%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL115-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n015.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 12:49:42 EDT 2022

% Result   : Unsatisfiable 2.26s 2.49s
% Output   : CNFRefutation 2.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :  127
%            Number of leaves      :  209
% Syntax   : Number of clauses     :  750 ( 376 unt;   0 nHn; 419 RR)
%            Number of literals    : 1306 (1305 equ; 558 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :   12 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  900 (  33 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
    implies(truth,X) = X ).

cnf(wajsberg_2,axiom,
    implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ).

cnf(wajsberg_3,axiom,
    implies(implies(X,Y),Y) = implies(implies(Y,X),X) ).

cnf(wajsberg_4,axiom,
    implies(implies(not(X),not(Y)),implies(Y,X)) = truth ).

cnf(prove_mv_39,negated_conjecture,
    implies(not(implies(a,b)),not(b)) != truth ).

cnf(refute_0_0,plain,
    implies(implies(X,implies(implies(X,X_25),X_25)),implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))) = truth,
    inference(subst,[],[wajsberg_2:[bind(Y,$fot(implies(implies(X,X_25),X_25)))]]) ).

cnf(refute_0_1,plain,
    implies(implies(truth,X_15),implies(implies(X_15,X_16),implies(truth,X_16))) = truth,
    inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(X_15)),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_2,plain,
    implies(truth,X_16) = X_16,
    inference(subst,[],[wajsberg_1:[bind(X,$fot(X_16))]]) ).

cnf(refute_0_3,plain,
    ( implies(implies(truth,X_15),implies(implies(X_15,X_16),implies(truth,X_16))) != truth
    | implies(truth,X_16) != X_16
    | implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_15),implies(implies(X_15,X_16),implies(truth,X_16))),truth) ),[0,1,1],$fot(X_16)]]) ).

cnf(refute_0_4,plain,
    ( implies(implies(truth,X_15),implies(implies(X_15,X_16),implies(truth,X_16))) != truth
    | implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)) = truth ),
    inference(resolve,[$cnf( $equal(implies(truth,X_16),X_16) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(truth,X_15),implies(implies(X_15,X_16),implies(truth,X_16))),truth) )],[refute_0_1,refute_0_4]) ).

cnf(refute_0_6,plain,
    implies(truth,X_15) = X_15,
    inference(subst,[],[wajsberg_1:[bind(X,$fot(X_15))]]) ).

cnf(refute_0_7,plain,
    implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)) = implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)),
    introduced(tautology,[refl,[$fot(implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)))]]) ).

cnf(refute_0_8,plain,
    ( implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)) != implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16))
    | implies(truth,X_15) != X_15
    | implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)) = implies(X_15,implies(implies(X_15,X_16),X_16)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)),implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16))) ),[1,0],$fot(X_15)]]) ).

cnf(refute_0_9,plain,
    ( implies(truth,X_15) != X_15
    | implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)) = implies(X_15,implies(implies(X_15,X_16),X_16)) ),
    inference(resolve,[$cnf( $equal(implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)),implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16))) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)) = implies(X_15,implies(implies(X_15,X_16),X_16)),
    inference(resolve,[$cnf( $equal(implies(truth,X_15),X_15) )],[refute_0_6,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)) != implies(X_15,implies(implies(X_15,X_16),X_16))
    | implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)) != truth
    | implies(X_15,implies(implies(X_15,X_16),X_16)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)),truth) ),[0],$fot(implies(X_15,implies(implies(X_15,X_16),X_16)))]]) ).

cnf(refute_0_12,plain,
    ( implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)) != truth
    | implies(X_15,implies(implies(X_15,X_16),X_16)) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)),implies(X_15,implies(implies(X_15,X_16),X_16))) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    implies(X_15,implies(implies(X_15,X_16),X_16)) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(truth,X_15),implies(implies(X_15,X_16),X_16)),truth) )],[refute_0_5,refute_0_12]) ).

cnf(refute_0_14,plain,
    implies(X,implies(implies(X,X_25),X_25)) = truth,
    inference(subst,[],[refute_0_13:[bind(X_15,$fot(X)),bind(X_16,$fot(X_25))]]) ).

cnf(refute_0_15,plain,
    ( implies(X,implies(implies(X,X_25),X_25)) != truth
    | implies(implies(X,implies(implies(X,X_25),X_25)),implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))) != truth
    | implies(truth,implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(implies(X,X_25),X_25)),implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))),truth) ),[0,0],$fot(truth)]]) ).

cnf(refute_0_16,plain,
    ( implies(implies(X,implies(implies(X,X_25),X_25)),implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))) != truth
    | implies(truth,implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))) = truth ),
    inference(resolve,[$cnf( $equal(implies(X,implies(implies(X,X_25),X_25)),truth) )],[refute_0_14,refute_0_15]) ).

cnf(refute_0_17,plain,
    implies(truth,implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(X,implies(implies(X,X_25),X_25)),implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))),truth) )],[refute_0_0,refute_0_16]) ).

cnf(refute_0_18,plain,
    implies(truth,implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))) = implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z)),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))))]]) ).

cnf(refute_0_19,plain,
    ( implies(truth,implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))) != implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))
    | implies(truth,implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))) != truth
    | implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))),truth) ),[0],$fot(implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z)))]]) ).

cnf(refute_0_20,plain,
    ( implies(truth,implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))) != truth
    | implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z)) = truth ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))),implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z)) = truth,
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X,X_25),X_25),Z),implies(X,Z))),truth) )],[refute_0_17,refute_0_20]) ).

cnf(refute_0_22,plain,
    implies(implies(implies(implies(X_80,X_82),X_82),implies(implies(not(X_82),not(X_80)),X_82)),implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))) = truth,
    inference(subst,[],[refute_0_21:[bind(X,$fot(X_80)),bind(Z,$fot(implies(implies(not(X_82),not(X_80)),X_82))),bind(X_25,$fot(X_82))]]) ).

cnf(refute_0_23,plain,
    implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))) = truth,
    inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(X),not(Y)))),bind(Y,$fot(implies(Y,X))),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_24,plain,
    ( implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))) != truth
    | implies(implies(not(X),not(Y)),implies(Y,X)) != truth
    | implies(truth,implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))),truth) ),[0,0],$fot(truth)]]) ).

cnf(refute_0_25,plain,
    ( implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))) != truth
    | implies(truth,implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[wajsberg_4,refute_0_24]) ).

cnf(refute_0_26,plain,
    implies(truth,implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))),truth) )],[refute_0_23,refute_0_25]) ).

cnf(refute_0_27,plain,
    implies(truth,implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))) = implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16)),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))))]]) ).

cnf(refute_0_28,plain,
    ( implies(truth,implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))) != implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))
    | implies(truth,implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))) != truth
    | implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))),truth) ),[0],$fot(implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16)))]]) ).

cnf(refute_0_29,plain,
    ( implies(truth,implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))) != truth
    | implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16)) = truth ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))),implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))) )],[refute_0_27,refute_0_28]) ).

cnf(refute_0_30,plain,
    implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16)) = truth,
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(Y,X),X_16),implies(implies(not(X),not(Y)),X_16))),truth) )],[refute_0_26,refute_0_29]) ).

cnf(refute_0_31,plain,
    implies(implies(implies(X_80,X_82),X_82),implies(implies(not(X_82),not(X_80)),X_82)) = truth,
    inference(subst,[],[refute_0_30:[bind(X,$fot(X_82)),bind(Y,$fot(X_80)),bind(X_16,$fot(X_82))]]) ).

cnf(refute_0_32,plain,
    ( implies(implies(implies(X_80,X_82),X_82),implies(implies(not(X_82),not(X_80)),X_82)) != truth
    | implies(implies(implies(implies(X_80,X_82),X_82),implies(implies(not(X_82),not(X_80)),X_82)),implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))) != truth
    | implies(truth,implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_80,X_82),X_82),implies(implies(not(X_82),not(X_80)),X_82)),implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))),truth) ),[0,0],$fot(truth)]]) ).

cnf(refute_0_33,plain,
    ( implies(implies(implies(implies(X_80,X_82),X_82),implies(implies(not(X_82),not(X_80)),X_82)),implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))) != truth
    | implies(truth,implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(X_80,X_82),X_82),implies(implies(not(X_82),not(X_80)),X_82)),truth) )],[refute_0_31,refute_0_32]) ).

cnf(refute_0_34,plain,
    implies(truth,implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_80,X_82),X_82),implies(implies(not(X_82),not(X_80)),X_82)),implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))),truth) )],[refute_0_22,refute_0_33]) ).

cnf(refute_0_35,plain,
    implies(truth,implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))) = implies(X_80,implies(implies(not(X_82),not(X_80)),X_82)),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))))]]) ).

cnf(refute_0_36,plain,
    ( implies(truth,implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))) != implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))
    | implies(truth,implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))) != truth
    | implies(X_80,implies(implies(not(X_82),not(X_80)),X_82)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))),truth) ),[0],$fot(implies(X_80,implies(implies(not(X_82),not(X_80)),X_82)))]]) ).

cnf(refute_0_37,plain,
    ( implies(truth,implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))) != truth
    | implies(X_80,implies(implies(not(X_82),not(X_80)),X_82)) = truth ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))),implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))) )],[refute_0_35,refute_0_36]) ).

cnf(refute_0_38,plain,
    implies(X_80,implies(implies(not(X_82),not(X_80)),X_82)) = truth,
    inference(resolve,[$cnf( $equal(implies(truth,implies(X_80,implies(implies(not(X_82),not(X_80)),X_82))),truth) )],[refute_0_34,refute_0_37]) ).

cnf(refute_0_39,plain,
    implies(not(Y),implies(implies(not(X_84),not(not(Y))),X_84)) = truth,
    inference(subst,[],[refute_0_38:[bind(X_80,$fot(not(Y))),bind(X_82,$fot(X_84))]]) ).

cnf(refute_0_40,plain,
    implies(implies(not(not(Y)),Y),Y) = implies(implies(Y,not(not(Y))),not(not(Y))),
    inference(subst,[],[wajsberg_3:[bind(X,$fot(not(not(Y))))]]) ).

cnf(refute_0_41,plain,
    implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(Y,X_4),X_4)) = truth,
    inference(subst,[],[wajsberg_4:[bind(X,$fot(X_4)),bind(Y,$fot(implies(Y,X_4)))]]) ).

cnf(refute_0_42,plain,
    implies(implies(X_4,Y),Y) = implies(implies(Y,X_4),X_4),
    inference(subst,[],[wajsberg_3:[bind(X,$fot(X_4))]]) ).

cnf(refute_0_43,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_44,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_45,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_43,refute_0_44]) ).

cnf(refute_0_46,plain,
    ( implies(implies(X_4,Y),Y) != implies(implies(Y,X_4),X_4)
    | implies(implies(Y,X_4),X_4) = implies(implies(X_4,Y),Y) ),
    inference(subst,[],[refute_0_45:[bind(X0,$fot(implies(implies(X_4,Y),Y))),bind(Y0,$fot(implies(implies(Y,X_4),X_4)))]]) ).

cnf(refute_0_47,plain,
    implies(implies(Y,X_4),X_4) = implies(implies(X_4,Y),Y),
    inference(resolve,[$cnf( $equal(implies(implies(X_4,Y),Y),implies(implies(Y,X_4),X_4)) )],[refute_0_42,refute_0_46]) ).

cnf(refute_0_48,plain,
    ( implies(implies(Y,X_4),X_4) != implies(implies(X_4,Y),Y)
    | implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(Y,X_4),X_4)) != truth
    | implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(X_4,Y),Y)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(Y,X_4),X_4)),truth) ),[0,1],$fot(implies(implies(X_4,Y),Y))]]) ).

cnf(refute_0_49,plain,
    ( implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(Y,X_4),X_4)) != truth
    | implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(X_4,Y),Y)) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(Y,X_4),X_4),implies(implies(X_4,Y),Y)) )],[refute_0_47,refute_0_48]) ).

cnf(refute_0_50,plain,
    implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(X_4,Y),Y)) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(Y,X_4),X_4)),truth) )],[refute_0_41,refute_0_49]) ).

cnf(refute_0_51,plain,
    implies(implies(not(X_19),not(implies(implies(Y,X_19),X_19))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) = truth,
    inference(subst,[],[refute_0_50:[bind(Y,$fot(implies(Y,X_19))),bind(X_4,$fot(X_19))]]) ).

cnf(refute_0_52,plain,
    implies(implies(X_19,Y),Y) = implies(implies(Y,X_19),X_19),
    inference(subst,[],[wajsberg_3:[bind(X,$fot(X_19))]]) ).

cnf(refute_0_53,plain,
    ( implies(implies(X_19,Y),Y) != implies(implies(Y,X_19),X_19)
    | implies(implies(Y,X_19),X_19) = implies(implies(X_19,Y),Y) ),
    inference(subst,[],[refute_0_45:[bind(X0,$fot(implies(implies(X_19,Y),Y))),bind(Y0,$fot(implies(implies(Y,X_19),X_19)))]]) ).

cnf(refute_0_54,plain,
    implies(implies(Y,X_19),X_19) = implies(implies(X_19,Y),Y),
    inference(resolve,[$cnf( $equal(implies(implies(X_19,Y),Y),implies(implies(Y,X_19),X_19)) )],[refute_0_52,refute_0_53]) ).

cnf(refute_0_55,plain,
    ( implies(implies(Y,X_19),X_19) != implies(implies(X_19,Y),Y)
    | implies(implies(not(X_19),not(implies(implies(Y,X_19),X_19))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) != truth
    | implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_19),not(implies(implies(Y,X_19),X_19))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))),truth) ),[0,0,1,0],$fot(implies(implies(X_19,Y),Y))]]) ).

cnf(refute_0_56,plain,
    ( implies(implies(not(X_19),not(implies(implies(Y,X_19),X_19))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) != truth
    | implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(Y,X_19),X_19),implies(implies(X_19,Y),Y)) )],[refute_0_54,refute_0_55]) ).

cnf(refute_0_57,plain,
    implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(X_19),not(implies(implies(Y,X_19),X_19))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))),truth) )],[refute_0_51,refute_0_56]) ).

cnf(refute_0_58,plain,
    ( implies(implies(X,Y),Y) != implies(implies(Y,X),X)
    | implies(implies(Y,X),X) = implies(implies(X,Y),Y) ),
    inference(subst,[],[refute_0_45:[bind(X0,$fot(implies(implies(X,Y),Y))),bind(Y0,$fot(implies(implies(Y,X),X)))]]) ).

cnf(refute_0_59,plain,
    implies(implies(Y,X),X) = implies(implies(X,Y),Y),
    inference(resolve,[$cnf( $equal(implies(implies(X,Y),Y),implies(implies(Y,X),X)) )],[wajsberg_3,refute_0_58]) ).

cnf(refute_0_60,plain,
    implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19)) = implies(implies(implies(Y,X_19),X_19),X_19),
    inference(subst,[],[refute_0_59:[bind(X,$fot(implies(Y,X_19))),bind(Y,$fot(X_19))]]) ).

cnf(refute_0_61,plain,
    implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) = implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))),
    introduced(tautology,[refl,[$fot(implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))))]]) ).

cnf(refute_0_62,plain,
    ( implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19)) != implies(implies(implies(Y,X_19),X_19),X_19)
    | implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) != implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19)))
    | implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) = implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))),implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19)))) ),[1,1],$fot(implies(implies(implies(Y,X_19),X_19),X_19))]]) ).

cnf(refute_0_63,plain,
    ( implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19)) != implies(implies(implies(Y,X_19),X_19),X_19)
    | implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) = implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19)) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))),implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19)))) )],[refute_0_61,refute_0_62]) ).

cnf(refute_0_64,plain,
    implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) = implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19)),
    inference(resolve,[$cnf( $equal(implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19)),implies(implies(implies(Y,X_19),X_19),X_19)) )],[refute_0_60,refute_0_63]) ).

cnf(refute_0_65,plain,
    ( implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) != implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19))
    | implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) != truth
    | implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))),truth) ),[0],$fot(implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19)))]]) ).

cnf(refute_0_66,plain,
    ( implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) != truth
    | implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19)) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))),implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19))) )],[refute_0_64,refute_0_65]) ).

cnf(refute_0_67,plain,
    implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19)) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))),truth) )],[refute_0_57,refute_0_66]) ).

cnf(refute_0_68,plain,
    implies(implies(not(not(not(Y))),not(implies(implies(not(not(Y)),Y),Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = truth,
    inference(subst,[],[refute_0_67:[bind(X_19,$fot(not(not(Y))))]]) ).

cnf(refute_0_69,plain,
    implies(implies(X_14,implies(not(X_16),not(truth))),implies(implies(implies(not(X_16),not(truth)),X_16),implies(X_14,X_16))) = truth,
    inference(subst,[],[wajsberg_2:[bind(X,$fot(X_14)),bind(Y,$fot(implies(not(X_16),not(truth)))),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_70,plain,
    implies(implies(not(X_4),not(truth)),implies(truth,X_4)) = truth,
    inference(subst,[],[wajsberg_4:[bind(X,$fot(X_4)),bind(Y,$fot(truth))]]) ).

cnf(refute_0_71,plain,
    implies(truth,X_4) = X_4,
    inference(subst,[],[wajsberg_1:[bind(X,$fot(X_4))]]) ).

cnf(refute_0_72,plain,
    ( implies(implies(not(X_4),not(truth)),implies(truth,X_4)) != truth
    | implies(truth,X_4) != X_4
    | implies(implies(not(X_4),not(truth)),X_4) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(truth)),implies(truth,X_4)),truth) ),[0,1],$fot(X_4)]]) ).

cnf(refute_0_73,plain,
    ( implies(implies(not(X_4),not(truth)),implies(truth,X_4)) != truth
    | implies(implies(not(X_4),not(truth)),X_4) = truth ),
    inference(resolve,[$cnf( $equal(implies(truth,X_4),X_4) )],[refute_0_71,refute_0_72]) ).

cnf(refute_0_74,plain,
    implies(implies(not(X_4),not(truth)),X_4) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(truth)),implies(truth,X_4)),truth) )],[refute_0_70,refute_0_73]) ).

cnf(refute_0_75,plain,
    implies(implies(not(X_16),not(truth)),X_16) = truth,
    inference(subst,[],[refute_0_74:[bind(X_4,$fot(X_16))]]) ).

cnf(refute_0_76,plain,
    ( implies(implies(X_14,implies(not(X_16),not(truth))),implies(implies(implies(not(X_16),not(truth)),X_16),implies(X_14,X_16))) != truth
    | implies(implies(not(X_16),not(truth)),X_16) != truth
    | implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_14,implies(not(X_16),not(truth))),implies(implies(implies(not(X_16),not(truth)),X_16),implies(X_14,X_16))),truth) ),[0,1,0],$fot(truth)]]) ).

cnf(refute_0_77,plain,
    ( implies(implies(X_14,implies(not(X_16),not(truth))),implies(implies(implies(not(X_16),not(truth)),X_16),implies(X_14,X_16))) != truth
    | implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_16),not(truth)),X_16),truth) )],[refute_0_75,refute_0_76]) ).

cnf(refute_0_78,plain,
    implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(X_14,implies(not(X_16),not(truth))),implies(implies(implies(not(X_16),not(truth)),X_16),implies(X_14,X_16))),truth) )],[refute_0_69,refute_0_77]) ).

cnf(refute_0_79,plain,
    implies(truth,implies(X_14,X_16)) = implies(X_14,X_16),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_14,X_16)))]]) ).

cnf(refute_0_80,plain,
    implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))) = implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))),
    introduced(tautology,[refl,[$fot(implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))))]]) ).

cnf(refute_0_81,plain,
    ( implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))) != implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16)))
    | implies(truth,implies(X_14,X_16)) != implies(X_14,X_16)
    | implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))) = implies(implies(X_14,implies(not(X_16),not(truth))),implies(X_14,X_16)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))),implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16)))) ),[1,1],$fot(implies(X_14,X_16))]]) ).

cnf(refute_0_82,plain,
    ( implies(truth,implies(X_14,X_16)) != implies(X_14,X_16)
    | implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))) = implies(implies(X_14,implies(not(X_16),not(truth))),implies(X_14,X_16)) ),
    inference(resolve,[$cnf( $equal(implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))),implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16)))) )],[refute_0_80,refute_0_81]) ).

cnf(refute_0_83,plain,
    implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))) = implies(implies(X_14,implies(not(X_16),not(truth))),implies(X_14,X_16)),
    inference(resolve,[$cnf( $equal(implies(truth,implies(X_14,X_16)),implies(X_14,X_16)) )],[refute_0_79,refute_0_82]) ).

cnf(refute_0_84,plain,
    ( implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))) != implies(implies(X_14,implies(not(X_16),not(truth))),implies(X_14,X_16))
    | implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))) != truth
    | implies(implies(X_14,implies(not(X_16),not(truth))),implies(X_14,X_16)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))),truth) ),[0],$fot(implies(implies(X_14,implies(not(X_16),not(truth))),implies(X_14,X_16)))]]) ).

cnf(refute_0_85,plain,
    ( implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))) != truth
    | implies(implies(X_14,implies(not(X_16),not(truth))),implies(X_14,X_16)) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))),implies(implies(X_14,implies(not(X_16),not(truth))),implies(X_14,X_16))) )],[refute_0_83,refute_0_84]) ).

cnf(refute_0_86,plain,
    implies(implies(X_14,implies(not(X_16),not(truth))),implies(X_14,X_16)) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(X_14,implies(not(X_16),not(truth))),implies(truth,implies(X_14,X_16))),truth) )],[refute_0_78,refute_0_85]) ).

cnf(refute_0_87,plain,
    implies(implies(implies(not(not(truth)),not(not(X_39))),implies(not(X_39),not(truth))),implies(implies(not(not(truth)),not(not(X_39))),X_39)) = truth,
    inference(subst,[],[refute_0_86:[bind(X_14,$fot(implies(not(not(truth)),not(not(X_39))))),bind(X_16,$fot(X_39))]]) ).

cnf(refute_0_88,plain,
    implies(implies(not(not(truth)),not(not(X_39))),implies(not(X_39),not(truth))) = truth,
    inference(subst,[],[wajsberg_4:[bind(X,$fot(not(truth))),bind(Y,$fot(not(X_39)))]]) ).

cnf(refute_0_89,plain,
    ( implies(implies(implies(not(not(truth)),not(not(X_39))),implies(not(X_39),not(truth))),implies(implies(not(not(truth)),not(not(X_39))),X_39)) != truth
    | implies(implies(not(not(truth)),not(not(X_39))),implies(not(X_39),not(truth))) != truth
    | implies(truth,implies(implies(not(not(truth)),not(not(X_39))),X_39)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_39))),implies(not(X_39),not(truth))),implies(implies(not(not(truth)),not(not(X_39))),X_39)),truth) ),[0,0],$fot(truth)]]) ).

cnf(refute_0_90,plain,
    ( implies(implies(implies(not(not(truth)),not(not(X_39))),implies(not(X_39),not(truth))),implies(implies(not(not(truth)),not(not(X_39))),X_39)) != truth
    | implies(truth,implies(implies(not(not(truth)),not(not(X_39))),X_39)) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_39))),implies(not(X_39),not(truth))),truth) )],[refute_0_88,refute_0_89]) ).

cnf(refute_0_91,plain,
    implies(truth,implies(implies(not(not(truth)),not(not(X_39))),X_39)) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_39))),implies(not(X_39),not(truth))),implies(implies(not(not(truth)),not(not(X_39))),X_39)),truth) )],[refute_0_87,refute_0_90]) ).

cnf(refute_0_92,plain,
    implies(truth,implies(implies(not(not(truth)),not(not(X_39))),X_39)) = implies(implies(not(not(truth)),not(not(X_39))),X_39),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(not(truth)),not(not(X_39))),X_39)))]]) ).

cnf(refute_0_93,plain,
    ( implies(truth,implies(implies(not(not(truth)),not(not(X_39))),X_39)) != implies(implies(not(not(truth)),not(not(X_39))),X_39)
    | implies(truth,implies(implies(not(not(truth)),not(not(X_39))),X_39)) != truth
    | implies(implies(not(not(truth)),not(not(X_39))),X_39) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_39))),X_39)),truth) ),[0],$fot(implies(implies(not(not(truth)),not(not(X_39))),X_39))]]) ).

