TSTP Solution File: LCL158-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL158-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 12:50:03 EDT 2022
% Result : Unsatisfiable 0.18s 0.56s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 74
% Number of leaves : 149
% Syntax : Number of clauses : 545 ( 281 unt; 0 nHn; 313 RR)
% Number of literals : 935 ( 934 equ; 394 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 575 ( 10 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(and_star_definition,axiom,
and_star(X,Y) = not(or(not(X),not(Y))) ).
cnf(false_definition,axiom,
not(truth) = falsehood ).
cnf(prove_alternative_wajsberg_axiom,negated_conjecture,
and_star(xor(truth,x),x) != falsehood ).
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( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( and(X,Y) != and(Y,X)
| and(Y,X) = and(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(and(Y,X)))]]) ).
cnf(refute_0_4,plain,
and(Y,X) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),and(Y,X)) )],[and_commutativity,refute_0_3]) ).
cnf(refute_0_5,plain,
and(xor(truth,x),x) = and(x,xor(truth,x)),
inference(subst,[],[refute_0_4:[bind(X,$fot(x)),bind(Y,$fot(xor(truth,x)))]]) ).
cnf(refute_0_6,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(or(not(X),not(Y)))))]]) ).
cnf(refute_0_7,plain,
not(or(not(X),not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[and_definition,refute_0_6]) ).
cnf(refute_0_8,plain,
( and_star(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) != and(X,Y)
| and_star(X,Y) = and(X,Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and_star(X,Y),and(X,Y)) ),[0],$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_9,plain,
( and_star(X,Y) != not(or(not(X),not(Y)))
| and_star(X,Y) = and(X,Y) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),and(X,Y)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
and_star(X,Y) = and(X,Y),
inference(resolve,[$cnf( $equal(and_star(X,Y),not(or(not(X),not(Y)))) )],[and_star_definition,refute_0_9]) ).
cnf(refute_0_11,plain,
and_star(xor(truth,x),x) = and(xor(truth,x),x),
inference(subst,[],[refute_0_10:[bind(X,$fot(xor(truth,x))),bind(Y,$fot(x))]]) ).
cnf(refute_0_12,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_13,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_12]) ).
cnf(refute_0_14,plain,
( and(xor(truth,x),x) != and(x,xor(truth,x))
| and_star(xor(truth,x),x) != and(xor(truth,x),x)
| and_star(xor(truth,x),x) = and(x,xor(truth,x)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and_star(xor(truth,x),x))),bind(Y0,$fot(and(xor(truth,x),x))),bind(Z0,$fot(and(x,xor(truth,x))))]]) ).
cnf(refute_0_15,plain,
( and(xor(truth,x),x) != and(x,xor(truth,x))
| and_star(xor(truth,x),x) = and(x,xor(truth,x)) ),
inference(resolve,[$cnf( $equal(and_star(xor(truth,x),x),and(xor(truth,x),x)) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
and_star(xor(truth,x),x) = and(x,xor(truth,x)),
inference(resolve,[$cnf( $equal(and(xor(truth,x),x),and(x,xor(truth,x))) )],[refute_0_5,refute_0_15]) ).
cnf(refute_0_17,plain,
( and(x,xor(truth,x)) != falsehood
| and_star(xor(truth,x),x) != and(x,xor(truth,x))
| and_star(xor(truth,x),x) = falsehood ),
introduced(tautology,[equality,[$cnf( $equal(and_star(xor(truth,x),x),and(x,xor(truth,x))) ),[1],$fot(falsehood)]]) ).
cnf(refute_0_18,plain,
( and(x,xor(truth,x)) != falsehood
| and_star(xor(truth,x),x) = falsehood ),
inference(resolve,[$cnf( $equal(and_star(xor(truth,x),x),and(x,xor(truth,x))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
and(x,xor(truth,x)) != falsehood,
inference(resolve,[$cnf( $equal(and_star(xor(truth,x),x),falsehood) )],[refute_0_18,prove_alternative_wajsberg_axiom]) ).
cnf(refute_0_20,plain,
or(not(X_81),Y) = implies(not(not(X_81)),Y),
inference(subst,[],[or_definition:[bind(X,$fot(not(X_81)))]]) ).
cnf(refute_0_21,plain,
implies(implies(not(not(X_61)),falsehood),falsehood) = implies(implies(falsehood,not(not(X_61))),not(not(X_61))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(not(X_61)))),bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_22,plain,
or(or(X_37,not(X_37)),X_39) = or(X_37,or(not(X_37),X_39)),
inference(subst,[],[or_associativity:[bind(X,$fot(X_37)),bind(Y,$fot(not(X_37))),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_23,plain,
or(X,not(X)) = implies(not(X),not(X)),
inference(subst,[],[or_definition:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_24,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_25,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[or_definition,refute_0_24]) ).
cnf(refute_0_26,plain,
implies(not(X),not(Y)) = or(X,not(Y)),
inference(subst,[],[refute_0_25:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_27,plain,
implies(implies(not(X),not(Y)),implies(Y,X)) = implies(implies(not(X),not(Y)),implies(Y,X)),
introduced(tautology,[refl,[$fot(implies(implies(not(X),not(Y)),implies(Y,X)))]]) ).
cnf(refute_0_28,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != implies(implies(not(X),not(Y)),implies(Y,X))
| implies(not(X),not(Y)) != or(X,not(Y))
| implies(implies(not(X),not(Y)),implies(Y,X)) = implies(or(X,not(Y)),implies(Y,X)) ),
introduced(tautology,[equality,[$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_29,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( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(not(X),not(Y)),implies(Y,X))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
implies(implies(not(X),not(Y)),implies(Y,X)) = implies(or(X,not(Y)),implies(Y,X)),
inference(resolve,[$cnf( $equal(implies(not(X),not(Y)),or(X,not(Y))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != implies(or(X,not(Y)),implies(Y,X))
| implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(or(X,not(Y)),implies(Y,X)) = truth ),
introduced(tautology,[equality,[$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_32,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(or(X,not(Y)),implies(Y,X)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(or(X,not(Y)),implies(Y,X))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
implies(or(X,not(Y)),implies(Y,X)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[wajsberg_4,refute_0_32]) ).
cnf(refute_0_34,plain,
implies(or(X_13,not(truth)),implies(truth,X_13)) = truth,
inference(subst,[],[refute_0_33:[bind(X,$fot(X_13)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_35,plain,
implies(truth,X_13) = X_13,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_36,plain,
( implies(or(X_13,not(truth)),implies(truth,X_13)) != truth
| implies(truth,X_13) != X_13
| implies(or(X_13,not(truth)),X_13) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_13,not(truth)),implies(truth,X_13)),truth) ),[0,1],$fot(X_13)]]) ).
