve,[$cnf( $equal(not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))),not(implies(or(X,not(or(X,X))),and(not(X),or(X,X))))) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))) = and(or(X,not(or(X,X))),or(X,not(or(X,X)))),
inference(resolve,[$cnf( $equal(not(implies(or(X,not(or(X,X))),and(not(X),or(X,X)))),and(or(X,not(or(X,X))),or(X,not(or(X,X))))) )],[refute_0_203,refute_0_277]) ).
cnf(refute_0_279,plain,
( not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))) != and(or(X,not(or(X,X))),or(X,not(or(X,X))))
| ~ is_a_theorem(not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))))
| is_a_theorem(and(or(X,not(or(X,X))),or(X,not(or(X,X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))))) ),[0],$fot(and(or(X,not(or(X,X))),or(X,not(or(X,X)))))]]) ).
cnf(refute_0_280,plain,
( ~ is_a_theorem(not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))))
| is_a_theorem(and(or(X,not(or(X,X))),or(X,not(or(X,X))))) ),
inference(resolve,[$cnf( $equal(not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X)))))),and(or(X,not(or(X,X))),or(X,not(or(X,X))))) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
is_a_theorem(and(or(X,not(or(X,X))),or(X,not(or(X,X))))),
inference(resolve,[$cnf( is_a_theorem(not(not(and(implies(not(X),and(not(X),not(X))),or(X,and(not(X),not(X))))))) )],[refute_0_193,refute_0_280]) ).
cnf(refute_0_282,plain,
is_a_theorem(and(or(X_415,not(or(X_415,X_415))),or(X_415,not(or(X_415,X_415))))),
inference(subst,[],[refute_0_281:[bind(X,$fot(X_415))]]) ).
cnf(refute_0_283,plain,
is_a_theorem(or(X_415,not(or(X_415,X_415)))),
inference(resolve,[$cnf( is_a_theorem(and(or(X_415,not(or(X_415,X_415))),or(X_415,not(or(X_415,X_415))))) )],[refute_0_282,refute_0_115]) ).
cnf(refute_0_284,plain,
is_a_theorem(or(X_1302,not(or(X_1302,X_1302)))),
inference(subst,[],[refute_0_283:[bind(X_415,$fot(X_1302))]]) ).
cnf(refute_0_285,plain,
( ~ kn3
| is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_286,plain,
kn3,
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_287,plain,
is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))),
inference(resolve,[$cnf( kn3 )],[refute_0_286,refute_0_285]) ).
cnf(refute_0_288,plain,
implies(X,or(X_11,not(X_10))) = not(and(X,not(or(X_11,not(X_10))))),
inference(subst,[],[refute_0_32:[bind(Y,$fot(or(X_11,not(X_10))))]]) ).
cnf(refute_0_289,plain,
( implies(X,or(X_11,not(X_10))) != not(and(X,not(or(X_11,not(X_10)))))
| not(or(X_11,not(X_10))) != and(not(X_11),X_10)
| implies(X,or(X_11,not(X_10))) = not(and(X,and(not(X_11),X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,or(X_11,not(X_10))),not(and(X,not(or(X_11,not(X_10)))))) ),[1,0,1],$fot(and(not(X_11),X_10))]]) ).
cnf(refute_0_290,plain,
( implies(X,or(X_11,not(X_10))) != not(and(X,not(or(X_11,not(X_10)))))
| implies(X,or(X_11,not(X_10))) = not(and(X,and(not(X_11),X_10))) ),
inference(resolve,[$cnf( $equal(not(or(X_11,not(X_10))),and(not(X_11),X_10)) )],[refute_0_197,refute_0_289]) ).
cnf(refute_0_291,plain,
implies(X,or(X_11,not(X_10))) = not(and(X,and(not(X_11),X_10))),
inference(resolve,[$cnf( $equal(implies(X,or(X_11,not(X_10))),not(and(X,not(or(X_11,not(X_10)))))) )],[refute_0_288,refute_0_290]) ).
cnf(refute_0_292,plain,
( implies(X,or(X_11,not(X_10))) != not(and(X,and(not(X_11),X_10)))
| not(and(X,and(not(X_11),X_10))) = implies(X,or(X_11,not(X_10))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,or(X_11,not(X_10))))),bind(Y0,$fot(not(and(X,and(not(X_11),X_10)))))]]) ).
cnf(refute_0_293,plain,
not(and(X,and(not(X_11),X_10))) = implies(X,or(X_11,not(X_10))),
inference(resolve,[$cnf( $equal(implies(X,or(X_11,not(X_10))),not(and(X,and(not(X_11),X_10)))) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
not(and(implies(P,Q),and(not(and(Q,R)),and(R,P)))) = implies(implies(P,Q),or(and(Q,R),not(and(R,P)))),
inference(subst,[],[refute_0_293:[bind(X,$fot(implies(P,Q))),bind(X_10,$fot(and(R,P))),bind(X_11,$fot(and(Q,R)))]]) ).
cnf(refute_0_295,plain,
implies(X_5,implies(X,not(Y))) = not(and(X_5,not(implies(X,not(Y))))),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_5)),bind(Y,$fot(implies(X,not(Y))))]]) ).
cnf(refute_0_296,plain,
( implies(X_5,implies(X,not(Y))) != not(and(X_5,not(implies(X,not(Y)))))
| not(implies(X,not(Y))) != and(X,Y)
| implies(X_5,implies(X,not(Y))) = not(and(X_5,and(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_5,implies(X,not(Y))),not(and(X_5,not(implies(X,not(Y)))))) ),[1,0,1],$fot(and(X,Y))]]) ).
cnf(refute_0_297,plain,
( implies(X_5,implies(X,not(Y))) != not(and(X_5,not(implies(X,not(Y)))))
| implies(X_5,implies(X,not(Y))) = not(and(X_5,and(X,Y))) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_53,refute_0_296]) ).
cnf(refute_0_298,plain,
implies(X_5,implies(X,not(Y))) = not(and(X_5,and(X,Y))),
inference(resolve,[$cnf( $equal(implies(X_5,implies(X,not(Y))),not(and(X_5,not(implies(X,not(Y)))))) )],[refute_0_295,refute_0_297]) ).
cnf(refute_0_299,plain,
implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) = not(and(implies(P,Q),and(not(and(Q,R)),and(R,P)))),
inference(subst,[],[refute_0_298:[bind(X,$fot(not(and(Q,R)))),bind(Y,$fot(and(R,P))),bind(X_5,$fot(implies(P,Q)))]]) ).
cnf(refute_0_300,plain,
( implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) != not(and(implies(P,Q),and(not(and(Q,R)),and(R,P))))
| not(and(implies(P,Q),and(not(and(Q,R)),and(R,P)))) != implies(implies(P,Q),or(and(Q,R),not(and(R,P))))
| implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) = implies(implies(P,Q),or(and(Q,R),not(and(R,P)))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))),bind(Y0,$fot(not(and(implies(P,Q),and(not(and(Q,R)),and(R,P)))))),bind(Z,$fot(implies(implies(P,Q),or(and(Q,R),not(and(R,P))))))]]) ).
cnf(refute_0_301,plain,
( not(and(implies(P,Q),and(not(and(Q,R)),and(R,P)))) != implies(implies(P,Q),or(and(Q,R),not(and(R,P))))
| implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) = implies(implies(P,Q),or(and(Q,R),not(and(R,P)))) ),
inference(resolve,[$cnf( $equal(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))),not(and(implies(P,Q),and(not(and(Q,R)),and(R,P))))) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) = implies(implies(P,Q),or(and(Q,R),not(and(R,P)))),
inference(resolve,[$cnf( $equal(not(and(implies(P,Q),and(not(and(Q,R)),and(R,P)))),implies(implies(P,Q),or(and(Q,R),not(and(R,P))))) )],[refute_0_294,refute_0_301]) ).
cnf(refute_0_303,plain,
( implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) != implies(implies(P,Q),or(and(Q,R),not(and(R,P))))
| ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| is_a_theorem(implies(implies(P,Q),or(and(Q,R),not(and(R,P))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),[0],$fot(implies(implies(P,Q),or(and(Q,R),not(and(R,P)))))]]) ).
cnf(refute_0_304,plain,
( ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| is_a_theorem(implies(implies(P,Q),or(and(Q,R),not(and(R,P))))) ),
inference(resolve,[$cnf( $equal(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))),implies(implies(P,Q),or(and(Q,R),not(and(R,P))))) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
is_a_theorem(implies(implies(P,Q),or(and(Q,R),not(and(R,P))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )],[refute_0_287,refute_0_304]) ).
cnf(refute_0_306,plain,
is_a_theorem(implies(implies(not(Y),X_109),or(and(X_109,X_110),not(and(X_110,not(Y)))))),
inference(subst,[],[refute_0_305:[bind(P,$fot(not(Y))),bind(Q,$fot(X_109)),bind(R,$fot(X_110))]]) ).
cnf(refute_0_307,plain,
implies(X_110,Y) = not(and(X_110,not(Y))),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_110))]]) ).
cnf(refute_0_308,plain,
( implies(X_110,Y) != not(and(X_110,not(Y)))
| not(and(X_110,not(Y))) = implies(X_110,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X_110,Y))),bind(Y0,$fot(not(and(X_110,not(Y)))))]]) ).
cnf(refute_0_309,plain,
not(and(X_110,not(Y))) = implies(X_110,Y),
inference(resolve,[$cnf( $equal(implies(X_110,Y),not(and(X_110,not(Y)))) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
( not(and(X_110,not(Y))) != implies(X_110,Y)
| ~ is_a_theorem(implies(implies(not(Y),X_109),or(and(X_109,X_110),not(and(X_110,not(Y))))))
| is_a_theorem(implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),X_109),or(and(X_109,X_110),not(and(X_110,not(Y)))))) ),[0,1,1],$fot(implies(X_110,Y))]]) ).
cnf(refute_0_311,plain,
( ~ is_a_theorem(implies(implies(not(Y),X_109),or(and(X_109,X_110),not(and(X_110,not(Y))))))
| is_a_theorem(implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y)))) ),
inference(resolve,[$cnf( $equal(not(and(X_110,not(Y))),implies(X_110,Y)) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
is_a_theorem(implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),X_109),or(and(X_109,X_110),not(and(X_110,not(Y)))))) )],[refute_0_306,refute_0_311]) ).
cnf(refute_0_313,plain,
implies(not(Y),X_109) = or(Y,X_109),
inference(subst,[],[refute_0_212:[bind(X,$fot(Y)),bind(Y,$fot(X_109))]]) ).
cnf(refute_0_314,plain,
implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y))) = implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y))),
introduced(tautology,[refl,[$fot(implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y))))]]) ).
cnf(refute_0_315,plain,
( implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y))) != implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y)))
| implies(not(Y),X_109) != or(Y,X_109)
| implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y))) = implies(or(Y,X_109),or(and(X_109,X_110),implies(X_110,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y))),implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y)))) ),[1,0],$fot(or(Y,X_109))]]) ).
cnf(refute_0_316,plain,
( implies(not(Y),X_109) != or(Y,X_109)
| implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y))) = implies(or(Y,X_109),or(and(X_109,X_110),implies(X_110,Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y))),implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y)))) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y))) = implies(or(Y,X_109),or(and(X_109,X_110),implies(X_110,Y))),
inference(resolve,[$cnf( $equal(implies(not(Y),X_109),or(Y,X_109)) )],[refute_0_313,refute_0_316]) ).
cnf(refute_0_318,plain,
( implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y))) != implies(or(Y,X_109),or(and(X_109,X_110),implies(X_110,Y)))
| ~ is_a_theorem(implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y))))
| is_a_theorem(implies(or(Y,X_109),or(and(X_109,X_110),implies(X_110,Y)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y)))) ),[0],$fot(implies(or(Y,X_109),or(and(X_109,X_110),implies(X_110,Y))))]]) ).
cnf(refute_0_319,plain,
( ~ is_a_theorem(implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y))))
| is_a_theorem(implies(or(Y,X_109),or(and(X_109,X_110),implies(X_110,Y)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y))),implies(or(Y,X_109),or(and(X_109,X_110),implies(X_110,Y)))) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
is_a_theorem(implies(or(Y,X_109),or(and(X_109,X_110),implies(X_110,Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),X_109),or(and(X_109,X_110),implies(X_110,Y)))) )],[refute_0_312,refute_0_319]) ).
cnf(refute_0_321,plain,
( ~ is_a_theorem(implies(or(Y,X_109),or(and(X_109,X_110),implies(X_110,Y))))
| ~ is_a_theorem(or(Y,X_109))
| is_a_theorem(or(and(X_109,X_110),implies(X_110,Y))) ),
inference(subst,[],[refute_0_64:[bind(X,$fot(or(Y,X_109))),bind(Y,$fot(or(and(X_109,X_110),implies(X_110,Y))))]]) ).
cnf(refute_0_322,plain,
( ~ is_a_theorem(or(Y,X_109))
| is_a_theorem(or(and(X_109,X_110),implies(X_110,Y))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(Y,X_109),or(and(X_109,X_110),implies(X_110,Y)))) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
( ~ is_a_theorem(or(X_1302,not(or(X_1302,X_1302))))
| is_a_theorem(or(and(not(or(X_1302,X_1302)),X_1304),implies(X_1304,X_1302))) ),
inference(subst,[],[refute_0_322:[bind(Y,$fot(X_1302)),bind(X_109,$fot(not(or(X_1302,X_1302)))),bind(X_110,$fot(X_1304))]]) ).
cnf(refute_0_324,plain,
is_a_theorem(or(and(not(or(X_1302,X_1302)),X_1304),implies(X_1304,X_1302))),
inference(resolve,[$cnf( is_a_theorem(or(X_1302,not(or(X_1302,X_1302)))) )],[refute_0_284,refute_0_323]) ).
cnf(refute_0_325,plain,
or(and(not(or(X_1302,X_1302)),X_1304),implies(X_1304,X_1302)) = implies(or(or(X_1302,X_1302),not(X_1304)),implies(X_1304,X_1302)),
inference(subst,[],[refute_0_209:[bind(Y,$fot(X_1304)),bind(X_13,$fot(implies(X_1304,X_1302))),bind(X_7,$fot(or(X_1302,X_1302)))]]) ).
cnf(refute_0_326,plain,
( or(and(not(or(X_1302,X_1302)),X_1304),implies(X_1304,X_1302)) != implies(or(or(X_1302,X_1302),not(X_1304)),implies(X_1304,X_1302))
| ~ is_a_theorem(or(and(not(or(X_1302,X_1302)),X_1304),implies(X_1304,X_1302)))
| is_a_theorem(implies(or(or(X_1302,X_1302),not(X_1304)),implies(X_1304,X_1302))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(or(X_1302,X_1302)),X_1304),implies(X_1304,X_1302))) ),[0],$fot(implies(or(or(X_1302,X_1302),not(X_1304)),implies(X_1304,X_1302)))]]) ).
cnf(refute_0_327,plain,
( ~ is_a_theorem(or(and(not(or(X_1302,X_1302)),X_1304),implies(X_1304,X_1302)))
| is_a_theorem(implies(or(or(X_1302,X_1302),not(X_1304)),implies(X_1304,X_1302))) ),
inference(resolve,[$cnf( $equal(or(and(not(or(X_1302,X_1302)),X_1304),implies(X_1304,X_1302)),implies(or(or(X_1302,X_1302),not(X_1304)),implies(X_1304,X_1302))) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
is_a_theorem(implies(or(or(X_1302,X_1302),not(X_1304)),implies(X_1304,X_1302))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(or(X_1302,X_1302)),X_1304),implies(X_1304,X_1302))) )],[refute_0_324,refute_0_327]) ).
cnf(refute_0_329,plain,
is_a_theorem(implies(or(or(X_1305,X_1305),not(not(X))),implies(not(X),X_1305))),
inference(subst,[],[refute_0_328:[bind(X_1302,$fot(X_1305)),bind(X_1304,$fot(not(X)))]]) ).
cnf(refute_0_330,plain,
or(X,X_1305) = implies(not(X),X_1305),
inference(subst,[],[refute_0_38:[bind(Y,$fot(X_1305))]]) ).
cnf(refute_0_331,plain,
( or(X,X_1305) != implies(not(X),X_1305)
| implies(not(X),X_1305) = or(X,X_1305) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_1305))),bind(Y0,$fot(implies(not(X),X_1305)))]]) ).
cnf(refute_0_332,plain,
implies(not(X),X_1305) = or(X,X_1305),
inference(resolve,[$cnf( $equal(or(X,X_1305),implies(not(X),X_1305)) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
( implies(not(X),X_1305) != or(X,X_1305)
| ~ is_a_theorem(implies(or(or(X_1305,X_1305),not(not(X))),implies(not(X),X_1305)))
| is_a_theorem(implies(or(or(X_1305,X_1305),not(not(X))),or(X,X_1305))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(or(X_1305,X_1305),not(not(X))),implies(not(X),X_1305))) ),[0,1],$fot(or(X,X_1305))]]) ).
cnf(refute_0_334,plain,
( ~ is_a_theorem(implies(or(or(X_1305,X_1305),not(not(X))),implies(not(X),X_1305)))
| is_a_theorem(implies(or(or(X_1305,X_1305),not(not(X))),or(X,X_1305))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_1305),or(X,X_1305)) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
is_a_theorem(implies(or(or(X_1305,X_1305),not(not(X))),or(X,X_1305))),
inference(resolve,[$cnf( is_a_theorem(implies(or(or(X_1305,X_1305),not(not(X))),implies(not(X),X_1305))) )],[refute_0_329,refute_0_334]) ).
cnf(refute_0_336,plain,
or(and(not(X),not(X_77)),X_78) = implies(implies(not(X),X_77),X_78),
inference(subst,[],[refute_0_155:[bind(X,$fot(not(X))),bind(Y,$fot(X_77)),bind(X_8,$fot(X_78))]]) ).
cnf(refute_0_337,plain,
or(X,X_77) = implies(not(X),X_77),
inference(subst,[],[refute_0_38:[bind(Y,$fot(X_77))]]) ).
cnf(refute_0_338,plain,
( or(X,X_77) != implies(not(X),X_77)
| implies(not(X),X_77) = or(X,X_77) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_77))),bind(Y0,$fot(implies(not(X),X_77)))]]) ).
