TSTP Solution File: LCL159-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL159-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 12:50:04 EDT 2022
% Result : Unsatisfiable 0.49s 0.69s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 133
% Number of leaves : 358
% Syntax : Number of clauses : 1236 ( 601 unt; 0 nHn; 729 RR)
% Number of literals : 2167 (2166 equ; 935 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 1270 ( 34 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(or_definition,axiom,
or(X,Y) = implies(not(X),Y) ).
cnf(or_associativity,axiom,
or(or(X,Y),Z) = or(X,or(Y,Z)) ).
cnf(or_commutativity,axiom,
or(X,Y) = or(Y,X) ).
cnf(and_definition,axiom,
and(X,Y) = not(or(not(X),not(Y))) ).
cnf(and_associativity,axiom,
and(and(X,Y),Z) = and(X,and(Y,Z)) ).
cnf(and_commutativity,axiom,
and(X,Y) = and(Y,X) ).
cnf(xor_definition,axiom,
xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ).
cnf(xor_commutativity,axiom,
xor(X,Y) = xor(Y,X) ).
cnf(false_definition,axiom,
not(truth) = falsehood ).
cnf(prove_alternative_wajsberg_axiom,negated_conjecture,
xor(x,xor(truth,y)) != xor(xor(x,truth),y) ).
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( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( xor(X,Y) != xor(Y,X)
| xor(Y,X) = xor(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(X,Y))),bind(Y0,$fot(xor(Y,X)))]]) ).
cnf(refute_0_4,plain,
xor(Y,X) = xor(X,Y),
inference(resolve,[$cnf( $equal(xor(X,Y),xor(Y,X)) )],[xor_commutativity,refute_0_3]) ).
cnf(refute_0_5,plain,
xor(x,truth) = xor(truth,x),
inference(subst,[],[refute_0_4:[bind(X,$fot(truth)),bind(Y,$fot(x))]]) ).
cnf(refute_0_6,plain,
xor(y,xor(x,truth)) = xor(y,xor(x,truth)),
introduced(tautology,[refl,[$fot(xor(y,xor(x,truth)))]]) ).
cnf(refute_0_7,plain,
( xor(x,truth) != xor(truth,x)
| xor(y,xor(x,truth)) != xor(y,xor(x,truth))
| xor(y,xor(x,truth)) = xor(y,xor(truth,x)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(y,xor(x,truth)),xor(y,xor(x,truth))) ),[1,1],$fot(xor(truth,x))]]) ).
cnf(refute_0_8,plain,
( xor(x,truth) != xor(truth,x)
| xor(y,xor(x,truth)) = xor(y,xor(truth,x)) ),
inference(resolve,[$cnf( $equal(xor(y,xor(x,truth)),xor(y,xor(x,truth))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
xor(y,xor(x,truth)) = xor(y,xor(truth,x)),
inference(resolve,[$cnf( $equal(xor(x,truth),xor(truth,x)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
xor(xor(x,truth),y) = xor(y,xor(x,truth)),
inference(subst,[],[refute_0_4:[bind(X,$fot(y)),bind(Y,$fot(xor(x,truth)))]]) ).
cnf(refute_0_11,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_12,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
( xor(xor(x,truth),y) != xor(y,xor(x,truth))
| xor(y,xor(x,truth)) != xor(y,xor(truth,x))
| xor(xor(x,truth),y) = xor(y,xor(truth,x)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(xor(xor(x,truth),y))),bind(Y0,$fot(xor(y,xor(x,truth)))),bind(Z0,$fot(xor(y,xor(truth,x))))]]) ).
cnf(refute_0_14,plain,
( xor(y,xor(x,truth)) != xor(y,xor(truth,x))
| xor(xor(x,truth),y) = xor(y,xor(truth,x)) ),
inference(resolve,[$cnf( $equal(xor(xor(x,truth),y),xor(y,xor(x,truth))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
xor(xor(x,truth),y) = xor(y,xor(truth,x)),
inference(resolve,[$cnf( $equal(xor(y,xor(x,truth)),xor(y,xor(truth,x))) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
( xor(x,xor(truth,y)) != xor(y,xor(truth,x))
| xor(xor(x,truth),y) != xor(y,xor(truth,x))
| xor(x,xor(truth,y)) = xor(xor(x,truth),y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(xor(x,xor(truth,y)),xor(xor(x,truth),y)) ),[1],$fot(xor(y,xor(truth,x)))]]) ).
cnf(refute_0_17,plain,
( xor(x,xor(truth,y)) != xor(y,xor(truth,x))
| xor(x,xor(truth,y)) = xor(xor(x,truth),y) ),
inference(resolve,[$cnf( $equal(xor(xor(x,truth),y),xor(y,xor(truth,x))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
xor(x,xor(truth,y)) != xor(y,xor(truth,x)),
inference(resolve,[$cnf( $equal(xor(x,xor(truth,y)),xor(xor(x,truth),y)) )],[refute_0_17,prove_alternative_wajsberg_axiom]) ).
cnf(refute_0_19,plain,
and(X_1,truth) = not(or(not(X_1),not(truth))),
inference(subst,[],[and_definition:[bind(X,$fot(X_1)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_20,plain,
( and(X_1,truth) != not(or(not(X_1),not(truth)))
| not(truth) != falsehood
| and(X_1,truth) = not(or(not(X_1),falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_1,truth),not(or(not(X_1),not(truth)))) ),[1,0,1],$fot(falsehood)]]) ).
cnf(refute_0_21,plain,
( and(X_1,truth) != not(or(not(X_1),not(truth)))
| and(X_1,truth) = not(or(not(X_1),falsehood)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_20]) ).
cnf(refute_0_22,plain,
and(X_1,truth) = not(or(not(X_1),falsehood)),
inference(resolve,[$cnf( $equal(and(X_1,truth),not(or(not(X_1),not(truth)))) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( or(X,Y) != or(Y,X)
| or(Y,X) = or(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(or(Y,X)))]]) ).
cnf(refute_0_24,plain,
or(Y,X) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),or(Y,X)) )],[or_commutativity,refute_0_23]) ).
cnf(refute_0_25,plain,
or(not(X_1),falsehood) = or(falsehood,not(X_1)),
inference(subst,[],[refute_0_24:[bind(X,$fot(falsehood)),bind(Y,$fot(not(X_1)))]]) ).
cnf(refute_0_26,plain,
not(or(not(X_1),falsehood)) = not(or(not(X_1),falsehood)),
introduced(tautology,[refl,[$fot(not(or(not(X_1),falsehood)))]]) ).
cnf(refute_0_27,plain,
( not(or(not(X_1),falsehood)) != not(or(not(X_1),falsehood))
| or(not(X_1),falsehood) != or(falsehood,not(X_1))
| not(or(not(X_1),falsehood)) = not(or(falsehood,not(X_1))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X_1),falsehood)),not(or(not(X_1),falsehood))) ),[1,0],$fot(or(falsehood,not(X_1)))]]) ).
cnf(refute_0_28,plain,
( or(not(X_1),falsehood) != or(falsehood,not(X_1))
| not(or(not(X_1),falsehood)) = not(or(falsehood,not(X_1))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_1),falsehood)),not(or(not(X_1),falsehood))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
not(or(not(X_1),falsehood)) = not(or(falsehood,not(X_1))),
inference(resolve,[$cnf( $equal(or(not(X_1),falsehood),or(falsehood,not(X_1))) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( and(X_1,truth) != not(or(not(X_1),falsehood))
| not(or(not(X_1),falsehood)) != not(or(falsehood,not(X_1)))
| and(X_1,truth) = not(or(falsehood,not(X_1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_1,truth),not(or(falsehood,not(X_1)))) ),[0],$fot(not(or(not(X_1),falsehood)))]]) ).
cnf(refute_0_31,plain,
( and(X_1,truth) != not(or(not(X_1),falsehood))
| and(X_1,truth) = not(or(falsehood,not(X_1))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_1),falsehood)),not(or(falsehood,not(X_1)))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
and(X_1,truth) = not(or(falsehood,not(X_1))),
inference(resolve,[$cnf( $equal(and(X_1,truth),not(or(not(X_1),falsehood))) )],[refute_0_22,refute_0_31]) ).
cnf(refute_0_33,plain,
and(or(falsehood,not(X_4)),truth) = not(or(falsehood,not(or(falsehood,not(X_4))))),
inference(subst,[],[refute_0_32:[bind(X_1,$fot(or(falsehood,not(X_4))))]]) ).
cnf(refute_0_34,plain,
and(X_4,truth) = not(or(falsehood,not(X_4))),
inference(subst,[],[refute_0_32:[bind(X_1,$fot(X_4))]]) ).
cnf(refute_0_35,plain,
( and(X_4,truth) != not(or(falsehood,not(X_4)))
| not(or(falsehood,not(X_4))) = and(X_4,truth) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_4,truth))),bind(Y0,$fot(not(or(falsehood,not(X_4)))))]]) ).
cnf(refute_0_36,plain,
not(or(falsehood,not(X_4))) = and(X_4,truth),
inference(resolve,[$cnf( $equal(and(X_4,truth),not(or(falsehood,not(X_4)))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( and(or(falsehood,not(X_4)),truth) != not(or(falsehood,not(or(falsehood,not(X_4)))))
| not(or(falsehood,not(X_4))) != and(X_4,truth)
| and(or(falsehood,not(X_4)),truth) = not(or(falsehood,and(X_4,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,not(X_4)),truth),not(or(falsehood,not(or(falsehood,not(X_4)))))) ),[1,0,1],$fot(and(X_4,truth))]]) ).
cnf(refute_0_38,plain,
( and(or(falsehood,not(X_4)),truth) != not(or(falsehood,not(or(falsehood,not(X_4)))))
| and(or(falsehood,not(X_4)),truth) = not(or(falsehood,and(X_4,truth))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_4))),and(X_4,truth)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
and(or(falsehood,not(X_4)),truth) = not(or(falsehood,and(X_4,truth))),
inference(resolve,[$cnf( $equal(and(or(falsehood,not(X_4)),truth),not(or(falsehood,not(or(falsehood,not(X_4)))))) )],[refute_0_33,refute_0_38]) ).
cnf(refute_0_40,plain,
and(truth,X_2) = not(or(not(truth),not(X_2))),
inference(subst,[],[and_definition:[bind(X,$fot(truth)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_41,plain,
( and(truth,X_2) != not(or(not(truth),not(X_2)))
| not(truth) != falsehood
| and(truth,X_2) = not(or(falsehood,not(X_2))) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,X_2),not(or(not(truth),not(X_2)))) ),[1,0,0],$fot(falsehood)]]) ).
cnf(refute_0_42,plain,
( and(truth,X_2) != not(or(not(truth),not(X_2)))
| and(truth,X_2) = not(or(falsehood,not(X_2))) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_41]) ).
cnf(refute_0_43,plain,
and(truth,X_2) = not(or(falsehood,not(X_2))),
inference(resolve,[$cnf( $equal(and(truth,X_2),not(or(not(truth),not(X_2)))) )],[refute_0_40,refute_0_42]) ).
cnf(refute_0_44,plain,
( and(X_1,truth) != not(or(falsehood,not(X_1)))
| not(or(falsehood,not(X_1))) = and(X_1,truth) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_1,truth))),bind(Y0,$fot(not(or(falsehood,not(X_1)))))]]) ).
cnf(refute_0_45,plain,
not(or(falsehood,not(X_1))) = and(X_1,truth),
inference(resolve,[$cnf( $equal(and(X_1,truth),not(or(falsehood,not(X_1)))) )],[refute_0_32,refute_0_44]) ).
cnf(refute_0_46,plain,
not(or(falsehood,not(X_2))) = and(X_2,truth),
inference(subst,[],[refute_0_45:[bind(X_1,$fot(X_2))]]) ).
cnf(refute_0_47,plain,
( and(truth,X_2) != not(or(falsehood,not(X_2)))
| not(or(falsehood,not(X_2))) != and(X_2,truth)
| and(truth,X_2) = and(X_2,truth) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(truth,X_2),and(X_2,truth)) ),[0],$fot(not(or(falsehood,not(X_2))))]]) ).
cnf(refute_0_48,plain,
( and(truth,X_2) != not(or(falsehood,not(X_2)))
| and(truth,X_2) = and(X_2,truth) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_2))),and(X_2,truth)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
and(truth,X_2) = and(X_2,truth),
inference(resolve,[$cnf( $equal(and(truth,X_2),not(or(falsehood,not(X_2)))) )],[refute_0_43,refute_0_48]) ).
cnf(refute_0_50,plain,
( and(truth,X_2) != and(X_2,truth)
| and(X_2,truth) = and(truth,X_2) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,X_2))),bind(Y0,$fot(and(X_2,truth)))]]) ).
cnf(refute_0_51,plain,
and(X_2,truth) = and(truth,X_2),
inference(resolve,[$cnf( $equal(and(truth,X_2),and(X_2,truth)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
and(or(falsehood,not(X_4)),truth) = and(truth,or(falsehood,not(X_4))),
inference(subst,[],[refute_0_51:[bind(X_2,$fot(or(falsehood,not(X_4))))]]) ).
cnf(refute_0_53,plain,
( and(or(falsehood,not(X_4)),truth) != and(truth,or(falsehood,not(X_4)))
| and(or(falsehood,not(X_4)),truth) != not(or(falsehood,and(X_4,truth)))
| and(truth,or(falsehood,not(X_4))) = not(or(falsehood,and(X_4,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,not(X_4)),truth),not(or(falsehood,and(X_4,truth)))) ),[0],$fot(and(truth,or(falsehood,not(X_4))))]]) ).
cnf(refute_0_54,plain,
( and(or(falsehood,not(X_4)),truth) != not(or(falsehood,and(X_4,truth)))
| and(truth,or(falsehood,not(X_4))) = not(or(falsehood,and(X_4,truth))) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,not(X_4)),truth),and(truth,or(falsehood,not(X_4)))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
and(truth,or(falsehood,not(X_4))) = not(or(falsehood,and(X_4,truth))),
inference(resolve,[$cnf( $equal(and(or(falsehood,not(X_4)),truth),not(or(falsehood,and(X_4,truth)))) )],[refute_0_39,refute_0_54]) ).
cnf(refute_0_56,plain,
and(truth,or(falsehood,not(X_27))) = not(or(falsehood,and(X_27,truth))),
inference(subst,[],[refute_0_55:[bind(X_4,$fot(X_27))]]) ).
cnf(refute_0_57,plain,
and(truth,X_27) = and(X_27,truth),
inference(subst,[],[and_commutativity:[bind(X,$fot(truth)),bind(Y,$fot(X_27))]]) ).
cnf(refute_0_58,plain,
( and(truth,X_27) != and(X_27,truth)
| and(X_27,truth) = and(truth,X_27) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,X_27))),bind(Y0,$fot(and(X_27,truth)))]]) ).
cnf(refute_0_59,plain,
and(X_27,truth) = and(truth,X_27),
inference(resolve,[$cnf( $equal(and(truth,X_27),and(X_27,truth)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( and(X_27,truth) != and(truth,X_27)
| and(truth,or(falsehood,not(X_27))) != not(or(falsehood,and(X_27,truth)))
| and(truth,or(falsehood,not(X_27))) = not(or(falsehood,and(truth,X_27))) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,or(falsehood,not(X_27))),not(or(falsehood,and(X_27,truth)))) ),[1,0,1],$fot(and(truth,X_27))]]) ).
cnf(refute_0_61,plain,
( and(truth,or(falsehood,not(X_27))) != not(or(falsehood,and(X_27,truth)))
| and(truth,or(falsehood,not(X_27))) = not(or(falsehood,and(truth,X_27))) ),
inference(resolve,[$cnf( $equal(and(X_27,truth),and(truth,X_27)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
and(truth,or(falsehood,not(X_27))) = not(or(falsehood,and(truth,X_27))),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,not(X_27))),not(or(falsehood,and(X_27,truth)))) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
( and(truth,or(falsehood,not(X_27))) != not(or(falsehood,and(X_27,truth)))
| and(truth,or(falsehood,not(X_27))) != not(or(falsehood,and(truth,X_27)))
| not(or(falsehood,and(X_27,truth))) = not(or(falsehood,and(truth,X_27))) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,or(falsehood,not(X_27))),not(or(falsehood,and(truth,X_27)))) ),[0],$fot(not(or(falsehood,and(X_27,truth))))]]) ).
cnf(refute_0_64,plain,
( and(truth,or(falsehood,not(X_27))) != not(or(falsehood,and(truth,X_27)))
| not(or(falsehood,and(X_27,truth))) = not(or(falsehood,and(truth,X_27))) ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,not(X_27))),not(or(falsehood,and(X_27,truth)))) )],[refute_0_56,refute_0_63]) ).
cnf(refute_0_65,plain,
not(or(falsehood,and(X_27,truth))) = not(or(falsehood,and(truth,X_27))),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,not(X_27))),not(or(falsehood,and(truth,X_27)))) )],[refute_0_62,refute_0_64]) ).
cnf(refute_0_66,plain,
xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = or(and(X_36,not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),
inference(subst,[],[xor_definition:[bind(X,$fot(X_36)),bind(Y,$fot(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))]]) ).
cnf(refute_0_67,plain,
and(truth,or(falsehood,not(or(falsehood,and(truth,or(falsehood,falsehood)))))) = not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))),
inference(subst,[],[refute_0_55:[bind(X_4,$fot(or(falsehood,and(truth,or(falsehood,falsehood)))))]]) ).
cnf(refute_0_68,plain,
and(or(falsehood,and(truth,truth)),truth) = not(or(falsehood,not(or(falsehood,and(truth,truth))))),
inference(subst,[],[refute_0_32:[bind(X_1,$fot(or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_69,plain,
and(or(falsehood,falsehood),truth) = not(or(falsehood,not(or(falsehood,falsehood)))),
inference(subst,[],[refute_0_32:[bind(X_1,$fot(or(falsehood,falsehood)))]]) ).
cnf(refute_0_70,plain,
and(truth,truth) = not(or(falsehood,not(truth))),
inference(subst,[],[refute_0_32:[bind(X_1,$fot(truth))]]) ).
cnf(refute_0_71,plain,
( and(truth,truth) != not(or(falsehood,not(truth)))
| not(truth) != falsehood
| and(truth,truth) = not(or(falsehood,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,truth),not(or(falsehood,not(truth)))) ),[1,0,1],$fot(falsehood)]]) ).
cnf(refute_0_72,plain,
( and(truth,truth) != not(or(falsehood,not(truth)))
| and(truth,truth) = not(or(falsehood,falsehood)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_71]) ).
cnf(refute_0_73,plain,
and(truth,truth) = not(or(falsehood,falsehood)),
inference(resolve,[$cnf( $equal(and(truth,truth),not(or(falsehood,not(truth)))) )],[refute_0_70,refute_0_72]) ).
cnf(refute_0_74,plain,
( and(truth,truth) != not(or(falsehood,falsehood))
| not(or(falsehood,falsehood)) = and(truth,truth) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,truth))),bind(Y0,$fot(not(or(falsehood,falsehood))))]]) ).
cnf(refute_0_75,plain,
not(or(falsehood,falsehood)) = and(truth,truth),
inference(resolve,[$cnf( $equal(and(truth,truth),not(or(falsehood,falsehood))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( and(or(falsehood,falsehood),truth) != not(or(falsehood,not(or(falsehood,falsehood))))
| not(or(falsehood,falsehood)) != and(truth,truth)
| and(or(falsehood,falsehood),truth) = not(or(falsehood,and(truth,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,not(or(falsehood,falsehood))))) ),[1,0,1],$fot(and(truth,truth))]]) ).
cnf(refute_0_77,plain,
( and(or(falsehood,falsehood),truth) != not(or(falsehood,not(or(falsehood,falsehood))))
| and(or(falsehood,falsehood),truth) = not(or(falsehood,and(truth,truth))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,falsehood)),and(truth,truth)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
and(or(falsehood,falsehood),truth) = not(or(falsehood,and(truth,truth))),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,not(or(falsehood,falsehood))))) )],[refute_0_69,refute_0_77]) ).
cnf(refute_0_79,plain,
and(or(falsehood,falsehood),truth) = and(truth,or(falsehood,falsehood)),
inference(subst,[],[refute_0_51:[bind(X_2,$fot(or(falsehood,falsehood)))]]) ).
cnf(refute_0_80,plain,
( and(or(falsehood,falsehood),truth) != and(truth,or(falsehood,falsehood))
| and(or(falsehood,falsehood),truth) != not(or(falsehood,and(truth,truth)))
| and(truth,or(falsehood,falsehood)) = not(or(falsehood,and(truth,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,and(truth,truth)))) ),[0],$fot(and(truth,or(falsehood,falsehood)))]]) ).
cnf(refute_0_81,plain,
( and(or(falsehood,falsehood),truth) != not(or(falsehood,and(truth,truth)))
| and(truth,or(falsehood,falsehood)) = not(or(falsehood,and(truth,truth))) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),truth),and(truth,or(falsehood,falsehood))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
and(truth,or(falsehood,falsehood)) = not(or(falsehood,and(truth,truth))),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,and(truth,truth)))) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
( and(truth,or(falsehood,falsehood)) != not(or(falsehood,and(truth,truth)))
| not(or(falsehood,and(truth,truth))) = and(truth,or(falsehood,falsehood)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,or(falsehood,falsehood)))),bind(Y0,$fot(not(or(falsehood,and(truth,truth)))))]]) ).
cnf(refute_0_84,plain,
not(or(falsehood,and(truth,truth))) = and(truth,or(falsehood,falsehood)),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),not(or(falsehood,and(truth,truth)))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
( and(or(falsehood,and(truth,truth)),truth) != not(or(falsehood,not(or(falsehood,and(truth,truth)))))
| not(or(falsehood,and(truth,truth))) != and(truth,or(falsehood,falsehood))
| and(or(falsehood,and(truth,truth)),truth) = not(or(falsehood,and(truth,or(falsehood,falsehood)))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,truth)),truth),not(or(falsehood,not(or(falsehood,and(truth,truth)))))) ),[1,0,1],$fot(and(truth,or(falsehood,falsehood)))]]) ).
cnf(refute_0_86,plain,
( and(or(falsehood,and(truth,truth)),truth) != not(or(falsehood,not(or(falsehood,and(truth,truth)))))
| and(or(falsehood,and(truth,truth)),truth) = not(or(falsehood,and(truth,or(falsehood,falsehood)))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,truth))),and(truth,or(falsehood,falsehood))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
and(or(falsehood,and(truth,truth)),truth) = not(or(falsehood,and(truth,or(falsehood,falsehood)))),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),truth),not(or(falsehood,not(or(falsehood,and(truth,truth)))))) )],[refute_0_68,refute_0_86]) ).
cnf(refute_0_88,plain,
and(or(falsehood,and(truth,truth)),truth) = and(truth,or(falsehood,and(truth,truth))),
inference(subst,[],[refute_0_51:[bind(X_2,$fot(or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_89,plain,
( and(or(falsehood,and(truth,truth)),truth) != and(truth,or(falsehood,and(truth,truth)))
| and(or(falsehood,and(truth,truth)),truth) != not(or(falsehood,and(truth,or(falsehood,falsehood))))
| and(truth,or(falsehood,and(truth,truth))) = not(or(falsehood,and(truth,or(falsehood,falsehood)))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,truth)),truth),not(or(falsehood,and(truth,or(falsehood,falsehood))))) ),[0],$fot(and(truth,or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_90,plain,
( and(or(falsehood,and(truth,truth)),truth) != not(or(falsehood,and(truth,or(falsehood,falsehood))))
| and(truth,or(falsehood,and(truth,truth))) = not(or(falsehood,and(truth,or(falsehood,falsehood)))) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),truth),and(truth,or(falsehood,and(truth,truth)))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
and(truth,or(falsehood,and(truth,truth))) = not(or(falsehood,and(truth,or(falsehood,falsehood)))),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),truth),not(or(falsehood,and(truth,or(falsehood,falsehood))))) )],[refute_0_87,refute_0_90]) ).
cnf(refute_0_92,plain,
( and(truth,or(falsehood,and(truth,truth))) != not(or(falsehood,and(truth,or(falsehood,falsehood))))
| not(or(falsehood,and(truth,or(falsehood,falsehood)))) = and(truth,or(falsehood,and(truth,truth))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,or(falsehood,and(truth,truth))))),bind(Y0,$fot(not(or(falsehood,and(truth,or(falsehood,falsehood))))))]]) ).
cnf(refute_0_93,plain,
not(or(falsehood,and(truth,or(falsehood,falsehood)))) = and(truth,or(falsehood,and(truth,truth))),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,and(truth,truth))),not(or(falsehood,and(truth,or(falsehood,falsehood))))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
( and(truth,or(falsehood,not(or(falsehood,and(truth,or(falsehood,falsehood)))))) != not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)))
| not(or(falsehood,and(truth,or(falsehood,falsehood)))) != and(truth,or(falsehood,and(truth,truth)))
| and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) = not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,or(falsehood,not(or(falsehood,and(truth,or(falsehood,falsehood)))))),not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)))) ),[0,1,1],$fot(and(truth,or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_95,plain,
( and(truth,or(falsehood,not(or(falsehood,and(truth,or(falsehood,falsehood)))))) != not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)))
| and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) = not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,or(falsehood,falsehood)))),and(truth,or(falsehood,and(truth,truth)))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) = not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,not(or(falsehood,and(truth,or(falsehood,falsehood)))))),not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)))) )],[refute_0_67,refute_0_95]) ).
cnf(refute_0_97,plain,
and(or(falsehood,and(truth,or(falsehood,falsehood))),truth) = and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))),
inference(subst,[],[refute_0_51:[bind(X_2,$fot(or(falsehood,and(truth,or(falsehood,falsehood)))))]]) ).
cnf(refute_0_98,plain,
or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)) = or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)),
introduced(tautology,[refl,[$fot(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)))]]) ).
cnf(refute_0_99,plain,
( and(or(falsehood,and(truth,or(falsehood,falsehood))),truth) != and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))
| or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)) != or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))
| or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)) = or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)),or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))) ),[1,1],$fot(and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))]]) ).
cnf(refute_0_100,plain,
( and(or(falsehood,and(truth,or(falsehood,falsehood))),truth) != and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))
| or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)) = or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)),or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)) = or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,or(falsehood,falsehood))),truth),and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))) = not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))),
introduced(tautology,[refl,[$fot(not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))))]]) ).
cnf(refute_0_103,plain,
( not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))) != not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)))
| or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)) != or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))
| not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))) = not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))),not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)))) ),[1,0],$fot(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))]]) ).
cnf(refute_0_104,plain,
( or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)) != or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))
| not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))) = not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))),not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))) = not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),
inference(resolve,[$cnf( $equal(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
( and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) != not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)))
| not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))) != not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))
| and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) = not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))),not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) ),[0],$fot(not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))))]]) ).
cnf(refute_0_107,plain,
( and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) != not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)))
| and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) = not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth))),not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) = not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))),not(or(falsehood,and(or(falsehood,and(truth,or(falsehood,falsehood))),truth)))) )],[refute_0_96,refute_0_107]) ).
cnf(refute_0_109,plain,
( and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) != not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))
| not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))))),bind(Y0,$fot(not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))))]]) ).
cnf(refute_0_110,plain,
not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))),not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
( not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) != and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))
| xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) != or(and(X_36,not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))
| xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),or(and(X_36,not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))) ),[1,0,1],$fot(and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))))]]) ).
cnf(refute_0_112,plain,
( xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) != or(and(X_36,not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))
| xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),
inference(resolve,[$cnf( $equal(xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),or(and(X_36,not(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))) )],[refute_0_66,refute_0_112]) ).
cnf(refute_0_114,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_115,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[or_definition,refute_0_114]) ).
cnf(refute_0_116,plain,
implies(not(X),not(Y)) = or(X,not(Y)),
inference(subst,[],[refute_0_115:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_117,plain,
implies(implies(not(X),not(Y)),implies(Y,X)) = implies(implies(not(X),not(Y)),implies(Y,X)),
introduced(tautology,[refl,[$fot(implies(implies(not(X),not(Y)),implies(Y,X)))]]) ).
cnf(refute_0_118,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != implies(implies(not(X),not(Y)),implies(Y,X))
| implies(not(X),not(Y)) != or(X,not(Y))
| implies(implies(not(X),not(Y)),implies(Y,X)) = implies(or(X,not(Y)),implies(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(not(X),not(Y)),implies(Y,X))) ),[1,0],$fot(or(X,not(Y)))]]) ).
cnf(refute_0_119,plain,
( implies(not(X),not(Y)) != or(X,not(Y))
| implies(implies(not(X),not(Y)),implies(Y,X)) = implies(or(X,not(Y)),implies(Y,X)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(not(X),not(Y)),implies(Y,X))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
implies(implies(not(X),not(Y)),implies(Y,X)) = implies(or(X,not(Y)),implies(Y,X)),
inference(resolve,[$cnf( $equal(implies(not(X),not(Y)),or(X,not(Y))) )],[refute_0_116,refute_0_119]) ).
cnf(refute_0_121,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != implies(or(X,not(Y)),implies(Y,X))
| implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(or(X,not(Y)),implies(Y,X)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) ),[0],$fot(implies(or(X,not(Y)),implies(Y,X)))]]) ).
cnf(refute_0_122,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(or(X,not(Y)),implies(Y,X)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(or(X,not(Y)),implies(Y,X))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
implies(or(X,not(Y)),implies(Y,X)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[wajsberg_4,refute_0_122]) ).
cnf(refute_0_124,plain,
implies(or(X_19,not(truth)),implies(truth,X_19)) = truth,
inference(subst,[],[refute_0_123:[bind(X,$fot(X_19)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_125,plain,
implies(truth,X_19) = X_19,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_126,plain,
( implies(or(X_19,not(truth)),implies(truth,X_19)) != truth
| implies(truth,X_19) != X_19
| implies(or(X_19,not(truth)),X_19) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_19,not(truth)),implies(truth,X_19)),truth) ),[0,1],$fot(X_19)]]) ).
cnf(refute_0_127,plain,
( implies(or(X_19,not(truth)),implies(truth,X_19)) != truth
| implies(or(X_19,not(truth)),X_19) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_19),X_19) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
implies(or(X_19,not(truth)),X_19) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_19,not(truth)),implies(truth,X_19)),truth) )],[refute_0_124,refute_0_127]) ).
cnf(refute_0_129,plain,
or(X_19,not(truth)) = or(X_19,not(truth)),
introduced(tautology,[refl,[$fot(or(X_19,not(truth)))]]) ).
cnf(refute_0_130,plain,
( not(truth) != falsehood
| or(X_19,not(truth)) != or(X_19,not(truth))
| or(X_19,not(truth)) = or(X_19,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_19,not(truth)),or(X_19,not(truth))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_131,plain,
( not(truth) != falsehood
| or(X_19,not(truth)) = or(X_19,falsehood) ),
inference(resolve,[$cnf( $equal(or(X_19,not(truth)),or(X_19,not(truth))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
or(X_19,not(truth)) = or(X_19,falsehood),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_131]) ).
cnf(refute_0_133,plain,
implies(or(X_19,not(truth)),X_19) = implies(or(X_19,not(truth)),X_19),
introduced(tautology,[refl,[$fot(implies(or(X_19,not(truth)),X_19))]]) ).
cnf(refute_0_134,plain,
( implies(or(X_19,not(truth)),X_19) != implies(or(X_19,not(truth)),X_19)
| or(X_19,not(truth)) != or(X_19,falsehood)
| implies(or(X_19,not(truth)),X_19) = implies(or(X_19,falsehood),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_19,not(truth)),X_19),implies(or(X_19,not(truth)),X_19)) ),[1,0],$fot(or(X_19,falsehood))]]) ).
cnf(refute_0_135,plain,
( or(X_19,not(truth)) != or(X_19,falsehood)
| implies(or(X_19,not(truth)),X_19) = implies(or(X_19,falsehood),X_19) ),
inference(resolve,[$cnf( $equal(implies(or(X_19,not(truth)),X_19),implies(or(X_19,not(truth)),X_19)) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
implies(or(X_19,not(truth)),X_19) = implies(or(X_19,falsehood),X_19),
inference(resolve,[$cnf( $equal(or(X_19,not(truth)),or(X_19,falsehood)) )],[refute_0_132,refute_0_135]) ).
cnf(refute_0_137,plain,
( implies(or(X_19,not(truth)),X_19) != implies(or(X_19,falsehood),X_19)
| implies(or(X_19,not(truth)),X_19) != truth
| implies(or(X_19,falsehood),X_19) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_19,not(truth)),X_19),truth) ),[0],$fot(implies(or(X_19,falsehood),X_19))]]) ).
cnf(refute_0_138,plain,
( implies(or(X_19,not(truth)),X_19) != truth
| implies(or(X_19,falsehood),X_19) = truth ),
inference(resolve,[$cnf( $equal(implies(or(X_19,not(truth)),X_19),implies(or(X_19,falsehood),X_19)) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
implies(or(X_19,falsehood),X_19) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_19,not(truth)),X_19),truth) )],[refute_0_128,refute_0_138]) ).
cnf(refute_0_140,plain,
implies(or(X_21,falsehood),X_21) = truth,
inference(subst,[],[refute_0_139:[bind(X_19,$fot(X_21))]]) ).
cnf(refute_0_141,plain,
or(falsehood,X_21) = or(X_21,falsehood),
inference(subst,[],[or_commutativity:[bind(X,$fot(falsehood)),bind(Y,$fot(X_21))]]) ).
cnf(refute_0_142,plain,
( or(falsehood,X_21) != or(X_21,falsehood)
| or(X_21,falsehood) = or(falsehood,X_21) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(falsehood,X_21))),bind(Y0,$fot(or(X_21,falsehood)))]]) ).
cnf(refute_0_143,plain,
or(X_21,falsehood) = or(falsehood,X_21),
inference(resolve,[$cnf( $equal(or(falsehood,X_21),or(X_21,falsehood)) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
( implies(or(X_21,falsehood),X_21) != truth
| or(X_21,falsehood) != or(falsehood,X_21)
| implies(or(falsehood,X_21),X_21) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_21,falsehood),X_21),truth) ),[0,0],$fot(or(falsehood,X_21))]]) ).
cnf(refute_0_145,plain,
( implies(or(X_21,falsehood),X_21) != truth
| implies(or(falsehood,X_21),X_21) = truth ),
inference(resolve,[$cnf( $equal(or(X_21,falsehood),or(falsehood,X_21)) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
implies(or(falsehood,X_21),X_21) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_21,falsehood),X_21),truth) )],[refute_0_140,refute_0_145]) ).
cnf(refute_0_147,plain,
implies(or(falsehood,or(X_47,and(truth,truth))),or(X_47,and(truth,truth))) = truth,
inference(subst,[],[refute_0_146:[bind(X_21,$fot(or(X_47,and(truth,truth))))]]) ).
cnf(refute_0_148,plain,
or(or(falsehood,and(truth,truth)),X_8) = implies(not(or(falsehood,and(truth,truth))),X_8),
inference(subst,[],[or_definition:[bind(X,$fot(or(falsehood,and(truth,truth)))),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_149,plain,
( not(or(falsehood,and(truth,truth))) != and(truth,or(falsehood,falsehood))
| or(or(falsehood,and(truth,truth)),X_8) != implies(not(or(falsehood,and(truth,truth))),X_8)
| or(or(falsehood,and(truth,truth)),X_8) = implies(and(truth,or(falsehood,falsehood)),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(falsehood,and(truth,truth)),X_8),implies(not(or(falsehood,and(truth,truth))),X_8)) ),[1,0],$fot(and(truth,or(falsehood,falsehood)))]]) ).
cnf(refute_0_150,plain,
( or(or(falsehood,and(truth,truth)),X_8) != implies(not(or(falsehood,and(truth,truth))),X_8)
| or(or(falsehood,and(truth,truth)),X_8) = implies(and(truth,or(falsehood,falsehood)),X_8) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,truth))),and(truth,or(falsehood,falsehood))) )],[refute_0_84,refute_0_149]) ).
cnf(refute_0_151,plain,
or(or(falsehood,and(truth,truth)),X_8) = implies(and(truth,or(falsehood,falsehood)),X_8),
inference(resolve,[$cnf( $equal(or(or(falsehood,and(truth,truth)),X_8),implies(not(or(falsehood,and(truth,truth))),X_8)) )],[refute_0_148,refute_0_150]) ).
cnf(refute_0_152,plain,
or(or(falsehood,and(truth,truth)),X_8) = or(falsehood,or(and(truth,truth),X_8)),
inference(subst,[],[or_associativity:[bind(X,$fot(falsehood)),bind(Y,$fot(and(truth,truth))),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_153,plain,
( or(or(falsehood,and(truth,truth)),X_8) != implies(and(truth,or(falsehood,falsehood)),X_8)
| or(or(falsehood,and(truth,truth)),X_8) != or(falsehood,or(and(truth,truth),X_8))
| or(falsehood,or(and(truth,truth),X_8)) = implies(and(truth,or(falsehood,falsehood)),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(falsehood,and(truth,truth)),X_8),implies(and(truth,or(falsehood,falsehood)),X_8)) ),[0],$fot(or(falsehood,or(and(truth,truth),X_8)))]]) ).
cnf(refute_0_154,plain,
( or(or(falsehood,and(truth,truth)),X_8) != implies(and(truth,or(falsehood,falsehood)),X_8)
| or(falsehood,or(and(truth,truth),X_8)) = implies(and(truth,or(falsehood,falsehood)),X_8) ),
inference(resolve,[$cnf( $equal(or(or(falsehood,and(truth,truth)),X_8),or(falsehood,or(and(truth,truth),X_8))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
or(falsehood,or(and(truth,truth),X_8)) = implies(and(truth,or(falsehood,falsehood)),X_8),
inference(resolve,[$cnf( $equal(or(or(falsehood,and(truth,truth)),X_8),implies(and(truth,or(falsehood,falsehood)),X_8)) )],[refute_0_151,refute_0_154]) ).
cnf(refute_0_156,plain,
or(falsehood,or(and(truth,truth),X_29)) = implies(and(truth,or(falsehood,falsehood)),X_29),
inference(subst,[],[refute_0_155:[bind(X_8,$fot(X_29))]]) ).
cnf(refute_0_157,plain,
or(X_29,and(truth,truth)) = or(and(truth,truth),X_29),
inference(subst,[],[or_commutativity:[bind(X,$fot(X_29)),bind(Y,$fot(and(truth,truth)))]]) ).
cnf(refute_0_158,plain,
( or(X_29,and(truth,truth)) != or(and(truth,truth),X_29)
| or(and(truth,truth),X_29) = or(X_29,and(truth,truth)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X_29,and(truth,truth)))),bind(Y0,$fot(or(and(truth,truth),X_29)))]]) ).
cnf(refute_0_159,plain,
or(and(truth,truth),X_29) = or(X_29,and(truth,truth)),
inference(resolve,[$cnf( $equal(or(X_29,and(truth,truth)),or(and(truth,truth),X_29)) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
( or(and(truth,truth),X_29) != or(X_29,and(truth,truth))
| or(falsehood,or(and(truth,truth),X_29)) != implies(and(truth,or(falsehood,falsehood)),X_29)
| or(falsehood,or(X_29,and(truth,truth))) = implies(and(truth,or(falsehood,falsehood)),X_29) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(and(truth,truth),X_29)),implies(and(truth,or(falsehood,falsehood)),X_29)) ),[0,1],$fot(or(X_29,and(truth,truth)))]]) ).
cnf(refute_0_161,plain,
( or(falsehood,or(and(truth,truth),X_29)) != implies(and(truth,or(falsehood,falsehood)),X_29)
| or(falsehood,or(X_29,and(truth,truth))) = implies(and(truth,or(falsehood,falsehood)),X_29) ),
inference(resolve,[$cnf( $equal(or(and(truth,truth),X_29),or(X_29,and(truth,truth))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
or(falsehood,or(X_29,and(truth,truth))) = implies(and(truth,or(falsehood,falsehood)),X_29),
inference(resolve,[$cnf( $equal(or(falsehood,or(and(truth,truth),X_29)),implies(and(truth,or(falsehood,falsehood)),X_29)) )],[refute_0_156,refute_0_161]) ).
cnf(refute_0_163,plain,
or(falsehood,or(X_47,and(truth,truth))) = implies(and(truth,or(falsehood,falsehood)),X_47),
inference(subst,[],[refute_0_162:[bind(X_29,$fot(X_47))]]) ).
cnf(refute_0_164,plain,
( implies(or(falsehood,or(X_47,and(truth,truth))),or(X_47,and(truth,truth))) != truth
| or(falsehood,or(X_47,and(truth,truth))) != implies(and(truth,or(falsehood,falsehood)),X_47)
| implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,or(X_47,and(truth,truth))),or(X_47,and(truth,truth))),truth) ),[0,0],$fot(implies(and(truth,or(falsehood,falsehood)),X_47))]]) ).
cnf(refute_0_165,plain,
( implies(or(falsehood,or(X_47,and(truth,truth))),or(X_47,and(truth,truth))) != truth
| implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,or(X_47,and(truth,truth))),implies(and(truth,or(falsehood,falsehood)),X_47)) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,or(X_47,and(truth,truth))),or(X_47,and(truth,truth))),truth) )],[refute_0_147,refute_0_165]) ).
cnf(refute_0_167,plain,
implies(truth,or(X_47,and(truth,truth))) = or(X_47,and(truth,truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(or(X_47,and(truth,truth))))]]) ).
cnf(refute_0_168,plain,
implies(implies(and(truth,or(falsehood,falsehood)),falsehood),implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(and(truth,or(falsehood,falsehood)))),bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_169,plain,
or(or(falsehood,falsehood),X_8) = implies(not(or(falsehood,falsehood)),X_8),
inference(subst,[],[or_definition:[bind(X,$fot(or(falsehood,falsehood))),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_170,plain,
( not(or(falsehood,falsehood)) != and(truth,truth)
| or(or(falsehood,falsehood),X_8) != implies(not(or(falsehood,falsehood)),X_8)
| or(or(falsehood,falsehood),X_8) = implies(and(truth,truth),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(falsehood,falsehood),X_8),implies(not(or(falsehood,falsehood)),X_8)) ),[1,0],$fot(and(truth,truth))]]) ).
