TSTP Solution File: LCL163-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL163-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n013.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 12:50:06 EDT 2022

% Result   : Unsatisfiable 0.19s 0.52s
% Output   : CNFRefutation 0.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   49
%            Number of leaves      :   78
% Syntax   : Number of clauses     :  255 ( 125 unt;   0 nHn; 131 RR)
%            Number of literals    :  442 ( 441 equ; 189 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :  434 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(axiom_1,axiom,
    not(X) = xor(X,truth) ).

cnf(axiom_2,axiom,
    xor(X,falsehood) = X ).

cnf(axiom_7,axiom,
    xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ).

cnf(axiom_8,axiom,
    and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ).

cnf(xor_commutativity,axiom,
    xor(X,Y) = xor(Y,X) ).

cnf(and_star_commutativity,axiom,
    and_star(X,Y) = and_star(Y,X) ).

cnf(false_definition,axiom,
    not(truth) = falsehood ).

cnf(implies_definition,axiom,
    implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ).

cnf(prove_wajsberg_axiom,negated_conjecture,
    implies(implies(x,y),y) != implies(implies(y,x),x) ).

cnf(refute_0_0,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_1,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_2,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( not(X) != xor(X,truth)
    | xor(X,truth) = not(X) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(not(X))),bind(Y0,$fot(xor(X,truth)))]]) ).

cnf(refute_0_4,plain,
    xor(X,truth) = not(X),
    inference(resolve,[$cnf( $equal(not(X),xor(X,truth)) )],[axiom_1,refute_0_3]) ).

cnf(refute_0_5,plain,
    xor(xor(X,truth),Y) = xor(xor(X,truth),Y),
    introduced(tautology,[refl,[$fot(xor(xor(X,truth),Y))]]) ).

cnf(refute_0_6,plain,
    ( xor(X,truth) != not(X)
    | xor(xor(X,truth),Y) != xor(xor(X,truth),Y)
    | xor(xor(X,truth),Y) = xor(not(X),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(xor(xor(X,truth),Y),xor(xor(X,truth),Y)) ),[1,0],$fot(not(X))]]) ).

cnf(refute_0_7,plain,
    ( xor(X,truth) != not(X)
    | xor(xor(X,truth),Y) = xor(not(X),Y) ),
    inference(resolve,[$cnf( $equal(xor(xor(X,truth),Y),xor(xor(X,truth),Y)) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    xor(xor(X,truth),Y) = xor(not(X),Y),
    inference(resolve,[$cnf( $equal(xor(X,truth),not(X)) )],[refute_0_4,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( xor(X,xor(truth,Y)) != xor(xor(X,truth),Y)
    | xor(xor(X,truth),Y) != xor(not(X),Y)
    | xor(X,xor(truth,Y)) = xor(not(X),Y) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(xor(X,xor(truth,Y)),xor(not(X),Y)) ),[0],$fot(xor(xor(X,truth),Y))]]) ).

cnf(refute_0_10,plain,
    ( xor(X,xor(truth,Y)) != xor(xor(X,truth),Y)
    | xor(X,xor(truth,Y)) = xor(not(X),Y) ),
    inference(resolve,[$cnf( $equal(xor(xor(X,truth),Y),xor(not(X),Y)) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    xor(X,xor(truth,Y)) = xor(not(X),Y),
    inference(resolve,[$cnf( $equal(xor(X,xor(truth,Y)),xor(xor(X,truth),Y)) )],[axiom_7,refute_0_10]) ).

cnf(refute_0_12,plain,
    xor(X_6,xor(truth,truth)) = xor(not(X_6),truth),
    inference(subst,[],[refute_0_11:[bind(X,$fot(X_6)),bind(Y,$fot(truth))]]) ).

cnf(refute_0_13,plain,
    not(not(X_6)) = xor(not(X_6),truth),
    inference(subst,[],[axiom_1:[bind(X,$fot(not(X_6)))]]) ).

cnf(refute_0_14,plain,
    ( not(not(X_6)) != xor(not(X_6),truth)
    | xor(not(X_6),truth) = not(not(X_6)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(not(not(X_6)))),bind(Y0,$fot(xor(not(X_6),truth)))]]) ).

cnf(refute_0_15,plain,
    xor(not(X_6),truth) = not(not(X_6)),
    inference(resolve,[$cnf( $equal(not(not(X_6)),xor(not(X_6),truth)) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( xor(X_6,xor(truth,truth)) != xor(not(X_6),truth)
    | xor(not(X_6),truth) != not(not(X_6))
    | xor(X_6,xor(truth,truth)) = not(not(X_6)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(xor(X_6,xor(truth,truth)),not(not(X_6))) ),[0],$fot(xor(not(X_6),truth))]]) ).

cnf(refute_0_17,plain,
    ( xor(X_6,xor(truth,truth)) != xor(not(X_6),truth)
    | xor(X_6,xor(truth,truth)) = not(not(X_6)) ),
    inference(resolve,[$cnf( $equal(xor(not(X_6),truth),not(not(X_6))) )],[refute_0_15,refute_0_16]) ).

cnf(refute_0_18,plain,
    xor(X_6,xor(truth,truth)) = not(not(X_6)),
    inference(resolve,[$cnf( $equal(xor(X_6,xor(truth,truth)),xor(not(X_6),truth)) )],[refute_0_12,refute_0_17]) ).

cnf(refute_0_19,plain,
    not(truth) = xor(truth,truth),
    inference(subst,[],[axiom_1:[bind(X,$fot(truth))]]) ).

cnf(refute_0_20,plain,
    ( not(truth) != xor(truth,truth)
    | xor(truth,truth) = not(truth) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(not(truth))),bind(Y0,$fot(xor(truth,truth)))]]) ).

cnf(refute_0_21,plain,
    xor(truth,truth) = not(truth),
    inference(resolve,[$cnf( $equal(not(truth),xor(truth,truth)) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( xor(X_6,xor(truth,truth)) != xor(not(X_6),truth)
    | xor(truth,truth) != not(truth)
    | xor(X_6,not(truth)) = xor(not(X_6),truth) ),
    introduced(tautology,[equality,[$cnf( $equal(xor(X_6,xor(truth,truth)),xor(not(X_6),truth)) ),[0,1],$fot(not(truth))]]) ).

cnf(refute_0_23,plain,
    ( xor(X_6,xor(truth,truth)) != xor(not(X_6),truth)
    | xor(X_6,not(truth)) = xor(not(X_6),truth) ),
    inference(resolve,[$cnf( $equal(xor(truth,truth),not(truth)) )],[refute_0_21,refute_0_22]) ).

cnf(refute_0_24,plain,
    xor(X_6,not(truth)) = xor(not(X_6),truth),
    inference(resolve,[$cnf( $equal(xor(X_6,xor(truth,truth)),xor(not(X_6),truth)) )],[refute_0_12,refute_0_23]) ).

cnf(refute_0_25,plain,
    xor(X_6,falsehood) = X_6,
    inference(subst,[],[axiom_2:[bind(X,$fot(X_6))]]) ).

cnf(refute_0_26,plain,
    xor(X_6,not(truth)) = xor(X_6,not(truth)),
    introduced(tautology,[refl,[$fot(xor(X_6,not(truth)))]]) ).

cnf(refute_0_27,plain,
    ( not(truth) != falsehood
    | xor(X_6,not(truth)) != xor(X_6,not(truth))
    | xor(X_6,not(truth)) = xor(X_6,falsehood) ),
    introduced(tautology,[equality,[$cnf( $equal(xor(X_6,not(truth)),xor(X_6,not(truth))) ),[1,1],$fot(falsehood)]]) ).

cnf(refute_0_28,plain,
    ( not(truth) != falsehood
    | xor(X_6,not(truth)) = xor(X_6,falsehood) ),
    inference(resolve,[$cnf( $equal(xor(X_6,not(truth)),xor(X_6,not(truth))) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    xor(X_6,not(truth)) = xor(X_6,falsehood),
    inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( Y0 != X0
    | Y0 != Z
    | X0 = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).

cnf(refute_0_31,plain,
    ( X0 != Y0
    | Y0 != Z
    | X0 = Z ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_30]) ).

cnf(refute_0_32,plain,
    ( xor(X_6,falsehood) != X_6
    | xor(X_6,not(truth)) != xor(X_6,falsehood)
    | xor(X_6,not(truth)) = X_6 ),
    inference(subst,[],[refute_0_31:[bind(X0,$fot(xor(X_6,not(truth)))),bind(Y0,$fot(xor(X_6,falsehood))),bind(Z,$fot(X_6))]]) ).

cnf(refute_0_33,plain,
    ( xor(X_6,falsehood) != X_6
    | xor(X_6,not(truth)) = X_6 ),
    inference(resolve,[$cnf( $equal(xor(X_6,not(truth)),xor(X_6,falsehood)) )],[refute_0_29,refute_0_32]) ).

cnf(refute_0_34,plain,
    xor(X_6,not(truth)) = X_6,
    inference(resolve,[$cnf( $equal(xor(X_6,falsehood),X_6) )],[refute_0_25,refute_0_33]) ).

cnf(refute_0_35,plain,
    ( xor(X_6,not(truth)) != X_6
    | xor(X_6,not(truth)) != xor(not(X_6),truth)
    | X_6 = xor(not(X_6),truth) ),
    introduced(tautology,[equality,[$cnf( $equal(xor(X_6,not(truth)),xor(not(X_6),truth)) ),[0],$fot(X_6)]]) ).

cnf(refute_0_36,plain,
    ( xor(X_6,not(truth)) != xor(not(X_6),truth)
    | X_6 = xor(not(X_6),truth) ),
    inference(resolve,[$cnf( $equal(xor(X_6,not(truth)),X_6) )],[refute_0_34,refute_0_35]) ).

cnf(refute_0_37,plain,
    ( xor(X,Y) != xor(Y,X)
    | xor(Y,X) = xor(X,Y) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(X,Y))),bind(Y0,$fot(xor(Y,X)))]]) ).

cnf(refute_0_38,plain,
    xor(Y,X) = xor(X,Y),
    inference(resolve,[$cnf( $equal(xor(X,Y),xor(Y,X)) )],[xor_commutativity,refute_0_37]) ).

cnf(refute_0_39,plain,
    xor(not(X_6),truth) = xor(truth,not(X_6)),
    inference(subst,[],[refute_0_38:[bind(X,$fot(truth)),bind(Y,$fot(not(X_6)))]]) ).

cnf(refute_0_40,plain,
    ( X_6 != xor(not(X_6),truth)
    | xor(not(X_6),truth) != xor(truth,not(X_6))
    | X_6 = xor(truth,not(X_6)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_6,xor(truth,not(X_6))) ),[0],$fot(xor(not(X_6),truth))]]) ).