cnf(refute_0_94,plain,
    ( implies(truth,implies(implies(not(not(truth)),not(not(X_39))),X_39)) != truth
    | implies(implies(not(not(truth)),not(not(X_39))),X_39) = truth ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_39))),X_39)),implies(implies(not(not(truth)),not(not(X_39))),X_39)) )],[refute_0_92,refute_0_93]) ).

cnf(refute_0_95,plain,
    implies(implies(not(not(truth)),not(not(X_39))),X_39) = truth,
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_39))),X_39)),truth) )],[refute_0_91,refute_0_94]) ).

cnf(refute_0_96,plain,
    implies(truth,not(not(X_39))) = not(not(X_39)),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(X_39))))]]) ).

cnf(refute_0_97,plain,
    implies(implies(X_14,implies(Y,X_16)),implies(implies(implies(Y,X_16),X_16),implies(X_14,X_16))) = truth,
    inference(subst,[],[wajsberg_2:[bind(X,$fot(X_14)),bind(Y,$fot(implies(Y,X_16))),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_98,plain,
    implies(implies(X_16,Y),Y) = implies(implies(Y,X_16),X_16),
    inference(subst,[],[wajsberg_3:[bind(X,$fot(X_16))]]) ).

cnf(refute_0_99,plain,
    ( implies(implies(X_16,Y),Y) != implies(implies(Y,X_16),X_16)
    | implies(implies(Y,X_16),X_16) = implies(implies(X_16,Y),Y) ),
    inference(subst,[],[refute_0_45:[bind(X0,$fot(implies(implies(X_16,Y),Y))),bind(Y0,$fot(implies(implies(Y,X_16),X_16)))]]) ).

cnf(refute_0_100,plain,
    implies(implies(Y,X_16),X_16) = implies(implies(X_16,Y),Y),
    inference(resolve,[$cnf( $equal(implies(implies(X_16,Y),Y),implies(implies(Y,X_16),X_16)) )],[refute_0_98,refute_0_99]) ).

cnf(refute_0_101,plain,
    ( implies(implies(Y,X_16),X_16) != implies(implies(X_16,Y),Y)
    | implies(implies(X_14,implies(Y,X_16)),implies(implies(implies(Y,X_16),X_16),implies(X_14,X_16))) != truth
    | implies(implies(X_14,implies(Y,X_16)),implies(implies(implies(X_16,Y),Y),implies(X_14,X_16))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_14,implies(Y,X_16)),implies(implies(implies(Y,X_16),X_16),implies(X_14,X_16))),truth) ),[0,1,0],$fot(implies(implies(X_16,Y),Y))]]) ).

cnf(refute_0_102,plain,
    ( implies(implies(X_14,implies(Y,X_16)),implies(implies(implies(Y,X_16),X_16),implies(X_14,X_16))) != truth
    | implies(implies(X_14,implies(Y,X_16)),implies(implies(implies(X_16,Y),Y),implies(X_14,X_16))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(Y,X_16),X_16),implies(implies(X_16,Y),Y)) )],[refute_0_100,refute_0_101]) ).

cnf(refute_0_103,plain,
    implies(implies(X_14,implies(Y,X_16)),implies(implies(implies(X_16,Y),Y),implies(X_14,X_16))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(X_14,implies(Y,X_16)),implies(implies(implies(Y,X_16),X_16),implies(X_14,X_16))),truth) )],[refute_0_97,refute_0_102]) ).

cnf(refute_0_104,plain,
    implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(implies(implies(not(not(truth)),not(truth)),not(truth)),implies(X_65,not(not(truth))))) = truth,
    inference(subst,[],[refute_0_103:[bind(Y,$fot(not(truth))),bind(X_14,$fot(X_65)),bind(X_16,$fot(not(not(truth))))]]) ).

cnf(refute_0_105,plain,
    implies(implies(not(not(truth)),not(truth)),not(truth)) = truth,
    inference(subst,[],[refute_0_74:[bind(X_4,$fot(not(truth)))]]) ).

cnf(refute_0_106,plain,
    ( implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(implies(implies(not(not(truth)),not(truth)),not(truth)),implies(X_65,not(not(truth))))) != truth
    | implies(implies(not(not(truth)),not(truth)),not(truth)) != truth
    | implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(implies(implies(not(not(truth)),not(truth)),not(truth)),implies(X_65,not(not(truth))))),truth) ),[0,1,0],$fot(truth)]]) ).

cnf(refute_0_107,plain,
    ( implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(implies(implies(not(not(truth)),not(truth)),not(truth)),implies(X_65,not(not(truth))))) != truth
    | implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),truth) )],[refute_0_105,refute_0_106]) ).

cnf(refute_0_108,plain,
    implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(implies(implies(not(not(truth)),not(truth)),not(truth)),implies(X_65,not(not(truth))))),truth) )],[refute_0_104,refute_0_107]) ).

cnf(refute_0_109,plain,
    implies(truth,implies(X_65,not(not(truth)))) = implies(X_65,not(not(truth))),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_65,not(not(truth)))))]]) ).

cnf(refute_0_110,plain,
    implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))) = implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))),
    introduced(tautology,[refl,[$fot(implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))))]]) ).

cnf(refute_0_111,plain,
    ( implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))) != implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth)))))
    | implies(truth,implies(X_65,not(not(truth)))) != implies(X_65,not(not(truth)))
    | implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))) = implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(X_65,not(not(truth)))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))),implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth)))))) ),[1,1],$fot(implies(X_65,not(not(truth))))]]) ).

cnf(refute_0_112,plain,
    ( implies(truth,implies(X_65,not(not(truth)))) != implies(X_65,not(not(truth)))
    | implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))) = implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(X_65,not(not(truth)))) ),
    inference(resolve,[$cnf( $equal(implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))),implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth)))))) )],[refute_0_110,refute_0_111]) ).

cnf(refute_0_113,plain,
    implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))) = implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(X_65,not(not(truth)))),
    inference(resolve,[$cnf( $equal(implies(truth,implies(X_65,not(not(truth)))),implies(X_65,not(not(truth)))) )],[refute_0_109,refute_0_112]) ).

cnf(refute_0_114,plain,
    ( implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))) != implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(X_65,not(not(truth))))
    | implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))) != truth
    | implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(X_65,not(not(truth)))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))),truth) ),[0],$fot(implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(X_65,not(not(truth)))))]]) ).

cnf(refute_0_115,plain,
    ( implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))) != truth
    | implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(X_65,not(not(truth)))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))),implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(X_65,not(not(truth))))) )],[refute_0_113,refute_0_114]) ).

cnf(refute_0_116,plain,
    implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(X_65,not(not(truth)))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(X_65,implies(not(truth),not(not(truth)))),implies(truth,implies(X_65,not(not(truth))))),truth) )],[refute_0_108,refute_0_115]) ).

cnf(refute_0_117,plain,
    implies(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))),implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) = truth,
    inference(subst,[],[refute_0_116:[bind(X_65,$fot(implies(not(truth),implies(not(not(not(truth))),not(truth)))))]]) ).

cnf(refute_0_118,plain,
    implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))) = truth,
    inference(subst,[],[refute_0_86:[bind(X_14,$fot(not(truth))),bind(X_16,$fot(not(not(truth))))]]) ).

cnf(refute_0_119,plain,
    ( implies(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))),implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) != truth
    | implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))) != truth
    | implies(truth,implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))),implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))),truth) ),[0,0],$fot(truth)]]) ).

cnf(refute_0_120,plain,
    ( implies(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))),implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) != truth
    | implies(truth,implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))),truth) )],[refute_0_118,refute_0_119]) ).

cnf(refute_0_121,plain,
    implies(truth,implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))),implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))),truth) )],[refute_0_117,refute_0_120]) ).

cnf(refute_0_122,plain,
    implies(truth,not(not(truth))) = not(not(truth)),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(truth))))]]) ).

cnf(refute_0_123,plain,
    implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(implies(X_16,truth),truth),X_16),implies(X_14,X_16))) = truth,
    inference(subst,[],[wajsberg_2:[bind(X,$fot(X_14)),bind(Y,$fot(implies(implies(X_16,truth),truth))),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_124,plain,
    implies(implies(X,X),X) = implies(implies(X,X),X),
    inference(subst,[],[wajsberg_3:[bind(Y,$fot(X))]]) ).

cnf(refute_0_125,plain,
    implies(implies(truth,X_2),X_2) = implies(implies(X_2,truth),truth),
    inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_2))]]) ).

cnf(refute_0_126,plain,
    implies(truth,X_2) = X_2,
    inference(subst,[],[wajsberg_1:[bind(X,$fot(X_2))]]) ).

cnf(refute_0_127,plain,
    ( implies(implies(truth,X_2),X_2) != implies(implies(X_2,truth),truth)
    | implies(truth,X_2) != X_2
    | implies(X_2,X_2) = implies(implies(X_2,truth),truth) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_2),X_2),implies(implies(X_2,truth),truth)) ),[0,0],$fot(X_2)]]) ).

cnf(refute_0_128,plain,
    ( implies(implies(truth,X_2),X_2) != implies(implies(X_2,truth),truth)
    | implies(X_2,X_2) = implies(implies(X_2,truth),truth) ),
    inference(resolve,[$cnf( $equal(implies(truth,X_2),X_2) )],[refute_0_126,refute_0_127]) ).

cnf(refute_0_129,plain,
    implies(X_2,X_2) = implies(implies(X_2,truth),truth),
    inference(resolve,[$cnf( $equal(implies(implies(truth,X_2),X_2),implies(implies(X_2,truth),truth)) )],[refute_0_125,refute_0_128]) ).

cnf(refute_0_130,plain,
    implies(X,X) = implies(implies(X,truth),truth),
    inference(subst,[],[refute_0_129:[bind(X_2,$fot(X))]]) ).

cnf(refute_0_131,plain,
    ( implies(X,X) != implies(implies(X,truth),truth)
    | implies(implies(X,X),X) != implies(implies(X,X),X)
    | implies(implies(X,X),X) = implies(implies(implies(X,truth),truth),X) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,X),X),implies(implies(X,X),X)) ),[1,0],$fot(implies(implies(X,truth),truth))]]) ).

cnf(refute_0_132,plain,
    ( implies(implies(X,X),X) != implies(implies(X,X),X)
    | implies(implies(X,X),X) = implies(implies(implies(X,truth),truth),X) ),
    inference(resolve,[$cnf( $equal(implies(X,X),implies(implies(X,truth),truth)) )],[refute_0_130,refute_0_131]) ).

cnf(refute_0_133,plain,
    implies(implies(X,X),X) = implies(implies(implies(X,truth),truth),X),
    inference(resolve,[$cnf( $equal(implies(implies(X,X),X),implies(implies(X,X),X)) )],[refute_0_124,refute_0_132]) ).

cnf(refute_0_134,plain,
    implies(implies(X_16,X_16),X_16) = implies(implies(implies(X_16,truth),truth),X_16),
    inference(subst,[],[refute_0_133:[bind(X,$fot(X_16))]]) ).

cnf(refute_0_135,plain,
    ( implies(implies(X_16,X_16),X_16) != implies(implies(implies(X_16,truth),truth),X_16)
    | implies(implies(implies(X_16,truth),truth),X_16) = implies(implies(X_16,X_16),X_16) ),
    inference(subst,[],[refute_0_45:[bind(X0,$fot(implies(implies(X_16,X_16),X_16))),bind(Y0,$fot(implies(implies(implies(X_16,truth),truth),X_16)))]]) ).

cnf(refute_0_136,plain,
    implies(implies(implies(X_16,truth),truth),X_16) = implies(implies(X_16,X_16),X_16),
    inference(resolve,[$cnf( $equal(implies(implies(X_16,X_16),X_16),implies(implies(implies(X_16,truth),truth),X_16)) )],[refute_0_134,refute_0_135]) ).

cnf(refute_0_137,plain,
    ( implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(implies(X_16,truth),truth),X_16),implies(X_14,X_16))) != truth
    | implies(implies(implies(X_16,truth),truth),X_16) != implies(implies(X_16,X_16),X_16)
    | implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(implies(X_16,truth),truth),X_16),implies(X_14,X_16))),truth) ),[0,1,0],$fot(implies(implies(X_16,X_16),X_16))]]) ).

cnf(refute_0_138,plain,
    ( implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(implies(X_16,truth),truth),X_16),implies(X_14,X_16))) != truth
    | implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(X_16,truth),truth),X_16),implies(implies(X_16,X_16),X_16)) )],[refute_0_136,refute_0_137]) ).

cnf(refute_0_139,plain,
    implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(implies(X_16,truth),truth),X_16),implies(X_14,X_16))),truth) )],[refute_0_123,refute_0_138]) ).

cnf(refute_0_140,plain,
    implies(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth),implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) = truth,
    inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth))),bind(Y,$fot(truth)),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_141,plain,
    implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)) = truth,
    inference(subst,[],[wajsberg_4:[bind(X,$fot(X_4)),bind(Y,$fot(X_4))]]) ).

cnf(refute_0_142,plain,
    implies(X_4,X_4) = implies(implies(X_4,truth),truth),
    inference(subst,[],[refute_0_129:[bind(X_2,$fot(X_4))]]) ).

cnf(refute_0_143,plain,
    ( implies(X_4,X_4) != implies(implies(X_4,truth),truth)
    | implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)) != truth
    | implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)),truth) ),[0,1],$fot(implies(implies(X_4,truth),truth))]]) ).

cnf(refute_0_144,plain,
    ( implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)) != truth
    | implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = truth ),
    inference(resolve,[$cnf( $equal(implies(X_4,X_4),implies(implies(X_4,truth),truth)) )],[refute_0_142,refute_0_143]) ).

cnf(refute_0_145,plain,
    implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)),truth) )],[refute_0_141,refute_0_144]) ).

cnf(refute_0_146,plain,
    implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),truth)) = truth,
    inference(subst,[],[refute_0_145:[bind(X_4,$fot(implies(implies(not(implies(not(truth),not(truth))),truth),truth)))]]) ).

cnf(refute_0_147,plain,
    implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(implies(not(truth),not(truth)),truth),truth)) = truth,
    inference(subst,[],[refute_0_145:[bind(X_4,$fot(implies(not(truth),not(truth))))]]) ).

cnf(refute_0_148,plain,
    implies(implies(not(truth),not(truth)),truth) = truth,
    inference(subst,[],[refute_0_74:[bind(X_4,$fot(truth))]]) ).

cnf(refute_0_149,plain,
    ( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(implies(not(truth),not(truth)),truth),truth)) != truth
    | implies(implies(not(truth),not(truth)),truth) != truth
    | implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(implies(not(truth),not(truth)),truth),truth)),truth) ),[0,1,0],$fot(truth)]]) ).

cnf(refute_0_150,plain,
    ( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(implies(not(truth),not(truth)),truth),truth)) != truth
    | implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(truth)),truth),truth) )],[refute_0_148,refute_0_149]) ).

cnf(refute_0_151,plain,
    implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(implies(not(truth),not(truth)),truth),truth)),truth) )],[refute_0_147,refute_0_150]) ).

cnf(refute_0_152,plain,
    implies(truth,truth) = truth,
    inference(subst,[],[wajsberg_1:[bind(X,$fot(truth))]]) ).

cnf(refute_0_153,plain,
    implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)),
    introduced(tautology,[refl,[$fot(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)))]]) ).

cnf(refute_0_154,plain,
    ( implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth))
    | implies(truth,truth) != truth
    | implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth))) ),[1,1],$fot(truth)]]) ).

cnf(refute_0_155,plain,
    ( implies(truth,truth) != truth
    | implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth))) )],[refute_0_153,refute_0_154]) ).

cnf(refute_0_156,plain,
    implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),
    inference(resolve,[$cnf( $equal(implies(truth,truth),truth) )],[refute_0_152,refute_0_155]) ).

cnf(refute_0_157,plain,
    implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))) = implies(implies(not(implies(not(truth),not(truth))),truth),truth),
    inference(subst,[],[refute_0_129:[bind(X_2,$fot(not(implies(not(truth),not(truth)))))]]) ).

cnf(refute_0_158,plain,
    implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),
    introduced(tautology,[refl,[$fot(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)))]]) ).

cnf(refute_0_159,plain,
    ( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) != implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth))
    | implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))) != implies(implies(not(implies(not(truth),not(truth))),truth),truth)
    | implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth))) ),[1,0],$fot(implies(implies(not(implies(not(truth),not(truth))),truth),truth))]]) ).

cnf(refute_0_160,plain,
    ( implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))) != implies(implies(not(implies(not(truth),not(truth))),truth),truth)
    | implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth))) )],[refute_0_158,refute_0_159]) ).

cnf(refute_0_161,plain,
    implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)),
    inference(resolve,[$cnf( $equal(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(not(implies(not(truth),not(truth))),truth),truth)) )],[refute_0_157,refute_0_160]) ).

cnf(refute_0_162,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_163,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_45,refute_0_162]) ).

cnf(refute_0_164,plain,
    ( implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)
    | implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth))
    | implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)))),bind(Y0,$fot(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)))),bind(Z0,$fot(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)))]]) ).

cnf(refute_0_165,plain,
    ( implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)
    | implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth))) )],[refute_0_161,refute_0_164]) ).

cnf(refute_0_166,plain,
    implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)) )],[refute_0_156,refute_0_165]) ).

cnf(refute_0_167,plain,
    ( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)
    | implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) != truth
    | implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),truth) ),[0],$fot(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth))]]) ).

cnf(refute_0_168,plain,
    ( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) != truth
    | implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)) )],[refute_0_166,refute_0_167]) ).

cnf(refute_0_169,plain,
    implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),truth) )],[refute_0_151,refute_0_168]) ).

cnf(refute_0_170,plain,
    ( implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) != truth
    | implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),truth)) != truth
    | implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),truth)),truth) ),[0,1,0],$fot(truth)]]) ).

cnf(refute_0_171,plain,
    ( implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),truth)) != truth
    | implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),truth) )],[refute_0_169,refute_0_170]) ).

cnf(refute_0_172,plain,
    implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),truth)),truth) )],[refute_0_146,refute_0_171]) ).

cnf(refute_0_173,plain,
    implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth)) = implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth)),
    introduced(tautology,[refl,[$fot(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth)))]]) ).

cnf(refute_0_174,plain,
    ( implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth)) != implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth))
    | implies(truth,truth) != truth
    | implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth)) = implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth)),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth))) ),[1,1],$fot(truth)]]) ).

cnf(refute_0_175,plain,
    ( implies(truth,truth) != truth
    | implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth)) = implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth)),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth))) )],[refute_0_173,refute_0_174]) ).

cnf(refute_0_176,plain,
    implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth)) = implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth),
    inference(resolve,[$cnf( $equal(implies(truth,truth),truth) )],[refute_0_152,refute_0_175]) ).

cnf(refute_0_177,plain,
    implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))) = implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),
    inference(subst,[],[refute_0_129:[bind(X_2,$fot(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))))]]) ).

cnf(refute_0_178,plain,
    implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)) = implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)),
    introduced(tautology,[refl,[$fot(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)))]]) ).

cnf(refute_0_179,plain,
    ( implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)) != implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth))
    | implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))) != implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth)
    | implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)) = implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)),implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth))) ),[1,0],$fot(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth))]]) ).

cnf(refute_0_180,plain,
    ( implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))) != implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth)
    | implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)) = implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth)) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)),implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth))) )],[refute_0_178,refute_0_179]) ).

cnf(refute_0_181,plain,
    implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)) = implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth)),
    inference(resolve,[$cnf( $equal(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth)) )],[refute_0_177,refute_0_180]) ).

cnf(refute_0_182,plain,
    ( implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth)) != implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth)
    | implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)) != implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth))
    | implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)) = implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)))),bind(Y0,$fot(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth)))),bind(Z0,$fot(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth)))]]) ).

cnf(refute_0_183,plain,
    ( implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth)) != implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth)
    | implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)) = implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth))) )],[refute_0_181,refute_0_182]) ).

cnf(refute_0_184,plain,
    implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)) = implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(truth,truth)),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth)) )],[refute_0_176,refute_0_183]) ).

cnf(refute_0_185,plain,
    ( implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)) != implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth)
    | implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)) != truth
    | implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)),truth) ),[0],$fot(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth))]]) ).

cnf(refute_0_186,plain,
    ( implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)) != truth
    | implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth)) )],[refute_0_184,refute_0_185]) ).

cnf(refute_0_187,plain,
    implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),implies(truth,truth)),truth) )],[refute_0_172,refute_0_186]) ).

cnf(refute_0_188,plain,
    ( implies(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth),implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) != truth
    | implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth) != truth
    | implies(truth,implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth),implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))),truth) ),[0,0],$fot(truth)]]) ).

cnf(refute_0_189,plain,
    ( implies(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth),implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) != truth
    | implies(truth,implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth),truth) )],[refute_0_187,refute_0_188]) ).

cnf(refute_0_190,plain,
    implies(truth,implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth),implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))),truth) )],[refute_0_140,refute_0_189]) ).

cnf(refute_0_191,plain,
    implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))) = truth,
    inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(implies(not(truth),truth))),bind(Z,$fot(truth))]]) ).

cnf(refute_0_192,plain,
    implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)) = truth,
    inference(subst,[],[wajsberg_4:[bind(X,$fot(X_5)),bind(Y,$fot(X_5))]]) ).

cnf(refute_0_193,plain,
    implies(not(X_5),not(X_5)) = implies(implies(not(X_5),truth),truth),
    inference(subst,[],[refute_0_129:[bind(X_2,$fot(not(X_5)))]]) ).

cnf(refute_0_194,plain,
    ( implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)) != truth
    | implies(not(X_5),not(X_5)) != implies(implies(not(X_5),truth),truth)
    | implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)),truth) ),[0,0],$fot(implies(implies(not(X_5),truth),truth))]]) ).

cnf(refute_0_195,plain,
    ( implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)) != truth
    | implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)) = truth ),
    inference(resolve,[$cnf( $equal(implies(not(X_5),not(X_5)),implies(implies(not(X_5),truth),truth)) )],[refute_0_193,refute_0_194]) ).

cnf(refute_0_196,plain,
    implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)),truth) )],[refute_0_192,refute_0_195]) ).

cnf(refute_0_197,plain,
    implies(implies(implies(not(truth),truth),truth),implies(truth,truth)) = truth,
    inference(subst,[],[refute_0_196:[bind(X_5,$fot(truth))]]) ).

cnf(refute_0_198,plain,
    ( implies(implies(implies(not(truth),truth),truth),implies(truth,truth)) != truth
    | implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))) != truth
    | implies(implies(truth,implies(not(truth),truth)),truth) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))),truth) ),[0,1],$fot(truth)]]) ).

cnf(refute_0_199,plain,
    ( implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))) != truth
    | implies(implies(truth,implies(not(truth),truth)),truth) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),truth),truth),implies(truth,truth)),truth) )],[refute_0_197,refute_0_198]) ).

cnf(refute_0_200,plain,
    implies(implies(truth,implies(not(truth),truth)),truth) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))),truth) )],[refute_0_191,refute_0_199]) ).

cnf(refute_0_201,plain,
    ( implies(X_2,X_2) != implies(implies(X_2,truth),truth)
    | implies(implies(X_2,truth),truth) = implies(X_2,X_2) ),
    inference(subst,[],[refute_0_45:[bind(X0,$fot(implies(X_2,X_2))),bind(Y0,$fot(implies(implies(X_2,truth),truth)))]]) ).

cnf(refute_0_202,plain,
    implies(implies(X_2,truth),truth) = implies(X_2,X_2),
    inference(resolve,[$cnf( $equal(implies(X_2,X_2),implies(implies(X_2,truth),truth)) )],[refute_0_129,refute_0_201]) ).

cnf(refute_0_203,plain,
    implies(implies(not(truth),truth),truth) = implies(not(truth),not(truth)),
    inference(subst,[],[refute_0_202:[bind(X_2,$fot(not(truth)))]]) ).

cnf(refute_0_204,plain,
    implies(truth,implies(not(truth),truth)) = implies(not(truth),truth),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(truth),truth)))]]) ).