cnf(refute_0_171,plain,
( or(or(falsehood,falsehood),X_8) != implies(not(or(falsehood,falsehood)),X_8)
| or(or(falsehood,falsehood),X_8) = implies(and(truth,truth),X_8) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,falsehood)),and(truth,truth)) )],[refute_0_75,refute_0_170]) ).
cnf(refute_0_172,plain,
or(or(falsehood,falsehood),X_8) = implies(and(truth,truth),X_8),
inference(resolve,[$cnf( $equal(or(or(falsehood,falsehood),X_8),implies(not(or(falsehood,falsehood)),X_8)) )],[refute_0_169,refute_0_171]) ).
cnf(refute_0_173,plain,
or(or(falsehood,falsehood),X_8) = or(falsehood,or(falsehood,X_8)),
inference(subst,[],[or_associativity:[bind(X,$fot(falsehood)),bind(Y,$fot(falsehood)),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_174,plain,
( or(or(falsehood,falsehood),X_8) != implies(and(truth,truth),X_8)
| or(or(falsehood,falsehood),X_8) != or(falsehood,or(falsehood,X_8))
| or(falsehood,or(falsehood,X_8)) = implies(and(truth,truth),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(falsehood,falsehood),X_8),implies(and(truth,truth),X_8)) ),[0],$fot(or(falsehood,or(falsehood,X_8)))]]) ).
cnf(refute_0_175,plain,
( or(or(falsehood,falsehood),X_8) != implies(and(truth,truth),X_8)
| or(falsehood,or(falsehood,X_8)) = implies(and(truth,truth),X_8) ),
inference(resolve,[$cnf( $equal(or(or(falsehood,falsehood),X_8),or(falsehood,or(falsehood,X_8))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
or(falsehood,or(falsehood,X_8)) = implies(and(truth,truth),X_8),
inference(resolve,[$cnf( $equal(or(or(falsehood,falsehood),X_8),implies(and(truth,truth),X_8)) )],[refute_0_172,refute_0_175]) ).
cnf(refute_0_177,plain,
or(falsehood,or(falsehood,X_17)) = implies(and(truth,truth),X_17),
inference(subst,[],[refute_0_176:[bind(X_8,$fot(X_17))]]) ).
cnf(refute_0_178,plain,
or(X_17,falsehood) = or(falsehood,X_17),
inference(subst,[],[or_commutativity:[bind(X,$fot(X_17)),bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_179,plain,
( or(X_17,falsehood) != or(falsehood,X_17)
| or(falsehood,X_17) = or(X_17,falsehood) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X_17,falsehood))),bind(Y0,$fot(or(falsehood,X_17)))]]) ).
cnf(refute_0_180,plain,
or(falsehood,X_17) = or(X_17,falsehood),
inference(resolve,[$cnf( $equal(or(X_17,falsehood),or(falsehood,X_17)) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
( or(falsehood,X_17) != or(X_17,falsehood)
| or(falsehood,or(falsehood,X_17)) != implies(and(truth,truth),X_17)
| or(falsehood,or(X_17,falsehood)) = implies(and(truth,truth),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(falsehood,X_17)),implies(and(truth,truth),X_17)) ),[0,1],$fot(or(X_17,falsehood))]]) ).
cnf(refute_0_182,plain,
( or(falsehood,or(falsehood,X_17)) != implies(and(truth,truth),X_17)
| or(falsehood,or(X_17,falsehood)) = implies(and(truth,truth),X_17) ),
inference(resolve,[$cnf( $equal(or(falsehood,X_17),or(X_17,falsehood)) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
or(falsehood,or(X_17,falsehood)) = implies(and(truth,truth),X_17),
inference(resolve,[$cnf( $equal(or(falsehood,or(falsehood,X_17)),implies(and(truth,truth),X_17)) )],[refute_0_177,refute_0_182]) ).
cnf(refute_0_184,plain,
or(falsehood,or(and(truth,truth),falsehood)) = implies(and(truth,truth),and(truth,truth)),
inference(subst,[],[refute_0_183:[bind(X_17,$fot(and(truth,truth)))]]) ).
cnf(refute_0_185,plain,
or(falsehood,or(and(truth,truth),falsehood)) = implies(and(truth,or(falsehood,falsehood)),falsehood),
inference(subst,[],[refute_0_155:[bind(X_8,$fot(falsehood))]]) ).
cnf(refute_0_186,plain,
( or(falsehood,or(and(truth,truth),falsehood)) != implies(and(truth,or(falsehood,falsehood)),falsehood)
| or(falsehood,or(and(truth,truth),falsehood)) != implies(and(truth,truth),and(truth,truth))
| implies(and(truth,or(falsehood,falsehood)),falsehood) = implies(and(truth,truth),and(truth,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(and(truth,truth),falsehood)),implies(and(truth,truth),and(truth,truth))) ),[0],$fot(implies(and(truth,or(falsehood,falsehood)),falsehood))]]) ).
cnf(refute_0_187,plain,
( or(falsehood,or(and(truth,truth),falsehood)) != implies(and(truth,truth),and(truth,truth))
| implies(and(truth,or(falsehood,falsehood)),falsehood) = implies(and(truth,truth),and(truth,truth)) ),
inference(resolve,[$cnf( $equal(or(falsehood,or(and(truth,truth),falsehood)),implies(and(truth,or(falsehood,falsehood)),falsehood)) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
implies(and(truth,or(falsehood,falsehood)),falsehood) = implies(and(truth,truth),and(truth,truth)),
inference(resolve,[$cnf( $equal(or(falsehood,or(and(truth,truth),falsehood)),implies(and(truth,truth),and(truth,truth))) )],[refute_0_184,refute_0_187]) ).
cnf(refute_0_189,plain,
implies(implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)),implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(and(truth,truth),truth))),bind(Y,$fot(implies(falsehood,falsehood))),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_190,plain,
implies(or(falsehood,implies(falsehood,falsehood)),implies(falsehood,falsehood)) = truth,
inference(subst,[],[refute_0_146:[bind(X_21,$fot(implies(falsehood,falsehood)))]]) ).
cnf(refute_0_191,plain,
or(falsehood,or(falsehood,truth)) = implies(and(truth,truth),truth),
inference(subst,[],[refute_0_176:[bind(X_8,$fot(truth))]]) ).
cnf(refute_0_192,plain,
or(truth,X_8) = implies(not(truth),X_8),
inference(subst,[],[or_definition:[bind(X,$fot(truth)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_193,plain,
( not(truth) != falsehood
| or(truth,X_8) != implies(not(truth),X_8)
| or(truth,X_8) = implies(falsehood,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(truth,X_8),implies(not(truth),X_8)) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_194,plain,
( or(truth,X_8) != implies(not(truth),X_8)
| or(truth,X_8) = implies(falsehood,X_8) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_193]) ).
cnf(refute_0_195,plain,
or(truth,X_8) = implies(falsehood,X_8),
inference(resolve,[$cnf( $equal(or(truth,X_8),implies(not(truth),X_8)) )],[refute_0_192,refute_0_194]) ).
cnf(refute_0_196,plain,
or(truth,X_8) = or(X_8,truth),
inference(subst,[],[or_commutativity:[bind(X,$fot(truth)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_197,plain,
( or(truth,X_8) != implies(falsehood,X_8)
| or(truth,X_8) != or(X_8,truth)
| or(X_8,truth) = implies(falsehood,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(truth,X_8),implies(falsehood,X_8)) ),[0],$fot(or(X_8,truth))]]) ).
cnf(refute_0_198,plain,
( or(truth,X_8) != implies(falsehood,X_8)
| or(X_8,truth) = implies(falsehood,X_8) ),
inference(resolve,[$cnf( $equal(or(truth,X_8),or(X_8,truth)) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
or(X_8,truth) = implies(falsehood,X_8),
inference(resolve,[$cnf( $equal(or(truth,X_8),implies(falsehood,X_8)) )],[refute_0_195,refute_0_198]) ).
cnf(refute_0_200,plain,
or(falsehood,truth) = implies(falsehood,falsehood),
inference(subst,[],[refute_0_199:[bind(X_8,$fot(falsehood))]]) ).
cnf(refute_0_201,plain,
( or(falsehood,or(falsehood,truth)) != implies(and(truth,truth),truth)
| or(falsehood,truth) != implies(falsehood,falsehood)
| or(falsehood,implies(falsehood,falsehood)) = implies(and(truth,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(falsehood,truth)),implies(and(truth,truth),truth)) ),[0,1],$fot(implies(falsehood,falsehood))]]) ).
cnf(refute_0_202,plain,
( or(falsehood,or(falsehood,truth)) != implies(and(truth,truth),truth)
| or(falsehood,implies(falsehood,falsehood)) = implies(and(truth,truth),truth) ),
inference(resolve,[$cnf( $equal(or(falsehood,truth),implies(falsehood,falsehood)) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
or(falsehood,implies(falsehood,falsehood)) = implies(and(truth,truth),truth),
inference(resolve,[$cnf( $equal(or(falsehood,or(falsehood,truth)),implies(and(truth,truth),truth)) )],[refute_0_191,refute_0_202]) ).
cnf(refute_0_204,plain,
( implies(or(falsehood,implies(falsehood,falsehood)),implies(falsehood,falsehood)) != truth
| or(falsehood,implies(falsehood,falsehood)) != implies(and(truth,truth),truth)
| implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,implies(falsehood,falsehood)),implies(falsehood,falsehood)),truth) ),[0,0],$fot(implies(and(truth,truth),truth))]]) ).
cnf(refute_0_205,plain,
( implies(or(falsehood,implies(falsehood,falsehood)),implies(falsehood,falsehood)) != truth
| implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,implies(falsehood,falsehood)),implies(and(truth,truth),truth)) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,implies(falsehood,falsehood)),implies(falsehood,falsehood)),truth) )],[refute_0_190,refute_0_205]) ).
cnf(refute_0_207,plain,
( implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)) != truth
| implies(implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)),implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))) != truth
| implies(truth,implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)),implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_208,plain,
( implies(implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)),implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))) != truth
| implies(truth,implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)),truth) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
implies(truth,implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)),implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))),truth) )],[refute_0_189,refute_0_208]) ).
cnf(refute_0_210,plain,
implies(truth,implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))) = implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))))]]) ).
cnf(refute_0_211,plain,
( implies(truth,implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))) != implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))
| implies(truth,implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))) != truth
| implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))),truth) ),[0],$fot(implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)))]]) ).
cnf(refute_0_212,plain,
( implies(truth,implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))) != truth
| implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))),implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))),truth) )],[refute_0_209,refute_0_212]) ).
cnf(refute_0_214,plain,
implies(truth,X_26) = X_26,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_26))]]) ).
cnf(refute_0_215,plain,
implies(implies(or(falsehood,and(truth,truth)),truth),implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(or(falsehood,and(truth,truth)))),bind(Y,$fot(truth)),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_216,plain,
implies(or(X,not(or(X,falsehood))),implies(or(X,falsehood),X)) = truth,
inference(subst,[],[refute_0_123:[bind(Y,$fot(or(X,falsehood)))]]) ).
cnf(refute_0_217,plain,
implies(or(X,falsehood),X) = truth,
inference(subst,[],[refute_0_139:[bind(X_19,$fot(X))]]) ).
cnf(refute_0_218,plain,
( implies(or(X,falsehood),X) != truth
| implies(or(X,not(or(X,falsehood))),implies(or(X,falsehood),X)) != truth
| implies(or(X,not(or(X,falsehood))),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X,not(or(X,falsehood))),implies(or(X,falsehood),X)),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_219,plain,
( implies(or(X,not(or(X,falsehood))),implies(or(X,falsehood),X)) != truth
| implies(or(X,not(or(X,falsehood))),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(or(X,falsehood),X),truth) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
implies(or(X,not(or(X,falsehood))),truth) = truth,
inference(resolve,[$cnf( $equal(implies(or(X,not(or(X,falsehood))),implies(or(X,falsehood),X)),truth) )],[refute_0_216,refute_0_219]) ).
cnf(refute_0_221,plain,
implies(or(falsehood,not(or(falsehood,falsehood))),truth) = truth,
inference(subst,[],[refute_0_220:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_222,plain,
( implies(or(falsehood,not(or(falsehood,falsehood))),truth) != truth
| not(or(falsehood,falsehood)) != and(truth,truth)
| implies(or(falsehood,and(truth,truth)),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,not(or(falsehood,falsehood))),truth),truth) ),[0,0,1],$fot(and(truth,truth))]]) ).
cnf(refute_0_223,plain,
( implies(or(falsehood,not(or(falsehood,falsehood))),truth) != truth
| implies(or(falsehood,and(truth,truth)),truth) = truth ),
inference(resolve,[$cnf( $equal(not(or(falsehood,falsehood)),and(truth,truth)) )],[refute_0_75,refute_0_222]) ).
cnf(refute_0_224,plain,
implies(or(falsehood,and(truth,truth)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,not(or(falsehood,falsehood))),truth),truth) )],[refute_0_221,refute_0_223]) ).
cnf(refute_0_225,plain,
( implies(implies(or(falsehood,and(truth,truth)),truth),implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) != truth
| implies(or(falsehood,and(truth,truth)),truth) != truth
| implies(truth,implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(or(falsehood,and(truth,truth)),truth),implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_226,plain,
( implies(implies(or(falsehood,and(truth,truth)),truth),implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) != truth
| implies(truth,implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) = truth ),
inference(resolve,[$cnf( $equal(implies(or(falsehood,and(truth,truth)),truth),truth) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
implies(truth,implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(or(falsehood,and(truth,truth)),truth),implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))),truth) )],[refute_0_215,refute_0_226]) ).
cnf(refute_0_228,plain,
implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26)) = implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26)))]]) ).
cnf(refute_0_229,plain,
( implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26)) != implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))
| implies(truth,X_26) != X_26
| implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26)) = implies(X_26,implies(or(falsehood,and(truth,truth)),X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26)),implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) ),[1,0],$fot(X_26)]]) ).
cnf(refute_0_230,plain,
( implies(truth,X_26) != X_26
| implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26)) = implies(X_26,implies(or(falsehood,and(truth,truth)),X_26)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26)),implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26)) = implies(X_26,implies(or(falsehood,and(truth,truth)),X_26)),
inference(resolve,[$cnf( $equal(implies(truth,X_26),X_26) )],[refute_0_214,refute_0_230]) ).
cnf(refute_0_232,plain,
implies(truth,implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) = implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))))]]) ).
cnf(refute_0_233,plain,
( implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26)) != implies(X_26,implies(or(falsehood,and(truth,truth)),X_26))
| implies(truth,implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) != implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))
| implies(truth,implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) = implies(X_26,implies(or(falsehood,and(truth,truth)),X_26)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(truth,implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))))),bind(Y0,$fot(implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26)))),bind(Z0,$fot(implies(X_26,implies(or(falsehood,and(truth,truth)),X_26))))]]) ).
cnf(refute_0_234,plain,
( implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26)) != implies(X_26,implies(or(falsehood,and(truth,truth)),X_26))
| implies(truth,implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) = implies(X_26,implies(or(falsehood,and(truth,truth)),X_26)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))),implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
implies(truth,implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) = implies(X_26,implies(or(falsehood,and(truth,truth)),X_26)),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26)),implies(X_26,implies(or(falsehood,and(truth,truth)),X_26))) )],[refute_0_231,refute_0_234]) ).
cnf(refute_0_236,plain,
( implies(truth,implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) != implies(X_26,implies(or(falsehood,and(truth,truth)),X_26))
| implies(truth,implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) != truth
| implies(X_26,implies(or(falsehood,and(truth,truth)),X_26)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))),truth) ),[0],$fot(implies(X_26,implies(or(falsehood,and(truth,truth)),X_26)))]]) ).
cnf(refute_0_237,plain,
( implies(truth,implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))) != truth
| implies(X_26,implies(or(falsehood,and(truth,truth)),X_26)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))),implies(X_26,implies(or(falsehood,and(truth,truth)),X_26))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
implies(X_26,implies(or(falsehood,and(truth,truth)),X_26)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_26),implies(or(falsehood,and(truth,truth)),X_26))),truth) )],[refute_0_227,refute_0_237]) ).
cnf(refute_0_239,plain,
implies(and(truth,truth),implies(or(falsehood,and(truth,truth)),and(truth,truth))) = truth,
inference(subst,[],[refute_0_238:[bind(X_26,$fot(and(truth,truth)))]]) ).
cnf(refute_0_240,plain,
implies(or(falsehood,and(truth,truth)),and(truth,truth)) = truth,
inference(subst,[],[refute_0_146:[bind(X_21,$fot(and(truth,truth)))]]) ).
cnf(refute_0_241,plain,
( implies(and(truth,truth),implies(or(falsehood,and(truth,truth)),and(truth,truth))) != truth
| implies(or(falsehood,and(truth,truth)),and(truth,truth)) != truth
| implies(and(truth,truth),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(truth,truth),implies(or(falsehood,and(truth,truth)),and(truth,truth))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_242,plain,
( implies(and(truth,truth),implies(or(falsehood,and(truth,truth)),and(truth,truth))) != truth
| implies(and(truth,truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(or(falsehood,and(truth,truth)),and(truth,truth)),truth) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
implies(and(truth,truth),truth) = truth,
inference(resolve,[$cnf( $equal(implies(and(truth,truth),implies(or(falsehood,and(truth,truth)),and(truth,truth))),truth) )],[refute_0_239,refute_0_242]) ).
cnf(refute_0_244,plain,
implies(implies(and(truth,truth),truth),X_26) = implies(implies(and(truth,truth),truth),X_26),
introduced(tautology,[refl,[$fot(implies(implies(and(truth,truth),truth),X_26))]]) ).
cnf(refute_0_245,plain,
( implies(and(truth,truth),truth) != truth
| implies(implies(and(truth,truth),truth),X_26) != implies(implies(and(truth,truth),truth),X_26)
| implies(implies(and(truth,truth),truth),X_26) = implies(truth,X_26) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(truth,truth),truth),X_26),implies(implies(and(truth,truth),truth),X_26)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_246,plain,
( implies(and(truth,truth),truth) != truth
| implies(implies(and(truth,truth),truth),X_26) = implies(truth,X_26) ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,truth),truth),X_26),implies(implies(and(truth,truth),truth),X_26)) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
implies(implies(and(truth,truth),truth),X_26) = implies(truth,X_26),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),truth),truth) )],[refute_0_243,refute_0_246]) ).
cnf(refute_0_248,plain,
( implies(implies(and(truth,truth),truth),X_26) != implies(truth,X_26)
| implies(truth,X_26) != X_26
| implies(implies(and(truth,truth),truth),X_26) = X_26 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(implies(and(truth,truth),truth),X_26))),bind(Y0,$fot(implies(truth,X_26))),bind(Z0,$fot(X_26))]]) ).
cnf(refute_0_249,plain,
( implies(truth,X_26) != X_26
| implies(implies(and(truth,truth),truth),X_26) = X_26 ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,truth),truth),X_26),implies(truth,X_26)) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
implies(implies(and(truth,truth),truth),X_26) = X_26,
inference(resolve,[$cnf( $equal(implies(truth,X_26),X_26) )],[refute_0_214,refute_0_249]) ).
cnf(refute_0_251,plain,
implies(X_26,implies(implies(and(truth,truth),truth),X_26)) = implies(X_26,implies(implies(and(truth,truth),truth),X_26)),
introduced(tautology,[refl,[$fot(implies(X_26,implies(implies(and(truth,truth),truth),X_26)))]]) ).
cnf(refute_0_252,plain,
( implies(X_26,implies(implies(and(truth,truth),truth),X_26)) != implies(X_26,implies(implies(and(truth,truth),truth),X_26))
| implies(implies(and(truth,truth),truth),X_26) != X_26
| implies(X_26,implies(implies(and(truth,truth),truth),X_26)) = implies(X_26,X_26) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_26,implies(implies(and(truth,truth),truth),X_26)),implies(X_26,implies(implies(and(truth,truth),truth),X_26))) ),[1,1],$fot(X_26)]]) ).
cnf(refute_0_253,plain,
( implies(implies(and(truth,truth),truth),X_26) != X_26
| implies(X_26,implies(implies(and(truth,truth),truth),X_26)) = implies(X_26,X_26) ),
inference(resolve,[$cnf( $equal(implies(X_26,implies(implies(and(truth,truth),truth),X_26)),implies(X_26,implies(implies(and(truth,truth),truth),X_26))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
implies(X_26,implies(implies(and(truth,truth),truth),X_26)) = implies(X_26,X_26),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,truth),truth),X_26),X_26) )],[refute_0_250,refute_0_253]) ).
cnf(refute_0_255,plain,
implies(truth,implies(falsehood,falsehood)) = implies(falsehood,falsehood),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(falsehood,falsehood)))]]) ).
cnf(refute_0_256,plain,
implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)) = implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)),
introduced(tautology,[refl,[$fot(implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)))]]) ).
cnf(refute_0_257,plain,
( implies(and(truth,truth),truth) != truth
| implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)) != implies(implies(and(truth,truth),truth),implies(falsehood,falsehood))
| implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)) = implies(truth,implies(falsehood,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)),implies(implies(and(truth,truth),truth),implies(falsehood,falsehood))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_258,plain,
( implies(and(truth,truth),truth) != truth
| implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)) = implies(truth,implies(falsehood,falsehood)) ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)),implies(implies(and(truth,truth),truth),implies(falsehood,falsehood))) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)) = implies(truth,implies(falsehood,falsehood)),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),truth),truth) )],[refute_0_243,refute_0_258]) ).
cnf(refute_0_260,plain,
( implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)) != implies(truth,implies(falsehood,falsehood))
| implies(truth,implies(falsehood,falsehood)) != implies(falsehood,falsehood)
| implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)) = implies(falsehood,falsehood) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)))),bind(Y0,$fot(implies(truth,implies(falsehood,falsehood)))),bind(Z0,$fot(implies(falsehood,falsehood)))]]) ).
cnf(refute_0_261,plain,
( implies(truth,implies(falsehood,falsehood)) != implies(falsehood,falsehood)
| implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)) = implies(falsehood,falsehood) ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)),implies(truth,implies(falsehood,falsehood))) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)) = implies(falsehood,falsehood),
inference(resolve,[$cnf( $equal(implies(truth,implies(falsehood,falsehood)),implies(falsehood,falsehood)) )],[refute_0_255,refute_0_261]) ).
cnf(refute_0_263,plain,
( implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)) != implies(falsehood,falsehood)
| implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)) != truth
| implies(falsehood,falsehood) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)),truth) ),[0],$fot(implies(falsehood,falsehood))]]) ).
cnf(refute_0_264,plain,
( implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)) != truth
| implies(falsehood,falsehood) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)),implies(falsehood,falsehood)) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
implies(falsehood,falsehood) = truth,
inference(resolve,[$cnf( $equal(implies(implies(and(truth,truth),truth),implies(falsehood,falsehood)),truth) )],[refute_0_206,refute_0_264]) ).
cnf(refute_0_266,plain,
implies(implies(falsehood,falsehood),X_26) = implies(implies(falsehood,falsehood),X_26),
introduced(tautology,[refl,[$fot(implies(implies(falsehood,falsehood),X_26))]]) ).
cnf(refute_0_267,plain,
( implies(falsehood,falsehood) != truth
| implies(implies(falsehood,falsehood),X_26) != implies(implies(falsehood,falsehood),X_26)
| implies(implies(falsehood,falsehood),X_26) = implies(truth,X_26) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,falsehood),X_26),implies(implies(falsehood,falsehood),X_26)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_268,plain,
( implies(falsehood,falsehood) != truth
| implies(implies(falsehood,falsehood),X_26) = implies(truth,X_26) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,falsehood),X_26),implies(implies(falsehood,falsehood),X_26)) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
implies(implies(falsehood,falsehood),X_26) = implies(truth,X_26),
inference(resolve,[$cnf( $equal(implies(falsehood,falsehood),truth) )],[refute_0_265,refute_0_268]) ).
cnf(refute_0_270,plain,
( implies(implies(falsehood,falsehood),X_26) != implies(truth,X_26)
| implies(truth,X_26) != X_26
| implies(implies(falsehood,falsehood),X_26) = X_26 ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(implies(falsehood,falsehood),X_26))),bind(Y0,$fot(implies(truth,X_26))),bind(Z0,$fot(X_26))]]) ).
cnf(refute_0_271,plain,
( implies(truth,X_26) != X_26
| implies(implies(falsehood,falsehood),X_26) = X_26 ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,falsehood),X_26),implies(truth,X_26)) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
implies(implies(falsehood,falsehood),X_26) = X_26,
inference(resolve,[$cnf( $equal(implies(truth,X_26),X_26) )],[refute_0_214,refute_0_271]) ).
cnf(refute_0_273,plain,
implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)) = implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)),
introduced(tautology,[refl,[$fot(implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)))]]) ).
cnf(refute_0_274,plain,
( implies(implies(falsehood,falsehood),X_26) != X_26
| implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)) != implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))
| implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)) = implies(X_26,implies(implies(and(truth,truth),truth),X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)),implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))) ),[1,0],$fot(X_26)]]) ).
cnf(refute_0_275,plain,
( implies(implies(falsehood,falsehood),X_26) != X_26
| implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)) = implies(X_26,implies(implies(and(truth,truth),truth),X_26)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)),implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26))) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)) = implies(X_26,implies(implies(and(truth,truth),truth),X_26)),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,falsehood),X_26),X_26) )],[refute_0_272,refute_0_275]) ).
cnf(refute_0_277,plain,
( implies(X_26,implies(implies(and(truth,truth),truth),X_26)) != implies(X_26,X_26)
| implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)) != implies(X_26,implies(implies(and(truth,truth),truth),X_26))
| implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)) = implies(X_26,X_26) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)))),bind(Y0,$fot(implies(X_26,implies(implies(and(truth,truth),truth),X_26)))),bind(Z0,$fot(implies(X_26,X_26)))]]) ).
cnf(refute_0_278,plain,
( implies(X_26,implies(implies(and(truth,truth),truth),X_26)) != implies(X_26,X_26)
| implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)) = implies(X_26,X_26) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)),implies(X_26,implies(implies(and(truth,truth),truth),X_26))) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)) = implies(X_26,X_26),
inference(resolve,[$cnf( $equal(implies(X_26,implies(implies(and(truth,truth),truth),X_26)),implies(X_26,X_26)) )],[refute_0_254,refute_0_278]) ).
cnf(refute_0_280,plain,
( implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)) != implies(X_26,X_26)
| implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)) != truth
| implies(X_26,X_26) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)),truth) ),[0],$fot(implies(X_26,X_26))]]) ).
cnf(refute_0_281,plain,
( implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)) != truth
| implies(X_26,X_26) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)),implies(X_26,X_26)) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
implies(X_26,X_26) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(falsehood,falsehood),X_26),implies(implies(and(truth,truth),truth),X_26)),truth) )],[refute_0_213,refute_0_281]) ).
cnf(refute_0_283,plain,
implies(and(truth,truth),and(truth,truth)) = truth,
inference(subst,[],[refute_0_282:[bind(X_26,$fot(and(truth,truth)))]]) ).
cnf(refute_0_284,plain,
( implies(and(truth,or(falsehood,falsehood)),falsehood) != implies(and(truth,truth),and(truth,truth))
| implies(and(truth,truth),and(truth,truth)) != truth
| implies(and(truth,or(falsehood,falsehood)),falsehood) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(and(truth,or(falsehood,falsehood)),falsehood),truth) ),[0],$fot(implies(and(truth,truth),and(truth,truth)))]]) ).
cnf(refute_0_285,plain,
( implies(and(truth,or(falsehood,falsehood)),falsehood) != implies(and(truth,truth),and(truth,truth))
| implies(and(truth,or(falsehood,falsehood)),falsehood) = truth ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),and(truth,truth)),truth) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
implies(and(truth,or(falsehood,falsehood)),falsehood) = truth,
inference(resolve,[$cnf( $equal(implies(and(truth,or(falsehood,falsehood)),falsehood),implies(and(truth,truth),and(truth,truth))) )],[refute_0_188,refute_0_285]) ).
cnf(refute_0_287,plain,
( implies(and(truth,or(falsehood,falsehood)),falsehood) != truth
| implies(implies(and(truth,or(falsehood,falsehood)),falsehood),implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))) != truth
| implies(truth,implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(truth,or(falsehood,falsehood)),falsehood),implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_288,plain,
( implies(implies(and(truth,or(falsehood,falsehood)),falsehood),implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))) != truth
| implies(truth,implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(and(truth,or(falsehood,falsehood)),falsehood),truth) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
implies(truth,implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(and(truth,or(falsehood,falsehood)),falsehood),implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))),truth) )],[refute_0_168,refute_0_288]) ).
cnf(refute_0_290,plain,
implies(truth,implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))) = implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))))]]) ).
cnf(refute_0_291,plain,
( implies(truth,implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))) != implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))
| implies(truth,implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))) != truth
| implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))),truth) ),[0],$fot(implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)))]]) ).
cnf(refute_0_292,plain,
( implies(truth,implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))) != truth
| implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))),implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))),truth) )],[refute_0_289,refute_0_292]) ).
cnf(refute_0_294,plain,
implies(truth,implies(and(truth,or(falsehood,falsehood)),Z)) = implies(and(truth,or(falsehood,falsehood)),Z),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(and(truth,or(falsehood,falsehood)),Z)))]]) ).
cnf(refute_0_295,plain,
implies(or(truth,not(X_20)),implies(X_20,truth)) = truth,
inference(subst,[],[refute_0_123:[bind(X,$fot(truth)),bind(Y,$fot(X_20))]]) ).
cnf(refute_0_296,plain,
or(truth,not(X_20)) = implies(falsehood,not(X_20)),
inference(subst,[],[refute_0_195:[bind(X_8,$fot(not(X_20)))]]) ).
cnf(refute_0_297,plain,
( implies(or(truth,not(X_20)),implies(X_20,truth)) != truth
| or(truth,not(X_20)) != implies(falsehood,not(X_20))
| implies(implies(falsehood,not(X_20)),implies(X_20,truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(truth,not(X_20)),implies(X_20,truth)),truth) ),[0,0],$fot(implies(falsehood,not(X_20)))]]) ).
cnf(refute_0_298,plain,
( implies(or(truth,not(X_20)),implies(X_20,truth)) != truth
| implies(implies(falsehood,not(X_20)),implies(X_20,truth)) = truth ),
inference(resolve,[$cnf( $equal(or(truth,not(X_20)),implies(falsehood,not(X_20))) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
implies(implies(falsehood,not(X_20)),implies(X_20,truth)) = truth,
inference(resolve,[$cnf( $equal(implies(or(truth,not(X_20)),implies(X_20,truth)),truth) )],[refute_0_295,refute_0_298]) ).
cnf(refute_0_300,plain,
implies(implies(falsehood,not(not(X))),implies(not(X),truth)) = truth,
inference(subst,[],[refute_0_299:[bind(X_20,$fot(not(X)))]]) ).
cnf(refute_0_301,plain,
or(X,truth) = implies(not(X),truth),
inference(subst,[],[or_definition:[bind(Y,$fot(truth))]]) ).
cnf(refute_0_302,plain,
( or(X,truth) != implies(not(X),truth)
| implies(not(X),truth) = or(X,truth) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,truth))),bind(Y0,$fot(implies(not(X),truth)))]]) ).
cnf(refute_0_303,plain,
implies(not(X),truth) = or(X,truth),
inference(resolve,[$cnf( $equal(or(X,truth),implies(not(X),truth)) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
( implies(implies(falsehood,not(not(X))),implies(not(X),truth)) != truth
| implies(not(X),truth) != or(X,truth)
| implies(implies(falsehood,not(not(X))),or(X,truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,not(not(X))),implies(not(X),truth)),truth) ),[0,1],$fot(or(X,truth))]]) ).
cnf(refute_0_305,plain,
( implies(implies(falsehood,not(not(X))),implies(not(X),truth)) != truth
| implies(implies(falsehood,not(not(X))),or(X,truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X),truth),or(X,truth)) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
implies(implies(falsehood,not(not(X))),or(X,truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(not(X))),implies(not(X),truth)),truth) )],[refute_0_300,refute_0_305]) ).
cnf(refute_0_307,plain,
or(X,truth) = implies(falsehood,X),
inference(subst,[],[refute_0_199:[bind(X_8,$fot(X))]]) ).
cnf(refute_0_308,plain,
implies(implies(falsehood,not(not(X))),or(X,truth)) = implies(implies(falsehood,not(not(X))),or(X,truth)),
introduced(tautology,[refl,[$fot(implies(implies(falsehood,not(not(X))),or(X,truth)))]]) ).
cnf(refute_0_309,plain,
( implies(implies(falsehood,not(not(X))),or(X,truth)) != implies(implies(falsehood,not(not(X))),or(X,truth))
| or(X,truth) != implies(falsehood,X)
| implies(implies(falsehood,not(not(X))),or(X,truth)) = implies(implies(falsehood,not(not(X))),implies(falsehood,X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,not(not(X))),or(X,truth)),implies(implies(falsehood,not(not(X))),or(X,truth))) ),[1,1],$fot(implies(falsehood,X))]]) ).
cnf(refute_0_310,plain,
( or(X,truth) != implies(falsehood,X)
| implies(implies(falsehood,not(not(X))),or(X,truth)) = implies(implies(falsehood,not(not(X))),implies(falsehood,X)) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(not(X))),or(X,truth)),implies(implies(falsehood,not(not(X))),or(X,truth))) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
implies(implies(falsehood,not(not(X))),or(X,truth)) = implies(implies(falsehood,not(not(X))),implies(falsehood,X)),
inference(resolve,[$cnf( $equal(or(X,truth),implies(falsehood,X)) )],[refute_0_307,refute_0_310]) ).
cnf(refute_0_312,plain,
( implies(implies(falsehood,not(not(X))),or(X,truth)) != implies(implies(falsehood,not(not(X))),implies(falsehood,X))
| implies(implies(falsehood,not(not(X))),or(X,truth)) != truth
| implies(implies(falsehood,not(not(X))),implies(falsehood,X)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,not(not(X))),or(X,truth)),truth) ),[0],$fot(implies(implies(falsehood,not(not(X))),implies(falsehood,X)))]]) ).
cnf(refute_0_313,plain,
( implies(implies(falsehood,not(not(X))),or(X,truth)) != truth
| implies(implies(falsehood,not(not(X))),implies(falsehood,X)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(not(X))),or(X,truth)),implies(implies(falsehood,not(not(X))),implies(falsehood,X))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
implies(implies(falsehood,not(not(X))),implies(falsehood,X)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(not(X))),or(X,truth)),truth) )],[refute_0_306,refute_0_313]) ).
cnf(refute_0_315,plain,
implies(truth,implies(falsehood,X)) = implies(falsehood,X),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(falsehood,X)))]]) ).
cnf(refute_0_316,plain,
implies(or(falsehood,implies(falsehood,not(X_46))),implies(falsehood,not(X_46))) = truth,
inference(subst,[],[refute_0_146:[bind(X_21,$fot(implies(falsehood,not(X_46))))]]) ).
cnf(refute_0_317,plain,
or(or(falsehood,not(X_1)),X_8) = implies(not(or(falsehood,not(X_1))),X_8),
inference(subst,[],[or_definition:[bind(X,$fot(or(falsehood,not(X_1)))),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_318,plain,
( not(or(falsehood,not(X_1))) != and(X_1,truth)
| or(or(falsehood,not(X_1)),X_8) != implies(not(or(falsehood,not(X_1))),X_8)
| or(or(falsehood,not(X_1)),X_8) = implies(and(X_1,truth),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(falsehood,not(X_1)),X_8),implies(not(or(falsehood,not(X_1))),X_8)) ),[1,0],$fot(and(X_1,truth))]]) ).
cnf(refute_0_319,plain,
( or(or(falsehood,not(X_1)),X_8) != implies(not(or(falsehood,not(X_1))),X_8)
| or(or(falsehood,not(X_1)),X_8) = implies(and(X_1,truth),X_8) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_1))),and(X_1,truth)) )],[refute_0_45,refute_0_318]) ).
cnf(refute_0_320,plain,
or(or(falsehood,not(X_1)),X_8) = implies(and(X_1,truth),X_8),
inference(resolve,[$cnf( $equal(or(or(falsehood,not(X_1)),X_8),implies(not(or(falsehood,not(X_1))),X_8)) )],[refute_0_317,refute_0_319]) ).
cnf(refute_0_321,plain,
or(or(falsehood,not(X_1)),X_8) = or(falsehood,or(not(X_1),X_8)),
inference(subst,[],[or_associativity:[bind(X,$fot(falsehood)),bind(Y,$fot(not(X_1))),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_322,plain,
( or(or(falsehood,not(X_1)),X_8) != implies(and(X_1,truth),X_8)
| or(or(falsehood,not(X_1)),X_8) != or(falsehood,or(not(X_1),X_8))
| or(falsehood,or(not(X_1),X_8)) = implies(and(X_1,truth),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(falsehood,not(X_1)),X_8),implies(and(X_1,truth),X_8)) ),[0],$fot(or(falsehood,or(not(X_1),X_8)))]]) ).
cnf(refute_0_323,plain,
( or(or(falsehood,not(X_1)),X_8) != implies(and(X_1,truth),X_8)
| or(falsehood,or(not(X_1),X_8)) = implies(and(X_1,truth),X_8) ),
inference(resolve,[$cnf( $equal(or(or(falsehood,not(X_1)),X_8),or(falsehood,or(not(X_1),X_8))) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
or(falsehood,or(not(X_1),X_8)) = implies(and(X_1,truth),X_8),
inference(resolve,[$cnf( $equal(or(or(falsehood,not(X_1)),X_8),implies(and(X_1,truth),X_8)) )],[refute_0_320,refute_0_323]) ).
cnf(refute_0_325,plain,
or(falsehood,or(not(X_34),truth)) = implies(and(X_34,truth),truth),
inference(subst,[],[refute_0_324:[bind(X_1,$fot(X_34)),bind(X_8,$fot(truth))]]) ).
cnf(refute_0_326,plain,
or(not(X_34),truth) = implies(falsehood,not(X_34)),
inference(subst,[],[refute_0_199:[bind(X_8,$fot(not(X_34)))]]) ).
cnf(refute_0_327,plain,
( or(falsehood,or(not(X_34),truth)) != implies(and(X_34,truth),truth)
| or(not(X_34),truth) != implies(falsehood,not(X_34))
| or(falsehood,implies(falsehood,not(X_34))) = implies(and(X_34,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(not(X_34),truth)),implies(and(X_34,truth),truth)) ),[0,1],$fot(implies(falsehood,not(X_34)))]]) ).
cnf(refute_0_328,plain,
( or(falsehood,or(not(X_34),truth)) != implies(and(X_34,truth),truth)
| or(falsehood,implies(falsehood,not(X_34))) = implies(and(X_34,truth),truth) ),
inference(resolve,[$cnf( $equal(or(not(X_34),truth),implies(falsehood,not(X_34))) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
or(falsehood,implies(falsehood,not(X_34))) = implies(and(X_34,truth),truth),
inference(resolve,[$cnf( $equal(or(falsehood,or(not(X_34),truth)),implies(and(X_34,truth),truth)) )],[refute_0_325,refute_0_328]) ).
cnf(refute_0_330,plain,
or(falsehood,implies(falsehood,not(X_46))) = implies(and(X_46,truth),truth),
inference(subst,[],[refute_0_329:[bind(X_34,$fot(X_46))]]) ).
cnf(refute_0_331,plain,
( implies(or(falsehood,implies(falsehood,not(X_46))),implies(falsehood,not(X_46))) != truth
| or(falsehood,implies(falsehood,not(X_46))) != implies(and(X_46,truth),truth)
| implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,implies(falsehood,not(X_46))),implies(falsehood,not(X_46))),truth) ),[0,0],$fot(implies(and(X_46,truth),truth))]]) ).
cnf(refute_0_332,plain,
( implies(or(falsehood,implies(falsehood,not(X_46))),implies(falsehood,not(X_46))) != truth
| implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,implies(falsehood,not(X_46))),implies(and(X_46,truth),truth)) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,implies(falsehood,not(X_46))),implies(falsehood,not(X_46))),truth) )],[refute_0_316,refute_0_332]) ).
cnf(refute_0_334,plain,
implies(truth,implies(falsehood,not(X_46))) = implies(falsehood,not(X_46)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(falsehood,not(X_46))))]]) ).
cnf(refute_0_335,plain,
implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),truth))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))))),bind(Z,$fot(truth))]]) ).
cnf(refute_0_336,plain,
implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),implies(implies(and(truth,or(falsehood,falsehood)),truth),implies(falsehood,and(truth,truth)))) = truth,
inference(subst,[],[refute_0_123:[bind(X,$fot(implies(falsehood,and(truth,truth)))),bind(Y,$fot(implies(and(truth,or(falsehood,falsehood)),truth)))]]) ).
cnf(refute_0_337,plain,
implies(or(falsehood,implies(falsehood,and(truth,truth))),implies(falsehood,and(truth,truth))) = truth,
inference(subst,[],[refute_0_146:[bind(X_21,$fot(implies(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_338,plain,
or(falsehood,or(and(truth,truth),truth)) = implies(and(truth,or(falsehood,falsehood)),truth),
inference(subst,[],[refute_0_155:[bind(X_8,$fot(truth))]]) ).
cnf(refute_0_339,plain,
or(and(truth,truth),truth) = implies(falsehood,and(truth,truth)),
inference(subst,[],[refute_0_199:[bind(X_8,$fot(and(truth,truth)))]]) ).
cnf(refute_0_340,plain,
( or(and(truth,truth),truth) != implies(falsehood,and(truth,truth))
| or(falsehood,or(and(truth,truth),truth)) != implies(and(truth,or(falsehood,falsehood)),truth)
| or(falsehood,implies(falsehood,and(truth,truth))) = implies(and(truth,or(falsehood,falsehood)),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(and(truth,truth),truth)),implies(and(truth,or(falsehood,falsehood)),truth)) ),[0,1],$fot(implies(falsehood,and(truth,truth)))]]) ).