cnf(refute_0_41,plain,
    ( X_6 != xor(not(X_6),truth)
    | X_6 = xor(truth,not(X_6)) ),
    inference(resolve,[$cnf( $equal(xor(not(X_6),truth),xor(truth,not(X_6))) )],[refute_0_39,refute_0_40]) ).

cnf(refute_0_42,plain,
    ( xor(X_6,not(truth)) != xor(not(X_6),truth)
    | X_6 = xor(truth,not(X_6)) ),
    inference(resolve,[$cnf( $equal(X_6,xor(not(X_6),truth)) )],[refute_0_36,refute_0_41]) ).

cnf(refute_0_43,plain,
    X_6 = xor(truth,not(X_6)),
    inference(resolve,[$cnf( $equal(xor(X_6,not(truth)),xor(not(X_6),truth)) )],[refute_0_24,refute_0_42]) ).

cnf(refute_0_44,plain,
    ( X_6 != xor(truth,not(X_6))
    | xor(truth,not(X_6)) = X_6 ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(X_6)),bind(Y0,$fot(xor(truth,not(X_6))))]]) ).

cnf(refute_0_45,plain,
    xor(truth,not(X_6)) = X_6,
    inference(resolve,[$cnf( $equal(X_6,xor(truth,not(X_6))) )],[refute_0_43,refute_0_44]) ).

cnf(refute_0_46,plain,
    ( xor(not(X_6),truth) != xor(truth,not(X_6))
    | xor(truth,not(X_6)) != X_6
    | xor(not(X_6),truth) = X_6 ),
    inference(subst,[],[refute_0_31:[bind(X0,$fot(xor(not(X_6),truth))),bind(Y0,$fot(xor(truth,not(X_6)))),bind(Z,$fot(X_6))]]) ).

cnf(refute_0_47,plain,
    ( xor(truth,not(X_6)) != X_6
    | xor(not(X_6),truth) = X_6 ),
    inference(resolve,[$cnf( $equal(xor(not(X_6),truth),xor(truth,not(X_6))) )],[refute_0_39,refute_0_46]) ).

cnf(refute_0_48,plain,
    xor(not(X_6),truth) = X_6,
    inference(resolve,[$cnf( $equal(xor(truth,not(X_6)),X_6) )],[refute_0_45,refute_0_47]) ).

cnf(refute_0_49,plain,
    ( xor(X_6,xor(truth,truth)) != xor(not(X_6),truth)
    | xor(not(X_6),truth) != X_6
    | xor(X_6,xor(truth,truth)) = X_6 ),
    inference(subst,[],[refute_0_31:[bind(X0,$fot(xor(X_6,xor(truth,truth)))),bind(Y0,$fot(xor(not(X_6),truth))),bind(Z,$fot(X_6))]]) ).

cnf(refute_0_50,plain,
    ( xor(not(X_6),truth) != X_6
    | xor(X_6,xor(truth,truth)) = X_6 ),
    inference(resolve,[$cnf( $equal(xor(X_6,xor(truth,truth)),xor(not(X_6),truth)) )],[refute_0_12,refute_0_49]) ).

cnf(refute_0_51,plain,
    xor(X_6,xor(truth,truth)) = X_6,
    inference(resolve,[$cnf( $equal(xor(not(X_6),truth),X_6) )],[refute_0_48,refute_0_50]) ).

cnf(refute_0_52,plain,
    ( xor(X_6,xor(truth,truth)) != X_6
    | xor(X_6,xor(truth,truth)) != not(not(X_6))
    | X_6 = not(not(X_6)) ),
    introduced(tautology,[equality,[$cnf( $equal(xor(X_6,xor(truth,truth)),not(not(X_6))) ),[0],$fot(X_6)]]) ).

cnf(refute_0_53,plain,
    ( xor(X_6,xor(truth,truth)) != not(not(X_6))
    | X_6 = not(not(X_6)) ),
    inference(resolve,[$cnf( $equal(xor(X_6,xor(truth,truth)),X_6) )],[refute_0_51,refute_0_52]) ).

cnf(refute_0_54,plain,
    X_6 = not(not(X_6)),
    inference(resolve,[$cnf( $equal(xor(X_6,xor(truth,truth)),not(not(X_6))) )],[refute_0_18,refute_0_53]) ).

cnf(refute_0_55,plain,
    implies(X_26,and_star(not(X_25),X_26)) = not(not(implies(X_26,and_star(not(X_25),X_26)))),
    inference(subst,[],[refute_0_54:[bind(X_6,$fot(implies(X_26,and_star(not(X_25),X_26))))]]) ).

cnf(refute_0_56,plain,
    xor(and_star(xor(truth,X),Y),truth) = not(and_star(xor(truth,X),Y)),
    inference(subst,[],[refute_0_4:[bind(X,$fot(and_star(xor(truth,X),Y)))]]) ).

cnf(refute_0_57,plain,
    and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,X),Y),truth),Y),
    introduced(tautology,[refl,[$fot(and_star(xor(and_star(xor(truth,X),Y),truth),Y))]]) ).

cnf(refute_0_58,plain,
    ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) != and_star(xor(and_star(xor(truth,X),Y),truth),Y)
    | xor(and_star(xor(truth,X),Y),truth) != not(and_star(xor(truth,X),Y))
    | and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(not(and_star(xor(truth,X),Y)),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(and_star(xor(and_star(xor(truth,X),Y),truth),Y),and_star(xor(and_star(xor(truth,X),Y),truth),Y)) ),[1,0],$fot(not(and_star(xor(truth,X),Y)))]]) ).

cnf(refute_0_59,plain,
    ( xor(and_star(xor(truth,X),Y),truth) != not(and_star(xor(truth,X),Y))
    | and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(not(and_star(xor(truth,X),Y)),Y) ),
    inference(resolve,[$cnf( $equal(and_star(xor(and_star(xor(truth,X),Y),truth),Y),and_star(xor(and_star(xor(truth,X),Y),truth),Y)) )],[refute_0_57,refute_0_58]) ).

cnf(refute_0_60,plain,
    and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(not(and_star(xor(truth,X),Y)),Y),
    inference(resolve,[$cnf( $equal(xor(and_star(xor(truth,X),Y),truth),not(and_star(xor(truth,X),Y))) )],[refute_0_56,refute_0_59]) ).

cnf(refute_0_61,plain,
    ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) != and_star(not(and_star(xor(truth,X),Y)),Y)
    | and_star(xor(and_star(xor(truth,X),Y),truth),Y) != and_star(xor(and_star(xor(truth,Y),X),truth),X)
    | and_star(not(and_star(xor(truth,X),Y)),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ),
    introduced(tautology,[equality,[$cnf( $equal(and_star(xor(and_star(xor(truth,X),Y),truth),Y),and_star(xor(and_star(xor(truth,Y),X),truth),X)) ),[0],$fot(and_star(not(and_star(xor(truth,X),Y)),Y))]]) ).

cnf(refute_0_62,plain,
    ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) != and_star(xor(and_star(xor(truth,Y),X),truth),X)
    | and_star(not(and_star(xor(truth,X),Y)),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ),
    inference(resolve,[$cnf( $equal(and_star(xor(and_star(xor(truth,X),Y),truth),Y),and_star(not(and_star(xor(truth,X),Y)),Y)) )],[refute_0_60,refute_0_61]) ).

cnf(refute_0_63,plain,
    xor(and_star(xor(truth,Y),X),truth) = not(and_star(xor(truth,Y),X)),
    inference(subst,[],[refute_0_4:[bind(X,$fot(and_star(xor(truth,Y),X)))]]) ).

cnf(refute_0_64,plain,
    and_star(xor(and_star(xor(truth,Y),X),truth),X) = and_star(xor(and_star(xor(truth,Y),X),truth),X),
    introduced(tautology,[refl,[$fot(and_star(xor(and_star(xor(truth,Y),X),truth),X))]]) ).

cnf(refute_0_65,plain,
    ( and_star(xor(and_star(xor(truth,Y),X),truth),X) != and_star(xor(and_star(xor(truth,Y),X),truth),X)
    | xor(and_star(xor(truth,Y),X),truth) != not(and_star(xor(truth,Y),X))
    | and_star(xor(and_star(xor(truth,Y),X),truth),X) = and_star(not(and_star(xor(truth,Y),X)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(and_star(xor(and_star(xor(truth,Y),X),truth),X),and_star(xor(and_star(xor(truth,Y),X),truth),X)) ),[1,0],$fot(not(and_star(xor(truth,Y),X)))]]) ).

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

cnf(refute_0_67,plain,
    and_star(xor(and_star(xor(truth,Y),X),truth),X) = and_star(not(and_star(xor(truth,Y),X)),X),
    inference(resolve,[$cnf( $equal(xor(and_star(xor(truth,Y),X),truth),not(and_star(xor(truth,Y),X))) )],[refute_0_63,refute_0_66]) ).

cnf(refute_0_68,plain,
    ( and_star(not(and_star(xor(truth,X),Y)),Y) != and_star(xor(and_star(xor(truth,Y),X),truth),X)
    | and_star(xor(and_star(xor(truth,Y),X),truth),X) != and_star(not(and_star(xor(truth,Y),X)),X)
    | and_star(not(and_star(xor(truth,X),Y)),Y) = and_star(not(and_star(xor(truth,Y),X)),X) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(and_star(not(and_star(xor(truth,X),Y)),Y),and_star(not(and_star(xor(truth,Y),X)),X)) ),[0],$fot(and_star(xor(and_star(xor(truth,Y),X),truth),X))]]) ).

cnf(refute_0_69,plain,
    ( and_star(not(and_star(xor(truth,X),Y)),Y) != and_star(xor(and_star(xor(truth,Y),X),truth),X)
    | and_star(not(and_star(xor(truth,X),Y)),Y) = and_star(not(and_star(xor(truth,Y),X)),X) ),
    inference(resolve,[$cnf( $equal(and_star(xor(and_star(xor(truth,Y),X),truth),X),and_star(not(and_star(xor(truth,Y),X)),X)) )],[refute_0_67,refute_0_68]) ).

cnf(refute_0_70,plain,
    ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) != and_star(xor(and_star(xor(truth,Y),X),truth),X)
    | and_star(not(and_star(xor(truth,X),Y)),Y) = and_star(not(and_star(xor(truth,Y),X)),X) ),
    inference(resolve,[$cnf( $equal(and_star(not(and_star(xor(truth,X),Y)),Y),and_star(xor(and_star(xor(truth,Y),X),truth),X)) )],[refute_0_62,refute_0_69]) ).