cnf(refute_0_205,plain,
    implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(truth,implies(not(truth),truth)),truth),
    introduced(tautology,[refl,[$fot(implies(implies(truth,implies(not(truth),truth)),truth))]]) ).

cnf(refute_0_206,plain,
    ( implies(implies(truth,implies(not(truth),truth)),truth) != implies(implies(truth,implies(not(truth),truth)),truth)
    | implies(truth,implies(not(truth),truth)) != implies(not(truth),truth)
    | implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(not(truth),truth),truth) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(implies(truth,implies(not(truth),truth)),truth)) ),[1,0],$fot(implies(not(truth),truth))]]) ).

cnf(refute_0_207,plain,
    ( implies(truth,implies(not(truth),truth)) != implies(not(truth),truth)
    | implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(not(truth),truth),truth) ),
    inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(implies(truth,implies(not(truth),truth)),truth)) )],[refute_0_205,refute_0_206]) ).

cnf(refute_0_208,plain,
    implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(not(truth),truth),truth),
    inference(resolve,[$cnf( $equal(implies(truth,implies(not(truth),truth)),implies(not(truth),truth)) )],[refute_0_204,refute_0_207]) ).

cnf(refute_0_209,plain,
    ( implies(implies(not(truth),truth),truth) != implies(not(truth),not(truth))
    | implies(implies(truth,implies(not(truth),truth)),truth) != implies(implies(not(truth),truth),truth)
    | implies(implies(truth,implies(not(truth),truth)),truth) = implies(not(truth),not(truth)) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(truth,implies(not(truth),truth)),truth))),bind(Y0,$fot(implies(implies(not(truth),truth),truth))),bind(Z0,$fot(implies(not(truth),not(truth))))]]) ).

cnf(refute_0_210,plain,
    ( implies(implies(not(truth),truth),truth) != implies(not(truth),not(truth))
    | implies(implies(truth,implies(not(truth),truth)),truth) = implies(not(truth),not(truth)) ),
    inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(implies(not(truth),truth),truth)) )],[refute_0_208,refute_0_209]) ).

cnf(refute_0_211,plain,
    implies(implies(truth,implies(not(truth),truth)),truth) = implies(not(truth),not(truth)),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),truth),truth),implies(not(truth),not(truth))) )],[refute_0_203,refute_0_210]) ).

cnf(refute_0_212,plain,
    ( implies(implies(truth,implies(not(truth),truth)),truth) != implies(not(truth),not(truth))
    | implies(implies(truth,implies(not(truth),truth)),truth) != truth
    | implies(not(truth),not(truth)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),truth) ),[0],$fot(implies(not(truth),not(truth)))]]) ).

cnf(refute_0_213,plain,
    ( implies(implies(truth,implies(not(truth),truth)),truth) != truth
    | implies(not(truth),not(truth)) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(not(truth),not(truth))) )],[refute_0_211,refute_0_212]) ).

cnf(refute_0_214,plain,
    implies(not(truth),not(truth)) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),truth) )],[refute_0_200,refute_0_213]) ).

cnf(refute_0_215,plain,
    ( implies(implies(not(truth),truth),truth) != implies(not(truth),not(truth))
    | implies(not(truth),not(truth)) != truth
    | implies(implies(not(truth),truth),truth) = truth ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(not(truth),truth),truth))),bind(Y0,$fot(implies(not(truth),not(truth)))),bind(Z0,$fot(truth))]]) ).

cnf(refute_0_216,plain,
    ( implies(not(truth),not(truth)) != truth
    | implies(implies(not(truth),truth),truth) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),truth),truth),implies(not(truth),not(truth))) )],[refute_0_203,refute_0_215]) ).

cnf(refute_0_217,plain,
    implies(implies(not(truth),truth),truth) = truth,
    inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_214,refute_0_216]) ).

cnf(refute_0_218,plain,
    not(implies(not(truth),not(truth))) = not(implies(not(truth),not(truth))),
    introduced(tautology,[refl,[$fot(not(implies(not(truth),not(truth))))]]) ).

cnf(refute_0_219,plain,
    ( implies(not(truth),not(truth)) != truth
    | not(implies(not(truth),not(truth))) != not(implies(not(truth),not(truth)))
    | not(implies(not(truth),not(truth))) = not(truth) ),
    introduced(tautology,[equality,[$cnf( $equal(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_220,plain,
    ( implies(not(truth),not(truth)) != truth
    | not(implies(not(truth),not(truth))) = not(truth) ),
    inference(resolve,[$cnf( $equal(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))) )],[refute_0_218,refute_0_219]) ).

cnf(refute_0_221,plain,
    not(implies(not(truth),not(truth))) = not(truth),
    inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_214,refute_0_220]) ).

cnf(refute_0_222,plain,
    implies(not(implies(not(truth),not(truth))),truth) = implies(not(implies(not(truth),not(truth))),truth),
    introduced(tautology,[refl,[$fot(implies(not(implies(not(truth),not(truth))),truth))]]) ).

cnf(refute_0_223,plain,
    ( implies(not(implies(not(truth),not(truth))),truth) != implies(not(implies(not(truth),not(truth))),truth)
    | not(implies(not(truth),not(truth))) != not(truth)
    | implies(not(implies(not(truth),not(truth))),truth) = implies(not(truth),truth) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(not(truth),not(truth))),truth),implies(not(implies(not(truth),not(truth))),truth)) ),[1,0],$fot(not(truth))]]) ).

cnf(refute_0_224,plain,
    ( not(implies(not(truth),not(truth))) != not(truth)
    | implies(not(implies(not(truth),not(truth))),truth) = implies(not(truth),truth) ),
    inference(resolve,[$cnf( $equal(implies(not(implies(not(truth),not(truth))),truth),implies(not(implies(not(truth),not(truth))),truth)) )],[refute_0_222,refute_0_223]) ).

cnf(refute_0_225,plain,
    implies(not(implies(not(truth),not(truth))),truth) = implies(not(truth),truth),
    inference(resolve,[$cnf( $equal(not(implies(not(truth),not(truth))),not(truth)) )],[refute_0_221,refute_0_224]) ).

cnf(refute_0_226,plain,
    implies(implies(not(implies(not(truth),not(truth))),truth),truth) = implies(implies(not(implies(not(truth),not(truth))),truth),truth),
    introduced(tautology,[refl,[$fot(implies(implies(not(implies(not(truth),not(truth))),truth),truth))]]) ).

cnf(refute_0_227,plain,
    ( implies(implies(not(implies(not(truth),not(truth))),truth),truth) != implies(implies(not(implies(not(truth),not(truth))),truth),truth)
    | implies(not(implies(not(truth),not(truth))),truth) != implies(not(truth),truth)
    | implies(implies(not(implies(not(truth),not(truth))),truth),truth) = implies(implies(not(truth),truth),truth) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(implies(not(implies(not(truth),not(truth))),truth),truth)) ),[1,0],$fot(implies(not(truth),truth))]]) ).

cnf(refute_0_228,plain,
    ( implies(not(implies(not(truth),not(truth))),truth) != implies(not(truth),truth)
    | implies(implies(not(implies(not(truth),not(truth))),truth),truth) = implies(implies(not(truth),truth),truth) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(implies(not(implies(not(truth),not(truth))),truth),truth)) )],[refute_0_226,refute_0_227]) ).

cnf(refute_0_229,plain,
    implies(implies(not(implies(not(truth),not(truth))),truth),truth) = implies(implies(not(truth),truth),truth),
    inference(resolve,[$cnf( $equal(implies(not(implies(not(truth),not(truth))),truth),implies(not(truth),truth)) )],[refute_0_225,refute_0_228]) ).

cnf(refute_0_230,plain,
    ( implies(implies(not(implies(not(truth),not(truth))),truth),truth) != implies(implies(not(truth),truth),truth)
    | implies(implies(not(truth),truth),truth) != truth
    | implies(implies(not(implies(not(truth),not(truth))),truth),truth) = truth ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),bind(Y0,$fot(implies(implies(not(truth),truth),truth))),bind(Z0,$fot(truth))]]) ).

cnf(refute_0_231,plain,
    ( implies(implies(not(truth),truth),truth) != truth
    | implies(implies(not(implies(not(truth),not(truth))),truth),truth) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(implies(not(truth),truth),truth)) )],[refute_0_229,refute_0_230]) ).

cnf(refute_0_232,plain,
    implies(implies(not(implies(not(truth),not(truth))),truth),truth) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),truth),truth),truth) )],[refute_0_217,refute_0_231]) ).

cnf(refute_0_233,plain,
    not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)) = not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),
    introduced(tautology,[refl,[$fot(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)))]]) ).

cnf(refute_0_234,plain,
    ( implies(implies(not(implies(not(truth),not(truth))),truth),truth) != truth
    | not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)) != not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))
    | not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)) = not(truth) ),
    introduced(tautology,[equality,[$cnf( $equal(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_235,plain,
    ( implies(implies(not(implies(not(truth),not(truth))),truth),truth) != truth
    | not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)) = not(truth) ),
    inference(resolve,[$cnf( $equal(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(implies(implies(not(implies(not(truth),not(truth))),truth),truth))) )],[refute_0_233,refute_0_234]) ).

cnf(refute_0_236,plain,
    not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)) = not(truth),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) )],[refute_0_232,refute_0_235]) ).

cnf(refute_0_237,plain,
    implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth) = implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),
    introduced(tautology,[refl,[$fot(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth))]]) ).

cnf(refute_0_238,plain,
    ( implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth) != implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth)
    | not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)) != not(truth)
    | implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth) = implies(not(truth),truth) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth)) ),[1,0],$fot(not(truth))]]) ).

cnf(refute_0_239,plain,
    ( not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)) != not(truth)
    | implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth) = implies(not(truth),truth) ),
    inference(resolve,[$cnf( $equal(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth)) )],[refute_0_237,refute_0_238]) ).

cnf(refute_0_240,plain,
    implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth) = implies(not(truth),truth),
    inference(resolve,[$cnf( $equal(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),not(truth)) )],[refute_0_236,refute_0_239]) ).

cnf(refute_0_241,plain,
    implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth) = implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),
    introduced(tautology,[refl,[$fot(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth))]]) ).

cnf(refute_0_242,plain,
    ( implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth) != implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth)
    | implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth) != implies(not(truth),truth)
    | implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth) = implies(implies(not(truth),truth),truth) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth)) ),[1,0],$fot(implies(not(truth),truth))]]) ).

cnf(refute_0_243,plain,
    ( implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth) != implies(not(truth),truth)
    | implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth) = implies(implies(not(truth),truth),truth) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth)) )],[refute_0_241,refute_0_242]) ).

cnf(refute_0_244,plain,
    implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth) = implies(implies(not(truth),truth),truth),
    inference(resolve,[$cnf( $equal(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),implies(not(truth),truth)) )],[refute_0_240,refute_0_243]) ).

cnf(refute_0_245,plain,
    ( implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth) != implies(implies(not(truth),truth),truth)
    | implies(implies(not(truth),truth),truth) != truth
    | implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth) = truth ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth))),bind(Y0,$fot(implies(implies(not(truth),truth),truth))),bind(Z0,$fot(truth))]]) ).

cnf(refute_0_246,plain,
    ( implies(implies(not(truth),truth),truth) != truth
    | implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),implies(implies(not(truth),truth),truth)) )],[refute_0_244,refute_0_245]) ).

cnf(refute_0_247,plain,
    implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),truth),truth),truth) )],[refute_0_217,refute_0_246]) ).

cnf(refute_0_248,plain,
    implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16) = implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16),
    introduced(tautology,[refl,[$fot(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))]]) ).

cnf(refute_0_249,plain,
    ( implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16) != implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)
    | implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth) != truth
    | implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16) = implies(truth,X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_250,plain,
    ( implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth) != truth
    | implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16) = implies(truth,X_16) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) )],[refute_0_248,refute_0_249]) ).

cnf(refute_0_251,plain,
    implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16) = implies(truth,X_16),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),truth) )],[refute_0_247,refute_0_250]) ).

cnf(refute_0_252,plain,
    ( implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16) != implies(truth,X_16)
    | implies(truth,X_16) != X_16
    | implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16) = X_16 ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))),bind(Y0,$fot(implies(truth,X_16))),bind(Z0,$fot(X_16))]]) ).

cnf(refute_0_253,plain,
    ( implies(truth,X_16) != X_16
    | implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16) = X_16 ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16),implies(truth,X_16)) )],[refute_0_251,refute_0_252]) ).

cnf(refute_0_254,plain,
    implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16) = X_16,
    inference(resolve,[$cnf( $equal(implies(truth,X_16),X_16) )],[refute_0_2,refute_0_253]) ).

cnf(refute_0_255,plain,
    implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) = implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)),
    introduced(tautology,[refl,[$fot(implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)))]]) ).

cnf(refute_0_256,plain,
    ( implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) != implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))
    | implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16) != X_16
    | implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) = implies(X_16,X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)),implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) ),[1,1],$fot(X_16)]]) ).

cnf(refute_0_257,plain,
    ( implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16) != X_16
    | implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) = implies(X_16,X_16) ),
    inference(resolve,[$cnf( $equal(implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)),implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) )],[refute_0_255,refute_0_256]) ).

cnf(refute_0_258,plain,
    implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) = implies(X_16,X_16),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16),X_16) )],[refute_0_254,refute_0_257]) ).

cnf(refute_0_259,plain,
    implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) = implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)),
    introduced(tautology,[refl,[$fot(implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)))]]) ).

cnf(refute_0_260,plain,
    ( implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) != implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))
    | implies(truth,X_16) != X_16
    | implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) = implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)),implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) ),[1,0],$fot(X_16)]]) ).

cnf(refute_0_261,plain,
    ( implies(truth,X_16) != X_16
    | implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) = implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) ),
    inference(resolve,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)),implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) )],[refute_0_259,refute_0_260]) ).

cnf(refute_0_262,plain,
    implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) = implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)),
    inference(resolve,[$cnf( $equal(implies(truth,X_16),X_16) )],[refute_0_2,refute_0_261]) ).

cnf(refute_0_263,plain,
    ( implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) != implies(X_16,X_16)
    | implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) != implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))
    | implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) = implies(X_16,X_16) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)))),bind(Y0,$fot(implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)))),bind(Z0,$fot(implies(X_16,X_16)))]]) ).

cnf(refute_0_264,plain,
    ( implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) != implies(X_16,X_16)
    | implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) = implies(X_16,X_16) ),
    inference(resolve,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)),implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) )],[refute_0_262,refute_0_263]) ).

cnf(refute_0_265,plain,
    implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) = implies(X_16,X_16),
    inference(resolve,[$cnf( $equal(implies(X_16,implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)),implies(X_16,X_16)) )],[refute_0_258,refute_0_264]) ).

cnf(refute_0_266,plain,
    implies(truth,implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) = implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))))]]) ).

cnf(refute_0_267,plain,
    ( implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) != implies(X_16,X_16)
    | implies(truth,implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) != implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))
    | implies(truth,implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) = implies(X_16,X_16) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(truth,implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))))),bind(Y0,$fot(implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)))),bind(Z0,$fot(implies(X_16,X_16)))]]) ).

cnf(refute_0_268,plain,
    ( implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)) != implies(X_16,X_16)
    | implies(truth,implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) = implies(X_16,X_16) ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))),implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) )],[refute_0_266,refute_0_267]) ).

cnf(refute_0_269,plain,
    implies(truth,implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) = implies(X_16,X_16),
    inference(resolve,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16)),implies(X_16,X_16)) )],[refute_0_265,refute_0_268]) ).

cnf(refute_0_270,plain,
    ( implies(truth,implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) != implies(X_16,X_16)
    | implies(truth,implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) != truth
    | implies(X_16,X_16) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))),truth) ),[0],$fot(implies(X_16,X_16))]]) ).

cnf(refute_0_271,plain,
    ( implies(truth,implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))) != truth
    | implies(X_16,X_16) = truth ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))),implies(X_16,X_16)) )],[refute_0_269,refute_0_270]) ).

cnf(refute_0_272,plain,
    implies(X_16,X_16) = truth,
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_16),implies(implies(implies(not(implies(implies(not(implies(not(truth),not(truth))),truth),truth)),truth),truth),X_16))),truth) )],[refute_0_190,refute_0_271]) ).

cnf(refute_0_273,plain,
    implies(implies(X_16,X_16),X_16) = implies(implies(X_16,X_16),X_16),
    introduced(tautology,[refl,[$fot(implies(implies(X_16,X_16),X_16))]]) ).

cnf(refute_0_274,plain,
    ( implies(X_16,X_16) != truth
    | implies(implies(X_16,X_16),X_16) != implies(implies(X_16,X_16),X_16)
    | implies(implies(X_16,X_16),X_16) = implies(truth,X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,X_16),X_16),implies(implies(X_16,X_16),X_16)) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_275,plain,
    ( implies(X_16,X_16) != truth
    | implies(implies(X_16,X_16),X_16) = implies(truth,X_16) ),
    inference(resolve,[$cnf( $equal(implies(implies(X_16,X_16),X_16),implies(implies(X_16,X_16),X_16)) )],[refute_0_273,refute_0_274]) ).

cnf(refute_0_276,plain,
    implies(implies(X_16,X_16),X_16) = implies(truth,X_16),
    inference(resolve,[$cnf( $equal(implies(X_16,X_16),truth) )],[refute_0_272,refute_0_275]) ).

cnf(refute_0_277,plain,
    ( implies(implies(X_16,X_16),X_16) != implies(truth,X_16)
    | implies(truth,X_16) != X_16
    | implies(implies(X_16,X_16),X_16) = X_16 ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(X_16,X_16),X_16))),bind(Y0,$fot(implies(truth,X_16))),bind(Z0,$fot(X_16))]]) ).

cnf(refute_0_278,plain,
    ( implies(truth,X_16) != X_16
    | implies(implies(X_16,X_16),X_16) = X_16 ),
    inference(resolve,[$cnf( $equal(implies(implies(X_16,X_16),X_16),implies(truth,X_16)) )],[refute_0_276,refute_0_277]) ).

cnf(refute_0_279,plain,
    implies(implies(X_16,X_16),X_16) = X_16,
    inference(resolve,[$cnf( $equal(implies(truth,X_16),X_16) )],[refute_0_2,refute_0_278]) ).

cnf(refute_0_280,plain,
    implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16)) = implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16)),
    introduced(tautology,[refl,[$fot(implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16)))]]) ).

cnf(refute_0_281,plain,
    ( implies(implies(X_16,X_16),X_16) != X_16
    | implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16)) != implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))
    | implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16)) = implies(X_16,implies(X_14,X_16)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))) ),[1,0],$fot(X_16)]]) ).

cnf(refute_0_282,plain,
    ( implies(implies(X_16,X_16),X_16) != X_16
    | implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16)) = implies(X_16,implies(X_14,X_16)) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))) )],[refute_0_280,refute_0_281]) ).

cnf(refute_0_283,plain,
    implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16)) = implies(X_16,implies(X_14,X_16)),
    inference(resolve,[$cnf( $equal(implies(implies(X_16,X_16),X_16),X_16) )],[refute_0_279,refute_0_282]) ).

cnf(refute_0_284,plain,
    implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))) = implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))),
    introduced(tautology,[refl,[$fot(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))))]]) ).

cnf(refute_0_285,plain,
    ( implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))) != implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16)))
    | implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16)) != implies(X_16,implies(X_14,X_16))
    | implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))) = implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))),implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16)))) ),[1,1],$fot(implies(X_16,implies(X_14,X_16)))]]) ).

cnf(refute_0_286,plain,
    ( implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16)) != implies(X_16,implies(X_14,X_16))
    | implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))) = implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) ),
    inference(resolve,[$cnf( $equal(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))),implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16)))) )],[refute_0_284,refute_0_285]) ).

cnf(refute_0_287,plain,
    implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))) = implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))),
    inference(resolve,[$cnf( $equal(implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16)),implies(X_16,implies(X_14,X_16))) )],[refute_0_283,refute_0_286]) ).

cnf(refute_0_288,plain,
    ( implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))) != implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16)))
    | implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))) != truth
    | implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))),truth) ),[0],$fot(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))))]]) ).

cnf(refute_0_289,plain,
    ( implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))) != truth
    | implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))),implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16)))) )],[refute_0_287,refute_0_288]) ).

cnf(refute_0_290,plain,
    implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(implies(implies(X_16,X_16),X_16),implies(X_14,X_16))),truth) )],[refute_0_139,refute_0_289]) ).

cnf(refute_0_291,plain,
    implies(truth,implies(X_16,implies(X_14,X_16))) = implies(X_16,implies(X_14,X_16)),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_16,implies(X_14,X_16))))]]) ).

cnf(refute_0_292,plain,
    implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))) = truth,
    inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(X_4),not(X_4)))),bind(Y,$fot(X_15)),bind(Z,$fot(implies(implies(X_4,truth),truth)))]]) ).

cnf(refute_0_293,plain,
    ( implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))) != truth
    | implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) != truth
    | implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))),truth) ),[0,1,1],$fot(truth)]]) ).

cnf(refute_0_294,plain,
    ( implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))) != truth
    | implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),truth) )],[refute_0_145,refute_0_293]) ).

cnf(refute_0_295,plain,
    implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))),truth) )],[refute_0_292,refute_0_294]) ).

cnf(refute_0_296,plain,
    implies(not(X_4),not(X_4)) = truth,
    inference(subst,[],[refute_0_272:[bind(X_16,$fot(not(X_4)))]]) ).

cnf(refute_0_297,plain,
    implies(implies(not(X_4),not(X_4)),X_15) = implies(implies(not(X_4),not(X_4)),X_15),
    introduced(tautology,[refl,[$fot(implies(implies(not(X_4),not(X_4)),X_15))]]) ).

cnf(refute_0_298,plain,
    ( implies(implies(not(X_4),not(X_4)),X_15) != implies(implies(not(X_4),not(X_4)),X_15)
    | implies(not(X_4),not(X_4)) != truth
    | implies(implies(not(X_4),not(X_4)),X_15) = implies(truth,X_15) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(not(X_4),not(X_4)),X_15)) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_299,plain,
    ( implies(not(X_4),not(X_4)) != truth
    | implies(implies(not(X_4),not(X_4)),X_15) = implies(truth,X_15) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(not(X_4),not(X_4)),X_15)) )],[refute_0_297,refute_0_298]) ).

cnf(refute_0_300,plain,
    implies(implies(not(X_4),not(X_4)),X_15) = implies(truth,X_15),
    inference(resolve,[$cnf( $equal(implies(not(X_4),not(X_4)),truth) )],[refute_0_296,refute_0_299]) ).

cnf(refute_0_301,plain,
    ( implies(implies(not(X_4),not(X_4)),X_15) != implies(truth,X_15)
    | implies(truth,X_15) != X_15
    | implies(implies(not(X_4),not(X_4)),X_15) = X_15 ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(not(X_4),not(X_4)),X_15))),bind(Y0,$fot(implies(truth,X_15))),bind(Z0,$fot(X_15))]]) ).

cnf(refute_0_302,plain,
    ( implies(truth,X_15) != X_15
    | implies(implies(not(X_4),not(X_4)),X_15) = X_15 ),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_15),implies(truth,X_15)) )],[refute_0_300,refute_0_301]) ).

cnf(refute_0_303,plain,
    implies(implies(not(X_4),not(X_4)),X_15) = X_15,
    inference(resolve,[$cnf( $equal(implies(truth,X_15),X_15) )],[refute_0_6,refute_0_302]) ).

cnf(refute_0_304,plain,
    implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) = implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)),
    introduced(tautology,[refl,[$fot(implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)))]]) ).

cnf(refute_0_305,plain,
    ( implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) != implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth))
    | implies(implies(not(X_4),not(X_4)),X_15) != X_15
    | implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) = implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)),implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth))) ),[1,0],$fot(X_15)]]) ).

cnf(refute_0_306,plain,
    ( implies(implies(not(X_4),not(X_4)),X_15) != X_15
    | implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) = implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)),implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth))) )],[refute_0_304,refute_0_305]) ).

cnf(refute_0_307,plain,
    implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) = implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_15),X_15) )],[refute_0_303,refute_0_306]) ).