cnf(refute_0_37,plain,
( implies(or(X_13,not(truth)),implies(truth,X_13)) != truth
| implies(or(X_13,not(truth)),X_13) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_13),X_13) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(or(X_13,not(truth)),X_13) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_13,not(truth)),implies(truth,X_13)),truth) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
or(X_13,not(truth)) = or(X_13,not(truth)),
introduced(tautology,[refl,[$fot(or(X_13,not(truth)))]]) ).
cnf(refute_0_40,plain,
( not(truth) != falsehood
| or(X_13,not(truth)) != or(X_13,not(truth))
| or(X_13,not(truth)) = or(X_13,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_13,not(truth)),or(X_13,not(truth))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_41,plain,
( not(truth) != falsehood
| or(X_13,not(truth)) = or(X_13,falsehood) ),
inference(resolve,[$cnf( $equal(or(X_13,not(truth)),or(X_13,not(truth))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
or(X_13,not(truth)) = or(X_13,falsehood),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_41]) ).
cnf(refute_0_43,plain,
implies(or(X_13,not(truth)),X_13) = implies(or(X_13,not(truth)),X_13),
introduced(tautology,[refl,[$fot(implies(or(X_13,not(truth)),X_13))]]) ).
cnf(refute_0_44,plain,
( implies(or(X_13,not(truth)),X_13) != implies(or(X_13,not(truth)),X_13)
| or(X_13,not(truth)) != or(X_13,falsehood)
| implies(or(X_13,not(truth)),X_13) = implies(or(X_13,falsehood),X_13) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_13,not(truth)),X_13),implies(or(X_13,not(truth)),X_13)) ),[1,0],$fot(or(X_13,falsehood))]]) ).
cnf(refute_0_45,plain,
( or(X_13,not(truth)) != or(X_13,falsehood)
| implies(or(X_13,not(truth)),X_13) = implies(or(X_13,falsehood),X_13) ),
inference(resolve,[$cnf( $equal(implies(or(X_13,not(truth)),X_13),implies(or(X_13,not(truth)),X_13)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
implies(or(X_13,not(truth)),X_13) = implies(or(X_13,falsehood),X_13),
inference(resolve,[$cnf( $equal(or(X_13,not(truth)),or(X_13,falsehood)) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
( implies(or(X_13,not(truth)),X_13) != implies(or(X_13,falsehood),X_13)
| implies(or(X_13,not(truth)),X_13) != truth
| implies(or(X_13,falsehood),X_13) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_13,not(truth)),X_13),truth) ),[0],$fot(implies(or(X_13,falsehood),X_13))]]) ).
cnf(refute_0_48,plain,
( implies(or(X_13,not(truth)),X_13) != truth
| implies(or(X_13,falsehood),X_13) = truth ),
inference(resolve,[$cnf( $equal(implies(or(X_13,not(truth)),X_13),implies(or(X_13,falsehood),X_13)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
implies(or(X_13,falsehood),X_13) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_13,not(truth)),X_13),truth) )],[refute_0_38,refute_0_48]) ).
cnf(refute_0_50,plain,
implies(or(X_15,falsehood),X_15) = truth,
inference(subst,[],[refute_0_49:[bind(X_13,$fot(X_15))]]) ).
cnf(refute_0_51,plain,
or(falsehood,X_15) = or(X_15,falsehood),
inference(subst,[],[or_commutativity:[bind(X,$fot(falsehood)),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_52,plain,
( or(falsehood,X_15) != or(X_15,falsehood)
| or(X_15,falsehood) = or(falsehood,X_15) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(falsehood,X_15))),bind(Y0,$fot(or(X_15,falsehood)))]]) ).
cnf(refute_0_53,plain,
or(X_15,falsehood) = or(falsehood,X_15),
inference(resolve,[$cnf( $equal(or(falsehood,X_15),or(X_15,falsehood)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( implies(or(X_15,falsehood),X_15) != truth
| or(X_15,falsehood) != or(falsehood,X_15)
| implies(or(falsehood,X_15),X_15) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_15,falsehood),X_15),truth) ),[0,0],$fot(or(falsehood,X_15))]]) ).
cnf(refute_0_55,plain,
( implies(or(X_15,falsehood),X_15) != truth
| implies(or(falsehood,X_15),X_15) = truth ),
inference(resolve,[$cnf( $equal(or(X_15,falsehood),or(falsehood,X_15)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
implies(or(falsehood,X_15),X_15) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_15,falsehood),X_15),truth) )],[refute_0_50,refute_0_55]) ).
cnf(refute_0_57,plain,
or(falsehood,Y) = implies(not(falsehood),Y),
inference(subst,[],[or_definition:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_58,plain,
implies(or(falsehood,not(falsehood)),not(falsehood)) = truth,
inference(subst,[],[refute_0_56:[bind(X_15,$fot(not(falsehood)))]]) ).
cnf(refute_0_59,plain,
implies(or(truth,falsehood),truth) = truth,
inference(subst,[],[refute_0_49:[bind(X_13,$fot(truth))]]) ).
cnf(refute_0_60,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_61,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_62,plain,
( or(truth,X_8) != implies(not(truth),X_8)
| or(truth,X_8) = implies(falsehood,X_8) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_61]) ).
cnf(refute_0_63,plain,
or(truth,X_8) = implies(falsehood,X_8),
inference(resolve,[$cnf( $equal(or(truth,X_8),implies(not(truth),X_8)) )],[refute_0_60,refute_0_62]) ).
cnf(refute_0_64,plain,
or(truth,falsehood) = implies(falsehood,falsehood),
inference(subst,[],[refute_0_63:[bind(X_8,$fot(falsehood))]]) ).
cnf(refute_0_65,plain,
( implies(or(truth,falsehood),truth) != truth
| or(truth,falsehood) != implies(falsehood,falsehood)
| implies(implies(falsehood,falsehood),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(truth,falsehood),truth),truth) ),[0,0],$fot(implies(falsehood,falsehood))]]) ).
cnf(refute_0_66,plain,
( implies(or(truth,falsehood),truth) != truth
| implies(implies(falsehood,falsehood),truth) = truth ),
inference(resolve,[$cnf( $equal(or(truth,falsehood),implies(falsehood,falsehood)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
implies(implies(falsehood,falsehood),truth) = truth,
inference(resolve,[$cnf( $equal(implies(or(truth,falsehood),truth),truth) )],[refute_0_59,refute_0_66]) ).
cnf(refute_0_68,plain,
implies(implies(truth,X_21),X_21) = implies(implies(X_21,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_21))]]) ).
cnf(refute_0_69,plain,
implies(truth,X_21) = X_21,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_21))]]) ).
cnf(refute_0_70,plain,
( implies(implies(truth,X_21),X_21) != implies(implies(X_21,truth),truth)
| implies(truth,X_21) != X_21
| implies(X_21,X_21) = implies(implies(X_21,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_21),X_21),implies(implies(X_21,truth),truth)) ),[0,0],$fot(X_21)]]) ).