cnf(refute_0_71,plain,
    and_star(not(and_star(xor(truth,X),Y)),Y) = and_star(not(and_star(xor(truth,Y),X)),X),
    inference(resolve,[$cnf( $equal(and_star(xor(and_star(xor(truth,X),Y),truth),Y),and_star(xor(and_star(xor(truth,Y),X),truth),X)) )],[axiom_8,refute_0_70]) ).

cnf(refute_0_72,plain,
    ( and_star(X,Y) != and_star(Y,X)
    | and_star(Y,X) = and_star(X,Y) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(and_star(X,Y))),bind(Y0,$fot(and_star(Y,X)))]]) ).

cnf(refute_0_73,plain,
    and_star(Y,X) = and_star(X,Y),
    inference(resolve,[$cnf( $equal(and_star(X,Y),and_star(Y,X)) )],[and_star_commutativity,refute_0_72]) ).

cnf(refute_0_74,plain,
    and_star(not(and_star(xor(truth,X),Y)),Y) = and_star(Y,not(and_star(xor(truth,X),Y))),
    inference(subst,[],[refute_0_73:[bind(X,$fot(Y)),bind(Y,$fot(not(and_star(xor(truth,X),Y))))]]) ).

cnf(refute_0_75,plain,
    ( and_star(not(and_star(xor(truth,X),Y)),Y) != and_star(Y,not(and_star(xor(truth,X),Y)))
    | and_star(not(and_star(xor(truth,X),Y)),Y) != and_star(not(and_star(xor(truth,Y),X)),X)
    | and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(not(and_star(xor(truth,Y),X)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(and_star(not(and_star(xor(truth,X),Y)),Y),and_star(not(and_star(xor(truth,Y),X)),X)) ),[0],$fot(and_star(Y,not(and_star(xor(truth,X),Y))))]]) ).

cnf(refute_0_76,plain,
    ( and_star(not(and_star(xor(truth,X),Y)),Y) != and_star(not(and_star(xor(truth,Y),X)),X)
    | and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(not(and_star(xor(truth,Y),X)),X) ),
    inference(resolve,[$cnf( $equal(and_star(not(and_star(xor(truth,X),Y)),Y),and_star(Y,not(and_star(xor(truth,X),Y)))) )],[refute_0_74,refute_0_75]) ).

cnf(refute_0_77,plain,
    and_star(not(and_star(xor(truth,Y),X)),X) = and_star(X,not(and_star(xor(truth,Y),X))),
    inference(subst,[],[refute_0_73:[bind(Y,$fot(not(and_star(xor(truth,Y),X))))]]) ).

cnf(refute_0_78,plain,
    ( and_star(Y,not(and_star(xor(truth,X),Y))) != and_star(not(and_star(xor(truth,Y),X)),X)
    | and_star(not(and_star(xor(truth,Y),X)),X) != and_star(X,not(and_star(xor(truth,Y),X)))
    | and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(X,not(and_star(xor(truth,Y),X))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(and_star(Y,not(and_star(xor(truth,X),Y))),and_star(X,not(and_star(xor(truth,Y),X)))) ),[0],$fot(and_star(not(and_star(xor(truth,Y),X)),X))]]) ).

cnf(refute_0_79,plain,
    ( and_star(Y,not(and_star(xor(truth,X),Y))) != and_star(not(and_star(xor(truth,Y),X)),X)
    | and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(X,not(and_star(xor(truth,Y),X))) ),
    inference(resolve,[$cnf( $equal(and_star(not(and_star(xor(truth,Y),X)),X),and_star(X,not(and_star(xor(truth,Y),X)))) )],[refute_0_77,refute_0_78]) ).

cnf(refute_0_80,plain,
    ( and_star(not(and_star(xor(truth,X),Y)),Y) != and_star(not(and_star(xor(truth,Y),X)),X)
    | and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(X,not(and_star(xor(truth,Y),X))) ),
    inference(resolve,[$cnf( $equal(and_star(Y,not(and_star(xor(truth,X),Y))),and_star(not(and_star(xor(truth,Y),X)),X)) )],[refute_0_76,refute_0_79]) ).

cnf(refute_0_81,plain,
    and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(X,not(and_star(xor(truth,Y),X))),
    inference(resolve,[$cnf( $equal(and_star(not(and_star(xor(truth,X),Y)),Y),and_star(not(and_star(xor(truth,Y),X)),X)) )],[refute_0_71,refute_0_80]) ).

cnf(refute_0_82,plain,
    not(X_9) = xor(truth,not(not(X_9))),
    inference(subst,[],[refute_0_43:[bind(X_6,$fot(not(X_9)))]]) ).

cnf(refute_0_83,plain,
    X_9 = not(not(X_9)),
    inference(subst,[],[refute_0_54:[bind(X_6,$fot(X_9))]]) ).

cnf(refute_0_84,plain,
    ( X_9 != not(not(X_9))
    | not(not(X_9)) = X_9 ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(X_9)),bind(Y0,$fot(not(not(X_9))))]]) ).

cnf(refute_0_85,plain,
    not(not(X_9)) = X_9,
    inference(resolve,[$cnf( $equal(X_9,not(not(X_9))) )],[refute_0_83,refute_0_84]) ).

cnf(refute_0_86,plain,
    ( not(X_9) != xor(truth,not(not(X_9)))
    | not(not(X_9)) != X_9
    | not(X_9) = xor(truth,X_9) ),
    introduced(tautology,[equality,[$cnf( $equal(not(X_9),xor(truth,not(not(X_9)))) ),[1,1],$fot(X_9)]]) ).

cnf(refute_0_87,plain,
    ( not(X_9) != xor(truth,not(not(X_9)))
    | not(X_9) = xor(truth,X_9) ),
    inference(resolve,[$cnf( $equal(not(not(X_9)),X_9) )],[refute_0_85,refute_0_86]) ).

cnf(refute_0_88,plain,
    not(X_9) = xor(truth,X_9),
    inference(resolve,[$cnf( $equal(not(X_9),xor(truth,not(not(X_9)))) )],[refute_0_82,refute_0_87]) ).

cnf(refute_0_89,plain,
    ( not(X_9) != xor(truth,X_9)
    | xor(truth,X_9) = not(X_9) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(not(X_9))),bind(Y0,$fot(xor(truth,X_9)))]]) ).

cnf(refute_0_90,plain,
    xor(truth,X_9) = not(X_9),
    inference(resolve,[$cnf( $equal(not(X_9),xor(truth,X_9)) )],[refute_0_88,refute_0_89]) ).

cnf(refute_0_91,plain,
    xor(truth,X) = not(X),
    inference(subst,[],[refute_0_90:[bind(X_9,$fot(X))]]) ).

cnf(refute_0_92,plain,
    and_star(xor(truth,X),Y) = and_star(xor(truth,X),Y),
    introduced(tautology,[refl,[$fot(and_star(xor(truth,X),Y))]]) ).

cnf(refute_0_93,plain,
    ( and_star(xor(truth,X),Y) != and_star(xor(truth,X),Y)
    | xor(truth,X) != not(X)
    | and_star(xor(truth,X),Y) = and_star(not(X),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(and_star(xor(truth,X),Y),and_star(xor(truth,X),Y)) ),[1,0],$fot(not(X))]]) ).

cnf(refute_0_94,plain,
    ( xor(truth,X) != not(X)
    | and_star(xor(truth,X),Y) = and_star(not(X),Y) ),
    inference(resolve,[$cnf( $equal(and_star(xor(truth,X),Y),and_star(xor(truth,X),Y)) )],[refute_0_92,refute_0_93]) ).

cnf(refute_0_95,plain,
    and_star(xor(truth,X),Y) = and_star(not(X),Y),
    inference(resolve,[$cnf( $equal(xor(truth,X),not(X)) )],[refute_0_91,refute_0_94]) ).

cnf(refute_0_96,plain,
    not(and_star(xor(truth,X),Y)) = not(and_star(xor(truth,X),Y)),
    introduced(tautology,[refl,[$fot(not(and_star(xor(truth,X),Y)))]]) ).

cnf(refute_0_97,plain,
    ( and_star(xor(truth,X),Y) != and_star(not(X),Y)
    | not(and_star(xor(truth,X),Y)) != not(and_star(xor(truth,X),Y))
    | not(and_star(xor(truth,X),Y)) = not(and_star(not(X),Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(not(and_star(xor(truth,X),Y)),not(and_star(xor(truth,X),Y))) ),[1,0],$fot(and_star(not(X),Y))]]) ).

cnf(refute_0_98,plain,
    ( and_star(xor(truth,X),Y) != and_star(not(X),Y)
    | not(and_star(xor(truth,X),Y)) = not(and_star(not(X),Y)) ),
    inference(resolve,[$cnf( $equal(not(and_star(xor(truth,X),Y)),not(and_star(xor(truth,X),Y))) )],[refute_0_96,refute_0_97]) ).

cnf(refute_0_99,plain,
    not(and_star(xor(truth,X),Y)) = not(and_star(not(X),Y)),
    inference(resolve,[$cnf( $equal(and_star(xor(truth,X),Y),and_star(not(X),Y)) )],[refute_0_95,refute_0_98]) ).

cnf(refute_0_100,plain,
    and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(Y,not(and_star(xor(truth,X),Y))),
    introduced(tautology,[refl,[$fot(and_star(Y,not(and_star(xor(truth,X),Y))))]]) ).

cnf(refute_0_101,plain,
    ( and_star(Y,not(and_star(xor(truth,X),Y))) != and_star(Y,not(and_star(xor(truth,X),Y)))
    | not(and_star(xor(truth,X),Y)) != not(and_star(not(X),Y))
    | and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(Y,not(and_star(not(X),Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(and_star(Y,not(and_star(xor(truth,X),Y))),and_star(Y,not(and_star(xor(truth,X),Y)))) ),[1,1],$fot(not(and_star(not(X),Y)))]]) ).

cnf(refute_0_102,plain,
    ( not(and_star(xor(truth,X),Y)) != not(and_star(not(X),Y))
    | and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(Y,not(and_star(not(X),Y))) ),
    inference(resolve,[$cnf( $equal(and_star(Y,not(and_star(xor(truth,X),Y))),and_star(Y,not(and_star(xor(truth,X),Y)))) )],[refute_0_100,refute_0_101]) ).

cnf(refute_0_103,plain,
    and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(Y,not(and_star(not(X),Y))),
    inference(resolve,[$cnf( $equal(not(and_star(xor(truth,X),Y)),not(and_star(not(X),Y))) )],[refute_0_99,refute_0_102]) ).