cnf(refute_0_308,plain,
    ( implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) != implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth))
    | implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) != truth
    | implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)),truth) ),[0],$fot(implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)))]]) ).

cnf(refute_0_309,plain,
    ( implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) != truth
    | implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)),implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth))) )],[refute_0_307,refute_0_308]) ).

cnf(refute_0_310,plain,
    implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_15),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)),truth) )],[refute_0_295,refute_0_309]) ).

cnf(refute_0_311,plain,
    implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))) = implies(implies(implies(not(X_7),not(X_7)),implies(implies(X_7,truth),truth)),implies(implies(X_7,truth),truth)),
    inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(implies(X_7,truth),truth))),bind(Y,$fot(implies(not(X_7),not(X_7))))]]) ).

cnf(refute_0_312,plain,
    implies(implies(not(X_7),not(X_7)),implies(implies(X_7,truth),truth)) = truth,
    inference(subst,[],[refute_0_145:[bind(X_4,$fot(X_7))]]) ).

cnf(refute_0_313,plain,
    ( implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))) != implies(implies(implies(not(X_7),not(X_7)),implies(implies(X_7,truth),truth)),implies(implies(X_7,truth),truth))
    | implies(implies(not(X_7),not(X_7)),implies(implies(X_7,truth),truth)) != truth
    | implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))) = implies(truth,implies(implies(X_7,truth),truth)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))),implies(implies(implies(not(X_7),not(X_7)),implies(implies(X_7,truth),truth)),implies(implies(X_7,truth),truth))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_314,plain,
    ( implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))) != implies(implies(implies(not(X_7),not(X_7)),implies(implies(X_7,truth),truth)),implies(implies(X_7,truth),truth))
    | implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))) = implies(truth,implies(implies(X_7,truth),truth)) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_7),not(X_7)),implies(implies(X_7,truth),truth)),truth) )],[refute_0_312,refute_0_313]) ).

cnf(refute_0_315,plain,
    implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))) = implies(truth,implies(implies(X_7,truth),truth)),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))),implies(implies(implies(not(X_7),not(X_7)),implies(implies(X_7,truth),truth)),implies(implies(X_7,truth),truth))) )],[refute_0_311,refute_0_314]) ).

cnf(refute_0_316,plain,
    implies(truth,implies(implies(X_7,truth),truth)) = implies(implies(X_7,truth),truth),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(X_7,truth),truth)))]]) ).

cnf(refute_0_317,plain,
    ( implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))) != implies(truth,implies(implies(X_7,truth),truth))
    | implies(truth,implies(implies(X_7,truth),truth)) != implies(implies(X_7,truth),truth)
    | implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))) = implies(implies(X_7,truth),truth) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))),implies(implies(X_7,truth),truth)) ),[0],$fot(implies(truth,implies(implies(X_7,truth),truth)))]]) ).

cnf(refute_0_318,plain,
    ( implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))) != implies(truth,implies(implies(X_7,truth),truth))
    | implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))) = implies(implies(X_7,truth),truth) ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_7,truth),truth)),implies(implies(X_7,truth),truth)) )],[refute_0_316,refute_0_317]) ).

cnf(refute_0_319,plain,
    implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))) = implies(implies(X_7,truth),truth),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))),implies(truth,implies(implies(X_7,truth),truth))) )],[refute_0_315,refute_0_318]) ).

cnf(refute_0_320,plain,
    implies(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) = truth,
    inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(X_4),not(X_4)))),bind(Y,$fot(implies(implies(X_4,truth),truth))),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_321,plain,
    ( implies(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) != truth
    | implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) != truth
    | implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))),truth) ),[0,0],$fot(truth)]]) ).

cnf(refute_0_322,plain,
    ( implies(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) != truth
    | implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),truth) )],[refute_0_145,refute_0_321]) ).

cnf(refute_0_323,plain,
    implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))),truth) )],[refute_0_320,refute_0_322]) ).

cnf(refute_0_324,plain,
    implies(implies(not(X_4),not(X_4)),X_16) = implies(implies(not(X_4),not(X_4)),X_16),
    introduced(tautology,[refl,[$fot(implies(implies(not(X_4),not(X_4)),X_16))]]) ).

cnf(refute_0_325,plain,
    ( implies(implies(not(X_4),not(X_4)),X_16) != implies(implies(not(X_4),not(X_4)),X_16)
    | implies(not(X_4),not(X_4)) != truth
    | implies(implies(not(X_4),not(X_4)),X_16) = implies(truth,X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_16),implies(implies(not(X_4),not(X_4)),X_16)) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_326,plain,
    ( implies(not(X_4),not(X_4)) != truth
    | implies(implies(not(X_4),not(X_4)),X_16) = implies(truth,X_16) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_16),implies(implies(not(X_4),not(X_4)),X_16)) )],[refute_0_324,refute_0_325]) ).

cnf(refute_0_327,plain,
    implies(implies(not(X_4),not(X_4)),X_16) = implies(truth,X_16),
    inference(resolve,[$cnf( $equal(implies(not(X_4),not(X_4)),truth) )],[refute_0_296,refute_0_326]) ).

cnf(refute_0_328,plain,
    ( implies(implies(not(X_4),not(X_4)),X_16) != implies(truth,X_16)
    | implies(truth,X_16) != X_16
    | implies(implies(not(X_4),not(X_4)),X_16) = X_16 ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(not(X_4),not(X_4)),X_16))),bind(Y0,$fot(implies(truth,X_16))),bind(Z0,$fot(X_16))]]) ).

cnf(refute_0_329,plain,
    ( implies(truth,X_16) != X_16
    | implies(implies(not(X_4),not(X_4)),X_16) = X_16 ),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_16),implies(truth,X_16)) )],[refute_0_327,refute_0_328]) ).

cnf(refute_0_330,plain,
    implies(implies(not(X_4),not(X_4)),X_16) = X_16,
    inference(resolve,[$cnf( $equal(implies(truth,X_16),X_16) )],[refute_0_2,refute_0_329]) ).

cnf(refute_0_331,plain,
    implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16)) = implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16)),
    introduced(tautology,[refl,[$fot(implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16)))]]) ).

cnf(refute_0_332,plain,
    ( implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16)) != implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))
    | implies(implies(not(X_4),not(X_4)),X_16) != X_16
    | implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16)) = implies(implies(implies(implies(X_4,truth),truth),X_16),X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16)),implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) ),[1,1],$fot(X_16)]]) ).

cnf(refute_0_333,plain,
    ( implies(implies(not(X_4),not(X_4)),X_16) != X_16
    | implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16)) = implies(implies(implies(implies(X_4,truth),truth),X_16),X_16) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16)),implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) )],[refute_0_331,refute_0_332]) ).

cnf(refute_0_334,plain,
    implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16)) = implies(implies(implies(implies(X_4,truth),truth),X_16),X_16),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_16),X_16) )],[refute_0_330,refute_0_333]) ).

cnf(refute_0_335,plain,
    implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) = implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16)),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))))]]) ).

cnf(refute_0_336,plain,
    ( implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16)) != implies(implies(implies(implies(X_4,truth),truth),X_16),X_16)
    | implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) != implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))
    | implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) = implies(implies(implies(implies(X_4,truth),truth),X_16),X_16) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))))),bind(Y0,$fot(implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16)))),bind(Z0,$fot(implies(implies(implies(implies(X_4,truth),truth),X_16),X_16)))]]) ).

cnf(refute_0_337,plain,
    ( implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16)) != implies(implies(implies(implies(X_4,truth),truth),X_16),X_16)
    | implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) = implies(implies(implies(implies(X_4,truth),truth),X_16),X_16) ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))),implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) )],[refute_0_335,refute_0_336]) ).

cnf(refute_0_338,plain,
    implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) = implies(implies(implies(implies(X_4,truth),truth),X_16),X_16),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16)),implies(implies(implies(implies(X_4,truth),truth),X_16),X_16)) )],[refute_0_334,refute_0_337]) ).

cnf(refute_0_339,plain,
    ( implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) != implies(implies(implies(implies(X_4,truth),truth),X_16),X_16)
    | implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) != truth
    | implies(implies(implies(implies(X_4,truth),truth),X_16),X_16) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))),truth) ),[0],$fot(implies(implies(implies(implies(X_4,truth),truth),X_16),X_16))]]) ).

cnf(refute_0_340,plain,
    ( implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))) != truth
    | implies(implies(implies(implies(X_4,truth),truth),X_16),X_16) = truth ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))),implies(implies(implies(implies(X_4,truth),truth),X_16),X_16)) )],[refute_0_338,refute_0_339]) ).

cnf(refute_0_341,plain,
    implies(implies(implies(implies(X_4,truth),truth),X_16),X_16) = truth,
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_16),implies(implies(not(X_4),not(X_4)),X_16))),truth) )],[refute_0_323,refute_0_340]) ).

cnf(refute_0_342,plain,
    implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))) = truth,
    inference(subst,[],[refute_0_341:[bind(X_16,$fot(implies(not(X_7),not(X_7)))),bind(X_4,$fot(X_7))]]) ).

cnf(refute_0_343,plain,
    ( implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))) != implies(implies(X_7,truth),truth)
    | implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))) != truth
    | truth = implies(implies(X_7,truth),truth) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))),implies(implies(X_7,truth),truth)) ),[0],$fot(truth)]]) ).

cnf(refute_0_344,plain,
    ( implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))) != implies(implies(X_7,truth),truth)
    | truth = implies(implies(X_7,truth),truth) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))),truth) )],[refute_0_342,refute_0_343]) ).

cnf(refute_0_345,plain,
    truth = implies(implies(X_7,truth),truth),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_7,truth),truth),implies(not(X_7),not(X_7))),implies(not(X_7),not(X_7))),implies(implies(X_7,truth),truth)) )],[refute_0_319,refute_0_344]) ).

cnf(refute_0_346,plain,
    ( truth != implies(implies(X_7,truth),truth)
    | implies(implies(X_7,truth),truth) = truth ),
    inference(subst,[],[refute_0_45:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(implies(X_7,truth),truth)))]]) ).

cnf(refute_0_347,plain,
    implies(implies(X_7,truth),truth) = truth,
    inference(resolve,[$cnf( $equal(truth,implies(implies(X_7,truth),truth)) )],[refute_0_345,refute_0_346]) ).

cnf(refute_0_348,plain,
    implies(implies(X_15,truth),truth) = truth,
    inference(subst,[],[refute_0_347:[bind(X_7,$fot(X_15))]]) ).

cnf(refute_0_349,plain,
    implies(implies(X_4,truth),truth) = truth,
    inference(subst,[],[refute_0_347:[bind(X_7,$fot(X_4))]]) ).

cnf(refute_0_350,plain,
    implies(X_15,implies(implies(X_4,truth),truth)) = implies(X_15,implies(implies(X_4,truth),truth)),
    introduced(tautology,[refl,[$fot(implies(X_15,implies(implies(X_4,truth),truth)))]]) ).

cnf(refute_0_351,plain,
    ( implies(X_15,implies(implies(X_4,truth),truth)) != implies(X_15,implies(implies(X_4,truth),truth))
    | implies(implies(X_4,truth),truth) != truth
    | implies(X_15,implies(implies(X_4,truth),truth)) = implies(X_15,truth) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(X_15,implies(implies(X_4,truth),truth)),implies(X_15,implies(implies(X_4,truth),truth))) ),[1,1],$fot(truth)]]) ).

cnf(refute_0_352,plain,
    ( implies(implies(X_4,truth),truth) != truth
    | implies(X_15,implies(implies(X_4,truth),truth)) = implies(X_15,truth) ),
    inference(resolve,[$cnf( $equal(implies(X_15,implies(implies(X_4,truth),truth)),implies(X_15,implies(implies(X_4,truth),truth))) )],[refute_0_350,refute_0_351]) ).

cnf(refute_0_353,plain,
    implies(X_15,implies(implies(X_4,truth),truth)) = implies(X_15,truth),
    inference(resolve,[$cnf( $equal(implies(implies(X_4,truth),truth),truth) )],[refute_0_349,refute_0_352]) ).

cnf(refute_0_354,plain,
    implies(implies(X_15,implies(implies(X_4,truth),truth)),truth) = implies(implies(X_15,implies(implies(X_4,truth),truth)),truth),
    introduced(tautology,[refl,[$fot(implies(implies(X_15,implies(implies(X_4,truth),truth)),truth))]]) ).

cnf(refute_0_355,plain,
    ( implies(X_15,implies(implies(X_4,truth),truth)) != implies(X_15,truth)
    | implies(implies(X_15,implies(implies(X_4,truth),truth)),truth) != implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)
    | implies(implies(X_15,implies(implies(X_4,truth),truth)),truth) = implies(implies(X_15,truth),truth) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_15,implies(implies(X_4,truth),truth)),truth),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) ),[1,0],$fot(implies(X_15,truth))]]) ).

cnf(refute_0_356,plain,
    ( implies(X_15,implies(implies(X_4,truth),truth)) != implies(X_15,truth)
    | implies(implies(X_15,implies(implies(X_4,truth),truth)),truth) = implies(implies(X_15,truth),truth) ),
    inference(resolve,[$cnf( $equal(implies(implies(X_15,implies(implies(X_4,truth),truth)),truth),implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) )],[refute_0_354,refute_0_355]) ).

cnf(refute_0_357,plain,
    implies(implies(X_15,implies(implies(X_4,truth),truth)),truth) = implies(implies(X_15,truth),truth),
    inference(resolve,[$cnf( $equal(implies(X_15,implies(implies(X_4,truth),truth)),implies(X_15,truth)) )],[refute_0_353,refute_0_356]) ).

cnf(refute_0_358,plain,
    ( implies(implies(X_15,implies(implies(X_4,truth),truth)),truth) != implies(implies(X_15,truth),truth)
    | implies(implies(X_15,truth),truth) != truth
    | implies(implies(X_15,implies(implies(X_4,truth),truth)),truth) = truth ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(X_15,implies(implies(X_4,truth),truth)),truth))),bind(Y0,$fot(implies(implies(X_15,truth),truth))),bind(Z0,$fot(truth))]]) ).

cnf(refute_0_359,plain,
    ( implies(implies(X_15,truth),truth) != truth
    | implies(implies(X_15,implies(implies(X_4,truth),truth)),truth) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(X_15,implies(implies(X_4,truth),truth)),truth),implies(implies(X_15,truth),truth)) )],[refute_0_357,refute_0_358]) ).

cnf(refute_0_360,plain,
    implies(implies(X_15,implies(implies(X_4,truth),truth)),truth) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(X_15,truth),truth),truth) )],[refute_0_348,refute_0_359]) ).

cnf(refute_0_361,plain,
    implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) = implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)),
    introduced(tautology,[refl,[$fot(implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)))]]) ).

cnf(refute_0_362,plain,
    ( implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) != implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth))
    | implies(implies(X_15,implies(implies(X_4,truth),truth)),truth) != truth
    | implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) = implies(X_15,truth) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)),implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth))) ),[1,1],$fot(truth)]]) ).

cnf(refute_0_363,plain,
    ( implies(implies(X_15,implies(implies(X_4,truth),truth)),truth) != truth
    | implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) = implies(X_15,truth) ),
    inference(resolve,[$cnf( $equal(implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)),implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth))) )],[refute_0_361,refute_0_362]) ).

cnf(refute_0_364,plain,
    implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) = implies(X_15,truth),
    inference(resolve,[$cnf( $equal(implies(implies(X_15,implies(implies(X_4,truth),truth)),truth),truth) )],[refute_0_360,refute_0_363]) ).

cnf(refute_0_365,plain,
    ( implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) != implies(X_15,truth)
    | implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) != truth
    | implies(X_15,truth) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)),truth) ),[0],$fot(implies(X_15,truth))]]) ).

cnf(refute_0_366,plain,
    ( implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)) != truth
    | implies(X_15,truth) = truth ),
    inference(resolve,[$cnf( $equal(implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)),implies(X_15,truth)) )],[refute_0_364,refute_0_365]) ).

cnf(refute_0_367,plain,
    implies(X_15,truth) = truth,
    inference(resolve,[$cnf( $equal(implies(X_15,implies(implies(X_15,implies(implies(X_4,truth),truth)),truth)),truth) )],[refute_0_310,refute_0_366]) ).

cnf(refute_0_368,plain,
    implies(X_14,truth) = truth,
    inference(subst,[],[refute_0_367:[bind(X_15,$fot(X_14))]]) ).

cnf(refute_0_369,plain,
    implies(implies(X_16,truth),truth) = truth,
    inference(subst,[],[refute_0_367:[bind(X_15,$fot(implies(X_16,truth)))]]) ).

cnf(refute_0_370,plain,
    implies(X_14,implies(implies(X_16,truth),truth)) = implies(X_14,implies(implies(X_16,truth),truth)),
    introduced(tautology,[refl,[$fot(implies(X_14,implies(implies(X_16,truth),truth)))]]) ).

cnf(refute_0_371,plain,
    ( implies(X_14,implies(implies(X_16,truth),truth)) != implies(X_14,implies(implies(X_16,truth),truth))
    | implies(implies(X_16,truth),truth) != truth
    | implies(X_14,implies(implies(X_16,truth),truth)) = implies(X_14,truth) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_14,implies(implies(X_16,truth),truth))) ),[1,1],$fot(truth)]]) ).

cnf(refute_0_372,plain,
    ( implies(implies(X_16,truth),truth) != truth
    | implies(X_14,implies(implies(X_16,truth),truth)) = implies(X_14,truth) ),
    inference(resolve,[$cnf( $equal(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_14,implies(implies(X_16,truth),truth))) )],[refute_0_370,refute_0_371]) ).

cnf(refute_0_373,plain,
    implies(X_14,implies(implies(X_16,truth),truth)) = implies(X_14,truth),
    inference(resolve,[$cnf( $equal(implies(implies(X_16,truth),truth),truth) )],[refute_0_369,refute_0_372]) ).

cnf(refute_0_374,plain,
    ( implies(X_14,implies(implies(X_16,truth),truth)) != implies(X_14,truth)
    | implies(X_14,truth) != truth
    | implies(X_14,implies(implies(X_16,truth),truth)) = truth ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(X_14,implies(implies(X_16,truth),truth)))),bind(Y0,$fot(implies(X_14,truth))),bind(Z0,$fot(truth))]]) ).

cnf(refute_0_375,plain,
    ( implies(X_14,truth) != truth
    | implies(X_14,implies(implies(X_16,truth),truth)) = truth ),
    inference(resolve,[$cnf( $equal(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_14,truth)) )],[refute_0_373,refute_0_374]) ).

cnf(refute_0_376,plain,
    implies(X_14,implies(implies(X_16,truth),truth)) = truth,
    inference(resolve,[$cnf( $equal(implies(X_14,truth),truth) )],[refute_0_368,refute_0_375]) ).

cnf(refute_0_377,plain,
    implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) = implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))),
    introduced(tautology,[refl,[$fot(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))))]]) ).

cnf(refute_0_378,plain,
    ( implies(X_14,implies(implies(X_16,truth),truth)) != truth
    | implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) != implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16)))
    | implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) = implies(truth,implies(X_16,implies(X_14,X_16))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))),implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16)))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_379,plain,
    ( implies(X_14,implies(implies(X_16,truth),truth)) != truth
    | implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) = implies(truth,implies(X_16,implies(X_14,X_16))) ),
    inference(resolve,[$cnf( $equal(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))),implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16)))) )],[refute_0_377,refute_0_378]) ).

cnf(refute_0_380,plain,
    implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) = implies(truth,implies(X_16,implies(X_14,X_16))),
    inference(resolve,[$cnf( $equal(implies(X_14,implies(implies(X_16,truth),truth)),truth) )],[refute_0_376,refute_0_379]) ).

cnf(refute_0_381,plain,
    ( implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) != implies(truth,implies(X_16,implies(X_14,X_16)))
    | implies(truth,implies(X_16,implies(X_14,X_16))) != implies(X_16,implies(X_14,X_16))
    | implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) = implies(X_16,implies(X_14,X_16)) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))))),bind(Y0,$fot(implies(truth,implies(X_16,implies(X_14,X_16))))),bind(Z0,$fot(implies(X_16,implies(X_14,X_16))))]]) ).

cnf(refute_0_382,plain,
    ( implies(truth,implies(X_16,implies(X_14,X_16))) != implies(X_16,implies(X_14,X_16))
    | implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) = implies(X_16,implies(X_14,X_16)) ),
    inference(resolve,[$cnf( $equal(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))),implies(truth,implies(X_16,implies(X_14,X_16)))) )],[refute_0_380,refute_0_381]) ).

cnf(refute_0_383,plain,
    implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) = implies(X_16,implies(X_14,X_16)),
    inference(resolve,[$cnf( $equal(implies(truth,implies(X_16,implies(X_14,X_16))),implies(X_16,implies(X_14,X_16))) )],[refute_0_291,refute_0_382]) ).

cnf(refute_0_384,plain,
    ( implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) != implies(X_16,implies(X_14,X_16))
    | implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) != truth
    | implies(X_16,implies(X_14,X_16)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))),truth) ),[0],$fot(implies(X_16,implies(X_14,X_16)))]]) ).

cnf(refute_0_385,plain,
    ( implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))) != truth
    | implies(X_16,implies(X_14,X_16)) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))),implies(X_16,implies(X_14,X_16))) )],[refute_0_383,refute_0_384]) ).

cnf(refute_0_386,plain,
    implies(X_16,implies(X_14,X_16)) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(X_14,implies(implies(X_16,truth),truth)),implies(X_16,implies(X_14,X_16))),truth) )],[refute_0_290,refute_0_385]) ).

cnf(refute_0_387,plain,
    implies(not(truth),implies(not(not(not(truth))),not(truth))) = truth,
    inference(subst,[],[refute_0_386:[bind(X_14,$fot(not(not(not(truth))))),bind(X_16,$fot(not(truth)))]]) ).

cnf(refute_0_388,plain,
    implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),
    introduced(tautology,[refl,[$fot(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))))]]) ).

cnf(refute_0_389,plain,
    ( implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) != implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))
    | implies(not(truth),implies(not(not(not(truth))),not(truth))) != truth
    | implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = implies(truth,not(not(truth))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_390,plain,
    ( implies(not(truth),implies(not(not(not(truth))),not(truth))) != truth
    | implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = implies(truth,not(not(truth))) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) )],[refute_0_388,refute_0_389]) ).

cnf(refute_0_391,plain,
    implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = implies(truth,not(not(truth))),
    inference(resolve,[$cnf( $equal(implies(not(truth),implies(not(not(not(truth))),not(truth))),truth) )],[refute_0_387,refute_0_390]) ).

cnf(refute_0_392,plain,
    ( implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) != implies(truth,not(not(truth)))
    | implies(truth,not(not(truth))) != not(not(truth))
    | implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = not(not(truth)) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))))),bind(Y0,$fot(implies(truth,not(not(truth))))),bind(Z0,$fot(not(not(truth))))]]) ).

cnf(refute_0_393,plain,
    ( implies(truth,not(not(truth))) != not(not(truth))
    | implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = not(not(truth)) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),implies(truth,not(not(truth)))) )],[refute_0_391,refute_0_392]) ).

cnf(refute_0_394,plain,
    implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = not(not(truth)),
    inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_122,refute_0_393]) ).

cnf(refute_0_395,plain,
    implies(truth,implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) = implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))))]]) ).

cnf(refute_0_396,plain,
    ( implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) != not(not(truth))
    | implies(truth,implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) != implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))
    | implies(truth,implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) = not(not(truth)) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(truth,implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))))),bind(Y0,$fot(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))))),bind(Z0,$fot(not(not(truth))))]]) ).

cnf(refute_0_397,plain,
    ( implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) != not(not(truth))
    | implies(truth,implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) = not(not(truth)) ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))),implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) )],[refute_0_395,refute_0_396]) ).

cnf(refute_0_398,plain,
    implies(truth,implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) = not(not(truth)),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),not(not(truth))) )],[refute_0_394,refute_0_397]) ).

cnf(refute_0_399,plain,
    ( implies(truth,implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) != not(not(truth))
    | implies(truth,implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) != truth
    | not(not(truth)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))),truth) ),[0],$fot(not(not(truth)))]]) ).