cnf(refute_0_341,plain,
( or(falsehood,or(and(truth,truth),truth)) != implies(and(truth,or(falsehood,falsehood)),truth)
| or(falsehood,implies(falsehood,and(truth,truth))) = implies(and(truth,or(falsehood,falsehood)),truth) ),
inference(resolve,[$cnf( $equal(or(and(truth,truth),truth),implies(falsehood,and(truth,truth))) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
or(falsehood,implies(falsehood,and(truth,truth))) = implies(and(truth,or(falsehood,falsehood)),truth),
inference(resolve,[$cnf( $equal(or(falsehood,or(and(truth,truth),truth)),implies(and(truth,or(falsehood,falsehood)),truth)) )],[refute_0_338,refute_0_341]) ).
cnf(refute_0_343,plain,
( implies(or(falsehood,implies(falsehood,and(truth,truth))),implies(falsehood,and(truth,truth))) != truth
| or(falsehood,implies(falsehood,and(truth,truth))) != implies(and(truth,or(falsehood,falsehood)),truth)
| implies(implies(and(truth,or(falsehood,falsehood)),truth),implies(falsehood,and(truth,truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,implies(falsehood,and(truth,truth))),implies(falsehood,and(truth,truth))),truth) ),[0,0],$fot(implies(and(truth,or(falsehood,falsehood)),truth))]]) ).
cnf(refute_0_344,plain,
( implies(or(falsehood,implies(falsehood,and(truth,truth))),implies(falsehood,and(truth,truth))) != truth
| implies(implies(and(truth,or(falsehood,falsehood)),truth),implies(falsehood,and(truth,truth))) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,implies(falsehood,and(truth,truth))),implies(and(truth,or(falsehood,falsehood)),truth)) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
implies(implies(and(truth,or(falsehood,falsehood)),truth),implies(falsehood,and(truth,truth))) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,implies(falsehood,and(truth,truth))),implies(falsehood,and(truth,truth))),truth) )],[refute_0_337,refute_0_344]) ).
cnf(refute_0_346,plain,
( implies(implies(and(truth,or(falsehood,falsehood)),truth),implies(falsehood,and(truth,truth))) != truth
| implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),implies(implies(and(truth,or(falsehood,falsehood)),truth),implies(falsehood,and(truth,truth)))) != truth
| implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),implies(implies(and(truth,or(falsehood,falsehood)),truth),implies(falsehood,and(truth,truth)))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_347,plain,
( implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),implies(implies(and(truth,or(falsehood,falsehood)),truth),implies(falsehood,and(truth,truth)))) != truth
| implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,or(falsehood,falsehood)),truth),implies(falsehood,and(truth,truth))),truth) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),truth) = truth,
inference(resolve,[$cnf( $equal(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),implies(implies(and(truth,or(falsehood,falsehood)),truth),implies(falsehood,and(truth,truth)))),truth) )],[refute_0_336,refute_0_347]) ).
cnf(refute_0_349,plain,
( implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),truth))) != truth
| implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),truth) != truth
| implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),truth))),truth) ),[0,1,1],$fot(truth)]]) ).
cnf(refute_0_350,plain,
( implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),truth))) != truth
| implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),truth),truth) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),truth))),truth) )],[refute_0_335,refute_0_350]) ).
cnf(refute_0_352,plain,
or(falsehood,implies(falsehood,not(or(not(X),not(Y))))) = implies(and(or(not(X),not(Y)),truth),truth),
inference(subst,[],[refute_0_329:[bind(X_34,$fot(or(not(X),not(Y))))]]) ).
cnf(refute_0_353,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(or(not(X),not(Y)))))]]) ).
cnf(refute_0_354,plain,
not(or(not(X),not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[and_definition,refute_0_353]) ).
cnf(refute_0_355,plain,
( not(or(not(X),not(Y))) != and(X,Y)
| or(falsehood,implies(falsehood,not(or(not(X),not(Y))))) != implies(and(or(not(X),not(Y)),truth),truth)
| or(falsehood,implies(falsehood,and(X,Y))) = implies(and(or(not(X),not(Y)),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,implies(falsehood,not(or(not(X),not(Y))))),implies(and(or(not(X),not(Y)),truth),truth)) ),[0,1,1],$fot(and(X,Y))]]) ).
cnf(refute_0_356,plain,
( or(falsehood,implies(falsehood,not(or(not(X),not(Y))))) != implies(and(or(not(X),not(Y)),truth),truth)
| or(falsehood,implies(falsehood,and(X,Y))) = implies(and(or(not(X),not(Y)),truth),truth) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),and(X,Y)) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
or(falsehood,implies(falsehood,and(X,Y))) = implies(and(or(not(X),not(Y)),truth),truth),
inference(resolve,[$cnf( $equal(or(falsehood,implies(falsehood,not(or(not(X),not(Y))))),implies(and(or(not(X),not(Y)),truth),truth)) )],[refute_0_352,refute_0_356]) ).
cnf(refute_0_358,plain,
or(or(falsehood,and(X,Y)),truth) = implies(falsehood,or(falsehood,and(X,Y))),
inference(subst,[],[refute_0_199:[bind(X_8,$fot(or(falsehood,and(X,Y))))]]) ).
cnf(refute_0_359,plain,
implies(not(or(falsehood,and(X,Y))),truth) = or(or(falsehood,and(X,Y)),truth),
inference(subst,[],[refute_0_115:[bind(X,$fot(or(falsehood,and(X,Y)))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_360,plain,
( implies(not(or(falsehood,and(X,Y))),truth) != or(or(falsehood,and(X,Y)),truth)
| or(or(falsehood,and(X,Y)),truth) != implies(falsehood,or(falsehood,and(X,Y)))
| implies(not(or(falsehood,and(X,Y))),truth) = implies(falsehood,or(falsehood,and(X,Y))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(not(or(falsehood,and(X,Y))),truth))),bind(Y0,$fot(or(or(falsehood,and(X,Y)),truth))),bind(Z0,$fot(implies(falsehood,or(falsehood,and(X,Y)))))]]) ).
cnf(refute_0_361,plain,
( or(or(falsehood,and(X,Y)),truth) != implies(falsehood,or(falsehood,and(X,Y)))
| implies(not(or(falsehood,and(X,Y))),truth) = implies(falsehood,or(falsehood,and(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(not(or(falsehood,and(X,Y))),truth),or(or(falsehood,and(X,Y)),truth)) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
implies(not(or(falsehood,and(X,Y))),truth) = implies(falsehood,or(falsehood,and(X,Y))),
inference(resolve,[$cnf( $equal(or(or(falsehood,and(X,Y)),truth),implies(falsehood,or(falsehood,and(X,Y)))) )],[refute_0_358,refute_0_361]) ).
cnf(refute_0_363,plain,
or(not(truth),and(X,Y)) = or(not(truth),and(X,Y)),
introduced(tautology,[refl,[$fot(or(not(truth),and(X,Y)))]]) ).
cnf(refute_0_364,plain,
( not(truth) != falsehood
| or(not(truth),and(X,Y)) != or(not(truth),and(X,Y))
| or(not(truth),and(X,Y)) = or(falsehood,and(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(truth),and(X,Y)),or(not(truth),and(X,Y))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_365,plain,
( not(truth) != falsehood
| or(not(truth),and(X,Y)) = or(falsehood,and(X,Y)) ),
inference(resolve,[$cnf( $equal(or(not(truth),and(X,Y)),or(not(truth),and(X,Y))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
or(not(truth),and(X,Y)) = or(falsehood,and(X,Y)),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_365]) ).
cnf(refute_0_367,plain,
not(or(not(truth),and(X,Y))) = not(or(not(truth),and(X,Y))),
introduced(tautology,[refl,[$fot(not(or(not(truth),and(X,Y))))]]) ).
cnf(refute_0_368,plain,
( not(or(not(truth),and(X,Y))) != not(or(not(truth),and(X,Y)))
| or(not(truth),and(X,Y)) != or(falsehood,and(X,Y))
| not(or(not(truth),and(X,Y))) = not(or(falsehood,and(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(truth),and(X,Y))),not(or(not(truth),and(X,Y)))) ),[1,0],$fot(or(falsehood,and(X,Y)))]]) ).
cnf(refute_0_369,plain,
( or(not(truth),and(X,Y)) != or(falsehood,and(X,Y))
| not(or(not(truth),and(X,Y))) = not(or(falsehood,and(X,Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(truth),and(X,Y))),not(or(not(truth),and(X,Y)))) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
not(or(not(truth),and(X,Y))) = not(or(falsehood,and(X,Y))),
inference(resolve,[$cnf( $equal(or(not(truth),and(X,Y)),or(falsehood,and(X,Y))) )],[refute_0_366,refute_0_369]) ).
cnf(refute_0_371,plain,
and(X,or(not(X_1),not(X_2))) = not(or(not(X),not(or(not(X_1),not(X_2))))),
inference(subst,[],[and_definition:[bind(Y,$fot(or(not(X_1),not(X_2))))]]) ).
cnf(refute_0_372,plain,
and(X_1,X_2) = not(or(not(X_1),not(X_2))),
inference(subst,[],[and_definition:[bind(X,$fot(X_1)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_373,plain,
( and(X_1,X_2) != not(or(not(X_1),not(X_2)))
| not(or(not(X_1),not(X_2))) = and(X_1,X_2) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_1,X_2))),bind(Y0,$fot(not(or(not(X_1),not(X_2)))))]]) ).
cnf(refute_0_374,plain,
not(or(not(X_1),not(X_2))) = and(X_1,X_2),
inference(resolve,[$cnf( $equal(and(X_1,X_2),not(or(not(X_1),not(X_2)))) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
( and(X,or(not(X_1),not(X_2))) != not(or(not(X),not(or(not(X_1),not(X_2)))))
| not(or(not(X_1),not(X_2))) != and(X_1,X_2)
| and(X,or(not(X_1),not(X_2))) = not(or(not(X),and(X_1,X_2))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,or(not(X_1),not(X_2))),not(or(not(X),not(or(not(X_1),not(X_2)))))) ),[1,0,1],$fot(and(X_1,X_2))]]) ).
cnf(refute_0_376,plain,
( and(X,or(not(X_1),not(X_2))) != not(or(not(X),not(or(not(X_1),not(X_2)))))
| and(X,or(not(X_1),not(X_2))) = not(or(not(X),and(X_1,X_2))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_1),not(X_2))),and(X_1,X_2)) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
and(X,or(not(X_1),not(X_2))) = not(or(not(X),and(X_1,X_2))),
inference(resolve,[$cnf( $equal(and(X,or(not(X_1),not(X_2))),not(or(not(X),not(or(not(X_1),not(X_2)))))) )],[refute_0_371,refute_0_376]) ).
cnf(refute_0_378,plain,
and(truth,or(not(X),not(Y))) = not(or(not(truth),and(X,Y))),
inference(subst,[],[refute_0_377:[bind(X,$fot(truth)),bind(X_1,$fot(X)),bind(X_2,$fot(Y))]]) ).
cnf(refute_0_379,plain,
( and(truth,or(not(X),not(Y))) != not(or(not(truth),and(X,Y)))
| not(or(not(truth),and(X,Y))) != not(or(falsehood,and(X,Y)))
| and(truth,or(not(X),not(Y))) = not(or(falsehood,and(X,Y))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(and(truth,or(not(X),not(Y))))),bind(Y0,$fot(not(or(not(truth),and(X,Y))))),bind(Z0,$fot(not(or(falsehood,and(X,Y)))))]]) ).
cnf(refute_0_380,plain,
( not(or(not(truth),and(X,Y))) != not(or(falsehood,and(X,Y)))
| and(truth,or(not(X),not(Y))) = not(or(falsehood,and(X,Y))) ),
inference(resolve,[$cnf( $equal(and(truth,or(not(X),not(Y))),not(or(not(truth),and(X,Y)))) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
and(truth,or(not(X),not(Y))) = not(or(falsehood,and(X,Y))),
inference(resolve,[$cnf( $equal(not(or(not(truth),and(X,Y))),not(or(falsehood,and(X,Y)))) )],[refute_0_370,refute_0_380]) ).
cnf(refute_0_382,plain,
implies(and(truth,or(not(X),not(Y))),truth) = implies(and(truth,or(not(X),not(Y))),truth),
introduced(tautology,[refl,[$fot(implies(and(truth,or(not(X),not(Y))),truth))]]) ).
cnf(refute_0_383,plain,
( and(truth,or(not(X),not(Y))) != not(or(falsehood,and(X,Y)))
| implies(and(truth,or(not(X),not(Y))),truth) != implies(and(truth,or(not(X),not(Y))),truth)
| implies(and(truth,or(not(X),not(Y))),truth) = implies(not(or(falsehood,and(X,Y))),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(truth,or(not(X),not(Y))),truth),implies(and(truth,or(not(X),not(Y))),truth)) ),[1,0],$fot(not(or(falsehood,and(X,Y))))]]) ).
cnf(refute_0_384,plain,
( and(truth,or(not(X),not(Y))) != not(or(falsehood,and(X,Y)))
| implies(and(truth,or(not(X),not(Y))),truth) = implies(not(or(falsehood,and(X,Y))),truth) ),
inference(resolve,[$cnf( $equal(implies(and(truth,or(not(X),not(Y))),truth),implies(and(truth,or(not(X),not(Y))),truth)) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
implies(and(truth,or(not(X),not(Y))),truth) = implies(not(or(falsehood,and(X,Y))),truth),
inference(resolve,[$cnf( $equal(and(truth,or(not(X),not(Y))),not(or(falsehood,and(X,Y)))) )],[refute_0_381,refute_0_384]) ).
cnf(refute_0_386,plain,
( implies(and(truth,or(not(X),not(Y))),truth) != implies(not(or(falsehood,and(X,Y))),truth)
| implies(not(or(falsehood,and(X,Y))),truth) != implies(falsehood,or(falsehood,and(X,Y)))
| implies(and(truth,or(not(X),not(Y))),truth) = implies(falsehood,or(falsehood,and(X,Y))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(and(truth,or(not(X),not(Y))),truth))),bind(Y0,$fot(implies(not(or(falsehood,and(X,Y))),truth))),bind(Z0,$fot(implies(falsehood,or(falsehood,and(X,Y)))))]]) ).
cnf(refute_0_387,plain,
( implies(not(or(falsehood,and(X,Y))),truth) != implies(falsehood,or(falsehood,and(X,Y)))
| implies(and(truth,or(not(X),not(Y))),truth) = implies(falsehood,or(falsehood,and(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(and(truth,or(not(X),not(Y))),truth),implies(not(or(falsehood,and(X,Y))),truth)) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
implies(and(truth,or(not(X),not(Y))),truth) = implies(falsehood,or(falsehood,and(X,Y))),
inference(resolve,[$cnf( $equal(implies(not(or(falsehood,and(X,Y))),truth),implies(falsehood,or(falsehood,and(X,Y)))) )],[refute_0_362,refute_0_387]) ).
cnf(refute_0_389,plain,
or(falsehood,or(not(X_34),X_35)) = implies(and(X_34,truth),X_35),
inference(subst,[],[refute_0_324:[bind(X_1,$fot(X_34)),bind(X_8,$fot(X_35))]]) ).
cnf(refute_0_390,plain,
and(truth,X_34) = and(X_34,truth),
inference(subst,[],[and_commutativity:[bind(X,$fot(truth)),bind(Y,$fot(X_34))]]) ).
cnf(refute_0_391,plain,
( and(truth,X_34) != and(X_34,truth)
| and(X_34,truth) = and(truth,X_34) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,X_34))),bind(Y0,$fot(and(X_34,truth)))]]) ).
cnf(refute_0_392,plain,
and(X_34,truth) = and(truth,X_34),
inference(resolve,[$cnf( $equal(and(truth,X_34),and(X_34,truth)) )],[refute_0_390,refute_0_391]) ).
cnf(refute_0_393,plain,
( and(X_34,truth) != and(truth,X_34)
| or(falsehood,or(not(X_34),X_35)) != implies(and(X_34,truth),X_35)
| or(falsehood,or(not(X_34),X_35)) = implies(and(truth,X_34),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(not(X_34),X_35)),implies(and(X_34,truth),X_35)) ),[1,0],$fot(and(truth,X_34))]]) ).
cnf(refute_0_394,plain,
( or(falsehood,or(not(X_34),X_35)) != implies(and(X_34,truth),X_35)
| or(falsehood,or(not(X_34),X_35)) = implies(and(truth,X_34),X_35) ),
inference(resolve,[$cnf( $equal(and(X_34,truth),and(truth,X_34)) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
or(falsehood,or(not(X_34),X_35)) = implies(and(truth,X_34),X_35),
inference(resolve,[$cnf( $equal(or(falsehood,or(not(X_34),X_35)),implies(and(X_34,truth),X_35)) )],[refute_0_389,refute_0_394]) ).
cnf(refute_0_396,plain,
( or(falsehood,or(not(X_34),X_35)) != implies(and(X_34,truth),X_35)
| or(falsehood,or(not(X_34),X_35)) != implies(and(truth,X_34),X_35)
| implies(and(X_34,truth),X_35) = implies(and(truth,X_34),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(not(X_34),X_35)),implies(and(truth,X_34),X_35)) ),[0],$fot(implies(and(X_34,truth),X_35))]]) ).
cnf(refute_0_397,plain,
( or(falsehood,or(not(X_34),X_35)) != implies(and(truth,X_34),X_35)
| implies(and(X_34,truth),X_35) = implies(and(truth,X_34),X_35) ),
inference(resolve,[$cnf( $equal(or(falsehood,or(not(X_34),X_35)),implies(and(X_34,truth),X_35)) )],[refute_0_389,refute_0_396]) ).
cnf(refute_0_398,plain,
implies(and(X_34,truth),X_35) = implies(and(truth,X_34),X_35),
inference(resolve,[$cnf( $equal(or(falsehood,or(not(X_34),X_35)),implies(and(truth,X_34),X_35)) )],[refute_0_395,refute_0_397]) ).
cnf(refute_0_399,plain,
implies(and(or(not(X),not(Y)),truth),truth) = implies(and(truth,or(not(X),not(Y))),truth),
inference(subst,[],[refute_0_398:[bind(X_34,$fot(or(not(X),not(Y)))),bind(X_35,$fot(truth))]]) ).
cnf(refute_0_400,plain,
( implies(and(or(not(X),not(Y)),truth),truth) != implies(and(truth,or(not(X),not(Y))),truth)
| implies(and(truth,or(not(X),not(Y))),truth) != implies(falsehood,or(falsehood,and(X,Y)))
| implies(and(or(not(X),not(Y)),truth),truth) = implies(falsehood,or(falsehood,and(X,Y))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(and(or(not(X),not(Y)),truth),truth))),bind(Y0,$fot(implies(and(truth,or(not(X),not(Y))),truth))),bind(Z0,$fot(implies(falsehood,or(falsehood,and(X,Y)))))]]) ).
cnf(refute_0_401,plain,
( implies(and(truth,or(not(X),not(Y))),truth) != implies(falsehood,or(falsehood,and(X,Y)))
| implies(and(or(not(X),not(Y)),truth),truth) = implies(falsehood,or(falsehood,and(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(and(or(not(X),not(Y)),truth),truth),implies(and(truth,or(not(X),not(Y))),truth)) )],[refute_0_399,refute_0_400]) ).
cnf(refute_0_402,plain,
implies(and(or(not(X),not(Y)),truth),truth) = implies(falsehood,or(falsehood,and(X,Y))),
inference(resolve,[$cnf( $equal(implies(and(truth,or(not(X),not(Y))),truth),implies(falsehood,or(falsehood,and(X,Y)))) )],[refute_0_388,refute_0_401]) ).
cnf(refute_0_403,plain,
( implies(and(or(not(X),not(Y)),truth),truth) != implies(falsehood,or(falsehood,and(X,Y)))
| or(falsehood,implies(falsehood,and(X,Y))) != implies(and(or(not(X),not(Y)),truth),truth)
| or(falsehood,implies(falsehood,and(X,Y))) = implies(falsehood,or(falsehood,and(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,implies(falsehood,and(X,Y))),implies(and(or(not(X),not(Y)),truth),truth)) ),[1],$fot(implies(falsehood,or(falsehood,and(X,Y))))]]) ).
cnf(refute_0_404,plain,
( or(falsehood,implies(falsehood,and(X,Y))) != implies(and(or(not(X),not(Y)),truth),truth)
| or(falsehood,implies(falsehood,and(X,Y))) = implies(falsehood,or(falsehood,and(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(and(or(not(X),not(Y)),truth),truth),implies(falsehood,or(falsehood,and(X,Y)))) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
or(falsehood,implies(falsehood,and(X,Y))) = implies(falsehood,or(falsehood,and(X,Y))),
inference(resolve,[$cnf( $equal(or(falsehood,implies(falsehood,and(X,Y))),implies(and(or(not(X),not(Y)),truth),truth)) )],[refute_0_357,refute_0_404]) ).
cnf(refute_0_406,plain,
or(falsehood,implies(falsehood,and(truth,truth))) = implies(falsehood,or(falsehood,and(truth,truth))),
inference(subst,[],[refute_0_405:[bind(X,$fot(truth)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_407,plain,
( or(falsehood,implies(falsehood,and(truth,truth))) != implies(and(truth,or(falsehood,falsehood)),truth)
| or(falsehood,implies(falsehood,and(truth,truth))) != implies(falsehood,or(falsehood,and(truth,truth)))
| implies(falsehood,or(falsehood,and(truth,truth))) = implies(and(truth,or(falsehood,falsehood)),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,implies(falsehood,and(truth,truth))),implies(and(truth,or(falsehood,falsehood)),truth)) ),[0],$fot(implies(falsehood,or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_408,plain,
( or(falsehood,implies(falsehood,and(truth,truth))) != implies(and(truth,or(falsehood,falsehood)),truth)
| implies(falsehood,or(falsehood,and(truth,truth))) = implies(and(truth,or(falsehood,falsehood)),truth) ),
inference(resolve,[$cnf( $equal(or(falsehood,implies(falsehood,and(truth,truth))),implies(falsehood,or(falsehood,and(truth,truth)))) )],[refute_0_406,refute_0_407]) ).
cnf(refute_0_409,plain,
implies(falsehood,or(falsehood,and(truth,truth))) = implies(and(truth,or(falsehood,falsehood)),truth),
inference(resolve,[$cnf( $equal(or(falsehood,implies(falsehood,and(truth,truth))),implies(and(truth,or(falsehood,falsehood)),truth)) )],[refute_0_342,refute_0_408]) ).
cnf(refute_0_410,plain,
( implies(falsehood,or(falsehood,and(truth,truth))) != implies(and(truth,or(falsehood,falsehood)),truth)
| implies(and(truth,or(falsehood,falsehood)),truth) = implies(falsehood,or(falsehood,and(truth,truth))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(falsehood,or(falsehood,and(truth,truth))))),bind(Y0,$fot(implies(and(truth,or(falsehood,falsehood)),truth)))]]) ).
cnf(refute_0_411,plain,
implies(and(truth,or(falsehood,falsehood)),truth) = implies(falsehood,or(falsehood,and(truth,truth))),
inference(resolve,[$cnf( $equal(implies(falsehood,or(falsehood,and(truth,truth))),implies(and(truth,or(falsehood,falsehood)),truth)) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
not(implies(and(truth,or(falsehood,falsehood)),truth)) = not(implies(and(truth,or(falsehood,falsehood)),truth)),
introduced(tautology,[refl,[$fot(not(implies(and(truth,or(falsehood,falsehood)),truth)))]]) ).
cnf(refute_0_413,plain,
( implies(and(truth,or(falsehood,falsehood)),truth) != implies(falsehood,or(falsehood,and(truth,truth)))
| not(implies(and(truth,or(falsehood,falsehood)),truth)) != not(implies(and(truth,or(falsehood,falsehood)),truth))
| not(implies(and(truth,or(falsehood,falsehood)),truth)) = not(implies(falsehood,or(falsehood,and(truth,truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(and(truth,or(falsehood,falsehood)),truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))) ),[1,0],$fot(implies(falsehood,or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_414,plain,
( implies(and(truth,or(falsehood,falsehood)),truth) != implies(falsehood,or(falsehood,and(truth,truth)))
| not(implies(and(truth,or(falsehood,falsehood)),truth)) = not(implies(falsehood,or(falsehood,and(truth,truth)))) ),
inference(resolve,[$cnf( $equal(not(implies(and(truth,or(falsehood,falsehood)),truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))) )],[refute_0_412,refute_0_413]) ).
cnf(refute_0_415,plain,
not(implies(and(truth,or(falsehood,falsehood)),truth)) = not(implies(falsehood,or(falsehood,and(truth,truth)))),
inference(resolve,[$cnf( $equal(implies(and(truth,or(falsehood,falsehood)),truth),implies(falsehood,or(falsehood,and(truth,truth)))) )],[refute_0_411,refute_0_414]) ).
cnf(refute_0_416,plain,
or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))) = or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),
introduced(tautology,[refl,[$fot(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))))]]) ).
cnf(refute_0_417,plain,
( not(implies(and(truth,or(falsehood,falsehood)),truth)) != not(implies(falsehood,or(falsehood,and(truth,truth))))
| or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))) != or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth)))
| or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))) = or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth)))) ),[1,1],$fot(not(implies(falsehood,or(falsehood,and(truth,truth)))))]]) ).
cnf(refute_0_418,plain,
( not(implies(and(truth,or(falsehood,falsehood)),truth)) != not(implies(falsehood,or(falsehood,and(truth,truth))))
| or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))) = or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))) ),
inference(resolve,[$cnf( $equal(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth)))) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))) = or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),
inference(resolve,[$cnf( $equal(not(implies(and(truth,or(falsehood,falsehood)),truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))) )],[refute_0_415,refute_0_418]) ).
cnf(refute_0_420,plain,
implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y) = implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),
introduced(tautology,[refl,[$fot(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y))]]) ).
cnf(refute_0_421,plain,
( implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y) != implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y)
| or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))) != or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth)))))
| implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y) = implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y)) ),[1,0],$fot(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))))]]) ).
cnf(refute_0_422,plain,
( or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))) != or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth)))))
| implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y) = implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y) ),
inference(resolve,[$cnf( $equal(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y)) )],[refute_0_420,refute_0_421]) ).
cnf(refute_0_423,plain,
implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y) = implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),
inference(resolve,[$cnf( $equal(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth)))))) )],[refute_0_419,refute_0_422]) ).
cnf(refute_0_424,plain,
implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)) = implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)),
introduced(tautology,[refl,[$fot(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)))]]) ).
cnf(refute_0_425,plain,
( implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)) != implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth))
| implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y) != implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y)
| implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)) = implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)),implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth))) ),[1,0],$fot(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y))]]) ).
cnf(refute_0_426,plain,
( implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y) != implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y)
| implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)) = implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)),implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth))) )],[refute_0_424,refute_0_425]) ).
cnf(refute_0_427,plain,
implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)) = implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)),
inference(resolve,[$cnf( $equal(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y)) )],[refute_0_423,refute_0_426]) ).
cnf(refute_0_428,plain,
( implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)) != implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth))
| implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)) != truth
| implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)),truth) ),[0],$fot(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)))]]) ).
cnf(refute_0_429,plain,
( implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)) != truth
| implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)),implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth))) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(and(truth,or(falsehood,falsehood)),truth))),Y),implies(implies(Y,truth),truth)),truth) )],[refute_0_351,refute_0_429]) ).
cnf(refute_0_431,plain,
implies(implies(truth,X_49),X_49) = implies(implies(X_49,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_49))]]) ).
cnf(refute_0_432,plain,
implies(truth,X_49) = X_49,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_49))]]) ).
cnf(refute_0_433,plain,
( implies(implies(truth,X_49),X_49) != implies(implies(X_49,truth),truth)
| implies(truth,X_49) != X_49
| implies(X_49,X_49) = implies(implies(X_49,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_49),X_49),implies(implies(X_49,truth),truth)) ),[0,0],$fot(X_49)]]) ).
cnf(refute_0_434,plain,
( implies(implies(truth,X_49),X_49) != implies(implies(X_49,truth),truth)
| implies(X_49,X_49) = implies(implies(X_49,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(truth,X_49),X_49) )],[refute_0_432,refute_0_433]) ).
cnf(refute_0_435,plain,
implies(X_49,X_49) = implies(implies(X_49,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_49),X_49),implies(implies(X_49,truth),truth)) )],[refute_0_431,refute_0_434]) ).
cnf(refute_0_436,plain,
implies(X_49,X_49) = truth,
inference(subst,[],[refute_0_282:[bind(X_26,$fot(X_49))]]) ).
cnf(refute_0_437,plain,
( implies(X_49,X_49) != implies(implies(X_49,truth),truth)
| implies(X_49,X_49) != truth
| truth = implies(implies(X_49,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_49,X_49),implies(implies(X_49,truth),truth)) ),[0],$fot(truth)]]) ).
cnf(refute_0_438,plain,
( implies(X_49,X_49) != implies(implies(X_49,truth),truth)
| truth = implies(implies(X_49,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(X_49,X_49),truth) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
truth = implies(implies(X_49,truth),truth),
inference(resolve,[$cnf( $equal(implies(X_49,X_49),implies(implies(X_49,truth),truth)) )],[refute_0_435,refute_0_438]) ).
cnf(refute_0_440,plain,
( truth != implies(implies(X_49,truth),truth)
| implies(implies(X_49,truth),truth) = truth ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(implies(X_49,truth),truth)))]]) ).
cnf(refute_0_441,plain,
implies(implies(X_49,truth),truth) = truth,
inference(resolve,[$cnf( $equal(truth,implies(implies(X_49,truth),truth)) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
implies(implies(Y,truth),truth) = truth,
inference(subst,[],[refute_0_441:[bind(X_49,$fot(Y))]]) ).
cnf(refute_0_443,plain,
implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)) = implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)),
introduced(tautology,[refl,[$fot(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)))]]) ).
cnf(refute_0_444,plain,
( implies(implies(Y,truth),truth) != truth
| implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)) != implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth))
| implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)) = implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)),implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_445,plain,
( implies(implies(Y,truth),truth) != truth
| implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)) = implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)),implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth))) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)) = implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth),
inference(resolve,[$cnf( $equal(implies(implies(Y,truth),truth),truth) )],[refute_0_442,refute_0_445]) ).
cnf(refute_0_447,plain,
( implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)) != implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth)
| implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)) != truth
| implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)),truth) ),[0],$fot(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth))]]) ).
cnf(refute_0_448,plain,
( implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)) != truth
| implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)),implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth)) )],[refute_0_446,refute_0_447]) ).
cnf(refute_0_449,plain,
implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(implies(Y,truth),truth)),truth) )],[refute_0_430,refute_0_448]) ).
cnf(refute_0_450,plain,
implies(truth,Y) = Y,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_451,plain,
implies(implies(truth,X_25),implies(implies(X_25,X_26),implies(truth,X_26))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(X_25)),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_452,plain,
( implies(implies(truth,X_25),implies(implies(X_25,X_26),implies(truth,X_26))) != truth
| implies(truth,X_26) != X_26
| implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_25),implies(implies(X_25,X_26),implies(truth,X_26))),truth) ),[0,1,1],$fot(X_26)]]) ).
cnf(refute_0_453,plain,
( implies(implies(truth,X_25),implies(implies(X_25,X_26),implies(truth,X_26))) != truth
| implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_26),X_26) )],[refute_0_214,refute_0_452]) ).
cnf(refute_0_454,plain,
implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_25),implies(implies(X_25,X_26),implies(truth,X_26))),truth) )],[refute_0_451,refute_0_453]) ).
cnf(refute_0_455,plain,
implies(truth,X_25) = X_25,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_25))]]) ).
cnf(refute_0_456,plain,
implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)) = implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)))]]) ).
cnf(refute_0_457,plain,
( implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)) != implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26))
| implies(truth,X_25) != X_25
| implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)) = implies(X_25,implies(implies(X_25,X_26),X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)),implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26))) ),[1,0],$fot(X_25)]]) ).
cnf(refute_0_458,plain,
( implies(truth,X_25) != X_25
| implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)) = implies(X_25,implies(implies(X_25,X_26),X_26)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)),implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26))) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)) = implies(X_25,implies(implies(X_25,X_26),X_26)),
inference(resolve,[$cnf( $equal(implies(truth,X_25),X_25) )],[refute_0_455,refute_0_458]) ).
cnf(refute_0_460,plain,
( implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)) != implies(X_25,implies(implies(X_25,X_26),X_26))
| implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)) != truth
| implies(X_25,implies(implies(X_25,X_26),X_26)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)),truth) ),[0],$fot(implies(X_25,implies(implies(X_25,X_26),X_26)))]]) ).
cnf(refute_0_461,plain,
( implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)) != truth
| implies(X_25,implies(implies(X_25,X_26),X_26)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)),implies(X_25,implies(implies(X_25,X_26),X_26))) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
implies(X_25,implies(implies(X_25,X_26),X_26)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_25),implies(implies(X_25,X_26),X_26)),truth) )],[refute_0_454,refute_0_461]) ).
cnf(refute_0_463,plain,
implies(and(truth,or(falsehood,falsehood)),implies(implies(and(truth,or(falsehood,falsehood)),truth),truth)) = truth,
inference(subst,[],[refute_0_462:[bind(X_25,$fot(and(truth,or(falsehood,falsehood)))),bind(X_26,$fot(truth))]]) ).
cnf(refute_0_464,plain,
( implies(and(truth,or(falsehood,falsehood)),implies(implies(and(truth,or(falsehood,falsehood)),truth),truth)) != truth
| implies(and(truth,or(falsehood,falsehood)),truth) != implies(falsehood,or(falsehood,and(truth,truth)))
| implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(truth,or(falsehood,falsehood)),implies(implies(and(truth,or(falsehood,falsehood)),truth),truth)),truth) ),[0,1,0],$fot(implies(falsehood,or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_465,plain,
( implies(and(truth,or(falsehood,falsehood)),implies(implies(and(truth,or(falsehood,falsehood)),truth),truth)) != truth
| implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(and(truth,or(falsehood,falsehood)),truth),implies(falsehood,or(falsehood,and(truth,truth)))) )],[refute_0_411,refute_0_464]) ).
cnf(refute_0_466,plain,
implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(and(truth,or(falsehood,falsehood)),implies(implies(and(truth,or(falsehood,falsehood)),truth),truth)),truth) )],[refute_0_463,refute_0_465]) ).
cnf(refute_0_467,plain,
implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))) = implies(implies(and(truth,or(falsehood,falsehood)),truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(and(truth,or(falsehood,falsehood))))]]) ).
cnf(refute_0_468,plain,
( implies(and(truth,or(falsehood,falsehood)),truth) != implies(falsehood,or(falsehood,and(truth,truth)))
| implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))) != implies(implies(and(truth,or(falsehood,falsehood)),truth),truth)
| implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))) = implies(implies(falsehood,or(falsehood,and(truth,truth))),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))),implies(implies(and(truth,or(falsehood,falsehood)),truth),truth)) ),[1,0],$fot(implies(falsehood,or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_469,plain,
( implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))) != implies(implies(and(truth,or(falsehood,falsehood)),truth),truth)
| implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))) = implies(implies(falsehood,or(falsehood,and(truth,truth))),truth) ),
inference(resolve,[$cnf( $equal(implies(and(truth,or(falsehood,falsehood)),truth),implies(falsehood,or(falsehood,and(truth,truth)))) )],[refute_0_411,refute_0_468]) ).
cnf(refute_0_470,plain,
implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))) = implies(implies(falsehood,or(falsehood,and(truth,truth))),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))),implies(implies(and(truth,or(falsehood,falsehood)),truth),truth)) )],[refute_0_467,refute_0_469]) ).
cnf(refute_0_471,plain,
implies(implies(and(truth,or(falsehood,falsehood)),truth),truth) = truth,
inference(subst,[],[refute_0_441:[bind(X_49,$fot(and(truth,or(falsehood,falsehood))))]]) ).
cnf(refute_0_472,plain,
( implies(implies(and(truth,or(falsehood,falsehood)),truth),truth) != truth
| implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))) != implies(implies(and(truth,or(falsehood,falsehood)),truth),truth)
| implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))) = truth ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))))),bind(Y0,$fot(implies(implies(and(truth,or(falsehood,falsehood)),truth),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_473,plain,
( implies(implies(and(truth,or(falsehood,falsehood)),truth),truth) != truth
| implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))),implies(implies(and(truth,or(falsehood,falsehood)),truth),truth)) )],[refute_0_467,refute_0_472]) ).
cnf(refute_0_474,plain,
implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(and(truth,or(falsehood,falsehood)),truth),truth),truth) )],[refute_0_471,refute_0_473]) ).
cnf(refute_0_475,plain,
( implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))) != implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)
| implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))) != truth
| truth = implies(implies(falsehood,or(falsehood,and(truth,truth))),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) ),[0],$fot(truth)]]) ).
cnf(refute_0_476,plain,
( implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))) != implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)
| truth = implies(implies(falsehood,or(falsehood,and(truth,truth))),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))),truth) )],[refute_0_474,refute_0_475]) ).
cnf(refute_0_477,plain,
truth = implies(implies(falsehood,or(falsehood,and(truth,truth))),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) )],[refute_0_470,refute_0_476]) ).
cnf(refute_0_478,plain,
( truth != implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)
| implies(implies(falsehood,or(falsehood,and(truth,truth))),truth) = truth ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)))]]) ).
cnf(refute_0_479,plain,
implies(implies(falsehood,or(falsehood,and(truth,truth))),truth) = truth,
inference(resolve,[$cnf( $equal(truth,implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) )],[refute_0_477,refute_0_478]) ).
cnf(refute_0_480,plain,
implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) = implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)),
introduced(tautology,[refl,[$fot(implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)))]]) ).
cnf(refute_0_481,plain,
( implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) != implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth))
| implies(implies(falsehood,or(falsehood,and(truth,truth))),truth) != truth
| implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) = implies(and(truth,or(falsehood,falsehood)),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)),implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_482,plain,
( implies(implies(falsehood,or(falsehood,and(truth,truth))),truth) != truth
| implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) = implies(and(truth,or(falsehood,falsehood)),truth) ),
inference(resolve,[$cnf( $equal(implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)),implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth))) )],[refute_0_480,refute_0_481]) ).
cnf(refute_0_483,plain,
implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) = implies(and(truth,or(falsehood,falsehood)),truth),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,or(falsehood,and(truth,truth))),truth),truth) )],[refute_0_479,refute_0_482]) ).
cnf(refute_0_484,plain,
( implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) != implies(and(truth,or(falsehood,falsehood)),truth)
| implies(and(truth,or(falsehood,falsehood)),truth) != implies(falsehood,or(falsehood,and(truth,truth)))
| implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) = implies(falsehood,or(falsehood,and(truth,truth))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)))),bind(Y0,$fot(implies(and(truth,or(falsehood,falsehood)),truth))),bind(Z0,$fot(implies(falsehood,or(falsehood,and(truth,truth)))))]]) ).
cnf(refute_0_485,plain,
( implies(and(truth,or(falsehood,falsehood)),truth) != implies(falsehood,or(falsehood,and(truth,truth)))
| implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) = implies(falsehood,or(falsehood,and(truth,truth))) ),
inference(resolve,[$cnf( $equal(implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)),implies(and(truth,or(falsehood,falsehood)),truth)) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) = implies(falsehood,or(falsehood,and(truth,truth))),
inference(resolve,[$cnf( $equal(implies(and(truth,or(falsehood,falsehood)),truth),implies(falsehood,or(falsehood,and(truth,truth)))) )],[refute_0_411,refute_0_485]) ).
cnf(refute_0_487,plain,
( implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) != implies(falsehood,or(falsehood,and(truth,truth)))
| implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) != truth
| implies(falsehood,or(falsehood,and(truth,truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)),truth) ),[0],$fot(implies(falsehood,or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_488,plain,
( implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)) != truth
| implies(falsehood,or(falsehood,and(truth,truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)),implies(falsehood,or(falsehood,and(truth,truth)))) )],[refute_0_486,refute_0_487]) ).
cnf(refute_0_489,plain,
implies(falsehood,or(falsehood,and(truth,truth))) = truth,
inference(resolve,[$cnf( $equal(implies(and(truth,or(falsehood,falsehood)),implies(implies(falsehood,or(falsehood,and(truth,truth))),truth)),truth) )],[refute_0_466,refute_0_488]) ).
cnf(refute_0_490,plain,
( implies(falsehood,or(falsehood,and(truth,truth))) != truth
| or(falsehood,implies(falsehood,and(truth,truth))) != implies(falsehood,or(falsehood,and(truth,truth)))
| or(falsehood,implies(falsehood,and(truth,truth))) = truth ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(or(falsehood,implies(falsehood,and(truth,truth))))),bind(Y0,$fot(implies(falsehood,or(falsehood,and(truth,truth))))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_491,plain,
( implies(falsehood,or(falsehood,and(truth,truth))) != truth
| or(falsehood,implies(falsehood,and(truth,truth))) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,implies(falsehood,and(truth,truth))),implies(falsehood,or(falsehood,and(truth,truth)))) )],[refute_0_406,refute_0_490]) ).
cnf(refute_0_492,plain,
or(falsehood,implies(falsehood,and(truth,truth))) = truth,
inference(resolve,[$cnf( $equal(implies(falsehood,or(falsehood,and(truth,truth))),truth) )],[refute_0_489,refute_0_491]) ).
cnf(refute_0_493,plain,
or(implies(falsehood,and(truth,truth)),falsehood) = or(falsehood,implies(falsehood,and(truth,truth))),
inference(subst,[],[refute_0_24:[bind(X,$fot(falsehood)),bind(Y,$fot(implies(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_494,plain,
( or(falsehood,implies(falsehood,and(truth,truth))) != truth
| or(implies(falsehood,and(truth,truth)),falsehood) != or(falsehood,implies(falsehood,and(truth,truth)))
| or(implies(falsehood,and(truth,truth)),falsehood) = truth ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(or(implies(falsehood,and(truth,truth)),falsehood))),bind(Y0,$fot(or(falsehood,implies(falsehood,and(truth,truth))))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_495,plain,
( or(falsehood,implies(falsehood,and(truth,truth))) != truth
| or(implies(falsehood,and(truth,truth)),falsehood) = truth ),
inference(resolve,[$cnf( $equal(or(implies(falsehood,and(truth,truth)),falsehood),or(falsehood,implies(falsehood,and(truth,truth)))) )],[refute_0_493,refute_0_494]) ).