cnf(refute_0_71,plain,
( implies(implies(truth,X_21),X_21) != implies(implies(X_21,truth),truth)
| implies(X_21,X_21) = implies(implies(X_21,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(truth,X_21),X_21) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
implies(X_21,X_21) = implies(implies(X_21,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_21),X_21),implies(implies(X_21,truth),truth)) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
implies(not(X),not(X)) = implies(implies(not(X),truth),truth),
inference(subst,[],[refute_0_72:[bind(X_21,$fot(not(X)))]]) ).
cnf(refute_0_74,plain,
( implies(not(X),not(X)) != implies(implies(not(X),truth),truth)
| or(X,not(X)) != implies(not(X),not(X))
| or(X,not(X)) = implies(implies(not(X),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(X)),implies(not(X),not(X))) ),[1],$fot(implies(implies(not(X),truth),truth))]]) ).
cnf(refute_0_75,plain,
( or(X,not(X)) != implies(not(X),not(X))
| or(X,not(X)) = implies(implies(not(X),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X)),implies(implies(not(X),truth),truth)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
or(X,not(X)) = implies(implies(not(X),truth),truth),
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(not(X),not(X))) )],[refute_0_23,refute_0_75]) ).
cnf(refute_0_77,plain,
or(X,truth) = or(truth,X),
inference(subst,[],[or_commutativity:[bind(Y,$fot(truth))]]) ).
cnf(refute_0_78,plain,
or(truth,X) = implies(falsehood,X),
inference(subst,[],[refute_0_63:[bind(X_8,$fot(X))]]) ).
cnf(refute_0_79,plain,
( or(X,truth) != or(truth,X)
| or(truth,X) != implies(falsehood,X)
| or(X,truth) = implies(falsehood,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(or(X,truth),implies(falsehood,X)) ),[0],$fot(or(truth,X))]]) ).
cnf(refute_0_80,plain,
( or(X,truth) != or(truth,X)
| or(X,truth) = implies(falsehood,X) ),
inference(resolve,[$cnf( $equal(or(truth,X),implies(falsehood,X)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
or(X,truth) = implies(falsehood,X),
inference(resolve,[$cnf( $equal(or(X,truth),or(truth,X)) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
implies(not(X),truth) = or(X,truth),
inference(subst,[],[refute_0_25:[bind(Y,$fot(truth))]]) ).
cnf(refute_0_83,plain,
( implies(not(X),truth) != or(X,truth)
| or(X,truth) != implies(falsehood,X)
| implies(not(X),truth) = implies(falsehood,X) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(not(X),truth))),bind(Y0,$fot(or(X,truth))),bind(Z0,$fot(implies(falsehood,X)))]]) ).
cnf(refute_0_84,plain,
( or(X,truth) != implies(falsehood,X)
| implies(not(X),truth) = implies(falsehood,X) ),
inference(resolve,[$cnf( $equal(implies(not(X),truth),or(X,truth)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
implies(not(X),truth) = implies(falsehood,X),
inference(resolve,[$cnf( $equal(or(X,truth),implies(falsehood,X)) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
implies(implies(not(X),truth),truth) = implies(implies(not(X),truth),truth),
introduced(tautology,[refl,[$fot(implies(implies(not(X),truth),truth))]]) ).
cnf(refute_0_87,plain,
( implies(implies(not(X),truth),truth) != implies(implies(not(X),truth),truth)
| implies(not(X),truth) != implies(falsehood,X)
| implies(implies(not(X),truth),truth) = implies(implies(falsehood,X),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),truth),truth),implies(implies(not(X),truth),truth)) ),[1,0],$fot(implies(falsehood,X))]]) ).
cnf(refute_0_88,plain,
( implies(not(X),truth) != implies(falsehood,X)
| implies(implies(not(X),truth),truth) = implies(implies(falsehood,X),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),truth),implies(implies(not(X),truth),truth)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
implies(implies(not(X),truth),truth) = implies(implies(falsehood,X),truth),
inference(resolve,[$cnf( $equal(implies(not(X),truth),implies(falsehood,X)) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
( implies(implies(not(X),truth),truth) != implies(implies(falsehood,X),truth)
| or(X,not(X)) != implies(implies(not(X),truth),truth)
| or(X,not(X)) = implies(implies(falsehood,X),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(X)),implies(implies(not(X),truth),truth)) ),[1],$fot(implies(implies(falsehood,X),truth))]]) ).
cnf(refute_0_91,plain,
( or(X,not(X)) != implies(implies(not(X),truth),truth)
| or(X,not(X)) = implies(implies(falsehood,X),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),truth),implies(implies(falsehood,X),truth)) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
or(X,not(X)) = implies(implies(falsehood,X),truth),
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(implies(not(X),truth),truth)) )],[refute_0_76,refute_0_91]) ).
cnf(refute_0_93,plain,
( or(X,not(X)) != implies(implies(falsehood,X),truth)
| implies(implies(falsehood,X),truth) = or(X,not(X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,not(X)))),bind(Y0,$fot(implies(implies(falsehood,X),truth)))]]) ).
cnf(refute_0_94,plain,
implies(implies(falsehood,X),truth) = or(X,not(X)),
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(implies(falsehood,X),truth)) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
implies(implies(falsehood,falsehood),truth) = or(falsehood,not(falsehood)),
inference(subst,[],[refute_0_94:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_96,plain,
( implies(implies(falsehood,falsehood),truth) != or(falsehood,not(falsehood))
| implies(implies(falsehood,falsehood),truth) != truth
| or(falsehood,not(falsehood)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,falsehood),truth),truth) ),[0],$fot(or(falsehood,not(falsehood)))]]) ).
cnf(refute_0_97,plain,
( implies(implies(falsehood,falsehood),truth) != truth
| or(falsehood,not(falsehood)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,falsehood),truth),or(falsehood,not(falsehood))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
or(falsehood,not(falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,falsehood),truth),truth) )],[refute_0_67,refute_0_97]) ).
cnf(refute_0_99,plain,
( implies(or(falsehood,not(falsehood)),not(falsehood)) != truth
| or(falsehood,not(falsehood)) != truth
| implies(truth,not(falsehood)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,not(falsehood)),not(falsehood)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_100,plain,
( implies(or(falsehood,not(falsehood)),not(falsehood)) != truth
| implies(truth,not(falsehood)) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,not(falsehood)),truth) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
implies(truth,not(falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,not(falsehood)),not(falsehood)),truth) )],[refute_0_58,refute_0_100]) ).
cnf(refute_0_102,plain,
implies(truth,not(falsehood)) = not(falsehood),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(falsehood)))]]) ).
cnf(refute_0_103,plain,
( implies(truth,not(falsehood)) != not(falsehood)
| implies(truth,not(falsehood)) != truth
| not(falsehood) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,not(falsehood)),truth) ),[0],$fot(not(falsehood))]]) ).