cnf(refute_0_400,plain,
    ( implies(truth,implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) != truth
    | not(not(truth)) = truth ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))),not(not(truth))) )],[refute_0_398,refute_0_399]) ).

cnf(refute_0_401,plain,
    not(not(truth)) = truth,
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))),truth) )],[refute_0_121,refute_0_400]) ).

cnf(refute_0_402,plain,
    implies(not(not(truth)),not(not(X_39))) = implies(not(not(truth)),not(not(X_39))),
    introduced(tautology,[refl,[$fot(implies(not(not(truth)),not(not(X_39))))]]) ).

cnf(refute_0_403,plain,
    ( implies(not(not(truth)),not(not(X_39))) != implies(not(not(truth)),not(not(X_39)))
    | not(not(truth)) != truth
    | implies(not(not(truth)),not(not(X_39))) = implies(truth,not(not(X_39))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(not(X_39))),implies(not(not(truth)),not(not(X_39)))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_404,plain,
    ( not(not(truth)) != truth
    | implies(not(not(truth)),not(not(X_39))) = implies(truth,not(not(X_39))) ),
    inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_39))),implies(not(not(truth)),not(not(X_39)))) )],[refute_0_402,refute_0_403]) ).

cnf(refute_0_405,plain,
    implies(not(not(truth)),not(not(X_39))) = implies(truth,not(not(X_39))),
    inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_401,refute_0_404]) ).

cnf(refute_0_406,plain,
    ( implies(not(not(truth)),not(not(X_39))) != implies(truth,not(not(X_39)))
    | implies(truth,not(not(X_39))) != not(not(X_39))
    | implies(not(not(truth)),not(not(X_39))) = not(not(X_39)) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(not(not(truth)),not(not(X_39))))),bind(Y0,$fot(implies(truth,not(not(X_39))))),bind(Z0,$fot(not(not(X_39))))]]) ).

cnf(refute_0_407,plain,
    ( implies(truth,not(not(X_39))) != not(not(X_39))
    | implies(not(not(truth)),not(not(X_39))) = not(not(X_39)) ),
    inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_39))),implies(truth,not(not(X_39)))) )],[refute_0_405,refute_0_406]) ).

cnf(refute_0_408,plain,
    implies(not(not(truth)),not(not(X_39))) = not(not(X_39)),
    inference(resolve,[$cnf( $equal(implies(truth,not(not(X_39))),not(not(X_39))) )],[refute_0_96,refute_0_407]) ).

cnf(refute_0_409,plain,
    implies(implies(not(not(truth)),not(not(X_39))),X_39) = implies(implies(not(not(truth)),not(not(X_39))),X_39),
    introduced(tautology,[refl,[$fot(implies(implies(not(not(truth)),not(not(X_39))),X_39))]]) ).

cnf(refute_0_410,plain,
    ( implies(implies(not(not(truth)),not(not(X_39))),X_39) != implies(implies(not(not(truth)),not(not(X_39))),X_39)
    | implies(not(not(truth)),not(not(X_39))) != not(not(X_39))
    | implies(implies(not(not(truth)),not(not(X_39))),X_39) = implies(not(not(X_39)),X_39) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_39))),X_39),implies(implies(not(not(truth)),not(not(X_39))),X_39)) ),[1,0],$fot(not(not(X_39)))]]) ).

cnf(refute_0_411,plain,
    ( implies(not(not(truth)),not(not(X_39))) != not(not(X_39))
    | implies(implies(not(not(truth)),not(not(X_39))),X_39) = implies(not(not(X_39)),X_39) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_39))),X_39),implies(implies(not(not(truth)),not(not(X_39))),X_39)) )],[refute_0_409,refute_0_410]) ).

cnf(refute_0_412,plain,
    implies(implies(not(not(truth)),not(not(X_39))),X_39) = implies(not(not(X_39)),X_39),
    inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_39))),not(not(X_39))) )],[refute_0_408,refute_0_411]) ).

cnf(refute_0_413,plain,
    ( implies(implies(not(not(truth)),not(not(X_39))),X_39) != implies(not(not(X_39)),X_39)
    | implies(implies(not(not(truth)),not(not(X_39))),X_39) != truth
    | implies(not(not(X_39)),X_39) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_39))),X_39),truth) ),[0],$fot(implies(not(not(X_39)),X_39))]]) ).

cnf(refute_0_414,plain,
    ( implies(implies(not(not(truth)),not(not(X_39))),X_39) != truth
    | implies(not(not(X_39)),X_39) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_39))),X_39),implies(not(not(X_39)),X_39)) )],[refute_0_412,refute_0_413]) ).

cnf(refute_0_415,plain,
    implies(not(not(X_39)),X_39) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_39))),X_39),truth) )],[refute_0_95,refute_0_414]) ).

cnf(refute_0_416,plain,
    implies(not(not(Y)),Y) = truth,
    inference(subst,[],[refute_0_415:[bind(X_39,$fot(Y))]]) ).

cnf(refute_0_417,plain,
    ( implies(implies(not(not(not(Y))),not(implies(implies(not(not(Y)),Y),Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) != truth
    | implies(not(not(Y)),Y) != truth
    | implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(Y))),not(implies(implies(not(not(Y)),Y),Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))),truth) ),[0,0,1,0,0],$fot(truth)]]) ).

cnf(refute_0_418,plain,
    ( implies(implies(not(not(not(Y))),not(implies(implies(not(not(Y)),Y),Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) != truth
    | implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = truth ),
    inference(resolve,[$cnf( $equal(implies(not(not(Y)),Y),truth) )],[refute_0_416,refute_0_417]) ).

cnf(refute_0_419,plain,
    implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(not(not(Y))),not(implies(implies(not(not(Y)),Y),Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))),truth) )],[refute_0_68,refute_0_418]) ).

cnf(refute_0_420,plain,
    implies(truth,implies(Y,not(not(Y)))) = implies(Y,not(not(Y))),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(Y,not(not(Y)))))]]) ).

cnf(refute_0_421,plain,
    implies(truth,Y) = Y,
    inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).

cnf(refute_0_422,plain,
    implies(implies(not(not(Y)),Y),Y) = implies(implies(not(not(Y)),Y),Y),
    introduced(tautology,[refl,[$fot(implies(implies(not(not(Y)),Y),Y))]]) ).

cnf(refute_0_423,plain,
    ( implies(implies(not(not(Y)),Y),Y) != implies(implies(not(not(Y)),Y),Y)
    | implies(not(not(Y)),Y) != truth
    | implies(implies(not(not(Y)),Y),Y) = implies(truth,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(not(not(Y)),Y),Y)) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_424,plain,
    ( implies(not(not(Y)),Y) != truth
    | implies(implies(not(not(Y)),Y),Y) = implies(truth,Y) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(not(not(Y)),Y),Y)) )],[refute_0_422,refute_0_423]) ).

cnf(refute_0_425,plain,
    implies(implies(not(not(Y)),Y),Y) = implies(truth,Y),
    inference(resolve,[$cnf( $equal(implies(not(not(Y)),Y),truth) )],[refute_0_416,refute_0_424]) ).

cnf(refute_0_426,plain,
    ( implies(implies(not(not(Y)),Y),Y) != implies(truth,Y)
    | implies(truth,Y) != Y
    | implies(implies(not(not(Y)),Y),Y) = Y ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(not(not(Y)),Y),Y))),bind(Y0,$fot(implies(truth,Y))),bind(Z0,$fot(Y))]]) ).

cnf(refute_0_427,plain,
    ( implies(truth,Y) != Y
    | implies(implies(not(not(Y)),Y),Y) = Y ),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,Y)) )],[refute_0_425,refute_0_426]) ).

cnf(refute_0_428,plain,
    implies(implies(not(not(Y)),Y),Y) = Y,
    inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_421,refute_0_427]) ).

cnf(refute_0_429,plain,
    implies(implies(implies(not(not(Y)),Y),Y),not(not(Y))) = implies(implies(implies(not(not(Y)),Y),Y),not(not(Y))),
    introduced(tautology,[refl,[$fot(implies(implies(implies(not(not(Y)),Y),Y),not(not(Y))))]]) ).

cnf(refute_0_430,plain,
    ( implies(implies(implies(not(not(Y)),Y),Y),not(not(Y))) != implies(implies(implies(not(not(Y)),Y),Y),not(not(Y)))
    | implies(implies(not(not(Y)),Y),Y) != Y
    | implies(implies(implies(not(not(Y)),Y),Y),not(not(Y))) = implies(Y,not(not(Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(Y)),Y),Y),not(not(Y))),implies(implies(implies(not(not(Y)),Y),Y),not(not(Y)))) ),[1,0],$fot(Y)]]) ).

cnf(refute_0_431,plain,
    ( implies(implies(not(not(Y)),Y),Y) != Y
    | implies(implies(implies(not(not(Y)),Y),Y),not(not(Y))) = implies(Y,not(not(Y))) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(Y)),Y),Y),not(not(Y))),implies(implies(implies(not(not(Y)),Y),Y),not(not(Y)))) )],[refute_0_429,refute_0_430]) ).

cnf(refute_0_432,plain,
    implies(implies(implies(not(not(Y)),Y),Y),not(not(Y))) = implies(Y,not(not(Y))),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),Y) )],[refute_0_428,refute_0_431]) ).

cnf(refute_0_433,plain,
    implies(implies(X,implies(X_1,X)),implies(X_1,X)) = implies(implies(implies(X_1,X),X),X),
    inference(subst,[],[wajsberg_3:[bind(Y,$fot(implies(X_1,X)))]]) ).

cnf(refute_0_434,plain,
    implies(implies(X_1,X),X) = implies(implies(X,X_1),X_1),
    inference(subst,[],[wajsberg_3:[bind(X,$fot(X_1)),bind(Y,$fot(X))]]) ).

cnf(refute_0_435,plain,
    ( implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X_1,X),X),X)
    | implies(implies(X_1,X),X) != implies(implies(X,X_1),X_1)
    | implies(implies(X,implies(X_1,X)),implies(X_1,X)) = implies(implies(implies(X,X_1),X_1),X) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X_1,X),X),X)) ),[1,0],$fot(implies(implies(X,X_1),X_1))]]) ).

cnf(refute_0_436,plain,
    ( implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X_1,X),X),X)
    | implies(implies(X,implies(X_1,X)),implies(X_1,X)) = implies(implies(implies(X,X_1),X_1),X) ),
    inference(resolve,[$cnf( $equal(implies(implies(X_1,X),X),implies(implies(X,X_1),X_1)) )],[refute_0_434,refute_0_435]) ).

cnf(refute_0_437,plain,
    implies(implies(X,implies(X_1,X)),implies(X_1,X)) = implies(implies(implies(X,X_1),X_1),X),
    inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X_1,X),X),X)) )],[refute_0_433,refute_0_436]) ).

cnf(refute_0_438,plain,
    ( implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X,X_1),X_1),X)
    | implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X_1,X),X),X)
    | implies(implies(implies(X_1,X),X),X) = implies(implies(implies(X,X_1),X_1),X) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X,X_1),X_1),X)) ),[0],$fot(implies(implies(implies(X_1,X),X),X))]]) ).

cnf(refute_0_439,plain,
    ( implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X,X_1),X_1),X)
    | implies(implies(implies(X_1,X),X),X) = implies(implies(implies(X,X_1),X_1),X) ),
    inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X_1,X),X),X)) )],[refute_0_433,refute_0_438]) ).

cnf(refute_0_440,plain,
    implies(implies(implies(X_1,X),X),X) = implies(implies(implies(X,X_1),X_1),X),
    inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X,X_1),X_1),X)) )],[refute_0_437,refute_0_439]) ).

cnf(refute_0_441,plain,
    implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))) = implies(implies(implies(not(not(Y)),Y),Y),not(not(Y))),
    inference(subst,[],[refute_0_440:[bind(X,$fot(not(not(Y)))),bind(X_1,$fot(Y))]]) ).

cnf(refute_0_442,plain,
    ( implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))) != implies(implies(implies(not(not(Y)),Y),Y),not(not(Y)))
    | implies(implies(implies(not(not(Y)),Y),Y),not(not(Y))) != implies(Y,not(not(Y)))
    | implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))) = implies(Y,not(not(Y))) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))))),bind(Y0,$fot(implies(implies(implies(not(not(Y)),Y),Y),not(not(Y))))),bind(Z0,$fot(implies(Y,not(not(Y)))))]]) ).

cnf(refute_0_443,plain,
    ( implies(implies(implies(not(not(Y)),Y),Y),not(not(Y))) != implies(Y,not(not(Y)))
    | implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))) = implies(Y,not(not(Y))) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))),implies(implies(implies(not(not(Y)),Y),Y),not(not(Y)))) )],[refute_0_441,refute_0_442]) ).

cnf(refute_0_444,plain,
    implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))) = implies(Y,not(not(Y))),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(Y)),Y),Y),not(not(Y))),implies(Y,not(not(Y)))) )],[refute_0_432,refute_0_443]) ).

cnf(refute_0_445,plain,
    implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))),
    introduced(tautology,[refl,[$fot(implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))))]]) ).

cnf(refute_0_446,plain,
    ( implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))) != implies(Y,not(not(Y)))
    | implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) != implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))))
    | implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = implies(truth,implies(Y,not(not(Y)))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))),implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))))) ),[1,1],$fot(implies(Y,not(not(Y))))]]) ).

cnf(refute_0_447,plain,
    ( implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))) != implies(Y,not(not(Y)))
    | implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = implies(truth,implies(Y,not(not(Y)))) ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))),implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))))) )],[refute_0_445,refute_0_446]) ).

cnf(refute_0_448,plain,
    implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = implies(truth,implies(Y,not(not(Y)))),
    inference(resolve,[$cnf( $equal(implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))),implies(Y,not(not(Y)))) )],[refute_0_444,refute_0_447]) ).

cnf(refute_0_449,plain,
    implies(not(Y),not(Y)) = truth,
    inference(subst,[],[refute_0_272:[bind(X_16,$fot(not(Y)))]]) ).

cnf(refute_0_450,plain,
    not(implies(truth,Y)) = not(implies(truth,Y)),
    introduced(tautology,[refl,[$fot(not(implies(truth,Y)))]]) ).

cnf(refute_0_451,plain,
    ( implies(truth,Y) != Y
    | not(implies(truth,Y)) != not(implies(truth,Y))
    | not(implies(truth,Y)) = not(Y) ),
    introduced(tautology,[equality,[$cnf( $equal(not(implies(truth,Y)),not(implies(truth,Y))) ),[1,0],$fot(Y)]]) ).

cnf(refute_0_452,plain,
    ( implies(truth,Y) != Y
    | not(implies(truth,Y)) = not(Y) ),
    inference(resolve,[$cnf( $equal(not(implies(truth,Y)),not(implies(truth,Y))) )],[refute_0_450,refute_0_451]) ).

cnf(refute_0_453,plain,
    not(implies(truth,Y)) = not(Y),
    inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_421,refute_0_452]) ).

cnf(refute_0_454,plain,
    implies(not(Y),not(implies(truth,Y))) = implies(not(Y),not(implies(truth,Y))),
    introduced(tautology,[refl,[$fot(implies(not(Y),not(implies(truth,Y))))]]) ).

cnf(refute_0_455,plain,
    ( implies(not(Y),not(implies(truth,Y))) != implies(not(Y),not(implies(truth,Y)))
    | not(implies(truth,Y)) != not(Y)
    | implies(not(Y),not(implies(truth,Y))) = implies(not(Y),not(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(Y),not(implies(truth,Y))),implies(not(Y),not(implies(truth,Y)))) ),[1,1],$fot(not(Y))]]) ).

cnf(refute_0_456,plain,
    ( not(implies(truth,Y)) != not(Y)
    | implies(not(Y),not(implies(truth,Y))) = implies(not(Y),not(Y)) ),
    inference(resolve,[$cnf( $equal(implies(not(Y),not(implies(truth,Y))),implies(not(Y),not(implies(truth,Y)))) )],[refute_0_454,refute_0_455]) ).

cnf(refute_0_457,plain,
    implies(not(Y),not(implies(truth,Y))) = implies(not(Y),not(Y)),
    inference(resolve,[$cnf( $equal(not(implies(truth,Y)),not(Y)) )],[refute_0_453,refute_0_456]) ).

cnf(refute_0_458,plain,
    implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(implies(implies(not(not(truth)),not(X_50)),implies(implies(not(truth),not(X_50)),not(X_50))),implies(implies(not(truth),not(X_50)),not(X_50))),
    inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(implies(not(truth),not(X_50)),not(X_50)))),bind(Y,$fot(implies(not(not(truth)),not(X_50))))]]) ).

cnf(refute_0_459,plain,
    implies(implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))),implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))) = truth,
    inference(subst,[],[refute_0_30:[bind(X,$fot(not(truth))),bind(Y,$fot(X_43)),bind(X_16,$fot(implies(implies(not(truth),not(X_43)),not(X_43))))]]) ).

cnf(refute_0_460,plain,
    implies(implies(implies(not(X_15),not(truth)),X_15),implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))) = truth,
    inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(X_15),not(truth)))),bind(Y,$fot(X_15)),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_461,plain,
    implies(implies(not(X_15),not(truth)),X_15) = truth,
    inference(subst,[],[refute_0_74:[bind(X_4,$fot(X_15))]]) ).

cnf(refute_0_462,plain,
    ( implies(implies(implies(not(X_15),not(truth)),X_15),implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))) != truth
    | implies(implies(not(X_15),not(truth)),X_15) != truth
    | implies(truth,implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_15),not(truth)),X_15),implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))),truth) ),[0,0],$fot(truth)]]) ).

cnf(refute_0_463,plain,
    ( implies(implies(implies(not(X_15),not(truth)),X_15),implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))) != truth
    | implies(truth,implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_15),not(truth)),X_15),truth) )],[refute_0_461,refute_0_462]) ).

cnf(refute_0_464,plain,
    implies(truth,implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_15),not(truth)),X_15),implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))),truth) )],[refute_0_460,refute_0_463]) ).

cnf(refute_0_465,plain,
    implies(truth,implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))) = implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16)),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))))]]) ).

cnf(refute_0_466,plain,
    ( implies(truth,implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))) != implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))
    | implies(truth,implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))) != truth
    | implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))),truth) ),[0],$fot(implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16)))]]) ).

cnf(refute_0_467,plain,
    ( implies(truth,implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))) != truth
    | implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16)) = truth ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))),implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))) )],[refute_0_465,refute_0_466]) ).

cnf(refute_0_468,plain,
    implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16)) = truth,
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_15,X_16),implies(implies(not(X_15),not(truth)),X_16))),truth) )],[refute_0_464,refute_0_467]) ).

cnf(refute_0_469,plain,
    implies(implies(X_22,not(truth)),implies(implies(not(X_22),not(truth)),not(truth))) = truth,
    inference(subst,[],[refute_0_468:[bind(X_15,$fot(X_22)),bind(X_16,$fot(not(truth)))]]) ).

cnf(refute_0_470,plain,
    implies(implies(not(truth),not(X_22)),not(X_22)) = implies(implies(not(X_22),not(truth)),not(truth)),
    inference(subst,[],[wajsberg_3:[bind(X,$fot(not(truth))),bind(Y,$fot(not(X_22)))]]) ).

cnf(refute_0_471,plain,
    ( implies(implies(not(truth),not(X_22)),not(X_22)) != implies(implies(not(X_22),not(truth)),not(truth))
    | implies(implies(not(X_22),not(truth)),not(truth)) = implies(implies(not(truth),not(X_22)),not(X_22)) ),
    inference(subst,[],[refute_0_45:[bind(X0,$fot(implies(implies(not(truth),not(X_22)),not(X_22)))),bind(Y0,$fot(implies(implies(not(X_22),not(truth)),not(truth))))]]) ).

cnf(refute_0_472,plain,
    implies(implies(not(X_22),not(truth)),not(truth)) = implies(implies(not(truth),not(X_22)),not(X_22)),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_22)),not(X_22)),implies(implies(not(X_22),not(truth)),not(truth))) )],[refute_0_470,refute_0_471]) ).

cnf(refute_0_473,plain,
    ( implies(implies(X_22,not(truth)),implies(implies(not(X_22),not(truth)),not(truth))) != truth
    | implies(implies(not(X_22),not(truth)),not(truth)) != implies(implies(not(truth),not(X_22)),not(X_22))
    | implies(implies(X_22,not(truth)),implies(implies(not(truth),not(X_22)),not(X_22))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_22,not(truth)),implies(implies(not(X_22),not(truth)),not(truth))),truth) ),[0,1],$fot(implies(implies(not(truth),not(X_22)),not(X_22)))]]) ).

cnf(refute_0_474,plain,
    ( implies(implies(X_22,not(truth)),implies(implies(not(X_22),not(truth)),not(truth))) != truth
    | implies(implies(X_22,not(truth)),implies(implies(not(truth),not(X_22)),not(X_22))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_22),not(truth)),not(truth)),implies(implies(not(truth),not(X_22)),not(X_22))) )],[refute_0_472,refute_0_473]) ).

cnf(refute_0_475,plain,
    implies(implies(X_22,not(truth)),implies(implies(not(truth),not(X_22)),not(X_22))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(X_22,not(truth)),implies(implies(not(X_22),not(truth)),not(truth))),truth) )],[refute_0_469,refute_0_474]) ).

cnf(refute_0_476,plain,
    implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))) = truth,
    inference(subst,[],[refute_0_475:[bind(X_22,$fot(X_43))]]) ).

cnf(refute_0_477,plain,
    ( implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))) != truth
    | implies(implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))),implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))) != truth
    | implies(truth,implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))),implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))),truth) ),[0,0],$fot(truth)]]) ).

cnf(refute_0_478,plain,
    ( implies(implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))),implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))) != truth
    | implies(truth,implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))),truth) )],[refute_0_476,refute_0_477]) ).

cnf(refute_0_479,plain,
    implies(truth,implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))),implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))),truth) )],[refute_0_459,refute_0_478]) ).

cnf(refute_0_480,plain,
    implies(truth,implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))) = implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43))),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))))]]) ).

cnf(refute_0_481,plain,
    ( implies(truth,implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))) != implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))
    | implies(truth,implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))) != truth
    | implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))),truth) ),[0],$fot(implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43))))]]) ).

cnf(refute_0_482,plain,
    ( implies(truth,implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))) != truth
    | implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43))) = truth ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))),implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))) )],[refute_0_480,refute_0_481]) ).

cnf(refute_0_483,plain,
    implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43))) = truth,
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43)))),truth) )],[refute_0_479,refute_0_482]) ).

cnf(refute_0_484,plain,
    implies(implies(not(not(truth)),not(X_50)),implies(implies(not(truth),not(X_50)),not(X_50))) = truth,
    inference(subst,[],[refute_0_483:[bind(X_43,$fot(X_50))]]) ).

cnf(refute_0_485,plain,
    ( implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) != implies(implies(implies(not(not(truth)),not(X_50)),implies(implies(not(truth),not(X_50)),not(X_50))),implies(implies(not(truth),not(X_50)),not(X_50)))
    | implies(implies(not(not(truth)),not(X_50)),implies(implies(not(truth),not(X_50)),not(X_50))) != truth
    | implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(truth,implies(implies(not(truth),not(X_50)),not(X_50))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))),implies(implies(implies(not(not(truth)),not(X_50)),implies(implies(not(truth),not(X_50)),not(X_50))),implies(implies(not(truth),not(X_50)),not(X_50)))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_486,plain,
    ( implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) != implies(implies(implies(not(not(truth)),not(X_50)),implies(implies(not(truth),not(X_50)),not(X_50))),implies(implies(not(truth),not(X_50)),not(X_50)))
    | implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(truth,implies(implies(not(truth),not(X_50)),not(X_50))) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(X_50)),implies(implies(not(truth),not(X_50)),not(X_50))),truth) )],[refute_0_484,refute_0_485]) ).

cnf(refute_0_487,plain,
    implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(truth,implies(implies(not(truth),not(X_50)),not(X_50))),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))),implies(implies(implies(not(not(truth)),not(X_50)),implies(implies(not(truth),not(X_50)),not(X_50))),implies(implies(not(truth),not(X_50)),not(X_50)))) )],[refute_0_458,refute_0_486]) ).