cnf(refute_0_339,plain,
implies(not(X),X_77) = or(X,X_77),
inference(resolve,[$cnf( $equal(or(X,X_77),implies(not(X),X_77)) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
( implies(not(X),X_77) != or(X,X_77)
| or(and(not(X),not(X_77)),X_78) != implies(implies(not(X),X_77),X_78)
| or(and(not(X),not(X_77)),X_78) = implies(or(X,X_77),X_78) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X),not(X_77)),X_78),implies(implies(not(X),X_77),X_78)) ),[1,0],$fot(or(X,X_77))]]) ).
cnf(refute_0_341,plain,
( or(and(not(X),not(X_77)),X_78) != implies(implies(not(X),X_77),X_78)
| or(and(not(X),not(X_77)),X_78) = implies(or(X,X_77),X_78) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_77),or(X,X_77)) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
or(and(not(X),not(X_77)),X_78) = implies(or(X,X_77),X_78),
inference(resolve,[$cnf( $equal(or(and(not(X),not(X_77)),X_78),implies(implies(not(X),X_77),X_78)) )],[refute_0_336,refute_0_341]) ).
cnf(refute_0_343,plain,
or(and(not(X),not(X_77)),X_78) = implies(or(X,not(not(X_77))),X_78),
inference(subst,[],[refute_0_209:[bind(Y,$fot(not(X_77))),bind(X_13,$fot(X_78)),bind(X_7,$fot(X))]]) ).
cnf(refute_0_344,plain,
( or(and(not(X),not(X_77)),X_78) != implies(or(X,X_77),X_78)
| or(and(not(X),not(X_77)),X_78) != implies(or(X,not(not(X_77))),X_78)
| implies(or(X,not(not(X_77))),X_78) = implies(or(X,X_77),X_78) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X),not(X_77)),X_78),implies(or(X,X_77),X_78)) ),[0],$fot(implies(or(X,not(not(X_77))),X_78))]]) ).
cnf(refute_0_345,plain,
( or(and(not(X),not(X_77)),X_78) != implies(or(X,X_77),X_78)
| implies(or(X,not(not(X_77))),X_78) = implies(or(X,X_77),X_78) ),
inference(resolve,[$cnf( $equal(or(and(not(X),not(X_77)),X_78),implies(or(X,not(not(X_77))),X_78)) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
implies(or(X,not(not(X_77))),X_78) = implies(or(X,X_77),X_78),
inference(resolve,[$cnf( $equal(or(and(not(X),not(X_77)),X_78),implies(or(X,X_77),X_78)) )],[refute_0_342,refute_0_345]) ).
cnf(refute_0_347,plain,
implies(or(or(X_1305,X_1305),not(not(X))),or(X,X_1305)) = implies(or(or(X_1305,X_1305),X),or(X,X_1305)),
inference(subst,[],[refute_0_346:[bind(X,$fot(or(X_1305,X_1305))),bind(X_77,$fot(X)),bind(X_78,$fot(or(X,X_1305)))]]) ).
cnf(refute_0_348,plain,
( implies(or(or(X_1305,X_1305),not(not(X))),or(X,X_1305)) != implies(or(or(X_1305,X_1305),X),or(X,X_1305))
| ~ is_a_theorem(implies(or(or(X_1305,X_1305),not(not(X))),or(X,X_1305)))
| is_a_theorem(implies(or(or(X_1305,X_1305),X),or(X,X_1305))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(or(X_1305,X_1305),not(not(X))),or(X,X_1305))) ),[0],$fot(implies(or(or(X_1305,X_1305),X),or(X,X_1305)))]]) ).
cnf(refute_0_349,plain,
( ~ is_a_theorem(implies(or(or(X_1305,X_1305),not(not(X))),or(X,X_1305)))
| is_a_theorem(implies(or(or(X_1305,X_1305),X),or(X,X_1305))) ),
inference(resolve,[$cnf( $equal(implies(or(or(X_1305,X_1305),not(not(X))),or(X,X_1305)),implies(or(or(X_1305,X_1305),X),or(X,X_1305))) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
is_a_theorem(implies(or(or(X_1305,X_1305),X),or(X,X_1305))),
inference(resolve,[$cnf( is_a_theorem(implies(or(or(X_1305,X_1305),not(not(X))),or(X,X_1305))) )],[refute_0_335,refute_0_349]) ).
cnf(refute_0_351,plain,
is_a_theorem(implies(or(or(not(X),not(X)),X_1310),or(X_1310,not(X)))),
inference(subst,[],[refute_0_350:[bind(X,$fot(X_1310)),bind(X_1305,$fot(not(X)))]]) ).
cnf(refute_0_352,plain,
implies(X,not(X)) = or(not(X),not(X)),
inference(subst,[],[refute_0_12:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_353,plain,
( implies(X,not(X)) != or(not(X),not(X))
| or(not(X),not(X)) = implies(X,not(X)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,not(X)))),bind(Y0,$fot(or(not(X),not(X))))]]) ).
cnf(refute_0_354,plain,
or(not(X),not(X)) = implies(X,not(X)),
inference(resolve,[$cnf( $equal(implies(X,not(X)),or(not(X),not(X))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
( or(not(X),not(X)) != implies(X,not(X))
| ~ is_a_theorem(implies(or(or(not(X),not(X)),X_1310),or(X_1310,not(X))))
| is_a_theorem(implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(or(not(X),not(X)),X_1310),or(X_1310,not(X)))) ),[0,0,0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_356,plain,
( ~ is_a_theorem(implies(or(or(not(X),not(X)),X_1310),or(X_1310,not(X))))
| is_a_theorem(implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
is_a_theorem(implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(or(not(X),not(X)),X_1310),or(X_1310,not(X)))) )],[refute_0_351,refute_0_356]) ).
cnf(refute_0_358,plain,
or(implies(X,not(Y)),X_8) = implies(not(implies(X,not(Y))),X_8),
inference(subst,[],[refute_0_38:[bind(X,$fot(implies(X,not(Y)))),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_359,plain,
( not(implies(X,not(Y))) != and(X,Y)
| or(implies(X,not(Y)),X_8) != implies(not(implies(X,not(Y))),X_8)
| or(implies(X,not(Y)),X_8) = implies(and(X,Y),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(X,not(Y)),X_8),implies(not(implies(X,not(Y))),X_8)) ),[1,0],$fot(and(X,Y))]]) ).
cnf(refute_0_360,plain,
( or(implies(X,not(Y)),X_8) != implies(not(implies(X,not(Y))),X_8)
| or(implies(X,not(Y)),X_8) = implies(and(X,Y),X_8) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_53,refute_0_359]) ).
cnf(refute_0_361,plain,
or(implies(X,not(Y)),X_8) = implies(and(X,Y),X_8),
inference(resolve,[$cnf( $equal(or(implies(X,not(Y)),X_8),implies(not(implies(X,not(Y))),X_8)) )],[refute_0_358,refute_0_360]) ).
cnf(refute_0_362,plain,
or(implies(X,not(X)),X_1310) = implies(and(X,X),X_1310),
inference(subst,[],[refute_0_361:[bind(Y,$fot(X)),bind(X_8,$fot(X_1310))]]) ).
cnf(refute_0_363,plain,
implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X))) = implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X))),
introduced(tautology,[refl,[$fot(implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X))))]]) ).
cnf(refute_0_364,plain,
( implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X))) != implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X)))
| or(implies(X,not(X)),X_1310) != implies(and(X,X),X_1310)
| implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X))) = implies(implies(and(X,X),X_1310),or(X_1310,not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X))),implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X)))) ),[1,0],$fot(implies(and(X,X),X_1310))]]) ).
cnf(refute_0_365,plain,
( or(implies(X,not(X)),X_1310) != implies(and(X,X),X_1310)
| implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X))) = implies(implies(and(X,X),X_1310),or(X_1310,not(X))) ),
inference(resolve,[$cnf( $equal(implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X))),implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X)))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X))) = implies(implies(and(X,X),X_1310),or(X_1310,not(X))),
inference(resolve,[$cnf( $equal(or(implies(X,not(X)),X_1310),implies(and(X,X),X_1310)) )],[refute_0_362,refute_0_365]) ).
cnf(refute_0_367,plain,
( implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X))) != implies(implies(and(X,X),X_1310),or(X_1310,not(X)))
| ~ is_a_theorem(implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X))))
| is_a_theorem(implies(implies(and(X,X),X_1310),or(X_1310,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X)))) ),[0],$fot(implies(implies(and(X,X),X_1310),or(X_1310,not(X))))]]) ).
cnf(refute_0_368,plain,
( ~ is_a_theorem(implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X))))
| is_a_theorem(implies(implies(and(X,X),X_1310),or(X_1310,not(X)))) ),
inference(resolve,[$cnf( $equal(implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X))),implies(implies(and(X,X),X_1310),or(X_1310,not(X)))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
is_a_theorem(implies(implies(and(X,X),X_1310),or(X_1310,not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(implies(X,not(X)),X_1310),or(X_1310,not(X)))) )],[refute_0_357,refute_0_368]) ).
cnf(refute_0_370,plain,
is_a_theorem(implies(implies(and(X_1312,X_1312),not(X)),or(not(X),not(X_1312)))),
inference(subst,[],[refute_0_369:[bind(X,$fot(X_1312)),bind(X_1310,$fot(not(X)))]]) ).
cnf(refute_0_371,plain,
implies(X,not(X_1312)) = or(not(X),not(X_1312)),
inference(subst,[],[refute_0_12:[bind(Y,$fot(not(X_1312)))]]) ).
cnf(refute_0_372,plain,
( implies(X,not(X_1312)) != or(not(X),not(X_1312))
| or(not(X),not(X_1312)) = implies(X,not(X_1312)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,not(X_1312)))),bind(Y0,$fot(or(not(X),not(X_1312))))]]) ).
cnf(refute_0_373,plain,
or(not(X),not(X_1312)) = implies(X,not(X_1312)),
inference(resolve,[$cnf( $equal(implies(X,not(X_1312)),or(not(X),not(X_1312))) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
( or(not(X),not(X_1312)) != implies(X,not(X_1312))
| ~ is_a_theorem(implies(implies(and(X_1312,X_1312),not(X)),or(not(X),not(X_1312))))
| is_a_theorem(implies(implies(and(X_1312,X_1312),not(X)),implies(X,not(X_1312)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(and(X_1312,X_1312),not(X)),or(not(X),not(X_1312)))) ),[0,1],$fot(implies(X,not(X_1312)))]]) ).
cnf(refute_0_375,plain,
( ~ is_a_theorem(implies(implies(and(X_1312,X_1312),not(X)),or(not(X),not(X_1312))))
| is_a_theorem(implies(implies(and(X_1312,X_1312),not(X)),implies(X,not(X_1312)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_1312)),implies(X,not(X_1312))) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
is_a_theorem(implies(implies(and(X_1312,X_1312),not(X)),implies(X,not(X_1312)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_1312,X_1312),not(X)),or(not(X),not(X_1312)))) )],[refute_0_370,refute_0_375]) ).
cnf(refute_0_377,plain,
implies(implies(and(X_1312,X_1312),not(X)),implies(X,not(X_1312))) = or(and(and(X_1312,X_1312),X),implies(X,not(X_1312))),
inference(subst,[],[refute_0_132:[bind(X,$fot(and(X_1312,X_1312))),bind(Y,$fot(X)),bind(X_13,$fot(implies(X,not(X_1312))))]]) ).
cnf(refute_0_378,plain,
( implies(implies(and(X_1312,X_1312),not(X)),implies(X,not(X_1312))) != or(and(and(X_1312,X_1312),X),implies(X,not(X_1312)))
| ~ is_a_theorem(implies(implies(and(X_1312,X_1312),not(X)),implies(X,not(X_1312))))
| is_a_theorem(or(and(and(X_1312,X_1312),X),implies(X,not(X_1312)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(and(X_1312,X_1312),not(X)),implies(X,not(X_1312)))) ),[0],$fot(or(and(and(X_1312,X_1312),X),implies(X,not(X_1312))))]]) ).
cnf(refute_0_379,plain,
( ~ is_a_theorem(implies(implies(and(X_1312,X_1312),not(X)),implies(X,not(X_1312))))
| is_a_theorem(or(and(and(X_1312,X_1312),X),implies(X,not(X_1312)))) ),
inference(resolve,[$cnf( $equal(implies(implies(and(X_1312,X_1312),not(X)),implies(X,not(X_1312))),or(and(and(X_1312,X_1312),X),implies(X,not(X_1312)))) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
is_a_theorem(or(and(and(X_1312,X_1312),X),implies(X,not(X_1312)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_1312,X_1312),not(X)),implies(X,not(X_1312)))) )],[refute_0_376,refute_0_379]) ).
cnf(refute_0_381,plain,
( ~ is_a_theorem(implies(not(X),X_296))
| ~ is_a_theorem(not(X))
| is_a_theorem(X_296) ),
inference(subst,[],[refute_0_64:[bind(X,$fot(not(X))),bind(Y,$fot(X_296))]]) ).
cnf(refute_0_382,plain,
or(X,X_296) = implies(not(X),X_296),
inference(subst,[],[refute_0_38:[bind(Y,$fot(X_296))]]) ).
cnf(refute_0_383,plain,
( or(X,X_296) != implies(not(X),X_296)
| implies(not(X),X_296) = or(X,X_296) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_296))),bind(Y0,$fot(implies(not(X),X_296)))]]) ).
cnf(refute_0_384,plain,
implies(not(X),X_296) = or(X,X_296),
inference(resolve,[$cnf( $equal(or(X,X_296),implies(not(X),X_296)) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
( implies(not(X),X_296) != or(X,X_296)
| ~ is_a_theorem(or(X,X_296))
| is_a_theorem(implies(not(X),X_296)) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(implies(not(X),X_296)) ),[0],$fot(or(X,X_296))]]) ).
cnf(refute_0_386,plain,
( ~ is_a_theorem(or(X,X_296))
| is_a_theorem(implies(not(X),X_296)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_296),or(X,X_296)) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
( ~ is_a_theorem(not(X))
| ~ is_a_theorem(or(X,X_296))
| is_a_theorem(X_296) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(X),X_296)) )],[refute_0_386,refute_0_381]) ).
cnf(refute_0_388,plain,
( ~ is_a_theorem(not(and(and(X_1312,X_1312),X)))
| ~ is_a_theorem(or(and(and(X_1312,X_1312),X),implies(X,not(X_1312))))
| is_a_theorem(implies(X,not(X_1312))) ),
inference(subst,[],[refute_0_387:[bind(X,$fot(and(and(X_1312,X_1312),X))),bind(X_296,$fot(implies(X,not(X_1312))))]]) ).
cnf(refute_0_389,plain,
( ~ is_a_theorem(not(and(and(X_1312,X_1312),X)))
| is_a_theorem(implies(X,not(X_1312))) ),
inference(resolve,[$cnf( is_a_theorem(or(and(and(X_1312,X_1312),X),implies(X,not(X_1312)))) )],[refute_0_380,refute_0_388]) ).
cnf(refute_0_390,plain,
( ~ is_a_theorem(not(and(and(not(X_5448),not(X_5448)),X_5448)))
| is_a_theorem(implies(X_5448,not(not(X_5448)))) ),
inference(subst,[],[refute_0_389:[bind(X,$fot(X_5448)),bind(X_1312,$fot(not(X_5448)))]]) ).
cnf(refute_0_391,plain,
is_a_theorem(implies(X_5448,not(not(X_5448)))),
inference(resolve,[$cnf( is_a_theorem(not(and(and(not(X_5448),not(X_5448)),X_5448))) )],[refute_0_111,refute_0_390]) ).
cnf(refute_0_392,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_393,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_394,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_393,refute_0_392]) ).
cnf(refute_0_395,plain,
( ~ is_a_theorem(equiv(X_96,not(not(X))))
| X_96 = not(not(X)) ),
inference(subst,[],[refute_0_394:[bind(X,$fot(X_96)),bind(Y,$fot(not(not(X))))]]) ).
cnf(refute_0_396,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_397,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_398,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_397,refute_0_396]) ).
cnf(refute_0_399,plain,
equiv(X_16,not(X)) = and(implies(X_16,not(X)),implies(not(X),X_16)),
inference(subst,[],[refute_0_398:[bind(X,$fot(X_16)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_400,plain,
or(X,X_16) = implies(not(X),X_16),
inference(subst,[],[refute_0_38:[bind(Y,$fot(X_16))]]) ).
cnf(refute_0_401,plain,
( or(X,X_16) != implies(not(X),X_16)
| implies(not(X),X_16) = or(X,X_16) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_16))),bind(Y0,$fot(implies(not(X),X_16)))]]) ).
cnf(refute_0_402,plain,
implies(not(X),X_16) = or(X,X_16),
inference(resolve,[$cnf( $equal(or(X,X_16),implies(not(X),X_16)) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
( equiv(X_16,not(X)) != and(implies(X_16,not(X)),implies(not(X),X_16))
| implies(not(X),X_16) != or(X,X_16)
| equiv(X_16,not(X)) = and(implies(X_16,not(X)),or(X,X_16)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_16,not(X)),and(implies(X_16,not(X)),implies(not(X),X_16))) ),[1,1],$fot(or(X,X_16))]]) ).
cnf(refute_0_404,plain,
( equiv(X_16,not(X)) != and(implies(X_16,not(X)),implies(not(X),X_16))
| equiv(X_16,not(X)) = and(implies(X_16,not(X)),or(X,X_16)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_16),or(X,X_16)) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
equiv(X_16,not(X)) = and(implies(X_16,not(X)),or(X,X_16)),
inference(resolve,[$cnf( $equal(equiv(X_16,not(X)),and(implies(X_16,not(X)),implies(not(X),X_16))) )],[refute_0_399,refute_0_404]) ).
cnf(refute_0_406,plain,
equiv(X_31,not(not(X))) = and(implies(X_31,not(not(X))),or(not(X),X_31)),
inference(subst,[],[refute_0_405:[bind(X,$fot(not(X))),bind(X_16,$fot(X_31))]]) ).
cnf(refute_0_407,plain,
implies(X,X_31) = or(not(X),X_31),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_31))]]) ).
cnf(refute_0_408,plain,
( implies(X,X_31) != or(not(X),X_31)
| or(not(X),X_31) = implies(X,X_31) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_31))),bind(Y0,$fot(or(not(X),X_31)))]]) ).