cnf(refute_0_496,plain,
or(implies(falsehood,and(truth,truth)),falsehood) = truth,
inference(resolve,[$cnf( $equal(or(falsehood,implies(falsehood,and(truth,truth))),truth) )],[refute_0_492,refute_0_495]) ).
cnf(refute_0_497,plain,
not(implies(falsehood,or(falsehood,and(truth,truth)))) = not(implies(falsehood,or(falsehood,and(truth,truth)))),
introduced(tautology,[refl,[$fot(not(implies(falsehood,or(falsehood,and(truth,truth)))))]]) ).
cnf(refute_0_498,plain,
( implies(falsehood,or(falsehood,and(truth,truth))) != truth
| not(implies(falsehood,or(falsehood,and(truth,truth)))) != not(implies(falsehood,or(falsehood,and(truth,truth))))
| not(implies(falsehood,or(falsehood,and(truth,truth)))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(falsehood,or(falsehood,and(truth,truth)))),not(implies(falsehood,or(falsehood,and(truth,truth))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_499,plain,
( implies(falsehood,or(falsehood,and(truth,truth))) != truth
| not(implies(falsehood,or(falsehood,and(truth,truth)))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(implies(falsehood,or(falsehood,and(truth,truth)))),not(implies(falsehood,or(falsehood,and(truth,truth))))) )],[refute_0_497,refute_0_498]) ).
cnf(refute_0_500,plain,
not(implies(falsehood,or(falsehood,and(truth,truth)))) = not(truth),
inference(resolve,[$cnf( $equal(implies(falsehood,or(falsehood,and(truth,truth))),truth) )],[refute_0_489,refute_0_499]) ).
cnf(refute_0_501,plain,
( not(implies(falsehood,or(falsehood,and(truth,truth)))) != not(truth)
| not(truth) != falsehood
| not(implies(falsehood,or(falsehood,and(truth,truth)))) = falsehood ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(not(implies(falsehood,or(falsehood,and(truth,truth)))))),bind(Y0,$fot(not(truth))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_502,plain,
( not(truth) != falsehood
| not(implies(falsehood,or(falsehood,and(truth,truth)))) = falsehood ),
inference(resolve,[$cnf( $equal(not(implies(falsehood,or(falsehood,and(truth,truth)))),not(truth)) )],[refute_0_500,refute_0_501]) ).
cnf(refute_0_503,plain,
not(implies(falsehood,or(falsehood,and(truth,truth)))) = falsehood,
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_502]) ).
cnf(refute_0_504,plain,
or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))) = or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),
introduced(tautology,[refl,[$fot(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))))]]) ).
cnf(refute_0_505,plain,
( not(implies(falsehood,or(falsehood,and(truth,truth)))) != falsehood
| or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))) != or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth)))))
| or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))) = or(implies(falsehood,and(truth,truth)),falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth)))))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_506,plain,
( not(implies(falsehood,or(falsehood,and(truth,truth)))) != falsehood
| or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))) = or(implies(falsehood,and(truth,truth)),falsehood) ),
inference(resolve,[$cnf( $equal(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth)))))) )],[refute_0_504,refute_0_505]) ).
cnf(refute_0_507,plain,
or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))) = or(implies(falsehood,and(truth,truth)),falsehood),
inference(resolve,[$cnf( $equal(not(implies(falsehood,or(falsehood,and(truth,truth)))),falsehood) )],[refute_0_503,refute_0_506]) ).
cnf(refute_0_508,plain,
( or(implies(falsehood,and(truth,truth)),falsehood) != truth
| or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))) != or(implies(falsehood,and(truth,truth)),falsehood)
| or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))) = truth ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))))),bind(Y0,$fot(or(implies(falsehood,and(truth,truth)),falsehood))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_509,plain,
( or(implies(falsehood,and(truth,truth)),falsehood) != truth
| or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))) = truth ),
inference(resolve,[$cnf( $equal(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),or(implies(falsehood,and(truth,truth)),falsehood)) )],[refute_0_507,refute_0_508]) ).
cnf(refute_0_510,plain,
or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))) = truth,
inference(resolve,[$cnf( $equal(or(implies(falsehood,and(truth,truth)),falsehood),truth) )],[refute_0_496,refute_0_509]) ).
cnf(refute_0_511,plain,
implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y) = implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),
introduced(tautology,[refl,[$fot(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y))]]) ).
cnf(refute_0_512,plain,
( implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y) != implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y)
| or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))) != truth
| implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_513,plain,
( or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))) != truth
| implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y)) )],[refute_0_511,refute_0_512]) ).
cnf(refute_0_514,plain,
implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),truth) )],[refute_0_510,refute_0_513]) ).
cnf(refute_0_515,plain,
( implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y) != implies(truth,Y)
| implies(truth,Y) != Y
| implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y) = Y ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y))),bind(Y0,$fot(implies(truth,Y))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_516,plain,
( implies(truth,Y) != Y
| implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y) = Y ),
inference(resolve,[$cnf( $equal(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),implies(truth,Y)) )],[refute_0_514,refute_0_515]) ).
cnf(refute_0_517,plain,
implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y) = Y,
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_450,refute_0_516]) ).
cnf(refute_0_518,plain,
implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth) = implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth),
introduced(tautology,[refl,[$fot(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth))]]) ).
cnf(refute_0_519,plain,
( implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth) != implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth)
| implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y) != Y
| implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth) = implies(Y,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth),implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth)) ),[1,0],$fot(Y)]]) ).
cnf(refute_0_520,plain,
( implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y) != Y
| implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth) = implies(Y,truth) ),
inference(resolve,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth),implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth)) )],[refute_0_518,refute_0_519]) ).
cnf(refute_0_521,plain,
implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth) = implies(Y,truth),
inference(resolve,[$cnf( $equal(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),Y) )],[refute_0_517,refute_0_520]) ).
cnf(refute_0_522,plain,
( implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth) != implies(Y,truth)
| implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth) != truth
| implies(Y,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth),truth) ),[0],$fot(implies(Y,truth))]]) ).
cnf(refute_0_523,plain,
( implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth) != truth
| implies(Y,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth),implies(Y,truth)) )],[refute_0_521,refute_0_522]) ).
cnf(refute_0_524,plain,
implies(Y,truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(or(implies(falsehood,and(truth,truth)),not(implies(falsehood,or(falsehood,and(truth,truth))))),Y),truth),truth) )],[refute_0_449,refute_0_523]) ).
cnf(refute_0_525,plain,
implies(and(X_46,truth),truth) = truth,
inference(subst,[],[refute_0_524:[bind(Y,$fot(and(X_46,truth)))]]) ).
cnf(refute_0_526,plain,
implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))) = implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))),
introduced(tautology,[refl,[$fot(implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))))]]) ).
cnf(refute_0_527,plain,
( implies(and(X_46,truth),truth) != truth
| implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))) != implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46)))
| implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))) = implies(truth,implies(falsehood,not(X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))),implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_528,plain,
( implies(and(X_46,truth),truth) != truth
| implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))) = implies(truth,implies(falsehood,not(X_46))) ),
inference(resolve,[$cnf( $equal(implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))),implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46)))) )],[refute_0_526,refute_0_527]) ).
cnf(refute_0_529,plain,
implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))) = implies(truth,implies(falsehood,not(X_46))),
inference(resolve,[$cnf( $equal(implies(and(X_46,truth),truth),truth) )],[refute_0_525,refute_0_528]) ).
cnf(refute_0_530,plain,
( implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))) != implies(truth,implies(falsehood,not(X_46)))
| implies(truth,implies(falsehood,not(X_46))) != implies(falsehood,not(X_46))
| implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))) = implies(falsehood,not(X_46)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))))),bind(Y0,$fot(implies(truth,implies(falsehood,not(X_46))))),bind(Z0,$fot(implies(falsehood,not(X_46))))]]) ).
cnf(refute_0_531,plain,
( implies(truth,implies(falsehood,not(X_46))) != implies(falsehood,not(X_46))
| implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))) = implies(falsehood,not(X_46)) ),
inference(resolve,[$cnf( $equal(implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))),implies(truth,implies(falsehood,not(X_46)))) )],[refute_0_529,refute_0_530]) ).
cnf(refute_0_532,plain,
implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))) = implies(falsehood,not(X_46)),
inference(resolve,[$cnf( $equal(implies(truth,implies(falsehood,not(X_46))),implies(falsehood,not(X_46))) )],[refute_0_334,refute_0_531]) ).
cnf(refute_0_533,plain,
( implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))) != implies(falsehood,not(X_46))
| implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))) != truth
| implies(falsehood,not(X_46)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))),truth) ),[0],$fot(implies(falsehood,not(X_46)))]]) ).
cnf(refute_0_534,plain,
( implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))) != truth
| implies(falsehood,not(X_46)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))),implies(falsehood,not(X_46))) )],[refute_0_532,refute_0_533]) ).
cnf(refute_0_535,plain,
implies(falsehood,not(X_46)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(and(X_46,truth),truth),implies(falsehood,not(X_46))),truth) )],[refute_0_333,refute_0_534]) ).
cnf(refute_0_536,plain,
implies(falsehood,not(not(X))) = truth,
inference(subst,[],[refute_0_535:[bind(X_46,$fot(not(X)))]]) ).
cnf(refute_0_537,plain,
implies(implies(falsehood,not(not(X))),implies(falsehood,X)) = implies(implies(falsehood,not(not(X))),implies(falsehood,X)),
introduced(tautology,[refl,[$fot(implies(implies(falsehood,not(not(X))),implies(falsehood,X)))]]) ).
cnf(refute_0_538,plain,
( implies(falsehood,not(not(X))) != truth
| implies(implies(falsehood,not(not(X))),implies(falsehood,X)) != implies(implies(falsehood,not(not(X))),implies(falsehood,X))
| implies(implies(falsehood,not(not(X))),implies(falsehood,X)) = implies(truth,implies(falsehood,X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,not(not(X))),implies(falsehood,X)),implies(implies(falsehood,not(not(X))),implies(falsehood,X))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_539,plain,
( implies(falsehood,not(not(X))) != truth
| implies(implies(falsehood,not(not(X))),implies(falsehood,X)) = implies(truth,implies(falsehood,X)) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(not(X))),implies(falsehood,X)),implies(implies(falsehood,not(not(X))),implies(falsehood,X))) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
implies(implies(falsehood,not(not(X))),implies(falsehood,X)) = implies(truth,implies(falsehood,X)),
inference(resolve,[$cnf( $equal(implies(falsehood,not(not(X))),truth) )],[refute_0_536,refute_0_539]) ).
cnf(refute_0_541,plain,
( implies(implies(falsehood,not(not(X))),implies(falsehood,X)) != implies(truth,implies(falsehood,X))
| implies(truth,implies(falsehood,X)) != implies(falsehood,X)
| implies(implies(falsehood,not(not(X))),implies(falsehood,X)) = implies(falsehood,X) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(implies(falsehood,not(not(X))),implies(falsehood,X)))),bind(Y0,$fot(implies(truth,implies(falsehood,X)))),bind(Z0,$fot(implies(falsehood,X)))]]) ).
cnf(refute_0_542,plain,
( implies(truth,implies(falsehood,X)) != implies(falsehood,X)
| implies(implies(falsehood,not(not(X))),implies(falsehood,X)) = implies(falsehood,X) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(not(X))),implies(falsehood,X)),implies(truth,implies(falsehood,X))) )],[refute_0_540,refute_0_541]) ).
cnf(refute_0_543,plain,
implies(implies(falsehood,not(not(X))),implies(falsehood,X)) = implies(falsehood,X),
inference(resolve,[$cnf( $equal(implies(truth,implies(falsehood,X)),implies(falsehood,X)) )],[refute_0_315,refute_0_542]) ).
cnf(refute_0_544,plain,
( implies(implies(falsehood,not(not(X))),implies(falsehood,X)) != implies(falsehood,X)
| implies(implies(falsehood,not(not(X))),implies(falsehood,X)) != truth
| implies(falsehood,X) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,not(not(X))),implies(falsehood,X)),truth) ),[0],$fot(implies(falsehood,X))]]) ).
cnf(refute_0_545,plain,
( implies(implies(falsehood,not(not(X))),implies(falsehood,X)) != truth
| implies(falsehood,X) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(not(X))),implies(falsehood,X)),implies(falsehood,X)) )],[refute_0_543,refute_0_544]) ).
cnf(refute_0_546,plain,
implies(falsehood,X) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(not(X))),implies(falsehood,X)),truth) )],[refute_0_314,refute_0_545]) ).
cnf(refute_0_547,plain,
implies(falsehood,Z) = truth,
inference(subst,[],[refute_0_546:[bind(X,$fot(Z))]]) ).
cnf(refute_0_548,plain,
implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)) = implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)),
introduced(tautology,[refl,[$fot(implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)))]]) ).
cnf(refute_0_549,plain,
( implies(falsehood,Z) != truth
| implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)) != implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))
| implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)) = implies(truth,implies(and(truth,or(falsehood,falsehood)),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)),implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_550,plain,
( implies(falsehood,Z) != truth
| implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)) = implies(truth,implies(and(truth,or(falsehood,falsehood)),Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)),implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z))) )],[refute_0_548,refute_0_549]) ).
cnf(refute_0_551,plain,
implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)) = implies(truth,implies(and(truth,or(falsehood,falsehood)),Z)),
inference(resolve,[$cnf( $equal(implies(falsehood,Z),truth) )],[refute_0_547,refute_0_550]) ).
cnf(refute_0_552,plain,
( implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)) != implies(truth,implies(and(truth,or(falsehood,falsehood)),Z))
| implies(truth,implies(and(truth,or(falsehood,falsehood)),Z)) != implies(and(truth,or(falsehood,falsehood)),Z)
| implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)) = implies(and(truth,or(falsehood,falsehood)),Z) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)))),bind(Y0,$fot(implies(truth,implies(and(truth,or(falsehood,falsehood)),Z)))),bind(Z0,$fot(implies(and(truth,or(falsehood,falsehood)),Z)))]]) ).
cnf(refute_0_553,plain,
( implies(truth,implies(and(truth,or(falsehood,falsehood)),Z)) != implies(and(truth,or(falsehood,falsehood)),Z)
| implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)) = implies(and(truth,or(falsehood,falsehood)),Z) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)),implies(truth,implies(and(truth,or(falsehood,falsehood)),Z))) )],[refute_0_551,refute_0_552]) ).
cnf(refute_0_554,plain,
implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)) = implies(and(truth,or(falsehood,falsehood)),Z),
inference(resolve,[$cnf( $equal(implies(truth,implies(and(truth,or(falsehood,falsehood)),Z)),implies(and(truth,or(falsehood,falsehood)),Z)) )],[refute_0_294,refute_0_553]) ).
cnf(refute_0_555,plain,
( implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)) != implies(and(truth,or(falsehood,falsehood)),Z)
| implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)) != truth
| implies(and(truth,or(falsehood,falsehood)),Z) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)),truth) ),[0],$fot(implies(and(truth,or(falsehood,falsehood)),Z))]]) ).
cnf(refute_0_556,plain,
( implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)) != truth
| implies(and(truth,or(falsehood,falsehood)),Z) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)),implies(and(truth,or(falsehood,falsehood)),Z)) )],[refute_0_554,refute_0_555]) ).
cnf(refute_0_557,plain,
implies(and(truth,or(falsehood,falsehood)),Z) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,Z),implies(and(truth,or(falsehood,falsehood)),Z)),truth) )],[refute_0_293,refute_0_556]) ).
cnf(refute_0_558,plain,
implies(and(truth,or(falsehood,falsehood)),X_47) = truth,
inference(subst,[],[refute_0_557:[bind(Z,$fot(X_47))]]) ).
cnf(refute_0_559,plain,
implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))) = implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))),
introduced(tautology,[refl,[$fot(implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))))]]) ).
cnf(refute_0_560,plain,
( implies(and(truth,or(falsehood,falsehood)),X_47) != truth
| implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))) != implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth)))
| implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))) = implies(truth,or(X_47,and(truth,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))),implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_561,plain,
( implies(and(truth,or(falsehood,falsehood)),X_47) != truth
| implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))) = implies(truth,or(X_47,and(truth,truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))),implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth)))) )],[refute_0_559,refute_0_560]) ).
cnf(refute_0_562,plain,
implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))) = implies(truth,or(X_47,and(truth,truth))),
inference(resolve,[$cnf( $equal(implies(and(truth,or(falsehood,falsehood)),X_47),truth) )],[refute_0_558,refute_0_561]) ).
cnf(refute_0_563,plain,
( implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))) != implies(truth,or(X_47,and(truth,truth)))
| implies(truth,or(X_47,and(truth,truth))) != or(X_47,and(truth,truth))
| implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))) = or(X_47,and(truth,truth)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))))),bind(Y0,$fot(implies(truth,or(X_47,and(truth,truth))))),bind(Z0,$fot(or(X_47,and(truth,truth))))]]) ).
cnf(refute_0_564,plain,
( implies(truth,or(X_47,and(truth,truth))) != or(X_47,and(truth,truth))
| implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))) = or(X_47,and(truth,truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))),implies(truth,or(X_47,and(truth,truth)))) )],[refute_0_562,refute_0_563]) ).
cnf(refute_0_565,plain,
implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))) = or(X_47,and(truth,truth)),
inference(resolve,[$cnf( $equal(implies(truth,or(X_47,and(truth,truth))),or(X_47,and(truth,truth))) )],[refute_0_167,refute_0_564]) ).
cnf(refute_0_566,plain,
( implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))) != or(X_47,and(truth,truth))
| implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))) != truth
| or(X_47,and(truth,truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))),truth) ),[0],$fot(or(X_47,and(truth,truth)))]]) ).
cnf(refute_0_567,plain,
( implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))) != truth
| or(X_47,and(truth,truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))),or(X_47,and(truth,truth))) )],[refute_0_565,refute_0_566]) ).
cnf(refute_0_568,plain,
or(X_47,and(truth,truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(and(truth,or(falsehood,falsehood)),X_47),or(X_47,and(truth,truth))),truth) )],[refute_0_166,refute_0_567]) ).
cnf(refute_0_569,plain,
or(falsehood,and(truth,truth)) = truth,
inference(subst,[],[refute_0_568:[bind(X_47,$fot(falsehood))]]) ).
cnf(refute_0_570,plain,
not(or(falsehood,and(truth,truth))) = not(or(falsehood,and(truth,truth))),
introduced(tautology,[refl,[$fot(not(or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_571,plain,
( not(or(falsehood,and(truth,truth))) != not(or(falsehood,and(truth,truth)))
| or(falsehood,and(truth,truth)) != truth
| not(or(falsehood,and(truth,truth))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,and(truth,truth))),not(or(falsehood,and(truth,truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_572,plain,
( or(falsehood,and(truth,truth)) != truth
| not(or(falsehood,and(truth,truth))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,truth))),not(or(falsehood,and(truth,truth)))) )],[refute_0_570,refute_0_571]) ).
cnf(refute_0_573,plain,
not(or(falsehood,and(truth,truth))) = not(truth),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),truth) )],[refute_0_569,refute_0_572]) ).
cnf(refute_0_574,plain,
( not(or(falsehood,and(truth,truth))) != not(truth)
| not(truth) != falsehood
| not(or(falsehood,and(truth,truth))) = falsehood ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(not(or(falsehood,and(truth,truth))))),bind(Y0,$fot(not(truth))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_575,plain,
( not(truth) != falsehood
| not(or(falsehood,and(truth,truth))) = falsehood ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,truth))),not(truth)) )],[refute_0_573,refute_0_574]) ).
cnf(refute_0_576,plain,
not(or(falsehood,and(truth,truth))) = falsehood,
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_575]) ).
cnf(refute_0_577,plain,
( and(truth,or(falsehood,falsehood)) != not(or(falsehood,and(truth,truth)))
| not(or(falsehood,and(truth,truth))) != falsehood
| and(truth,or(falsehood,falsehood)) = falsehood ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(truth,or(falsehood,falsehood)),falsehood) ),[0],$fot(not(or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_578,plain,
( and(truth,or(falsehood,falsehood)) != not(or(falsehood,and(truth,truth)))
| and(truth,or(falsehood,falsehood)) = falsehood ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,truth))),falsehood) )],[refute_0_576,refute_0_577]) ).
cnf(refute_0_579,plain,
and(truth,or(falsehood,falsehood)) = falsehood,
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),not(or(falsehood,and(truth,truth)))) )],[refute_0_82,refute_0_578]) ).
cnf(refute_0_580,plain,
or(falsehood,and(truth,or(falsehood,falsehood))) = or(falsehood,and(truth,or(falsehood,falsehood))),
introduced(tautology,[refl,[$fot(or(falsehood,and(truth,or(falsehood,falsehood))))]]) ).
cnf(refute_0_581,plain,
( and(truth,or(falsehood,falsehood)) != falsehood
| or(falsehood,and(truth,or(falsehood,falsehood))) != or(falsehood,and(truth,or(falsehood,falsehood)))
| or(falsehood,and(truth,or(falsehood,falsehood))) = or(falsehood,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,falsehood))),or(falsehood,and(truth,or(falsehood,falsehood)))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_582,plain,
( and(truth,or(falsehood,falsehood)) != falsehood
| or(falsehood,and(truth,or(falsehood,falsehood))) = or(falsehood,falsehood) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,falsehood))),or(falsehood,and(truth,or(falsehood,falsehood)))) )],[refute_0_580,refute_0_581]) ).
cnf(refute_0_583,plain,
or(falsehood,and(truth,or(falsehood,falsehood))) = or(falsehood,falsehood),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),falsehood) )],[refute_0_579,refute_0_582]) ).
cnf(refute_0_584,plain,
and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))) = and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))),
introduced(tautology,[refl,[$fot(and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))]]) ).
cnf(refute_0_585,plain,
( and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))) != and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))
| or(falsehood,and(truth,or(falsehood,falsehood))) != or(falsehood,falsehood)
| and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))) = and(truth,or(falsehood,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))),and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))) ),[1,1],$fot(or(falsehood,falsehood))]]) ).
cnf(refute_0_586,plain,
( or(falsehood,and(truth,or(falsehood,falsehood))) != or(falsehood,falsehood)
| and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))) = and(truth,or(falsehood,falsehood)) ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))),and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))) )],[refute_0_584,refute_0_585]) ).
cnf(refute_0_587,plain,
and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))) = and(truth,or(falsehood,falsehood)),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,falsehood))),or(falsehood,falsehood)) )],[refute_0_583,refute_0_586]) ).
cnf(refute_0_588,plain,
( and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))) != and(truth,or(falsehood,falsehood))
| and(truth,or(falsehood,falsehood)) != falsehood
| and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))) = falsehood ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),bind(Y0,$fot(and(truth,or(falsehood,falsehood)))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_589,plain,
( and(truth,or(falsehood,falsehood)) != falsehood
| and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))) = falsehood ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))),and(truth,or(falsehood,falsehood))) )],[refute_0_587,refute_0_588]) ).
cnf(refute_0_590,plain,
and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))) = falsehood,
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),falsehood) )],[refute_0_579,refute_0_589]) ).
cnf(refute_0_591,plain,
or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))) = or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))),
introduced(tautology,[refl,[$fot(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))]]) ).
cnf(refute_0_592,plain,
( and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))) != falsehood
| or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))) != or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))
| or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))) = or(falsehood,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_593,plain,
( and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))) != falsehood
| or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))) = or(falsehood,falsehood) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) )],[refute_0_591,refute_0_592]) ).
cnf(refute_0_594,plain,
or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))) = or(falsehood,falsehood),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))),falsehood) )],[refute_0_590,refute_0_593]) ).
cnf(refute_0_595,plain,
xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),
introduced(tautology,[refl,[$fot(xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))]]) ).
cnf(refute_0_596,plain,
( or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))) != or(falsehood,falsehood)
| xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) != xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))
| xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = xor(X_36,or(falsehood,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) ),[1,1],$fot(or(falsehood,falsehood))]]) ).
cnf(refute_0_597,plain,
( or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))) != or(falsehood,falsehood)
| xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = xor(X_36,or(falsehood,falsehood)) ),
inference(resolve,[$cnf( $equal(xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) )],[refute_0_595,refute_0_596]) ).
cnf(refute_0_598,plain,
xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = xor(X_36,or(falsehood,falsehood)),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))),or(falsehood,falsehood)) )],[refute_0_594,refute_0_597]) ).
cnf(refute_0_599,plain,
( xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) != or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))
| xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) != xor(X_36,or(falsehood,falsehood))
| xor(X_36,or(falsehood,falsehood)) = or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))) ),[0],$fot(xor(X_36,or(falsehood,falsehood)))]]) ).
cnf(refute_0_600,plain,
( xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) != or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))
| xor(X_36,or(falsehood,falsehood)) = or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) ),
inference(resolve,[$cnf( $equal(xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),xor(X_36,or(falsehood,falsehood))) )],[refute_0_598,refute_0_599]) ).
cnf(refute_0_601,plain,
or(and(X_36,and(truth,truth)),falsehood) = or(falsehood,and(X_36,and(truth,truth))),
inference(subst,[],[refute_0_24:[bind(X,$fot(falsehood)),bind(Y,$fot(and(X_36,and(truth,truth))))]]) ).
cnf(refute_0_602,plain,
and(X,or(falsehood,and(truth,or(falsehood,falsehood)))) = not(or(not(X),not(or(falsehood,and(truth,or(falsehood,falsehood)))))),
inference(subst,[],[and_definition:[bind(Y,$fot(or(falsehood,and(truth,or(falsehood,falsehood)))))]]) ).
cnf(refute_0_603,plain,
( and(X,or(falsehood,and(truth,or(falsehood,falsehood)))) != not(or(not(X),not(or(falsehood,and(truth,or(falsehood,falsehood))))))
| not(or(falsehood,and(truth,or(falsehood,falsehood)))) != and(truth,or(falsehood,and(truth,truth)))
| and(X,or(falsehood,and(truth,or(falsehood,falsehood)))) = not(or(not(X),and(truth,or(falsehood,and(truth,truth))))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,or(falsehood,and(truth,or(falsehood,falsehood)))),not(or(not(X),not(or(falsehood,and(truth,or(falsehood,falsehood))))))) ),[1,0,1],$fot(and(truth,or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_604,plain,
( and(X,or(falsehood,and(truth,or(falsehood,falsehood)))) != not(or(not(X),not(or(falsehood,and(truth,or(falsehood,falsehood))))))
| and(X,or(falsehood,and(truth,or(falsehood,falsehood)))) = not(or(not(X),and(truth,or(falsehood,and(truth,truth))))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,or(falsehood,falsehood)))),and(truth,or(falsehood,and(truth,truth)))) )],[refute_0_93,refute_0_603]) ).
cnf(refute_0_605,plain,
and(X,or(falsehood,and(truth,or(falsehood,falsehood)))) = not(or(not(X),and(truth,or(falsehood,and(truth,truth))))),
inference(resolve,[$cnf( $equal(and(X,or(falsehood,and(truth,or(falsehood,falsehood)))),not(or(not(X),not(or(falsehood,and(truth,or(falsehood,falsehood))))))) )],[refute_0_602,refute_0_604]) ).
cnf(refute_0_606,plain,
and(X,or(falsehood,and(truth,or(falsehood,falsehood)))) = and(X,or(falsehood,and(truth,or(falsehood,falsehood)))),
introduced(tautology,[refl,[$fot(and(X,or(falsehood,and(truth,or(falsehood,falsehood)))))]]) ).
cnf(refute_0_607,plain,
( and(X,or(falsehood,and(truth,or(falsehood,falsehood)))) != and(X,or(falsehood,and(truth,or(falsehood,falsehood))))
| or(falsehood,and(truth,or(falsehood,falsehood))) != or(falsehood,falsehood)
| and(X,or(falsehood,and(truth,or(falsehood,falsehood)))) = and(X,or(falsehood,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,or(falsehood,and(truth,or(falsehood,falsehood)))),and(X,or(falsehood,and(truth,or(falsehood,falsehood))))) ),[1,1],$fot(or(falsehood,falsehood))]]) ).
cnf(refute_0_608,plain,
( or(falsehood,and(truth,or(falsehood,falsehood))) != or(falsehood,falsehood)
| and(X,or(falsehood,and(truth,or(falsehood,falsehood)))) = and(X,or(falsehood,falsehood)) ),
inference(resolve,[$cnf( $equal(and(X,or(falsehood,and(truth,or(falsehood,falsehood)))),and(X,or(falsehood,and(truth,or(falsehood,falsehood))))) )],[refute_0_606,refute_0_607]) ).
cnf(refute_0_609,plain,
and(X,or(falsehood,and(truth,or(falsehood,falsehood)))) = and(X,or(falsehood,falsehood)),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,falsehood))),or(falsehood,falsehood)) )],[refute_0_583,refute_0_608]) ).
cnf(refute_0_610,plain,
( and(X,or(falsehood,and(truth,or(falsehood,falsehood)))) != and(X,or(falsehood,falsehood))
| and(X,or(falsehood,and(truth,or(falsehood,falsehood)))) != not(or(not(X),and(truth,or(falsehood,and(truth,truth)))))
| and(X,or(falsehood,falsehood)) = not(or(not(X),and(truth,or(falsehood,and(truth,truth))))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,or(falsehood,and(truth,or(falsehood,falsehood)))),not(or(not(X),and(truth,or(falsehood,and(truth,truth)))))) ),[0],$fot(and(X,or(falsehood,falsehood)))]]) ).
cnf(refute_0_611,plain,
( and(X,or(falsehood,and(truth,or(falsehood,falsehood)))) != not(or(not(X),and(truth,or(falsehood,and(truth,truth)))))
| and(X,or(falsehood,falsehood)) = not(or(not(X),and(truth,or(falsehood,and(truth,truth))))) ),
inference(resolve,[$cnf( $equal(and(X,or(falsehood,and(truth,or(falsehood,falsehood)))),and(X,or(falsehood,falsehood))) )],[refute_0_609,refute_0_610]) ).
cnf(refute_0_612,plain,
or(not(X),and(truth,truth)) = truth,
inference(subst,[],[refute_0_568:[bind(X_47,$fot(not(X)))]]) ).
cnf(refute_0_613,plain,
and(truth,or(falsehood,and(truth,truth))) = and(truth,or(falsehood,and(truth,truth))),
introduced(tautology,[refl,[$fot(and(truth,or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_614,plain,
( and(truth,or(falsehood,and(truth,truth))) != and(truth,or(falsehood,and(truth,truth)))
| or(falsehood,and(truth,truth)) != truth
| and(truth,or(falsehood,and(truth,truth))) = and(truth,truth) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,or(falsehood,and(truth,truth))),and(truth,or(falsehood,and(truth,truth)))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_615,plain,
( or(falsehood,and(truth,truth)) != truth
| and(truth,or(falsehood,and(truth,truth))) = and(truth,truth) ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,and(truth,truth))),and(truth,or(falsehood,and(truth,truth)))) )],[refute_0_613,refute_0_614]) ).
cnf(refute_0_616,plain,
and(truth,or(falsehood,and(truth,truth))) = and(truth,truth),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),truth) )],[refute_0_569,refute_0_615]) ).
cnf(refute_0_617,plain,
or(not(X),and(truth,or(falsehood,and(truth,truth)))) = or(not(X),and(truth,or(falsehood,and(truth,truth)))),
introduced(tautology,[refl,[$fot(or(not(X),and(truth,or(falsehood,and(truth,truth)))))]]) ).
cnf(refute_0_618,plain,
( and(truth,or(falsehood,and(truth,truth))) != and(truth,truth)
| or(not(X),and(truth,or(falsehood,and(truth,truth)))) != or(not(X),and(truth,or(falsehood,and(truth,truth))))
| or(not(X),and(truth,or(falsehood,and(truth,truth)))) = or(not(X),and(truth,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X),and(truth,or(falsehood,and(truth,truth)))),or(not(X),and(truth,or(falsehood,and(truth,truth))))) ),[1,1],$fot(and(truth,truth))]]) ).
cnf(refute_0_619,plain,
( and(truth,or(falsehood,and(truth,truth))) != and(truth,truth)
| or(not(X),and(truth,or(falsehood,and(truth,truth)))) = or(not(X),and(truth,truth)) ),
inference(resolve,[$cnf( $equal(or(not(X),and(truth,or(falsehood,and(truth,truth)))),or(not(X),and(truth,or(falsehood,and(truth,truth))))) )],[refute_0_617,refute_0_618]) ).
cnf(refute_0_620,plain,
or(not(X),and(truth,or(falsehood,and(truth,truth)))) = or(not(X),and(truth,truth)),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,and(truth,truth))),and(truth,truth)) )],[refute_0_616,refute_0_619]) ).
cnf(refute_0_621,plain,
( or(not(X),and(truth,or(falsehood,and(truth,truth)))) != or(not(X),and(truth,truth))
| or(not(X),and(truth,truth)) != truth
| or(not(X),and(truth,or(falsehood,and(truth,truth)))) = truth ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(or(not(X),and(truth,or(falsehood,and(truth,truth)))))),bind(Y0,$fot(or(not(X),and(truth,truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_622,plain,
( or(not(X),and(truth,truth)) != truth
| or(not(X),and(truth,or(falsehood,and(truth,truth)))) = truth ),
inference(resolve,[$cnf( $equal(or(not(X),and(truth,or(falsehood,and(truth,truth)))),or(not(X),and(truth,truth))) )],[refute_0_620,refute_0_621]) ).
cnf(refute_0_623,plain,
or(not(X),and(truth,or(falsehood,and(truth,truth)))) = truth,
inference(resolve,[$cnf( $equal(or(not(X),and(truth,truth)),truth) )],[refute_0_612,refute_0_622]) ).
cnf(refute_0_624,plain,
not(or(not(X),and(truth,or(falsehood,and(truth,truth))))) = not(or(not(X),and(truth,or(falsehood,and(truth,truth))))),
introduced(tautology,[refl,[$fot(not(or(not(X),and(truth,or(falsehood,and(truth,truth))))))]]) ).
cnf(refute_0_625,plain,
( not(or(not(X),and(truth,or(falsehood,and(truth,truth))))) != not(or(not(X),and(truth,or(falsehood,and(truth,truth)))))
| or(not(X),and(truth,or(falsehood,and(truth,truth)))) != truth
| not(or(not(X),and(truth,or(falsehood,and(truth,truth))))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),and(truth,or(falsehood,and(truth,truth))))),not(or(not(X),and(truth,or(falsehood,and(truth,truth)))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_626,plain,
( or(not(X),and(truth,or(falsehood,and(truth,truth)))) != truth
| not(or(not(X),and(truth,or(falsehood,and(truth,truth))))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(or(not(X),and(truth,or(falsehood,and(truth,truth))))),not(or(not(X),and(truth,or(falsehood,and(truth,truth)))))) )],[refute_0_624,refute_0_625]) ).
cnf(refute_0_627,plain,
not(or(not(X),and(truth,or(falsehood,and(truth,truth))))) = not(truth),
inference(resolve,[$cnf( $equal(or(not(X),and(truth,or(falsehood,and(truth,truth)))),truth) )],[refute_0_623,refute_0_626]) ).
cnf(refute_0_628,plain,
( not(or(not(X),and(truth,or(falsehood,and(truth,truth))))) != not(truth)
| not(truth) != falsehood
| not(or(not(X),and(truth,or(falsehood,and(truth,truth))))) = falsehood ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(not(or(not(X),and(truth,or(falsehood,and(truth,truth))))))),bind(Y0,$fot(not(truth))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_629,plain,
( not(truth) != falsehood
| not(or(not(X),and(truth,or(falsehood,and(truth,truth))))) = falsehood ),
inference(resolve,[$cnf( $equal(not(or(not(X),and(truth,or(falsehood,and(truth,truth))))),not(truth)) )],[refute_0_627,refute_0_628]) ).
cnf(refute_0_630,plain,
not(or(not(X),and(truth,or(falsehood,and(truth,truth))))) = falsehood,
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_629]) ).
cnf(refute_0_631,plain,
( and(X,or(falsehood,falsehood)) != not(or(not(X),and(truth,or(falsehood,and(truth,truth)))))
| not(or(not(X),and(truth,or(falsehood,and(truth,truth))))) != falsehood
| and(X,or(falsehood,falsehood)) = falsehood ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,or(falsehood,falsehood)),falsehood) ),[0],$fot(not(or(not(X),and(truth,or(falsehood,and(truth,truth))))))]]) ).
cnf(refute_0_632,plain,
( and(X,or(falsehood,falsehood)) != not(or(not(X),and(truth,or(falsehood,and(truth,truth)))))
| and(X,or(falsehood,falsehood)) = falsehood ),
inference(resolve,[$cnf( $equal(not(or(not(X),and(truth,or(falsehood,and(truth,truth))))),falsehood) )],[refute_0_630,refute_0_631]) ).
cnf(refute_0_633,plain,
( and(X,or(falsehood,and(truth,or(falsehood,falsehood)))) != not(or(not(X),and(truth,or(falsehood,and(truth,truth)))))
| and(X,or(falsehood,falsehood)) = falsehood ),
inference(resolve,[$cnf( $equal(and(X,or(falsehood,falsehood)),not(or(not(X),and(truth,or(falsehood,and(truth,truth)))))) )],[refute_0_611,refute_0_632]) ).
cnf(refute_0_634,plain,
and(X,or(falsehood,falsehood)) = falsehood,
inference(resolve,[$cnf( $equal(and(X,or(falsehood,and(truth,or(falsehood,falsehood)))),not(or(not(X),and(truth,or(falsehood,and(truth,truth)))))) )],[refute_0_605,refute_0_633]) ).
cnf(refute_0_635,plain,
and(not(X_36),or(falsehood,falsehood)) = falsehood,
inference(subst,[],[refute_0_634:[bind(X,$fot(not(X_36)))]]) ).
cnf(refute_0_636,plain,
and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),
introduced(tautology,[refl,[$fot(and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))]]) ).
cnf(refute_0_637,plain,
( and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) != and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))
| or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))) != or(falsehood,falsehood)
| and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = and(not(X_36),or(falsehood,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) ),[1,1],$fot(or(falsehood,falsehood))]]) ).
cnf(refute_0_638,plain,
( or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))) != or(falsehood,falsehood)
| and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = and(not(X_36),or(falsehood,falsehood)) ),
inference(resolve,[$cnf( $equal(and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) )],[refute_0_636,refute_0_637]) ).
cnf(refute_0_639,plain,
and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = and(not(X_36),or(falsehood,falsehood)),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))),or(falsehood,falsehood)) )],[refute_0_594,refute_0_638]) ).
cnf(refute_0_640,plain,
( and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) != and(not(X_36),or(falsehood,falsehood))
| and(not(X_36),or(falsehood,falsehood)) != falsehood
| and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = falsehood ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))),bind(Y0,$fot(and(not(X_36),or(falsehood,falsehood)))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_641,plain,
( and(not(X_36),or(falsehood,falsehood)) != falsehood
| and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = falsehood ),
inference(resolve,[$cnf( $equal(and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),and(not(X_36),or(falsehood,falsehood))) )],[refute_0_639,refute_0_640]) ).
cnf(refute_0_642,plain,
and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) = falsehood,
inference(resolve,[$cnf( $equal(and(not(X_36),or(falsehood,falsehood)),falsehood) )],[refute_0_635,refute_0_641]) ).
cnf(refute_0_643,plain,
or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) = or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),
introduced(tautology,[refl,[$fot(or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))))]]) ).
cnf(refute_0_644,plain,
( and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) != falsehood
| or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) != or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))
| or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) = or(and(X_36,and(truth,truth)),falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_645,plain,
( and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) != falsehood
| or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) = or(and(X_36,and(truth,truth)),falsehood) ),
inference(resolve,[$cnf( $equal(or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))) )],[refute_0_643,refute_0_644]) ).
cnf(refute_0_646,plain,
or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) = or(and(X_36,and(truth,truth)),falsehood),
inference(resolve,[$cnf( $equal(and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),falsehood) )],[refute_0_642,refute_0_645]) ).
cnf(refute_0_647,plain,
or(falsehood,and(truth,or(falsehood,and(truth,truth)))) = or(falsehood,and(truth,or(falsehood,and(truth,truth)))),
introduced(tautology,[refl,[$fot(or(falsehood,and(truth,or(falsehood,and(truth,truth)))))]]) ).
cnf(refute_0_648,plain,
( and(truth,or(falsehood,and(truth,truth))) != and(truth,truth)
| or(falsehood,and(truth,or(falsehood,and(truth,truth)))) != or(falsehood,and(truth,or(falsehood,and(truth,truth))))
| or(falsehood,and(truth,or(falsehood,and(truth,truth)))) = or(falsehood,and(truth,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,and(truth,truth)))),or(falsehood,and(truth,or(falsehood,and(truth,truth))))) ),[1,1],$fot(and(truth,truth))]]) ).
cnf(refute_0_649,plain,
( and(truth,or(falsehood,and(truth,truth))) != and(truth,truth)
| or(falsehood,and(truth,or(falsehood,and(truth,truth)))) = or(falsehood,and(truth,truth)) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,and(truth,truth)))),or(falsehood,and(truth,or(falsehood,and(truth,truth))))) )],[refute_0_647,refute_0_648]) ).
cnf(refute_0_650,plain,
or(falsehood,and(truth,or(falsehood,and(truth,truth)))) = or(falsehood,and(truth,truth)),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,and(truth,truth))),and(truth,truth)) )],[refute_0_616,refute_0_649]) ).