cnf(refute_0_104,plain,
( implies(truth,not(falsehood)) != truth
| not(falsehood) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,not(falsehood)),not(falsehood)) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
not(falsehood) = truth,
inference(resolve,[$cnf( $equal(implies(truth,not(falsehood)),truth) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
( not(falsehood) != truth
| or(falsehood,Y) != implies(not(falsehood),Y)
| or(falsehood,Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,Y),implies(not(falsehood),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_107,plain,
( or(falsehood,Y) != implies(not(falsehood),Y)
| or(falsehood,Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
or(falsehood,Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(or(falsehood,Y),implies(not(falsehood),Y)) )],[refute_0_57,refute_0_107]) ).
cnf(refute_0_109,plain,
implies(truth,Y) = Y,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_110,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_111,plain,
( or(falsehood,Y) != implies(truth,Y)
| or(falsehood,Y) = Y ),
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
or(falsehood,Y) = Y,
inference(resolve,[$cnf( $equal(or(falsehood,Y),implies(truth,Y)) )],[refute_0_108,refute_0_111]) ).
cnf(refute_0_113,plain,
or(falsehood,X_15) = X_15,
inference(subst,[],[refute_0_112:[bind(Y,$fot(X_15))]]) ).
cnf(refute_0_114,plain,
implies(or(falsehood,X_15),X_15) = implies(or(falsehood,X_15),X_15),
introduced(tautology,[refl,[$fot(implies(or(falsehood,X_15),X_15))]]) ).
cnf(refute_0_115,plain,
( implies(or(falsehood,X_15),X_15) != implies(or(falsehood,X_15),X_15)
| or(falsehood,X_15) != X_15
| implies(or(falsehood,X_15),X_15) = implies(X_15,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,X_15),X_15),implies(or(falsehood,X_15),X_15)) ),[1,0],$fot(X_15)]]) ).
cnf(refute_0_116,plain,
( or(falsehood,X_15) != X_15
| implies(or(falsehood,X_15),X_15) = implies(X_15,X_15) ),
inference(resolve,[$cnf( $equal(implies(or(falsehood,X_15),X_15),implies(or(falsehood,X_15),X_15)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
implies(or(falsehood,X_15),X_15) = implies(X_15,X_15),
inference(resolve,[$cnf( $equal(or(falsehood,X_15),X_15) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
( implies(or(falsehood,X_15),X_15) != implies(X_15,X_15)
| implies(or(falsehood,X_15),X_15) != truth
| implies(X_15,X_15) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,X_15),X_15),truth) ),[0],$fot(implies(X_15,X_15))]]) ).
cnf(refute_0_119,plain,
( implies(or(falsehood,X_15),X_15) != truth
| implies(X_15,X_15) = truth ),
inference(resolve,[$cnf( $equal(implies(or(falsehood,X_15),X_15),implies(X_15,X_15)) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
implies(X_15,X_15) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,X_15),X_15),truth) )],[refute_0_56,refute_0_119]) ).
cnf(refute_0_121,plain,
implies(not(X),not(X)) = truth,
inference(subst,[],[refute_0_120:[bind(X_15,$fot(not(X)))]]) ).
cnf(refute_0_122,plain,
( implies(not(X),not(X)) != truth
| or(X,not(X)) != implies(not(X),not(X))
| or(X,not(X)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(X)),implies(not(X),not(X))) ),[1],$fot(truth)]]) ).
cnf(refute_0_123,plain,
( or(X,not(X)) != implies(not(X),not(X))
| or(X,not(X)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X)),truth) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
or(X,not(X)) = truth,
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(not(X),not(X))) )],[refute_0_23,refute_0_123]) ).
cnf(refute_0_125,plain,
or(X_37,not(X_37)) = truth,
inference(subst,[],[refute_0_124:[bind(X,$fot(X_37))]]) ).
cnf(refute_0_126,plain,
( or(X_37,not(X_37)) != truth
| or(or(X_37,not(X_37)),X_39) != or(X_37,or(not(X_37),X_39))
| or(truth,X_39) = or(X_37,or(not(X_37),X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(X_37,not(X_37)),X_39),or(X_37,or(not(X_37),X_39))) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_127,plain,
( or(or(X_37,not(X_37)),X_39) != or(X_37,or(not(X_37),X_39))
| or(truth,X_39) = or(X_37,or(not(X_37),X_39)) ),
inference(resolve,[$cnf( $equal(or(X_37,not(X_37)),truth) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
or(truth,X_39) = or(X_37,or(not(X_37),X_39)),
inference(resolve,[$cnf( $equal(or(or(X_37,not(X_37)),X_39),or(X_37,or(not(X_37),X_39))) )],[refute_0_22,refute_0_127]) ).
cnf(refute_0_129,plain,
or(truth,X_39) = implies(falsehood,X_39),
inference(subst,[],[refute_0_63:[bind(X_8,$fot(X_39))]]) ).
cnf(refute_0_130,plain,
( or(truth,X_39) != implies(falsehood,X_39)
| or(truth,X_39) != or(X_37,or(not(X_37),X_39))
| implies(falsehood,X_39) = or(X_37,or(not(X_37),X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(or(truth,X_39),or(X_37,or(not(X_37),X_39))) ),[0],$fot(implies(falsehood,X_39))]]) ).
cnf(refute_0_131,plain,
( or(truth,X_39) != or(X_37,or(not(X_37),X_39))
| implies(falsehood,X_39) = or(X_37,or(not(X_37),X_39)) ),
inference(resolve,[$cnf( $equal(or(truth,X_39),implies(falsehood,X_39)) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
implies(falsehood,X_39) = or(X_37,or(not(X_37),X_39)),
inference(resolve,[$cnf( $equal(or(truth,X_39),or(X_37,or(not(X_37),X_39))) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
implies(falsehood,not(not(X_51))) = or(X_51,or(not(X_51),not(not(X_51)))),
inference(subst,[],[refute_0_132:[bind(X_37,$fot(X_51)),bind(X_39,$fot(not(not(X_51))))]]) ).
cnf(refute_0_134,plain,
or(not(X_51),not(not(X_51))) = truth,
inference(subst,[],[refute_0_124:[bind(X,$fot(not(X_51)))]]) ).
cnf(refute_0_135,plain,
( implies(falsehood,not(not(X_51))) != or(X_51,or(not(X_51),not(not(X_51))))
| or(not(X_51),not(not(X_51))) != truth
| implies(falsehood,not(not(X_51))) = or(X_51,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(falsehood,not(not(X_51))),or(X_51,or(not(X_51),not(not(X_51))))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_136,plain,
( implies(falsehood,not(not(X_51))) != or(X_51,or(not(X_51),not(not(X_51))))
| implies(falsehood,not(not(X_51))) = or(X_51,truth) ),
inference(resolve,[$cnf( $equal(or(not(X_51),not(not(X_51))),truth) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
implies(falsehood,not(not(X_51))) = or(X_51,truth),
inference(resolve,[$cnf( $equal(implies(falsehood,not(not(X_51))),or(X_51,or(not(X_51),not(not(X_51))))) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
or(X_51,truth) = implies(falsehood,X_51),
inference(subst,[],[refute_0_81:[bind(X,$fot(X_51))]]) ).