cnf(refute_0_104,plain,
    ( and_star(Y,not(and_star(xor(truth,X),Y))) != and_star(X,not(and_star(xor(truth,Y),X)))
    | and_star(Y,not(and_star(xor(truth,X),Y))) != and_star(Y,not(and_star(not(X),Y)))
    | and_star(Y,not(and_star(not(X),Y))) = and_star(X,not(and_star(xor(truth,Y),X))) ),
    introduced(tautology,[equality,[$cnf( $equal(and_star(Y,not(and_star(xor(truth,X),Y))),and_star(X,not(and_star(xor(truth,Y),X)))) ),[0],$fot(and_star(Y,not(and_star(not(X),Y))))]]) ).

cnf(refute_0_105,plain,
    ( and_star(Y,not(and_star(xor(truth,X),Y))) != and_star(X,not(and_star(xor(truth,Y),X)))
    | and_star(Y,not(and_star(not(X),Y))) = and_star(X,not(and_star(xor(truth,Y),X))) ),
    inference(resolve,[$cnf( $equal(and_star(Y,not(and_star(xor(truth,X),Y))),and_star(Y,not(and_star(not(X),Y)))) )],[refute_0_103,refute_0_104]) ).

cnf(refute_0_106,plain,
    xor(truth,Y) = not(Y),
    inference(subst,[],[refute_0_90:[bind(X_9,$fot(Y))]]) ).

cnf(refute_0_107,plain,
    and_star(xor(truth,Y),X) = and_star(xor(truth,Y),X),
    introduced(tautology,[refl,[$fot(and_star(xor(truth,Y),X))]]) ).

cnf(refute_0_108,plain,
    ( and_star(xor(truth,Y),X) != and_star(xor(truth,Y),X)
    | xor(truth,Y) != not(Y)
    | and_star(xor(truth,Y),X) = and_star(not(Y),X) ),
    introduced(tautology,[equality,[$cnf( $equal(and_star(xor(truth,Y),X),and_star(xor(truth,Y),X)) ),[1,0],$fot(not(Y))]]) ).

cnf(refute_0_109,plain,
    ( xor(truth,Y) != not(Y)
    | and_star(xor(truth,Y),X) = and_star(not(Y),X) ),
    inference(resolve,[$cnf( $equal(and_star(xor(truth,Y),X),and_star(xor(truth,Y),X)) )],[refute_0_107,refute_0_108]) ).

cnf(refute_0_110,plain,
    and_star(xor(truth,Y),X) = and_star(not(Y),X),
    inference(resolve,[$cnf( $equal(xor(truth,Y),not(Y)) )],[refute_0_106,refute_0_109]) ).

cnf(refute_0_111,plain,
    not(and_star(xor(truth,Y),X)) = not(and_star(xor(truth,Y),X)),
    introduced(tautology,[refl,[$fot(not(and_star(xor(truth,Y),X)))]]) ).

cnf(refute_0_112,plain,
    ( and_star(xor(truth,Y),X) != and_star(not(Y),X)
    | not(and_star(xor(truth,Y),X)) != not(and_star(xor(truth,Y),X))
    | not(and_star(xor(truth,Y),X)) = not(and_star(not(Y),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(not(and_star(xor(truth,Y),X)),not(and_star(xor(truth,Y),X))) ),[1,0],$fot(and_star(not(Y),X))]]) ).

cnf(refute_0_113,plain,
    ( and_star(xor(truth,Y),X) != and_star(not(Y),X)
    | not(and_star(xor(truth,Y),X)) = not(and_star(not(Y),X)) ),
    inference(resolve,[$cnf( $equal(not(and_star(xor(truth,Y),X)),not(and_star(xor(truth,Y),X))) )],[refute_0_111,refute_0_112]) ).

cnf(refute_0_114,plain,
    not(and_star(xor(truth,Y),X)) = not(and_star(not(Y),X)),
    inference(resolve,[$cnf( $equal(and_star(xor(truth,Y),X),and_star(not(Y),X)) )],[refute_0_110,refute_0_113]) ).

cnf(refute_0_115,plain,
    and_star(X,not(and_star(xor(truth,Y),X))) = and_star(X,not(and_star(xor(truth,Y),X))),
    introduced(tautology,[refl,[$fot(and_star(X,not(and_star(xor(truth,Y),X))))]]) ).

cnf(refute_0_116,plain,
    ( and_star(X,not(and_star(xor(truth,Y),X))) != and_star(X,not(and_star(xor(truth,Y),X)))
    | not(and_star(xor(truth,Y),X)) != not(and_star(not(Y),X))
    | and_star(X,not(and_star(xor(truth,Y),X))) = and_star(X,not(and_star(not(Y),X))) ),
    introduced(tautology,[equality,[$cnf( $equal(and_star(X,not(and_star(xor(truth,Y),X))),and_star(X,not(and_star(xor(truth,Y),X)))) ),[1,1],$fot(not(and_star(not(Y),X)))]]) ).

cnf(refute_0_117,plain,
    ( not(and_star(xor(truth,Y),X)) != not(and_star(not(Y),X))
    | and_star(X,not(and_star(xor(truth,Y),X))) = and_star(X,not(and_star(not(Y),X))) ),
    inference(resolve,[$cnf( $equal(and_star(X,not(and_star(xor(truth,Y),X))),and_star(X,not(and_star(xor(truth,Y),X)))) )],[refute_0_115,refute_0_116]) ).

cnf(refute_0_118,plain,
    and_star(X,not(and_star(xor(truth,Y),X))) = and_star(X,not(and_star(not(Y),X))),
    inference(resolve,[$cnf( $equal(not(and_star(xor(truth,Y),X)),not(and_star(not(Y),X))) )],[refute_0_114,refute_0_117]) ).

cnf(refute_0_119,plain,
    ( and_star(X,not(and_star(xor(truth,Y),X))) != and_star(X,not(and_star(not(Y),X)))
    | and_star(Y,not(and_star(not(X),Y))) != and_star(X,not(and_star(xor(truth,Y),X)))
    | and_star(Y,not(and_star(not(X),Y))) = and_star(X,not(and_star(not(Y),X))) ),
    introduced(tautology,[equality,[$cnf( $equal(and_star(Y,not(and_star(not(X),Y))),and_star(X,not(and_star(xor(truth,Y),X)))) ),[1],$fot(and_star(X,not(and_star(not(Y),X))))]]) ).

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

cnf(refute_0_121,plain,
    ( and_star(Y,not(and_star(xor(truth,X),Y))) != and_star(X,not(and_star(xor(truth,Y),X)))
    | and_star(Y,not(and_star(not(X),Y))) = and_star(X,not(and_star(not(Y),X))) ),
    inference(resolve,[$cnf( $equal(and_star(Y,not(and_star(not(X),Y))),and_star(X,not(and_star(xor(truth,Y),X)))) )],[refute_0_105,refute_0_120]) ).

cnf(refute_0_122,plain,
    and_star(Y,not(and_star(not(X),Y))) = and_star(X,not(and_star(not(Y),X))),
    inference(resolve,[$cnf( $equal(and_star(Y,not(and_star(xor(truth,X),Y))),and_star(X,not(and_star(xor(truth,Y),X)))) )],[refute_0_81,refute_0_121]) ).

cnf(refute_0_123,plain,
    and_star(X_14,not(X_15)) = not(not(and_star(X_14,not(X_15)))),
    inference(subst,[],[refute_0_54:[bind(X_6,$fot(and_star(X_14,not(X_15))))]]) ).

cnf(refute_0_124,plain,
    and_star(X,xor(truth,Y)) = and_star(X,xor(truth,Y)),
    introduced(tautology,[refl,[$fot(and_star(X,xor(truth,Y)))]]) ).

cnf(refute_0_125,plain,
    ( and_star(X,xor(truth,Y)) != and_star(X,xor(truth,Y))
    | xor(truth,Y) != not(Y)
    | and_star(X,xor(truth,Y)) = and_star(X,not(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(and_star(X,xor(truth,Y)),and_star(X,xor(truth,Y))) ),[1,1],$fot(not(Y))]]) ).

cnf(refute_0_126,plain,
    ( xor(truth,Y) != not(Y)
    | and_star(X,xor(truth,Y)) = and_star(X,not(Y)) ),
    inference(resolve,[$cnf( $equal(and_star(X,xor(truth,Y)),and_star(X,xor(truth,Y))) )],[refute_0_124,refute_0_125]) ).

cnf(refute_0_127,plain,
    and_star(X,xor(truth,Y)) = and_star(X,not(Y)),
    inference(resolve,[$cnf( $equal(xor(truth,Y),not(Y)) )],[refute_0_106,refute_0_126]) ).

cnf(refute_0_128,plain,
    not(and_star(X,xor(truth,Y))) = not(and_star(X,xor(truth,Y))),
    introduced(tautology,[refl,[$fot(not(and_star(X,xor(truth,Y))))]]) ).

cnf(refute_0_129,plain,
    ( and_star(X,xor(truth,Y)) != and_star(X,not(Y))
    | not(and_star(X,xor(truth,Y))) != not(and_star(X,xor(truth,Y)))
    | not(and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(not(and_star(X,xor(truth,Y))),not(and_star(X,xor(truth,Y)))) ),[1,0],$fot(and_star(X,not(Y)))]]) ).

cnf(refute_0_130,plain,
    ( and_star(X,xor(truth,Y)) != and_star(X,not(Y))
    | not(and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))) ),
    inference(resolve,[$cnf( $equal(not(and_star(X,xor(truth,Y))),not(and_star(X,xor(truth,Y)))) )],[refute_0_128,refute_0_129]) ).

cnf(refute_0_131,plain,
    not(and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))),
    inference(resolve,[$cnf( $equal(and_star(X,xor(truth,Y)),and_star(X,not(Y))) )],[refute_0_127,refute_0_130]) ).

cnf(refute_0_132,plain,
    xor(truth,and_star(X,xor(truth,Y))) = not(and_star(X,xor(truth,Y))),
    inference(subst,[],[refute_0_90:[bind(X_9,$fot(and_star(X,xor(truth,Y))))]]) ).

cnf(refute_0_133,plain,
    ( not(and_star(X,xor(truth,Y))) != not(and_star(X,not(Y)))
    | xor(truth,and_star(X,xor(truth,Y))) != not(and_star(X,xor(truth,Y)))
    | xor(truth,and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))) ),
    inference(subst,[],[refute_0_31:[bind(X0,$fot(xor(truth,and_star(X,xor(truth,Y))))),bind(Y0,$fot(not(and_star(X,xor(truth,Y))))),bind(Z,$fot(not(and_star(X,not(Y)))))]]) ).

cnf(refute_0_134,plain,
    ( not(and_star(X,xor(truth,Y))) != not(and_star(X,not(Y)))
    | xor(truth,and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))) ),
    inference(resolve,[$cnf( $equal(xor(truth,and_star(X,xor(truth,Y))),not(and_star(X,xor(truth,Y)))) )],[refute_0_132,refute_0_133]) ).