cnf(refute_0_488,plain,
    implies(truth,implies(implies(not(truth),not(X_50)),not(X_50))) = implies(implies(not(truth),not(X_50)),not(X_50)),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(truth),not(X_50)),not(X_50))))]]) ).

cnf(refute_0_489,plain,
    ( implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) != implies(truth,implies(implies(not(truth),not(X_50)),not(X_50)))
    | implies(truth,implies(implies(not(truth),not(X_50)),not(X_50))) != implies(implies(not(truth),not(X_50)),not(X_50))
    | implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(implies(not(truth),not(X_50)),not(X_50)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))),implies(implies(not(truth),not(X_50)),not(X_50))) ),[0],$fot(implies(truth,implies(implies(not(truth),not(X_50)),not(X_50))))]]) ).

cnf(refute_0_490,plain,
    ( implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) != implies(truth,implies(implies(not(truth),not(X_50)),not(X_50)))
    | implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(implies(not(truth),not(X_50)),not(X_50)) ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(truth),not(X_50)),not(X_50))),implies(implies(not(truth),not(X_50)),not(X_50))) )],[refute_0_488,refute_0_489]) ).

cnf(refute_0_491,plain,
    implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(implies(not(truth),not(X_50)),not(X_50)),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))),implies(truth,implies(implies(not(truth),not(X_50)),not(X_50)))) )],[refute_0_487,refute_0_490]) ).

cnf(refute_0_492,plain,
    implies(implies(X,implies(implies(X_21,X),X)),implies(implies(X_21,X),X)) = implies(implies(implies(implies(X_21,X),X),X),X),
    inference(subst,[],[wajsberg_3:[bind(Y,$fot(implies(implies(X_21,X),X)))]]) ).

cnf(refute_0_493,plain,
    implies(implies(implies(X_21,X),X),X) = implies(implies(implies(X,X_21),X_21),X),
    inference(subst,[],[refute_0_440:[bind(X_1,$fot(X_21))]]) ).

cnf(refute_0_494,plain,
    ( implies(implies(X,implies(implies(X_21,X),X)),implies(implies(X_21,X),X)) != implies(implies(implies(implies(X_21,X),X),X),X)
    | implies(implies(implies(X_21,X),X),X) != implies(implies(implies(X,X_21),X_21),X)
    | implies(implies(X,implies(implies(X_21,X),X)),implies(implies(X_21,X),X)) = implies(implies(implies(implies(X,X_21),X_21),X),X) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(implies(X_21,X),X)),implies(implies(X_21,X),X)),implies(implies(implies(implies(X_21,X),X),X),X)) ),[1,0],$fot(implies(implies(implies(X,X_21),X_21),X))]]) ).

cnf(refute_0_495,plain,
    ( implies(implies(X,implies(implies(X_21,X),X)),implies(implies(X_21,X),X)) != implies(implies(implies(implies(X_21,X),X),X),X)
    | implies(implies(X,implies(implies(X_21,X),X)),implies(implies(X_21,X),X)) = implies(implies(implies(implies(X,X_21),X_21),X),X) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(X_21,X),X),X),implies(implies(implies(X,X_21),X_21),X)) )],[refute_0_493,refute_0_494]) ).

cnf(refute_0_496,plain,
    implies(implies(X,implies(implies(X_21,X),X)),implies(implies(X_21,X),X)) = implies(implies(implies(implies(X,X_21),X_21),X),X),
    inference(resolve,[$cnf( $equal(implies(implies(X,implies(implies(X_21,X),X)),implies(implies(X_21,X),X)),implies(implies(implies(implies(X_21,X),X),X),X)) )],[refute_0_492,refute_0_495]) ).

cnf(refute_0_497,plain,
    ( implies(implies(X,implies(implies(X_21,X),X)),implies(implies(X_21,X),X)) != implies(implies(implies(implies(X,X_21),X_21),X),X)
    | implies(implies(X,implies(implies(X_21,X),X)),implies(implies(X_21,X),X)) != implies(implies(implies(implies(X_21,X),X),X),X)
    | implies(implies(implies(implies(X_21,X),X),X),X) = implies(implies(implies(implies(X,X_21),X_21),X),X) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(implies(X_21,X),X)),implies(implies(X_21,X),X)),implies(implies(implies(implies(X,X_21),X_21),X),X)) ),[0],$fot(implies(implies(implies(implies(X_21,X),X),X),X))]]) ).

cnf(refute_0_498,plain,
    ( implies(implies(X,implies(implies(X_21,X),X)),implies(implies(X_21,X),X)) != implies(implies(implies(implies(X,X_21),X_21),X),X)
    | implies(implies(implies(implies(X_21,X),X),X),X) = implies(implies(implies(implies(X,X_21),X_21),X),X) ),
    inference(resolve,[$cnf( $equal(implies(implies(X,implies(implies(X_21,X),X)),implies(implies(X_21,X),X)),implies(implies(implies(implies(X_21,X),X),X),X)) )],[refute_0_492,refute_0_497]) ).

cnf(refute_0_499,plain,
    implies(implies(implies(implies(X_21,X),X),X),X) = implies(implies(implies(implies(X,X_21),X_21),X),X),
    inference(resolve,[$cnf( $equal(implies(implies(X,implies(implies(X_21,X),X)),implies(implies(X_21,X),X)),implies(implies(implies(implies(X,X_21),X_21),X),X)) )],[refute_0_496,refute_0_498]) ).

cnf(refute_0_500,plain,
    implies(implies(implies(implies(Y,X_25),X_25),Y),Y) = implies(implies(Y,implies(implies(Y,X_25),X_25)),implies(implies(Y,X_25),X_25)),
    inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(implies(Y,X_25),X_25)))]]) ).

cnf(refute_0_501,plain,
    implies(Y,implies(implies(Y,X_25),X_25)) = truth,
    inference(subst,[],[refute_0_13:[bind(X_15,$fot(Y)),bind(X_16,$fot(X_25))]]) ).

cnf(refute_0_502,plain,
    ( implies(Y,implies(implies(Y,X_25),X_25)) != truth
    | implies(implies(implies(implies(Y,X_25),X_25),Y),Y) != implies(implies(Y,implies(implies(Y,X_25),X_25)),implies(implies(Y,X_25),X_25))
    | implies(implies(implies(implies(Y,X_25),X_25),Y),Y) = implies(truth,implies(implies(Y,X_25),X_25)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(Y,X_25),X_25),Y),Y),implies(implies(Y,implies(implies(Y,X_25),X_25)),implies(implies(Y,X_25),X_25))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_503,plain,
    ( implies(implies(implies(implies(Y,X_25),X_25),Y),Y) != implies(implies(Y,implies(implies(Y,X_25),X_25)),implies(implies(Y,X_25),X_25))
    | implies(implies(implies(implies(Y,X_25),X_25),Y),Y) = implies(truth,implies(implies(Y,X_25),X_25)) ),
    inference(resolve,[$cnf( $equal(implies(Y,implies(implies(Y,X_25),X_25)),truth) )],[refute_0_501,refute_0_502]) ).

cnf(refute_0_504,plain,
    implies(implies(implies(implies(Y,X_25),X_25),Y),Y) = implies(truth,implies(implies(Y,X_25),X_25)),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_25),X_25),Y),Y),implies(implies(Y,implies(implies(Y,X_25),X_25)),implies(implies(Y,X_25),X_25))) )],[refute_0_500,refute_0_503]) ).

cnf(refute_0_505,plain,
    implies(truth,implies(implies(Y,X_25),X_25)) = implies(implies(Y,X_25),X_25),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(Y,X_25),X_25)))]]) ).

cnf(refute_0_506,plain,
    ( implies(implies(implies(implies(Y,X_25),X_25),Y),Y) != implies(truth,implies(implies(Y,X_25),X_25))
    | implies(truth,implies(implies(Y,X_25),X_25)) != implies(implies(Y,X_25),X_25)
    | implies(implies(implies(implies(Y,X_25),X_25),Y),Y) = implies(implies(Y,X_25),X_25) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(implies(Y,X_25),X_25),Y),Y),implies(implies(Y,X_25),X_25)) ),[0],$fot(implies(truth,implies(implies(Y,X_25),X_25)))]]) ).

cnf(refute_0_507,plain,
    ( implies(implies(implies(implies(Y,X_25),X_25),Y),Y) != implies(truth,implies(implies(Y,X_25),X_25))
    | implies(implies(implies(implies(Y,X_25),X_25),Y),Y) = implies(implies(Y,X_25),X_25) ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(Y,X_25),X_25)),implies(implies(Y,X_25),X_25)) )],[refute_0_505,refute_0_506]) ).

cnf(refute_0_508,plain,
    implies(implies(implies(implies(Y,X_25),X_25),Y),Y) = implies(implies(Y,X_25),X_25),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_25),X_25),Y),Y),implies(truth,implies(implies(Y,X_25),X_25))) )],[refute_0_504,refute_0_507]) ).

cnf(refute_0_509,plain,
    implies(implies(implies(implies(X,X_21),X_21),X),X) = implies(implies(X,X_21),X_21),
    inference(subst,[],[refute_0_508:[bind(Y,$fot(X)),bind(X_25,$fot(X_21))]]) ).

cnf(refute_0_510,plain,
    ( implies(implies(implies(implies(X,X_21),X_21),X),X) != implies(implies(X,X_21),X_21)
    | implies(implies(implies(implies(X_21,X),X),X),X) != implies(implies(implies(implies(X,X_21),X_21),X),X)
    | implies(implies(implies(implies(X_21,X),X),X),X) = implies(implies(X,X_21),X_21) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_21,X),X),X),X),implies(implies(implies(implies(X,X_21),X_21),X),X)) ),[1],$fot(implies(implies(X,X_21),X_21))]]) ).

cnf(refute_0_511,plain,
    ( implies(implies(implies(implies(X_21,X),X),X),X) != implies(implies(implies(implies(X,X_21),X_21),X),X)
    | implies(implies(implies(implies(X_21,X),X),X),X) = implies(implies(X,X_21),X_21) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X,X_21),X_21),X),X),implies(implies(X,X_21),X_21)) )],[refute_0_509,refute_0_510]) ).

cnf(refute_0_512,plain,
    implies(implies(implies(implies(X_21,X),X),X),X) = implies(implies(X,X_21),X_21),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_21,X),X),X),X),implies(implies(implies(implies(X,X_21),X_21),X),X)) )],[refute_0_499,refute_0_511]) ).

cnf(refute_0_513,plain,
    implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50)) = implies(implies(not(X_50),not(truth)),not(truth)),
    inference(subst,[],[refute_0_512:[bind(X,$fot(not(X_50))),bind(X_21,$fot(not(truth)))]]) ).

cnf(refute_0_514,plain,
    implies(truth,not(X_50)) = not(X_50),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(not(X_50)))]]) ).

cnf(refute_0_515,plain,
    implies(not(not(truth)),not(X_50)) = implies(not(not(truth)),not(X_50)),
    introduced(tautology,[refl,[$fot(implies(not(not(truth)),not(X_50)))]]) ).

cnf(refute_0_516,plain,
    ( implies(not(not(truth)),not(X_50)) != implies(not(not(truth)),not(X_50))
    | not(not(truth)) != truth
    | implies(not(not(truth)),not(X_50)) = implies(truth,not(X_50)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(X_50)),implies(not(not(truth)),not(X_50))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_517,plain,
    ( not(not(truth)) != truth
    | implies(not(not(truth)),not(X_50)) = implies(truth,not(X_50)) ),
    inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(X_50)),implies(not(not(truth)),not(X_50))) )],[refute_0_515,refute_0_516]) ).

cnf(refute_0_518,plain,
    implies(not(not(truth)),not(X_50)) = implies(truth,not(X_50)),
    inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_401,refute_0_517]) ).

cnf(refute_0_519,plain,
    ( implies(not(not(truth)),not(X_50)) != implies(truth,not(X_50))
    | implies(truth,not(X_50)) != not(X_50)
    | implies(not(not(truth)),not(X_50)) = not(X_50) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(not(not(truth)),not(X_50)))),bind(Y0,$fot(implies(truth,not(X_50)))),bind(Z0,$fot(not(X_50)))]]) ).

cnf(refute_0_520,plain,
    ( implies(truth,not(X_50)) != not(X_50)
    | implies(not(not(truth)),not(X_50)) = not(X_50) ),
    inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(X_50)),implies(truth,not(X_50))) )],[refute_0_518,refute_0_519]) ).

cnf(refute_0_521,plain,
    implies(not(not(truth)),not(X_50)) = not(X_50),
    inference(resolve,[$cnf( $equal(implies(truth,not(X_50)),not(X_50)) )],[refute_0_514,refute_0_520]) ).

cnf(refute_0_522,plain,
    implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))) = implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),
    introduced(tautology,[refl,[$fot(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))))]]) ).

cnf(refute_0_523,plain,
    ( implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))) != implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50)))
    | implies(not(not(truth)),not(X_50)) != not(X_50)
    | implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))) = implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50)))) ),[1,1],$fot(not(X_50))]]) ).

cnf(refute_0_524,plain,
    ( implies(not(not(truth)),not(X_50)) != not(X_50)
    | implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))) = implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50)) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50)))) )],[refute_0_522,refute_0_523]) ).

cnf(refute_0_525,plain,
    implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))) = implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50)),
    inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(X_50)),not(X_50)) )],[refute_0_521,refute_0_524]) ).

cnf(refute_0_526,plain,
    implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))) = implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),
    introduced(tautology,[refl,[$fot(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))))]]) ).

cnf(refute_0_527,plain,
    ( implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))) != implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50)))
    | implies(not(not(truth)),not(X_50)) != not(X_50)
    | implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))) = implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50)))) ),[1,1],$fot(not(X_50))]]) ).

cnf(refute_0_528,plain,
    ( implies(not(not(truth)),not(X_50)) != not(X_50)
    | implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))) = implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50)))) )],[refute_0_526,refute_0_527]) ).

cnf(refute_0_529,plain,
    implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))) = implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),
    inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(X_50)),not(X_50)) )],[refute_0_521,refute_0_528]) ).

cnf(refute_0_530,plain,
    implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))),
    introduced(tautology,[refl,[$fot(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))))]]) ).

cnf(refute_0_531,plain,
    ( implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) != implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50)))
    | implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))) != implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50))
    | implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))),implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50)))) ),[1,0],$fot(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)))]]) ).

cnf(refute_0_532,plain,
    ( implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))) != implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50))
    | implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))),implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50)))) )],[refute_0_530,refute_0_531]) ).

cnf(refute_0_533,plain,
    implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50))) )],[refute_0_529,refute_0_532]) ).

cnf(refute_0_534,plain,
    ( implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) != implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50)))
    | implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))) != implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50))
    | implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50)) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))))),bind(Y0,$fot(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))))),bind(Z0,$fot(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50))))]]) ).

cnf(refute_0_535,plain,
    ( implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))) != implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50))
    | implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50)) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))),implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50)))) )],[refute_0_533,refute_0_534]) ).

cnf(refute_0_536,plain,
    implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50)),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50))) )],[refute_0_525,refute_0_535]) ).

cnf(refute_0_537,plain,
    ( implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) != implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50))
    | implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50)) != implies(implies(not(X_50),not(truth)),not(truth))
    | implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(implies(not(X_50),not(truth)),not(truth)) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))))),bind(Y0,$fot(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50)))),bind(Z0,$fot(implies(implies(not(X_50),not(truth)),not(truth))))]]) ).

cnf(refute_0_538,plain,
    ( implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50)) != implies(implies(not(X_50),not(truth)),not(truth))
    | implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(implies(not(X_50),not(truth)),not(truth)) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))),implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50))) )],[refute_0_536,refute_0_537]) ).

cnf(refute_0_539,plain,
    implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) = implies(implies(not(X_50),not(truth)),not(truth)),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)),not(X_50)),implies(implies(not(X_50),not(truth)),not(truth))) )],[refute_0_513,refute_0_538]) ).

cnf(refute_0_540,plain,
    ( implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) != implies(implies(not(X_50),not(truth)),not(truth))
    | implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) != implies(implies(not(truth),not(X_50)),not(X_50))
    | implies(implies(not(X_50),not(truth)),not(truth)) = implies(implies(not(truth),not(X_50)),not(X_50)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))),implies(implies(not(truth),not(X_50)),not(X_50))) ),[0],$fot(implies(implies(not(X_50),not(truth)),not(truth)))]]) ).

cnf(refute_0_541,plain,
    ( implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))) != implies(implies(not(truth),not(X_50)),not(X_50))
    | implies(implies(not(X_50),not(truth)),not(truth)) = implies(implies(not(truth),not(X_50)),not(X_50)) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))),implies(implies(not(X_50),not(truth)),not(truth))) )],[refute_0_539,refute_0_540]) ).

cnf(refute_0_542,plain,
    implies(implies(not(X_50),not(truth)),not(truth)) = implies(implies(not(truth),not(X_50)),not(X_50)),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_50)),not(X_50)),implies(not(not(truth)),not(X_50))),implies(not(not(truth)),not(X_50))),implies(implies(not(truth),not(X_50)),not(X_50))) )],[refute_0_491,refute_0_541]) ).

cnf(refute_0_543,plain,
    implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) = implies(implies(implies(X_28,not(truth)),implies(implies(not(truth),not(X_28)),not(X_28))),implies(implies(not(truth),not(X_28)),not(X_28))),
    inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(implies(not(truth),not(X_28)),not(X_28)))),bind(Y,$fot(implies(X_28,not(truth))))]]) ).

cnf(refute_0_544,plain,
    implies(implies(X_28,not(truth)),implies(implies(not(truth),not(X_28)),not(X_28))) = truth,
    inference(subst,[],[refute_0_475:[bind(X_22,$fot(X_28))]]) ).

cnf(refute_0_545,plain,
    ( implies(implies(X_28,not(truth)),implies(implies(not(truth),not(X_28)),not(X_28))) != truth
    | implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) != implies(implies(implies(X_28,not(truth)),implies(implies(not(truth),not(X_28)),not(X_28))),implies(implies(not(truth),not(X_28)),not(X_28)))
    | implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) = implies(truth,implies(implies(not(truth),not(X_28)),not(X_28))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))),implies(implies(implies(X_28,not(truth)),implies(implies(not(truth),not(X_28)),not(X_28))),implies(implies(not(truth),not(X_28)),not(X_28)))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_546,plain,
    ( implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) != implies(implies(implies(X_28,not(truth)),implies(implies(not(truth),not(X_28)),not(X_28))),implies(implies(not(truth),not(X_28)),not(X_28)))
    | implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) = implies(truth,implies(implies(not(truth),not(X_28)),not(X_28))) ),
    inference(resolve,[$cnf( $equal(implies(implies(X_28,not(truth)),implies(implies(not(truth),not(X_28)),not(X_28))),truth) )],[refute_0_544,refute_0_545]) ).

cnf(refute_0_547,plain,
    implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) = implies(truth,implies(implies(not(truth),not(X_28)),not(X_28))),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))),implies(implies(implies(X_28,not(truth)),implies(implies(not(truth),not(X_28)),not(X_28))),implies(implies(not(truth),not(X_28)),not(X_28)))) )],[refute_0_543,refute_0_546]) ).

cnf(refute_0_548,plain,
    implies(truth,implies(implies(not(truth),not(X_28)),not(X_28))) = implies(implies(not(truth),not(X_28)),not(X_28)),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(truth),not(X_28)),not(X_28))))]]) ).

cnf(refute_0_549,plain,
    ( implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) != implies(truth,implies(implies(not(truth),not(X_28)),not(X_28)))
    | implies(truth,implies(implies(not(truth),not(X_28)),not(X_28))) != implies(implies(not(truth),not(X_28)),not(X_28))
    | implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) = implies(implies(not(truth),not(X_28)),not(X_28)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))),implies(implies(not(truth),not(X_28)),not(X_28))) ),[0],$fot(implies(truth,implies(implies(not(truth),not(X_28)),not(X_28))))]]) ).

cnf(refute_0_550,plain,
    ( implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) != implies(truth,implies(implies(not(truth),not(X_28)),not(X_28)))
    | implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) = implies(implies(not(truth),not(X_28)),not(X_28)) ),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(truth),not(X_28)),not(X_28))),implies(implies(not(truth),not(X_28)),not(X_28))) )],[refute_0_548,refute_0_549]) ).

cnf(refute_0_551,plain,
    implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) = implies(implies(not(truth),not(X_28)),not(X_28)),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))),implies(truth,implies(implies(not(truth),not(X_28)),not(X_28)))) )],[refute_0_547,refute_0_550]) ).

cnf(refute_0_552,plain,
    implies(truth,implies(X_28,not(truth))) = implies(X_28,not(truth)),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_28,not(truth))))]]) ).

cnf(refute_0_553,plain,
    implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))) = truth,
    inference(subst,[],[wajsberg_4:[bind(X,$fot(not(truth)))]]) ).

cnf(refute_0_554,plain,
    ( implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))) != truth
    | not(not(truth)) != truth
    | implies(implies(truth,not(Y)),implies(Y,not(truth))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))),truth) ),[0,0,0],$fot(truth)]]) ).

cnf(refute_0_555,plain,
    ( implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))) != truth
    | implies(implies(truth,not(Y)),implies(Y,not(truth))) = truth ),
    inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_401,refute_0_554]) ).

cnf(refute_0_556,plain,
    implies(implies(truth,not(Y)),implies(Y,not(truth))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))),truth) )],[refute_0_553,refute_0_555]) ).

cnf(refute_0_557,plain,
    implies(truth,not(Y)) = not(Y),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(not(Y)))]]) ).

cnf(refute_0_558,plain,
    implies(implies(truth,not(Y)),implies(Y,not(truth))) = implies(implies(truth,not(Y)),implies(Y,not(truth))),
    introduced(tautology,[refl,[$fot(implies(implies(truth,not(Y)),implies(Y,not(truth))))]]) ).

cnf(refute_0_559,plain,
    ( implies(implies(truth,not(Y)),implies(Y,not(truth))) != implies(implies(truth,not(Y)),implies(Y,not(truth)))
    | implies(truth,not(Y)) != not(Y)
    | implies(implies(truth,not(Y)),implies(Y,not(truth))) = implies(not(Y),implies(Y,not(truth))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),implies(implies(truth,not(Y)),implies(Y,not(truth)))) ),[1,0],$fot(not(Y))]]) ).

cnf(refute_0_560,plain,
    ( implies(truth,not(Y)) != not(Y)
    | implies(implies(truth,not(Y)),implies(Y,not(truth))) = implies(not(Y),implies(Y,not(truth))) ),
    inference(resolve,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),implies(implies(truth,not(Y)),implies(Y,not(truth)))) )],[refute_0_558,refute_0_559]) ).

cnf(refute_0_561,plain,
    implies(implies(truth,not(Y)),implies(Y,not(truth))) = implies(not(Y),implies(Y,not(truth))),
    inference(resolve,[$cnf( $equal(implies(truth,not(Y)),not(Y)) )],[refute_0_557,refute_0_560]) ).

cnf(refute_0_562,plain,
    ( implies(implies(truth,not(Y)),implies(Y,not(truth))) != implies(not(Y),implies(Y,not(truth)))
    | implies(implies(truth,not(Y)),implies(Y,not(truth))) != truth
    | implies(not(Y),implies(Y,not(truth))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),truth) ),[0],$fot(implies(not(Y),implies(Y,not(truth))))]]) ).

cnf(refute_0_563,plain,
    ( implies(implies(truth,not(Y)),implies(Y,not(truth))) != truth
    | implies(not(Y),implies(Y,not(truth))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),implies(not(Y),implies(Y,not(truth)))) )],[refute_0_561,refute_0_562]) ).

cnf(refute_0_564,plain,
    implies(not(Y),implies(Y,not(truth))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),truth) )],[refute_0_556,refute_0_563]) ).

cnf(refute_0_565,plain,
    implies(not(X_28),implies(X_28,not(truth))) = truth,
    inference(subst,[],[refute_0_564:[bind(Y,$fot(X_28))]]) ).

cnf(refute_0_566,plain,
    implies(truth,not(X_28)) = not(X_28),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(not(X_28)))]]) ).

cnf(refute_0_567,plain,
    implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(Y,X))) = truth,
    inference(subst,[],[refute_0_50:[bind(Y,$fot(implies(Y,X))),bind(X_4,$fot(implies(not(X),not(Y))))]]) ).