cnf(refute_0_139,plain,
( implies(falsehood,not(not(X_51))) != or(X_51,truth)
| or(X_51,truth) != implies(falsehood,X_51)
| implies(falsehood,not(not(X_51))) = implies(falsehood,X_51) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(falsehood,not(not(X_51))),implies(falsehood,X_51)) ),[0],$fot(or(X_51,truth))]]) ).
cnf(refute_0_140,plain,
( implies(falsehood,not(not(X_51))) != or(X_51,truth)
| implies(falsehood,not(not(X_51))) = implies(falsehood,X_51) ),
inference(resolve,[$cnf( $equal(or(X_51,truth),implies(falsehood,X_51)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
implies(falsehood,not(not(X_51))) = implies(falsehood,X_51),
inference(resolve,[$cnf( $equal(implies(falsehood,not(not(X_51))),or(X_51,truth)) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
implies(falsehood,not(not(X_61))) = implies(falsehood,X_61),
inference(subst,[],[refute_0_141:[bind(X_51,$fot(X_61))]]) ).
cnf(refute_0_143,plain,
( implies(falsehood,not(not(X_61))) != implies(falsehood,X_61)
| implies(implies(not(not(X_61)),falsehood),falsehood) != implies(implies(falsehood,not(not(X_61))),not(not(X_61)))
| implies(implies(not(not(X_61)),falsehood),falsehood) = implies(implies(falsehood,X_61),not(not(X_61))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(X_61)),falsehood),falsehood),implies(implies(falsehood,not(not(X_61))),not(not(X_61)))) ),[1,0],$fot(implies(falsehood,X_61))]]) ).
cnf(refute_0_144,plain,
( implies(implies(not(not(X_61)),falsehood),falsehood) != implies(implies(falsehood,not(not(X_61))),not(not(X_61)))
| implies(implies(not(not(X_61)),falsehood),falsehood) = implies(implies(falsehood,X_61),not(not(X_61))) ),
inference(resolve,[$cnf( $equal(implies(falsehood,not(not(X_61))),implies(falsehood,X_61)) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
implies(implies(not(not(X_61)),falsehood),falsehood) = implies(implies(falsehood,X_61),not(not(X_61))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(X_61)),falsehood),falsehood),implies(implies(falsehood,not(not(X_61))),not(not(X_61)))) )],[refute_0_21,refute_0_144]) ).
cnf(refute_0_146,plain,
or(X,falsehood) = or(falsehood,X),
inference(subst,[],[or_commutativity:[bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_147,plain,
or(falsehood,X) = X,
inference(subst,[],[refute_0_112:[bind(Y,$fot(X))]]) ).
cnf(refute_0_148,plain,
( or(X,falsehood) != or(falsehood,X)
| or(falsehood,X) != X
| or(X,falsehood) = X ),
introduced(tautology,[equality,[$cnf( ~ $equal(or(X,falsehood),X) ),[0],$fot(or(falsehood,X))]]) ).
cnf(refute_0_149,plain,
( or(X,falsehood) != or(falsehood,X)
| or(X,falsehood) = X ),
inference(resolve,[$cnf( $equal(or(falsehood,X),X) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
or(X,falsehood) = X,
inference(resolve,[$cnf( $equal(or(X,falsehood),or(falsehood,X)) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
or(X_61,falsehood) = X_61,
inference(subst,[],[refute_0_150:[bind(X,$fot(X_61))]]) ).
cnf(refute_0_152,plain,
implies(not(X_61),falsehood) = or(X_61,falsehood),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_61)),bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_153,plain,
( implies(not(X_61),falsehood) != or(X_61,falsehood)
| or(X_61,falsehood) != X_61
| implies(not(X_61),falsehood) = X_61 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(not(X_61),falsehood))),bind(Y0,$fot(or(X_61,falsehood))),bind(Z0,$fot(X_61))]]) ).
cnf(refute_0_154,plain,
( or(X_61,falsehood) != X_61
| implies(not(X_61),falsehood) = X_61 ),
inference(resolve,[$cnf( $equal(implies(not(X_61),falsehood),or(X_61,falsehood)) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
implies(not(X_61),falsehood) = X_61,
inference(resolve,[$cnf( $equal(or(X_61,falsehood),X_61) )],[refute_0_151,refute_0_154]) ).
cnf(refute_0_156,plain,
or(not(X_61),falsehood) = not(X_61),
inference(subst,[],[refute_0_150:[bind(X,$fot(not(X_61)))]]) ).
cnf(refute_0_157,plain,
implies(not(not(X_61)),falsehood) = or(not(X_61),falsehood),
inference(subst,[],[refute_0_25:[bind(X,$fot(not(X_61))),bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_158,plain,
( implies(not(not(X_61)),falsehood) != or(not(X_61),falsehood)
| or(not(X_61),falsehood) != not(X_61)
| implies(not(not(X_61)),falsehood) = not(X_61) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(not(not(X_61)),falsehood))),bind(Y0,$fot(or(not(X_61),falsehood))),bind(Z0,$fot(not(X_61)))]]) ).
cnf(refute_0_159,plain,
( or(not(X_61),falsehood) != not(X_61)
| implies(not(not(X_61)),falsehood) = not(X_61) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_61)),falsehood),or(not(X_61),falsehood)) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
implies(not(not(X_61)),falsehood) = not(X_61),
inference(resolve,[$cnf( $equal(or(not(X_61),falsehood),not(X_61)) )],[refute_0_156,refute_0_159]) ).
cnf(refute_0_161,plain,
implies(implies(not(not(X_61)),falsehood),falsehood) = implies(implies(not(not(X_61)),falsehood),falsehood),
introduced(tautology,[refl,[$fot(implies(implies(not(not(X_61)),falsehood),falsehood))]]) ).
cnf(refute_0_162,plain,
( implies(implies(not(not(X_61)),falsehood),falsehood) != implies(implies(not(not(X_61)),falsehood),falsehood)
| implies(not(not(X_61)),falsehood) != not(X_61)
| implies(implies(not(not(X_61)),falsehood),falsehood) = implies(not(X_61),falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(X_61)),falsehood),falsehood),implies(implies(not(not(X_61)),falsehood),falsehood)) ),[1,0],$fot(not(X_61))]]) ).