cnf(refute_0_651,plain,
( or(falsehood,and(truth,or(falsehood,and(truth,truth)))) != or(falsehood,and(truth,truth))
| or(falsehood,and(truth,truth)) != truth
| or(falsehood,and(truth,or(falsehood,and(truth,truth)))) = truth ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),bind(Y0,$fot(or(falsehood,and(truth,truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_652,plain,
( or(falsehood,and(truth,truth)) != truth
| or(falsehood,and(truth,or(falsehood,and(truth,truth)))) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,and(truth,truth)))),or(falsehood,and(truth,truth))) )],[refute_0_650,refute_0_651]) ).
cnf(refute_0_653,plain,
or(falsehood,and(truth,or(falsehood,and(truth,truth)))) = truth,
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),truth) )],[refute_0_569,refute_0_652]) ).
cnf(refute_0_654,plain,
and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) = and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))),
introduced(tautology,[refl,[$fot(and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))))]]) ).
cnf(refute_0_655,plain,
( and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) != and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))
| or(falsehood,and(truth,or(falsehood,and(truth,truth)))) != truth
| and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) = and(truth,truth) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))),and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_656,plain,
( or(falsehood,and(truth,or(falsehood,and(truth,truth)))) != truth
| and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) = and(truth,truth) ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))),and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) = and(truth,truth),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,and(truth,truth)))),truth) )],[refute_0_653,refute_0_656]) ).
cnf(refute_0_658,plain,
and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))) = and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),
introduced(tautology,[refl,[$fot(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))))]]) ).
cnf(refute_0_659,plain,
( and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))) != and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))))
| and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) != and(truth,truth)
| and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))) = and(X_36,and(truth,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))))) ),[1,1],$fot(and(truth,truth))]]) ).
cnf(refute_0_660,plain,
( and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))) != and(truth,truth)
| and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))) = and(X_36,and(truth,truth)) ),
inference(resolve,[$cnf( $equal(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))))) )],[refute_0_658,refute_0_659]) ).
cnf(refute_0_661,plain,
and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))) = and(X_36,and(truth,truth)),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth))))),and(truth,truth)) )],[refute_0_657,refute_0_660]) ).
cnf(refute_0_662,plain,
or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) = or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),
introduced(tautology,[refl,[$fot(or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))))]]) ).
cnf(refute_0_663,plain,
( and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))) != and(X_36,and(truth,truth))
| or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) != or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))
| or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) = or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))) ),[1,0],$fot(and(X_36,and(truth,truth)))]]) ).
cnf(refute_0_664,plain,
( and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))) != and(X_36,and(truth,truth))
| or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) = or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) ),
inference(resolve,[$cnf( $equal(or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))) )],[refute_0_662,refute_0_663]) ).
cnf(refute_0_665,plain,
or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) = or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),
inference(resolve,[$cnf( $equal(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(X_36,and(truth,truth))) )],[refute_0_661,refute_0_664]) ).
cnf(refute_0_666,plain,
( or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) != or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))
| or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) != or(and(X_36,and(truth,truth)),falsehood)
| or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) = or(and(X_36,and(truth,truth)),falsehood) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))))),bind(Y0,$fot(or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))))),bind(Z0,$fot(or(and(X_36,and(truth,truth)),falsehood)))]]) ).
cnf(refute_0_667,plain,
( or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) != or(and(X_36,and(truth,truth)),falsehood)
| or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) = or(and(X_36,and(truth,truth)),falsehood) ),
inference(resolve,[$cnf( $equal(or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))) )],[refute_0_665,refute_0_666]) ).
cnf(refute_0_668,plain,
or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) = or(and(X_36,and(truth,truth)),falsehood),
inference(resolve,[$cnf( $equal(or(and(X_36,and(truth,truth)),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),or(and(X_36,and(truth,truth)),falsehood)) )],[refute_0_646,refute_0_667]) ).
cnf(refute_0_669,plain,
( or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) != or(and(X_36,and(truth,truth)),falsehood)
| or(and(X_36,and(truth,truth)),falsehood) != or(falsehood,and(X_36,and(truth,truth)))
| or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) = or(falsehood,and(X_36,and(truth,truth))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))))),bind(Y0,$fot(or(and(X_36,and(truth,truth)),falsehood))),bind(Z0,$fot(or(falsehood,and(X_36,and(truth,truth)))))]]) ).
cnf(refute_0_670,plain,
( or(and(X_36,and(truth,truth)),falsehood) != or(falsehood,and(X_36,and(truth,truth)))
| or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) = or(falsehood,and(X_36,and(truth,truth))) ),
inference(resolve,[$cnf( $equal(or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),or(and(X_36,and(truth,truth)),falsehood)) )],[refute_0_668,refute_0_669]) ).
cnf(refute_0_671,plain,
or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) = or(falsehood,and(X_36,and(truth,truth))),
inference(resolve,[$cnf( $equal(or(and(X_36,and(truth,truth)),falsehood),or(falsehood,and(X_36,and(truth,truth)))) )],[refute_0_601,refute_0_670]) ).
cnf(refute_0_672,plain,
( or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))) != or(falsehood,and(X_36,and(truth,truth)))
| xor(X_36,or(falsehood,falsehood)) != or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))
| xor(X_36,or(falsehood,falsehood)) = or(falsehood,and(X_36,and(truth,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_36,or(falsehood,falsehood)),or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))) ),[1],$fot(or(falsehood,and(X_36,and(truth,truth))))]]) ).
cnf(refute_0_673,plain,
( xor(X_36,or(falsehood,falsehood)) != or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))
| xor(X_36,or(falsehood,falsehood)) = or(falsehood,and(X_36,and(truth,truth))) ),
inference(resolve,[$cnf( $equal(or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood))))))),or(falsehood,and(X_36,and(truth,truth)))) )],[refute_0_671,refute_0_672]) ).
cnf(refute_0_674,plain,
( xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))) != or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))
| xor(X_36,or(falsehood,falsehood)) = or(falsehood,and(X_36,and(truth,truth))) ),
inference(resolve,[$cnf( $equal(xor(X_36,or(falsehood,falsehood)),or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))) )],[refute_0_600,refute_0_673]) ).
cnf(refute_0_675,plain,
xor(X_36,or(falsehood,falsehood)) = or(falsehood,and(X_36,and(truth,truth))),
inference(resolve,[$cnf( $equal(xor(X_36,or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))),or(and(X_36,and(truth,or(falsehood,and(truth,or(falsehood,and(truth,truth)))))),and(not(X_36),or(falsehood,and(truth,or(falsehood,and(truth,or(falsehood,falsehood)))))))) )],[refute_0_113,refute_0_674]) ).
cnf(refute_0_676,plain,
implies(implies(X,falsehood),falsehood) = implies(implies(falsehood,X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_677,plain,
( implies(falsehood,X) != truth
| implies(implies(X,falsehood),falsehood) != implies(implies(falsehood,X),X)
| implies(implies(X,falsehood),falsehood) = implies(truth,X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,falsehood),falsehood),implies(implies(falsehood,X),X)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_678,plain,
( implies(implies(X,falsehood),falsehood) != implies(implies(falsehood,X),X)
| implies(implies(X,falsehood),falsehood) = implies(truth,X) ),
inference(resolve,[$cnf( $equal(implies(falsehood,X),truth) )],[refute_0_546,refute_0_677]) ).
cnf(refute_0_679,plain,
implies(implies(X,falsehood),falsehood) = implies(truth,X),
inference(resolve,[$cnf( $equal(implies(implies(X,falsehood),falsehood),implies(implies(falsehood,X),X)) )],[refute_0_676,refute_0_678]) ).
cnf(refute_0_680,plain,
( implies(implies(X,falsehood),falsehood) != implies(truth,X)
| implies(truth,X) != X
| implies(implies(X,falsehood),falsehood) = X ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X,falsehood),falsehood),X) ),[0],$fot(implies(truth,X))]]) ).
cnf(refute_0_681,plain,
( implies(implies(X,falsehood),falsehood) != implies(truth,X)
| implies(implies(X,falsehood),falsehood) = X ),
inference(resolve,[$cnf( $equal(implies(truth,X),X) )],[wajsberg_1,refute_0_680]) ).
cnf(refute_0_682,plain,
implies(implies(X,falsehood),falsehood) = X,
inference(resolve,[$cnf( $equal(implies(implies(X,falsehood),falsehood),implies(truth,X)) )],[refute_0_679,refute_0_681]) ).
cnf(refute_0_683,plain,
implies(implies(or(falsehood,falsehood),falsehood),falsehood) = or(falsehood,falsehood),
inference(subst,[],[refute_0_682:[bind(X,$fot(or(falsehood,falsehood)))]]) ).
cnf(refute_0_684,plain,
implies(or(falsehood,falsehood),falsehood) = truth,
inference(subst,[],[refute_0_146:[bind(X_21,$fot(falsehood))]]) ).
cnf(refute_0_685,plain,
( implies(implies(or(falsehood,falsehood),falsehood),falsehood) != or(falsehood,falsehood)
| implies(or(falsehood,falsehood),falsehood) != truth
| implies(truth,falsehood) = or(falsehood,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(or(falsehood,falsehood),falsehood),falsehood),or(falsehood,falsehood)) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_686,plain,
( implies(implies(or(falsehood,falsehood),falsehood),falsehood) != or(falsehood,falsehood)
| implies(truth,falsehood) = or(falsehood,falsehood) ),
inference(resolve,[$cnf( $equal(implies(or(falsehood,falsehood),falsehood),truth) )],[refute_0_684,refute_0_685]) ).
cnf(refute_0_687,plain,
implies(truth,falsehood) = or(falsehood,falsehood),
inference(resolve,[$cnf( $equal(implies(implies(or(falsehood,falsehood),falsehood),falsehood),or(falsehood,falsehood)) )],[refute_0_683,refute_0_686]) ).
cnf(refute_0_688,plain,
implies(truth,falsehood) = falsehood,
inference(subst,[],[wajsberg_1:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_689,plain,
( implies(truth,falsehood) != falsehood
| implies(truth,falsehood) != or(falsehood,falsehood)
| falsehood = or(falsehood,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,falsehood),or(falsehood,falsehood)) ),[0],$fot(falsehood)]]) ).
cnf(refute_0_690,plain,
( implies(truth,falsehood) != or(falsehood,falsehood)
| falsehood = or(falsehood,falsehood) ),
inference(resolve,[$cnf( $equal(implies(truth,falsehood),falsehood) )],[refute_0_688,refute_0_689]) ).
cnf(refute_0_691,plain,
falsehood = or(falsehood,falsehood),
inference(resolve,[$cnf( $equal(implies(truth,falsehood),or(falsehood,falsehood)) )],[refute_0_687,refute_0_690]) ).
cnf(refute_0_692,plain,
( falsehood != or(falsehood,falsehood)
| or(falsehood,falsehood) = falsehood ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(falsehood)),bind(Y0,$fot(or(falsehood,falsehood)))]]) ).
cnf(refute_0_693,plain,
or(falsehood,falsehood) = falsehood,
inference(resolve,[$cnf( $equal(falsehood,or(falsehood,falsehood)) )],[refute_0_691,refute_0_692]) ).
cnf(refute_0_694,plain,
xor(X_36,or(falsehood,falsehood)) = xor(X_36,or(falsehood,falsehood)),
introduced(tautology,[refl,[$fot(xor(X_36,or(falsehood,falsehood)))]]) ).
cnf(refute_0_695,plain,
( or(falsehood,falsehood) != falsehood
| xor(X_36,or(falsehood,falsehood)) != xor(X_36,or(falsehood,falsehood))
| xor(X_36,or(falsehood,falsehood)) = xor(X_36,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_36,or(falsehood,falsehood)),xor(X_36,or(falsehood,falsehood))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_696,plain,
( or(falsehood,falsehood) != falsehood
| xor(X_36,or(falsehood,falsehood)) = xor(X_36,falsehood) ),
inference(resolve,[$cnf( $equal(xor(X_36,or(falsehood,falsehood)),xor(X_36,or(falsehood,falsehood))) )],[refute_0_694,refute_0_695]) ).
cnf(refute_0_697,plain,
xor(X_36,or(falsehood,falsehood)) = xor(X_36,falsehood),
inference(resolve,[$cnf( $equal(or(falsehood,falsehood),falsehood) )],[refute_0_693,refute_0_696]) ).
cnf(refute_0_698,plain,
( xor(X_36,or(falsehood,falsehood)) != or(falsehood,and(X_36,and(truth,truth)))
| xor(X_36,or(falsehood,falsehood)) != xor(X_36,falsehood)
| xor(X_36,falsehood) = or(falsehood,and(X_36,and(truth,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_36,or(falsehood,falsehood)),or(falsehood,and(X_36,and(truth,truth)))) ),[0],$fot(xor(X_36,falsehood))]]) ).
cnf(refute_0_699,plain,
( xor(X_36,or(falsehood,falsehood)) != or(falsehood,and(X_36,and(truth,truth)))
| xor(X_36,falsehood) = or(falsehood,and(X_36,and(truth,truth))) ),
inference(resolve,[$cnf( $equal(xor(X_36,or(falsehood,falsehood)),xor(X_36,falsehood)) )],[refute_0_697,refute_0_698]) ).
cnf(refute_0_700,plain,
not(or(falsehood,falsehood)) = not(or(falsehood,falsehood)),
introduced(tautology,[refl,[$fot(not(or(falsehood,falsehood)))]]) ).
cnf(refute_0_701,plain,
( not(or(falsehood,falsehood)) != not(or(falsehood,falsehood))
| or(falsehood,falsehood) != falsehood
| not(or(falsehood,falsehood)) = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,falsehood)),not(or(falsehood,falsehood))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_702,plain,
( or(falsehood,falsehood) != falsehood
| not(or(falsehood,falsehood)) = not(falsehood) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,falsehood)),not(or(falsehood,falsehood))) )],[refute_0_700,refute_0_701]) ).
cnf(refute_0_703,plain,
not(or(falsehood,falsehood)) = not(falsehood),
inference(resolve,[$cnf( $equal(or(falsehood,falsehood),falsehood) )],[refute_0_693,refute_0_702]) ).
cnf(refute_0_704,plain,
( and(truth,truth) != not(or(falsehood,falsehood))
| not(or(falsehood,falsehood)) != not(falsehood)
| and(truth,truth) = not(falsehood) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(truth,truth),not(falsehood)) ),[0],$fot(not(or(falsehood,falsehood)))]]) ).
cnf(refute_0_705,plain,
( and(truth,truth) != not(or(falsehood,falsehood))
| and(truth,truth) = not(falsehood) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,falsehood)),not(falsehood)) )],[refute_0_703,refute_0_704]) ).
cnf(refute_0_706,plain,
and(truth,truth) = not(falsehood),
inference(resolve,[$cnf( $equal(and(truth,truth),not(or(falsehood,falsehood))) )],[refute_0_73,refute_0_705]) ).
cnf(refute_0_707,plain,
and(X_36,and(truth,truth)) = and(X_36,and(truth,truth)),
introduced(tautology,[refl,[$fot(and(X_36,and(truth,truth)))]]) ).
cnf(refute_0_708,plain,
( and(X_36,and(truth,truth)) != and(X_36,and(truth,truth))
| and(truth,truth) != not(falsehood)
| and(X_36,and(truth,truth)) = and(X_36,not(falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_36,and(truth,truth)),and(X_36,and(truth,truth))) ),[1,1],$fot(not(falsehood))]]) ).
cnf(refute_0_709,plain,
( and(truth,truth) != not(falsehood)
| and(X_36,and(truth,truth)) = and(X_36,not(falsehood)) ),
inference(resolve,[$cnf( $equal(and(X_36,and(truth,truth)),and(X_36,and(truth,truth))) )],[refute_0_707,refute_0_708]) ).
cnf(refute_0_710,plain,
and(X_36,and(truth,truth)) = and(X_36,not(falsehood)),
inference(resolve,[$cnf( $equal(and(truth,truth),not(falsehood)) )],[refute_0_706,refute_0_709]) ).
cnf(refute_0_711,plain,
or(falsehood,and(X_36,and(truth,truth))) = or(falsehood,and(X_36,and(truth,truth))),
introduced(tautology,[refl,[$fot(or(falsehood,and(X_36,and(truth,truth))))]]) ).
cnf(refute_0_712,plain,
( and(X_36,and(truth,truth)) != and(X_36,not(falsehood))
| or(falsehood,and(X_36,and(truth,truth))) != or(falsehood,and(X_36,and(truth,truth)))
| or(falsehood,and(X_36,and(truth,truth))) = or(falsehood,and(X_36,not(falsehood))) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,and(X_36,and(truth,truth))),or(falsehood,and(X_36,and(truth,truth)))) ),[1,1],$fot(and(X_36,not(falsehood)))]]) ).
cnf(refute_0_713,plain,
( and(X_36,and(truth,truth)) != and(X_36,not(falsehood))
| or(falsehood,and(X_36,and(truth,truth))) = or(falsehood,and(X_36,not(falsehood))) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(X_36,and(truth,truth))),or(falsehood,and(X_36,and(truth,truth)))) )],[refute_0_711,refute_0_712]) ).
cnf(refute_0_714,plain,
or(falsehood,and(X_36,and(truth,truth))) = or(falsehood,and(X_36,not(falsehood))),
inference(resolve,[$cnf( $equal(and(X_36,and(truth,truth)),and(X_36,not(falsehood))) )],[refute_0_710,refute_0_713]) ).
cnf(refute_0_715,plain,
( or(falsehood,and(X_36,and(truth,truth))) != or(falsehood,and(X_36,not(falsehood)))
| xor(X_36,falsehood) != or(falsehood,and(X_36,and(truth,truth)))
| xor(X_36,falsehood) = or(falsehood,and(X_36,not(falsehood))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_36,falsehood),or(falsehood,and(X_36,and(truth,truth)))) ),[1],$fot(or(falsehood,and(X_36,not(falsehood))))]]) ).
cnf(refute_0_716,plain,
( xor(X_36,falsehood) != or(falsehood,and(X_36,and(truth,truth)))
| xor(X_36,falsehood) = or(falsehood,and(X_36,not(falsehood))) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(X_36,and(truth,truth))),or(falsehood,and(X_36,not(falsehood)))) )],[refute_0_714,refute_0_715]) ).
cnf(refute_0_717,plain,
( xor(X_36,or(falsehood,falsehood)) != or(falsehood,and(X_36,and(truth,truth)))
| xor(X_36,falsehood) = or(falsehood,and(X_36,not(falsehood))) ),
inference(resolve,[$cnf( $equal(xor(X_36,falsehood),or(falsehood,and(X_36,and(truth,truth)))) )],[refute_0_699,refute_0_716]) ).
cnf(refute_0_718,plain,
xor(X_36,falsehood) = or(falsehood,and(X_36,not(falsehood))),
inference(resolve,[$cnf( $equal(xor(X_36,or(falsehood,falsehood)),or(falsehood,and(X_36,and(truth,truth)))) )],[refute_0_675,refute_0_717]) ).
cnf(refute_0_719,plain,
implies(implies(not(X),falsehood),falsehood) = not(X),
inference(subst,[],[refute_0_682:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_720,plain,
or(X,falsehood) = implies(not(X),falsehood),
inference(subst,[],[or_definition:[bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_721,plain,
( or(X,falsehood) != implies(not(X),falsehood)
| implies(not(X),falsehood) = or(X,falsehood) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,falsehood))),bind(Y0,$fot(implies(not(X),falsehood)))]]) ).
cnf(refute_0_722,plain,
implies(not(X),falsehood) = or(X,falsehood),
inference(resolve,[$cnf( $equal(or(X,falsehood),implies(not(X),falsehood)) )],[refute_0_720,refute_0_721]) ).
cnf(refute_0_723,plain,
( implies(implies(not(X),falsehood),falsehood) != not(X)
| implies(not(X),falsehood) != or(X,falsehood)
| implies(or(X,falsehood),falsehood) = not(X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),falsehood),falsehood),not(X)) ),[0,0],$fot(or(X,falsehood))]]) ).
cnf(refute_0_724,plain,
( implies(implies(not(X),falsehood),falsehood) != not(X)
| implies(or(X,falsehood),falsehood) = not(X) ),
inference(resolve,[$cnf( $equal(implies(not(X),falsehood),or(X,falsehood)) )],[refute_0_722,refute_0_723]) ).
cnf(refute_0_725,plain,
implies(or(X,falsehood),falsehood) = not(X),
inference(resolve,[$cnf( $equal(implies(implies(not(X),falsehood),falsehood),not(X)) )],[refute_0_719,refute_0_724]) ).
cnf(refute_0_726,plain,
implies(or(falsehood,falsehood),falsehood) = not(falsehood),
inference(subst,[],[refute_0_725:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_727,plain,
( implies(or(falsehood,falsehood),falsehood) != not(falsehood)
| implies(or(falsehood,falsehood),falsehood) != truth
| not(falsehood) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,falsehood),falsehood),truth) ),[0],$fot(not(falsehood))]]) ).
cnf(refute_0_728,plain,
( implies(or(falsehood,falsehood),falsehood) != truth
| not(falsehood) = truth ),
inference(resolve,[$cnf( $equal(implies(or(falsehood,falsehood),falsehood),not(falsehood)) )],[refute_0_726,refute_0_727]) ).
cnf(refute_0_729,plain,
not(falsehood) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,falsehood),falsehood),truth) )],[refute_0_684,refute_0_728]) ).
cnf(refute_0_730,plain,
and(X_36,not(falsehood)) = and(X_36,not(falsehood)),
introduced(tautology,[refl,[$fot(and(X_36,not(falsehood)))]]) ).
cnf(refute_0_731,plain,
( and(X_36,not(falsehood)) != and(X_36,not(falsehood))
| not(falsehood) != truth
| and(X_36,not(falsehood)) = and(X_36,truth) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_36,not(falsehood)),and(X_36,not(falsehood))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_732,plain,
( not(falsehood) != truth
| and(X_36,not(falsehood)) = and(X_36,truth) ),
inference(resolve,[$cnf( $equal(and(X_36,not(falsehood)),and(X_36,not(falsehood))) )],[refute_0_730,refute_0_731]) ).
cnf(refute_0_733,plain,
and(X_36,not(falsehood)) = and(X_36,truth),
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_729,refute_0_732]) ).
cnf(refute_0_734,plain,
or(falsehood,and(X_36,not(falsehood))) = or(falsehood,and(X_36,not(falsehood))),
introduced(tautology,[refl,[$fot(or(falsehood,and(X_36,not(falsehood))))]]) ).
cnf(refute_0_735,plain,
( and(X_36,not(falsehood)) != and(X_36,truth)
| or(falsehood,and(X_36,not(falsehood))) != or(falsehood,and(X_36,not(falsehood)))
| or(falsehood,and(X_36,not(falsehood))) = or(falsehood,and(X_36,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,and(X_36,not(falsehood))),or(falsehood,and(X_36,not(falsehood)))) ),[1,1],$fot(and(X_36,truth))]]) ).
cnf(refute_0_736,plain,
( and(X_36,not(falsehood)) != and(X_36,truth)
| or(falsehood,and(X_36,not(falsehood))) = or(falsehood,and(X_36,truth)) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(X_36,not(falsehood))),or(falsehood,and(X_36,not(falsehood)))) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
or(falsehood,and(X_36,not(falsehood))) = or(falsehood,and(X_36,truth)),
inference(resolve,[$cnf( $equal(and(X_36,not(falsehood)),and(X_36,truth)) )],[refute_0_733,refute_0_736]) ).
cnf(refute_0_738,plain,
( or(falsehood,and(X_36,not(falsehood))) != or(falsehood,and(X_36,truth))
| xor(X_36,falsehood) != or(falsehood,and(X_36,not(falsehood)))
| xor(X_36,falsehood) = or(falsehood,and(X_36,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_36,falsehood),or(falsehood,and(X_36,not(falsehood)))) ),[1],$fot(or(falsehood,and(X_36,truth)))]]) ).
cnf(refute_0_739,plain,
( xor(X_36,falsehood) != or(falsehood,and(X_36,not(falsehood)))
| xor(X_36,falsehood) = or(falsehood,and(X_36,truth)) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(X_36,not(falsehood))),or(falsehood,and(X_36,truth))) )],[refute_0_737,refute_0_738]) ).
cnf(refute_0_740,plain,
xor(X_36,falsehood) = or(falsehood,and(X_36,truth)),
inference(resolve,[$cnf( $equal(xor(X_36,falsehood),or(falsehood,and(X_36,not(falsehood)))) )],[refute_0_718,refute_0_739]) ).
cnf(refute_0_741,plain,
( xor(X_36,falsehood) != or(falsehood,and(X_36,truth))
| or(falsehood,and(X_36,truth)) = xor(X_36,falsehood) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(X_36,falsehood))),bind(Y0,$fot(or(falsehood,and(X_36,truth))))]]) ).
cnf(refute_0_742,plain,
or(falsehood,and(X_36,truth)) = xor(X_36,falsehood),
inference(resolve,[$cnf( $equal(xor(X_36,falsehood),or(falsehood,and(X_36,truth))) )],[refute_0_740,refute_0_741]) ).
cnf(refute_0_743,plain,
or(falsehood,and(X_27,truth)) = xor(X_27,falsehood),
inference(subst,[],[refute_0_742:[bind(X_36,$fot(X_27))]]) ).
cnf(refute_0_744,plain,
not(or(falsehood,and(X_27,truth))) = not(or(falsehood,and(X_27,truth))),
introduced(tautology,[refl,[$fot(not(or(falsehood,and(X_27,truth))))]]) ).
cnf(refute_0_745,plain,
( not(or(falsehood,and(X_27,truth))) != not(or(falsehood,and(X_27,truth)))
| or(falsehood,and(X_27,truth)) != xor(X_27,falsehood)
| not(or(falsehood,and(X_27,truth))) = not(xor(X_27,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,and(X_27,truth))),not(or(falsehood,and(X_27,truth)))) ),[1,0],$fot(xor(X_27,falsehood))]]) ).
cnf(refute_0_746,plain,
( or(falsehood,and(X_27,truth)) != xor(X_27,falsehood)
| not(or(falsehood,and(X_27,truth))) = not(xor(X_27,falsehood)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(X_27,truth))),not(or(falsehood,and(X_27,truth)))) )],[refute_0_744,refute_0_745]) ).
cnf(refute_0_747,plain,
not(or(falsehood,and(X_27,truth))) = not(xor(X_27,falsehood)),
inference(resolve,[$cnf( $equal(or(falsehood,and(X_27,truth)),xor(X_27,falsehood)) )],[refute_0_743,refute_0_746]) ).
cnf(refute_0_748,plain,
( not(or(falsehood,and(X_27,truth))) != not(or(falsehood,and(truth,X_27)))
| not(or(falsehood,and(X_27,truth))) != not(xor(X_27,falsehood))
| not(xor(X_27,falsehood)) = not(or(falsehood,and(truth,X_27))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,and(X_27,truth))),not(or(falsehood,and(truth,X_27)))) ),[0],$fot(not(xor(X_27,falsehood)))]]) ).
cnf(refute_0_749,plain,
( not(or(falsehood,and(X_27,truth))) != not(or(falsehood,and(truth,X_27)))
| not(xor(X_27,falsehood)) = not(or(falsehood,and(truth,X_27))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(X_27,truth))),not(xor(X_27,falsehood))) )],[refute_0_747,refute_0_748]) ).
cnf(refute_0_750,plain,
not(xor(X_27,falsehood)) = not(or(falsehood,and(truth,X_27))),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(X_27,truth))),not(or(falsehood,and(truth,X_27)))) )],[refute_0_65,refute_0_749]) ).
cnf(refute_0_751,plain,
or(falsehood,Y) = implies(not(falsehood),Y),
inference(subst,[],[or_definition:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_752,plain,
( not(falsehood) != truth
| or(falsehood,Y) != implies(not(falsehood),Y)
| or(falsehood,Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,Y),implies(not(falsehood),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_753,plain,
( or(falsehood,Y) != implies(not(falsehood),Y)
| or(falsehood,Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_729,refute_0_752]) ).
cnf(refute_0_754,plain,
or(falsehood,Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(or(falsehood,Y),implies(not(falsehood),Y)) )],[refute_0_751,refute_0_753]) ).
cnf(refute_0_755,plain,
( implies(truth,Y) != Y
| or(falsehood,Y) != implies(truth,Y)
| or(falsehood,Y) = Y ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,Y),implies(truth,Y)) ),[1],$fot(Y)]]) ).
cnf(refute_0_756,plain,
( or(falsehood,Y) != implies(truth,Y)
| or(falsehood,Y) = Y ),
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_450,refute_0_755]) ).
cnf(refute_0_757,plain,
or(falsehood,Y) = Y,
inference(resolve,[$cnf( $equal(or(falsehood,Y),implies(truth,Y)) )],[refute_0_754,refute_0_756]) ).
cnf(refute_0_758,plain,
or(falsehood,and(truth,X_27)) = and(truth,X_27),
inference(subst,[],[refute_0_757:[bind(Y,$fot(and(truth,X_27)))]]) ).
cnf(refute_0_759,plain,
not(or(falsehood,and(truth,X_27))) = not(or(falsehood,and(truth,X_27))),
introduced(tautology,[refl,[$fot(not(or(falsehood,and(truth,X_27))))]]) ).
cnf(refute_0_760,plain,
( not(or(falsehood,and(truth,X_27))) != not(or(falsehood,and(truth,X_27)))
| or(falsehood,and(truth,X_27)) != and(truth,X_27)
| not(or(falsehood,and(truth,X_27))) = not(and(truth,X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,and(truth,X_27))),not(or(falsehood,and(truth,X_27)))) ),[1,0],$fot(and(truth,X_27))]]) ).
cnf(refute_0_761,plain,
( or(falsehood,and(truth,X_27)) != and(truth,X_27)
| not(or(falsehood,and(truth,X_27))) = not(and(truth,X_27)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,X_27))),not(or(falsehood,and(truth,X_27)))) )],[refute_0_759,refute_0_760]) ).
cnf(refute_0_762,plain,
not(or(falsehood,and(truth,X_27))) = not(and(truth,X_27)),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,X_27)),and(truth,X_27)) )],[refute_0_758,refute_0_761]) ).
cnf(refute_0_763,plain,
( not(or(falsehood,and(truth,X_27))) != not(and(truth,X_27))
| not(xor(X_27,falsehood)) != not(or(falsehood,and(truth,X_27)))
| not(xor(X_27,falsehood)) = not(and(truth,X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(not(xor(X_27,falsehood)),not(or(falsehood,and(truth,X_27)))) ),[1],$fot(not(and(truth,X_27)))]]) ).
cnf(refute_0_764,plain,
( not(xor(X_27,falsehood)) != not(or(falsehood,and(truth,X_27)))
| not(xor(X_27,falsehood)) = not(and(truth,X_27)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,X_27))),not(and(truth,X_27))) )],[refute_0_762,refute_0_763]) ).
cnf(refute_0_765,plain,
not(xor(X_27,falsehood)) = not(and(truth,X_27)),
inference(resolve,[$cnf( $equal(not(xor(X_27,falsehood)),not(or(falsehood,and(truth,X_27)))) )],[refute_0_750,refute_0_764]) ).
cnf(refute_0_766,plain,
xor(or(falsehood,and(truth,truth)),X_37) = or(and(or(falsehood,and(truth,truth)),not(X_37)),and(not(or(falsehood,and(truth,truth))),X_37)),
inference(subst,[],[xor_definition:[bind(X,$fot(or(falsehood,and(truth,truth)))),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_767,plain,
( not(or(falsehood,and(truth,truth))) != and(truth,or(falsehood,falsehood))
| xor(or(falsehood,and(truth,truth)),X_37) != or(and(or(falsehood,and(truth,truth)),not(X_37)),and(not(or(falsehood,and(truth,truth))),X_37))
| xor(or(falsehood,and(truth,truth)),X_37) = or(and(or(falsehood,and(truth,truth)),not(X_37)),and(and(truth,or(falsehood,falsehood)),X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(or(falsehood,and(truth,truth)),X_37),or(and(or(falsehood,and(truth,truth)),not(X_37)),and(not(or(falsehood,and(truth,truth))),X_37))) ),[1,1,0],$fot(and(truth,or(falsehood,falsehood)))]]) ).
cnf(refute_0_768,plain,
( xor(or(falsehood,and(truth,truth)),X_37) != or(and(or(falsehood,and(truth,truth)),not(X_37)),and(not(or(falsehood,and(truth,truth))),X_37))
| xor(or(falsehood,and(truth,truth)),X_37) = or(and(or(falsehood,and(truth,truth)),not(X_37)),and(and(truth,or(falsehood,falsehood)),X_37)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,truth))),and(truth,or(falsehood,falsehood))) )],[refute_0_84,refute_0_767]) ).
cnf(refute_0_769,plain,
xor(or(falsehood,and(truth,truth)),X_37) = or(and(or(falsehood,and(truth,truth)),not(X_37)),and(and(truth,or(falsehood,falsehood)),X_37)),
inference(resolve,[$cnf( $equal(xor(or(falsehood,and(truth,truth)),X_37),or(and(or(falsehood,and(truth,truth)),not(X_37)),and(not(or(falsehood,and(truth,truth))),X_37))) )],[refute_0_766,refute_0_768]) ).
cnf(refute_0_770,plain,
and(and(truth,or(falsehood,falsehood)),X_37) = and(truth,and(or(falsehood,falsehood),X_37)),
inference(subst,[],[and_associativity:[bind(X,$fot(truth)),bind(Y,$fot(or(falsehood,falsehood))),bind(Z,$fot(X_37))]]) ).
cnf(refute_0_771,plain,
or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37))) = or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37))),
introduced(tautology,[refl,[$fot(or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37))))]]) ).
cnf(refute_0_772,plain,
( and(and(truth,or(falsehood,falsehood)),X_37) != and(truth,and(or(falsehood,falsehood),X_37))
| or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37))) != or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37)))
| or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37))) = or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37))),or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37)))) ),[1,0],$fot(and(truth,and(or(falsehood,falsehood),X_37)))]]) ).
cnf(refute_0_773,plain,
( and(and(truth,or(falsehood,falsehood)),X_37) != and(truth,and(or(falsehood,falsehood),X_37))
| or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37))) = or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37))),or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37)))) )],[refute_0_771,refute_0_772]) ).
cnf(refute_0_774,plain,
or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37))) = or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))),
inference(resolve,[$cnf( $equal(and(and(truth,or(falsehood,falsehood)),X_37),and(truth,and(or(falsehood,falsehood),X_37))) )],[refute_0_770,refute_0_773]) ).
cnf(refute_0_775,plain,
or(and(or(falsehood,and(truth,truth)),not(X_37)),and(and(truth,or(falsehood,falsehood)),X_37)) = or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37))),
inference(subst,[],[refute_0_24:[bind(X,$fot(and(and(truth,or(falsehood,falsehood)),X_37))),bind(Y,$fot(and(or(falsehood,and(truth,truth)),not(X_37))))]]) ).
cnf(refute_0_776,plain,
( or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37))) != or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))
| or(and(or(falsehood,and(truth,truth)),not(X_37)),and(and(truth,or(falsehood,falsehood)),X_37)) != or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37)))
| or(and(or(falsehood,and(truth,truth)),not(X_37)),and(and(truth,or(falsehood,falsehood)),X_37)) = or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(or(and(or(falsehood,and(truth,truth)),not(X_37)),and(and(truth,or(falsehood,falsehood)),X_37)))),bind(Y0,$fot(or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37))))),bind(Z0,$fot(or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))))]]) ).
cnf(refute_0_777,plain,
( or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37))) != or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))
| or(and(or(falsehood,and(truth,truth)),not(X_37)),and(and(truth,or(falsehood,falsehood)),X_37)) = or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(or(falsehood,and(truth,truth)),not(X_37)),and(and(truth,or(falsehood,falsehood)),X_37)),or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37)))) )],[refute_0_775,refute_0_776]) ).
cnf(refute_0_778,plain,
or(and(or(falsehood,and(truth,truth)),not(X_37)),and(and(truth,or(falsehood,falsehood)),X_37)) = or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))),
inference(resolve,[$cnf( $equal(or(and(and(truth,or(falsehood,falsehood)),X_37),and(or(falsehood,and(truth,truth)),not(X_37))),or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))) )],[refute_0_774,refute_0_777]) ).
cnf(refute_0_779,plain,
( or(and(or(falsehood,and(truth,truth)),not(X_37)),and(and(truth,or(falsehood,falsehood)),X_37)) != or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))
| xor(or(falsehood,and(truth,truth)),X_37) != or(and(or(falsehood,and(truth,truth)),not(X_37)),and(and(truth,or(falsehood,falsehood)),X_37))
| xor(or(falsehood,and(truth,truth)),X_37) = or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(or(falsehood,and(truth,truth)),X_37),or(and(or(falsehood,and(truth,truth)),not(X_37)),and(and(truth,or(falsehood,falsehood)),X_37))) ),[1],$fot(or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))))]]) ).
cnf(refute_0_780,plain,
( xor(or(falsehood,and(truth,truth)),X_37) != or(and(or(falsehood,and(truth,truth)),not(X_37)),and(and(truth,or(falsehood,falsehood)),X_37))
| xor(or(falsehood,and(truth,truth)),X_37) = or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(or(falsehood,and(truth,truth)),not(X_37)),and(and(truth,or(falsehood,falsehood)),X_37)),or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))) )],[refute_0_778,refute_0_779]) ).
cnf(refute_0_781,plain,
xor(or(falsehood,and(truth,truth)),X_37) = or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))),
inference(resolve,[$cnf( $equal(xor(or(falsehood,and(truth,truth)),X_37),or(and(or(falsehood,and(truth,truth)),not(X_37)),and(and(truth,or(falsehood,falsehood)),X_37))) )],[refute_0_769,refute_0_780]) ).
cnf(refute_0_782,plain,
xor(or(falsehood,and(truth,truth)),X_37) = xor(or(falsehood,and(truth,truth)),X_37),
introduced(tautology,[refl,[$fot(xor(or(falsehood,and(truth,truth)),X_37))]]) ).
cnf(refute_0_783,plain,
( or(falsehood,and(truth,truth)) != truth
| xor(or(falsehood,and(truth,truth)),X_37) != xor(or(falsehood,and(truth,truth)),X_37)
| xor(or(falsehood,and(truth,truth)),X_37) = xor(truth,X_37) ),
introduced(tautology,[equality,[$cnf( $equal(xor(or(falsehood,and(truth,truth)),X_37),xor(or(falsehood,and(truth,truth)),X_37)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_784,plain,
( or(falsehood,and(truth,truth)) != truth
| xor(or(falsehood,and(truth,truth)),X_37) = xor(truth,X_37) ),
inference(resolve,[$cnf( $equal(xor(or(falsehood,and(truth,truth)),X_37),xor(or(falsehood,and(truth,truth)),X_37)) )],[refute_0_782,refute_0_783]) ).
cnf(refute_0_785,plain,
xor(or(falsehood,and(truth,truth)),X_37) = xor(truth,X_37),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),truth) )],[refute_0_569,refute_0_784]) ).
cnf(refute_0_786,plain,
( xor(or(falsehood,and(truth,truth)),X_37) != or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))
| xor(or(falsehood,and(truth,truth)),X_37) != xor(truth,X_37)
| xor(truth,X_37) = or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(or(falsehood,and(truth,truth)),X_37),or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))) ),[0],$fot(xor(truth,X_37))]]) ).
cnf(refute_0_787,plain,
( xor(or(falsehood,and(truth,truth)),X_37) != or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))
| xor(truth,X_37) = or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) ),
inference(resolve,[$cnf( $equal(xor(or(falsehood,and(truth,truth)),X_37),xor(truth,X_37)) )],[refute_0_785,refute_0_786]) ).
cnf(refute_0_788,plain,
and(or(falsehood,and(truth,truth)),not(X_37)) = and(or(falsehood,and(truth,truth)),not(X_37)),
introduced(tautology,[refl,[$fot(and(or(falsehood,and(truth,truth)),not(X_37)))]]) ).
cnf(refute_0_789,plain,
( and(or(falsehood,and(truth,truth)),not(X_37)) != and(or(falsehood,and(truth,truth)),not(X_37))
| or(falsehood,and(truth,truth)) != truth
| and(or(falsehood,and(truth,truth)),not(X_37)) = and(truth,not(X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,truth)),not(X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_790,plain,
( or(falsehood,and(truth,truth)) != truth
| and(or(falsehood,and(truth,truth)),not(X_37)) = and(truth,not(X_37)) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),not(X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) )],[refute_0_788,refute_0_789]) ).
cnf(refute_0_791,plain,
and(or(falsehood,and(truth,truth)),not(X_37)) = and(truth,not(X_37)),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),truth) )],[refute_0_569,refute_0_790]) ).
cnf(refute_0_792,plain,
or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37))) = or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37))),
introduced(tautology,[refl,[$fot(or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37))))]]) ).
cnf(refute_0_793,plain,
( and(or(falsehood,and(truth,truth)),not(X_37)) != and(truth,not(X_37))
| or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37))) != or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37)))
| or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37))) = or(and(falsehood,truth),and(truth,not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37))),or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37)))) ),[1,1],$fot(and(truth,not(X_37)))]]) ).
cnf(refute_0_794,plain,
( and(or(falsehood,and(truth,truth)),not(X_37)) != and(truth,not(X_37))
| or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37))) = or(and(falsehood,truth),and(truth,not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37))),or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37)))) )],[refute_0_792,refute_0_793]) ).
cnf(refute_0_795,plain,
or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37))) = or(and(falsehood,truth),and(truth,not(X_37))),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),not(X_37)),and(truth,not(X_37))) )],[refute_0_791,refute_0_794]) ).
cnf(refute_0_796,plain,
and(or(falsehood,and(truth,truth)),Y) = not(or(not(or(falsehood,and(truth,truth))),not(Y))),
inference(subst,[],[and_definition:[bind(X,$fot(or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_797,plain,
( and(or(falsehood,and(truth,truth)),Y) != not(or(not(or(falsehood,and(truth,truth))),not(Y)))
| not(or(falsehood,and(truth,truth))) != and(truth,or(falsehood,falsehood))
| and(or(falsehood,and(truth,truth)),Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),not(or(not(or(falsehood,and(truth,truth))),not(Y)))) ),[1,0,0],$fot(and(truth,or(falsehood,falsehood)))]]) ).