cnf(refute_0_135,plain,
    xor(truth,and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))),
    inference(resolve,[$cnf( $equal(not(and_star(X,xor(truth,Y))),not(and_star(X,not(Y)))) )],[refute_0_131,refute_0_134]) ).

cnf(refute_0_136,plain,
    ( implies(X,Y) != xor(truth,and_star(X,xor(truth,Y)))
    | xor(truth,and_star(X,xor(truth,Y))) != not(and_star(X,not(Y)))
    | implies(X,Y) = not(and_star(X,not(Y))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,Y),not(and_star(X,not(Y)))) ),[0],$fot(xor(truth,and_star(X,xor(truth,Y))))]]) ).

cnf(refute_0_137,plain,
    ( implies(X,Y) != xor(truth,and_star(X,xor(truth,Y)))
    | implies(X,Y) = not(and_star(X,not(Y))) ),
    inference(resolve,[$cnf( $equal(xor(truth,and_star(X,xor(truth,Y))),not(and_star(X,not(Y)))) )],[refute_0_135,refute_0_136]) ).

cnf(refute_0_138,plain,
    implies(X,Y) = not(and_star(X,not(Y))),
    inference(resolve,[$cnf( $equal(implies(X,Y),xor(truth,and_star(X,xor(truth,Y)))) )],[implies_definition,refute_0_137]) ).

cnf(refute_0_139,plain,
    implies(X_14,X_15) = not(and_star(X_14,not(X_15))),
    inference(subst,[],[refute_0_138:[bind(X,$fot(X_14)),bind(Y,$fot(X_15))]]) ).

cnf(refute_0_140,plain,
    ( implies(X_14,X_15) != not(and_star(X_14,not(X_15)))
    | not(and_star(X_14,not(X_15))) = implies(X_14,X_15) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_14,X_15))),bind(Y0,$fot(not(and_star(X_14,not(X_15)))))]]) ).

cnf(refute_0_141,plain,
    not(and_star(X_14,not(X_15))) = implies(X_14,X_15),
    inference(resolve,[$cnf( $equal(implies(X_14,X_15),not(and_star(X_14,not(X_15)))) )],[refute_0_139,refute_0_140]) ).

cnf(refute_0_142,plain,
    ( and_star(X_14,not(X_15)) != not(not(and_star(X_14,not(X_15))))
    | not(and_star(X_14,not(X_15))) != implies(X_14,X_15)
    | and_star(X_14,not(X_15)) = not(implies(X_14,X_15)) ),
    introduced(tautology,[equality,[$cnf( $equal(and_star(X_14,not(X_15)),not(not(and_star(X_14,not(X_15))))) ),[1,0],$fot(implies(X_14,X_15))]]) ).

cnf(refute_0_143,plain,
    ( and_star(X_14,not(X_15)) != not(not(and_star(X_14,not(X_15))))
    | and_star(X_14,not(X_15)) = not(implies(X_14,X_15)) ),
    inference(resolve,[$cnf( $equal(not(and_star(X_14,not(X_15))),implies(X_14,X_15)) )],[refute_0_141,refute_0_142]) ).

cnf(refute_0_144,plain,
    and_star(X_14,not(X_15)) = not(implies(X_14,X_15)),
    inference(resolve,[$cnf( $equal(and_star(X_14,not(X_15)),not(not(and_star(X_14,not(X_15))))) )],[refute_0_123,refute_0_143]) ).

cnf(refute_0_145,plain,
    and_star(Y,not(and_star(not(X),Y))) = not(implies(Y,and_star(not(X),Y))),
    inference(subst,[],[refute_0_144:[bind(X_14,$fot(Y)),bind(X_15,$fot(and_star(not(X),Y)))]]) ).

cnf(refute_0_146,plain,
    ( and_star(Y,not(and_star(not(X),Y))) != and_star(X,not(and_star(not(Y),X)))
    | and_star(Y,not(and_star(not(X),Y))) != not(implies(Y,and_star(not(X),Y)))
    | not(implies(Y,and_star(not(X),Y))) = and_star(X,not(and_star(not(Y),X))) ),
    introduced(tautology,[equality,[$cnf( $equal(and_star(Y,not(and_star(not(X),Y))),and_star(X,not(and_star(not(Y),X)))) ),[0],$fot(not(implies(Y,and_star(not(X),Y))))]]) ).

cnf(refute_0_147,plain,
    ( and_star(Y,not(and_star(not(X),Y))) != and_star(X,not(and_star(not(Y),X)))
    | not(implies(Y,and_star(not(X),Y))) = and_star(X,not(and_star(not(Y),X))) ),
    inference(resolve,[$cnf( $equal(and_star(Y,not(and_star(not(X),Y))),not(implies(Y,and_star(not(X),Y)))) )],[refute_0_145,refute_0_146]) ).

cnf(refute_0_148,plain,
    and_star(X,not(and_star(not(Y),X))) = not(implies(X,and_star(not(Y),X))),
    inference(subst,[],[refute_0_144:[bind(X_14,$fot(X)),bind(X_15,$fot(and_star(not(Y),X)))]]) ).

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

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

cnf(refute_0_151,plain,
    ( and_star(Y,not(and_star(not(X),Y))) != and_star(X,not(and_star(not(Y),X)))
    | not(implies(Y,and_star(not(X),Y))) = not(implies(X,and_star(not(Y),X))) ),
    inference(resolve,[$cnf( $equal(not(implies(Y,and_star(not(X),Y))),and_star(X,not(and_star(not(Y),X)))) )],[refute_0_147,refute_0_150]) ).

cnf(refute_0_152,plain,
    not(implies(Y,and_star(not(X),Y))) = not(implies(X,and_star(not(Y),X))),
    inference(resolve,[$cnf( $equal(and_star(Y,not(and_star(not(X),Y))),and_star(X,not(and_star(not(Y),X)))) )],[refute_0_122,refute_0_151]) ).

cnf(refute_0_153,plain,
    not(implies(X_26,and_star(not(X_25),X_26))) = not(implies(X_25,and_star(not(X_26),X_25))),
    inference(subst,[],[refute_0_152:[bind(X,$fot(X_25)),bind(Y,$fot(X_26))]]) ).

cnf(refute_0_154,plain,
    ( implies(X_26,and_star(not(X_25),X_26)) != not(not(implies(X_26,and_star(not(X_25),X_26))))
    | not(implies(X_26,and_star(not(X_25),X_26))) != not(implies(X_25,and_star(not(X_26),X_25)))
    | implies(X_26,and_star(not(X_25),X_26)) = not(not(implies(X_25,and_star(not(X_26),X_25)))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(X_26,and_star(not(X_25),X_26)),not(not(implies(X_26,and_star(not(X_25),X_26))))) ),[1,0],$fot(not(implies(X_25,and_star(not(X_26),X_25))))]]) ).

cnf(refute_0_155,plain,
    ( implies(X_26,and_star(not(X_25),X_26)) != not(not(implies(X_26,and_star(not(X_25),X_26))))
    | implies(X_26,and_star(not(X_25),X_26)) = not(not(implies(X_25,and_star(not(X_26),X_25)))) ),
    inference(resolve,[$cnf( $equal(not(implies(X_26,and_star(not(X_25),X_26))),not(implies(X_25,and_star(not(X_26),X_25)))) )],[refute_0_153,refute_0_154]) ).

cnf(refute_0_156,plain,
    implies(X_26,and_star(not(X_25),X_26)) = not(not(implies(X_25,and_star(not(X_26),X_25)))),
    inference(resolve,[$cnf( $equal(implies(X_26,and_star(not(X_25),X_26)),not(not(implies(X_26,and_star(not(X_25),X_26))))) )],[refute_0_55,refute_0_155]) ).

cnf(refute_0_157,plain,
    ( X_6 != not(not(X_6))
    | not(not(X_6)) = X_6 ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(X_6)),bind(Y0,$fot(not(not(X_6))))]]) ).

cnf(refute_0_158,plain,
    not(not(X_6)) = X_6,
    inference(resolve,[$cnf( $equal(X_6,not(not(X_6))) )],[refute_0_54,refute_0_157]) ).

cnf(refute_0_159,plain,
    not(not(implies(X_25,and_star(not(X_26),X_25)))) = implies(X_25,and_star(not(X_26),X_25)),
    inference(subst,[],[refute_0_158:[bind(X_6,$fot(implies(X_25,and_star(not(X_26),X_25))))]]) ).

cnf(refute_0_160,plain,
    ( implies(X_26,and_star(not(X_25),X_26)) != not(not(implies(X_25,and_star(not(X_26),X_25))))
    | not(not(implies(X_25,and_star(not(X_26),X_25)))) != implies(X_25,and_star(not(X_26),X_25))
    | implies(X_26,and_star(not(X_25),X_26)) = implies(X_25,and_star(not(X_26),X_25)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_26,and_star(not(X_25),X_26)),implies(X_25,and_star(not(X_26),X_25))) ),[0],$fot(not(not(implies(X_25,and_star(not(X_26),X_25)))))]]) ).

cnf(refute_0_161,plain,
    ( implies(X_26,and_star(not(X_25),X_26)) != not(not(implies(X_25,and_star(not(X_26),X_25))))
    | implies(X_26,and_star(not(X_25),X_26)) = implies(X_25,and_star(not(X_26),X_25)) ),
    inference(resolve,[$cnf( $equal(not(not(implies(X_25,and_star(not(X_26),X_25)))),implies(X_25,and_star(not(X_26),X_25))) )],[refute_0_159,refute_0_160]) ).

cnf(refute_0_162,plain,
    implies(X_26,and_star(not(X_25),X_26)) = implies(X_25,and_star(not(X_26),X_25)),
    inference(resolve,[$cnf( $equal(implies(X_26,and_star(not(X_25),X_26)),not(not(implies(X_25,and_star(not(X_26),X_25))))) )],[refute_0_156,refute_0_161]) ).

cnf(refute_0_163,plain,
    implies(X_26,and_star(not(not(X_38)),X_26)) = implies(not(X_38),and_star(not(X_26),not(X_38))),
    inference(subst,[],[refute_0_162:[bind(X_25,$fot(not(X_38)))]]) ).

cnf(refute_0_164,plain,
    and_star(not(X_26),not(X_38)) = not(implies(not(X_26),X_38)),
    inference(subst,[],[refute_0_144:[bind(X_14,$fot(not(X_26))),bind(X_15,$fot(X_38))]]) ).