cnf(refute_0_163,plain,
( implies(not(not(X_61)),falsehood) != not(X_61)
| implies(implies(not(not(X_61)),falsehood),falsehood) = implies(not(X_61),falsehood) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(X_61)),falsehood),falsehood),implies(implies(not(not(X_61)),falsehood),falsehood)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
implies(implies(not(not(X_61)),falsehood),falsehood) = implies(not(X_61),falsehood),
inference(resolve,[$cnf( $equal(implies(not(not(X_61)),falsehood),not(X_61)) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
( implies(implies(not(not(X_61)),falsehood),falsehood) != implies(not(X_61),falsehood)
| implies(not(X_61),falsehood) != X_61
| implies(implies(not(not(X_61)),falsehood),falsehood) = X_61 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(implies(not(not(X_61)),falsehood),falsehood))),bind(Y0,$fot(implies(not(X_61),falsehood))),bind(Z0,$fot(X_61))]]) ).
cnf(refute_0_166,plain,
( implies(not(X_61),falsehood) != X_61
| implies(implies(not(not(X_61)),falsehood),falsehood) = X_61 ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(X_61)),falsehood),falsehood),implies(not(X_61),falsehood)) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
implies(implies(not(not(X_61)),falsehood),falsehood) = X_61,
inference(resolve,[$cnf( $equal(implies(not(X_61),falsehood),X_61) )],[refute_0_155,refute_0_166]) ).
cnf(refute_0_168,plain,
( implies(implies(not(not(X_61)),falsehood),falsehood) != X_61
| implies(implies(not(not(X_61)),falsehood),falsehood) != implies(implies(falsehood,X_61),not(not(X_61)))
| X_61 = implies(implies(falsehood,X_61),not(not(X_61))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(X_61)),falsehood),falsehood),implies(implies(falsehood,X_61),not(not(X_61)))) ),[0],$fot(X_61)]]) ).
cnf(refute_0_169,plain,
( implies(implies(not(not(X_61)),falsehood),falsehood) != implies(implies(falsehood,X_61),not(not(X_61)))
| X_61 = implies(implies(falsehood,X_61),not(not(X_61))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(X_61)),falsehood),falsehood),X_61) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
X_61 = implies(implies(falsehood,X_61),not(not(X_61))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(X_61)),falsehood),falsehood),implies(implies(falsehood,X_61),not(not(X_61)))) )],[refute_0_145,refute_0_169]) ).
cnf(refute_0_171,plain,
implies(truth,not(not(X_61))) = not(not(X_61)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(X_61))))]]) ).
cnf(refute_0_172,plain,
implies(implies(truth,X_31),implies(implies(X_31,X_32),implies(truth,X_32))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(X_31)),bind(Z,$fot(X_32))]]) ).
cnf(refute_0_173,plain,
implies(truth,X_32) = X_32,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_32))]]) ).
cnf(refute_0_174,plain,
( implies(implies(truth,X_31),implies(implies(X_31,X_32),implies(truth,X_32))) != truth
| implies(truth,X_32) != X_32
| implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_31),implies(implies(X_31,X_32),implies(truth,X_32))),truth) ),[0,1,1],$fot(X_32)]]) ).
cnf(refute_0_175,plain,
( implies(implies(truth,X_31),implies(implies(X_31,X_32),implies(truth,X_32))) != truth
| implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_32),X_32) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_31),implies(implies(X_31,X_32),implies(truth,X_32))),truth) )],[refute_0_172,refute_0_175]) ).
cnf(refute_0_177,plain,
implies(truth,X_31) = X_31,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_31))]]) ).
cnf(refute_0_178,plain,
implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)) = implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)))]]) ).
cnf(refute_0_179,plain,
( implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)) != implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32))
| implies(truth,X_31) != X_31
| implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)) = implies(X_31,implies(implies(X_31,X_32),X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)),implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32))) ),[1,0],$fot(X_31)]]) ).
cnf(refute_0_180,plain,
( implies(truth,X_31) != X_31
| implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)) = implies(X_31,implies(implies(X_31,X_32),X_32)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)),implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)) = implies(X_31,implies(implies(X_31,X_32),X_32)),
inference(resolve,[$cnf( $equal(implies(truth,X_31),X_31) )],[refute_0_177,refute_0_180]) ).
cnf(refute_0_182,plain,
( implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)) != implies(X_31,implies(implies(X_31,X_32),X_32))
| implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)) != truth
| implies(X_31,implies(implies(X_31,X_32),X_32)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)),truth) ),[0],$fot(implies(X_31,implies(implies(X_31,X_32),X_32)))]]) ).
cnf(refute_0_183,plain,
( implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)) != truth
| implies(X_31,implies(implies(X_31,X_32),X_32)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)),implies(X_31,implies(implies(X_31,X_32),X_32))) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
implies(X_31,implies(implies(X_31,X_32),X_32)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_31),implies(implies(X_31,X_32),X_32)),truth) )],[refute_0_176,refute_0_183]) ).
cnf(refute_0_185,plain,
implies(falsehood,implies(implies(falsehood,not(not(X_61))),not(not(X_61)))) = truth,
inference(subst,[],[refute_0_184:[bind(X_31,$fot(falsehood)),bind(X_32,$fot(not(not(X_61))))]]) ).
cnf(refute_0_186,plain,
( implies(falsehood,implies(implies(falsehood,not(not(X_61))),not(not(X_61)))) != truth
| implies(falsehood,not(not(X_61))) != implies(falsehood,X_61)
| implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(falsehood,implies(implies(falsehood,not(not(X_61))),not(not(X_61)))),truth) ),[0,1,0],$fot(implies(falsehood,X_61))]]) ).
cnf(refute_0_187,plain,
( implies(falsehood,implies(implies(falsehood,not(not(X_61))),not(not(X_61)))) != truth
| implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))) = truth ),
inference(resolve,[$cnf( $equal(implies(falsehood,not(not(X_61))),implies(falsehood,X_61)) )],[refute_0_142,refute_0_186]) ).
cnf(refute_0_188,plain,
implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))) = truth,
inference(resolve,[$cnf( $equal(implies(falsehood,implies(implies(falsehood,not(not(X_61))),not(not(X_61)))),truth) )],[refute_0_185,refute_0_187]) ).
cnf(refute_0_189,plain,
( X_61 != implies(implies(falsehood,X_61),not(not(X_61)))
| implies(implies(falsehood,X_61),not(not(X_61))) = X_61 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_61)),bind(Y0,$fot(implies(implies(falsehood,X_61),not(not(X_61)))))]]) ).
cnf(refute_0_190,plain,
implies(implies(falsehood,X_61),not(not(X_61))) = X_61,
inference(resolve,[$cnf( $equal(X_61,implies(implies(falsehood,X_61),not(not(X_61)))) )],[refute_0_170,refute_0_189]) ).
cnf(refute_0_191,plain,
implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))) = implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))),
introduced(tautology,[refl,[$fot(implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))))]]) ).
cnf(refute_0_192,plain,
( implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))) != implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61))))
| implies(implies(falsehood,X_61),not(not(X_61))) != X_61
| implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))) = implies(falsehood,X_61) ),
introduced(tautology,[equality,[$cnf( $equal(implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))),implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61))))) ),[1,1],$fot(X_61)]]) ).