cnf(refute_0_409,plain,
or(not(X),X_31) = implies(X,X_31),
inference(resolve,[$cnf( $equal(implies(X,X_31),or(not(X),X_31)) )],[refute_0_407,refute_0_408]) ).
cnf(refute_0_410,plain,
( equiv(X_31,not(not(X))) != and(implies(X_31,not(not(X))),or(not(X),X_31))
| or(not(X),X_31) != implies(X,X_31)
| equiv(X_31,not(not(X))) = and(implies(X_31,not(not(X))),implies(X,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_31,not(not(X))),and(implies(X_31,not(not(X))),or(not(X),X_31))) ),[1,1],$fot(implies(X,X_31))]]) ).
cnf(refute_0_411,plain,
( equiv(X_31,not(not(X))) != and(implies(X_31,not(not(X))),or(not(X),X_31))
| equiv(X_31,not(not(X))) = and(implies(X_31,not(not(X))),implies(X,X_31)) ),
inference(resolve,[$cnf( $equal(or(not(X),X_31),implies(X,X_31)) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
equiv(X_31,not(not(X))) = and(implies(X_31,not(not(X))),implies(X,X_31)),
inference(resolve,[$cnf( $equal(equiv(X_31,not(not(X))),and(implies(X_31,not(not(X))),or(not(X),X_31))) )],[refute_0_406,refute_0_411]) ).
cnf(refute_0_413,plain,
( equiv(X,Y) != and(implies(X,Y),implies(Y,X))
| and(implies(X,Y),implies(Y,X)) = equiv(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(X,Y))),bind(Y0,$fot(and(implies(X,Y),implies(Y,X))))]]) ).
cnf(refute_0_414,plain,
and(implies(X,Y),implies(Y,X)) = equiv(X,Y),
inference(resolve,[$cnf( $equal(equiv(X,Y),and(implies(X,Y),implies(Y,X))) )],[refute_0_398,refute_0_413]) ).
cnf(refute_0_415,plain,
and(implies(X_31,X),implies(X,X_31)) = equiv(X_31,X),
inference(subst,[],[refute_0_414:[bind(X,$fot(X_31)),bind(Y,$fot(X))]]) ).
cnf(refute_0_416,plain,
not(and(X_31,not(X))) = implies(X_31,X),
inference(subst,[],[refute_0_34:[bind(X,$fot(X_31)),bind(Y,$fot(X))]]) ).
cnf(refute_0_417,plain,
and(not(and(X_31,not(X))),implies(X,X_31)) = and(not(and(X_31,not(X))),implies(X,X_31)),
introduced(tautology,[refl,[$fot(and(not(and(X_31,not(X))),implies(X,X_31)))]]) ).
cnf(refute_0_418,plain,
( and(not(and(X_31,not(X))),implies(X,X_31)) != and(not(and(X_31,not(X))),implies(X,X_31))
| not(and(X_31,not(X))) != implies(X_31,X)
| and(not(and(X_31,not(X))),implies(X,X_31)) = and(implies(X_31,X),implies(X,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(X_31,not(X))),implies(X,X_31)),and(not(and(X_31,not(X))),implies(X,X_31))) ),[1,0],$fot(implies(X_31,X))]]) ).
cnf(refute_0_419,plain,
( not(and(X_31,not(X))) != implies(X_31,X)
| and(not(and(X_31,not(X))),implies(X,X_31)) = and(implies(X_31,X),implies(X,X_31)) ),
inference(resolve,[$cnf( $equal(and(not(and(X_31,not(X))),implies(X,X_31)),and(not(and(X_31,not(X))),implies(X,X_31))) )],[refute_0_417,refute_0_418]) ).
cnf(refute_0_420,plain,
and(not(and(X_31,not(X))),implies(X,X_31)) = and(implies(X_31,X),implies(X,X_31)),
inference(resolve,[$cnf( $equal(not(and(X_31,not(X))),implies(X_31,X)) )],[refute_0_416,refute_0_419]) ).
cnf(refute_0_421,plain,
( and(implies(X_31,X),implies(X,X_31)) != equiv(X_31,X)
| and(not(and(X_31,not(X))),implies(X,X_31)) != and(implies(X_31,X),implies(X,X_31))
| and(not(and(X_31,not(X))),implies(X,X_31)) = equiv(X_31,X) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(and(not(and(X_31,not(X))),implies(X,X_31)))),bind(Y0,$fot(and(implies(X_31,X),implies(X,X_31)))),bind(Z,$fot(equiv(X_31,X)))]]) ).
cnf(refute_0_422,plain,
( and(implies(X_31,X),implies(X,X_31)) != equiv(X_31,X)
| and(not(and(X_31,not(X))),implies(X,X_31)) = equiv(X_31,X) ),
inference(resolve,[$cnf( $equal(and(not(and(X_31,not(X))),implies(X,X_31)),and(implies(X_31,X),implies(X,X_31))) )],[refute_0_420,refute_0_421]) ).
cnf(refute_0_423,plain,
and(not(and(X_31,not(X))),implies(X,X_31)) = equiv(X_31,X),
inference(resolve,[$cnf( $equal(and(implies(X_31,X),implies(X,X_31)),equiv(X_31,X)) )],[refute_0_415,refute_0_422]) ).
cnf(refute_0_424,plain,
and(not(not(implies(X,not(Y)))),X_32) = and(implies(X,not(Y)),X_32),
inference(subst,[],[refute_0_57:[bind(Y,$fot(X_32)),bind(X_12,$fot(implies(X,not(Y))))]]) ).
cnf(refute_0_425,plain,
( and(not(not(implies(X,not(Y)))),X_32) != and(implies(X,not(Y)),X_32)
| not(implies(X,not(Y))) != and(X,Y)
| and(not(and(X,Y)),X_32) = and(implies(X,not(Y)),X_32) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(implies(X,not(Y)))),X_32),and(implies(X,not(Y)),X_32)) ),[0,0,0],$fot(and(X,Y))]]) ).
cnf(refute_0_426,plain,
( and(not(not(implies(X,not(Y)))),X_32) != and(implies(X,not(Y)),X_32)
| and(not(and(X,Y)),X_32) = and(implies(X,not(Y)),X_32) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_53,refute_0_425]) ).
cnf(refute_0_427,plain,
and(not(and(X,Y)),X_32) = and(implies(X,not(Y)),X_32),
inference(resolve,[$cnf( $equal(and(not(not(implies(X,not(Y)))),X_32),and(implies(X,not(Y)),X_32)) )],[refute_0_424,refute_0_426]) ).
cnf(refute_0_428,plain,
( and(not(and(X,Y)),X_32) != and(implies(X,not(Y)),X_32)
| and(implies(X,not(Y)),X_32) = and(not(and(X,Y)),X_32) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(not(and(X,Y)),X_32))),bind(Y0,$fot(and(implies(X,not(Y)),X_32)))]]) ).
cnf(refute_0_429,plain,
and(implies(X,not(Y)),X_32) = and(not(and(X,Y)),X_32),
inference(resolve,[$cnf( $equal(and(not(and(X,Y)),X_32),and(implies(X,not(Y)),X_32)) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
and(implies(X_31,not(not(X))),implies(X,X_31)) = and(not(and(X_31,not(X))),implies(X,X_31)),
inference(subst,[],[refute_0_429:[bind(X,$fot(X_31)),bind(Y,$fot(not(X))),bind(X_32,$fot(implies(X,X_31)))]]) ).
cnf(refute_0_431,plain,
( and(implies(X_31,not(not(X))),implies(X,X_31)) != and(not(and(X_31,not(X))),implies(X,X_31))
| and(not(and(X_31,not(X))),implies(X,X_31)) != equiv(X_31,X)
| and(implies(X_31,not(not(X))),implies(X,X_31)) = equiv(X_31,X) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(and(implies(X_31,not(not(X))),implies(X,X_31)))),bind(Y0,$fot(and(not(and(X_31,not(X))),implies(X,X_31)))),bind(Z,$fot(equiv(X_31,X)))]]) ).
cnf(refute_0_432,plain,
( and(not(and(X_31,not(X))),implies(X,X_31)) != equiv(X_31,X)
| and(implies(X_31,not(not(X))),implies(X,X_31)) = equiv(X_31,X) ),
inference(resolve,[$cnf( $equal(and(implies(X_31,not(not(X))),implies(X,X_31)),and(not(and(X_31,not(X))),implies(X,X_31))) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
and(implies(X_31,not(not(X))),implies(X,X_31)) = equiv(X_31,X),
inference(resolve,[$cnf( $equal(and(not(and(X_31,not(X))),implies(X,X_31)),equiv(X_31,X)) )],[refute_0_423,refute_0_432]) ).
cnf(refute_0_434,plain,
( and(implies(X_31,not(not(X))),implies(X,X_31)) != equiv(X_31,X)
| equiv(X_31,not(not(X))) != and(implies(X_31,not(not(X))),implies(X,X_31))
| equiv(X_31,not(not(X))) = equiv(X_31,X) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_31,not(not(X))),and(implies(X_31,not(not(X))),implies(X,X_31))) ),[1],$fot(equiv(X_31,X))]]) ).
cnf(refute_0_435,plain,
( equiv(X_31,not(not(X))) != and(implies(X_31,not(not(X))),implies(X,X_31))
| equiv(X_31,not(not(X))) = equiv(X_31,X) ),
inference(resolve,[$cnf( $equal(and(implies(X_31,not(not(X))),implies(X,X_31)),equiv(X_31,X)) )],[refute_0_433,refute_0_434]) ).
cnf(refute_0_436,plain,
equiv(X_31,not(not(X))) = equiv(X_31,X),
inference(resolve,[$cnf( $equal(equiv(X_31,not(not(X))),and(implies(X_31,not(not(X))),implies(X,X_31))) )],[refute_0_412,refute_0_435]) ).
cnf(refute_0_437,plain,
equiv(X_96,not(not(X))) = equiv(X_96,X),
inference(subst,[],[refute_0_436:[bind(X_31,$fot(X_96))]]) ).
cnf(refute_0_438,plain,
( equiv(X_96,not(not(X))) != equiv(X_96,X)
| ~ is_a_theorem(equiv(X_96,X))
| is_a_theorem(equiv(X_96,not(not(X)))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(equiv(X_96,not(not(X)))) ),[0],$fot(equiv(X_96,X))]]) ).
cnf(refute_0_439,plain,
( ~ is_a_theorem(equiv(X_96,X))
| is_a_theorem(equiv(X_96,not(not(X)))) ),
inference(resolve,[$cnf( $equal(equiv(X_96,not(not(X))),equiv(X_96,X)) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
( ~ is_a_theorem(equiv(X_96,X))
| X_96 = not(not(X)) ),
inference(resolve,[$cnf( is_a_theorem(equiv(X_96,not(not(X)))) )],[refute_0_439,refute_0_395]) ).
cnf(refute_0_441,plain,
( ~ is_a_theorem(equiv(X_5451,X_5451))
| X_5451 = not(not(X_5451)) ),
inference(subst,[],[refute_0_440:[bind(X,$fot(X_5451)),bind(X_96,$fot(X_5451))]]) ).
cnf(refute_0_442,plain,
( ~ is_a_theorem(implies(X_5450,not(not(X_5450))))
| is_a_theorem(and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450))))) ),
inference(subst,[],[refute_0_89:[bind(X_295,$fot(implies(X_5450,not(not(X_5450)))))]]) ).
cnf(refute_0_443,plain,
is_a_theorem(implies(X_5450,not(not(X_5450)))),
inference(subst,[],[refute_0_391:[bind(X_5448,$fot(X_5450))]]) ).
cnf(refute_0_444,plain,
is_a_theorem(and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_5450,not(not(X_5450)))) )],[refute_0_443,refute_0_442]) ).
cnf(refute_0_445,plain,
and(Y,Y) = not(implies(Y,not(Y))),
inference(subst,[],[refute_0_25:[bind(X,$fot(Y))]]) ).
cnf(refute_0_446,plain,
( ~ is_a_theorem(equiv(or(X_3643,X_3643),or(X_3643,X_3643)))
| or(X_3643,X_3643) = not(not(or(X_3643,X_3643))) ),
inference(subst,[],[refute_0_440:[bind(X,$fot(or(X_3643,X_3643))),bind(X_96,$fot(or(X_3643,X_3643)))]]) ).
cnf(refute_0_447,plain,
is_a_theorem(implies(implies(X_16,X_16),and(implies(X_16,X_16),implies(X_16,X_16)))),
inference(subst,[],[refute_0_86:[bind(P,$fot(implies(X_16,X_16)))]]) ).
cnf(refute_0_448,plain,
equiv(X_16,X_16) = and(implies(X_16,X_16),implies(X_16,X_16)),
inference(subst,[],[refute_0_398:[bind(X,$fot(X_16)),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_449,plain,
( equiv(X_16,X_16) != and(implies(X_16,X_16),implies(X_16,X_16))
| and(implies(X_16,X_16),implies(X_16,X_16)) = equiv(X_16,X_16) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(X_16,X_16))),bind(Y0,$fot(and(implies(X_16,X_16),implies(X_16,X_16))))]]) ).
cnf(refute_0_450,plain,
and(implies(X_16,X_16),implies(X_16,X_16)) = equiv(X_16,X_16),
inference(resolve,[$cnf( $equal(equiv(X_16,X_16),and(implies(X_16,X_16),implies(X_16,X_16))) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
( and(implies(X_16,X_16),implies(X_16,X_16)) != equiv(X_16,X_16)
| ~ is_a_theorem(implies(implies(X_16,X_16),and(implies(X_16,X_16),implies(X_16,X_16))))
| is_a_theorem(implies(implies(X_16,X_16),equiv(X_16,X_16))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_16,X_16),and(implies(X_16,X_16),implies(X_16,X_16)))) ),[0,1],$fot(equiv(X_16,X_16))]]) ).
cnf(refute_0_452,plain,
( ~ is_a_theorem(implies(implies(X_16,X_16),and(implies(X_16,X_16),implies(X_16,X_16))))
| is_a_theorem(implies(implies(X_16,X_16),equiv(X_16,X_16))) ),
inference(resolve,[$cnf( $equal(and(implies(X_16,X_16),implies(X_16,X_16)),equiv(X_16,X_16)) )],[refute_0_450,refute_0_451]) ).
cnf(refute_0_453,plain,
is_a_theorem(implies(implies(X_16,X_16),equiv(X_16,X_16))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_16,X_16),and(implies(X_16,X_16),implies(X_16,X_16)))) )],[refute_0_447,refute_0_452]) ).
cnf(refute_0_454,plain,
( ~ is_a_theorem(implies(X_16,X_16))
| ~ is_a_theorem(implies(implies(X_16,X_16),equiv(X_16,X_16)))
| is_a_theorem(equiv(X_16,X_16)) ),
inference(subst,[],[refute_0_64:[bind(X,$fot(implies(X_16,X_16))),bind(Y,$fot(equiv(X_16,X_16)))]]) ).
cnf(refute_0_455,plain,
( ~ is_a_theorem(implies(X_16,X_16))
| is_a_theorem(equiv(X_16,X_16)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_16,X_16),equiv(X_16,X_16))) )],[refute_0_453,refute_0_454]) ).
cnf(refute_0_456,plain,
( ~ is_a_theorem(implies(or(X_3641,X_3641),or(X_3641,X_3641)))
| is_a_theorem(equiv(or(X_3641,X_3641),or(X_3641,X_3641))) ),
inference(subst,[],[refute_0_455:[bind(X_16,$fot(or(X_3641,X_3641)))]]) ).
cnf(refute_0_457,plain,
is_a_theorem(implies(not(X_7),and(not(X_7),not(X_7)))),
inference(subst,[],[refute_0_86:[bind(P,$fot(not(X_7)))]]) ).
cnf(refute_0_458,plain,
or(X_7,and(not(X_7),not(X_7))) = implies(not(X_7),and(not(X_7),not(X_7))),
inference(subst,[],[refute_0_38:[bind(X,$fot(X_7)),bind(Y,$fot(and(not(X_7),not(X_7))))]]) ).
cnf(refute_0_459,plain,
( or(X_7,and(not(X_7),not(X_7))) != implies(not(X_7),and(not(X_7),not(X_7)))
| implies(not(X_7),and(not(X_7),not(X_7))) = or(X_7,and(not(X_7),not(X_7))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X_7,and(not(X_7),not(X_7))))),bind(Y0,$fot(implies(not(X_7),and(not(X_7),not(X_7)))))]]) ).
cnf(refute_0_460,plain,
implies(not(X_7),and(not(X_7),not(X_7))) = or(X_7,and(not(X_7),not(X_7))),
inference(resolve,[$cnf( $equal(or(X_7,and(not(X_7),not(X_7))),implies(not(X_7),and(not(X_7),not(X_7)))) )],[refute_0_458,refute_0_459]) ).
cnf(refute_0_461,plain,
( implies(not(X_7),and(not(X_7),not(X_7))) != or(X_7,and(not(X_7),not(X_7)))
| ~ is_a_theorem(implies(not(X_7),and(not(X_7),not(X_7))))
| is_a_theorem(or(X_7,and(not(X_7),not(X_7)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X_7),and(not(X_7),not(X_7)))) ),[0],$fot(or(X_7,and(not(X_7),not(X_7))))]]) ).
cnf(refute_0_462,plain,
( ~ is_a_theorem(implies(not(X_7),and(not(X_7),not(X_7))))
| is_a_theorem(or(X_7,and(not(X_7),not(X_7)))) ),
inference(resolve,[$cnf( $equal(implies(not(X_7),and(not(X_7),not(X_7))),or(X_7,and(not(X_7),not(X_7)))) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
is_a_theorem(or(X_7,and(not(X_7),not(X_7)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_7),and(not(X_7),not(X_7)))) )],[refute_0_457,refute_0_462]) ).
cnf(refute_0_464,plain,
or(X_7,and(not(X_7),not(X_7))) = not(and(not(X_7),or(X_7,X_7))),
inference(subst,[],[refute_0_237:[bind(X,$fot(X_7)),bind(X_143,$fot(X_7)),bind(X_145,$fot(X_7))]]) ).