cnf(refute_0_798,plain,
( and(or(falsehood,and(truth,truth)),Y) != not(or(not(or(falsehood,and(truth,truth))),not(Y)))
| and(or(falsehood,and(truth,truth)),Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,truth))),and(truth,or(falsehood,falsehood))) )],[refute_0_84,refute_0_797]) ).
cnf(refute_0_799,plain,
and(or(falsehood,and(truth,truth)),Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),not(or(not(or(falsehood,and(truth,truth))),not(Y)))) )],[refute_0_796,refute_0_798]) ).
cnf(refute_0_800,plain,
and(or(falsehood,and(truth,truth)),Y) = and(or(falsehood,and(truth,truth)),Y),
introduced(tautology,[refl,[$fot(and(or(falsehood,and(truth,truth)),Y))]]) ).
cnf(refute_0_801,plain,
( and(or(falsehood,and(truth,truth)),Y) != and(or(falsehood,and(truth,truth)),Y)
| or(falsehood,and(truth,truth)) != truth
| and(or(falsehood,and(truth,truth)),Y) = and(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),and(or(falsehood,and(truth,truth)),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_802,plain,
( or(falsehood,and(truth,truth)) != truth
| and(or(falsehood,and(truth,truth)),Y) = and(truth,Y) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),and(or(falsehood,and(truth,truth)),Y)) )],[refute_0_800,refute_0_801]) ).
cnf(refute_0_803,plain,
and(or(falsehood,and(truth,truth)),Y) = and(truth,Y),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),truth) )],[refute_0_569,refute_0_802]) ).
cnf(refute_0_804,plain,
( and(or(falsehood,and(truth,truth)),Y) != and(truth,Y)
| and(or(falsehood,and(truth,truth)),Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) ),[0],$fot(and(truth,Y))]]) ).
cnf(refute_0_805,plain,
( and(or(falsehood,and(truth,truth)),Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),and(truth,Y)) )],[refute_0_803,refute_0_804]) ).
cnf(refute_0_806,plain,
not(or(falsehood,not(Y))) = and(Y,truth),
inference(subst,[],[refute_0_45:[bind(X_1,$fot(Y))]]) ).
cnf(refute_0_807,plain,
or(and(truth,or(falsehood,falsehood)),not(Y)) = or(and(truth,or(falsehood,falsehood)),not(Y)),
introduced(tautology,[refl,[$fot(or(and(truth,or(falsehood,falsehood)),not(Y)))]]) ).
cnf(refute_0_808,plain,
( and(truth,or(falsehood,falsehood)) != falsehood
| or(and(truth,or(falsehood,falsehood)),not(Y)) != or(and(truth,or(falsehood,falsehood)),not(Y))
| or(and(truth,or(falsehood,falsehood)),not(Y)) = or(falsehood,not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(truth,or(falsehood,falsehood)),not(Y)),or(and(truth,or(falsehood,falsehood)),not(Y))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_809,plain,
( and(truth,or(falsehood,falsehood)) != falsehood
| or(and(truth,or(falsehood,falsehood)),not(Y)) = or(falsehood,not(Y)) ),
inference(resolve,[$cnf( $equal(or(and(truth,or(falsehood,falsehood)),not(Y)),or(and(truth,or(falsehood,falsehood)),not(Y))) )],[refute_0_807,refute_0_808]) ).
cnf(refute_0_810,plain,
or(and(truth,or(falsehood,falsehood)),not(Y)) = or(falsehood,not(Y)),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),falsehood) )],[refute_0_579,refute_0_809]) ).
cnf(refute_0_811,plain,
not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(or(and(truth,or(falsehood,falsehood)),not(Y))),
introduced(tautology,[refl,[$fot(not(or(and(truth,or(falsehood,falsehood)),not(Y))))]]) ).
cnf(refute_0_812,plain,
( not(or(and(truth,or(falsehood,falsehood)),not(Y))) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| or(and(truth,or(falsehood,falsehood)),not(Y)) != or(falsehood,not(Y))
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(or(falsehood,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(and(truth,or(falsehood,falsehood)),not(Y))),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) ),[1,0],$fot(or(falsehood,not(Y)))]]) ).
cnf(refute_0_813,plain,
( or(and(truth,or(falsehood,falsehood)),not(Y)) != or(falsehood,not(Y))
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(or(falsehood,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(and(truth,or(falsehood,falsehood)),not(Y))),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) )],[refute_0_811,refute_0_812]) ).
cnf(refute_0_814,plain,
not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(or(falsehood,not(Y))),
inference(resolve,[$cnf( $equal(or(and(truth,or(falsehood,falsehood)),not(Y)),or(falsehood,not(Y))) )],[refute_0_810,refute_0_813]) ).
cnf(refute_0_815,plain,
( not(or(and(truth,or(falsehood,falsehood)),not(Y))) != not(or(falsehood,not(Y)))
| not(or(falsehood,not(Y))) != and(Y,truth)
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) = and(Y,truth) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(not(or(and(truth,or(falsehood,falsehood)),not(Y))))),bind(Y0,$fot(not(or(falsehood,not(Y))))),bind(Z0,$fot(and(Y,truth)))]]) ).
cnf(refute_0_816,plain,
( not(or(falsehood,not(Y))) != and(Y,truth)
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) = and(Y,truth) ),
inference(resolve,[$cnf( $equal(not(or(and(truth,or(falsehood,falsehood)),not(Y))),not(or(falsehood,not(Y)))) )],[refute_0_814,refute_0_815]) ).
cnf(refute_0_817,plain,
not(or(and(truth,or(falsehood,falsehood)),not(Y))) = and(Y,truth),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(Y))),and(Y,truth)) )],[refute_0_806,refute_0_816]) ).
cnf(refute_0_818,plain,
( and(truth,Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) != and(Y,truth)
| and(truth,Y) = and(Y,truth) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(truth,Y),and(Y,truth)) ),[0],$fot(not(or(and(truth,or(falsehood,falsehood)),not(Y))))]]) ).
cnf(refute_0_819,plain,
( and(truth,Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = and(Y,truth) ),
inference(resolve,[$cnf( $equal(not(or(and(truth,or(falsehood,falsehood)),not(Y))),and(Y,truth)) )],[refute_0_817,refute_0_818]) ).
cnf(refute_0_820,plain,
( and(or(falsehood,and(truth,truth)),Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = and(Y,truth) ),
inference(resolve,[$cnf( $equal(and(truth,Y),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) )],[refute_0_805,refute_0_819]) ).
cnf(refute_0_821,plain,
and(truth,Y) = and(Y,truth),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) )],[refute_0_799,refute_0_820]) ).
cnf(refute_0_822,plain,
and(truth,falsehood) = and(falsehood,truth),
inference(subst,[],[refute_0_821:[bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_823,plain,
and(or(falsehood,and(truth,or(falsehood,falsehood))),Y) = not(or(not(or(falsehood,and(truth,or(falsehood,falsehood)))),not(Y))),
inference(subst,[],[and_definition:[bind(X,$fot(or(falsehood,and(truth,or(falsehood,falsehood)))))]]) ).
cnf(refute_0_824,plain,
( and(or(falsehood,and(truth,or(falsehood,falsehood))),Y) != not(or(not(or(falsehood,and(truth,or(falsehood,falsehood)))),not(Y)))
| not(or(falsehood,and(truth,or(falsehood,falsehood)))) != and(truth,or(falsehood,and(truth,truth)))
| and(or(falsehood,and(truth,or(falsehood,falsehood))),Y) = not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,or(falsehood,falsehood))),Y),not(or(not(or(falsehood,and(truth,or(falsehood,falsehood)))),not(Y)))) ),[1,0,0],$fot(and(truth,or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_825,plain,
( and(or(falsehood,and(truth,or(falsehood,falsehood))),Y) != not(or(not(or(falsehood,and(truth,or(falsehood,falsehood)))),not(Y)))
| and(or(falsehood,and(truth,or(falsehood,falsehood))),Y) = not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,or(falsehood,falsehood)))),and(truth,or(falsehood,and(truth,truth)))) )],[refute_0_93,refute_0_824]) ).
cnf(refute_0_826,plain,
and(or(falsehood,and(truth,or(falsehood,falsehood))),Y) = not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,or(falsehood,falsehood))),Y),not(or(not(or(falsehood,and(truth,or(falsehood,falsehood)))),not(Y)))) )],[refute_0_823,refute_0_825]) ).
cnf(refute_0_827,plain,
and(or(falsehood,and(truth,or(falsehood,falsehood))),Y) = and(or(falsehood,and(truth,or(falsehood,falsehood))),Y),
introduced(tautology,[refl,[$fot(and(or(falsehood,and(truth,or(falsehood,falsehood))),Y))]]) ).
cnf(refute_0_828,plain,
( and(or(falsehood,and(truth,or(falsehood,falsehood))),Y) != and(or(falsehood,and(truth,or(falsehood,falsehood))),Y)
| or(falsehood,and(truth,or(falsehood,falsehood))) != or(falsehood,falsehood)
| and(or(falsehood,and(truth,or(falsehood,falsehood))),Y) = and(or(falsehood,falsehood),Y) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,or(falsehood,falsehood))),Y),and(or(falsehood,and(truth,or(falsehood,falsehood))),Y)) ),[1,0],$fot(or(falsehood,falsehood))]]) ).
cnf(refute_0_829,plain,
( or(falsehood,and(truth,or(falsehood,falsehood))) != or(falsehood,falsehood)
| and(or(falsehood,and(truth,or(falsehood,falsehood))),Y) = and(or(falsehood,falsehood),Y) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,or(falsehood,falsehood))),Y),and(or(falsehood,and(truth,or(falsehood,falsehood))),Y)) )],[refute_0_827,refute_0_828]) ).
cnf(refute_0_830,plain,
and(or(falsehood,and(truth,or(falsehood,falsehood))),Y) = and(or(falsehood,falsehood),Y),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,falsehood))),or(falsehood,falsehood)) )],[refute_0_583,refute_0_829]) ).
cnf(refute_0_831,plain,
( and(or(falsehood,and(truth,or(falsehood,falsehood))),Y) != and(or(falsehood,falsehood),Y)
| and(or(falsehood,and(truth,or(falsehood,falsehood))),Y) != not(or(and(truth,or(falsehood,and(truth,truth))),not(Y)))
| and(or(falsehood,falsehood),Y) = not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,or(falsehood,falsehood))),Y),not(or(and(truth,or(falsehood,and(truth,truth))),not(Y)))) ),[0],$fot(and(or(falsehood,falsehood),Y))]]) ).
cnf(refute_0_832,plain,
( and(or(falsehood,and(truth,or(falsehood,falsehood))),Y) != not(or(and(truth,or(falsehood,and(truth,truth))),not(Y)))
| and(or(falsehood,falsehood),Y) = not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,or(falsehood,falsehood))),Y),and(or(falsehood,falsehood),Y)) )],[refute_0_830,refute_0_831]) ).
cnf(refute_0_833,plain,
implies(or(falsehood,or(and(truth,truth),X_29)),or(and(truth,truth),X_29)) = truth,
inference(subst,[],[refute_0_146:[bind(X_21,$fot(or(and(truth,truth),X_29)))]]) ).
cnf(refute_0_834,plain,
( implies(or(falsehood,or(and(truth,truth),X_29)),or(and(truth,truth),X_29)) != truth
| or(falsehood,or(and(truth,truth),X_29)) != implies(and(truth,or(falsehood,falsehood)),X_29)
| implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,or(and(truth,truth),X_29)),or(and(truth,truth),X_29)),truth) ),[0,0],$fot(implies(and(truth,or(falsehood,falsehood)),X_29))]]) ).
cnf(refute_0_835,plain,
( implies(or(falsehood,or(and(truth,truth),X_29)),or(and(truth,truth),X_29)) != truth
| implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,or(and(truth,truth),X_29)),implies(and(truth,or(falsehood,falsehood)),X_29)) )],[refute_0_156,refute_0_834]) ).
cnf(refute_0_836,plain,
implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,or(and(truth,truth),X_29)),or(and(truth,truth),X_29)),truth) )],[refute_0_833,refute_0_835]) ).
cnf(refute_0_837,plain,
implies(truth,or(and(truth,truth),X_29)) = or(and(truth,truth),X_29),
inference(subst,[],[wajsberg_1:[bind(X,$fot(or(and(truth,truth),X_29)))]]) ).
cnf(refute_0_838,plain,
implies(and(truth,or(falsehood,falsehood)),X_29) = truth,
inference(subst,[],[refute_0_557:[bind(Z,$fot(X_29))]]) ).
cnf(refute_0_839,plain,
implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)) = implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)),
introduced(tautology,[refl,[$fot(implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)))]]) ).
cnf(refute_0_840,plain,
( implies(and(truth,or(falsehood,falsehood)),X_29) != truth
| implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)) != implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29))
| implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)) = implies(truth,or(and(truth,truth),X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)),implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_841,plain,
( implies(and(truth,or(falsehood,falsehood)),X_29) != truth
| implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)) = implies(truth,or(and(truth,truth),X_29)) ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)),implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29))) )],[refute_0_839,refute_0_840]) ).
cnf(refute_0_842,plain,
implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)) = implies(truth,or(and(truth,truth),X_29)),
inference(resolve,[$cnf( $equal(implies(and(truth,or(falsehood,falsehood)),X_29),truth) )],[refute_0_838,refute_0_841]) ).
cnf(refute_0_843,plain,
( implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)) != implies(truth,or(and(truth,truth),X_29))
| implies(truth,or(and(truth,truth),X_29)) != or(and(truth,truth),X_29)
| implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)) = or(and(truth,truth),X_29) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)))),bind(Y0,$fot(implies(truth,or(and(truth,truth),X_29)))),bind(Z0,$fot(or(and(truth,truth),X_29)))]]) ).
cnf(refute_0_844,plain,
( implies(truth,or(and(truth,truth),X_29)) != or(and(truth,truth),X_29)
| implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)) = or(and(truth,truth),X_29) ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)),implies(truth,or(and(truth,truth),X_29))) )],[refute_0_842,refute_0_843]) ).
cnf(refute_0_845,plain,
implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)) = or(and(truth,truth),X_29),
inference(resolve,[$cnf( $equal(implies(truth,or(and(truth,truth),X_29)),or(and(truth,truth),X_29)) )],[refute_0_837,refute_0_844]) ).
cnf(refute_0_846,plain,
( implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)) != or(and(truth,truth),X_29)
| implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)) != truth
| or(and(truth,truth),X_29) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)),truth) ),[0],$fot(or(and(truth,truth),X_29))]]) ).
cnf(refute_0_847,plain,
( implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)) != truth
| or(and(truth,truth),X_29) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)),or(and(truth,truth),X_29)) )],[refute_0_845,refute_0_846]) ).
cnf(refute_0_848,plain,
or(and(truth,truth),X_29) = truth,
inference(resolve,[$cnf( $equal(implies(implies(and(truth,or(falsehood,falsehood)),X_29),or(and(truth,truth),X_29)),truth) )],[refute_0_836,refute_0_847]) ).
cnf(refute_0_849,plain,
or(and(truth,truth),not(Y)) = truth,
inference(subst,[],[refute_0_848:[bind(X_29,$fot(not(Y)))]]) ).
cnf(refute_0_850,plain,
or(and(truth,or(falsehood,and(truth,truth))),not(Y)) = or(and(truth,or(falsehood,and(truth,truth))),not(Y)),
introduced(tautology,[refl,[$fot(or(and(truth,or(falsehood,and(truth,truth))),not(Y)))]]) ).
cnf(refute_0_851,plain,
( and(truth,or(falsehood,and(truth,truth))) != and(truth,truth)
| or(and(truth,or(falsehood,and(truth,truth))),not(Y)) != or(and(truth,or(falsehood,and(truth,truth))),not(Y))
| or(and(truth,or(falsehood,and(truth,truth))),not(Y)) = or(and(truth,truth),not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(truth,or(falsehood,and(truth,truth))),not(Y)),or(and(truth,or(falsehood,and(truth,truth))),not(Y))) ),[1,0],$fot(and(truth,truth))]]) ).
cnf(refute_0_852,plain,
( and(truth,or(falsehood,and(truth,truth))) != and(truth,truth)
| or(and(truth,or(falsehood,and(truth,truth))),not(Y)) = or(and(truth,truth),not(Y)) ),
inference(resolve,[$cnf( $equal(or(and(truth,or(falsehood,and(truth,truth))),not(Y)),or(and(truth,or(falsehood,and(truth,truth))),not(Y))) )],[refute_0_850,refute_0_851]) ).
cnf(refute_0_853,plain,
or(and(truth,or(falsehood,and(truth,truth))),not(Y)) = or(and(truth,truth),not(Y)),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,and(truth,truth))),and(truth,truth)) )],[refute_0_616,refute_0_852]) ).
cnf(refute_0_854,plain,
( or(and(truth,or(falsehood,and(truth,truth))),not(Y)) != or(and(truth,truth),not(Y))
| or(and(truth,truth),not(Y)) != truth
| or(and(truth,or(falsehood,and(truth,truth))),not(Y)) = truth ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(or(and(truth,or(falsehood,and(truth,truth))),not(Y)))),bind(Y0,$fot(or(and(truth,truth),not(Y)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_855,plain,
( or(and(truth,truth),not(Y)) != truth
| or(and(truth,or(falsehood,and(truth,truth))),not(Y)) = truth ),
inference(resolve,[$cnf( $equal(or(and(truth,or(falsehood,and(truth,truth))),not(Y)),or(and(truth,truth),not(Y))) )],[refute_0_853,refute_0_854]) ).
cnf(refute_0_856,plain,
or(and(truth,or(falsehood,and(truth,truth))),not(Y)) = truth,
inference(resolve,[$cnf( $equal(or(and(truth,truth),not(Y)),truth) )],[refute_0_849,refute_0_855]) ).
cnf(refute_0_857,plain,
not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))) = not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))),
introduced(tautology,[refl,[$fot(not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))))]]) ).
cnf(refute_0_858,plain,
( not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))) != not(or(and(truth,or(falsehood,and(truth,truth))),not(Y)))
| or(and(truth,or(falsehood,and(truth,truth))),not(Y)) != truth
| not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))),not(or(and(truth,or(falsehood,and(truth,truth))),not(Y)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_859,plain,
( or(and(truth,or(falsehood,and(truth,truth))),not(Y)) != truth
| not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))),not(or(and(truth,or(falsehood,and(truth,truth))),not(Y)))) )],[refute_0_857,refute_0_858]) ).
cnf(refute_0_860,plain,
not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))) = not(truth),
inference(resolve,[$cnf( $equal(or(and(truth,or(falsehood,and(truth,truth))),not(Y)),truth) )],[refute_0_856,refute_0_859]) ).
cnf(refute_0_861,plain,
( not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))) != not(truth)
| not(truth) != falsehood
| not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))) = falsehood ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))))),bind(Y0,$fot(not(truth))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_862,plain,
( not(truth) != falsehood
| not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))) = falsehood ),
inference(resolve,[$cnf( $equal(not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))),not(truth)) )],[refute_0_860,refute_0_861]) ).
cnf(refute_0_863,plain,
not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))) = falsehood,
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_862]) ).
cnf(refute_0_864,plain,
( and(or(falsehood,falsehood),Y) != not(or(and(truth,or(falsehood,and(truth,truth))),not(Y)))
| not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))) != falsehood
| and(or(falsehood,falsehood),Y) = falsehood ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(or(falsehood,falsehood),Y),falsehood) ),[0],$fot(not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))))]]) ).
cnf(refute_0_865,plain,
( and(or(falsehood,falsehood),Y) != not(or(and(truth,or(falsehood,and(truth,truth))),not(Y)))
| and(or(falsehood,falsehood),Y) = falsehood ),
inference(resolve,[$cnf( $equal(not(or(and(truth,or(falsehood,and(truth,truth))),not(Y))),falsehood) )],[refute_0_863,refute_0_864]) ).
cnf(refute_0_866,plain,
( and(or(falsehood,and(truth,or(falsehood,falsehood))),Y) != not(or(and(truth,or(falsehood,and(truth,truth))),not(Y)))
| and(or(falsehood,falsehood),Y) = falsehood ),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),Y),not(or(and(truth,or(falsehood,and(truth,truth))),not(Y)))) )],[refute_0_832,refute_0_865]) ).
cnf(refute_0_867,plain,
and(or(falsehood,falsehood),Y) = falsehood,
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,or(falsehood,falsehood))),Y),not(or(and(truth,or(falsehood,and(truth,truth))),not(Y)))) )],[refute_0_826,refute_0_866]) ).
cnf(refute_0_868,plain,
and(or(falsehood,falsehood),X_37) = falsehood,
inference(subst,[],[refute_0_867:[bind(Y,$fot(X_37))]]) ).
cnf(refute_0_869,plain,
and(truth,and(or(falsehood,falsehood),X_37)) = and(truth,and(or(falsehood,falsehood),X_37)),
introduced(tautology,[refl,[$fot(and(truth,and(or(falsehood,falsehood),X_37)))]]) ).
cnf(refute_0_870,plain,
( and(or(falsehood,falsehood),X_37) != falsehood
| and(truth,and(or(falsehood,falsehood),X_37)) != and(truth,and(or(falsehood,falsehood),X_37))
| and(truth,and(or(falsehood,falsehood),X_37)) = and(truth,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,and(or(falsehood,falsehood),X_37)),and(truth,and(or(falsehood,falsehood),X_37))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_871,plain,
( and(or(falsehood,falsehood),X_37) != falsehood
| and(truth,and(or(falsehood,falsehood),X_37)) = and(truth,falsehood) ),
inference(resolve,[$cnf( $equal(and(truth,and(or(falsehood,falsehood),X_37)),and(truth,and(or(falsehood,falsehood),X_37))) )],[refute_0_869,refute_0_870]) ).
cnf(refute_0_872,plain,
and(truth,and(or(falsehood,falsehood),X_37)) = and(truth,falsehood),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),X_37),falsehood) )],[refute_0_868,refute_0_871]) ).
cnf(refute_0_873,plain,
( and(truth,and(or(falsehood,falsehood),X_37)) != and(truth,falsehood)
| and(truth,falsehood) != and(falsehood,truth)
| and(truth,and(or(falsehood,falsehood),X_37)) = and(falsehood,truth) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(and(truth,and(or(falsehood,falsehood),X_37)))),bind(Y0,$fot(and(truth,falsehood))),bind(Z0,$fot(and(falsehood,truth)))]]) ).
cnf(refute_0_874,plain,
( and(truth,falsehood) != and(falsehood,truth)
| and(truth,and(or(falsehood,falsehood),X_37)) = and(falsehood,truth) ),
inference(resolve,[$cnf( $equal(and(truth,and(or(falsehood,falsehood),X_37)),and(truth,falsehood)) )],[refute_0_872,refute_0_873]) ).
cnf(refute_0_875,plain,
and(truth,and(or(falsehood,falsehood),X_37)) = and(falsehood,truth),
inference(resolve,[$cnf( $equal(and(truth,falsehood),and(falsehood,truth)) )],[refute_0_822,refute_0_874]) ).
cnf(refute_0_876,plain,
or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) = or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))),
introduced(tautology,[refl,[$fot(or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))))]]) ).
cnf(refute_0_877,plain,
( and(truth,and(or(falsehood,falsehood),X_37)) != and(falsehood,truth)
| or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) != or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))
| or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) = or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))),or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))) ),[1,0],$fot(and(falsehood,truth))]]) ).
cnf(refute_0_878,plain,
( and(truth,and(or(falsehood,falsehood),X_37)) != and(falsehood,truth)
| or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) = or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))),or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))) )],[refute_0_876,refute_0_877]) ).
cnf(refute_0_879,plain,
or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) = or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37))),
inference(resolve,[$cnf( $equal(and(truth,and(or(falsehood,falsehood),X_37)),and(falsehood,truth)) )],[refute_0_875,refute_0_878]) ).
cnf(refute_0_880,plain,
( or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37))) != or(and(falsehood,truth),and(truth,not(X_37)))
| or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) != or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37)))
| or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) = or(and(falsehood,truth),and(truth,not(X_37))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))))),bind(Y0,$fot(or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37))))),bind(Z0,$fot(or(and(falsehood,truth),and(truth,not(X_37)))))]]) ).
cnf(refute_0_881,plain,
( or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37))) != or(and(falsehood,truth),and(truth,not(X_37)))
| or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) = or(and(falsehood,truth),and(truth,not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))),or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37)))) )],[refute_0_879,refute_0_880]) ).
cnf(refute_0_882,plain,
or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) = or(and(falsehood,truth),and(truth,not(X_37))),
inference(resolve,[$cnf( $equal(or(and(falsehood,truth),and(or(falsehood,and(truth,truth)),not(X_37))),or(and(falsehood,truth),and(truth,not(X_37)))) )],[refute_0_795,refute_0_881]) ).
cnf(refute_0_883,plain,
( or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))) != or(and(falsehood,truth),and(truth,not(X_37)))
| xor(truth,X_37) != or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))
| xor(truth,X_37) = or(and(falsehood,truth),and(truth,not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_37),or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))) ),[1],$fot(or(and(falsehood,truth),and(truth,not(X_37))))]]) ).
cnf(refute_0_884,plain,
( xor(truth,X_37) != or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))
| xor(truth,X_37) = or(and(falsehood,truth),and(truth,not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37))),or(and(falsehood,truth),and(truth,not(X_37)))) )],[refute_0_882,refute_0_883]) ).
cnf(refute_0_885,plain,
( xor(or(falsehood,and(truth,truth)),X_37) != or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))
| xor(truth,X_37) = or(and(falsehood,truth),and(truth,not(X_37))) ),
inference(resolve,[$cnf( $equal(xor(truth,X_37),or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))) )],[refute_0_787,refute_0_884]) ).
cnf(refute_0_886,plain,
xor(truth,X_37) = or(and(falsehood,truth),and(truth,not(X_37))),
inference(resolve,[$cnf( $equal(xor(or(falsehood,and(truth,truth)),X_37),or(and(truth,and(or(falsehood,falsehood),X_37)),and(or(falsehood,and(truth,truth)),not(X_37)))) )],[refute_0_781,refute_0_885]) ).
cnf(refute_0_887,plain,
and(or(falsehood,falsehood),Y) = and(or(falsehood,falsehood),Y),
introduced(tautology,[refl,[$fot(and(or(falsehood,falsehood),Y))]]) ).
cnf(refute_0_888,plain,
( and(or(falsehood,falsehood),Y) != and(or(falsehood,falsehood),Y)
| or(falsehood,falsehood) != falsehood
| and(or(falsehood,falsehood),Y) = and(falsehood,Y) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,falsehood),Y),and(or(falsehood,falsehood),Y)) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_889,plain,
( or(falsehood,falsehood) != falsehood
| and(or(falsehood,falsehood),Y) = and(falsehood,Y) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),Y),and(or(falsehood,falsehood),Y)) )],[refute_0_887,refute_0_888]) ).
cnf(refute_0_890,plain,
and(or(falsehood,falsehood),Y) = and(falsehood,Y),
inference(resolve,[$cnf( $equal(or(falsehood,falsehood),falsehood) )],[refute_0_693,refute_0_889]) ).
cnf(refute_0_891,plain,
( and(or(falsehood,falsehood),Y) != and(falsehood,Y)
| and(or(falsehood,falsehood),Y) != falsehood
| and(falsehood,Y) = falsehood ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,falsehood),Y),falsehood) ),[0],$fot(and(falsehood,Y))]]) ).
cnf(refute_0_892,plain,
( and(or(falsehood,falsehood),Y) != falsehood
| and(falsehood,Y) = falsehood ),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),Y),and(falsehood,Y)) )],[refute_0_890,refute_0_891]) ).
cnf(refute_0_893,plain,
and(falsehood,Y) = falsehood,
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),Y),falsehood) )],[refute_0_867,refute_0_892]) ).
cnf(refute_0_894,plain,
and(falsehood,truth) = falsehood,
inference(subst,[],[refute_0_893:[bind(Y,$fot(truth))]]) ).
cnf(refute_0_895,plain,
or(and(falsehood,truth),and(truth,not(X_37))) = or(and(falsehood,truth),and(truth,not(X_37))),
introduced(tautology,[refl,[$fot(or(and(falsehood,truth),and(truth,not(X_37))))]]) ).
cnf(refute_0_896,plain,
( and(falsehood,truth) != falsehood
| or(and(falsehood,truth),and(truth,not(X_37))) != or(and(falsehood,truth),and(truth,not(X_37)))
| or(and(falsehood,truth),and(truth,not(X_37))) = or(falsehood,and(truth,not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(falsehood,truth),and(truth,not(X_37))),or(and(falsehood,truth),and(truth,not(X_37)))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_897,plain,
( and(falsehood,truth) != falsehood
| or(and(falsehood,truth),and(truth,not(X_37))) = or(falsehood,and(truth,not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,truth),and(truth,not(X_37))),or(and(falsehood,truth),and(truth,not(X_37)))) )],[refute_0_895,refute_0_896]) ).
cnf(refute_0_898,plain,
or(and(falsehood,truth),and(truth,not(X_37))) = or(falsehood,and(truth,not(X_37))),
inference(resolve,[$cnf( $equal(and(falsehood,truth),falsehood) )],[refute_0_894,refute_0_897]) ).
cnf(refute_0_899,plain,
( or(and(falsehood,truth),and(truth,not(X_37))) != or(falsehood,and(truth,not(X_37)))
| xor(truth,X_37) != or(and(falsehood,truth),and(truth,not(X_37)))
| xor(truth,X_37) = or(falsehood,and(truth,not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_37),or(and(falsehood,truth),and(truth,not(X_37)))) ),[1],$fot(or(falsehood,and(truth,not(X_37))))]]) ).
cnf(refute_0_900,plain,
( xor(truth,X_37) != or(and(falsehood,truth),and(truth,not(X_37)))
| xor(truth,X_37) = or(falsehood,and(truth,not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,truth),and(truth,not(X_37))),or(falsehood,and(truth,not(X_37)))) )],[refute_0_898,refute_0_899]) ).
cnf(refute_0_901,plain,
xor(truth,X_37) = or(falsehood,and(truth,not(X_37))),
inference(resolve,[$cnf( $equal(xor(truth,X_37),or(and(falsehood,truth),and(truth,not(X_37)))) )],[refute_0_886,refute_0_900]) ).
cnf(refute_0_902,plain,
or(falsehood,and(X_4,truth)) = xor(X_4,falsehood),
inference(subst,[],[refute_0_742:[bind(X_36,$fot(X_4))]]) ).
cnf(refute_0_903,plain,
not(or(falsehood,and(X_4,truth))) = not(or(falsehood,and(X_4,truth))),
introduced(tautology,[refl,[$fot(not(or(falsehood,and(X_4,truth))))]]) ).
cnf(refute_0_904,plain,
( not(or(falsehood,and(X_4,truth))) != not(or(falsehood,and(X_4,truth)))
| or(falsehood,and(X_4,truth)) != xor(X_4,falsehood)
| not(or(falsehood,and(X_4,truth))) = not(xor(X_4,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,and(X_4,truth))),not(or(falsehood,and(X_4,truth)))) ),[1,0],$fot(xor(X_4,falsehood))]]) ).
cnf(refute_0_905,plain,
( or(falsehood,and(X_4,truth)) != xor(X_4,falsehood)
| not(or(falsehood,and(X_4,truth))) = not(xor(X_4,falsehood)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(X_4,truth))),not(or(falsehood,and(X_4,truth)))) )],[refute_0_903,refute_0_904]) ).
cnf(refute_0_906,plain,
not(or(falsehood,and(X_4,truth))) = not(xor(X_4,falsehood)),
inference(resolve,[$cnf( $equal(or(falsehood,and(X_4,truth)),xor(X_4,falsehood)) )],[refute_0_902,refute_0_905]) ).
cnf(refute_0_907,plain,
( and(truth,or(falsehood,not(X_4))) != not(or(falsehood,and(X_4,truth)))
| not(or(falsehood,and(X_4,truth))) != not(xor(X_4,falsehood))
| and(truth,or(falsehood,not(X_4))) = not(xor(X_4,falsehood)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(truth,or(falsehood,not(X_4))),not(xor(X_4,falsehood))) ),[0],$fot(not(or(falsehood,and(X_4,truth))))]]) ).
cnf(refute_0_908,plain,
( and(truth,or(falsehood,not(X_4))) != not(or(falsehood,and(X_4,truth)))
| and(truth,or(falsehood,not(X_4))) = not(xor(X_4,falsehood)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(X_4,truth))),not(xor(X_4,falsehood))) )],[refute_0_906,refute_0_907]) ).
cnf(refute_0_909,plain,
and(truth,or(falsehood,not(X_4))) = not(xor(X_4,falsehood)),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,not(X_4))),not(or(falsehood,and(X_4,truth)))) )],[refute_0_55,refute_0_908]) ).
cnf(refute_0_910,plain,
or(falsehood,not(X_4)) = not(X_4),
inference(subst,[],[refute_0_757:[bind(Y,$fot(not(X_4)))]]) ).
cnf(refute_0_911,plain,
and(truth,or(falsehood,not(X_4))) = and(truth,or(falsehood,not(X_4))),
introduced(tautology,[refl,[$fot(and(truth,or(falsehood,not(X_4))))]]) ).
cnf(refute_0_912,plain,
( and(truth,or(falsehood,not(X_4))) != and(truth,or(falsehood,not(X_4)))
| or(falsehood,not(X_4)) != not(X_4)
| and(truth,or(falsehood,not(X_4))) = and(truth,not(X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,or(falsehood,not(X_4))),and(truth,or(falsehood,not(X_4)))) ),[1,1],$fot(not(X_4))]]) ).
cnf(refute_0_913,plain,
( or(falsehood,not(X_4)) != not(X_4)
| and(truth,or(falsehood,not(X_4))) = and(truth,not(X_4)) ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,not(X_4))),and(truth,or(falsehood,not(X_4)))) )],[refute_0_911,refute_0_912]) ).
cnf(refute_0_914,plain,
and(truth,or(falsehood,not(X_4))) = and(truth,not(X_4)),
inference(resolve,[$cnf( $equal(or(falsehood,not(X_4)),not(X_4)) )],[refute_0_910,refute_0_913]) ).
cnf(refute_0_915,plain,
( and(truth,or(falsehood,not(X_4))) != and(truth,not(X_4))
| and(truth,or(falsehood,not(X_4))) != not(xor(X_4,falsehood))
| and(truth,not(X_4)) = not(xor(X_4,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,or(falsehood,not(X_4))),not(xor(X_4,falsehood))) ),[0],$fot(and(truth,not(X_4)))]]) ).
cnf(refute_0_916,plain,
( and(truth,or(falsehood,not(X_4))) != not(xor(X_4,falsehood))
| and(truth,not(X_4)) = not(xor(X_4,falsehood)) ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,not(X_4))),and(truth,not(X_4))) )],[refute_0_914,refute_0_915]) ).
cnf(refute_0_917,plain,
and(truth,not(X_4)) = not(xor(X_4,falsehood)),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,not(X_4))),not(xor(X_4,falsehood))) )],[refute_0_909,refute_0_916]) ).
cnf(refute_0_918,plain,
not(xor(X_4,falsehood)) = not(and(truth,X_4)),
inference(subst,[],[refute_0_765:[bind(X_27,$fot(X_4))]]) ).
cnf(refute_0_919,plain,
( and(truth,not(X_4)) != not(xor(X_4,falsehood))
| not(xor(X_4,falsehood)) != not(and(truth,X_4))
| and(truth,not(X_4)) = not(and(truth,X_4)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(truth,not(X_4)),not(and(truth,X_4))) ),[0],$fot(not(xor(X_4,falsehood)))]]) ).
cnf(refute_0_920,plain,
( and(truth,not(X_4)) != not(xor(X_4,falsehood))
| and(truth,not(X_4)) = not(and(truth,X_4)) ),
inference(resolve,[$cnf( $equal(not(xor(X_4,falsehood)),not(and(truth,X_4))) )],[refute_0_918,refute_0_919]) ).
cnf(refute_0_921,plain,
and(truth,not(X_4)) = not(and(truth,X_4)),
inference(resolve,[$cnf( $equal(and(truth,not(X_4)),not(xor(X_4,falsehood))) )],[refute_0_917,refute_0_920]) ).
cnf(refute_0_922,plain,
and(truth,not(X_37)) = not(and(truth,X_37)),
inference(subst,[],[refute_0_921:[bind(X_4,$fot(X_37))]]) ).
cnf(refute_0_923,plain,
or(falsehood,and(truth,not(X_37))) = and(truth,not(X_37)),
inference(subst,[],[refute_0_757:[bind(Y,$fot(and(truth,not(X_37))))]]) ).
cnf(refute_0_924,plain,
( and(truth,not(X_37)) != not(and(truth,X_37))
| or(falsehood,and(truth,not(X_37))) != and(truth,not(X_37))
| or(falsehood,and(truth,not(X_37))) = not(and(truth,X_37)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(or(falsehood,and(truth,not(X_37))))),bind(Y0,$fot(and(truth,not(X_37)))),bind(Z0,$fot(not(and(truth,X_37))))]]) ).
cnf(refute_0_925,plain,
( and(truth,not(X_37)) != not(and(truth,X_37))
| or(falsehood,and(truth,not(X_37))) = not(and(truth,X_37)) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,not(X_37))),and(truth,not(X_37))) )],[refute_0_923,refute_0_924]) ).
cnf(refute_0_926,plain,
or(falsehood,and(truth,not(X_37))) = not(and(truth,X_37)),
inference(resolve,[$cnf( $equal(and(truth,not(X_37)),not(and(truth,X_37))) )],[refute_0_922,refute_0_925]) ).
cnf(refute_0_927,plain,
( or(falsehood,and(truth,not(X_37))) != not(and(truth,X_37))
| xor(truth,X_37) != or(falsehood,and(truth,not(X_37)))
| xor(truth,X_37) = not(and(truth,X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_37),or(falsehood,and(truth,not(X_37)))) ),[1],$fot(not(and(truth,X_37)))]]) ).
cnf(refute_0_928,plain,
( xor(truth,X_37) != or(falsehood,and(truth,not(X_37)))
| xor(truth,X_37) = not(and(truth,X_37)) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,not(X_37))),not(and(truth,X_37))) )],[refute_0_926,refute_0_927]) ).
cnf(refute_0_929,plain,
xor(truth,X_37) = not(and(truth,X_37)),
inference(resolve,[$cnf( $equal(xor(truth,X_37),or(falsehood,and(truth,not(X_37)))) )],[refute_0_901,refute_0_928]) ).
cnf(refute_0_930,plain,
( xor(truth,X_37) != not(and(truth,X_37))
| not(and(truth,X_37)) = xor(truth,X_37) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(truth,X_37))),bind(Y0,$fot(not(and(truth,X_37))))]]) ).
cnf(refute_0_931,plain,
not(and(truth,X_37)) = xor(truth,X_37),
inference(resolve,[$cnf( $equal(xor(truth,X_37),not(and(truth,X_37))) )],[refute_0_929,refute_0_930]) ).
cnf(refute_0_932,plain,
not(and(truth,X_27)) = xor(truth,X_27),
inference(subst,[],[refute_0_931:[bind(X_37,$fot(X_27))]]) ).
cnf(refute_0_933,plain,
( not(and(truth,X_27)) != xor(truth,X_27)
| not(xor(X_27,falsehood)) != not(and(truth,X_27))
| not(xor(X_27,falsehood)) = xor(truth,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(not(xor(X_27,falsehood)),not(and(truth,X_27))) ),[1],$fot(xor(truth,X_27))]]) ).
cnf(refute_0_934,plain,
( not(xor(X_27,falsehood)) != not(and(truth,X_27))
| not(xor(X_27,falsehood)) = xor(truth,X_27) ),
inference(resolve,[$cnf( $equal(not(and(truth,X_27)),xor(truth,X_27)) )],[refute_0_932,refute_0_933]) ).
cnf(refute_0_935,plain,
not(xor(X_27,falsehood)) = xor(truth,X_27),
inference(resolve,[$cnf( $equal(not(xor(X_27,falsehood)),not(and(truth,X_27))) )],[refute_0_765,refute_0_934]) ).
cnf(refute_0_936,plain,
or(falsehood,not(X_1)) = not(X_1),
inference(subst,[],[refute_0_757:[bind(Y,$fot(not(X_1)))]]) ).
cnf(refute_0_937,plain,
not(or(falsehood,not(X_1))) = not(or(falsehood,not(X_1))),
introduced(tautology,[refl,[$fot(not(or(falsehood,not(X_1))))]]) ).
cnf(refute_0_938,plain,
( not(or(falsehood,not(X_1))) != not(or(falsehood,not(X_1)))
| or(falsehood,not(X_1)) != not(X_1)
| not(or(falsehood,not(X_1))) = not(not(X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,not(X_1))),not(or(falsehood,not(X_1)))) ),[1,0],$fot(not(X_1))]]) ).
cnf(refute_0_939,plain,
( or(falsehood,not(X_1)) != not(X_1)
| not(or(falsehood,not(X_1))) = not(not(X_1)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_1))),not(or(falsehood,not(X_1)))) )],[refute_0_937,refute_0_938]) ).
cnf(refute_0_940,plain,
not(or(falsehood,not(X_1))) = not(not(X_1)),
inference(resolve,[$cnf( $equal(or(falsehood,not(X_1)),not(X_1)) )],[refute_0_936,refute_0_939]) ).
cnf(refute_0_941,plain,
( and(X_1,truth) != not(or(falsehood,not(X_1)))
| not(or(falsehood,not(X_1))) != not(not(X_1))
| and(X_1,truth) = not(not(X_1)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_1,truth),not(not(X_1))) ),[0],$fot(not(or(falsehood,not(X_1))))]]) ).
cnf(refute_0_942,plain,
( and(X_1,truth) != not(or(falsehood,not(X_1)))
| and(X_1,truth) = not(not(X_1)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_1))),not(not(X_1))) )],[refute_0_940,refute_0_941]) ).
cnf(refute_0_943,plain,
and(X_1,truth) = not(not(X_1)),
inference(resolve,[$cnf( $equal(and(X_1,truth),not(or(falsehood,not(X_1)))) )],[refute_0_32,refute_0_942]) ).