cnf(refute_0_193,plain,
( implies(implies(falsehood,X_61),not(not(X_61))) != X_61
| implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))) = implies(falsehood,X_61) ),
inference(resolve,[$cnf( $equal(implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))),implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61))))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))) = implies(falsehood,X_61),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,X_61),not(not(X_61))),X_61) )],[refute_0_190,refute_0_193]) ).
cnf(refute_0_195,plain,
( implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))) != implies(falsehood,X_61)
| implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))) != truth
| implies(falsehood,X_61) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))),truth) ),[0],$fot(implies(falsehood,X_61))]]) ).
cnf(refute_0_196,plain,
( implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))) != truth
| implies(falsehood,X_61) = truth ),
inference(resolve,[$cnf( $equal(implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))),implies(falsehood,X_61)) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
implies(falsehood,X_61) = truth,
inference(resolve,[$cnf( $equal(implies(falsehood,implies(implies(falsehood,X_61),not(not(X_61)))),truth) )],[refute_0_188,refute_0_196]) ).
cnf(refute_0_198,plain,
implies(implies(falsehood,X_61),not(not(X_61))) = implies(implies(falsehood,X_61),not(not(X_61))),
introduced(tautology,[refl,[$fot(implies(implies(falsehood,X_61),not(not(X_61))))]]) ).
cnf(refute_0_199,plain,
( implies(falsehood,X_61) != truth
| implies(implies(falsehood,X_61),not(not(X_61))) != implies(implies(falsehood,X_61),not(not(X_61)))
| implies(implies(falsehood,X_61),not(not(X_61))) = implies(truth,not(not(X_61))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,X_61),not(not(X_61))),implies(implies(falsehood,X_61),not(not(X_61)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_200,plain,
( implies(falsehood,X_61) != truth
| implies(implies(falsehood,X_61),not(not(X_61))) = implies(truth,not(not(X_61))) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,X_61),not(not(X_61))),implies(implies(falsehood,X_61),not(not(X_61)))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
implies(implies(falsehood,X_61),not(not(X_61))) = implies(truth,not(not(X_61))),
inference(resolve,[$cnf( $equal(implies(falsehood,X_61),truth) )],[refute_0_197,refute_0_200]) ).
cnf(refute_0_202,plain,
( implies(implies(falsehood,X_61),not(not(X_61))) != implies(truth,not(not(X_61)))
| implies(truth,not(not(X_61))) != not(not(X_61))
| implies(implies(falsehood,X_61),not(not(X_61))) = not(not(X_61)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(implies(falsehood,X_61),not(not(X_61))))),bind(Y0,$fot(implies(truth,not(not(X_61))))),bind(Z0,$fot(not(not(X_61))))]]) ).
cnf(refute_0_203,plain,
( implies(truth,not(not(X_61))) != not(not(X_61))
| implies(implies(falsehood,X_61),not(not(X_61))) = not(not(X_61)) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,X_61),not(not(X_61))),implies(truth,not(not(X_61)))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
implies(implies(falsehood,X_61),not(not(X_61))) = not(not(X_61)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(X_61))),not(not(X_61))) )],[refute_0_171,refute_0_203]) ).
cnf(refute_0_205,plain,
( X_61 != implies(implies(falsehood,X_61),not(not(X_61)))
| implies(implies(falsehood,X_61),not(not(X_61))) != not(not(X_61))
| X_61 = not(not(X_61)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_61,not(not(X_61))) ),[0],$fot(implies(implies(falsehood,X_61),not(not(X_61))))]]) ).
cnf(refute_0_206,plain,
( X_61 != implies(implies(falsehood,X_61),not(not(X_61)))
| X_61 = not(not(X_61)) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,X_61),not(not(X_61))),not(not(X_61))) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
X_61 = not(not(X_61)),
inference(resolve,[$cnf( $equal(X_61,implies(implies(falsehood,X_61),not(not(X_61)))) )],[refute_0_170,refute_0_206]) ).
cnf(refute_0_208,plain,
X_81 = not(not(X_81)),
inference(subst,[],[refute_0_207:[bind(X_61,$fot(X_81))]]) ).
cnf(refute_0_209,plain,
( X_81 != not(not(X_81))
| not(not(X_81)) = X_81 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_81)),bind(Y0,$fot(not(not(X_81))))]]) ).
cnf(refute_0_210,plain,
not(not(X_81)) = X_81,
inference(resolve,[$cnf( $equal(X_81,not(not(X_81))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
( not(not(X_81)) != X_81
| or(not(X_81),Y) != implies(not(not(X_81)),Y)
| or(not(X_81),Y) = implies(X_81,Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X_81),Y),implies(not(not(X_81)),Y)) ),[1,0],$fot(X_81)]]) ).
cnf(refute_0_212,plain,
( or(not(X_81),Y) != implies(not(not(X_81)),Y)
| or(not(X_81),Y) = implies(X_81,Y) ),
inference(resolve,[$cnf( $equal(not(not(X_81)),X_81) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
or(not(X_81),Y) = implies(X_81,Y),
inference(resolve,[$cnf( $equal(or(not(X_81),Y),implies(not(not(X_81)),Y)) )],[refute_0_20,refute_0_212]) ).
cnf(refute_0_214,plain,
or(not(implies(X,Y)),and(not(X),Y)) = implies(implies(X,Y),and(not(X),Y)),
inference(subst,[],[refute_0_213:[bind(Y,$fot(and(not(X),Y))),bind(X_81,$fot(implies(X,Y)))]]) ).
cnf(refute_0_215,plain,
and(X,not(X_81)) = not(or(not(X),not(not(X_81)))),
inference(subst,[],[and_definition:[bind(Y,$fot(not(X_81)))]]) ).
cnf(refute_0_216,plain,
( and(X,not(X_81)) != not(or(not(X),not(not(X_81))))
| not(not(X_81)) != X_81
| and(X,not(X_81)) = not(or(not(X),X_81)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,not(X_81)),not(or(not(X),not(not(X_81))))) ),[1,0,1],$fot(X_81)]]) ).
cnf(refute_0_217,plain,
( and(X,not(X_81)) != not(or(not(X),not(not(X_81))))
| and(X,not(X_81)) = not(or(not(X),X_81)) ),
inference(resolve,[$cnf( $equal(not(not(X_81)),X_81) )],[refute_0_210,refute_0_216]) ).
cnf(refute_0_218,plain,
and(X,not(X_81)) = not(or(not(X),X_81)),
inference(resolve,[$cnf( $equal(and(X,not(X_81)),not(or(not(X),not(not(X_81))))) )],[refute_0_215,refute_0_217]) ).
cnf(refute_0_219,plain,
or(not(X),X_81) = implies(X,X_81),
inference(subst,[],[refute_0_213:[bind(Y,$fot(X_81)),bind(X_81,$fot(X))]]) ).