cnf(refute_0_465,plain,
( or(X_7,and(not(X_7),not(X_7))) != not(and(not(X_7),or(X_7,X_7)))
| ~ is_a_theorem(or(X_7,and(not(X_7),not(X_7))))
| is_a_theorem(not(and(not(X_7),or(X_7,X_7)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_7,and(not(X_7),not(X_7)))) ),[0],$fot(not(and(not(X_7),or(X_7,X_7))))]]) ).
cnf(refute_0_466,plain,
( ~ is_a_theorem(or(X_7,and(not(X_7),not(X_7))))
| is_a_theorem(not(and(not(X_7),or(X_7,X_7)))) ),
inference(resolve,[$cnf( $equal(or(X_7,and(not(X_7),not(X_7))),not(and(not(X_7),or(X_7,X_7)))) )],[refute_0_464,refute_0_465]) ).
cnf(refute_0_467,plain,
is_a_theorem(not(and(not(X_7),or(X_7,X_7)))),
inference(resolve,[$cnf( is_a_theorem(or(X_7,and(not(X_7),not(X_7)))) )],[refute_0_463,refute_0_466]) ).
cnf(refute_0_468,plain,
is_a_theorem(implies(and(X_33,not(X_88)),not(not(X_33)))),
inference(subst,[],[refute_0_61:[bind(Q,$fot(not(X_88)))]]) ).
cnf(refute_0_469,plain,
implies(and(X_33,not(X_88)),not(not(X_33))) = or(implies(X_33,X_88),not(not(X_33))),
inference(subst,[],[refute_0_72:[bind(X,$fot(X_33)),bind(Y,$fot(X_88)),bind(X_13,$fot(not(not(X_33))))]]) ).
cnf(refute_0_470,plain,
( implies(and(X_33,not(X_88)),not(not(X_33))) != or(implies(X_33,X_88),not(not(X_33)))
| ~ is_a_theorem(implies(and(X_33,not(X_88)),not(not(X_33))))
| is_a_theorem(or(implies(X_33,X_88),not(not(X_33)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(X_33,not(X_88)),not(not(X_33)))) ),[0],$fot(or(implies(X_33,X_88),not(not(X_33))))]]) ).
cnf(refute_0_471,plain,
( ~ is_a_theorem(implies(and(X_33,not(X_88)),not(not(X_33))))
| is_a_theorem(or(implies(X_33,X_88),not(not(X_33)))) ),
inference(resolve,[$cnf( $equal(implies(and(X_33,not(X_88)),not(not(X_33))),or(implies(X_33,X_88),not(not(X_33)))) )],[refute_0_469,refute_0_470]) ).
cnf(refute_0_472,plain,
is_a_theorem(or(implies(X_33,X_88),not(not(X_33)))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_33,not(X_88)),not(not(X_33)))) )],[refute_0_468,refute_0_471]) ).
cnf(refute_0_473,plain,
is_a_theorem(or(implies(not(X),X_95),not(not(not(X))))),
inference(subst,[],[refute_0_472:[bind(X_33,$fot(not(X))),bind(X_88,$fot(X_95))]]) ).
cnf(refute_0_474,plain,
or(X,X_95) = implies(not(X),X_95),
inference(subst,[],[refute_0_38:[bind(Y,$fot(X_95))]]) ).
cnf(refute_0_475,plain,
( or(X,X_95) != implies(not(X),X_95)
| implies(not(X),X_95) = or(X,X_95) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_95))),bind(Y0,$fot(implies(not(X),X_95)))]]) ).
cnf(refute_0_476,plain,
implies(not(X),X_95) = or(X,X_95),
inference(resolve,[$cnf( $equal(or(X,X_95),implies(not(X),X_95)) )],[refute_0_474,refute_0_475]) ).
cnf(refute_0_477,plain,
( implies(not(X),X_95) != or(X,X_95)
| ~ is_a_theorem(or(implies(not(X),X_95),not(not(not(X)))))
| is_a_theorem(or(or(X,X_95),not(not(not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(not(X),X_95),not(not(not(X))))) ),[0,0],$fot(or(X,X_95))]]) ).
cnf(refute_0_478,plain,
( ~ is_a_theorem(or(implies(not(X),X_95),not(not(not(X)))))
| is_a_theorem(or(or(X,X_95),not(not(not(X))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_95),or(X,X_95)) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
is_a_theorem(or(or(X,X_95),not(not(not(X))))),
inference(resolve,[$cnf( is_a_theorem(or(implies(not(X),X_95),not(not(not(X))))) )],[refute_0_473,refute_0_478]) ).
cnf(refute_0_480,plain,
is_a_theorem(or(or(not(X),X_117),not(not(not(not(X)))))),
inference(subst,[],[refute_0_479:[bind(X,$fot(not(X))),bind(X_95,$fot(X_117))]]) ).
cnf(refute_0_481,plain,
implies(X,X_117) = or(not(X),X_117),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_117))]]) ).
cnf(refute_0_482,plain,
( implies(X,X_117) != or(not(X),X_117)
| or(not(X),X_117) = implies(X,X_117) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_117))),bind(Y0,$fot(or(not(X),X_117)))]]) ).
cnf(refute_0_483,plain,
or(not(X),X_117) = implies(X,X_117),
inference(resolve,[$cnf( $equal(implies(X,X_117),or(not(X),X_117)) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
( or(not(X),X_117) != implies(X,X_117)
| ~ is_a_theorem(or(or(not(X),X_117),not(not(not(not(X))))))
| is_a_theorem(or(implies(X,X_117),not(not(not(not(X)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(or(not(X),X_117),not(not(not(not(X)))))) ),[0,0],$fot(implies(X,X_117))]]) ).
cnf(refute_0_485,plain,
( ~ is_a_theorem(or(or(not(X),X_117),not(not(not(not(X))))))
| is_a_theorem(or(implies(X,X_117),not(not(not(not(X)))))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_117),implies(X,X_117)) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
is_a_theorem(or(implies(X,X_117),not(not(not(not(X)))))),
inference(resolve,[$cnf( is_a_theorem(or(or(not(X),X_117),not(not(not(not(X)))))) )],[refute_0_480,refute_0_485]) ).
cnf(refute_0_487,plain,
is_a_theorem(or(implies(not(X),X_248),not(not(not(not(not(X))))))),
inference(subst,[],[refute_0_486:[bind(X,$fot(not(X))),bind(X_117,$fot(X_248))]]) ).
cnf(refute_0_488,plain,
or(X,X_248) = implies(not(X),X_248),
inference(subst,[],[refute_0_38:[bind(Y,$fot(X_248))]]) ).
cnf(refute_0_489,plain,
( or(X,X_248) != implies(not(X),X_248)
| implies(not(X),X_248) = or(X,X_248) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_248))),bind(Y0,$fot(implies(not(X),X_248)))]]) ).
cnf(refute_0_490,plain,
implies(not(X),X_248) = or(X,X_248),
inference(resolve,[$cnf( $equal(or(X,X_248),implies(not(X),X_248)) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
( implies(not(X),X_248) != or(X,X_248)
| ~ is_a_theorem(or(implies(not(X),X_248),not(not(not(not(not(X)))))))
| is_a_theorem(or(or(X,X_248),not(not(not(not(not(X))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(not(X),X_248),not(not(not(not(not(X))))))) ),[0,0],$fot(or(X,X_248))]]) ).
cnf(refute_0_492,plain,
( ~ is_a_theorem(or(implies(not(X),X_248),not(not(not(not(not(X)))))))
| is_a_theorem(or(or(X,X_248),not(not(not(not(not(X))))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_248),or(X,X_248)) )],[refute_0_490,refute_0_491]) ).
cnf(refute_0_493,plain,
is_a_theorem(or(or(X,X_248),not(not(not(not(not(X))))))),
inference(resolve,[$cnf( is_a_theorem(or(implies(not(X),X_248),not(not(not(not(not(X))))))) )],[refute_0_487,refute_0_492]) ).
cnf(refute_0_494,plain,
is_a_theorem(or(or(not(X),X_270),not(not(not(not(not(not(X)))))))),
inference(subst,[],[refute_0_493:[bind(X,$fot(not(X))),bind(X_248,$fot(X_270))]]) ).
cnf(refute_0_495,plain,
implies(X,X_270) = or(not(X),X_270),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_270))]]) ).
cnf(refute_0_496,plain,
( implies(X,X_270) != or(not(X),X_270)
| or(not(X),X_270) = implies(X,X_270) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_270))),bind(Y0,$fot(or(not(X),X_270)))]]) ).
cnf(refute_0_497,plain,
or(not(X),X_270) = implies(X,X_270),
inference(resolve,[$cnf( $equal(implies(X,X_270),or(not(X),X_270)) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
( or(not(X),X_270) != implies(X,X_270)
| ~ is_a_theorem(or(or(not(X),X_270),not(not(not(not(not(not(X))))))))
| is_a_theorem(or(implies(X,X_270),not(not(not(not(not(not(X)))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(or(not(X),X_270),not(not(not(not(not(not(X)))))))) ),[0,0],$fot(implies(X,X_270))]]) ).
cnf(refute_0_499,plain,
( ~ is_a_theorem(or(or(not(X),X_270),not(not(not(not(not(not(X))))))))
| is_a_theorem(or(implies(X,X_270),not(not(not(not(not(not(X)))))))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_270),implies(X,X_270)) )],[refute_0_497,refute_0_498]) ).
cnf(refute_0_500,plain,
is_a_theorem(or(implies(X,X_270),not(not(not(not(not(not(X)))))))),
inference(resolve,[$cnf( is_a_theorem(or(or(not(X),X_270),not(not(not(not(not(not(X)))))))) )],[refute_0_494,refute_0_499]) ).
cnf(refute_0_501,plain,
( ~ is_a_theorem(or(implies(X,X_270),not(not(not(not(not(not(X))))))))
| is_a_theorem(or(and(not(not(not(not(not(not(X)))))),X_1304),implies(X_1304,implies(X,X_270)))) ),
inference(subst,[],[refute_0_322:[bind(Y,$fot(implies(X,X_270))),bind(X_109,$fot(not(not(not(not(not(not(X)))))))),bind(X_110,$fot(X_1304))]]) ).
cnf(refute_0_502,plain,
is_a_theorem(or(and(not(not(not(not(not(not(X)))))),X_1304),implies(X_1304,implies(X,X_270)))),
inference(resolve,[$cnf( is_a_theorem(or(implies(X,X_270),not(not(not(not(not(not(X)))))))) )],[refute_0_500,refute_0_501]) ).
cnf(refute_0_503,plain,
implies(implies(X,not(X_1304)),implies(X_1304,implies(X,X_270))) = or(and(X,X_1304),implies(X_1304,implies(X,X_270))),
inference(subst,[],[refute_0_132:[bind(Y,$fot(X_1304)),bind(X_13,$fot(implies(X_1304,implies(X,X_270))))]]) ).
cnf(refute_0_504,plain,
or(not(X),not(X_1304)) = implies(X,not(X_1304)),
inference(subst,[],[refute_0_17:[bind(Y,$fot(not(X_1304)))]]) ).
cnf(refute_0_505,plain,
implies(not(not(X)),not(X_1304)) = or(not(X),not(X_1304)),
inference(subst,[],[refute_0_212:[bind(X,$fot(not(X))),bind(Y,$fot(not(X_1304)))]]) ).
cnf(refute_0_506,plain,
( implies(not(not(X)),not(X_1304)) != or(not(X),not(X_1304))
| or(not(X),not(X_1304)) != implies(X,not(X_1304))
| implies(not(not(X)),not(X_1304)) = implies(X,not(X_1304)) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(implies(not(not(X)),not(X_1304)))),bind(Y0,$fot(or(not(X),not(X_1304)))),bind(Z,$fot(implies(X,not(X_1304))))]]) ).
cnf(refute_0_507,plain,
( or(not(X),not(X_1304)) != implies(X,not(X_1304))
| implies(not(not(X)),not(X_1304)) = implies(X,not(X_1304)) ),
inference(resolve,[$cnf( $equal(implies(not(not(X)),not(X_1304)),or(not(X),not(X_1304))) )],[refute_0_505,refute_0_506]) ).
cnf(refute_0_508,plain,
implies(not(not(X)),not(X_1304)) = implies(X,not(X_1304)),
inference(resolve,[$cnf( $equal(or(not(X),not(X_1304)),implies(X,not(X_1304))) )],[refute_0_504,refute_0_507]) ).
cnf(refute_0_509,plain,
or(not(not(not(X))),not(X_1304)) = implies(not(not(X)),not(X_1304)),
inference(subst,[],[refute_0_17:[bind(X,$fot(not(not(X)))),bind(Y,$fot(not(X_1304)))]]) ).
cnf(refute_0_510,plain,
( implies(not(not(X)),not(X_1304)) != implies(X,not(X_1304))
| or(not(not(not(X))),not(X_1304)) != implies(not(not(X)),not(X_1304))
| or(not(not(not(X))),not(X_1304)) = implies(X,not(X_1304)) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(or(not(not(not(X))),not(X_1304)))),bind(Y0,$fot(implies(not(not(X)),not(X_1304)))),bind(Z,$fot(implies(X,not(X_1304))))]]) ).
cnf(refute_0_511,plain,
( implies(not(not(X)),not(X_1304)) != implies(X,not(X_1304))
| or(not(not(not(X))),not(X_1304)) = implies(X,not(X_1304)) ),
inference(resolve,[$cnf( $equal(or(not(not(not(X))),not(X_1304)),implies(not(not(X)),not(X_1304))) )],[refute_0_509,refute_0_510]) ).
cnf(refute_0_512,plain,
or(not(not(not(X))),not(X_1304)) = implies(X,not(X_1304)),
inference(resolve,[$cnf( $equal(implies(not(not(X)),not(X_1304)),implies(X,not(X_1304))) )],[refute_0_508,refute_0_511]) ).
cnf(refute_0_513,plain,
implies(not(not(not(not(X)))),not(X_1304)) = or(not(not(not(X))),not(X_1304)),
inference(subst,[],[refute_0_212:[bind(X,$fot(not(not(not(X))))),bind(Y,$fot(not(X_1304)))]]) ).
cnf(refute_0_514,plain,
( implies(not(not(not(not(X)))),not(X_1304)) != or(not(not(not(X))),not(X_1304))
| or(not(not(not(X))),not(X_1304)) != implies(X,not(X_1304))
| implies(not(not(not(not(X)))),not(X_1304)) = implies(X,not(X_1304)) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(implies(not(not(not(not(X)))),not(X_1304)))),bind(Y0,$fot(or(not(not(not(X))),not(X_1304)))),bind(Z,$fot(implies(X,not(X_1304))))]]) ).
cnf(refute_0_515,plain,
( or(not(not(not(X))),not(X_1304)) != implies(X,not(X_1304))
| implies(not(not(not(not(X)))),not(X_1304)) = implies(X,not(X_1304)) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(X)))),not(X_1304)),or(not(not(not(X))),not(X_1304))) )],[refute_0_513,refute_0_514]) ).
cnf(refute_0_516,plain,
implies(not(not(not(not(X)))),not(X_1304)) = implies(X,not(X_1304)),
inference(resolve,[$cnf( $equal(or(not(not(not(X))),not(X_1304)),implies(X,not(X_1304))) )],[refute_0_512,refute_0_515]) ).
cnf(refute_0_517,plain,
or(not(not(not(not(not(X))))),not(X_1304)) = implies(not(not(not(not(X)))),not(X_1304)),
inference(subst,[],[refute_0_17:[bind(X,$fot(not(not(not(not(X)))))),bind(Y,$fot(not(X_1304)))]]) ).
cnf(refute_0_518,plain,
( implies(not(not(not(not(X)))),not(X_1304)) != implies(X,not(X_1304))
| or(not(not(not(not(not(X))))),not(X_1304)) != implies(not(not(not(not(X)))),not(X_1304))
| or(not(not(not(not(not(X))))),not(X_1304)) = implies(X,not(X_1304)) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(or(not(not(not(not(not(X))))),not(X_1304)))),bind(Y0,$fot(implies(not(not(not(not(X)))),not(X_1304)))),bind(Z,$fot(implies(X,not(X_1304))))]]) ).
cnf(refute_0_519,plain,
( implies(not(not(not(not(X)))),not(X_1304)) != implies(X,not(X_1304))
| or(not(not(not(not(not(X))))),not(X_1304)) = implies(X,not(X_1304)) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(X))))),not(X_1304)),implies(not(not(not(not(X)))),not(X_1304))) )],[refute_0_517,refute_0_518]) ).
cnf(refute_0_520,plain,
or(not(not(not(not(not(X))))),not(X_1304)) = implies(X,not(X_1304)),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(X)))),not(X_1304)),implies(X,not(X_1304))) )],[refute_0_516,refute_0_519]) ).
cnf(refute_0_521,plain,
implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))) = implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))),
introduced(tautology,[refl,[$fot(implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))))]]) ).
cnf(refute_0_522,plain,
( implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))) != implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270)))
| or(not(not(not(not(not(X))))),not(X_1304)) != implies(X,not(X_1304))
| implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))) = implies(implies(X,not(X_1304)),implies(X_1304,implies(X,X_270))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))),implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270)))) ),[1,0],$fot(implies(X,not(X_1304)))]]) ).
cnf(refute_0_523,plain,
( or(not(not(not(not(not(X))))),not(X_1304)) != implies(X,not(X_1304))
| implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))) = implies(implies(X,not(X_1304)),implies(X_1304,implies(X,X_270))) ),
inference(resolve,[$cnf( $equal(implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))),implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270)))) )],[refute_0_521,refute_0_522]) ).
cnf(refute_0_524,plain,
implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))) = implies(implies(X,not(X_1304)),implies(X_1304,implies(X,X_270))),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(X))))),not(X_1304)),implies(X,not(X_1304))) )],[refute_0_520,refute_0_523]) ).
cnf(refute_0_525,plain,
( implies(implies(X,not(X_1304)),implies(X_1304,implies(X,X_270))) != or(and(X,X_1304),implies(X_1304,implies(X,X_270)))
| implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))) != implies(implies(X,not(X_1304)),implies(X_1304,implies(X,X_270)))
| implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))) = or(and(X,X_1304),implies(X_1304,implies(X,X_270))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))))),bind(Y0,$fot(implies(implies(X,not(X_1304)),implies(X_1304,implies(X,X_270))))),bind(Z,$fot(or(and(X,X_1304),implies(X_1304,implies(X,X_270)))))]]) ).