cnf(refute_0_568,plain,
    ( implies(implies(not(X),not(Y)),implies(Y,X)) != truth
    | implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(Y,X))) != truth
    | implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(Y,X))),truth) ),[0,1,0],$fot(truth)]]) ).

cnf(refute_0_569,plain,
    ( implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(Y,X))) != truth
    | implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[wajsberg_4,refute_0_568]) ).

cnf(refute_0_570,plain,
    implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(Y,X))),truth) )],[refute_0_567,refute_0_569]) ).

cnf(refute_0_571,plain,
    implies(truth,implies(Y,X)) = implies(Y,X),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(Y,X)))]]) ).

cnf(refute_0_572,plain,
    implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))) = implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))),
    introduced(tautology,[refl,[$fot(implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))))]]) ).

cnf(refute_0_573,plain,
    ( implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))) != implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X)))
    | implies(truth,implies(Y,X)) != implies(Y,X)
    | implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))) = implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(Y,X)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))),implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X)))) ),[1,1],$fot(implies(Y,X))]]) ).

cnf(refute_0_574,plain,
    ( implies(truth,implies(Y,X)) != implies(Y,X)
    | implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))) = implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(Y,X)) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))),implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X)))) )],[refute_0_572,refute_0_573]) ).

cnf(refute_0_575,plain,
    implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))) = implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(Y,X)),
    inference(resolve,[$cnf( $equal(implies(truth,implies(Y,X)),implies(Y,X)) )],[refute_0_571,refute_0_574]) ).

cnf(refute_0_576,plain,
    ( implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))) != implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(Y,X))
    | implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))) != truth
    | implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(Y,X)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))),truth) ),[0],$fot(implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(Y,X)))]]) ).

cnf(refute_0_577,plain,
    ( implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))) != truth
    | implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(Y,X)) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))),implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(Y,X))) )],[refute_0_575,refute_0_576]) ).

cnf(refute_0_578,plain,
    implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(Y,X)) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(X),not(Y))),not(implies(implies(Y,X),implies(not(X),not(Y))))),implies(truth,implies(Y,X))),truth) )],[refute_0_570,refute_0_577]) ).

cnf(refute_0_579,plain,
    implies(implies(not(implies(not(X),not(not(truth)))),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) = truth,
    inference(subst,[],[refute_0_578:[bind(Y,$fot(not(truth)))]]) ).

cnf(refute_0_580,plain,
    ( implies(implies(not(implies(not(X),not(not(truth)))),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) != truth
    | not(not(truth)) != truth
    | implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(X),not(not(truth)))),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)),truth) ),[0,0,0,0,1],$fot(truth)]]) ).

cnf(refute_0_581,plain,
    ( implies(implies(not(implies(not(X),not(not(truth)))),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) != truth
    | implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) = truth ),
    inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_401,refute_0_580]) ).

cnf(refute_0_582,plain,
    implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(X),not(not(truth)))),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)),truth) )],[refute_0_579,refute_0_581]) ).

cnf(refute_0_583,plain,
    implies(truth,implies(not(truth),X)) = implies(not(truth),X),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(truth),X)))]]) ).

cnf(refute_0_584,plain,
    implies(implies(not(truth),X),truth) = truth,
    inference(subst,[],[refute_0_367:[bind(X_15,$fot(implies(not(truth),X)))]]) ).

cnf(refute_0_585,plain,
    implies(not(X),truth) = truth,
    inference(subst,[],[refute_0_367:[bind(X_15,$fot(not(X)))]]) ).

cnf(refute_0_586,plain,
    implies(not(X),not(not(truth))) = implies(not(X),not(not(truth))),
    introduced(tautology,[refl,[$fot(implies(not(X),not(not(truth))))]]) ).

cnf(refute_0_587,plain,
    ( implies(not(X),not(not(truth))) != implies(not(X),not(not(truth)))
    | not(not(truth)) != truth
    | implies(not(X),not(not(truth))) = implies(not(X),truth) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(X),not(not(truth))),implies(not(X),not(not(truth)))) ),[1,1],$fot(truth)]]) ).

cnf(refute_0_588,plain,
    ( not(not(truth)) != truth
    | implies(not(X),not(not(truth))) = implies(not(X),truth) ),
    inference(resolve,[$cnf( $equal(implies(not(X),not(not(truth))),implies(not(X),not(not(truth)))) )],[refute_0_586,refute_0_587]) ).

cnf(refute_0_589,plain,
    implies(not(X),not(not(truth))) = implies(not(X),truth),
    inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_401,refute_0_588]) ).

cnf(refute_0_590,plain,
    ( implies(not(X),not(not(truth))) != implies(not(X),truth)
    | implies(not(X),truth) != truth
    | implies(not(X),not(not(truth))) = truth ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(not(X),not(not(truth))))),bind(Y0,$fot(implies(not(X),truth))),bind(Z0,$fot(truth))]]) ).

cnf(refute_0_591,plain,
    ( implies(not(X),truth) != truth
    | implies(not(X),not(not(truth))) = truth ),
    inference(resolve,[$cnf( $equal(implies(not(X),not(not(truth))),implies(not(X),truth)) )],[refute_0_589,refute_0_590]) ).

cnf(refute_0_592,plain,
    implies(not(X),not(not(truth))) = truth,
    inference(resolve,[$cnf( $equal(implies(not(X),truth),truth) )],[refute_0_585,refute_0_591]) ).

cnf(refute_0_593,plain,
    implies(implies(not(truth),X),implies(not(X),not(not(truth)))) = implies(implies(not(truth),X),implies(not(X),not(not(truth)))),
    introduced(tautology,[refl,[$fot(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))]]) ).

cnf(refute_0_594,plain,
    ( implies(implies(not(truth),X),implies(not(X),not(not(truth)))) != implies(implies(not(truth),X),implies(not(X),not(not(truth))))
    | implies(not(X),not(not(truth))) != truth
    | implies(implies(not(truth),X),implies(not(X),not(not(truth)))) = implies(implies(not(truth),X),truth) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),X),implies(not(X),not(not(truth)))),implies(implies(not(truth),X),implies(not(X),not(not(truth))))) ),[1,1],$fot(truth)]]) ).

cnf(refute_0_595,plain,
    ( implies(not(X),not(not(truth))) != truth
    | implies(implies(not(truth),X),implies(not(X),not(not(truth)))) = implies(implies(not(truth),X),truth) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),X),implies(not(X),not(not(truth)))),implies(implies(not(truth),X),implies(not(X),not(not(truth))))) )],[refute_0_593,refute_0_594]) ).

cnf(refute_0_596,plain,
    implies(implies(not(truth),X),implies(not(X),not(not(truth)))) = implies(implies(not(truth),X),truth),
    inference(resolve,[$cnf( $equal(implies(not(X),not(not(truth))),truth) )],[refute_0_592,refute_0_595]) ).

cnf(refute_0_597,plain,
    ( implies(implies(not(truth),X),implies(not(X),not(not(truth)))) != implies(implies(not(truth),X),truth)
    | implies(implies(not(truth),X),truth) != truth
    | implies(implies(not(truth),X),implies(not(X),not(not(truth)))) = truth ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),bind(Y0,$fot(implies(implies(not(truth),X),truth))),bind(Z0,$fot(truth))]]) ).

cnf(refute_0_598,plain,
    ( implies(implies(not(truth),X),truth) != truth
    | implies(implies(not(truth),X),implies(not(X),not(not(truth)))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),X),implies(not(X),not(not(truth)))),implies(implies(not(truth),X),truth)) )],[refute_0_596,refute_0_597]) ).

cnf(refute_0_599,plain,
    implies(implies(not(truth),X),implies(not(X),not(not(truth)))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),X),truth),truth) )],[refute_0_584,refute_0_598]) ).

cnf(refute_0_600,plain,
    not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))) = not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))),
    introduced(tautology,[refl,[$fot(not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))))]]) ).

cnf(refute_0_601,plain,
    ( implies(implies(not(truth),X),implies(not(X),not(not(truth)))) != truth
    | not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))) != not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))
    | not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))) = not(truth) ),
    introduced(tautology,[equality,[$cnf( $equal(not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_602,plain,
    ( implies(implies(not(truth),X),implies(not(X),not(not(truth)))) != truth
    | not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))) = not(truth) ),
    inference(resolve,[$cnf( $equal(not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) )],[refute_0_600,refute_0_601]) ).

cnf(refute_0_603,plain,
    not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))) = not(truth),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),X),implies(not(X),not(not(truth)))),truth) )],[refute_0_599,refute_0_602]) ).

cnf(refute_0_604,plain,
    implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) = implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),
    introduced(tautology,[refl,[$fot(implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))))]]) ).

cnf(refute_0_605,plain,
    ( implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) != implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))))
    | not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))) != not(truth)
    | implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) = implies(not(truth),not(truth)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))))) ),[1,1],$fot(not(truth))]]) ).

cnf(refute_0_606,plain,
    ( not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))) != not(truth)
    | implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) = implies(not(truth),not(truth)) ),
    inference(resolve,[$cnf( $equal(implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))))) )],[refute_0_604,refute_0_605]) ).

cnf(refute_0_607,plain,
    implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) = implies(not(truth),not(truth)),
    inference(resolve,[$cnf( $equal(not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))),not(truth)) )],[refute_0_603,refute_0_606]) ).

cnf(refute_0_608,plain,
    not(implies(not(X),truth)) = not(implies(not(X),truth)),
    introduced(tautology,[refl,[$fot(not(implies(not(X),truth)))]]) ).

cnf(refute_0_609,plain,
    ( implies(not(X),truth) != truth
    | not(implies(not(X),truth)) != not(implies(not(X),truth))
    | not(implies(not(X),truth)) = not(truth) ),
    introduced(tautology,[equality,[$cnf( $equal(not(implies(not(X),truth)),not(implies(not(X),truth))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_610,plain,
    ( implies(not(X),truth) != truth
    | not(implies(not(X),truth)) = not(truth) ),
    inference(resolve,[$cnf( $equal(not(implies(not(X),truth)),not(implies(not(X),truth))) )],[refute_0_608,refute_0_609]) ).

cnf(refute_0_611,plain,
    not(implies(not(X),truth)) = not(truth),
    inference(resolve,[$cnf( $equal(implies(not(X),truth),truth) )],[refute_0_585,refute_0_610]) ).

cnf(refute_0_612,plain,
    implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) = implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),
    introduced(tautology,[refl,[$fot(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))))]]) ).

cnf(refute_0_613,plain,
    ( implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) != implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))))
    | not(implies(not(X),truth)) != not(truth)
    | implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) = implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))))) ),[1,0],$fot(not(truth))]]) ).

cnf(refute_0_614,plain,
    ( not(implies(not(X),truth)) != not(truth)
    | implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) = implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) ),
    inference(resolve,[$cnf( $equal(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))))) )],[refute_0_612,refute_0_613]) ).

cnf(refute_0_615,plain,
    implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) = implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),
    inference(resolve,[$cnf( $equal(not(implies(not(X),truth)),not(truth)) )],[refute_0_611,refute_0_614]) ).

cnf(refute_0_616,plain,
    ( implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) != implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))))
    | implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) != implies(not(truth),not(truth))
    | implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) = implies(not(truth),not(truth)) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))))),bind(Y0,$fot(implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))))),bind(Z0,$fot(implies(not(truth),not(truth))))]]) ).

cnf(refute_0_617,plain,
    ( implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) != implies(not(truth),not(truth))
    | implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) = implies(not(truth),not(truth)) ),
    inference(resolve,[$cnf( $equal(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth))))))) )],[refute_0_615,refute_0_616]) ).

cnf(refute_0_618,plain,
    implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) = implies(not(truth),not(truth)),
    inference(resolve,[$cnf( $equal(implies(not(truth),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),not(truth))) )],[refute_0_607,refute_0_617]) ).

cnf(refute_0_619,plain,
    ( implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) != implies(not(truth),not(truth))
    | implies(not(truth),not(truth)) != truth
    | implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) = truth ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))))),bind(Y0,$fot(implies(not(truth),not(truth)))),bind(Z0,$fot(truth))]]) ).

cnf(refute_0_620,plain,
    ( implies(not(truth),not(truth)) != truth
    | implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) = truth ),
    inference(resolve,[$cnf( $equal(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),not(truth))) )],[refute_0_618,refute_0_619]) ).

cnf(refute_0_621,plain,
    implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) = truth,
    inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_214,refute_0_620]) ).

cnf(refute_0_622,plain,
    implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) = implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)),
    introduced(tautology,[refl,[$fot(implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)))]]) ).

cnf(refute_0_623,plain,
    ( implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) != implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X))
    | implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) != truth
    | implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) = implies(truth,implies(not(truth),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)),implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_624,plain,
    ( implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))) != truth
    | implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) = implies(truth,implies(not(truth),X)) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)),implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X))) )],[refute_0_622,refute_0_623]) ).

cnf(refute_0_625,plain,
    implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) = implies(truth,implies(not(truth),X)),
    inference(resolve,[$cnf( $equal(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),truth) )],[refute_0_621,refute_0_624]) ).

cnf(refute_0_626,plain,
    ( implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) != implies(truth,implies(not(truth),X))
    | implies(truth,implies(not(truth),X)) != implies(not(truth),X)
    | implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) = implies(not(truth),X) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)))),bind(Y0,$fot(implies(truth,implies(not(truth),X)))),bind(Z0,$fot(implies(not(truth),X)))]]) ).

cnf(refute_0_627,plain,
    ( implies(truth,implies(not(truth),X)) != implies(not(truth),X)
    | implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) = implies(not(truth),X) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)),implies(truth,implies(not(truth),X))) )],[refute_0_625,refute_0_626]) ).

cnf(refute_0_628,plain,
    implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) = implies(not(truth),X),
    inference(resolve,[$cnf( $equal(implies(truth,implies(not(truth),X)),implies(not(truth),X)) )],[refute_0_583,refute_0_627]) ).

cnf(refute_0_629,plain,
    ( implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) != implies(not(truth),X)
    | implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) != truth
    | implies(not(truth),X) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)),truth) ),[0],$fot(implies(not(truth),X))]]) ).

cnf(refute_0_630,plain,
    ( implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)) != truth
    | implies(not(truth),X) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)),implies(not(truth),X)) )],[refute_0_628,refute_0_629]) ).

cnf(refute_0_631,plain,
    implies(not(truth),X) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(X),truth)),not(implies(implies(not(truth),X),implies(not(X),not(not(truth)))))),implies(not(truth),X)),truth) )],[refute_0_582,refute_0_630]) ).

cnf(refute_0_632,plain,
    implies(not(truth),not(X_28)) = truth,
    inference(subst,[],[refute_0_631:[bind(X,$fot(not(X_28)))]]) ).

cnf(refute_0_633,plain,
    implies(implies(not(truth),not(X_28)),not(X_28)) = implies(implies(not(truth),not(X_28)),not(X_28)),
    introduced(tautology,[refl,[$fot(implies(implies(not(truth),not(X_28)),not(X_28)))]]) ).

cnf(refute_0_634,plain,
    ( implies(implies(not(truth),not(X_28)),not(X_28)) != implies(implies(not(truth),not(X_28)),not(X_28))
    | implies(not(truth),not(X_28)) != truth
    | implies(implies(not(truth),not(X_28)),not(X_28)) = implies(truth,not(X_28)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(X_28)),not(X_28)),implies(implies(not(truth),not(X_28)),not(X_28))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_635,plain,
    ( implies(not(truth),not(X_28)) != truth
    | implies(implies(not(truth),not(X_28)),not(X_28)) = implies(truth,not(X_28)) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_28)),not(X_28)),implies(implies(not(truth),not(X_28)),not(X_28))) )],[refute_0_633,refute_0_634]) ).

cnf(refute_0_636,plain,
    implies(implies(not(truth),not(X_28)),not(X_28)) = implies(truth,not(X_28)),
    inference(resolve,[$cnf( $equal(implies(not(truth),not(X_28)),truth) )],[refute_0_632,refute_0_635]) ).

cnf(refute_0_637,plain,
    ( implies(implies(not(truth),not(X_28)),not(X_28)) != implies(truth,not(X_28))
    | implies(truth,not(X_28)) != not(X_28)
    | implies(implies(not(truth),not(X_28)),not(X_28)) = not(X_28) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(not(truth),not(X_28)),not(X_28)))),bind(Y0,$fot(implies(truth,not(X_28)))),bind(Z0,$fot(not(X_28)))]]) ).

cnf(refute_0_638,plain,
    ( implies(truth,not(X_28)) != not(X_28)
    | implies(implies(not(truth),not(X_28)),not(X_28)) = not(X_28) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_28)),not(X_28)),implies(truth,not(X_28))) )],[refute_0_636,refute_0_637]) ).

cnf(refute_0_639,plain,
    implies(implies(not(truth),not(X_28)),not(X_28)) = not(X_28),
    inference(resolve,[$cnf( $equal(implies(truth,not(X_28)),not(X_28)) )],[refute_0_566,refute_0_638]) ).

cnf(refute_0_640,plain,
    implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))) = implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),
    introduced(tautology,[refl,[$fot(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))))]]) ).

cnf(refute_0_641,plain,
    ( implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))) != implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth)))
    | implies(implies(not(truth),not(X_28)),not(X_28)) != not(X_28)
    | implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))) = implies(not(X_28),implies(X_28,not(truth))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth)))) ),[1,0],$fot(not(X_28))]]) ).

cnf(refute_0_642,plain,
    ( implies(implies(not(truth),not(X_28)),not(X_28)) != not(X_28)
    | implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))) = implies(not(X_28),implies(X_28,not(truth))) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth)))) )],[refute_0_640,refute_0_641]) ).

cnf(refute_0_643,plain,
    implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))) = implies(not(X_28),implies(X_28,not(truth))),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_28)),not(X_28)),not(X_28)) )],[refute_0_639,refute_0_642]) ).

cnf(refute_0_644,plain,
    ( implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))) != implies(not(X_28),implies(X_28,not(truth)))
    | implies(not(X_28),implies(X_28,not(truth))) != truth
    | implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))) = truth ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))))),bind(Y0,$fot(implies(not(X_28),implies(X_28,not(truth))))),bind(Z0,$fot(truth))]]) ).

cnf(refute_0_645,plain,
    ( implies(not(X_28),implies(X_28,not(truth))) != truth
    | implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(not(X_28),implies(X_28,not(truth)))) )],[refute_0_643,refute_0_644]) ).

cnf(refute_0_646,plain,
    implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))) = truth,
    inference(resolve,[$cnf( $equal(implies(not(X_28),implies(X_28,not(truth))),truth) )],[refute_0_565,refute_0_645]) ).

cnf(refute_0_647,plain,
    implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) = implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))),
    introduced(tautology,[refl,[$fot(implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))))]]) ).

cnf(refute_0_648,plain,
    ( implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) != implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth)))
    | implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))) != truth
    | implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) = implies(truth,implies(X_28,not(truth))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))),implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth)))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_649,plain,
    ( implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))) != truth
    | implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) = implies(truth,implies(X_28,not(truth))) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))),implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth)))) )],[refute_0_647,refute_0_648]) ).

cnf(refute_0_650,plain,
    implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) = implies(truth,implies(X_28,not(truth))),
    inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),truth) )],[refute_0_646,refute_0_649]) ).

cnf(refute_0_651,plain,
    ( implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) != implies(truth,implies(X_28,not(truth)))
    | implies(truth,implies(X_28,not(truth))) != implies(X_28,not(truth))
    | implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) = implies(X_28,not(truth)) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))))),bind(Y0,$fot(implies(truth,implies(X_28,not(truth))))),bind(Z0,$fot(implies(X_28,not(truth))))]]) ).

cnf(refute_0_652,plain,
    ( implies(truth,implies(X_28,not(truth))) != implies(X_28,not(truth))
    | implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) = implies(X_28,not(truth)) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))),implies(truth,implies(X_28,not(truth)))) )],[refute_0_650,refute_0_651]) ).

cnf(refute_0_653,plain,
    implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) = implies(X_28,not(truth)),
    inference(resolve,[$cnf( $equal(implies(truth,implies(X_28,not(truth))),implies(X_28,not(truth))) )],[refute_0_552,refute_0_652]) ).

cnf(refute_0_654,plain,
    ( implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) != implies(X_28,not(truth))
    | implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) != implies(implies(not(truth),not(X_28)),not(X_28))
    | implies(X_28,not(truth)) = implies(implies(not(truth),not(X_28)),not(X_28)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))),implies(implies(not(truth),not(X_28)),not(X_28))) ),[0],$fot(implies(X_28,not(truth)))]]) ).

cnf(refute_0_655,plain,
    ( implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) != implies(implies(not(truth),not(X_28)),not(X_28))
    | implies(X_28,not(truth)) = implies(implies(not(truth),not(X_28)),not(X_28)) ),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))),implies(X_28,not(truth))) )],[refute_0_653,refute_0_654]) ).

cnf(refute_0_656,plain,
    ( implies(X_28,not(truth)) != implies(implies(not(truth),not(X_28)),not(X_28))
    | implies(implies(not(truth),not(X_28)),not(X_28)) != not(X_28)
    | implies(X_28,not(truth)) = not(X_28) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_28,not(truth)),not(X_28)) ),[0],$fot(implies(implies(not(truth),not(X_28)),not(X_28)))]]) ).

cnf(refute_0_657,plain,
    ( implies(X_28,not(truth)) != implies(implies(not(truth),not(X_28)),not(X_28))
    | implies(X_28,not(truth)) = not(X_28) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_28)),not(X_28)),not(X_28)) )],[refute_0_639,refute_0_656]) ).

cnf(refute_0_658,plain,
    ( implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))) != implies(implies(not(truth),not(X_28)),not(X_28))
    | implies(X_28,not(truth)) = not(X_28) ),
    inference(resolve,[$cnf( $equal(implies(X_28,not(truth)),implies(implies(not(truth),not(X_28)),not(X_28))) )],[refute_0_655,refute_0_657]) ).

cnf(refute_0_659,plain,
    implies(X_28,not(truth)) = not(X_28),
    inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_28)),not(X_28)),implies(X_28,not(truth))),implies(X_28,not(truth))),implies(implies(not(truth),not(X_28)),not(X_28))) )],[refute_0_551,refute_0_658]) ).

cnf(refute_0_660,plain,
    implies(not(X_50),not(truth)) = not(not(X_50)),
    inference(subst,[],[refute_0_659:[bind(X_28,$fot(not(X_50)))]]) ).

cnf(refute_0_661,plain,
    not(implies(not(X_50),not(truth))) = not(implies(not(X_50),not(truth))),
    introduced(tautology,[refl,[$fot(not(implies(not(X_50),not(truth))))]]) ).

cnf(refute_0_662,plain,
    ( implies(not(X_50),not(truth)) != not(not(X_50))
    | not(implies(not(X_50),not(truth))) != not(implies(not(X_50),not(truth)))
    | not(implies(not(X_50),not(truth))) = not(not(not(X_50))) ),
    introduced(tautology,[equality,[$cnf( $equal(not(implies(not(X_50),not(truth))),not(implies(not(X_50),not(truth)))) ),[1,0],$fot(not(not(X_50)))]]) ).

cnf(refute_0_663,plain,
    ( implies(not(X_50),not(truth)) != not(not(X_50))
    | not(implies(not(X_50),not(truth))) = not(not(not(X_50))) ),
    inference(resolve,[$cnf( $equal(not(implies(not(X_50),not(truth))),not(implies(not(X_50),not(truth)))) )],[refute_0_661,refute_0_662]) ).

cnf(refute_0_664,plain,
    not(implies(not(X_50),not(truth))) = not(not(not(X_50))),
    inference(resolve,[$cnf( $equal(implies(not(X_50),not(truth)),not(not(X_50))) )],[refute_0_660,refute_0_663]) ).

cnf(refute_0_665,plain,
    implies(implies(not(X_50),not(truth)),not(truth)) = not(implies(not(X_50),not(truth))),
    inference(subst,[],[refute_0_659:[bind(X_28,$fot(implies(not(X_50),not(truth))))]]) ).