cnf(refute_0_165,plain,
    ( and_star(not(X_26),not(X_38)) != not(implies(not(X_26),X_38))
    | implies(X_26,and_star(not(not(X_38)),X_26)) != implies(not(X_38),and_star(not(X_26),not(X_38)))
    | implies(X_26,and_star(not(not(X_38)),X_26)) = implies(not(X_38),not(implies(not(X_26),X_38))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(X_26,and_star(not(not(X_38)),X_26)),implies(not(X_38),and_star(not(X_26),not(X_38)))) ),[1,1],$fot(not(implies(not(X_26),X_38)))]]) ).

cnf(refute_0_166,plain,
    ( implies(X_26,and_star(not(not(X_38)),X_26)) != implies(not(X_38),and_star(not(X_26),not(X_38)))
    | implies(X_26,and_star(not(not(X_38)),X_26)) = implies(not(X_38),not(implies(not(X_26),X_38))) ),
    inference(resolve,[$cnf( $equal(and_star(not(X_26),not(X_38)),not(implies(not(X_26),X_38))) )],[refute_0_164,refute_0_165]) ).

cnf(refute_0_167,plain,
    implies(X_26,and_star(not(not(X_38)),X_26)) = implies(not(X_38),not(implies(not(X_26),X_38))),
    inference(resolve,[$cnf( $equal(implies(X_26,and_star(not(not(X_38)),X_26)),implies(not(X_38),and_star(not(X_26),not(X_38)))) )],[refute_0_163,refute_0_166]) ).

cnf(refute_0_168,plain,
    not(not(X_38)) = X_38,
    inference(subst,[],[refute_0_158:[bind(X_6,$fot(X_38))]]) ).

cnf(refute_0_169,plain,
    and_star(not(not(X_38)),X_26) = and_star(not(not(X_38)),X_26),
    introduced(tautology,[refl,[$fot(and_star(not(not(X_38)),X_26))]]) ).

cnf(refute_0_170,plain,
    ( and_star(not(not(X_38)),X_26) != and_star(not(not(X_38)),X_26)
    | not(not(X_38)) != X_38
    | and_star(not(not(X_38)),X_26) = and_star(X_38,X_26) ),
    introduced(tautology,[equality,[$cnf( $equal(and_star(not(not(X_38)),X_26),and_star(not(not(X_38)),X_26)) ),[1,0],$fot(X_38)]]) ).

cnf(refute_0_171,plain,
    ( not(not(X_38)) != X_38
    | and_star(not(not(X_38)),X_26) = and_star(X_38,X_26) ),
    inference(resolve,[$cnf( $equal(and_star(not(not(X_38)),X_26),and_star(not(not(X_38)),X_26)) )],[refute_0_169,refute_0_170]) ).

cnf(refute_0_172,plain,
    and_star(not(not(X_38)),X_26) = and_star(X_38,X_26),
    inference(resolve,[$cnf( $equal(not(not(X_38)),X_38) )],[refute_0_168,refute_0_171]) ).

cnf(refute_0_173,plain,
    implies(X_26,and_star(not(not(X_38)),X_26)) = implies(X_26,and_star(not(not(X_38)),X_26)),
    introduced(tautology,[refl,[$fot(implies(X_26,and_star(not(not(X_38)),X_26)))]]) ).

cnf(refute_0_174,plain,
    ( and_star(not(not(X_38)),X_26) != and_star(X_38,X_26)
    | implies(X_26,and_star(not(not(X_38)),X_26)) != implies(X_26,and_star(not(not(X_38)),X_26))
    | implies(X_26,and_star(not(not(X_38)),X_26)) = implies(X_26,and_star(X_38,X_26)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(X_26,and_star(not(not(X_38)),X_26)),implies(X_26,and_star(not(not(X_38)),X_26))) ),[1,1],$fot(and_star(X_38,X_26))]]) ).

cnf(refute_0_175,plain,
    ( and_star(not(not(X_38)),X_26) != and_star(X_38,X_26)
    | implies(X_26,and_star(not(not(X_38)),X_26)) = implies(X_26,and_star(X_38,X_26)) ),
    inference(resolve,[$cnf( $equal(implies(X_26,and_star(not(not(X_38)),X_26)),implies(X_26,and_star(not(not(X_38)),X_26))) )],[refute_0_173,refute_0_174]) ).

cnf(refute_0_176,plain,
    implies(X_26,and_star(not(not(X_38)),X_26)) = implies(X_26,and_star(X_38,X_26)),
    inference(resolve,[$cnf( $equal(and_star(not(not(X_38)),X_26),and_star(X_38,X_26)) )],[refute_0_172,refute_0_175]) ).

cnf(refute_0_177,plain,
    ( implies(X_26,and_star(not(not(X_38)),X_26)) != implies(X_26,and_star(X_38,X_26))
    | implies(X_26,and_star(not(not(X_38)),X_26)) != implies(not(X_38),not(implies(not(X_26),X_38)))
    | implies(X_26,and_star(X_38,X_26)) = implies(not(X_38),not(implies(not(X_26),X_38))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(X_26,and_star(not(not(X_38)),X_26)),implies(not(X_38),not(implies(not(X_26),X_38)))) ),[0],$fot(implies(X_26,and_star(X_38,X_26)))]]) ).

cnf(refute_0_178,plain,
    ( implies(X_26,and_star(not(not(X_38)),X_26)) != implies(not(X_38),not(implies(not(X_26),X_38)))
    | implies(X_26,and_star(X_38,X_26)) = implies(not(X_38),not(implies(not(X_26),X_38))) ),
    inference(resolve,[$cnf( $equal(implies(X_26,and_star(not(not(X_38)),X_26)),implies(X_26,and_star(X_38,X_26))) )],[refute_0_176,refute_0_177]) ).

cnf(refute_0_179,plain,
    implies(X_14,not(X_6)) = not(and_star(X_14,not(not(X_6)))),
    inference(subst,[],[refute_0_138:[bind(X,$fot(X_14)),bind(Y,$fot(not(X_6)))]]) ).

cnf(refute_0_180,plain,
    ( implies(X_14,not(X_6)) != not(and_star(X_14,not(not(X_6))))
    | not(not(X_6)) != X_6
    | implies(X_14,not(X_6)) = not(and_star(X_14,X_6)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(X_14,not(X_6)),not(and_star(X_14,not(not(X_6))))) ),[1,0,1],$fot(X_6)]]) ).

cnf(refute_0_181,plain,
    ( implies(X_14,not(X_6)) != not(and_star(X_14,not(not(X_6))))
    | implies(X_14,not(X_6)) = not(and_star(X_14,X_6)) ),
    inference(resolve,[$cnf( $equal(not(not(X_6)),X_6) )],[refute_0_158,refute_0_180]) ).

cnf(refute_0_182,plain,
    implies(X_14,not(X_6)) = not(and_star(X_14,X_6)),
    inference(resolve,[$cnf( $equal(implies(X_14,not(X_6)),not(and_star(X_14,not(not(X_6))))) )],[refute_0_179,refute_0_181]) ).

cnf(refute_0_183,plain,
    implies(not(X_38),not(implies(not(X_26),X_38))) = not(and_star(not(X_38),implies(not(X_26),X_38))),
    inference(subst,[],[refute_0_182:[bind(X_14,$fot(not(X_38))),bind(X_6,$fot(implies(not(X_26),X_38)))]]) ).

cnf(refute_0_184,plain,
    ( implies(X_26,and_star(X_38,X_26)) != implies(not(X_38),not(implies(not(X_26),X_38)))
    | implies(not(X_38),not(implies(not(X_26),X_38))) != not(and_star(not(X_38),implies(not(X_26),X_38)))
    | implies(X_26,and_star(X_38,X_26)) = not(and_star(not(X_38),implies(not(X_26),X_38))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_26,and_star(X_38,X_26)),not(and_star(not(X_38),implies(not(X_26),X_38)))) ),[0],$fot(implies(not(X_38),not(implies(not(X_26),X_38))))]]) ).

cnf(refute_0_185,plain,
    ( implies(X_26,and_star(X_38,X_26)) != implies(not(X_38),not(implies(not(X_26),X_38)))
    | implies(X_26,and_star(X_38,X_26)) = not(and_star(not(X_38),implies(not(X_26),X_38))) ),
    inference(resolve,[$cnf( $equal(implies(not(X_38),not(implies(not(X_26),X_38))),not(and_star(not(X_38),implies(not(X_26),X_38)))) )],[refute_0_183,refute_0_184]) ).

cnf(refute_0_186,plain,
    ( implies(X_26,and_star(not(not(X_38)),X_26)) != implies(not(X_38),not(implies(not(X_26),X_38)))
    | implies(X_26,and_star(X_38,X_26)) = not(and_star(not(X_38),implies(not(X_26),X_38))) ),
    inference(resolve,[$cnf( $equal(implies(X_26,and_star(X_38,X_26)),implies(not(X_38),not(implies(not(X_26),X_38)))) )],[refute_0_178,refute_0_185]) ).

cnf(refute_0_187,plain,
    implies(X_26,and_star(X_38,X_26)) = not(and_star(not(X_38),implies(not(X_26),X_38))),
    inference(resolve,[$cnf( $equal(implies(X_26,and_star(not(not(X_38)),X_26)),implies(not(X_38),not(implies(not(X_26),X_38)))) )],[refute_0_167,refute_0_186]) ).

cnf(refute_0_188,plain,
    not(not(implies(implies(not(X_26),X_38),X_38))) = implies(implies(not(X_26),X_38),X_38),
    inference(subst,[],[refute_0_158:[bind(X_6,$fot(implies(implies(not(X_26),X_38),X_38)))]]) ).

cnf(refute_0_189,plain,
    and_star(not(X_38),Y) = and_star(Y,not(X_38)),
    inference(subst,[],[and_star_commutativity:[bind(X,$fot(not(X_38)))]]) ).

cnf(refute_0_190,plain,
    and_star(Y,not(X_38)) = not(implies(Y,X_38)),
    inference(subst,[],[refute_0_144:[bind(X_14,$fot(Y)),bind(X_15,$fot(X_38))]]) ).

cnf(refute_0_191,plain,
    ( and_star(Y,not(X_38)) != not(implies(Y,X_38))
    | and_star(not(X_38),Y) != and_star(Y,not(X_38))
    | and_star(not(X_38),Y) = not(implies(Y,X_38)) ),
    introduced(tautology,[equality,[$cnf( $equal(and_star(not(X_38),Y),and_star(Y,not(X_38))) ),[1],$fot(not(implies(Y,X_38)))]]) ).

cnf(refute_0_192,plain,
    ( and_star(not(X_38),Y) != and_star(Y,not(X_38))
    | and_star(not(X_38),Y) = not(implies(Y,X_38)) ),
    inference(resolve,[$cnf( $equal(and_star(Y,not(X_38)),not(implies(Y,X_38))) )],[refute_0_190,refute_0_191]) ).