cnf(refute_0_944,plain,
and(X_36,truth) = not(not(X_36)),
inference(subst,[],[refute_0_943:[bind(X_1,$fot(X_36))]]) ).
cnf(refute_0_945,plain,
or(falsehood,and(X_36,truth)) = and(X_36,truth),
inference(subst,[],[refute_0_757:[bind(Y,$fot(and(X_36,truth)))]]) ).
cnf(refute_0_946,plain,
( and(X_36,truth) != not(not(X_36))
| or(falsehood,and(X_36,truth)) != and(X_36,truth)
| or(falsehood,and(X_36,truth)) = not(not(X_36)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(or(falsehood,and(X_36,truth)))),bind(Y0,$fot(and(X_36,truth))),bind(Z0,$fot(not(not(X_36))))]]) ).
cnf(refute_0_947,plain,
( and(X_36,truth) != not(not(X_36))
| or(falsehood,and(X_36,truth)) = not(not(X_36)) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(X_36,truth)),and(X_36,truth)) )],[refute_0_945,refute_0_946]) ).
cnf(refute_0_948,plain,
or(falsehood,and(X_36,truth)) = not(not(X_36)),
inference(resolve,[$cnf( $equal(and(X_36,truth),not(not(X_36))) )],[refute_0_944,refute_0_947]) ).
cnf(refute_0_949,plain,
( or(falsehood,and(X_36,truth)) != not(not(X_36))
| xor(X_36,falsehood) != or(falsehood,and(X_36,truth))
| xor(X_36,falsehood) = not(not(X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_36,falsehood),or(falsehood,and(X_36,truth))) ),[1],$fot(not(not(X_36)))]]) ).
cnf(refute_0_950,plain,
( xor(X_36,falsehood) != or(falsehood,and(X_36,truth))
| xor(X_36,falsehood) = not(not(X_36)) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(X_36,truth)),not(not(X_36))) )],[refute_0_948,refute_0_949]) ).
cnf(refute_0_951,plain,
xor(X_36,falsehood) = not(not(X_36)),
inference(resolve,[$cnf( $equal(xor(X_36,falsehood),or(falsehood,and(X_36,truth))) )],[refute_0_740,refute_0_950]) ).
cnf(refute_0_952,plain,
xor(X_27,falsehood) = not(not(X_27)),
inference(subst,[],[refute_0_951:[bind(X_36,$fot(X_27))]]) ).
cnf(refute_0_953,plain,
not(xor(X_27,falsehood)) = not(xor(X_27,falsehood)),
introduced(tautology,[refl,[$fot(not(xor(X_27,falsehood)))]]) ).
cnf(refute_0_954,plain,
( not(xor(X_27,falsehood)) != not(xor(X_27,falsehood))
| xor(X_27,falsehood) != not(not(X_27))
| not(xor(X_27,falsehood)) = not(not(not(X_27))) ),
introduced(tautology,[equality,[$cnf( $equal(not(xor(X_27,falsehood)),not(xor(X_27,falsehood))) ),[1,0],$fot(not(not(X_27)))]]) ).
cnf(refute_0_955,plain,
( xor(X_27,falsehood) != not(not(X_27))
| not(xor(X_27,falsehood)) = not(not(not(X_27))) ),
inference(resolve,[$cnf( $equal(not(xor(X_27,falsehood)),not(xor(X_27,falsehood))) )],[refute_0_953,refute_0_954]) ).
cnf(refute_0_956,plain,
not(xor(X_27,falsehood)) = not(not(not(X_27))),
inference(resolve,[$cnf( $equal(xor(X_27,falsehood),not(not(X_27))) )],[refute_0_952,refute_0_955]) ).
cnf(refute_0_957,plain,
( not(xor(X_27,falsehood)) != not(not(not(X_27)))
| not(xor(X_27,falsehood)) != xor(truth,X_27)
| not(not(not(X_27))) = xor(truth,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(not(xor(X_27,falsehood)),xor(truth,X_27)) ),[0],$fot(not(not(not(X_27))))]]) ).
cnf(refute_0_958,plain,
( not(xor(X_27,falsehood)) != xor(truth,X_27)
| not(not(not(X_27))) = xor(truth,X_27) ),
inference(resolve,[$cnf( $equal(not(xor(X_27,falsehood)),not(not(not(X_27)))) )],[refute_0_956,refute_0_957]) ).
cnf(refute_0_959,plain,
not(not(not(X_27))) = xor(truth,X_27),
inference(resolve,[$cnf( $equal(not(xor(X_27,falsehood)),xor(truth,X_27)) )],[refute_0_935,refute_0_958]) ).
cnf(refute_0_960,plain,
implies(not(falsehood),X_17) = or(falsehood,X_17),
inference(subst,[],[refute_0_115:[bind(X,$fot(falsehood)),bind(Y,$fot(X_17))]]) ).
cnf(refute_0_961,plain,
implies(and(truth,truth),X_17) = implies(and(truth,truth),X_17),
introduced(tautology,[refl,[$fot(implies(and(truth,truth),X_17))]]) ).
cnf(refute_0_962,plain,
( and(truth,truth) != not(falsehood)
| implies(and(truth,truth),X_17) != implies(and(truth,truth),X_17)
| implies(and(truth,truth),X_17) = implies(not(falsehood),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(truth,truth),X_17),implies(and(truth,truth),X_17)) ),[1,0],$fot(not(falsehood))]]) ).
cnf(refute_0_963,plain,
( and(truth,truth) != not(falsehood)
| implies(and(truth,truth),X_17) = implies(not(falsehood),X_17) ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),X_17),implies(and(truth,truth),X_17)) )],[refute_0_961,refute_0_962]) ).
cnf(refute_0_964,plain,
implies(and(truth,truth),X_17) = implies(not(falsehood),X_17),
inference(resolve,[$cnf( $equal(and(truth,truth),not(falsehood)) )],[refute_0_706,refute_0_963]) ).
cnf(refute_0_965,plain,
( implies(and(truth,truth),X_17) != implies(not(falsehood),X_17)
| implies(not(falsehood),X_17) != or(falsehood,X_17)
| implies(and(truth,truth),X_17) = or(falsehood,X_17) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(and(truth,truth),X_17))),bind(Y0,$fot(implies(not(falsehood),X_17))),bind(Z0,$fot(or(falsehood,X_17)))]]) ).
cnf(refute_0_966,plain,
( implies(not(falsehood),X_17) != or(falsehood,X_17)
| implies(and(truth,truth),X_17) = or(falsehood,X_17) ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),X_17),implies(not(falsehood),X_17)) )],[refute_0_964,refute_0_965]) ).
cnf(refute_0_967,plain,
implies(and(truth,truth),X_17) = or(falsehood,X_17),
inference(resolve,[$cnf( $equal(implies(not(falsehood),X_17),or(falsehood,X_17)) )],[refute_0_960,refute_0_966]) ).
cnf(refute_0_968,plain,
( implies(and(truth,truth),X_17) != or(falsehood,X_17)
| or(falsehood,or(X_17,falsehood)) != implies(and(truth,truth),X_17)
| or(falsehood,or(X_17,falsehood)) = or(falsehood,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(X_17,falsehood)),implies(and(truth,truth),X_17)) ),[1],$fot(or(falsehood,X_17))]]) ).
cnf(refute_0_969,plain,
( or(falsehood,or(X_17,falsehood)) != implies(and(truth,truth),X_17)
| or(falsehood,or(X_17,falsehood)) = or(falsehood,X_17) ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),X_17),or(falsehood,X_17)) )],[refute_0_967,refute_0_968]) ).
cnf(refute_0_970,plain,
or(falsehood,or(X_17,falsehood)) = or(falsehood,X_17),
inference(resolve,[$cnf( $equal(or(falsehood,or(X_17,falsehood)),implies(and(truth,truth),X_17)) )],[refute_0_183,refute_0_969]) ).
cnf(refute_0_971,plain,
or(falsehood,or(X_17,falsehood)) = or(X_17,falsehood),
inference(subst,[],[refute_0_757:[bind(Y,$fot(or(X_17,falsehood)))]]) ).
cnf(refute_0_972,plain,
( or(falsehood,or(X_17,falsehood)) != or(X_17,falsehood)
| or(falsehood,or(X_17,falsehood)) != or(falsehood,X_17)
| or(X_17,falsehood) = or(falsehood,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(X_17,falsehood)),or(falsehood,X_17)) ),[0],$fot(or(X_17,falsehood))]]) ).
cnf(refute_0_973,plain,
( or(falsehood,or(X_17,falsehood)) != or(falsehood,X_17)
| or(X_17,falsehood) = or(falsehood,X_17) ),
inference(resolve,[$cnf( $equal(or(falsehood,or(X_17,falsehood)),or(X_17,falsehood)) )],[refute_0_971,refute_0_972]) ).
cnf(refute_0_974,plain,
or(falsehood,X_17) = X_17,
inference(subst,[],[refute_0_757:[bind(Y,$fot(X_17))]]) ).
cnf(refute_0_975,plain,
( or(X_17,falsehood) != or(falsehood,X_17)
| or(falsehood,X_17) != X_17
| or(X_17,falsehood) = X_17 ),
introduced(tautology,[equality,[$cnf( ~ $equal(or(X_17,falsehood),X_17) ),[0],$fot(or(falsehood,X_17))]]) ).
cnf(refute_0_976,plain,
( or(X_17,falsehood) != or(falsehood,X_17)
| or(X_17,falsehood) = X_17 ),
inference(resolve,[$cnf( $equal(or(falsehood,X_17),X_17) )],[refute_0_974,refute_0_975]) ).
cnf(refute_0_977,plain,
( or(falsehood,or(X_17,falsehood)) != or(falsehood,X_17)
| or(X_17,falsehood) = X_17 ),
inference(resolve,[$cnf( $equal(or(X_17,falsehood),or(falsehood,X_17)) )],[refute_0_973,refute_0_976]) ).
cnf(refute_0_978,plain,
or(X_17,falsehood) = X_17,
inference(resolve,[$cnf( $equal(or(falsehood,or(X_17,falsehood)),or(falsehood,X_17)) )],[refute_0_970,refute_0_977]) ).
cnf(refute_0_979,plain,
or(X,falsehood) = X,
inference(subst,[],[refute_0_978:[bind(X_17,$fot(X))]]) ).
cnf(refute_0_980,plain,
implies(or(X,falsehood),falsehood) = implies(or(X,falsehood),falsehood),
introduced(tautology,[refl,[$fot(implies(or(X,falsehood),falsehood))]]) ).
cnf(refute_0_981,plain,
( implies(or(X,falsehood),falsehood) != implies(or(X,falsehood),falsehood)
| or(X,falsehood) != X
| implies(or(X,falsehood),falsehood) = implies(X,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X,falsehood),falsehood),implies(or(X,falsehood),falsehood)) ),[1,0],$fot(X)]]) ).
cnf(refute_0_982,plain,
( or(X,falsehood) != X
| implies(or(X,falsehood),falsehood) = implies(X,falsehood) ),
inference(resolve,[$cnf( $equal(implies(or(X,falsehood),falsehood),implies(or(X,falsehood),falsehood)) )],[refute_0_980,refute_0_981]) ).
cnf(refute_0_983,plain,
implies(or(X,falsehood),falsehood) = implies(X,falsehood),
inference(resolve,[$cnf( $equal(or(X,falsehood),X) )],[refute_0_979,refute_0_982]) ).
cnf(refute_0_984,plain,
( implies(or(X,falsehood),falsehood) != implies(X,falsehood)
| implies(or(X,falsehood),falsehood) != not(X)
| implies(X,falsehood) = not(X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X,falsehood),falsehood),not(X)) ),[0],$fot(implies(X,falsehood))]]) ).
cnf(refute_0_985,plain,
( implies(or(X,falsehood),falsehood) != not(X)
| implies(X,falsehood) = not(X) ),
inference(resolve,[$cnf( $equal(implies(or(X,falsehood),falsehood),implies(X,falsehood)) )],[refute_0_983,refute_0_984]) ).
cnf(refute_0_986,plain,
implies(X,falsehood) = not(X),
inference(resolve,[$cnf( $equal(implies(or(X,falsehood),falsehood),not(X)) )],[refute_0_725,refute_0_985]) ).
cnf(refute_0_987,plain,
not(implies(X,falsehood)) = not(implies(X,falsehood)),
introduced(tautology,[refl,[$fot(not(implies(X,falsehood)))]]) ).
cnf(refute_0_988,plain,
( implies(X,falsehood) != not(X)
| not(implies(X,falsehood)) != not(implies(X,falsehood))
| not(implies(X,falsehood)) = not(not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X,falsehood)),not(implies(X,falsehood))) ),[1,0],$fot(not(X))]]) ).
cnf(refute_0_989,plain,
( implies(X,falsehood) != not(X)
| not(implies(X,falsehood)) = not(not(X)) ),
inference(resolve,[$cnf( $equal(not(implies(X,falsehood)),not(implies(X,falsehood))) )],[refute_0_987,refute_0_988]) ).
cnf(refute_0_990,plain,
not(implies(X,falsehood)) = not(not(X)),
inference(resolve,[$cnf( $equal(implies(X,falsehood),not(X)) )],[refute_0_986,refute_0_989]) ).
cnf(refute_0_991,plain,
implies(implies(X,falsehood),falsehood) = not(implies(X,falsehood)),
inference(subst,[],[refute_0_986:[bind(X,$fot(implies(X,falsehood)))]]) ).
cnf(refute_0_992,plain,
( implies(implies(X,falsehood),falsehood) != not(implies(X,falsehood))
| not(implies(X,falsehood)) != not(not(X))
| implies(implies(X,falsehood),falsehood) = not(not(X)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(implies(X,falsehood),falsehood))),bind(Y0,$fot(not(implies(X,falsehood)))),bind(Z0,$fot(not(not(X))))]]) ).
cnf(refute_0_993,plain,
( not(implies(X,falsehood)) != not(not(X))
| implies(implies(X,falsehood),falsehood) = not(not(X)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,falsehood),falsehood),not(implies(X,falsehood))) )],[refute_0_991,refute_0_992]) ).
cnf(refute_0_994,plain,
implies(implies(X,falsehood),falsehood) = not(not(X)),
inference(resolve,[$cnf( $equal(not(implies(X,falsehood)),not(not(X))) )],[refute_0_990,refute_0_993]) ).
cnf(refute_0_995,plain,
( implies(implies(X,falsehood),falsehood) != X
| implies(implies(X,falsehood),falsehood) != not(not(X))
| not(not(X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,falsehood),falsehood),X) ),[0],$fot(not(not(X)))]]) ).
cnf(refute_0_996,plain,
( implies(implies(X,falsehood),falsehood) != X
| not(not(X)) = X ),
inference(resolve,[$cnf( $equal(implies(implies(X,falsehood),falsehood),not(not(X))) )],[refute_0_994,refute_0_995]) ).
cnf(refute_0_997,plain,
not(not(X)) = X,
inference(resolve,[$cnf( $equal(implies(implies(X,falsehood),falsehood),X) )],[refute_0_682,refute_0_996]) ).
cnf(refute_0_998,plain,
not(not(not(X_27))) = not(X_27),
inference(subst,[],[refute_0_997:[bind(X,$fot(not(X_27)))]]) ).
cnf(refute_0_999,plain,
( not(not(not(X_27))) != not(X_27)
| not(not(not(X_27))) != xor(truth,X_27)
| not(X_27) = xor(truth,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(not(X_27))),xor(truth,X_27)) ),[0],$fot(not(X_27))]]) ).
cnf(refute_0_1000,plain,
( not(not(not(X_27))) != xor(truth,X_27)
| not(X_27) = xor(truth,X_27) ),
inference(resolve,[$cnf( $equal(not(not(not(X_27))),not(X_27)) )],[refute_0_998,refute_0_999]) ).
cnf(refute_0_1001,plain,
not(X_27) = xor(truth,X_27),
inference(resolve,[$cnf( $equal(not(not(not(X_27))),xor(truth,X_27)) )],[refute_0_959,refute_0_1000]) ).
cnf(refute_0_1002,plain,
( not(X_27) != xor(truth,X_27)
| xor(truth,X_27) = not(X_27) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(not(X_27))),bind(Y0,$fot(xor(truth,X_27)))]]) ).
cnf(refute_0_1003,plain,
xor(truth,X_27) = not(X_27),
inference(resolve,[$cnf( $equal(not(X_27),xor(truth,X_27)) )],[refute_0_1001,refute_0_1002]) ).
cnf(refute_0_1004,plain,
xor(truth,y) = not(y),
inference(subst,[],[refute_0_1003:[bind(X_27,$fot(y))]]) ).
cnf(refute_0_1005,plain,
xor(x,xor(truth,y)) = xor(x,xor(truth,y)),
introduced(tautology,[refl,[$fot(xor(x,xor(truth,y)))]]) ).
cnf(refute_0_1006,plain,
( xor(truth,y) != not(y)
| xor(x,xor(truth,y)) != xor(x,xor(truth,y))
| xor(x,xor(truth,y)) = xor(x,not(y)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(x,xor(truth,y)),xor(x,xor(truth,y))) ),[1,1],$fot(not(y))]]) ).
cnf(refute_0_1007,plain,
( xor(truth,y) != not(y)
| xor(x,xor(truth,y)) = xor(x,not(y)) ),
inference(resolve,[$cnf( $equal(xor(x,xor(truth,y)),xor(x,xor(truth,y))) )],[refute_0_1005,refute_0_1006]) ).
cnf(refute_0_1008,plain,
xor(x,xor(truth,y)) = xor(x,not(y)),
inference(resolve,[$cnf( $equal(xor(truth,y),not(y)) )],[refute_0_1004,refute_0_1007]) ).
cnf(refute_0_1009,plain,
( xor(x,not(y)) != xor(y,xor(truth,x))
| xor(x,xor(truth,y)) != xor(x,not(y))
| xor(x,xor(truth,y)) = xor(y,xor(truth,x)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(x,xor(truth,y)),xor(x,not(y))) ),[1],$fot(xor(y,xor(truth,x)))]]) ).
cnf(refute_0_1010,plain,
( xor(x,not(y)) != xor(y,xor(truth,x))
| xor(x,xor(truth,y)) = xor(y,xor(truth,x)) ),
inference(resolve,[$cnf( $equal(xor(x,xor(truth,y)),xor(x,not(y))) )],[refute_0_1008,refute_0_1009]) ).
cnf(refute_0_1011,plain,
xor(truth,x) = not(x),
inference(subst,[],[refute_0_1003:[bind(X_27,$fot(x))]]) ).
cnf(refute_0_1012,plain,
xor(y,xor(truth,x)) = xor(y,xor(truth,x)),
introduced(tautology,[refl,[$fot(xor(y,xor(truth,x)))]]) ).
cnf(refute_0_1013,plain,
( xor(truth,x) != not(x)
| xor(y,xor(truth,x)) != xor(y,xor(truth,x))
| xor(y,xor(truth,x)) = xor(y,not(x)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(y,xor(truth,x)),xor(y,xor(truth,x))) ),[1,1],$fot(not(x))]]) ).
cnf(refute_0_1014,plain,
( xor(truth,x) != not(x)
| xor(y,xor(truth,x)) = xor(y,not(x)) ),
inference(resolve,[$cnf( $equal(xor(y,xor(truth,x)),xor(y,xor(truth,x))) )],[refute_0_1012,refute_0_1013]) ).
cnf(refute_0_1015,plain,
xor(y,xor(truth,x)) = xor(y,not(x)),
inference(resolve,[$cnf( $equal(xor(truth,x),not(x)) )],[refute_0_1011,refute_0_1014]) ).
cnf(refute_0_1016,plain,
( xor(x,not(y)) != xor(y,not(x))
| xor(y,xor(truth,x)) != xor(y,not(x))
| xor(x,not(y)) = xor(y,xor(truth,x)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(xor(x,not(y)),xor(y,xor(truth,x))) ),[1],$fot(xor(y,not(x)))]]) ).
cnf(refute_0_1017,plain,
( xor(x,not(y)) != xor(y,not(x))
| xor(x,not(y)) = xor(y,xor(truth,x)) ),
inference(resolve,[$cnf( $equal(xor(y,xor(truth,x)),xor(y,not(x))) )],[refute_0_1015,refute_0_1016]) ).
cnf(refute_0_1018,plain,
( xor(x,not(y)) != xor(y,not(x))
| xor(x,xor(truth,y)) = xor(y,xor(truth,x)) ),
inference(resolve,[$cnf( $equal(xor(x,not(y)),xor(y,xor(truth,x))) )],[refute_0_1017,refute_0_1010]) ).
cnf(refute_0_1019,plain,
xor(x,not(y)) != xor(y,not(x)),
inference(resolve,[$cnf( $equal(xor(x,xor(truth,y)),xor(y,xor(truth,x))) )],[refute_0_1018,refute_0_18]) ).
cnf(refute_0_1020,plain,
xor(X_36,X_37) = or(and(X_36,not(X_37)),and(not(X_36),X_37)),
inference(subst,[],[xor_definition:[bind(X,$fot(X_36)),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_1021,plain,
and(not(X_37),X_36) = and(X_36,not(X_37)),
inference(subst,[],[and_commutativity:[bind(X,$fot(not(X_37))),bind(Y,$fot(X_36))]]) ).
cnf(refute_0_1022,plain,
( and(not(X_37),X_36) != and(X_36,not(X_37))
| and(X_36,not(X_37)) = and(not(X_37),X_36) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(not(X_37),X_36))),bind(Y0,$fot(and(X_36,not(X_37))))]]) ).
cnf(refute_0_1023,plain,
and(X_36,not(X_37)) = and(not(X_37),X_36),
inference(resolve,[$cnf( $equal(and(not(X_37),X_36),and(X_36,not(X_37))) )],[refute_0_1021,refute_0_1022]) ).
cnf(refute_0_1024,plain,
( and(X_36,not(X_37)) != and(not(X_37),X_36)
| xor(X_36,X_37) != or(and(X_36,not(X_37)),and(not(X_36),X_37))
| xor(X_36,X_37) = or(and(not(X_37),X_36),and(not(X_36),X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_36,X_37),or(and(X_36,not(X_37)),and(not(X_36),X_37))) ),[1,0],$fot(and(not(X_37),X_36))]]) ).
cnf(refute_0_1025,plain,
( xor(X_36,X_37) != or(and(X_36,not(X_37)),and(not(X_36),X_37))
| xor(X_36,X_37) = or(and(not(X_37),X_36),and(not(X_36),X_37)) ),
inference(resolve,[$cnf( $equal(and(X_36,not(X_37)),and(not(X_37),X_36)) )],[refute_0_1023,refute_0_1024]) ).
cnf(refute_0_1026,plain,
xor(X_36,X_37) = or(and(not(X_37),X_36),and(not(X_36),X_37)),
inference(resolve,[$cnf( $equal(xor(X_36,X_37),or(and(X_36,not(X_37)),and(not(X_36),X_37))) )],[refute_0_1020,refute_0_1025]) ).
cnf(refute_0_1027,plain,
xor(not(X_90),X_37) = or(and(not(X_37),not(X_90)),and(not(not(X_90)),X_37)),
inference(subst,[],[refute_0_1026:[bind(X_36,$fot(not(X_90)))]]) ).
cnf(refute_0_1028,plain,
and(X,or(falsehood,not(X_4))) = not(or(not(X),not(or(falsehood,not(X_4))))),
inference(subst,[],[and_definition:[bind(Y,$fot(or(falsehood,not(X_4))))]]) ).
cnf(refute_0_1029,plain,
( and(X,or(falsehood,not(X_4))) != not(or(not(X),not(or(falsehood,not(X_4)))))
| not(or(falsehood,not(X_4))) != and(X_4,truth)
| and(X,or(falsehood,not(X_4))) = not(or(not(X),and(X_4,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,or(falsehood,not(X_4))),not(or(not(X),not(or(falsehood,not(X_4)))))) ),[1,0,1],$fot(and(X_4,truth))]]) ).
cnf(refute_0_1030,plain,
( and(X,or(falsehood,not(X_4))) != not(or(not(X),not(or(falsehood,not(X_4)))))
| and(X,or(falsehood,not(X_4))) = not(or(not(X),and(X_4,truth))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_4))),and(X_4,truth)) )],[refute_0_36,refute_0_1029]) ).
cnf(refute_0_1031,plain,
and(X,or(falsehood,not(X_4))) = not(or(not(X),and(X_4,truth))),
inference(resolve,[$cnf( $equal(and(X,or(falsehood,not(X_4))),not(or(not(X),not(or(falsehood,not(X_4)))))) )],[refute_0_1028,refute_0_1030]) ).
cnf(refute_0_1032,plain,
and(X,or(falsehood,not(X_4))) = and(X,or(falsehood,not(X_4))),
introduced(tautology,[refl,[$fot(and(X,or(falsehood,not(X_4))))]]) ).
cnf(refute_0_1033,plain,
( and(X,or(falsehood,not(X_4))) != and(X,or(falsehood,not(X_4)))
| or(falsehood,not(X_4)) != not(X_4)
| and(X,or(falsehood,not(X_4))) = and(X,not(X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,or(falsehood,not(X_4))),and(X,or(falsehood,not(X_4)))) ),[1,1],$fot(not(X_4))]]) ).
cnf(refute_0_1034,plain,
( or(falsehood,not(X_4)) != not(X_4)
| and(X,or(falsehood,not(X_4))) = and(X,not(X_4)) ),
inference(resolve,[$cnf( $equal(and(X,or(falsehood,not(X_4))),and(X,or(falsehood,not(X_4)))) )],[refute_0_1032,refute_0_1033]) ).
cnf(refute_0_1035,plain,
and(X,or(falsehood,not(X_4))) = and(X,not(X_4)),
inference(resolve,[$cnf( $equal(or(falsehood,not(X_4)),not(X_4)) )],[refute_0_910,refute_0_1034]) ).
cnf(refute_0_1036,plain,
( and(X,or(falsehood,not(X_4))) != and(X,not(X_4))
| and(X,or(falsehood,not(X_4))) != not(or(not(X),and(X_4,truth)))
| and(X,not(X_4)) = not(or(not(X),and(X_4,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,or(falsehood,not(X_4))),not(or(not(X),and(X_4,truth)))) ),[0],$fot(and(X,not(X_4)))]]) ).
cnf(refute_0_1037,plain,
( and(X,or(falsehood,not(X_4))) != not(or(not(X),and(X_4,truth)))
| and(X,not(X_4)) = not(or(not(X),and(X_4,truth))) ),
inference(resolve,[$cnf( $equal(and(X,or(falsehood,not(X_4))),and(X,not(X_4))) )],[refute_0_1035,refute_0_1036]) ).
cnf(refute_0_1038,plain,
not(not(X_1)) = X_1,
inference(subst,[],[refute_0_997:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_1039,plain,
( and(X_1,truth) != not(not(X_1))
| not(not(X_1)) != X_1
| and(X_1,truth) = X_1 ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_1,truth),X_1) ),[0],$fot(not(not(X_1)))]]) ).
cnf(refute_0_1040,plain,
( and(X_1,truth) != not(not(X_1))
| and(X_1,truth) = X_1 ),
inference(resolve,[$cnf( $equal(not(not(X_1)),X_1) )],[refute_0_1038,refute_0_1039]) ).
cnf(refute_0_1041,plain,
and(X_1,truth) = X_1,
inference(resolve,[$cnf( $equal(and(X_1,truth),not(not(X_1))) )],[refute_0_943,refute_0_1040]) ).
cnf(refute_0_1042,plain,
and(X_4,truth) = X_4,
inference(subst,[],[refute_0_1041:[bind(X_1,$fot(X_4))]]) ).
cnf(refute_0_1043,plain,
implies(X,and(X_4,truth)) = implies(X,and(X_4,truth)),
introduced(tautology,[refl,[$fot(implies(X,and(X_4,truth)))]]) ).
cnf(refute_0_1044,plain,
( and(X_4,truth) != X_4
| implies(X,and(X_4,truth)) != implies(X,and(X_4,truth))
| implies(X,and(X_4,truth)) = implies(X,X_4) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,and(X_4,truth)),implies(X,and(X_4,truth))) ),[1,1],$fot(X_4)]]) ).
cnf(refute_0_1045,plain,
( and(X_4,truth) != X_4
| implies(X,and(X_4,truth)) = implies(X,X_4) ),
inference(resolve,[$cnf( $equal(implies(X,and(X_4,truth)),implies(X,and(X_4,truth))) )],[refute_0_1043,refute_0_1044]) ).
cnf(refute_0_1046,plain,
implies(X,and(X_4,truth)) = implies(X,X_4),
inference(resolve,[$cnf( $equal(and(X_4,truth),X_4) )],[refute_0_1042,refute_0_1045]) ).
cnf(refute_0_1047,plain,
or(falsehood,or(not(X_1),X_8)) = or(not(X_1),X_8),
inference(subst,[],[refute_0_757:[bind(Y,$fot(or(not(X_1),X_8)))]]) ).
cnf(refute_0_1048,plain,
( or(falsehood,or(not(X_1),X_8)) != implies(and(X_1,truth),X_8)
| or(falsehood,or(not(X_1),X_8)) != or(not(X_1),X_8)
| or(not(X_1),X_8) = implies(and(X_1,truth),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(not(X_1),X_8)),implies(and(X_1,truth),X_8)) ),[0],$fot(or(not(X_1),X_8))]]) ).
cnf(refute_0_1049,plain,
( or(falsehood,or(not(X_1),X_8)) != implies(and(X_1,truth),X_8)
| or(not(X_1),X_8) = implies(and(X_1,truth),X_8) ),
inference(resolve,[$cnf( $equal(or(falsehood,or(not(X_1),X_8)),or(not(X_1),X_8)) )],[refute_0_1047,refute_0_1048]) ).
cnf(refute_0_1050,plain,
implies(and(X_1,truth),X_8) = implies(and(X_1,truth),X_8),
introduced(tautology,[refl,[$fot(implies(and(X_1,truth),X_8))]]) ).
cnf(refute_0_1051,plain,
( and(X_1,truth) != X_1
| implies(and(X_1,truth),X_8) != implies(and(X_1,truth),X_8)
| implies(and(X_1,truth),X_8) = implies(X_1,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(X_1,truth),X_8),implies(and(X_1,truth),X_8)) ),[1,0],$fot(X_1)]]) ).
cnf(refute_0_1052,plain,
( and(X_1,truth) != X_1
| implies(and(X_1,truth),X_8) = implies(X_1,X_8) ),
inference(resolve,[$cnf( $equal(implies(and(X_1,truth),X_8),implies(and(X_1,truth),X_8)) )],[refute_0_1050,refute_0_1051]) ).
cnf(refute_0_1053,plain,
implies(and(X_1,truth),X_8) = implies(X_1,X_8),
inference(resolve,[$cnf( $equal(and(X_1,truth),X_1) )],[refute_0_1041,refute_0_1052]) ).
cnf(refute_0_1054,plain,
( implies(and(X_1,truth),X_8) != implies(X_1,X_8)
| or(not(X_1),X_8) != implies(and(X_1,truth),X_8)
| or(not(X_1),X_8) = implies(X_1,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X_1),X_8),implies(and(X_1,truth),X_8)) ),[1],$fot(implies(X_1,X_8))]]) ).
cnf(refute_0_1055,plain,
( or(not(X_1),X_8) != implies(and(X_1,truth),X_8)
| or(not(X_1),X_8) = implies(X_1,X_8) ),
inference(resolve,[$cnf( $equal(implies(and(X_1,truth),X_8),implies(X_1,X_8)) )],[refute_0_1053,refute_0_1054]) ).
cnf(refute_0_1056,plain,
( or(falsehood,or(not(X_1),X_8)) != implies(and(X_1,truth),X_8)
| or(not(X_1),X_8) = implies(X_1,X_8) ),
inference(resolve,[$cnf( $equal(or(not(X_1),X_8),implies(and(X_1,truth),X_8)) )],[refute_0_1049,refute_0_1055]) ).
cnf(refute_0_1057,plain,
or(not(X_1),X_8) = implies(X_1,X_8),
inference(resolve,[$cnf( $equal(or(falsehood,or(not(X_1),X_8)),implies(and(X_1,truth),X_8)) )],[refute_0_324,refute_0_1056]) ).
cnf(refute_0_1058,plain,
or(not(X),and(X_4,truth)) = implies(X,and(X_4,truth)),
inference(subst,[],[refute_0_1057:[bind(X_1,$fot(X)),bind(X_8,$fot(and(X_4,truth)))]]) ).
cnf(refute_0_1059,plain,
( implies(X,and(X_4,truth)) != implies(X,X_4)
| or(not(X),and(X_4,truth)) != implies(X,and(X_4,truth))
| or(not(X),and(X_4,truth)) = implies(X,X_4) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(or(not(X),and(X_4,truth)))),bind(Y0,$fot(implies(X,and(X_4,truth)))),bind(Z0,$fot(implies(X,X_4)))]]) ).
cnf(refute_0_1060,plain,
( implies(X,and(X_4,truth)) != implies(X,X_4)
| or(not(X),and(X_4,truth)) = implies(X,X_4) ),
inference(resolve,[$cnf( $equal(or(not(X),and(X_4,truth)),implies(X,and(X_4,truth))) )],[refute_0_1058,refute_0_1059]) ).
cnf(refute_0_1061,plain,
or(not(X),and(X_4,truth)) = implies(X,X_4),
inference(resolve,[$cnf( $equal(implies(X,and(X_4,truth)),implies(X,X_4)) )],[refute_0_1046,refute_0_1060]) ).
cnf(refute_0_1062,plain,
not(or(not(X),and(X_4,truth))) = not(or(not(X),and(X_4,truth))),
introduced(tautology,[refl,[$fot(not(or(not(X),and(X_4,truth))))]]) ).
cnf(refute_0_1063,plain,
( not(or(not(X),and(X_4,truth))) != not(or(not(X),and(X_4,truth)))
| or(not(X),and(X_4,truth)) != implies(X,X_4)
| not(or(not(X),and(X_4,truth))) = not(implies(X,X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),and(X_4,truth))),not(or(not(X),and(X_4,truth)))) ),[1,0],$fot(implies(X,X_4))]]) ).
cnf(refute_0_1064,plain,
( or(not(X),and(X_4,truth)) != implies(X,X_4)
| not(or(not(X),and(X_4,truth))) = not(implies(X,X_4)) ),
inference(resolve,[$cnf( $equal(not(or(not(X),and(X_4,truth))),not(or(not(X),and(X_4,truth)))) )],[refute_0_1062,refute_0_1063]) ).
cnf(refute_0_1065,plain,
not(or(not(X),and(X_4,truth))) = not(implies(X,X_4)),
inference(resolve,[$cnf( $equal(or(not(X),and(X_4,truth)),implies(X,X_4)) )],[refute_0_1061,refute_0_1064]) ).
cnf(refute_0_1066,plain,
( and(X,not(X_4)) != not(or(not(X),and(X_4,truth)))
| not(or(not(X),and(X_4,truth))) != not(implies(X,X_4))
| and(X,not(X_4)) = not(implies(X,X_4)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,not(X_4)),not(implies(X,X_4))) ),[0],$fot(not(or(not(X),and(X_4,truth))))]]) ).
cnf(refute_0_1067,plain,
( and(X,not(X_4)) != not(or(not(X),and(X_4,truth)))
| and(X,not(X_4)) = not(implies(X,X_4)) ),
inference(resolve,[$cnf( $equal(not(or(not(X),and(X_4,truth))),not(implies(X,X_4))) )],[refute_0_1065,refute_0_1066]) ).
cnf(refute_0_1068,plain,
( and(X,or(falsehood,not(X_4))) != not(or(not(X),and(X_4,truth)))
| and(X,not(X_4)) = not(implies(X,X_4)) ),
inference(resolve,[$cnf( $equal(and(X,not(X_4)),not(or(not(X),and(X_4,truth)))) )],[refute_0_1037,refute_0_1067]) ).
cnf(refute_0_1069,plain,
and(X,not(X_4)) = not(implies(X,X_4)),
inference(resolve,[$cnf( $equal(and(X,or(falsehood,not(X_4))),not(or(not(X),and(X_4,truth)))) )],[refute_0_1031,refute_0_1068]) ).
cnf(refute_0_1070,plain,
and(not(X_37),not(X_90)) = not(implies(not(X_37),X_90)),
inference(subst,[],[refute_0_1069:[bind(X,$fot(not(X_37))),bind(X_4,$fot(X_90))]]) ).
cnf(refute_0_1071,plain,
( and(not(X_37),not(X_90)) != not(implies(not(X_37),X_90))
| xor(not(X_90),X_37) != or(and(not(X_37),not(X_90)),and(not(not(X_90)),X_37))
| xor(not(X_90),X_37) = or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(not(X_90),X_37),or(and(not(X_37),not(X_90)),and(not(not(X_90)),X_37))) ),[1,0],$fot(not(implies(not(X_37),X_90)))]]) ).
cnf(refute_0_1072,plain,
( xor(not(X_90),X_37) != or(and(not(X_37),not(X_90)),and(not(not(X_90)),X_37))
| xor(not(X_90),X_37) = or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37)) ),
inference(resolve,[$cnf( $equal(and(not(X_37),not(X_90)),not(implies(not(X_37),X_90))) )],[refute_0_1070,refute_0_1071]) ).
cnf(refute_0_1073,plain,
xor(not(X_90),X_37) = or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37)),
inference(resolve,[$cnf( $equal(xor(not(X_90),X_37),or(and(not(X_37),not(X_90)),and(not(not(X_90)),X_37))) )],[refute_0_1027,refute_0_1072]) ).
cnf(refute_0_1074,plain,
xor(X,not(X_65)) = or(and(X,not(not(X_65))),and(not(X),not(X_65))),
inference(subst,[],[xor_definition:[bind(Y,$fot(not(X_65)))]]) ).
cnf(refute_0_1075,plain,
not(not(X_65)) = X_65,
inference(subst,[],[refute_0_997:[bind(X,$fot(X_65))]]) ).
cnf(refute_0_1076,plain,
( not(not(X_65)) != X_65
| xor(X,not(X_65)) != or(and(X,not(not(X_65))),and(not(X),not(X_65)))
| xor(X,not(X_65)) = or(and(X,X_65),and(not(X),not(X_65))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X,not(X_65)),or(and(X,not(not(X_65))),and(not(X),not(X_65)))) ),[1,0,1],$fot(X_65)]]) ).
cnf(refute_0_1077,plain,
( xor(X,not(X_65)) != or(and(X,not(not(X_65))),and(not(X),not(X_65)))
| xor(X,not(X_65)) = or(and(X,X_65),and(not(X),not(X_65))) ),
inference(resolve,[$cnf( $equal(not(not(X_65)),X_65) )],[refute_0_1075,refute_0_1076]) ).
cnf(refute_0_1078,plain,
xor(X,not(X_65)) = or(and(X,X_65),and(not(X),not(X_65))),
inference(resolve,[$cnf( $equal(xor(X,not(X_65)),or(and(X,not(not(X_65))),and(not(X),not(X_65)))) )],[refute_0_1074,refute_0_1077]) ).
cnf(refute_0_1079,plain,
xor(or(falsehood,not(X_1)),X_37) = or(and(or(falsehood,not(X_1)),not(X_37)),and(not(or(falsehood,not(X_1))),X_37)),
inference(subst,[],[xor_definition:[bind(X,$fot(or(falsehood,not(X_1)))),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_1080,plain,
( not(or(falsehood,not(X_1))) != and(X_1,truth)
| xor(or(falsehood,not(X_1)),X_37) != or(and(or(falsehood,not(X_1)),not(X_37)),and(not(or(falsehood,not(X_1))),X_37))
| xor(or(falsehood,not(X_1)),X_37) = or(and(or(falsehood,not(X_1)),not(X_37)),and(and(X_1,truth),X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(or(falsehood,not(X_1)),X_37),or(and(or(falsehood,not(X_1)),not(X_37)),and(not(or(falsehood,not(X_1))),X_37))) ),[1,1,0],$fot(and(X_1,truth))]]) ).
cnf(refute_0_1081,plain,
( xor(or(falsehood,not(X_1)),X_37) != or(and(or(falsehood,not(X_1)),not(X_37)),and(not(or(falsehood,not(X_1))),X_37))
| xor(or(falsehood,not(X_1)),X_37) = or(and(or(falsehood,not(X_1)),not(X_37)),and(and(X_1,truth),X_37)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_1))),and(X_1,truth)) )],[refute_0_45,refute_0_1080]) ).
cnf(refute_0_1082,plain,
xor(or(falsehood,not(X_1)),X_37) = or(and(or(falsehood,not(X_1)),not(X_37)),and(and(X_1,truth),X_37)),
inference(resolve,[$cnf( $equal(xor(or(falsehood,not(X_1)),X_37),or(and(or(falsehood,not(X_1)),not(X_37)),and(not(or(falsehood,not(X_1))),X_37))) )],[refute_0_1079,refute_0_1081]) ).
cnf(refute_0_1083,plain,
and(and(X_1,truth),X_37) = and(X_1,and(truth,X_37)),
inference(subst,[],[and_associativity:[bind(X,$fot(X_1)),bind(Y,$fot(truth)),bind(Z,$fot(X_37))]]) ).
cnf(refute_0_1084,plain,
or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37))) = or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37))),
introduced(tautology,[refl,[$fot(or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37))))]]) ).
cnf(refute_0_1085,plain,
( and(and(X_1,truth),X_37) != and(X_1,and(truth,X_37))
| or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37))) != or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37)))
| or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37))) = or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37))),or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37)))) ),[1,0],$fot(and(X_1,and(truth,X_37)))]]) ).
cnf(refute_0_1086,plain,
( and(and(X_1,truth),X_37) != and(X_1,and(truth,X_37))
| or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37))) = or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37))),or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37)))) )],[refute_0_1084,refute_0_1085]) ).
cnf(refute_0_1087,plain,
or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37))) = or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))),
inference(resolve,[$cnf( $equal(and(and(X_1,truth),X_37),and(X_1,and(truth,X_37))) )],[refute_0_1083,refute_0_1086]) ).
cnf(refute_0_1088,plain,
or(and(or(falsehood,not(X_1)),not(X_37)),and(and(X_1,truth),X_37)) = or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37))),
inference(subst,[],[refute_0_24:[bind(X,$fot(and(and(X_1,truth),X_37))),bind(Y,$fot(and(or(falsehood,not(X_1)),not(X_37))))]]) ).