cnf(refute_0_666,plain,
    ( implies(implies(not(X_50),not(truth)),not(truth)) != not(implies(not(X_50),not(truth)))
    | not(implies(not(X_50),not(truth))) != not(not(not(X_50)))
    | implies(implies(not(X_50),not(truth)),not(truth)) = not(not(not(X_50))) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(not(X_50),not(truth)),not(truth)))),bind(Y0,$fot(not(implies(not(X_50),not(truth))))),bind(Z0,$fot(not(not(not(X_50)))))]]) ).

cnf(refute_0_667,plain,
    ( not(implies(not(X_50),not(truth))) != not(not(not(X_50)))
    | implies(implies(not(X_50),not(truth)),not(truth)) = not(not(not(X_50))) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_50),not(truth)),not(truth)),not(implies(not(X_50),not(truth)))) )],[refute_0_665,refute_0_666]) ).

cnf(refute_0_668,plain,
    implies(implies(not(X_50),not(truth)),not(truth)) = not(not(not(X_50))),
    inference(resolve,[$cnf( $equal(not(implies(not(X_50),not(truth))),not(not(not(X_50)))) )],[refute_0_664,refute_0_667]) ).

cnf(refute_0_669,plain,
    ( implies(implies(not(X_50),not(truth)),not(truth)) != implies(implies(not(truth),not(X_50)),not(X_50))
    | implies(implies(not(X_50),not(truth)),not(truth)) != not(not(not(X_50)))
    | not(not(not(X_50))) = implies(implies(not(truth),not(X_50)),not(X_50)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_50),not(truth)),not(truth)),implies(implies(not(truth),not(X_50)),not(X_50))) ),[0],$fot(not(not(not(X_50))))]]) ).

cnf(refute_0_670,plain,
    ( implies(implies(not(X_50),not(truth)),not(truth)) != implies(implies(not(truth),not(X_50)),not(X_50))
    | not(not(not(X_50))) = implies(implies(not(truth),not(X_50)),not(X_50)) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_50),not(truth)),not(truth)),not(not(not(X_50)))) )],[refute_0_668,refute_0_669]) ).

cnf(refute_0_671,plain,
    implies(not(truth),not(X_50)) = truth,
    inference(subst,[],[refute_0_631:[bind(X,$fot(not(X_50)))]]) ).

cnf(refute_0_672,plain,
    implies(implies(not(truth),not(X_50)),not(X_50)) = implies(implies(not(truth),not(X_50)),not(X_50)),
    introduced(tautology,[refl,[$fot(implies(implies(not(truth),not(X_50)),not(X_50)))]]) ).

cnf(refute_0_673,plain,
    ( implies(implies(not(truth),not(X_50)),not(X_50)) != implies(implies(not(truth),not(X_50)),not(X_50))
    | implies(not(truth),not(X_50)) != truth
    | implies(implies(not(truth),not(X_50)),not(X_50)) = implies(truth,not(X_50)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(X_50)),not(X_50)),implies(implies(not(truth),not(X_50)),not(X_50))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_674,plain,
    ( implies(not(truth),not(X_50)) != truth
    | implies(implies(not(truth),not(X_50)),not(X_50)) = implies(truth,not(X_50)) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_50)),not(X_50)),implies(implies(not(truth),not(X_50)),not(X_50))) )],[refute_0_672,refute_0_673]) ).

cnf(refute_0_675,plain,
    implies(implies(not(truth),not(X_50)),not(X_50)) = implies(truth,not(X_50)),
    inference(resolve,[$cnf( $equal(implies(not(truth),not(X_50)),truth) )],[refute_0_671,refute_0_674]) ).

cnf(refute_0_676,plain,
    ( implies(implies(not(truth),not(X_50)),not(X_50)) != implies(truth,not(X_50))
    | implies(truth,not(X_50)) != not(X_50)
    | implies(implies(not(truth),not(X_50)),not(X_50)) = not(X_50) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(not(truth),not(X_50)),not(X_50)))),bind(Y0,$fot(implies(truth,not(X_50)))),bind(Z0,$fot(not(X_50)))]]) ).

cnf(refute_0_677,plain,
    ( implies(truth,not(X_50)) != not(X_50)
    | implies(implies(not(truth),not(X_50)),not(X_50)) = not(X_50) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_50)),not(X_50)),implies(truth,not(X_50))) )],[refute_0_675,refute_0_676]) ).

cnf(refute_0_678,plain,
    implies(implies(not(truth),not(X_50)),not(X_50)) = not(X_50),
    inference(resolve,[$cnf( $equal(implies(truth,not(X_50)),not(X_50)) )],[refute_0_514,refute_0_677]) ).

cnf(refute_0_679,plain,
    ( implies(implies(not(truth),not(X_50)),not(X_50)) != not(X_50)
    | not(not(not(X_50))) != implies(implies(not(truth),not(X_50)),not(X_50))
    | not(not(not(X_50))) = not(X_50) ),
    introduced(tautology,[equality,[$cnf( $equal(not(not(not(X_50))),implies(implies(not(truth),not(X_50)),not(X_50))) ),[1],$fot(not(X_50))]]) ).

cnf(refute_0_680,plain,
    ( not(not(not(X_50))) != implies(implies(not(truth),not(X_50)),not(X_50))
    | not(not(not(X_50))) = not(X_50) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_50)),not(X_50)),not(X_50)) )],[refute_0_678,refute_0_679]) ).

cnf(refute_0_681,plain,
    ( implies(implies(not(X_50),not(truth)),not(truth)) != implies(implies(not(truth),not(X_50)),not(X_50))
    | not(not(not(X_50))) = not(X_50) ),
    inference(resolve,[$cnf( $equal(not(not(not(X_50))),implies(implies(not(truth),not(X_50)),not(X_50))) )],[refute_0_670,refute_0_680]) ).

cnf(refute_0_682,plain,
    not(not(not(X_50))) = not(X_50),
    inference(resolve,[$cnf( $equal(implies(implies(not(X_50),not(truth)),not(truth)),implies(implies(not(truth),not(X_50)),not(X_50))) )],[refute_0_542,refute_0_681]) ).

cnf(refute_0_683,plain,
    not(not(not(Y))) = not(Y),
    inference(subst,[],[refute_0_682:[bind(X_50,$fot(Y))]]) ).

cnf(refute_0_684,plain,
    implies(not(not(not(Y))),not(implies(truth,Y))) = implies(not(not(not(Y))),not(implies(truth,Y))),
    introduced(tautology,[refl,[$fot(implies(not(not(not(Y))),not(implies(truth,Y))))]]) ).

cnf(refute_0_685,plain,
    ( implies(not(not(not(Y))),not(implies(truth,Y))) != implies(not(not(not(Y))),not(implies(truth,Y)))
    | not(not(not(Y))) != not(Y)
    | implies(not(not(not(Y))),not(implies(truth,Y))) = implies(not(Y),not(implies(truth,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(not(not(Y))),not(implies(truth,Y))),implies(not(not(not(Y))),not(implies(truth,Y)))) ),[1,0],$fot(not(Y))]]) ).

cnf(refute_0_686,plain,
    ( not(not(not(Y))) != not(Y)
    | implies(not(not(not(Y))),not(implies(truth,Y))) = implies(not(Y),not(implies(truth,Y))) ),
    inference(resolve,[$cnf( $equal(implies(not(not(not(Y))),not(implies(truth,Y))),implies(not(not(not(Y))),not(implies(truth,Y)))) )],[refute_0_684,refute_0_685]) ).

cnf(refute_0_687,plain,
    implies(not(not(not(Y))),not(implies(truth,Y))) = implies(not(Y),not(implies(truth,Y))),
    inference(resolve,[$cnf( $equal(not(not(not(Y))),not(Y)) )],[refute_0_683,refute_0_686]) ).

cnf(refute_0_688,plain,
    ( implies(not(Y),not(implies(truth,Y))) != implies(not(Y),not(Y))
    | implies(not(not(not(Y))),not(implies(truth,Y))) != implies(not(Y),not(implies(truth,Y)))
    | implies(not(not(not(Y))),not(implies(truth,Y))) = implies(not(Y),not(Y)) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(not(not(not(Y))),not(implies(truth,Y))))),bind(Y0,$fot(implies(not(Y),not(implies(truth,Y))))),bind(Z0,$fot(implies(not(Y),not(Y))))]]) ).

cnf(refute_0_689,plain,
    ( implies(not(Y),not(implies(truth,Y))) != implies(not(Y),not(Y))
    | implies(not(not(not(Y))),not(implies(truth,Y))) = implies(not(Y),not(Y)) ),
    inference(resolve,[$cnf( $equal(implies(not(not(not(Y))),not(implies(truth,Y))),implies(not(Y),not(implies(truth,Y)))) )],[refute_0_687,refute_0_688]) ).

cnf(refute_0_690,plain,
    implies(not(not(not(Y))),not(implies(truth,Y))) = implies(not(Y),not(Y)),
    inference(resolve,[$cnf( $equal(implies(not(Y),not(implies(truth,Y))),implies(not(Y),not(Y))) )],[refute_0_457,refute_0_689]) ).

cnf(refute_0_691,plain,
    ( implies(not(Y),not(Y)) != truth
    | implies(not(not(not(Y))),not(implies(truth,Y))) != implies(not(Y),not(Y))
    | implies(not(not(not(Y))),not(implies(truth,Y))) = truth ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(not(not(not(Y))),not(implies(truth,Y))))),bind(Y0,$fot(implies(not(Y),not(Y)))),bind(Z0,$fot(truth))]]) ).

cnf(refute_0_692,plain,
    ( implies(not(Y),not(Y)) != truth
    | implies(not(not(not(Y))),not(implies(truth,Y))) = truth ),
    inference(resolve,[$cnf( $equal(implies(not(not(not(Y))),not(implies(truth,Y))),implies(not(Y),not(Y))) )],[refute_0_690,refute_0_691]) ).

cnf(refute_0_693,plain,
    implies(not(not(not(Y))),not(implies(truth,Y))) = truth,
    inference(resolve,[$cnf( $equal(implies(not(Y),not(Y)),truth) )],[refute_0_449,refute_0_692]) ).

cnf(refute_0_694,plain,
    implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))),
    introduced(tautology,[refl,[$fot(implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))))]]) ).

cnf(refute_0_695,plain,
    ( implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) != implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))))
    | implies(not(not(not(Y))),not(implies(truth,Y))) != truth
    | implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))),implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_696,plain,
    ( implies(not(not(not(Y))),not(implies(truth,Y))) != truth
    | implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))),implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))))) )],[refute_0_694,refute_0_695]) ).

cnf(refute_0_697,plain,
    implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))),
    inference(resolve,[$cnf( $equal(implies(not(not(not(Y))),not(implies(truth,Y))),truth) )],[refute_0_693,refute_0_696]) ).

cnf(refute_0_698,plain,
    ( implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) != implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))))
    | implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) != implies(truth,implies(Y,not(not(Y))))
    | implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = implies(truth,implies(Y,not(not(Y)))) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))))),bind(Y0,$fot(implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))))),bind(Z0,$fot(implies(truth,implies(Y,not(not(Y))))))]]) ).

cnf(refute_0_699,plain,
    ( implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) != implies(truth,implies(Y,not(not(Y))))
    | implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = implies(truth,implies(Y,not(not(Y)))) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))),implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y))))) )],[refute_0_697,refute_0_698]) ).

cnf(refute_0_700,plain,
    implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = implies(truth,implies(Y,not(not(Y)))),
    inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))),implies(truth,implies(Y,not(not(Y))))) )],[refute_0_448,refute_0_699]) ).

cnf(refute_0_701,plain,
    ( implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) != implies(truth,implies(Y,not(not(Y))))
    | implies(truth,implies(Y,not(not(Y)))) != implies(Y,not(not(Y)))
    | implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = implies(Y,not(not(Y))) ),
    inference(subst,[],[refute_0_163:[bind(X0,$fot(implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))))),bind(Y0,$fot(implies(truth,implies(Y,not(not(Y)))))),bind(Z0,$fot(implies(Y,not(not(Y)))))]]) ).

cnf(refute_0_702,plain,
    ( implies(truth,implies(Y,not(not(Y)))) != implies(Y,not(not(Y)))
    | implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = implies(Y,not(not(Y))) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))),implies(truth,implies(Y,not(not(Y))))) )],[refute_0_700,refute_0_701]) ).

cnf(refute_0_703,plain,
    implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) = implies(Y,not(not(Y))),
    inference(resolve,[$cnf( $equal(implies(truth,implies(Y,not(not(Y)))),implies(Y,not(not(Y)))) )],[refute_0_420,refute_0_702]) ).

cnf(refute_0_704,plain,
    ( implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) != implies(Y,not(not(Y)))
    | implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) != truth
    | implies(Y,not(not(Y))) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))),truth) ),[0],$fot(implies(Y,not(not(Y))))]]) ).

cnf(refute_0_705,plain,
    ( implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))) != truth
    | implies(Y,not(not(Y))) = truth ),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))),implies(Y,not(not(Y)))) )],[refute_0_703,refute_0_704]) ).

cnf(refute_0_706,plain,
    implies(Y,not(not(Y))) = truth,
    inference(resolve,[$cnf( $equal(implies(implies(not(not(not(Y))),not(implies(truth,Y))),implies(implies(implies(Y,not(not(Y))),not(not(Y))),not(not(Y)))),truth) )],[refute_0_419,refute_0_705]) ).

cnf(refute_0_707,plain,
    ( implies(Y,not(not(Y))) != truth
    | implies(implies(not(not(Y)),Y),Y) != implies(implies(Y,not(not(Y))),not(not(Y)))
    | implies(implies(not(not(Y)),Y),Y) = implies(truth,not(not(Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(Y,not(not(Y))),not(not(Y)))) ),[1,0],$fot(truth)]]) ).

cnf(refute_0_708,plain,
    ( implies(implies(not(not(Y)),Y),Y) != implies(implies(Y,not(not(Y))),not(not(Y)))
    | implies(implies(not(not(Y)),Y),Y) = implies(truth,not(not(Y))) ),
    inference(resolve,[$cnf( $equal(implies(Y,not(not(Y))),truth) )],[refute_0_706,refute_0_707]) ).

cnf(refute_0_709,plain,
    implies(implies(not(not(Y)),Y),Y) = implies(truth,not(not(Y))),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(Y,not(not(Y))),not(not(Y)))) )],[refute_0_40,refute_0_708]) ).

cnf(refute_0_710,plain,
    ( implies(implies(not(not(Y)),Y),Y) != Y
    | implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
    | Y = implies(truth,not(not(Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,not(not(Y)))) ),[0],$fot(Y)]]) ).

cnf(refute_0_711,plain,
    ( implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
    | Y = implies(truth,not(not(Y))) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),Y) )],[refute_0_428,refute_0_710]) ).

cnf(refute_0_712,plain,
    implies(truth,not(not(Y))) = not(not(Y)),
    inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(Y))))]]) ).

cnf(refute_0_713,plain,
    ( Y != implies(truth,not(not(Y)))
    | implies(truth,not(not(Y))) != not(not(Y))
    | Y = not(not(Y)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(Y,not(not(Y))) ),[0],$fot(implies(truth,not(not(Y))))]]) ).

cnf(refute_0_714,plain,
    ( Y != implies(truth,not(not(Y)))
    | Y = not(not(Y)) ),
    inference(resolve,[$cnf( $equal(implies(truth,not(not(Y))),not(not(Y))) )],[refute_0_712,refute_0_713]) ).

cnf(refute_0_715,plain,
    ( implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
    | Y = not(not(Y)) ),
    inference(resolve,[$cnf( $equal(Y,implies(truth,not(not(Y)))) )],[refute_0_711,refute_0_714]) ).

cnf(refute_0_716,plain,
    Y = not(not(Y)),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,not(not(Y)))) )],[refute_0_709,refute_0_715]) ).

cnf(refute_0_717,plain,
    ( Y != not(not(Y))
    | not(not(Y)) = Y ),
    inference(subst,[],[refute_0_45:[bind(X0,$fot(Y)),bind(Y0,$fot(not(not(Y))))]]) ).

cnf(refute_0_718,plain,
    not(not(Y)) = Y,
    inference(resolve,[$cnf( $equal(Y,not(not(Y))) )],[refute_0_716,refute_0_717]) ).

cnf(refute_0_719,plain,
    ( implies(not(Y),implies(implies(not(X_84),not(not(Y))),X_84)) != truth
    | not(not(Y)) != Y
    | implies(not(Y),implies(implies(not(X_84),Y),X_84)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(Y),implies(implies(not(X_84),not(not(Y))),X_84)),truth) ),[0,1,0,1],$fot(Y)]]) ).

cnf(refute_0_720,plain,
    ( implies(not(Y),implies(implies(not(X_84),not(not(Y))),X_84)) != truth
    | implies(not(Y),implies(implies(not(X_84),Y),X_84)) = truth ),
    inference(resolve,[$cnf( $equal(not(not(Y)),Y) )],[refute_0_718,refute_0_719]) ).

cnf(refute_0_721,plain,
    implies(not(Y),implies(implies(not(X_84),Y),X_84)) = truth,
    inference(resolve,[$cnf( $equal(implies(not(Y),implies(implies(not(X_84),not(not(Y))),X_84)),truth) )],[refute_0_39,refute_0_720]) ).

cnf(refute_0_722,plain,
    implies(not(implies(X_132,not(X_84))),implies(implies(not(X_84),implies(X_132,not(X_84))),X_84)) = truth,
    inference(subst,[],[refute_0_721:[bind(Y,$fot(implies(X_132,not(X_84))))]]) ).

cnf(refute_0_723,plain,
    implies(not(X_84),implies(X_132,not(X_84))) = truth,
    inference(subst,[],[refute_0_386:[bind(X_14,$fot(X_132)),bind(X_16,$fot(not(X_84)))]]) ).

cnf(refute_0_724,plain,
    ( implies(not(X_84),implies(X_132,not(X_84))) != truth
    | implies(not(implies(X_132,not(X_84))),implies(implies(not(X_84),implies(X_132,not(X_84))),X_84)) != truth
    | implies(not(implies(X_132,not(X_84))),implies(truth,X_84)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X_132,not(X_84))),implies(implies(not(X_84),implies(X_132,not(X_84))),X_84)),truth) ),[0,1,0],$fot(truth)]]) ).

cnf(refute_0_725,plain,
    ( implies(not(implies(X_132,not(X_84))),implies(implies(not(X_84),implies(X_132,not(X_84))),X_84)) != truth
    | implies(not(implies(X_132,not(X_84))),implies(truth,X_84)) = truth ),
    inference(resolve,[$cnf( $equal(implies(not(X_84),implies(X_132,not(X_84))),truth) )],[refute_0_723,refute_0_724]) ).

cnf(refute_0_726,plain,
    implies(not(implies(X_132,not(X_84))),implies(truth,X_84)) = truth,
    inference(resolve,[$cnf( $equal(implies(not(implies(X_132,not(X_84))),implies(implies(not(X_84),implies(X_132,not(X_84))),X_84)),truth) )],[refute_0_722,refute_0_725]) ).

cnf(refute_0_727,plain,
    implies(truth,X_84) = X_84,
    inference(subst,[],[wajsberg_1:[bind(X,$fot(X_84))]]) ).

cnf(refute_0_728,plain,
    implies(not(implies(X_132,not(X_84))),implies(truth,X_84)) = implies(not(implies(X_132,not(X_84))),implies(truth,X_84)),
    introduced(tautology,[refl,[$fot(implies(not(implies(X_132,not(X_84))),implies(truth,X_84)))]]) ).

cnf(refute_0_729,plain,
    ( implies(not(implies(X_132,not(X_84))),implies(truth,X_84)) != implies(not(implies(X_132,not(X_84))),implies(truth,X_84))
    | implies(truth,X_84) != X_84
    | implies(not(implies(X_132,not(X_84))),implies(truth,X_84)) = implies(not(implies(X_132,not(X_84))),X_84) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X_132,not(X_84))),implies(truth,X_84)),implies(not(implies(X_132,not(X_84))),implies(truth,X_84))) ),[1,1],$fot(X_84)]]) ).

cnf(refute_0_730,plain,
    ( implies(truth,X_84) != X_84
    | implies(not(implies(X_132,not(X_84))),implies(truth,X_84)) = implies(not(implies(X_132,not(X_84))),X_84) ),
    inference(resolve,[$cnf( $equal(implies(not(implies(X_132,not(X_84))),implies(truth,X_84)),implies(not(implies(X_132,not(X_84))),implies(truth,X_84))) )],[refute_0_728,refute_0_729]) ).

cnf(refute_0_731,plain,
    implies(not(implies(X_132,not(X_84))),implies(truth,X_84)) = implies(not(implies(X_132,not(X_84))),X_84),
    inference(resolve,[$cnf( $equal(implies(truth,X_84),X_84) )],[refute_0_727,refute_0_730]) ).

cnf(refute_0_732,plain,
    ( implies(not(implies(X_132,not(X_84))),implies(truth,X_84)) != implies(not(implies(X_132,not(X_84))),X_84)
    | implies(not(implies(X_132,not(X_84))),implies(truth,X_84)) != truth
    | implies(not(implies(X_132,not(X_84))),X_84) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X_132,not(X_84))),implies(truth,X_84)),truth) ),[0],$fot(implies(not(implies(X_132,not(X_84))),X_84))]]) ).

cnf(refute_0_733,plain,
    ( implies(not(implies(X_132,not(X_84))),implies(truth,X_84)) != truth
    | implies(not(implies(X_132,not(X_84))),X_84) = truth ),
    inference(resolve,[$cnf( $equal(implies(not(implies(X_132,not(X_84))),implies(truth,X_84)),implies(not(implies(X_132,not(X_84))),X_84)) )],[refute_0_731,refute_0_732]) ).

cnf(refute_0_734,plain,
    implies(not(implies(X_132,not(X_84))),X_84) = truth,
    inference(resolve,[$cnf( $equal(implies(not(implies(X_132,not(X_84))),implies(truth,X_84)),truth) )],[refute_0_726,refute_0_733]) ).

cnf(refute_0_735,plain,
    implies(not(implies(X_143,not(not(Y)))),not(Y)) = truth,
    inference(subst,[],[refute_0_734:[bind(X_132,$fot(X_143)),bind(X_84,$fot(not(Y)))]]) ).

cnf(refute_0_736,plain,
    ( implies(not(implies(X_143,not(not(Y)))),not(Y)) != truth
    | not(not(Y)) != Y
    | implies(not(implies(X_143,Y)),not(Y)) = truth ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X_143,not(not(Y)))),not(Y)),truth) ),[0,0,0,1],$fot(Y)]]) ).

cnf(refute_0_737,plain,
    ( implies(not(implies(X_143,not(not(Y)))),not(Y)) != truth
    | implies(not(implies(X_143,Y)),not(Y)) = truth ),
    inference(resolve,[$cnf( $equal(not(not(Y)),Y) )],[refute_0_718,refute_0_736]) ).

cnf(refute_0_738,plain,
    implies(not(implies(X_143,Y)),not(Y)) = truth,
    inference(resolve,[$cnf( $equal(implies(not(implies(X_143,not(not(Y)))),not(Y)),truth) )],[refute_0_735,refute_0_737]) ).

cnf(refute_0_739,plain,
    implies(not(implies(a,b)),not(b)) = truth,
    inference(subst,[],[refute_0_738:[bind(Y,$fot(b)),bind(X_143,$fot(a))]]) ).

cnf(refute_0_740,plain,
    ( implies(not(implies(a,b)),not(b)) != truth
    | truth != truth
    | implies(not(implies(a,b)),not(b)) = truth ),
    introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(implies(a,b)),not(b)),truth) ),[0],$fot(truth)]]) ).

cnf(refute_0_741,plain,
    ( truth != truth
    | implies(not(implies(a,b)),not(b)) = truth ),
    inference(resolve,[$cnf( $equal(implies(not(implies(a,b)),not(b)),truth) )],[refute_0_739,refute_0_740]) ).

cnf(refute_0_742,plain,
    truth != truth,
    inference(resolve,[$cnf( $equal(implies(not(implies(a,b)),not(b)),truth) )],[refute_0_741,prove_mv_39]) ).

cnf(refute_0_743,plain,
    truth = truth,
    introduced(tautology,[refl,[$fot(truth)]]) ).

cnf(refute_0_744,plain,
    $false,
    inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_743,refute_0_742]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : LCL115-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.35  % Computer : n015.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sun Jul  3 14:09:30 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.26/2.49  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.26/2.49  
% 2.26/2.49  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.42/2.62  
%------------------------------------------------------------------------------