cnf(refute_0_526,plain,
( implies(implies(X,not(X_1304)),implies(X_1304,implies(X,X_270))) != or(and(X,X_1304),implies(X_1304,implies(X,X_270)))
| implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))) = or(and(X,X_1304),implies(X_1304,implies(X,X_270))) ),
inference(resolve,[$cnf( $equal(implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))),implies(implies(X,not(X_1304)),implies(X_1304,implies(X,X_270)))) )],[refute_0_524,refute_0_525]) ).
cnf(refute_0_527,plain,
implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))) = or(and(X,X_1304),implies(X_1304,implies(X,X_270))),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X_1304)),implies(X_1304,implies(X,X_270))),or(and(X,X_1304),implies(X_1304,implies(X,X_270)))) )],[refute_0_503,refute_0_526]) ).
cnf(refute_0_528,plain,
or(and(not(not(not(not(not(not(X)))))),X_1304),implies(X_1304,implies(X,X_270))) = implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))),
inference(subst,[],[refute_0_209:[bind(Y,$fot(X_1304)),bind(X_13,$fot(implies(X_1304,implies(X,X_270)))),bind(X_7,$fot(not(not(not(not(not(X)))))))]]) ).
cnf(refute_0_529,plain,
( implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))) != or(and(X,X_1304),implies(X_1304,implies(X,X_270)))
| or(and(not(not(not(not(not(not(X)))))),X_1304),implies(X_1304,implies(X,X_270))) != implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270)))
| or(and(not(not(not(not(not(not(X)))))),X_1304),implies(X_1304,implies(X,X_270))) = or(and(X,X_1304),implies(X_1304,implies(X,X_270))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(or(and(not(not(not(not(not(not(X)))))),X_1304),implies(X_1304,implies(X,X_270))))),bind(Y0,$fot(implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))))),bind(Z,$fot(or(and(X,X_1304),implies(X_1304,implies(X,X_270)))))]]) ).
cnf(refute_0_530,plain,
( implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))) != or(and(X,X_1304),implies(X_1304,implies(X,X_270)))
| or(and(not(not(not(not(not(not(X)))))),X_1304),implies(X_1304,implies(X,X_270))) = or(and(X,X_1304),implies(X_1304,implies(X,X_270))) ),
inference(resolve,[$cnf( $equal(or(and(not(not(not(not(not(not(X)))))),X_1304),implies(X_1304,implies(X,X_270))),implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270)))) )],[refute_0_528,refute_0_529]) ).
cnf(refute_0_531,plain,
or(and(not(not(not(not(not(not(X)))))),X_1304),implies(X_1304,implies(X,X_270))) = or(and(X,X_1304),implies(X_1304,implies(X,X_270))),
inference(resolve,[$cnf( $equal(implies(or(not(not(not(not(not(X))))),not(X_1304)),implies(X_1304,implies(X,X_270))),or(and(X,X_1304),implies(X_1304,implies(X,X_270)))) )],[refute_0_527,refute_0_530]) ).
cnf(refute_0_532,plain,
( or(and(not(not(not(not(not(not(X)))))),X_1304),implies(X_1304,implies(X,X_270))) != or(and(X,X_1304),implies(X_1304,implies(X,X_270)))
| ~ is_a_theorem(or(and(not(not(not(not(not(not(X)))))),X_1304),implies(X_1304,implies(X,X_270))))
| is_a_theorem(or(and(X,X_1304),implies(X_1304,implies(X,X_270)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(not(not(not(not(not(X)))))),X_1304),implies(X_1304,implies(X,X_270)))) ),[0],$fot(or(and(X,X_1304),implies(X_1304,implies(X,X_270))))]]) ).
cnf(refute_0_533,plain,
( ~ is_a_theorem(or(and(not(not(not(not(not(not(X)))))),X_1304),implies(X_1304,implies(X,X_270))))
| is_a_theorem(or(and(X,X_1304),implies(X_1304,implies(X,X_270)))) ),
inference(resolve,[$cnf( $equal(or(and(not(not(not(not(not(not(X)))))),X_1304),implies(X_1304,implies(X,X_270))),or(and(X,X_1304),implies(X_1304,implies(X,X_270)))) )],[refute_0_531,refute_0_532]) ).
cnf(refute_0_534,plain,
is_a_theorem(or(and(X,X_1304),implies(X_1304,implies(X,X_270)))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(not(not(not(not(not(X)))))),X_1304),implies(X_1304,implies(X,X_270)))) )],[refute_0_502,refute_0_533]) ).
cnf(refute_0_535,plain,
( ~ is_a_theorem(not(and(X,X_1304)))
| ~ is_a_theorem(or(and(X,X_1304),implies(X_1304,implies(X,X_270))))
| is_a_theorem(implies(X_1304,implies(X,X_270))) ),
inference(subst,[],[refute_0_387:[bind(X,$fot(and(X,X_1304))),bind(X_296,$fot(implies(X_1304,implies(X,X_270))))]]) ).
cnf(refute_0_536,plain,
( ~ is_a_theorem(not(and(X,X_1304)))
| is_a_theorem(implies(X_1304,implies(X,X_270))) ),
inference(resolve,[$cnf( is_a_theorem(or(and(X,X_1304),implies(X_1304,implies(X,X_270)))) )],[refute_0_534,refute_0_535]) ).
cnf(refute_0_537,plain,
( ~ is_a_theorem(not(and(not(X_7),or(X_7,X_7))))
| is_a_theorem(implies(or(X_7,X_7),implies(not(X_7),X_3640))) ),
inference(subst,[],[refute_0_536:[bind(X,$fot(not(X_7))),bind(X_1304,$fot(or(X_7,X_7))),bind(X_270,$fot(X_3640))]]) ).
cnf(refute_0_538,plain,
is_a_theorem(implies(or(X_7,X_7),implies(not(X_7),X_3640))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(X_7),or(X_7,X_7)))) )],[refute_0_467,refute_0_537]) ).
cnf(refute_0_539,plain,
implies(not(X_7),X_3640) = or(X_7,X_3640),
inference(subst,[],[refute_0_212:[bind(X,$fot(X_7)),bind(Y,$fot(X_3640))]]) ).
cnf(refute_0_540,plain,
implies(or(X_7,X_7),implies(not(X_7),X_3640)) = implies(or(X_7,X_7),implies(not(X_7),X_3640)),
introduced(tautology,[refl,[$fot(implies(or(X_7,X_7),implies(not(X_7),X_3640)))]]) ).
cnf(refute_0_541,plain,
( implies(not(X_7),X_3640) != or(X_7,X_3640)
| implies(or(X_7,X_7),implies(not(X_7),X_3640)) != implies(or(X_7,X_7),implies(not(X_7),X_3640))
| implies(or(X_7,X_7),implies(not(X_7),X_3640)) = implies(or(X_7,X_7),or(X_7,X_3640)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_7,X_7),implies(not(X_7),X_3640)),implies(or(X_7,X_7),implies(not(X_7),X_3640))) ),[1,1],$fot(or(X_7,X_3640))]]) ).
cnf(refute_0_542,plain,
( implies(not(X_7),X_3640) != or(X_7,X_3640)
| implies(or(X_7,X_7),implies(not(X_7),X_3640)) = implies(or(X_7,X_7),or(X_7,X_3640)) ),
inference(resolve,[$cnf( $equal(implies(or(X_7,X_7),implies(not(X_7),X_3640)),implies(or(X_7,X_7),implies(not(X_7),X_3640))) )],[refute_0_540,refute_0_541]) ).
cnf(refute_0_543,plain,
implies(or(X_7,X_7),implies(not(X_7),X_3640)) = implies(or(X_7,X_7),or(X_7,X_3640)),
inference(resolve,[$cnf( $equal(implies(not(X_7),X_3640),or(X_7,X_3640)) )],[refute_0_539,refute_0_542]) ).
cnf(refute_0_544,plain,
( implies(or(X_7,X_7),implies(not(X_7),X_3640)) != implies(or(X_7,X_7),or(X_7,X_3640))
| ~ is_a_theorem(implies(or(X_7,X_7),implies(not(X_7),X_3640)))
| is_a_theorem(implies(or(X_7,X_7),or(X_7,X_3640))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_7,X_7),implies(not(X_7),X_3640))) ),[0],$fot(implies(or(X_7,X_7),or(X_7,X_3640)))]]) ).
cnf(refute_0_545,plain,
( ~ is_a_theorem(implies(or(X_7,X_7),implies(not(X_7),X_3640)))
| is_a_theorem(implies(or(X_7,X_7),or(X_7,X_3640))) ),
inference(resolve,[$cnf( $equal(implies(or(X_7,X_7),implies(not(X_7),X_3640)),implies(or(X_7,X_7),or(X_7,X_3640))) )],[refute_0_543,refute_0_544]) ).
cnf(refute_0_546,plain,
is_a_theorem(implies(or(X_7,X_7),or(X_7,X_3640))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_7,X_7),implies(not(X_7),X_3640))) )],[refute_0_538,refute_0_545]) ).
cnf(refute_0_547,plain,
is_a_theorem(implies(or(X_3641,X_3641),or(X_3641,X_3641))),
inference(subst,[],[refute_0_546:[bind(X_3640,$fot(X_3641)),bind(X_7,$fot(X_3641))]]) ).
cnf(refute_0_548,plain,
is_a_theorem(equiv(or(X_3641,X_3641),or(X_3641,X_3641))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_3641,X_3641),or(X_3641,X_3641))) )],[refute_0_547,refute_0_456]) ).
cnf(refute_0_549,plain,
is_a_theorem(equiv(or(X_3643,X_3643),or(X_3643,X_3643))),
inference(subst,[],[refute_0_548:[bind(X_3641,$fot(X_3643))]]) ).
cnf(refute_0_550,plain,
or(X_3643,X_3643) = not(not(or(X_3643,X_3643))),
inference(resolve,[$cnf( is_a_theorem(equiv(or(X_3643,X_3643),or(X_3643,X_3643))) )],[refute_0_549,refute_0_446]) ).
cnf(refute_0_551,plain,
or(not(X),not(X)) = not(not(or(not(X),not(X)))),
inference(subst,[],[refute_0_550:[bind(X_3643,$fot(not(X)))]]) ).
cnf(refute_0_552,plain,
( or(not(X),not(X)) != implies(X,not(X))
| or(not(X),not(X)) != not(not(or(not(X),not(X))))
| or(not(X),not(X)) = not(not(implies(X,not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X),not(X)),not(not(or(not(X),not(X))))) ),[1,0,0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_553,plain,
( or(not(X),not(X)) != not(not(or(not(X),not(X))))
| or(not(X),not(X)) = not(not(implies(X,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_354,refute_0_552]) ).
cnf(refute_0_554,plain,
or(not(X),not(X)) = not(not(implies(X,not(X)))),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),not(not(or(not(X),not(X))))) )],[refute_0_551,refute_0_553]) ).
cnf(refute_0_555,plain,
( or(not(X),not(X)) != implies(X,not(X))
| or(not(X),not(X)) != not(not(implies(X,not(X))))
| implies(X,not(X)) = not(not(implies(X,not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X),not(X)),not(not(implies(X,not(X))))) ),[0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_556,plain,
( or(not(X),not(X)) != not(not(implies(X,not(X))))
| implies(X,not(X)) = not(not(implies(X,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_354,refute_0_555]) ).
cnf(refute_0_557,plain,
not(implies(X,not(X))) = and(X,X),
inference(subst,[],[refute_0_53:[bind(Y,$fot(X))]]) ).
cnf(refute_0_558,plain,
not(not(implies(X,not(X)))) = not(not(implies(X,not(X)))),
introduced(tautology,[refl,[$fot(not(not(implies(X,not(X)))))]]) ).
cnf(refute_0_559,plain,
( not(implies(X,not(X))) != and(X,X)
| not(not(implies(X,not(X)))) != not(not(implies(X,not(X))))
| not(not(implies(X,not(X)))) = not(and(X,X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(X,not(X)))),not(not(implies(X,not(X))))) ),[1,0],$fot(and(X,X))]]) ).
cnf(refute_0_560,plain,
( not(implies(X,not(X))) != and(X,X)
| not(not(implies(X,not(X)))) = not(and(X,X)) ),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(X)))),not(not(implies(X,not(X))))) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
not(not(implies(X,not(X)))) = not(and(X,X)),
inference(resolve,[$cnf( $equal(not(implies(X,not(X))),and(X,X)) )],[refute_0_557,refute_0_560]) ).
cnf(refute_0_562,plain,
( implies(X,not(X)) != not(not(implies(X,not(X))))
| not(not(implies(X,not(X)))) != not(and(X,X))
| implies(X,not(X)) = not(and(X,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,not(X)),not(and(X,X))) ),[0],$fot(not(not(implies(X,not(X)))))]]) ).
cnf(refute_0_563,plain,
( implies(X,not(X)) != not(not(implies(X,not(X))))
| implies(X,not(X)) = not(and(X,X)) ),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(X)))),not(and(X,X))) )],[refute_0_561,refute_0_562]) ).
cnf(refute_0_564,plain,
( or(not(X),not(X)) != not(not(implies(X,not(X))))
| implies(X,not(X)) = not(and(X,X)) ),
inference(resolve,[$cnf( $equal(implies(X,not(X)),not(not(implies(X,not(X))))) )],[refute_0_556,refute_0_563]) ).
cnf(refute_0_565,plain,
implies(X,not(X)) = not(and(X,X)),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),not(not(implies(X,not(X))))) )],[refute_0_554,refute_0_564]) ).
cnf(refute_0_566,plain,
implies(Y,not(Y)) = not(and(Y,Y)),
inference(subst,[],[refute_0_565:[bind(X,$fot(Y))]]) ).
cnf(refute_0_567,plain,
( and(Y,Y) != not(implies(Y,not(Y)))
| implies(Y,not(Y)) != not(and(Y,Y))
| and(Y,Y) = not(not(and(Y,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(Y,Y),not(implies(Y,not(Y)))) ),[1,0],$fot(not(and(Y,Y)))]]) ).
cnf(refute_0_568,plain,
( and(Y,Y) != not(implies(Y,not(Y)))
| and(Y,Y) = not(not(and(Y,Y))) ),
inference(resolve,[$cnf( $equal(implies(Y,not(Y)),not(and(Y,Y))) )],[refute_0_566,refute_0_567]) ).
cnf(refute_0_569,plain,
and(Y,Y) = not(not(and(Y,Y))),
inference(resolve,[$cnf( $equal(and(Y,Y),not(implies(Y,not(Y)))) )],[refute_0_445,refute_0_568]) ).
cnf(refute_0_570,plain,
and(implies(X,X),implies(X,X)) = not(not(and(implies(X,X),implies(X,X)))),
inference(subst,[],[refute_0_569:[bind(Y,$fot(implies(X,X)))]]) ).
cnf(refute_0_571,plain,
equiv(X,X) = and(implies(X,X),implies(X,X)),
inference(subst,[],[refute_0_398:[bind(Y,$fot(X))]]) ).
cnf(refute_0_572,plain,
( equiv(X,X) != and(implies(X,X),implies(X,X))
| and(implies(X,X),implies(X,X)) = equiv(X,X) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(X,X))),bind(Y0,$fot(and(implies(X,X),implies(X,X))))]]) ).
cnf(refute_0_573,plain,
and(implies(X,X),implies(X,X)) = equiv(X,X),
inference(resolve,[$cnf( $equal(equiv(X,X),and(implies(X,X),implies(X,X))) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
( and(implies(X,X),implies(X,X)) != equiv(X,X)
| and(implies(X,X),implies(X,X)) != not(not(and(implies(X,X),implies(X,X))))
| and(implies(X,X),implies(X,X)) = not(not(equiv(X,X))) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(X,X),implies(X,X)),not(not(and(implies(X,X),implies(X,X))))) ),[1,0,0],$fot(equiv(X,X))]]) ).
cnf(refute_0_575,plain,
( and(implies(X,X),implies(X,X)) != not(not(and(implies(X,X),implies(X,X))))
| and(implies(X,X),implies(X,X)) = not(not(equiv(X,X))) ),
inference(resolve,[$cnf( $equal(and(implies(X,X),implies(X,X)),equiv(X,X)) )],[refute_0_573,refute_0_574]) ).
cnf(refute_0_576,plain,
and(implies(X,X),implies(X,X)) = not(not(equiv(X,X))),
inference(resolve,[$cnf( $equal(and(implies(X,X),implies(X,X)),not(not(and(implies(X,X),implies(X,X))))) )],[refute_0_570,refute_0_575]) ).
cnf(refute_0_577,plain,
( and(implies(X,X),implies(X,X)) != equiv(X,X)
| and(implies(X,X),implies(X,X)) != not(not(equiv(X,X)))
| equiv(X,X) = not(not(equiv(X,X))) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(X,X),implies(X,X)),not(not(equiv(X,X)))) ),[0],$fot(equiv(X,X))]]) ).
cnf(refute_0_578,plain,
( and(implies(X,X),implies(X,X)) != not(not(equiv(X,X)))
| equiv(X,X) = not(not(equiv(X,X))) ),
inference(resolve,[$cnf( $equal(and(implies(X,X),implies(X,X)),equiv(X,X)) )],[refute_0_573,refute_0_577]) ).
cnf(refute_0_579,plain,
equiv(X,X) = not(not(equiv(X,X))),
inference(resolve,[$cnf( $equal(and(implies(X,X),implies(X,X)),not(not(equiv(X,X)))) )],[refute_0_576,refute_0_578]) ).
cnf(refute_0_580,plain,
( equiv(X,X) != not(not(equiv(X,X)))
| not(not(equiv(X,X))) = equiv(X,X) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(X,X))),bind(Y0,$fot(not(not(equiv(X,X)))))]]) ).
cnf(refute_0_581,plain,
not(not(equiv(X,X))) = equiv(X,X),
inference(resolve,[$cnf( $equal(equiv(X,X),not(not(equiv(X,X)))) )],[refute_0_579,refute_0_580]) ).
cnf(refute_0_582,plain,
not(not(equiv(X_5450,X_5450))) = equiv(X_5450,X_5450),
inference(subst,[],[refute_0_581:[bind(X,$fot(X_5450))]]) ).