cnf(refute_0_193,plain,
    and_star(not(X_38),Y) = not(implies(Y,X_38)),
    inference(resolve,[$cnf( $equal(and_star(not(X_38),Y),and_star(Y,not(X_38))) )],[refute_0_189,refute_0_192]) ).

cnf(refute_0_194,plain,
    and_star(not(X_38),implies(not(X_26),X_38)) = not(implies(implies(not(X_26),X_38),X_38)),
    inference(subst,[],[refute_0_193:[bind(Y,$fot(implies(not(X_26),X_38)))]]) ).

cnf(refute_0_195,plain,
    not(and_star(not(X_38),implies(not(X_26),X_38))) = not(and_star(not(X_38),implies(not(X_26),X_38))),
    introduced(tautology,[refl,[$fot(not(and_star(not(X_38),implies(not(X_26),X_38))))]]) ).

cnf(refute_0_196,plain,
    ( and_star(not(X_38),implies(not(X_26),X_38)) != not(implies(implies(not(X_26),X_38),X_38))
    | not(and_star(not(X_38),implies(not(X_26),X_38))) != not(and_star(not(X_38),implies(not(X_26),X_38)))
    | not(and_star(not(X_38),implies(not(X_26),X_38))) = not(not(implies(implies(not(X_26),X_38),X_38))) ),
    introduced(tautology,[equality,[$cnf( $equal(not(and_star(not(X_38),implies(not(X_26),X_38))),not(and_star(not(X_38),implies(not(X_26),X_38)))) ),[1,0],$fot(not(implies(implies(not(X_26),X_38),X_38)))]]) ).

cnf(refute_0_197,plain,
    ( and_star(not(X_38),implies(not(X_26),X_38)) != not(implies(implies(not(X_26),X_38),X_38))
    | not(and_star(not(X_38),implies(not(X_26),X_38))) = not(not(implies(implies(not(X_26),X_38),X_38))) ),
    inference(resolve,[$cnf( $equal(not(and_star(not(X_38),implies(not(X_26),X_38))),not(and_star(not(X_38),implies(not(X_26),X_38)))) )],[refute_0_195,refute_0_196]) ).

cnf(refute_0_198,plain,
    not(and_star(not(X_38),implies(not(X_26),X_38))) = not(not(implies(implies(not(X_26),X_38),X_38))),
    inference(resolve,[$cnf( $equal(and_star(not(X_38),implies(not(X_26),X_38)),not(implies(implies(not(X_26),X_38),X_38))) )],[refute_0_194,refute_0_197]) ).

cnf(refute_0_199,plain,
    ( not(and_star(not(X_38),implies(not(X_26),X_38))) != not(not(implies(implies(not(X_26),X_38),X_38)))
    | not(not(implies(implies(not(X_26),X_38),X_38))) != implies(implies(not(X_26),X_38),X_38)
    | not(and_star(not(X_38),implies(not(X_26),X_38))) = implies(implies(not(X_26),X_38),X_38) ),
    inference(subst,[],[refute_0_31:[bind(X0,$fot(not(and_star(not(X_38),implies(not(X_26),X_38))))),bind(Y0,$fot(not(not(implies(implies(not(X_26),X_38),X_38))))),bind(Z,$fot(implies(implies(not(X_26),X_38),X_38)))]]) ).

cnf(refute_0_200,plain,
    ( not(not(implies(implies(not(X_26),X_38),X_38))) != implies(implies(not(X_26),X_38),X_38)
    | not(and_star(not(X_38),implies(not(X_26),X_38))) = implies(implies(not(X_26),X_38),X_38) ),
    inference(resolve,[$cnf( $equal(not(and_star(not(X_38),implies(not(X_26),X_38))),not(not(implies(implies(not(X_26),X_38),X_38)))) )],[refute_0_198,refute_0_199]) ).

cnf(refute_0_201,plain,
    not(and_star(not(X_38),implies(not(X_26),X_38))) = implies(implies(not(X_26),X_38),X_38),
    inference(resolve,[$cnf( $equal(not(not(implies(implies(not(X_26),X_38),X_38))),implies(implies(not(X_26),X_38),X_38)) )],[refute_0_188,refute_0_200]) ).

cnf(refute_0_202,plain,
    ( implies(X_26,and_star(X_38,X_26)) != not(and_star(not(X_38),implies(not(X_26),X_38)))
    | not(and_star(not(X_38),implies(not(X_26),X_38))) != implies(implies(not(X_26),X_38),X_38)
    | implies(X_26,and_star(X_38,X_26)) = implies(implies(not(X_26),X_38),X_38) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_26,and_star(X_38,X_26)),implies(implies(not(X_26),X_38),X_38)) ),[0],$fot(not(and_star(not(X_38),implies(not(X_26),X_38))))]]) ).

cnf(refute_0_203,plain,
    ( implies(X_26,and_star(X_38,X_26)) != not(and_star(not(X_38),implies(not(X_26),X_38)))
    | implies(X_26,and_star(X_38,X_26)) = implies(implies(not(X_26),X_38),X_38) ),
    inference(resolve,[$cnf( $equal(not(and_star(not(X_38),implies(not(X_26),X_38))),implies(implies(not(X_26),X_38),X_38)) )],[refute_0_201,refute_0_202]) ).

cnf(refute_0_204,plain,
    implies(X_26,and_star(X_38,X_26)) = implies(implies(not(X_26),X_38),X_38),
    inference(resolve,[$cnf( $equal(implies(X_26,and_star(X_38,X_26)),not(and_star(not(X_38),implies(not(X_26),X_38)))) )],[refute_0_187,refute_0_203]) ).

cnf(refute_0_205,plain,
    implies(not(X_15),and_star(X_53,not(X_15))) = implies(implies(not(not(X_15)),X_53),X_53),
    inference(subst,[],[refute_0_204:[bind(X_26,$fot(not(X_15))),bind(X_38,$fot(X_53))]]) ).

cnf(refute_0_206,plain,
    and_star(X_53,not(X_15)) = not(implies(X_53,X_15)),
    inference(subst,[],[refute_0_144:[bind(X_14,$fot(X_53))]]) ).

cnf(refute_0_207,plain,
    ( and_star(X_53,not(X_15)) != not(implies(X_53,X_15))
    | implies(not(X_15),and_star(X_53,not(X_15))) != implies(implies(not(not(X_15)),X_53),X_53)
    | implies(not(X_15),not(implies(X_53,X_15))) = implies(implies(not(not(X_15)),X_53),X_53) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(X_15),and_star(X_53,not(X_15))),implies(implies(not(not(X_15)),X_53),X_53)) ),[0,1],$fot(not(implies(X_53,X_15)))]]) ).

cnf(refute_0_208,plain,
    ( implies(not(X_15),and_star(X_53,not(X_15))) != implies(implies(not(not(X_15)),X_53),X_53)
    | implies(not(X_15),not(implies(X_53,X_15))) = implies(implies(not(not(X_15)),X_53),X_53) ),
    inference(resolve,[$cnf( $equal(and_star(X_53,not(X_15)),not(implies(X_53,X_15))) )],[refute_0_206,refute_0_207]) ).

cnf(refute_0_209,plain,
    implies(not(X_15),not(implies(X_53,X_15))) = implies(implies(not(not(X_15)),X_53),X_53),
    inference(resolve,[$cnf( $equal(implies(not(X_15),and_star(X_53,not(X_15))),implies(implies(not(not(X_15)),X_53),X_53)) )],[refute_0_205,refute_0_208]) ).

cnf(refute_0_210,plain,
    not(not(implies(implies(X_53,X_15),X_15))) = implies(implies(X_53,X_15),X_15),
    inference(subst,[],[refute_0_158:[bind(X_6,$fot(implies(implies(X_53,X_15),X_15)))]]) ).

cnf(refute_0_211,plain,
    and_star(not(X_15),implies(X_53,X_15)) = not(implies(implies(X_53,X_15),X_15)),
    inference(subst,[],[refute_0_193:[bind(Y,$fot(implies(X_53,X_15))),bind(X_38,$fot(X_15))]]) ).

cnf(refute_0_212,plain,
    not(and_star(not(X_15),implies(X_53,X_15))) = not(and_star(not(X_15),implies(X_53,X_15))),
    introduced(tautology,[refl,[$fot(not(and_star(not(X_15),implies(X_53,X_15))))]]) ).

cnf(refute_0_213,plain,
    ( and_star(not(X_15),implies(X_53,X_15)) != not(implies(implies(X_53,X_15),X_15))
    | not(and_star(not(X_15),implies(X_53,X_15))) != not(and_star(not(X_15),implies(X_53,X_15)))
    | not(and_star(not(X_15),implies(X_53,X_15))) = not(not(implies(implies(X_53,X_15),X_15))) ),
    introduced(tautology,[equality,[$cnf( $equal(not(and_star(not(X_15),implies(X_53,X_15))),not(and_star(not(X_15),implies(X_53,X_15)))) ),[1,0],$fot(not(implies(implies(X_53,X_15),X_15)))]]) ).

cnf(refute_0_214,plain,
    ( and_star(not(X_15),implies(X_53,X_15)) != not(implies(implies(X_53,X_15),X_15))
    | not(and_star(not(X_15),implies(X_53,X_15))) = not(not(implies(implies(X_53,X_15),X_15))) ),
    inference(resolve,[$cnf( $equal(not(and_star(not(X_15),implies(X_53,X_15))),not(and_star(not(X_15),implies(X_53,X_15)))) )],[refute_0_212,refute_0_213]) ).

cnf(refute_0_215,plain,
    not(and_star(not(X_15),implies(X_53,X_15))) = not(not(implies(implies(X_53,X_15),X_15))),
    inference(resolve,[$cnf( $equal(and_star(not(X_15),implies(X_53,X_15)),not(implies(implies(X_53,X_15),X_15))) )],[refute_0_211,refute_0_214]) ).

cnf(refute_0_216,plain,
    ( not(and_star(not(X_15),implies(X_53,X_15))) != not(not(implies(implies(X_53,X_15),X_15)))
    | not(not(implies(implies(X_53,X_15),X_15))) != implies(implies(X_53,X_15),X_15)
    | not(and_star(not(X_15),implies(X_53,X_15))) = implies(implies(X_53,X_15),X_15) ),
    inference(subst,[],[refute_0_31:[bind(X0,$fot(not(and_star(not(X_15),implies(X_53,X_15))))),bind(Y0,$fot(not(not(implies(implies(X_53,X_15),X_15))))),bind(Z,$fot(implies(implies(X_53,X_15),X_15)))]]) ).