cnf(refute_0_1089,plain,
( or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37))) != or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))
| or(and(or(falsehood,not(X_1)),not(X_37)),and(and(X_1,truth),X_37)) != or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37)))
| or(and(or(falsehood,not(X_1)),not(X_37)),and(and(X_1,truth),X_37)) = or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(or(and(or(falsehood,not(X_1)),not(X_37)),and(and(X_1,truth),X_37)))),bind(Y0,$fot(or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37))))),bind(Z0,$fot(or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))))]]) ).
cnf(refute_0_1090,plain,
( or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37))) != or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))
| or(and(or(falsehood,not(X_1)),not(X_37)),and(and(X_1,truth),X_37)) = or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(or(falsehood,not(X_1)),not(X_37)),and(and(X_1,truth),X_37)),or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37)))) )],[refute_0_1088,refute_0_1089]) ).
cnf(refute_0_1091,plain,
or(and(or(falsehood,not(X_1)),not(X_37)),and(and(X_1,truth),X_37)) = or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))),
inference(resolve,[$cnf( $equal(or(and(and(X_1,truth),X_37),and(or(falsehood,not(X_1)),not(X_37))),or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))) )],[refute_0_1087,refute_0_1090]) ).
cnf(refute_0_1092,plain,
( or(and(or(falsehood,not(X_1)),not(X_37)),and(and(X_1,truth),X_37)) != or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))
| xor(or(falsehood,not(X_1)),X_37) != or(and(or(falsehood,not(X_1)),not(X_37)),and(and(X_1,truth),X_37))
| xor(or(falsehood,not(X_1)),X_37) = or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(or(falsehood,not(X_1)),X_37),or(and(or(falsehood,not(X_1)),not(X_37)),and(and(X_1,truth),X_37))) ),[1],$fot(or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))))]]) ).
cnf(refute_0_1093,plain,
( xor(or(falsehood,not(X_1)),X_37) != or(and(or(falsehood,not(X_1)),not(X_37)),and(and(X_1,truth),X_37))
| xor(or(falsehood,not(X_1)),X_37) = or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(or(falsehood,not(X_1)),not(X_37)),and(and(X_1,truth),X_37)),or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))) )],[refute_0_1091,refute_0_1092]) ).
cnf(refute_0_1094,plain,
xor(or(falsehood,not(X_1)),X_37) = or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))),
inference(resolve,[$cnf( $equal(xor(or(falsehood,not(X_1)),X_37),or(and(or(falsehood,not(X_1)),not(X_37)),and(and(X_1,truth),X_37))) )],[refute_0_1082,refute_0_1093]) ).
cnf(refute_0_1095,plain,
xor(or(falsehood,not(X_1)),X_37) = xor(or(falsehood,not(X_1)),X_37),
introduced(tautology,[refl,[$fot(xor(or(falsehood,not(X_1)),X_37))]]) ).
cnf(refute_0_1096,plain,
( or(falsehood,not(X_1)) != not(X_1)
| xor(or(falsehood,not(X_1)),X_37) != xor(or(falsehood,not(X_1)),X_37)
| xor(or(falsehood,not(X_1)),X_37) = xor(not(X_1),X_37) ),
introduced(tautology,[equality,[$cnf( $equal(xor(or(falsehood,not(X_1)),X_37),xor(or(falsehood,not(X_1)),X_37)) ),[1,0],$fot(not(X_1))]]) ).
cnf(refute_0_1097,plain,
( or(falsehood,not(X_1)) != not(X_1)
| xor(or(falsehood,not(X_1)),X_37) = xor(not(X_1),X_37) ),
inference(resolve,[$cnf( $equal(xor(or(falsehood,not(X_1)),X_37),xor(or(falsehood,not(X_1)),X_37)) )],[refute_0_1095,refute_0_1096]) ).
cnf(refute_0_1098,plain,
xor(or(falsehood,not(X_1)),X_37) = xor(not(X_1),X_37),
inference(resolve,[$cnf( $equal(or(falsehood,not(X_1)),not(X_1)) )],[refute_0_936,refute_0_1097]) ).
cnf(refute_0_1099,plain,
( xor(or(falsehood,not(X_1)),X_37) != or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))
| xor(or(falsehood,not(X_1)),X_37) != xor(not(X_1),X_37)
| xor(not(X_1),X_37) = or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(or(falsehood,not(X_1)),X_37),or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))) ),[0],$fot(xor(not(X_1),X_37))]]) ).
cnf(refute_0_1100,plain,
( xor(or(falsehood,not(X_1)),X_37) != or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))
| xor(not(X_1),X_37) = or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))) ),
inference(resolve,[$cnf( $equal(xor(or(falsehood,not(X_1)),X_37),xor(not(X_1),X_37)) )],[refute_0_1098,refute_0_1099]) ).
cnf(refute_0_1101,plain,
and(or(falsehood,not(X_1)),not(X_37)) = and(or(falsehood,not(X_1)),not(X_37)),
introduced(tautology,[refl,[$fot(and(or(falsehood,not(X_1)),not(X_37)))]]) ).
cnf(refute_0_1102,plain,
( and(or(falsehood,not(X_1)),not(X_37)) != and(or(falsehood,not(X_1)),not(X_37))
| or(falsehood,not(X_1)) != not(X_1)
| and(or(falsehood,not(X_1)),not(X_37)) = and(not(X_1),not(X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,not(X_1)),not(X_37)),and(or(falsehood,not(X_1)),not(X_37))) ),[1,0],$fot(not(X_1))]]) ).
cnf(refute_0_1103,plain,
( or(falsehood,not(X_1)) != not(X_1)
| and(or(falsehood,not(X_1)),not(X_37)) = and(not(X_1),not(X_37)) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,not(X_1)),not(X_37)),and(or(falsehood,not(X_1)),not(X_37))) )],[refute_0_1101,refute_0_1102]) ).
cnf(refute_0_1104,plain,
and(or(falsehood,not(X_1)),not(X_37)) = and(not(X_1),not(X_37)),
inference(resolve,[$cnf( $equal(or(falsehood,not(X_1)),not(X_1)) )],[refute_0_936,refute_0_1103]) ).
cnf(refute_0_1105,plain,
or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))) = or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))),
introduced(tautology,[refl,[$fot(or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))))]]) ).
cnf(refute_0_1106,plain,
( and(or(falsehood,not(X_1)),not(X_37)) != and(not(X_1),not(X_37))
| or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))) != or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))
| or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))) = or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))),or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))) ),[1,1],$fot(and(not(X_1),not(X_37)))]]) ).
cnf(refute_0_1107,plain,
( and(or(falsehood,not(X_1)),not(X_37)) != and(not(X_1),not(X_37))
| or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))) = or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))),or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))) )],[refute_0_1105,refute_0_1106]) ).
cnf(refute_0_1108,plain,
or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))) = or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))),
inference(resolve,[$cnf( $equal(and(or(falsehood,not(X_1)),not(X_37)),and(not(X_1),not(X_37))) )],[refute_0_1104,refute_0_1107]) ).
cnf(refute_0_1109,plain,
( or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))) != or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37)))
| xor(not(X_1),X_37) != or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))
| xor(not(X_1),X_37) = or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(not(X_1),X_37),or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))) ),[1],$fot(or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))))]]) ).
cnf(refute_0_1110,plain,
( xor(not(X_1),X_37) != or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))
| xor(not(X_1),X_37) = or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37))),or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37)))) )],[refute_0_1108,refute_0_1109]) ).
cnf(refute_0_1111,plain,
( xor(or(falsehood,not(X_1)),X_37) != or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))
| xor(not(X_1),X_37) = or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))) ),
inference(resolve,[$cnf( $equal(xor(not(X_1),X_37),or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))) )],[refute_0_1100,refute_0_1110]) ).
cnf(refute_0_1112,plain,
xor(not(X_1),X_37) = or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))),
inference(resolve,[$cnf( $equal(xor(or(falsehood,not(X_1)),X_37),or(and(X_1,and(truth,X_37)),and(or(falsehood,not(X_1)),not(X_37)))) )],[refute_0_1094,refute_0_1111]) ).
cnf(refute_0_1113,plain,
and(X_2,truth) = X_2,
inference(subst,[],[refute_0_1041:[bind(X_1,$fot(X_2))]]) ).
cnf(refute_0_1114,plain,
( and(X_2,truth) != X_2
| and(truth,X_2) != and(X_2,truth)
| and(truth,X_2) = X_2 ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,X_2),and(X_2,truth)) ),[1],$fot(X_2)]]) ).
cnf(refute_0_1115,plain,
( and(truth,X_2) != and(X_2,truth)
| and(truth,X_2) = X_2 ),
inference(resolve,[$cnf( $equal(and(X_2,truth),X_2) )],[refute_0_1113,refute_0_1114]) ).
cnf(refute_0_1116,plain,
and(truth,X_2) = X_2,
inference(resolve,[$cnf( $equal(and(truth,X_2),and(X_2,truth)) )],[refute_0_49,refute_0_1115]) ).
cnf(refute_0_1117,plain,
and(truth,X_37) = X_37,
inference(subst,[],[refute_0_1116:[bind(X_2,$fot(X_37))]]) ).
cnf(refute_0_1118,plain,
and(X_1,and(truth,X_37)) = and(X_1,and(truth,X_37)),
introduced(tautology,[refl,[$fot(and(X_1,and(truth,X_37)))]]) ).
cnf(refute_0_1119,plain,
( and(X_1,and(truth,X_37)) != and(X_1,and(truth,X_37))
| and(truth,X_37) != X_37
| and(X_1,and(truth,X_37)) = and(X_1,X_37) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_1,and(truth,X_37)),and(X_1,and(truth,X_37))) ),[1,1],$fot(X_37)]]) ).
cnf(refute_0_1120,plain,
( and(truth,X_37) != X_37
| and(X_1,and(truth,X_37)) = and(X_1,X_37) ),
inference(resolve,[$cnf( $equal(and(X_1,and(truth,X_37)),and(X_1,and(truth,X_37))) )],[refute_0_1118,refute_0_1119]) ).
cnf(refute_0_1121,plain,
and(X_1,and(truth,X_37)) = and(X_1,X_37),
inference(resolve,[$cnf( $equal(and(truth,X_37),X_37) )],[refute_0_1117,refute_0_1120]) ).
cnf(refute_0_1122,plain,
or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))) = or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))),
introduced(tautology,[refl,[$fot(or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))))]]) ).
cnf(refute_0_1123,plain,
( and(X_1,and(truth,X_37)) != and(X_1,X_37)
| or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))) != or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37)))
| or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))) = or(and(X_1,X_37),and(not(X_1),not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))),or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37)))) ),[1,0],$fot(and(X_1,X_37))]]) ).
cnf(refute_0_1124,plain,
( and(X_1,and(truth,X_37)) != and(X_1,X_37)
| or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))) = or(and(X_1,X_37),and(not(X_1),not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))),or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37)))) )],[refute_0_1122,refute_0_1123]) ).
cnf(refute_0_1125,plain,
or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))) = or(and(X_1,X_37),and(not(X_1),not(X_37))),
inference(resolve,[$cnf( $equal(and(X_1,and(truth,X_37)),and(X_1,X_37)) )],[refute_0_1121,refute_0_1124]) ).
cnf(refute_0_1126,plain,
( or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))) != or(and(X_1,X_37),and(not(X_1),not(X_37)))
| xor(not(X_1),X_37) != or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37)))
| xor(not(X_1),X_37) = or(and(X_1,X_37),and(not(X_1),not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(not(X_1),X_37),or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37)))) ),[1],$fot(or(and(X_1,X_37),and(not(X_1),not(X_37))))]]) ).
cnf(refute_0_1127,plain,
( xor(not(X_1),X_37) != or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37)))
| xor(not(X_1),X_37) = or(and(X_1,X_37),and(not(X_1),not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37))),or(and(X_1,X_37),and(not(X_1),not(X_37)))) )],[refute_0_1125,refute_0_1126]) ).
cnf(refute_0_1128,plain,
xor(not(X_1),X_37) = or(and(X_1,X_37),and(not(X_1),not(X_37))),
inference(resolve,[$cnf( $equal(xor(not(X_1),X_37),or(and(X_1,and(truth,X_37)),and(not(X_1),not(X_37)))) )],[refute_0_1112,refute_0_1127]) ).
cnf(refute_0_1129,plain,
( xor(not(X_1),X_37) != or(and(X_1,X_37),and(not(X_1),not(X_37)))
| or(and(X_1,X_37),and(not(X_1),not(X_37))) = xor(not(X_1),X_37) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(not(X_1),X_37))),bind(Y0,$fot(or(and(X_1,X_37),and(not(X_1),not(X_37)))))]]) ).
cnf(refute_0_1130,plain,
or(and(X_1,X_37),and(not(X_1),not(X_37))) = xor(not(X_1),X_37),
inference(resolve,[$cnf( $equal(xor(not(X_1),X_37),or(and(X_1,X_37),and(not(X_1),not(X_37)))) )],[refute_0_1128,refute_0_1129]) ).
cnf(refute_0_1131,plain,
or(and(X,X_65),and(not(X),not(X_65))) = xor(not(X),X_65),
inference(subst,[],[refute_0_1130:[bind(X_1,$fot(X)),bind(X_37,$fot(X_65))]]) ).
cnf(refute_0_1132,plain,
( or(and(X,X_65),and(not(X),not(X_65))) != xor(not(X),X_65)
| xor(X,not(X_65)) != or(and(X,X_65),and(not(X),not(X_65)))
| xor(X,not(X_65)) = xor(not(X),X_65) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X,not(X_65)),or(and(X,X_65),and(not(X),not(X_65)))) ),[1],$fot(xor(not(X),X_65))]]) ).
cnf(refute_0_1133,plain,
( xor(X,not(X_65)) != or(and(X,X_65),and(not(X),not(X_65)))
| xor(X,not(X_65)) = xor(not(X),X_65) ),
inference(resolve,[$cnf( $equal(or(and(X,X_65),and(not(X),not(X_65))),xor(not(X),X_65)) )],[refute_0_1131,refute_0_1132]) ).
cnf(refute_0_1134,plain,
xor(X,not(X_65)) = xor(not(X),X_65),
inference(resolve,[$cnf( $equal(xor(X,not(X_65)),or(and(X,X_65),and(not(X),not(X_65)))) )],[refute_0_1078,refute_0_1133]) ).
cnf(refute_0_1135,plain,
( xor(X,not(X_65)) != xor(not(X),X_65)
| xor(not(X),X_65) = xor(X,not(X_65)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(X,not(X_65)))),bind(Y0,$fot(xor(not(X),X_65)))]]) ).
cnf(refute_0_1136,plain,
xor(not(X),X_65) = xor(X,not(X_65)),
inference(resolve,[$cnf( $equal(xor(X,not(X_65)),xor(not(X),X_65)) )],[refute_0_1134,refute_0_1135]) ).
cnf(refute_0_1137,plain,
xor(not(X_90),X_37) = xor(X_90,not(X_37)),
inference(subst,[],[refute_0_1136:[bind(X,$fot(X_90)),bind(X_65,$fot(X_37))]]) ).
cnf(refute_0_1138,plain,
( xor(not(X_90),X_37) != or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37))
| xor(not(X_90),X_37) != xor(X_90,not(X_37))
| xor(X_90,not(X_37)) = or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(not(X_90),X_37),or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37))) ),[0],$fot(xor(X_90,not(X_37)))]]) ).
cnf(refute_0_1139,plain,
( xor(not(X_90),X_37) != or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37))
| xor(X_90,not(X_37)) = or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37)) ),
inference(resolve,[$cnf( $equal(xor(not(X_90),X_37),xor(X_90,not(X_37))) )],[refute_0_1137,refute_0_1138]) ).
cnf(refute_0_1140,plain,
and(X_37,not(X_36)) = and(not(X_36),X_37),
inference(subst,[],[and_commutativity:[bind(X,$fot(X_37)),bind(Y,$fot(not(X_36)))]]) ).
cnf(refute_0_1141,plain,
( and(X_37,not(X_36)) != and(not(X_36),X_37)
| and(not(X_36),X_37) = and(X_37,not(X_36)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_37,not(X_36)))),bind(Y0,$fot(and(not(X_36),X_37)))]]) ).
cnf(refute_0_1142,plain,
and(not(X_36),X_37) = and(X_37,not(X_36)),
inference(resolve,[$cnf( $equal(and(X_37,not(X_36)),and(not(X_36),X_37)) )],[refute_0_1140,refute_0_1141]) ).
cnf(refute_0_1143,plain,
( and(not(X_36),X_37) != and(X_37,not(X_36))
| xor(X_36,X_37) != or(and(X_36,not(X_37)),and(not(X_36),X_37))
| xor(X_36,X_37) = or(and(X_36,not(X_37)),and(X_37,not(X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_36,X_37),or(and(X_36,not(X_37)),and(not(X_36),X_37))) ),[1,1],$fot(and(X_37,not(X_36)))]]) ).
cnf(refute_0_1144,plain,
( xor(X_36,X_37) != or(and(X_36,not(X_37)),and(not(X_36),X_37))
| xor(X_36,X_37) = or(and(X_36,not(X_37)),and(X_37,not(X_36))) ),
inference(resolve,[$cnf( $equal(and(not(X_36),X_37),and(X_37,not(X_36))) )],[refute_0_1142,refute_0_1143]) ).
cnf(refute_0_1145,plain,
xor(X_36,X_37) = or(and(X_36,not(X_37)),and(X_37,not(X_36))),
inference(resolve,[$cnf( $equal(xor(X_36,X_37),or(and(X_36,not(X_37)),and(not(X_36),X_37))) )],[refute_0_1020,refute_0_1144]) ).
cnf(refute_0_1146,plain,
xor(not(X),X_73) = or(and(not(X),not(X_73)),and(X_73,not(not(X)))),
inference(subst,[],[refute_0_1145:[bind(X_36,$fot(not(X))),bind(X_37,$fot(X_73))]]) ).
cnf(refute_0_1147,plain,
( not(not(X)) != X
| xor(not(X),X_73) != or(and(not(X),not(X_73)),and(X_73,not(not(X))))
| xor(not(X),X_73) = or(and(not(X),not(X_73)),and(X_73,X)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(not(X),X_73),or(and(not(X),not(X_73)),and(X_73,not(not(X))))) ),[1,1,1],$fot(X)]]) ).
cnf(refute_0_1148,plain,
( xor(not(X),X_73) != or(and(not(X),not(X_73)),and(X_73,not(not(X))))
| xor(not(X),X_73) = or(and(not(X),not(X_73)),and(X_73,X)) ),
inference(resolve,[$cnf( $equal(not(not(X)),X) )],[refute_0_997,refute_0_1147]) ).
cnf(refute_0_1149,plain,
xor(not(X),X_73) = or(and(not(X),not(X_73)),and(X_73,X)),
inference(resolve,[$cnf( $equal(xor(not(X),X_73),or(and(not(X),not(X_73)),and(X_73,not(not(X))))) )],[refute_0_1146,refute_0_1148]) ).
cnf(refute_0_1150,plain,
xor(not(X),X_73) = xor(X,not(X_73)),
inference(subst,[],[refute_0_1136:[bind(X_65,$fot(X_73))]]) ).
cnf(refute_0_1151,plain,
( xor(not(X),X_73) != or(and(not(X),not(X_73)),and(X_73,X))
| xor(not(X),X_73) != xor(X,not(X_73))
| xor(X,not(X_73)) = or(and(not(X),not(X_73)),and(X_73,X)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(not(X),X_73),or(and(not(X),not(X_73)),and(X_73,X))) ),[0],$fot(xor(X,not(X_73)))]]) ).
cnf(refute_0_1152,plain,
( xor(not(X),X_73) != or(and(not(X),not(X_73)),and(X_73,X))
| xor(X,not(X_73)) = or(and(not(X),not(X_73)),and(X_73,X)) ),
inference(resolve,[$cnf( $equal(xor(not(X),X_73),xor(X,not(X_73))) )],[refute_0_1150,refute_0_1151]) ).
cnf(refute_0_1153,plain,
or(and(not(X),not(X_73)),and(X_73,X)) = or(and(X_73,X),and(not(X),not(X_73))),
inference(subst,[],[refute_0_24:[bind(X,$fot(and(X_73,X))),bind(Y,$fot(and(not(X),not(X_73))))]]) ).
cnf(refute_0_1154,plain,
( or(and(not(X),not(X_73)),and(X_73,X)) != or(and(X_73,X),and(not(X),not(X_73)))
| xor(X,not(X_73)) != or(and(not(X),not(X_73)),and(X_73,X))
| xor(X,not(X_73)) = or(and(X_73,X),and(not(X),not(X_73))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X,not(X_73)),or(and(not(X),not(X_73)),and(X_73,X))) ),[1],$fot(or(and(X_73,X),and(not(X),not(X_73))))]]) ).
cnf(refute_0_1155,plain,
( xor(X,not(X_73)) != or(and(not(X),not(X_73)),and(X_73,X))
| xor(X,not(X_73)) = or(and(X_73,X),and(not(X),not(X_73))) ),
inference(resolve,[$cnf( $equal(or(and(not(X),not(X_73)),and(X_73,X)),or(and(X_73,X),and(not(X),not(X_73)))) )],[refute_0_1153,refute_0_1154]) ).
cnf(refute_0_1156,plain,
( xor(not(X),X_73) != or(and(not(X),not(X_73)),and(X_73,X))
| xor(X,not(X_73)) = or(and(X_73,X),and(not(X),not(X_73))) ),
inference(resolve,[$cnf( $equal(xor(X,not(X_73)),or(and(not(X),not(X_73)),and(X_73,X))) )],[refute_0_1152,refute_0_1155]) ).
cnf(refute_0_1157,plain,
xor(X,not(X_73)) = or(and(X_73,X),and(not(X),not(X_73))),
inference(resolve,[$cnf( $equal(xor(not(X),X_73),or(and(not(X),not(X_73)),and(X_73,X))) )],[refute_0_1149,refute_0_1156]) ).
cnf(refute_0_1158,plain,
or(X_35,not(X_34)) = or(not(X_34),X_35),
inference(subst,[],[or_commutativity:[bind(X,$fot(X_35)),bind(Y,$fot(not(X_34)))]]) ).
cnf(refute_0_1159,plain,
or(not(X_34),X_35) = implies(X_34,X_35),
inference(subst,[],[refute_0_1057:[bind(X_1,$fot(X_34)),bind(X_8,$fot(X_35))]]) ).
cnf(refute_0_1160,plain,
( or(X_35,not(X_34)) != or(not(X_34),X_35)
| or(not(X_34),X_35) != implies(X_34,X_35)
| or(X_35,not(X_34)) = implies(X_34,X_35) ),
introduced(tautology,[equality,[$cnf( ~ $equal(or(X_35,not(X_34)),implies(X_34,X_35)) ),[0],$fot(or(not(X_34),X_35))]]) ).
cnf(refute_0_1161,plain,
( or(X_35,not(X_34)) != or(not(X_34),X_35)
| or(X_35,not(X_34)) = implies(X_34,X_35) ),
inference(resolve,[$cnf( $equal(or(not(X_34),X_35),implies(X_34,X_35)) )],[refute_0_1159,refute_0_1160]) ).
cnf(refute_0_1162,plain,
or(X_35,not(X_34)) = implies(X_34,X_35),
inference(resolve,[$cnf( $equal(or(X_35,not(X_34)),or(not(X_34),X_35)) )],[refute_0_1158,refute_0_1161]) ).
cnf(refute_0_1163,plain,
or(and(X_73,X),not(or(X,X_73))) = implies(or(X,X_73),and(X_73,X)),
inference(subst,[],[refute_0_1162:[bind(X_34,$fot(or(X,X_73))),bind(X_35,$fot(and(X_73,X)))]]) ).
cnf(refute_0_1164,plain,
implies(not(X),X_73) = or(X,X_73),
inference(subst,[],[refute_0_115:[bind(Y,$fot(X_73))]]) ).
cnf(refute_0_1165,plain,
not(implies(not(X),X_73)) = not(implies(not(X),X_73)),
introduced(tautology,[refl,[$fot(not(implies(not(X),X_73)))]]) ).
cnf(refute_0_1166,plain,
( implies(not(X),X_73) != or(X,X_73)
| not(implies(not(X),X_73)) != not(implies(not(X),X_73))
| not(implies(not(X),X_73)) = not(or(X,X_73)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(X),X_73)),not(implies(not(X),X_73))) ),[1,0],$fot(or(X,X_73))]]) ).
cnf(refute_0_1167,plain,
( implies(not(X),X_73) != or(X,X_73)
| not(implies(not(X),X_73)) = not(or(X,X_73)) ),
inference(resolve,[$cnf( $equal(not(implies(not(X),X_73)),not(implies(not(X),X_73))) )],[refute_0_1165,refute_0_1166]) ).
cnf(refute_0_1168,plain,
not(implies(not(X),X_73)) = not(or(X,X_73)),
inference(resolve,[$cnf( $equal(implies(not(X),X_73),or(X,X_73)) )],[refute_0_1164,refute_0_1167]) ).
cnf(refute_0_1169,plain,
and(not(X),not(X_73)) = not(implies(not(X),X_73)),
inference(subst,[],[refute_0_1069:[bind(X,$fot(not(X))),bind(X_4,$fot(X_73))]]) ).
cnf(refute_0_1170,plain,
( and(not(X),not(X_73)) != not(implies(not(X),X_73))
| not(implies(not(X),X_73)) != not(or(X,X_73))
| and(not(X),not(X_73)) = not(or(X,X_73)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(and(not(X),not(X_73)))),bind(Y0,$fot(not(implies(not(X),X_73)))),bind(Z0,$fot(not(or(X,X_73))))]]) ).
cnf(refute_0_1171,plain,
( not(implies(not(X),X_73)) != not(or(X,X_73))
| and(not(X),not(X_73)) = not(or(X,X_73)) ),
inference(resolve,[$cnf( $equal(and(not(X),not(X_73)),not(implies(not(X),X_73))) )],[refute_0_1169,refute_0_1170]) ).
cnf(refute_0_1172,plain,
and(not(X),not(X_73)) = not(or(X,X_73)),
inference(resolve,[$cnf( $equal(not(implies(not(X),X_73)),not(or(X,X_73))) )],[refute_0_1168,refute_0_1171]) ).
cnf(refute_0_1173,plain,
or(and(X_73,X),and(not(X),not(X_73))) = or(and(X_73,X),and(not(X),not(X_73))),
introduced(tautology,[refl,[$fot(or(and(X_73,X),and(not(X),not(X_73))))]]) ).
cnf(refute_0_1174,plain,
( and(not(X),not(X_73)) != not(or(X,X_73))
| or(and(X_73,X),and(not(X),not(X_73))) != or(and(X_73,X),and(not(X),not(X_73)))
| or(and(X_73,X),and(not(X),not(X_73))) = or(and(X_73,X),not(or(X,X_73))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_73,X),and(not(X),not(X_73))),or(and(X_73,X),and(not(X),not(X_73)))) ),[1,1],$fot(not(or(X,X_73)))]]) ).
cnf(refute_0_1175,plain,
( and(not(X),not(X_73)) != not(or(X,X_73))
| or(and(X_73,X),and(not(X),not(X_73))) = or(and(X_73,X),not(or(X,X_73))) ),
inference(resolve,[$cnf( $equal(or(and(X_73,X),and(not(X),not(X_73))),or(and(X_73,X),and(not(X),not(X_73)))) )],[refute_0_1173,refute_0_1174]) ).
cnf(refute_0_1176,plain,
or(and(X_73,X),and(not(X),not(X_73))) = or(and(X_73,X),not(or(X,X_73))),
inference(resolve,[$cnf( $equal(and(not(X),not(X_73)),not(or(X,X_73))) )],[refute_0_1172,refute_0_1175]) ).
cnf(refute_0_1177,plain,
( or(and(X_73,X),and(not(X),not(X_73))) != or(and(X_73,X),not(or(X,X_73)))
| or(and(X_73,X),not(or(X,X_73))) != implies(or(X,X_73),and(X_73,X))
| or(and(X_73,X),and(not(X),not(X_73))) = implies(or(X,X_73),and(X_73,X)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(or(and(X_73,X),and(not(X),not(X_73))))),bind(Y0,$fot(or(and(X_73,X),not(or(X,X_73))))),bind(Z0,$fot(implies(or(X,X_73),and(X_73,X))))]]) ).
cnf(refute_0_1178,plain,
( or(and(X_73,X),not(or(X,X_73))) != implies(or(X,X_73),and(X_73,X))
| or(and(X_73,X),and(not(X),not(X_73))) = implies(or(X,X_73),and(X_73,X)) ),
inference(resolve,[$cnf( $equal(or(and(X_73,X),and(not(X),not(X_73))),or(and(X_73,X),not(or(X,X_73)))) )],[refute_0_1176,refute_0_1177]) ).
cnf(refute_0_1179,plain,
or(and(X_73,X),and(not(X),not(X_73))) = implies(or(X,X_73),and(X_73,X)),
inference(resolve,[$cnf( $equal(or(and(X_73,X),not(or(X,X_73))),implies(or(X,X_73),and(X_73,X))) )],[refute_0_1163,refute_0_1178]) ).
cnf(refute_0_1180,plain,
( or(and(X_73,X),and(not(X),not(X_73))) != implies(or(X,X_73),and(X_73,X))
| xor(X,not(X_73)) != or(and(X_73,X),and(not(X),not(X_73)))
| xor(X,not(X_73)) = implies(or(X,X_73),and(X_73,X)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X,not(X_73)),or(and(X_73,X),and(not(X),not(X_73)))) ),[1],$fot(implies(or(X,X_73),and(X_73,X)))]]) ).
cnf(refute_0_1181,plain,
( xor(X,not(X_73)) != or(and(X_73,X),and(not(X),not(X_73)))
| xor(X,not(X_73)) = implies(or(X,X_73),and(X_73,X)) ),
inference(resolve,[$cnf( $equal(or(and(X_73,X),and(not(X),not(X_73))),implies(or(X,X_73),and(X_73,X))) )],[refute_0_1179,refute_0_1180]) ).
cnf(refute_0_1182,plain,
xor(X,not(X_73)) = implies(or(X,X_73),and(X_73,X)),
inference(resolve,[$cnf( $equal(xor(X,not(X_73)),or(and(X_73,X),and(not(X),not(X_73)))) )],[refute_0_1157,refute_0_1181]) ).
cnf(refute_0_1183,plain,
( xor(X,not(X_73)) != implies(or(X,X_73),and(X_73,X))
| implies(or(X,X_73),and(X_73,X)) = xor(X,not(X_73)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(X,not(X_73)))),bind(Y0,$fot(implies(or(X,X_73),and(X_73,X))))]]) ).
cnf(refute_0_1184,plain,
implies(or(X,X_73),and(X_73,X)) = xor(X,not(X_73)),
inference(resolve,[$cnf( $equal(xor(X,not(X_73)),implies(or(X,X_73),and(X_73,X))) )],[refute_0_1182,refute_0_1183]) ).
cnf(refute_0_1185,plain,
implies(or(X_37,X_90),and(X_90,X_37)) = xor(X_37,not(X_90)),
inference(subst,[],[refute_0_1184:[bind(X,$fot(X_37)),bind(X_73,$fot(X_90))]]) ).
cnf(refute_0_1186,plain,
not(not(X_90)) = X_90,
inference(subst,[],[refute_0_997:[bind(X,$fot(X_90))]]) ).
cnf(refute_0_1187,plain,
and(not(not(X_90)),X_37) = and(not(not(X_90)),X_37),
introduced(tautology,[refl,[$fot(and(not(not(X_90)),X_37))]]) ).
cnf(refute_0_1188,plain,
( and(not(not(X_90)),X_37) != and(not(not(X_90)),X_37)
| not(not(X_90)) != X_90
| and(not(not(X_90)),X_37) = and(X_90,X_37) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X_90)),X_37),and(not(not(X_90)),X_37)) ),[1,0],$fot(X_90)]]) ).
cnf(refute_0_1189,plain,
( not(not(X_90)) != X_90
| and(not(not(X_90)),X_37) = and(X_90,X_37) ),
inference(resolve,[$cnf( $equal(and(not(not(X_90)),X_37),and(not(not(X_90)),X_37)) )],[refute_0_1187,refute_0_1188]) ).
cnf(refute_0_1190,plain,
and(not(not(X_90)),X_37) = and(X_90,X_37),
inference(resolve,[$cnf( $equal(not(not(X_90)),X_90) )],[refute_0_1186,refute_0_1189]) ).
cnf(refute_0_1191,plain,
implies(or(X_37,X_90),and(not(not(X_90)),X_37)) = implies(or(X_37,X_90),and(not(not(X_90)),X_37)),
introduced(tautology,[refl,[$fot(implies(or(X_37,X_90),and(not(not(X_90)),X_37)))]]) ).
cnf(refute_0_1192,plain,
( and(not(not(X_90)),X_37) != and(X_90,X_37)
| implies(or(X_37,X_90),and(not(not(X_90)),X_37)) != implies(or(X_37,X_90),and(not(not(X_90)),X_37))
| implies(or(X_37,X_90),and(not(not(X_90)),X_37)) = implies(or(X_37,X_90),and(X_90,X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_37,X_90),and(not(not(X_90)),X_37)),implies(or(X_37,X_90),and(not(not(X_90)),X_37))) ),[1,1],$fot(and(X_90,X_37))]]) ).
cnf(refute_0_1193,plain,
( and(not(not(X_90)),X_37) != and(X_90,X_37)
| implies(or(X_37,X_90),and(not(not(X_90)),X_37)) = implies(or(X_37,X_90),and(X_90,X_37)) ),
inference(resolve,[$cnf( $equal(implies(or(X_37,X_90),and(not(not(X_90)),X_37)),implies(or(X_37,X_90),and(not(not(X_90)),X_37))) )],[refute_0_1191,refute_0_1192]) ).
cnf(refute_0_1194,plain,
implies(or(X_37,X_90),and(not(not(X_90)),X_37)) = implies(or(X_37,X_90),and(X_90,X_37)),
inference(resolve,[$cnf( $equal(and(not(not(X_90)),X_37),and(X_90,X_37)) )],[refute_0_1190,refute_0_1193]) ).
cnf(refute_0_1195,plain,
implies(not(X_37),X_90) = or(X_37,X_90),
inference(subst,[],[refute_0_115:[bind(X,$fot(X_37)),bind(Y,$fot(X_90))]]) ).
cnf(refute_0_1196,plain,
implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)) = implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)),
introduced(tautology,[refl,[$fot(implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)))]]) ).
cnf(refute_0_1197,plain,
( implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)) != implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37))
| implies(not(X_37),X_90) != or(X_37,X_90)
| implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)) = implies(or(X_37,X_90),and(not(not(X_90)),X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)),implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37))) ),[1,0],$fot(or(X_37,X_90))]]) ).
cnf(refute_0_1198,plain,
( implies(not(X_37),X_90) != or(X_37,X_90)
| implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)) = implies(or(X_37,X_90),and(not(not(X_90)),X_37)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)),implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37))) )],[refute_0_1196,refute_0_1197]) ).
cnf(refute_0_1199,plain,
implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)) = implies(or(X_37,X_90),and(not(not(X_90)),X_37)),
inference(resolve,[$cnf( $equal(implies(not(X_37),X_90),or(X_37,X_90)) )],[refute_0_1195,refute_0_1198]) ).
cnf(refute_0_1200,plain,
( implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)) != implies(or(X_37,X_90),and(not(not(X_90)),X_37))
| implies(or(X_37,X_90),and(not(not(X_90)),X_37)) != implies(or(X_37,X_90),and(X_90,X_37))
| implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)) = implies(or(X_37,X_90),and(X_90,X_37)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)))),bind(Y0,$fot(implies(or(X_37,X_90),and(not(not(X_90)),X_37)))),bind(Z0,$fot(implies(or(X_37,X_90),and(X_90,X_37))))]]) ).
cnf(refute_0_1201,plain,
( implies(or(X_37,X_90),and(not(not(X_90)),X_37)) != implies(or(X_37,X_90),and(X_90,X_37))
| implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)) = implies(or(X_37,X_90),and(X_90,X_37)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)),implies(or(X_37,X_90),and(not(not(X_90)),X_37))) )],[refute_0_1199,refute_0_1200]) ).
cnf(refute_0_1202,plain,
implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)) = implies(or(X_37,X_90),and(X_90,X_37)),
inference(resolve,[$cnf( $equal(implies(or(X_37,X_90),and(not(not(X_90)),X_37)),implies(or(X_37,X_90),and(X_90,X_37))) )],[refute_0_1194,refute_0_1201]) ).
cnf(refute_0_1203,plain,
( implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)) != implies(or(X_37,X_90),and(X_90,X_37))
| implies(or(X_37,X_90),and(X_90,X_37)) != xor(X_37,not(X_90))
| implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)) = xor(X_37,not(X_90)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)))),bind(Y0,$fot(implies(or(X_37,X_90),and(X_90,X_37)))),bind(Z0,$fot(xor(X_37,not(X_90))))]]) ).
cnf(refute_0_1204,plain,
( implies(or(X_37,X_90),and(X_90,X_37)) != xor(X_37,not(X_90))
| implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)) = xor(X_37,not(X_90)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)),implies(or(X_37,X_90),and(X_90,X_37))) )],[refute_0_1202,refute_0_1203]) ).
cnf(refute_0_1205,plain,
implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)) = xor(X_37,not(X_90)),
inference(resolve,[$cnf( $equal(implies(or(X_37,X_90),and(X_90,X_37)),xor(X_37,not(X_90))) )],[refute_0_1185,refute_0_1204]) ).
cnf(refute_0_1206,plain,
or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37)) = implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)),
inference(subst,[],[refute_0_1057:[bind(X_1,$fot(implies(not(X_37),X_90))),bind(X_8,$fot(and(not(not(X_90)),X_37)))]]) ).
cnf(refute_0_1207,plain,
( implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)) != xor(X_37,not(X_90))
| or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37)) != implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37))
| or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37)) = xor(X_37,not(X_90)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37)))),bind(Y0,$fot(implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)))),bind(Z0,$fot(xor(X_37,not(X_90))))]]) ).
cnf(refute_0_1208,plain,
( implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)) != xor(X_37,not(X_90))
| or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37)) = xor(X_37,not(X_90)) ),
inference(resolve,[$cnf( $equal(or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37)),implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37))) )],[refute_0_1206,refute_0_1207]) ).
cnf(refute_0_1209,plain,
or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37)) = xor(X_37,not(X_90)),
inference(resolve,[$cnf( $equal(implies(implies(not(X_37),X_90),and(not(not(X_90)),X_37)),xor(X_37,not(X_90))) )],[refute_0_1205,refute_0_1208]) ).
cnf(refute_0_1210,plain,
( or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37)) != xor(X_37,not(X_90))
| xor(X_90,not(X_37)) != or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37))
| xor(X_90,not(X_37)) = xor(X_37,not(X_90)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_90,not(X_37)),or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37))) ),[1],$fot(xor(X_37,not(X_90)))]]) ).
cnf(refute_0_1211,plain,
( xor(X_90,not(X_37)) != or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37))
| xor(X_90,not(X_37)) = xor(X_37,not(X_90)) ),
inference(resolve,[$cnf( $equal(or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37)),xor(X_37,not(X_90))) )],[refute_0_1209,refute_0_1210]) ).
cnf(refute_0_1212,plain,
( xor(not(X_90),X_37) != or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37))
| xor(X_90,not(X_37)) = xor(X_37,not(X_90)) ),
inference(resolve,[$cnf( $equal(xor(X_90,not(X_37)),or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37))) )],[refute_0_1139,refute_0_1211]) ).
cnf(refute_0_1213,plain,
xor(X_90,not(X_37)) = xor(X_37,not(X_90)),
inference(resolve,[$cnf( $equal(xor(not(X_90),X_37),or(not(implies(not(X_37),X_90)),and(not(not(X_90)),X_37))) )],[refute_0_1073,refute_0_1212]) ).
cnf(refute_0_1214,plain,
( xor(X_90,not(X_37)) != xor(X_37,not(X_90))
| xor(X_37,not(X_90)) = xor(X_90,not(X_37)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(X_90,not(X_37)))),bind(Y0,$fot(xor(X_37,not(X_90))))]]) ).
cnf(refute_0_1215,plain,
xor(X_37,not(X_90)) = xor(X_90,not(X_37)),
inference(resolve,[$cnf( $equal(xor(X_90,not(X_37)),xor(X_37,not(X_90))) )],[refute_0_1213,refute_0_1214]) ).
cnf(refute_0_1216,plain,
xor(y,not(x)) = xor(x,not(y)),
inference(subst,[],[refute_0_1215:[bind(X_37,$fot(y)),bind(X_90,$fot(x))]]) ).
cnf(refute_0_1217,plain,
( xor(x,not(y)) != xor(x,not(y))
| xor(y,not(x)) != xor(x,not(y))
| xor(x,not(y)) = xor(y,not(x)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(xor(x,not(y)),xor(y,not(x))) ),[1],$fot(xor(x,not(y)))]]) ).
cnf(refute_0_1218,plain,
( xor(x,not(y)) != xor(x,not(y))
| xor(x,not(y)) = xor(y,not(x)) ),
inference(resolve,[$cnf( $equal(xor(y,not(x)),xor(x,not(y))) )],[refute_0_1216,refute_0_1217]) ).
cnf(refute_0_1219,plain,
xor(x,not(y)) != xor(x,not(y)),
inference(resolve,[$cnf( $equal(xor(x,not(y)),xor(y,not(x))) )],[refute_0_1218,refute_0_1019]) ).
cnf(refute_0_1220,plain,
xor(x,not(y)) = xor(x,not(y)),
introduced(tautology,[refl,[$fot(xor(x,not(y)))]]) ).
cnf(refute_0_1221,plain,
$false,
inference(resolve,[$cnf( $equal(xor(x,not(y)),xor(x,not(y))) )],[refute_0_1220,refute_0_1219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL159-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 2 10:29:23 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.49/0.69 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.49/0.69
% 0.49/0.69 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.61/0.85
%------------------------------------------------------------------------------