cnf(refute_0_583,plain,
and(implies(X_5450,X_5450),implies(X_5450,X_5450)) = equiv(X_5450,X_5450),
inference(subst,[],[refute_0_414:[bind(X,$fot(X_5450)),bind(Y,$fot(X_5450))]]) ).
cnf(refute_0_584,plain,
not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))) = not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))),
introduced(tautology,[refl,[$fot(not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))))]]) ).
cnf(refute_0_585,plain,
( and(implies(X_5450,X_5450),implies(X_5450,X_5450)) != equiv(X_5450,X_5450)
| not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))) != not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))
| not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))) = not(equiv(X_5450,X_5450)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))),not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))) ),[1,0],$fot(equiv(X_5450,X_5450))]]) ).
cnf(refute_0_586,plain,
( and(implies(X_5450,X_5450),implies(X_5450,X_5450)) != equiv(X_5450,X_5450)
| not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))) = not(equiv(X_5450,X_5450)) ),
inference(resolve,[$cnf( $equal(not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))),not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))) )],[refute_0_584,refute_0_585]) ).
cnf(refute_0_587,plain,
not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))) = not(equiv(X_5450,X_5450)),
inference(resolve,[$cnf( $equal(and(implies(X_5450,X_5450),implies(X_5450,X_5450)),equiv(X_5450,X_5450)) )],[refute_0_583,refute_0_586]) ).
cnf(refute_0_588,plain,
implies(implies(X_5450,X_5450),and(X_5450,not(X_5450))) = not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))),
inference(subst,[],[refute_0_166:[bind(X,$fot(implies(X_5450,X_5450))),bind(X_5,$fot(X_5450)),bind(X_6,$fot(X_5450))]]) ).
cnf(refute_0_589,plain,
or(and(X_5450,not(X_5450)),and(X_5450,not(X_5450))) = implies(implies(X_5450,X_5450),and(X_5450,not(X_5450))),
inference(subst,[],[refute_0_155:[bind(X,$fot(X_5450)),bind(Y,$fot(X_5450)),bind(X_8,$fot(and(X_5450,not(X_5450))))]]) ).
cnf(refute_0_590,plain,
( implies(implies(X_5450,X_5450),and(X_5450,not(X_5450))) != not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))
| or(and(X_5450,not(X_5450)),and(X_5450,not(X_5450))) != implies(implies(X_5450,X_5450),and(X_5450,not(X_5450)))
| or(and(X_5450,not(X_5450)),and(X_5450,not(X_5450))) = not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(or(and(X_5450,not(X_5450)),and(X_5450,not(X_5450))))),bind(Y0,$fot(implies(implies(X_5450,X_5450),and(X_5450,not(X_5450))))),bind(Z,$fot(not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))))]]) ).
cnf(refute_0_591,plain,
( implies(implies(X_5450,X_5450),and(X_5450,not(X_5450))) != not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))
| or(and(X_5450,not(X_5450)),and(X_5450,not(X_5450))) = not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))) ),
inference(resolve,[$cnf( $equal(or(and(X_5450,not(X_5450)),and(X_5450,not(X_5450))),implies(implies(X_5450,X_5450),and(X_5450,not(X_5450)))) )],[refute_0_589,refute_0_590]) ).
cnf(refute_0_592,plain,
or(and(X_5450,not(X_5450)),and(X_5450,not(X_5450))) = not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))),
inference(resolve,[$cnf( $equal(implies(implies(X_5450,X_5450),and(X_5450,not(X_5450))),not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))) )],[refute_0_588,refute_0_591]) ).
cnf(refute_0_593,plain,
not(and(not(and(X_5450,not(X_5450))),implies(X_5450,X_5450))) = or(and(X_5450,not(X_5450)),and(X_5450,not(X_5450))),
inference(subst,[],[refute_0_240:[bind(X,$fot(and(X_5450,not(X_5450)))),bind(X_47,$fot(X_5450)),bind(X_48,$fot(X_5450))]]) ).
cnf(refute_0_594,plain,
( not(and(not(and(X_5450,not(X_5450))),implies(X_5450,X_5450))) != or(and(X_5450,not(X_5450)),and(X_5450,not(X_5450)))
| or(and(X_5450,not(X_5450)),and(X_5450,not(X_5450))) != not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))
| not(and(not(and(X_5450,not(X_5450))),implies(X_5450,X_5450))) = not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(not(and(not(and(X_5450,not(X_5450))),implies(X_5450,X_5450))))),bind(Y0,$fot(or(and(X_5450,not(X_5450)),and(X_5450,not(X_5450))))),bind(Z,$fot(not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))))]]) ).
cnf(refute_0_595,plain,
( or(and(X_5450,not(X_5450)),and(X_5450,not(X_5450))) != not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))
| not(and(not(and(X_5450,not(X_5450))),implies(X_5450,X_5450))) = not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))) ),
inference(resolve,[$cnf( $equal(not(and(not(and(X_5450,not(X_5450))),implies(X_5450,X_5450))),or(and(X_5450,not(X_5450)),and(X_5450,not(X_5450)))) )],[refute_0_593,refute_0_594]) ).
cnf(refute_0_596,plain,
not(and(not(and(X_5450,not(X_5450))),implies(X_5450,X_5450))) = not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))),
inference(resolve,[$cnf( $equal(or(and(X_5450,not(X_5450)),and(X_5450,not(X_5450))),not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))) )],[refute_0_592,refute_0_595]) ).
cnf(refute_0_597,plain,
implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))) = not(and(not(and(X_5450,not(X_5450))),implies(X_5450,X_5450))),
inference(subst,[],[refute_0_166:[bind(X,$fot(not(and(X_5450,not(X_5450))))),bind(X_5,$fot(X_5450)),bind(X_6,$fot(X_5450))]]) ).
cnf(refute_0_598,plain,
( implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))) != not(and(not(and(X_5450,not(X_5450))),implies(X_5450,X_5450)))
| not(and(not(and(X_5450,not(X_5450))),implies(X_5450,X_5450))) != not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))
| implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))) = not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))))),bind(Y0,$fot(not(and(not(and(X_5450,not(X_5450))),implies(X_5450,X_5450))))),bind(Z,$fot(not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))))]]) ).
cnf(refute_0_599,plain,
( not(and(not(and(X_5450,not(X_5450))),implies(X_5450,X_5450))) != not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))
| implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))) = not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))) ),
inference(resolve,[$cnf( $equal(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))),not(and(not(and(X_5450,not(X_5450))),implies(X_5450,X_5450)))) )],[refute_0_597,refute_0_598]) ).
cnf(refute_0_600,plain,
implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))) = not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))),
inference(resolve,[$cnf( $equal(not(and(not(and(X_5450,not(X_5450))),implies(X_5450,X_5450))),not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))) )],[refute_0_596,refute_0_599]) ).
cnf(refute_0_601,plain,
( implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))) != not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))
| not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))) != not(equiv(X_5450,X_5450))
| implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))) = not(equiv(X_5450,X_5450)) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))))),bind(Y0,$fot(not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))))),bind(Z,$fot(not(equiv(X_5450,X_5450))))]]) ).
cnf(refute_0_602,plain,
( not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))) != not(equiv(X_5450,X_5450))
| implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))) = not(equiv(X_5450,X_5450)) ),
inference(resolve,[$cnf( $equal(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))),not(and(implies(X_5450,X_5450),implies(X_5450,X_5450)))) )],[refute_0_600,refute_0_601]) ).
cnf(refute_0_603,plain,
implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))) = not(equiv(X_5450,X_5450)),
inference(resolve,[$cnf( $equal(not(and(implies(X_5450,X_5450),implies(X_5450,X_5450))),not(equiv(X_5450,X_5450))) )],[refute_0_587,refute_0_602]) ).
cnf(refute_0_604,plain,
not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))) = not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))),
introduced(tautology,[refl,[$fot(not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))))]]) ).
cnf(refute_0_605,plain,
( implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))) != not(equiv(X_5450,X_5450))
| not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))) != not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))))
| not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))) = not(not(equiv(X_5450,X_5450))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))),not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))))) ),[1,0],$fot(not(equiv(X_5450,X_5450)))]]) ).
cnf(refute_0_606,plain,
( implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))) != not(equiv(X_5450,X_5450))
| not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))) = not(not(equiv(X_5450,X_5450))) ),
inference(resolve,[$cnf( $equal(not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))),not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))))) )],[refute_0_604,refute_0_605]) ).
cnf(refute_0_607,plain,
not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))) = not(not(equiv(X_5450,X_5450))),
inference(resolve,[$cnf( $equal(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))),not(equiv(X_5450,X_5450))) )],[refute_0_603,refute_0_606]) ).
cnf(refute_0_608,plain,
( not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))) != not(not(equiv(X_5450,X_5450)))
| not(not(equiv(X_5450,X_5450))) != equiv(X_5450,X_5450)
| not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))) = equiv(X_5450,X_5450) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))))),bind(Y0,$fot(not(not(equiv(X_5450,X_5450))))),bind(Z,$fot(equiv(X_5450,X_5450)))]]) ).
cnf(refute_0_609,plain,
( not(not(equiv(X_5450,X_5450))) != equiv(X_5450,X_5450)
| not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))) = equiv(X_5450,X_5450) ),
inference(resolve,[$cnf( $equal(not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))),not(not(equiv(X_5450,X_5450)))) )],[refute_0_607,refute_0_608]) ).
cnf(refute_0_610,plain,
not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))) = equiv(X_5450,X_5450),
inference(resolve,[$cnf( $equal(not(not(equiv(X_5450,X_5450))),equiv(X_5450,X_5450)) )],[refute_0_582,refute_0_609]) ).
cnf(refute_0_611,plain,
and(not(and(X_5450,not(X_5450))),implies(X_5450,not(not(X_5450)))) = not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))),
inference(subst,[],[refute_0_124:[bind(X,$fot(not(and(X_5450,not(X_5450))))),bind(X_1,$fot(X_5450)),bind(X_2,$fot(not(X_5450)))]]) ).
cnf(refute_0_612,plain,
and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))) = and(not(and(X_5450,not(X_5450))),implies(X_5450,not(not(X_5450)))),
inference(subst,[],[refute_0_429:[bind(X,$fot(X_5450)),bind(Y,$fot(not(X_5450))),bind(X_32,$fot(implies(X_5450,not(not(X_5450)))))]]) ).
cnf(refute_0_613,plain,
( and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))) != and(not(and(X_5450,not(X_5450))),implies(X_5450,not(not(X_5450))))
| and(not(and(X_5450,not(X_5450))),implies(X_5450,not(not(X_5450)))) != not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))))
| and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))) = not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))))),bind(Y0,$fot(and(not(and(X_5450,not(X_5450))),implies(X_5450,not(not(X_5450)))))),bind(Z,$fot(not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))))))]]) ).
cnf(refute_0_614,plain,
( and(not(and(X_5450,not(X_5450))),implies(X_5450,not(not(X_5450)))) != not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))))
| and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))) = not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))) ),
inference(resolve,[$cnf( $equal(and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))),and(not(and(X_5450,not(X_5450))),implies(X_5450,not(not(X_5450))))) )],[refute_0_612,refute_0_613]) ).
cnf(refute_0_615,plain,
and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))) = not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))),
inference(resolve,[$cnf( $equal(and(not(and(X_5450,not(X_5450))),implies(X_5450,not(not(X_5450)))),not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))))) )],[refute_0_611,refute_0_614]) ).
cnf(refute_0_616,plain,
( and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))) != not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))))
| not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))) != equiv(X_5450,X_5450)
| and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))) = equiv(X_5450,X_5450) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))))),bind(Y0,$fot(not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))))),bind(Z,$fot(equiv(X_5450,X_5450)))]]) ).
cnf(refute_0_617,plain,
( not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))) != equiv(X_5450,X_5450)
| and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))) = equiv(X_5450,X_5450) ),
inference(resolve,[$cnf( $equal(and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))),not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450))))) )],[refute_0_615,refute_0_616]) ).
cnf(refute_0_618,plain,
and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))) = equiv(X_5450,X_5450),
inference(resolve,[$cnf( $equal(not(implies(not(and(X_5450,not(X_5450))),and(X_5450,not(X_5450)))),equiv(X_5450,X_5450)) )],[refute_0_610,refute_0_617]) ).
cnf(refute_0_619,plain,
( and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))) != equiv(X_5450,X_5450)
| ~ is_a_theorem(and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))))
| is_a_theorem(equiv(X_5450,X_5450)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450))))) ),[0],$fot(equiv(X_5450,X_5450))]]) ).
cnf(refute_0_620,plain,
( ~ is_a_theorem(and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))))
| is_a_theorem(equiv(X_5450,X_5450)) ),
inference(resolve,[$cnf( $equal(and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450)))),equiv(X_5450,X_5450)) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
is_a_theorem(equiv(X_5450,X_5450)),
inference(resolve,[$cnf( is_a_theorem(and(implies(X_5450,not(not(X_5450))),implies(X_5450,not(not(X_5450))))) )],[refute_0_444,refute_0_620]) ).
cnf(refute_0_622,plain,
is_a_theorem(equiv(X_5451,X_5451)),
inference(subst,[],[refute_0_621:[bind(X_5450,$fot(X_5451))]]) ).
cnf(refute_0_623,plain,
X_5451 = not(not(X_5451)),
inference(resolve,[$cnf( is_a_theorem(equiv(X_5451,X_5451)) )],[refute_0_622,refute_0_441]) ).
cnf(refute_0_624,plain,
( X_5451 != not(not(X_5451))
| not(not(X_5451)) = X_5451 ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(X_5451)),bind(Y0,$fot(not(not(X_5451))))]]) ).
cnf(refute_0_625,plain,
not(not(X_5451)) = X_5451,
inference(resolve,[$cnf( $equal(X_5451,not(not(X_5451))) )],[refute_0_623,refute_0_624]) ).
cnf(refute_0_626,plain,
not(not(implies(X_5448,X_5448))) = implies(X_5448,X_5448),
inference(subst,[],[refute_0_625:[bind(X_5451,$fot(implies(X_5448,X_5448)))]]) ).
cnf(refute_0_627,plain,
( ~ is_a_theorem(equiv(X,and(X_281,not(X_282))))
| X = and(X_281,not(X_282)) ),
inference(subst,[],[refute_0_394:[bind(Y,$fot(and(X_281,not(X_282))))]]) ).
cnf(refute_0_628,plain,
equiv(X,and(X_47,not(X_48))) = and(implies(X,and(X_47,not(X_48))),implies(and(X_47,not(X_48)),X)),
inference(subst,[],[refute_0_398:[bind(Y,$fot(and(X_47,not(X_48))))]]) ).
cnf(refute_0_629,plain,
implies(X,and(X_47,not(X_48))) = not(and(X,implies(X_47,X_48))),
inference(subst,[],[refute_0_166:[bind(X_5,$fot(X_47)),bind(X_6,$fot(X_48))]]) ).
cnf(refute_0_630,plain,
( equiv(X,and(X_47,not(X_48))) != and(implies(X,and(X_47,not(X_48))),implies(and(X_47,not(X_48)),X))
| implies(X,and(X_47,not(X_48))) != not(and(X,implies(X_47,X_48)))
| equiv(X,and(X_47,not(X_48))) = and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X,and(X_47,not(X_48))),and(implies(X,and(X_47,not(X_48))),implies(and(X_47,not(X_48)),X))) ),[1,0],$fot(not(and(X,implies(X_47,X_48))))]]) ).
cnf(refute_0_631,plain,
( equiv(X,and(X_47,not(X_48))) != and(implies(X,and(X_47,not(X_48))),implies(and(X_47,not(X_48)),X))
| equiv(X,and(X_47,not(X_48))) = and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)) ),
inference(resolve,[$cnf( $equal(implies(X,and(X_47,not(X_48))),not(and(X,implies(X_47,X_48)))) )],[refute_0_629,refute_0_630]) ).
cnf(refute_0_632,plain,
equiv(X,and(X_47,not(X_48))) = and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)),
inference(resolve,[$cnf( $equal(equiv(X,and(X_47,not(X_48))),and(implies(X,and(X_47,not(X_48))),implies(and(X_47,not(X_48)),X))) )],[refute_0_628,refute_0_631]) ).
cnf(refute_0_633,plain,
and(not(not(implies(X_16,not(X)))),or(X,X_16)) = and(implies(X_16,not(X)),or(X,X_16)),
inference(subst,[],[refute_0_57:[bind(Y,$fot(or(X,X_16))),bind(X_12,$fot(implies(X_16,not(X))))]]) ).
cnf(refute_0_634,plain,
( equiv(X_16,not(X)) != and(implies(X_16,not(X)),or(X,X_16))
| and(implies(X_16,not(X)),or(X,X_16)) = equiv(X_16,not(X)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(X_16,not(X)))),bind(Y0,$fot(and(implies(X_16,not(X)),or(X,X_16))))]]) ).
cnf(refute_0_635,plain,
and(implies(X_16,not(X)),or(X,X_16)) = equiv(X_16,not(X)),
inference(resolve,[$cnf( $equal(equiv(X_16,not(X)),and(implies(X_16,not(X)),or(X,X_16))) )],[refute_0_405,refute_0_634]) ).
cnf(refute_0_636,plain,
( and(implies(X_16,not(X)),or(X,X_16)) != equiv(X_16,not(X))
| and(not(not(implies(X_16,not(X)))),or(X,X_16)) != and(implies(X_16,not(X)),or(X,X_16))
| and(not(not(implies(X_16,not(X)))),or(X,X_16)) = equiv(X_16,not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(implies(X_16,not(X)))),or(X,X_16)),and(implies(X_16,not(X)),or(X,X_16))) ),[1],$fot(equiv(X_16,not(X)))]]) ).
cnf(refute_0_637,plain,
( and(not(not(implies(X_16,not(X)))),or(X,X_16)) != and(implies(X_16,not(X)),or(X,X_16))
| and(not(not(implies(X_16,not(X)))),or(X,X_16)) = equiv(X_16,not(X)) ),
inference(resolve,[$cnf( $equal(and(implies(X_16,not(X)),or(X,X_16)),equiv(X_16,not(X))) )],[refute_0_635,refute_0_636]) ).