cnf(refute_0_217,plain,
    ( not(not(implies(implies(X_53,X_15),X_15))) != implies(implies(X_53,X_15),X_15)
    | not(and_star(not(X_15),implies(X_53,X_15))) = implies(implies(X_53,X_15),X_15) ),
    inference(resolve,[$cnf( $equal(not(and_star(not(X_15),implies(X_53,X_15))),not(not(implies(implies(X_53,X_15),X_15)))) )],[refute_0_215,refute_0_216]) ).

cnf(refute_0_218,plain,
    not(and_star(not(X_15),implies(X_53,X_15))) = implies(implies(X_53,X_15),X_15),
    inference(resolve,[$cnf( $equal(not(not(implies(implies(X_53,X_15),X_15))),implies(implies(X_53,X_15),X_15)) )],[refute_0_210,refute_0_217]) ).

cnf(refute_0_219,plain,
    implies(not(X_15),not(implies(X_53,X_15))) = not(and_star(not(X_15),implies(X_53,X_15))),
    inference(subst,[],[refute_0_182:[bind(X_14,$fot(not(X_15))),bind(X_6,$fot(implies(X_53,X_15)))]]) ).

cnf(refute_0_220,plain,
    ( implies(not(X_15),not(implies(X_53,X_15))) != not(and_star(not(X_15),implies(X_53,X_15)))
    | not(and_star(not(X_15),implies(X_53,X_15))) != implies(implies(X_53,X_15),X_15)
    | implies(not(X_15),not(implies(X_53,X_15))) = implies(implies(X_53,X_15),X_15) ),
    inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(not(X_15),not(implies(X_53,X_15))))),bind(Y0,$fot(not(and_star(not(X_15),implies(X_53,X_15))))),bind(Z,$fot(implies(implies(X_53,X_15),X_15)))]]) ).

cnf(refute_0_221,plain,
    ( not(and_star(not(X_15),implies(X_53,X_15))) != implies(implies(X_53,X_15),X_15)
    | implies(not(X_15),not(implies(X_53,X_15))) = implies(implies(X_53,X_15),X_15) ),
    inference(resolve,[$cnf( $equal(implies(not(X_15),not(implies(X_53,X_15))),not(and_star(not(X_15),implies(X_53,X_15)))) )],[refute_0_219,refute_0_220]) ).

cnf(refute_0_222,plain,
    implies(not(X_15),not(implies(X_53,X_15))) = implies(implies(X_53,X_15),X_15),
    inference(resolve,[$cnf( $equal(not(and_star(not(X_15),implies(X_53,X_15))),implies(implies(X_53,X_15),X_15)) )],[refute_0_218,refute_0_221]) ).

cnf(refute_0_223,plain,
    ( implies(not(X_15),not(implies(X_53,X_15))) != implies(implies(X_53,X_15),X_15)
    | implies(not(X_15),not(implies(X_53,X_15))) != implies(implies(not(not(X_15)),X_53),X_53)
    | implies(implies(X_53,X_15),X_15) = implies(implies(not(not(X_15)),X_53),X_53) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(X_15),not(implies(X_53,X_15))),implies(implies(not(not(X_15)),X_53),X_53)) ),[0],$fot(implies(implies(X_53,X_15),X_15))]]) ).

cnf(refute_0_224,plain,
    ( implies(not(X_15),not(implies(X_53,X_15))) != implies(implies(not(not(X_15)),X_53),X_53)
    | implies(implies(X_53,X_15),X_15) = implies(implies(not(not(X_15)),X_53),X_53) ),
    inference(resolve,[$cnf( $equal(implies(not(X_15),not(implies(X_53,X_15))),implies(implies(X_53,X_15),X_15)) )],[refute_0_222,refute_0_223]) ).

cnf(refute_0_225,plain,
    not(not(X_15)) = X_15,
    inference(subst,[],[refute_0_158:[bind(X_6,$fot(X_15))]]) ).

cnf(refute_0_226,plain,
    implies(not(not(X_15)),X_53) = implies(not(not(X_15)),X_53),
    introduced(tautology,[refl,[$fot(implies(not(not(X_15)),X_53))]]) ).

cnf(refute_0_227,plain,
    ( implies(not(not(X_15)),X_53) != implies(not(not(X_15)),X_53)
    | not(not(X_15)) != X_15
    | implies(not(not(X_15)),X_53) = implies(X_15,X_53) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(not(not(X_15)),X_53),implies(not(not(X_15)),X_53)) ),[1,0],$fot(X_15)]]) ).

cnf(refute_0_228,plain,
    ( not(not(X_15)) != X_15
    | implies(not(not(X_15)),X_53) = implies(X_15,X_53) ),
    inference(resolve,[$cnf( $equal(implies(not(not(X_15)),X_53),implies(not(not(X_15)),X_53)) )],[refute_0_226,refute_0_227]) ).

cnf(refute_0_229,plain,
    implies(not(not(X_15)),X_53) = implies(X_15,X_53),
    inference(resolve,[$cnf( $equal(not(not(X_15)),X_15) )],[refute_0_225,refute_0_228]) ).

cnf(refute_0_230,plain,
    implies(implies(not(not(X_15)),X_53),X_53) = implies(implies(not(not(X_15)),X_53),X_53),
    introduced(tautology,[refl,[$fot(implies(implies(not(not(X_15)),X_53),X_53))]]) ).

cnf(refute_0_231,plain,
    ( implies(implies(not(not(X_15)),X_53),X_53) != implies(implies(not(not(X_15)),X_53),X_53)
    | implies(not(not(X_15)),X_53) != implies(X_15,X_53)
    | implies(implies(not(not(X_15)),X_53),X_53) = implies(implies(X_15,X_53),X_53) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(X_15)),X_53),X_53),implies(implies(not(not(X_15)),X_53),X_53)) ),[1,0],$fot(implies(X_15,X_53))]]) ).

cnf(refute_0_232,plain,
    ( implies(not(not(X_15)),X_53) != implies(X_15,X_53)
    | implies(implies(not(not(X_15)),X_53),X_53) = implies(implies(X_15,X_53),X_53) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(X_15)),X_53),X_53),implies(implies(not(not(X_15)),X_53),X_53)) )],[refute_0_230,refute_0_231]) ).

cnf(refute_0_233,plain,
    implies(implies(not(not(X_15)),X_53),X_53) = implies(implies(X_15,X_53),X_53),
    inference(resolve,[$cnf( $equal(implies(not(not(X_15)),X_53),implies(X_15,X_53)) )],[refute_0_229,refute_0_232]) ).

cnf(refute_0_234,plain,
    ( implies(implies(X_53,X_15),X_15) != implies(implies(not(not(X_15)),X_53),X_53)
    | implies(implies(not(not(X_15)),X_53),X_53) != implies(implies(X_15,X_53),X_53)
    | implies(implies(X_53,X_15),X_15) = implies(implies(X_15,X_53),X_53) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X_53,X_15),X_15),implies(implies(X_15,X_53),X_53)) ),[0],$fot(implies(implies(not(not(X_15)),X_53),X_53))]]) ).

cnf(refute_0_235,plain,
    ( implies(implies(X_53,X_15),X_15) != implies(implies(not(not(X_15)),X_53),X_53)
    | implies(implies(X_53,X_15),X_15) = implies(implies(X_15,X_53),X_53) ),
    inference(resolve,[$cnf( $equal(implies(implies(not(not(X_15)),X_53),X_53),implies(implies(X_15,X_53),X_53)) )],[refute_0_233,refute_0_234]) ).

cnf(refute_0_236,plain,
    ( implies(not(X_15),not(implies(X_53,X_15))) != implies(implies(not(not(X_15)),X_53),X_53)
    | implies(implies(X_53,X_15),X_15) = implies(implies(X_15,X_53),X_53) ),
    inference(resolve,[$cnf( $equal(implies(implies(X_53,X_15),X_15),implies(implies(not(not(X_15)),X_53),X_53)) )],[refute_0_224,refute_0_235]) ).

cnf(refute_0_237,plain,
    implies(implies(X_53,X_15),X_15) = implies(implies(X_15,X_53),X_53),
    inference(resolve,[$cnf( $equal(implies(not(X_15),not(implies(X_53,X_15))),implies(implies(not(not(X_15)),X_53),X_53)) )],[refute_0_209,refute_0_236]) ).

cnf(refute_0_238,plain,
    ( implies(implies(X_53,X_15),X_15) != implies(implies(X_15,X_53),X_53)
    | implies(implies(X_15,X_53),X_53) = implies(implies(X_53,X_15),X_15) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(X_53,X_15),X_15))),bind(Y0,$fot(implies(implies(X_15,X_53),X_53)))]]) ).

cnf(refute_0_239,plain,
    implies(implies(X_15,X_53),X_53) = implies(implies(X_53,X_15),X_15),
    inference(resolve,[$cnf( $equal(implies(implies(X_53,X_15),X_15),implies(implies(X_15,X_53),X_53)) )],[refute_0_237,refute_0_238]) ).

cnf(refute_0_240,plain,
    implies(implies(y,x),x) = implies(implies(x,y),y),
    inference(subst,[],[refute_0_239:[bind(X_15,$fot(y)),bind(X_53,$fot(x))]]) ).

cnf(refute_0_241,plain,
    ( implies(implies(x,y),y) != implies(implies(x,y),y)
    | implies(implies(y,x),x) != implies(implies(x,y),y)
    | implies(implies(x,y),y) = implies(implies(y,x),x) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(x,y),y),implies(implies(y,x),x)) ),[1],$fot(implies(implies(x,y),y))]]) ).

cnf(refute_0_242,plain,
    ( implies(implies(x,y),y) != implies(implies(x,y),y)
    | implies(implies(x,y),y) = implies(implies(y,x),x) ),
    inference(resolve,[$cnf( $equal(implies(implies(y,x),x),implies(implies(x,y),y)) )],[refute_0_240,refute_0_241]) ).

cnf(refute_0_243,plain,
    implies(implies(x,y),y) != implies(implies(x,y),y),
    inference(resolve,[$cnf( $equal(implies(implies(x,y),y),implies(implies(y,x),x)) )],[refute_0_242,prove_wajsberg_axiom]) ).

cnf(refute_0_244,plain,
    implies(implies(x,y),y) = implies(implies(x,y),y),
    introduced(tautology,[refl,[$fot(implies(implies(x,y),y))]]) ).

cnf(refute_0_245,plain,
    $false,
    inference(resolve,[$cnf( $equal(implies(implies(x,y),y),implies(implies(x,y),y)) )],[refute_0_244,refute_0_243]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : LCL163-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n013.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul  4 19:17:44 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.52  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.52  
% 0.19/0.52  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.38/0.55  
%------------------------------------------------------------------------------