cnf(refute_0_638,plain,
and(not(not(implies(X_16,not(X)))),or(X,X_16)) = equiv(X_16,not(X)),
inference(resolve,[$cnf( $equal(and(not(not(implies(X_16,not(X)))),or(X,X_16)),and(implies(X_16,not(X)),or(X,X_16))) )],[refute_0_633,refute_0_637]) ).
cnf(refute_0_639,plain,
and(implies(X_16,not(X)),or(X,X_16)) = and(not(and(X_16,X)),or(X,X_16)),
inference(subst,[],[refute_0_429:[bind(X,$fot(X_16)),bind(Y,$fot(X)),bind(X_32,$fot(or(X,X_16)))]]) ).
cnf(refute_0_640,plain,
( and(implies(X_16,not(X)),or(X,X_16)) != and(not(and(X_16,X)),or(X,X_16))
| and(not(not(implies(X_16,not(X)))),or(X,X_16)) != and(implies(X_16,not(X)),or(X,X_16))
| and(not(not(implies(X_16,not(X)))),or(X,X_16)) = and(not(and(X_16,X)),or(X,X_16)) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(and(not(not(implies(X_16,not(X)))),or(X,X_16)))),bind(Y0,$fot(and(implies(X_16,not(X)),or(X,X_16)))),bind(Z,$fot(and(not(and(X_16,X)),or(X,X_16))))]]) ).
cnf(refute_0_641,plain,
( and(implies(X_16,not(X)),or(X,X_16)) != and(not(and(X_16,X)),or(X,X_16))
| and(not(not(implies(X_16,not(X)))),or(X,X_16)) = and(not(and(X_16,X)),or(X,X_16)) ),
inference(resolve,[$cnf( $equal(and(not(not(implies(X_16,not(X)))),or(X,X_16)),and(implies(X_16,not(X)),or(X,X_16))) )],[refute_0_633,refute_0_640]) ).
cnf(refute_0_642,plain,
and(not(not(implies(X_16,not(X)))),or(X,X_16)) = and(not(and(X_16,X)),or(X,X_16)),
inference(resolve,[$cnf( $equal(and(implies(X_16,not(X)),or(X,X_16)),and(not(and(X_16,X)),or(X,X_16))) )],[refute_0_639,refute_0_641]) ).
cnf(refute_0_643,plain,
( and(not(not(implies(X_16,not(X)))),or(X,X_16)) != and(not(and(X_16,X)),or(X,X_16))
| and(not(not(implies(X_16,not(X)))),or(X,X_16)) != equiv(X_16,not(X))
| and(not(and(X_16,X)),or(X,X_16)) = equiv(X_16,not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(implies(X_16,not(X)))),or(X,X_16)),equiv(X_16,not(X))) ),[0],$fot(and(not(and(X_16,X)),or(X,X_16)))]]) ).
cnf(refute_0_644,plain,
( and(not(not(implies(X_16,not(X)))),or(X,X_16)) != equiv(X_16,not(X))
| and(not(and(X_16,X)),or(X,X_16)) = equiv(X_16,not(X)) ),
inference(resolve,[$cnf( $equal(and(not(not(implies(X_16,not(X)))),or(X,X_16)),and(not(and(X_16,X)),or(X,X_16))) )],[refute_0_642,refute_0_643]) ).
cnf(refute_0_645,plain,
and(not(and(X_16,X)),or(X,X_16)) = equiv(X_16,not(X)),
inference(resolve,[$cnf( $equal(and(not(not(implies(X_16,not(X)))),or(X,X_16)),equiv(X_16,not(X))) )],[refute_0_638,refute_0_644]) ).
cnf(refute_0_646,plain,
and(not(and(X,implies(X_47,X_48))),or(implies(X_47,X_48),X)) = equiv(X,not(implies(X_47,X_48))),
inference(subst,[],[refute_0_645:[bind(X,$fot(implies(X_47,X_48))),bind(X_16,$fot(X))]]) ).
cnf(refute_0_647,plain,
implies(and(X_47,not(X_48)),X) = or(implies(X_47,X_48),X),
inference(subst,[],[refute_0_72:[bind(X,$fot(X_47)),bind(Y,$fot(X_48)),bind(X_13,$fot(X))]]) ).
cnf(refute_0_648,plain,
and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)) = and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)),
introduced(tautology,[refl,[$fot(and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)))]]) ).
cnf(refute_0_649,plain,
( and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)) != and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X))
| implies(and(X_47,not(X_48)),X) != or(implies(X_47,X_48),X)
| and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)) = and(not(and(X,implies(X_47,X_48))),or(implies(X_47,X_48),X)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)),and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X))) ),[1,1],$fot(or(implies(X_47,X_48),X))]]) ).
cnf(refute_0_650,plain,
( implies(and(X_47,not(X_48)),X) != or(implies(X_47,X_48),X)
| and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)) = and(not(and(X,implies(X_47,X_48))),or(implies(X_47,X_48),X)) ),
inference(resolve,[$cnf( $equal(and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)),and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X))) )],[refute_0_648,refute_0_649]) ).
cnf(refute_0_651,plain,
and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)) = and(not(and(X,implies(X_47,X_48))),or(implies(X_47,X_48),X)),
inference(resolve,[$cnf( $equal(implies(and(X_47,not(X_48)),X),or(implies(X_47,X_48),X)) )],[refute_0_647,refute_0_650]) ).
cnf(refute_0_652,plain,
( and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)) != and(not(and(X,implies(X_47,X_48))),or(implies(X_47,X_48),X))
| and(not(and(X,implies(X_47,X_48))),or(implies(X_47,X_48),X)) != equiv(X,not(implies(X_47,X_48)))
| and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)) = equiv(X,not(implies(X_47,X_48))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)))),bind(Y0,$fot(and(not(and(X,implies(X_47,X_48))),or(implies(X_47,X_48),X)))),bind(Z,$fot(equiv(X,not(implies(X_47,X_48)))))]]) ).
cnf(refute_0_653,plain,
( and(not(and(X,implies(X_47,X_48))),or(implies(X_47,X_48),X)) != equiv(X,not(implies(X_47,X_48)))
| and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)) = equiv(X,not(implies(X_47,X_48))) ),
inference(resolve,[$cnf( $equal(and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)),and(not(and(X,implies(X_47,X_48))),or(implies(X_47,X_48),X))) )],[refute_0_651,refute_0_652]) ).
cnf(refute_0_654,plain,
and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)) = equiv(X,not(implies(X_47,X_48))),
inference(resolve,[$cnf( $equal(and(not(and(X,implies(X_47,X_48))),or(implies(X_47,X_48),X)),equiv(X,not(implies(X_47,X_48)))) )],[refute_0_646,refute_0_653]) ).
cnf(refute_0_655,plain,
( and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)) != equiv(X,not(implies(X_47,X_48)))
| equiv(X,and(X_47,not(X_48))) != and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X))
| equiv(X,and(X_47,not(X_48))) = equiv(X,not(implies(X_47,X_48))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X,and(X_47,not(X_48))),and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X))) ),[1],$fot(equiv(X,not(implies(X_47,X_48))))]]) ).
cnf(refute_0_656,plain,
( equiv(X,and(X_47,not(X_48))) != and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X))
| equiv(X,and(X_47,not(X_48))) = equiv(X,not(implies(X_47,X_48))) ),
inference(resolve,[$cnf( $equal(and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X)),equiv(X,not(implies(X_47,X_48)))) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
equiv(X,and(X_47,not(X_48))) = equiv(X,not(implies(X_47,X_48))),
inference(resolve,[$cnf( $equal(equiv(X,and(X_47,not(X_48))),and(not(and(X,implies(X_47,X_48))),implies(and(X_47,not(X_48)),X))) )],[refute_0_632,refute_0_656]) ).
cnf(refute_0_658,plain,
equiv(X,and(X_281,not(X_282))) = equiv(X,not(implies(X_281,X_282))),
inference(subst,[],[refute_0_657:[bind(X_47,$fot(X_281)),bind(X_48,$fot(X_282))]]) ).
cnf(refute_0_659,plain,
( equiv(X,and(X_281,not(X_282))) != equiv(X,not(implies(X_281,X_282)))
| ~ is_a_theorem(equiv(X,not(implies(X_281,X_282))))
| is_a_theorem(equiv(X,and(X_281,not(X_282)))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(equiv(X,and(X_281,not(X_282)))) ),[0],$fot(equiv(X,not(implies(X_281,X_282))))]]) ).
cnf(refute_0_660,plain,
( ~ is_a_theorem(equiv(X,not(implies(X_281,X_282))))
| is_a_theorem(equiv(X,and(X_281,not(X_282)))) ),
inference(resolve,[$cnf( $equal(equiv(X,and(X_281,not(X_282))),equiv(X,not(implies(X_281,X_282)))) )],[refute_0_658,refute_0_659]) ).
cnf(refute_0_661,plain,
( ~ is_a_theorem(equiv(X,not(implies(X_281,X_282))))
| X = and(X_281,not(X_282)) ),
inference(resolve,[$cnf( is_a_theorem(equiv(X,and(X_281,not(X_282)))) )],[refute_0_660,refute_0_627]) ).
cnf(refute_0_662,plain,
( ~ is_a_theorem(equiv(not(implies(X_281,X_282)),not(implies(X_281,X_282))))
| not(implies(X_281,X_282)) = and(X_281,not(X_282)) ),
inference(subst,[],[refute_0_661:[bind(X,$fot(not(implies(X_281,X_282))))]]) ).
cnf(refute_0_663,plain,
is_a_theorem(equiv(not(implies(X_281,X_282)),not(implies(X_281,X_282)))),
inference(subst,[],[refute_0_621:[bind(X_5450,$fot(not(implies(X_281,X_282))))]]) ).
cnf(refute_0_664,plain,
not(implies(X_281,X_282)) = and(X_281,not(X_282)),
inference(resolve,[$cnf( is_a_theorem(equiv(not(implies(X_281,X_282)),not(implies(X_281,X_282)))) )],[refute_0_663,refute_0_662]) ).
cnf(refute_0_665,plain,
( not(implies(X_281,X_282)) != and(X_281,not(X_282))
| and(X_281,not(X_282)) = not(implies(X_281,X_282)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(not(implies(X_281,X_282)))),bind(Y0,$fot(and(X_281,not(X_282))))]]) ).
cnf(refute_0_666,plain,
and(X_281,not(X_282)) = not(implies(X_281,X_282)),
inference(resolve,[$cnf( $equal(not(implies(X_281,X_282)),and(X_281,not(X_282))) )],[refute_0_664,refute_0_665]) ).
cnf(refute_0_667,plain,
and(X_5448,not(X_5448)) = not(implies(X_5448,X_5448)),
inference(subst,[],[refute_0_666:[bind(X_281,$fot(X_5448)),bind(X_282,$fot(X_5448))]]) ).
cnf(refute_0_668,plain,
not(and(X_5448,not(X_5448))) = not(and(X_5448,not(X_5448))),
introduced(tautology,[refl,[$fot(not(and(X_5448,not(X_5448))))]]) ).
cnf(refute_0_669,plain,
( and(X_5448,not(X_5448)) != not(implies(X_5448,X_5448))
| not(and(X_5448,not(X_5448))) != not(and(X_5448,not(X_5448)))
| not(and(X_5448,not(X_5448))) = not(not(implies(X_5448,X_5448))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(X_5448,not(X_5448))),not(and(X_5448,not(X_5448)))) ),[1,0],$fot(not(implies(X_5448,X_5448)))]]) ).
cnf(refute_0_670,plain,
( and(X_5448,not(X_5448)) != not(implies(X_5448,X_5448))
| not(and(X_5448,not(X_5448))) = not(not(implies(X_5448,X_5448))) ),
inference(resolve,[$cnf( $equal(not(and(X_5448,not(X_5448))),not(and(X_5448,not(X_5448)))) )],[refute_0_668,refute_0_669]) ).
cnf(refute_0_671,plain,
not(and(X_5448,not(X_5448))) = not(not(implies(X_5448,X_5448))),
inference(resolve,[$cnf( $equal(and(X_5448,not(X_5448)),not(implies(X_5448,X_5448))) )],[refute_0_667,refute_0_670]) ).
cnf(refute_0_672,plain,
( not(and(X_5448,not(X_5448))) != not(not(implies(X_5448,X_5448)))
| not(not(implies(X_5448,X_5448))) != implies(X_5448,X_5448)
| not(and(X_5448,not(X_5448))) = implies(X_5448,X_5448) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(not(and(X_5448,not(X_5448))))),bind(Y0,$fot(not(not(implies(X_5448,X_5448))))),bind(Z,$fot(implies(X_5448,X_5448)))]]) ).
cnf(refute_0_673,plain,
( not(not(implies(X_5448,X_5448))) != implies(X_5448,X_5448)
| not(and(X_5448,not(X_5448))) = implies(X_5448,X_5448) ),
inference(resolve,[$cnf( $equal(not(and(X_5448,not(X_5448))),not(not(implies(X_5448,X_5448)))) )],[refute_0_671,refute_0_672]) ).
cnf(refute_0_674,plain,
not(and(X_5448,not(X_5448))) = implies(X_5448,X_5448),
inference(resolve,[$cnf( $equal(not(not(implies(X_5448,X_5448))),implies(X_5448,X_5448)) )],[refute_0_626,refute_0_673]) ).
cnf(refute_0_675,plain,
( ~ is_a_theorem(equiv(X,implies(X_127,not(X_128))))
| X = implies(X_127,not(X_128)) ),
inference(subst,[],[refute_0_394:[bind(Y,$fot(implies(X_127,not(X_128))))]]) ).
cnf(refute_0_676,plain,
equiv(X,implies(X_49,not(X_50))) = and(implies(X,implies(X_49,not(X_50))),implies(implies(X_49,not(X_50)),X)),
inference(subst,[],[refute_0_398:[bind(Y,$fot(implies(X_49,not(X_50))))]]) ).
cnf(refute_0_677,plain,
implies(X,implies(X_49,not(X_50))) = not(and(X,and(X_49,X_50))),
inference(subst,[],[refute_0_298:[bind(X,$fot(X_49)),bind(Y,$fot(X_50)),bind(X_5,$fot(X))]]) ).
cnf(refute_0_678,plain,
( equiv(X,implies(X_49,not(X_50))) != and(implies(X,implies(X_49,not(X_50))),implies(implies(X_49,not(X_50)),X))
| implies(X,implies(X_49,not(X_50))) != not(and(X,and(X_49,X_50)))
| equiv(X,implies(X_49,not(X_50))) = and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X,implies(X_49,not(X_50))),and(implies(X,implies(X_49,not(X_50))),implies(implies(X_49,not(X_50)),X))) ),[1,0],$fot(not(and(X,and(X_49,X_50))))]]) ).
cnf(refute_0_679,plain,
( equiv(X,implies(X_49,not(X_50))) != and(implies(X,implies(X_49,not(X_50))),implies(implies(X_49,not(X_50)),X))
| equiv(X,implies(X_49,not(X_50))) = and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)) ),
inference(resolve,[$cnf( $equal(implies(X,implies(X_49,not(X_50))),not(and(X,and(X_49,X_50)))) )],[refute_0_677,refute_0_678]) ).
cnf(refute_0_680,plain,
equiv(X,implies(X_49,not(X_50))) = and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)),
inference(resolve,[$cnf( $equal(equiv(X,implies(X_49,not(X_50))),and(implies(X,implies(X_49,not(X_50))),implies(implies(X_49,not(X_50)),X))) )],[refute_0_676,refute_0_679]) ).
cnf(refute_0_681,plain,
and(not(and(X,and(X_49,X_50))),or(and(X_49,X_50),X)) = equiv(X,not(and(X_49,X_50))),
inference(subst,[],[refute_0_645:[bind(X,$fot(and(X_49,X_50))),bind(X_16,$fot(X))]]) ).
cnf(refute_0_682,plain,
implies(implies(X_49,not(X_50)),X) = or(and(X_49,X_50),X),
inference(subst,[],[refute_0_132:[bind(X,$fot(X_49)),bind(Y,$fot(X_50)),bind(X_13,$fot(X))]]) ).
cnf(refute_0_683,plain,
and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)) = and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)),
introduced(tautology,[refl,[$fot(and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)))]]) ).
cnf(refute_0_684,plain,
( and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)) != and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X))
| implies(implies(X_49,not(X_50)),X) != or(and(X_49,X_50),X)
| and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)) = and(not(and(X,and(X_49,X_50))),or(and(X_49,X_50),X)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)),and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X))) ),[1,1],$fot(or(and(X_49,X_50),X))]]) ).
cnf(refute_0_685,plain,
( implies(implies(X_49,not(X_50)),X) != or(and(X_49,X_50),X)
| and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)) = and(not(and(X,and(X_49,X_50))),or(and(X_49,X_50),X)) ),
inference(resolve,[$cnf( $equal(and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)),and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X))) )],[refute_0_683,refute_0_684]) ).
cnf(refute_0_686,plain,
and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)) = and(not(and(X,and(X_49,X_50))),or(and(X_49,X_50),X)),
inference(resolve,[$cnf( $equal(implies(implies(X_49,not(X_50)),X),or(and(X_49,X_50),X)) )],[refute_0_682,refute_0_685]) ).
cnf(refute_0_687,plain,
( and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)) != and(not(and(X,and(X_49,X_50))),or(and(X_49,X_50),X))
| and(not(and(X,and(X_49,X_50))),or(and(X_49,X_50),X)) != equiv(X,not(and(X_49,X_50)))
| and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)) = equiv(X,not(and(X_49,X_50))) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)))),bind(Y0,$fot(and(not(and(X,and(X_49,X_50))),or(and(X_49,X_50),X)))),bind(Z,$fot(equiv(X,not(and(X_49,X_50)))))]]) ).
cnf(refute_0_688,plain,
( and(not(and(X,and(X_49,X_50))),or(and(X_49,X_50),X)) != equiv(X,not(and(X_49,X_50)))
| and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)) = equiv(X,not(and(X_49,X_50))) ),
inference(resolve,[$cnf( $equal(and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)),and(not(and(X,and(X_49,X_50))),or(and(X_49,X_50),X))) )],[refute_0_686,refute_0_687]) ).
cnf(refute_0_689,plain,
and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)) = equiv(X,not(and(X_49,X_50))),
inference(resolve,[$cnf( $equal(and(not(and(X,and(X_49,X_50))),or(and(X_49,X_50),X)),equiv(X,not(and(X_49,X_50)))) )],[refute_0_681,refute_0_688]) ).
cnf(refute_0_690,plain,
( and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)) != equiv(X,not(and(X_49,X_50)))
| equiv(X,implies(X_49,not(X_50))) != and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X))
| equiv(X,implies(X_49,not(X_50))) = equiv(X,not(and(X_49,X_50))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X,implies(X_49,not(X_50))),and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X))) ),[1],$fot(equiv(X,not(and(X_49,X_50))))]]) ).
cnf(refute_0_691,plain,
( equiv(X,implies(X_49,not(X_50))) != and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X))
| equiv(X,implies(X_49,not(X_50))) = equiv(X,not(and(X_49,X_50))) ),
inference(resolve,[$cnf( $equal(and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X)),equiv(X,not(and(X_49,X_50)))) )],[refute_0_689,refute_0_690]) ).
cnf(refute_0_692,plain,
equiv(X,implies(X_49,not(X_50))) = equiv(X,not(and(X_49,X_50))),
inference(resolve,[$cnf( $equal(equiv(X,implies(X_49,not(X_50))),and(not(and(X,and(X_49,X_50))),implies(implies(X_49,not(X_50)),X))) )],[refute_0_680,refute_0_691]) ).
cnf(refute_0_693,plain,
equiv(X,implies(X_127,not(X_128))) = equiv(X,not(and(X_127,X_128))),
inference(subst,[],[refute_0_692:[bind(X_49,$fot(X_127)),bind(X_50,$fot(X_128))]]) ).
cnf(refute_0_694,plain,
( equiv(X,implies(X_127,not(X_128))) != equiv(X,not(and(X_127,X_128)))
| ~ is_a_theorem(equiv(X,not(and(X_127,X_128))))
| is_a_theorem(equiv(X,implies(X_127,not(X_128)))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(equiv(X,implies(X_127,not(X_128)))) ),[0],$fot(equiv(X,not(and(X_127,X_128))))]]) ).
cnf(refute_0_695,plain,
( ~ is_a_theorem(equiv(X,not(and(X_127,X_128))))
| is_a_theorem(equiv(X,implies(X_127,not(X_128)))) ),
inference(resolve,[$cnf( $equal(equiv(X,implies(X_127,not(X_128))),equiv(X,not(and(X_127,X_128)))) )],[refute_0_693,refute_0_694]) ).
cnf(refute_0_696,plain,
( ~ is_a_theorem(equiv(X,not(and(X_127,X_128))))
| X = implies(X_127,not(X_128)) ),
inference(resolve,[$cnf( is_a_theorem(equiv(X,implies(X_127,not(X_128)))) )],[refute_0_695,refute_0_675]) ).
cnf(refute_0_697,plain,
( ~ is_a_theorem(equiv(not(and(X_127,X_128)),not(and(X_127,X_128))))
| not(and(X_127,X_128)) = implies(X_127,not(X_128)) ),
inference(subst,[],[refute_0_696:[bind(X,$fot(not(and(X_127,X_128))))]]) ).
cnf(refute_0_698,plain,
is_a_theorem(equiv(not(and(X_127,X_128)),not(and(X_127,X_128)))),
inference(subst,[],[refute_0_621:[bind(X_5450,$fot(not(and(X_127,X_128))))]]) ).
cnf(refute_0_699,plain,
not(and(X_127,X_128)) = implies(X_127,not(X_128)),
inference(resolve,[$cnf( is_a_theorem(equiv(not(and(X_127,X_128)),not(and(X_127,X_128)))) )],[refute_0_698,refute_0_697]) ).
cnf(refute_0_700,plain,
( not(and(X_127,X_128)) != implies(X_127,not(X_128))
| implies(X_127,not(X_128)) = not(and(X_127,X_128)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(not(and(X_127,X_128)))),bind(Y0,$fot(implies(X_127,not(X_128))))]]) ).
cnf(refute_0_701,plain,
implies(X_127,not(X_128)) = not(and(X_127,X_128)),
inference(resolve,[$cnf( $equal(not(and(X_127,X_128)),implies(X_127,not(X_128))) )],[refute_0_699,refute_0_700]) ).
cnf(refute_0_702,plain,
implies(X_5448,not(not(X_5448))) = not(and(X_5448,not(X_5448))),
inference(subst,[],[refute_0_701:[bind(X_127,$fot(X_5448)),bind(X_128,$fot(not(X_5448)))]]) ).
cnf(refute_0_703,plain,
( implies(X_5448,not(not(X_5448))) != not(and(X_5448,not(X_5448)))
| not(and(X_5448,not(X_5448))) != implies(X_5448,X_5448)
| implies(X_5448,not(not(X_5448))) = implies(X_5448,X_5448) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(implies(X_5448,not(not(X_5448))))),bind(Y0,$fot(not(and(X_5448,not(X_5448))))),bind(Z,$fot(implies(X_5448,X_5448)))]]) ).
cnf(refute_0_704,plain,
( not(and(X_5448,not(X_5448))) != implies(X_5448,X_5448)
| implies(X_5448,not(not(X_5448))) = implies(X_5448,X_5448) ),
inference(resolve,[$cnf( $equal(implies(X_5448,not(not(X_5448))),not(and(X_5448,not(X_5448)))) )],[refute_0_702,refute_0_703]) ).
cnf(refute_0_705,plain,
implies(X_5448,not(not(X_5448))) = implies(X_5448,X_5448),
inference(resolve,[$cnf( $equal(not(and(X_5448,not(X_5448))),implies(X_5448,X_5448)) )],[refute_0_674,refute_0_704]) ).
cnf(refute_0_706,plain,
( implies(X_5448,not(not(X_5448))) != implies(X_5448,X_5448)
| ~ is_a_theorem(implies(X_5448,not(not(X_5448))))
| is_a_theorem(implies(X_5448,X_5448)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_5448,not(not(X_5448)))) ),[0],$fot(implies(X_5448,X_5448))]]) ).
cnf(refute_0_707,plain,
( ~ is_a_theorem(implies(X_5448,not(not(X_5448))))
| is_a_theorem(implies(X_5448,X_5448)) ),
inference(resolve,[$cnf( $equal(implies(X_5448,not(not(X_5448))),implies(X_5448,X_5448)) )],[refute_0_705,refute_0_706]) ).
cnf(refute_0_708,plain,
is_a_theorem(implies(X_5448,X_5448)),
inference(resolve,[$cnf( is_a_theorem(implies(X_5448,not(not(X_5448)))) )],[refute_0_391,refute_0_707]) ).
cnf(refute_0_709,plain,
is_a_theorem(implies(and(X_5639,X_5639),and(X_5639,X_5639))),
inference(subst,[],[refute_0_708:[bind(X_5448,$fot(and(X_5639,X_5639)))]]) ).
cnf(refute_0_710,plain,
( ~ is_a_theorem(not(and(and(X_5449,X_5449),not(Y))))
| is_a_theorem(implies(not(Y),not(X_5449))) ),
inference(subst,[],[refute_0_389:[bind(X,$fot(not(Y))),bind(X_1312,$fot(X_5449))]]) ).
cnf(refute_0_711,plain,
implies(and(X_5449,X_5449),Y) = not(and(and(X_5449,X_5449),not(Y))),
inference(subst,[],[refute_0_32:[bind(X,$fot(and(X_5449,X_5449)))]]) ).
cnf(refute_0_712,plain,
( implies(and(X_5449,X_5449),Y) != not(and(and(X_5449,X_5449),not(Y)))
| not(and(and(X_5449,X_5449),not(Y))) = implies(and(X_5449,X_5449),Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(and(X_5449,X_5449),Y))),bind(Y0,$fot(not(and(and(X_5449,X_5449),not(Y)))))]]) ).
cnf(refute_0_713,plain,
not(and(and(X_5449,X_5449),not(Y))) = implies(and(X_5449,X_5449),Y),
inference(resolve,[$cnf( $equal(implies(and(X_5449,X_5449),Y),not(and(and(X_5449,X_5449),not(Y)))) )],[refute_0_711,refute_0_712]) ).
cnf(refute_0_714,plain,
( not(and(and(X_5449,X_5449),not(Y))) != implies(and(X_5449,X_5449),Y)
| ~ is_a_theorem(implies(and(X_5449,X_5449),Y))
| is_a_theorem(not(and(and(X_5449,X_5449),not(Y)))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(not(and(and(X_5449,X_5449),not(Y)))) ),[0],$fot(implies(and(X_5449,X_5449),Y))]]) ).
cnf(refute_0_715,plain,
( ~ is_a_theorem(implies(and(X_5449,X_5449),Y))
| is_a_theorem(not(and(and(X_5449,X_5449),not(Y)))) ),
inference(resolve,[$cnf( $equal(not(and(and(X_5449,X_5449),not(Y))),implies(and(X_5449,X_5449),Y)) )],[refute_0_713,refute_0_714]) ).
cnf(refute_0_716,plain,
( ~ is_a_theorem(implies(and(X_5449,X_5449),Y))
| is_a_theorem(implies(not(Y),not(X_5449))) ),
inference(resolve,[$cnf( is_a_theorem(not(and(and(X_5449,X_5449),not(Y)))) )],[refute_0_715,refute_0_710]) ).
cnf(refute_0_717,plain,
implies(not(Y),not(X_5449)) = or(Y,not(X_5449)),
inference(subst,[],[refute_0_212:[bind(X,$fot(Y)),bind(Y,$fot(not(X_5449)))]]) ).
cnf(refute_0_718,plain,
( implies(not(Y),not(X_5449)) != or(Y,not(X_5449))
| ~ is_a_theorem(implies(not(Y),not(X_5449)))
| is_a_theorem(or(Y,not(X_5449))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(Y),not(X_5449))) ),[0],$fot(or(Y,not(X_5449)))]]) ).
cnf(refute_0_719,plain,
( ~ is_a_theorem(implies(not(Y),not(X_5449)))
| is_a_theorem(or(Y,not(X_5449))) ),
inference(resolve,[$cnf( $equal(implies(not(Y),not(X_5449)),or(Y,not(X_5449))) )],[refute_0_717,refute_0_718]) ).
cnf(refute_0_720,plain,
( ~ is_a_theorem(implies(and(X_5449,X_5449),Y))
| is_a_theorem(or(Y,not(X_5449))) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(Y),not(X_5449))) )],[refute_0_716,refute_0_719]) ).
cnf(refute_0_721,plain,
( ~ is_a_theorem(implies(and(X_5639,X_5639),and(X_5639,X_5639)))
| is_a_theorem(or(and(X_5639,X_5639),not(X_5639))) ),
inference(subst,[],[refute_0_720:[bind(Y,$fot(and(X_5639,X_5639))),bind(X_5449,$fot(X_5639))]]) ).
cnf(refute_0_722,plain,
is_a_theorem(or(and(X_5639,X_5639),not(X_5639))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_5639,X_5639),and(X_5639,X_5639))) )],[refute_0_709,refute_0_721]) ).
cnf(refute_0_723,plain,
is_a_theorem(or(and(not(X_5451),not(X_5451)),not(not(X_5451)))),
inference(subst,[],[refute_0_722:[bind(X_5639,$fot(not(X_5451)))]]) ).
cnf(refute_0_724,plain,
( not(not(X_5451)) != X_5451
| ~ is_a_theorem(or(and(not(X_5451),not(X_5451)),not(not(X_5451))))
| is_a_theorem(or(and(not(X_5451),not(X_5451)),X_5451)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(X_5451),not(X_5451)),not(not(X_5451)))) ),[0,1],$fot(X_5451)]]) ).
cnf(refute_0_725,plain,
( ~ is_a_theorem(or(and(not(X_5451),not(X_5451)),not(not(X_5451))))
| is_a_theorem(or(and(not(X_5451),not(X_5451)),X_5451)) ),
inference(resolve,[$cnf( $equal(not(not(X_5451)),X_5451) )],[refute_0_625,refute_0_724]) ).
cnf(refute_0_726,plain,
is_a_theorem(or(and(not(X_5451),not(X_5451)),X_5451)),
inference(resolve,[$cnf( is_a_theorem(or(and(not(X_5451),not(X_5451)),not(not(X_5451)))) )],[refute_0_723,refute_0_725]) ).
cnf(refute_0_727,plain,
or(X_5451,not(not(X_5451))) = or(X_5451,not(not(X_5451))),
introduced(tautology,[refl,[$fot(or(X_5451,not(not(X_5451))))]]) ).
cnf(refute_0_728,plain,
( not(not(X_5451)) != X_5451
| or(X_5451,not(not(X_5451))) != or(X_5451,not(not(X_5451)))
| or(X_5451,not(not(X_5451))) = or(X_5451,X_5451) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_5451,not(not(X_5451))),or(X_5451,not(not(X_5451)))) ),[1,1],$fot(X_5451)]]) ).
cnf(refute_0_729,plain,
( not(not(X_5451)) != X_5451
| or(X_5451,not(not(X_5451))) = or(X_5451,X_5451) ),
inference(resolve,[$cnf( $equal(or(X_5451,not(not(X_5451))),or(X_5451,not(not(X_5451)))) )],[refute_0_727,refute_0_728]) ).
cnf(refute_0_730,plain,
or(X_5451,not(not(X_5451))) = or(X_5451,X_5451),
inference(resolve,[$cnf( $equal(not(not(X_5451)),X_5451) )],[refute_0_625,refute_0_729]) ).
cnf(refute_0_731,plain,
implies(or(X_5451,not(not(X_5451))),X_5451) = implies(or(X_5451,not(not(X_5451))),X_5451),
introduced(tautology,[refl,[$fot(implies(or(X_5451,not(not(X_5451))),X_5451))]]) ).
cnf(refute_0_732,plain,
( implies(or(X_5451,not(not(X_5451))),X_5451) != implies(or(X_5451,not(not(X_5451))),X_5451)
| or(X_5451,not(not(X_5451))) != or(X_5451,X_5451)
| implies(or(X_5451,not(not(X_5451))),X_5451) = implies(or(X_5451,X_5451),X_5451) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_5451,not(not(X_5451))),X_5451),implies(or(X_5451,not(not(X_5451))),X_5451)) ),[1,0],$fot(or(X_5451,X_5451))]]) ).
cnf(refute_0_733,plain,
( or(X_5451,not(not(X_5451))) != or(X_5451,X_5451)
| implies(or(X_5451,not(not(X_5451))),X_5451) = implies(or(X_5451,X_5451),X_5451) ),
inference(resolve,[$cnf( $equal(implies(or(X_5451,not(not(X_5451))),X_5451),implies(or(X_5451,not(not(X_5451))),X_5451)) )],[refute_0_731,refute_0_732]) ).
cnf(refute_0_734,plain,
implies(or(X_5451,not(not(X_5451))),X_5451) = implies(or(X_5451,X_5451),X_5451),
inference(resolve,[$cnf( $equal(or(X_5451,not(not(X_5451))),or(X_5451,X_5451)) )],[refute_0_730,refute_0_733]) ).
cnf(refute_0_735,plain,
or(and(not(X_5451),not(X_5451)),X_5451) = implies(or(X_5451,not(not(X_5451))),X_5451),
inference(subst,[],[refute_0_209:[bind(Y,$fot(not(X_5451))),bind(X_13,$fot(X_5451)),bind(X_7,$fot(X_5451))]]) ).
cnf(refute_0_736,plain,
( implies(or(X_5451,not(not(X_5451))),X_5451) != implies(or(X_5451,X_5451),X_5451)
| or(and(not(X_5451),not(X_5451)),X_5451) != implies(or(X_5451,not(not(X_5451))),X_5451)
| or(and(not(X_5451),not(X_5451)),X_5451) = implies(or(X_5451,X_5451),X_5451) ),
inference(subst,[],[refute_0_144:[bind(X0,$fot(or(and(not(X_5451),not(X_5451)),X_5451))),bind(Y0,$fot(implies(or(X_5451,not(not(X_5451))),X_5451))),bind(Z,$fot(implies(or(X_5451,X_5451),X_5451)))]]) ).
cnf(refute_0_737,plain,
( implies(or(X_5451,not(not(X_5451))),X_5451) != implies(or(X_5451,X_5451),X_5451)
| or(and(not(X_5451),not(X_5451)),X_5451) = implies(or(X_5451,X_5451),X_5451) ),
inference(resolve,[$cnf( $equal(or(and(not(X_5451),not(X_5451)),X_5451),implies(or(X_5451,not(not(X_5451))),X_5451)) )],[refute_0_735,refute_0_736]) ).
cnf(refute_0_738,plain,
or(and(not(X_5451),not(X_5451)),X_5451) = implies(or(X_5451,X_5451),X_5451),
inference(resolve,[$cnf( $equal(implies(or(X_5451,not(not(X_5451))),X_5451),implies(or(X_5451,X_5451),X_5451)) )],[refute_0_734,refute_0_737]) ).
cnf(refute_0_739,plain,
( or(and(not(X_5451),not(X_5451)),X_5451) != implies(or(X_5451,X_5451),X_5451)
| ~ is_a_theorem(or(and(not(X_5451),not(X_5451)),X_5451))
| is_a_theorem(implies(or(X_5451,X_5451),X_5451)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(X_5451),not(X_5451)),X_5451)) ),[0],$fot(implies(or(X_5451,X_5451),X_5451))]]) ).
cnf(refute_0_740,plain,
( ~ is_a_theorem(or(and(not(X_5451),not(X_5451)),X_5451))
| is_a_theorem(implies(or(X_5451,X_5451),X_5451)) ),
inference(resolve,[$cnf( $equal(or(and(not(X_5451),not(X_5451)),X_5451),implies(or(X_5451,X_5451),X_5451)) )],[refute_0_738,refute_0_739]) ).
cnf(refute_0_741,plain,
is_a_theorem(implies(or(X_5451,X_5451),X_5451)),
inference(resolve,[$cnf( is_a_theorem(or(and(not(X_5451),not(X_5451)),X_5451)) )],[refute_0_726,refute_0_740]) ).
cnf(refute_0_742,plain,
is_a_theorem(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6)),
inference(subst,[],[refute_0_741:[bind(X_5451,$fot(skolemFOFtoCNF_P_6))]]) ).
cnf(refute_0_743,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6)) )],[refute_0_742,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL518+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 04:22:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 108.06/108.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 108.06/108.25
% 108.06/108.25 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 108.12/108.36
%------------------------------------------------------------------------------