cnf(refute_0_220,plain,
not(or(not(X),X_81)) = not(or(not(X),X_81)),
introduced(tautology,[refl,[$fot(not(or(not(X),X_81)))]]) ).
cnf(refute_0_221,plain,
( not(or(not(X),X_81)) != not(or(not(X),X_81))
| or(not(X),X_81) != implies(X,X_81)
| not(or(not(X),X_81)) = not(implies(X,X_81)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),X_81)),not(or(not(X),X_81))) ),[1,0],$fot(implies(X,X_81))]]) ).
cnf(refute_0_222,plain,
( or(not(X),X_81) != implies(X,X_81)
| not(or(not(X),X_81)) = not(implies(X,X_81)) ),
inference(resolve,[$cnf( $equal(not(or(not(X),X_81)),not(or(not(X),X_81))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
not(or(not(X),X_81)) = not(implies(X,X_81)),
inference(resolve,[$cnf( $equal(or(not(X),X_81),implies(X,X_81)) )],[refute_0_219,refute_0_222]) ).
cnf(refute_0_224,plain,
( and(X,not(X_81)) != not(or(not(X),X_81))
| not(or(not(X),X_81)) != not(implies(X,X_81))
| and(X,not(X_81)) = not(implies(X,X_81)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,not(X_81)),not(implies(X,X_81))) ),[0],$fot(not(or(not(X),X_81)))]]) ).
cnf(refute_0_225,plain,
( and(X,not(X_81)) != not(or(not(X),X_81))
| and(X,not(X_81)) = not(implies(X,X_81)) ),
inference(resolve,[$cnf( $equal(not(or(not(X),X_81)),not(implies(X,X_81))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
and(X,not(X_81)) = not(implies(X,X_81)),
inference(resolve,[$cnf( $equal(and(X,not(X_81)),not(or(not(X),X_81))) )],[refute_0_218,refute_0_225]) ).
cnf(refute_0_227,plain,
and(X,not(Y)) = not(implies(X,Y)),
inference(subst,[],[refute_0_226:[bind(X_81,$fot(Y))]]) ).
cnf(refute_0_228,plain,
or(and(X,not(Y)),and(not(X),Y)) = or(and(X,not(Y)),and(not(X),Y)),
introduced(tautology,[refl,[$fot(or(and(X,not(Y)),and(not(X),Y)))]]) ).
cnf(refute_0_229,plain,
( and(X,not(Y)) != not(implies(X,Y))
| or(and(X,not(Y)),and(not(X),Y)) != or(and(X,not(Y)),and(not(X),Y))
| or(and(X,not(Y)),and(not(X),Y)) = or(not(implies(X,Y)),and(not(X),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X,not(Y)),and(not(X),Y)),or(and(X,not(Y)),and(not(X),Y))) ),[1,0],$fot(not(implies(X,Y)))]]) ).
cnf(refute_0_230,plain,
( and(X,not(Y)) != not(implies(X,Y))
| or(and(X,not(Y)),and(not(X),Y)) = or(not(implies(X,Y)),and(not(X),Y)) ),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),and(not(X),Y)),or(and(X,not(Y)),and(not(X),Y))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
or(and(X,not(Y)),and(not(X),Y)) = or(not(implies(X,Y)),and(not(X),Y)),
inference(resolve,[$cnf( $equal(and(X,not(Y)),not(implies(X,Y))) )],[refute_0_227,refute_0_230]) ).
cnf(refute_0_232,plain,
( or(and(X,not(Y)),and(not(X),Y)) != or(not(implies(X,Y)),and(not(X),Y))
| or(not(implies(X,Y)),and(not(X),Y)) != implies(implies(X,Y),and(not(X),Y))
| or(and(X,not(Y)),and(not(X),Y)) = implies(implies(X,Y),and(not(X),Y)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(and(X,not(Y)),and(not(X),Y)))),bind(Y0,$fot(or(not(implies(X,Y)),and(not(X),Y)))),bind(Z0,$fot(implies(implies(X,Y),and(not(X),Y))))]]) ).
cnf(refute_0_233,plain,
( or(not(implies(X,Y)),and(not(X),Y)) != implies(implies(X,Y),and(not(X),Y))
| or(and(X,not(Y)),and(not(X),Y)) = implies(implies(X,Y),and(not(X),Y)) ),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),and(not(X),Y)),or(not(implies(X,Y)),and(not(X),Y))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
or(and(X,not(Y)),and(not(X),Y)) = implies(implies(X,Y),and(not(X),Y)),
inference(resolve,[$cnf( $equal(or(not(implies(X,Y)),and(not(X),Y)),implies(implies(X,Y),and(not(X),Y))) )],[refute_0_214,refute_0_233]) ).
cnf(refute_0_235,plain,
( or(and(X,not(Y)),and(not(X),Y)) != implies(implies(X,Y),and(not(X),Y))
| xor(X,Y) != or(and(X,not(Y)),and(not(X),Y))
| xor(X,Y) = implies(implies(X,Y),and(not(X),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X,Y),or(and(X,not(Y)),and(not(X),Y))) ),[1],$fot(implies(implies(X,Y),and(not(X),Y)))]]) ).
cnf(refute_0_236,plain,
( xor(X,Y) != or(and(X,not(Y)),and(not(X),Y))
| xor(X,Y) = implies(implies(X,Y),and(not(X),Y)) ),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),and(not(X),Y)),implies(implies(X,Y),and(not(X),Y))) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
xor(X,Y) = implies(implies(X,Y),and(not(X),Y)),
inference(resolve,[$cnf( $equal(xor(X,Y),or(and(X,not(Y)),and(not(X),Y))) )],[xor_definition,refute_0_236]) ).
cnf(refute_0_238,plain,
xor(truth,X_85) = implies(implies(truth,X_85),and(not(truth),X_85)),
inference(subst,[],[refute_0_237:[bind(X,$fot(truth)),bind(Y,$fot(X_85))]]) ).
cnf(refute_0_239,plain,
( not(truth) != falsehood
| xor(truth,X_85) != implies(implies(truth,X_85),and(not(truth),X_85))
| xor(truth,X_85) = implies(implies(truth,X_85),and(falsehood,X_85)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_85),implies(implies(truth,X_85),and(not(truth),X_85))) ),[1,1,0],$fot(falsehood)]]) ).
cnf(refute_0_240,plain,
( xor(truth,X_85) != implies(implies(truth,X_85),and(not(truth),X_85))
| xor(truth,X_85) = implies(implies(truth,X_85),and(falsehood,X_85)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_239]) ).
cnf(refute_0_241,plain,
xor(truth,X_85) = implies(implies(truth,X_85),and(falsehood,X_85)),
inference(resolve,[$cnf( $equal(xor(truth,X_85),implies(implies(truth,X_85),and(not(truth),X_85))) )],[refute_0_238,refute_0_240]) ).
cnf(refute_0_242,plain,
and(falsehood,Y) = not(or(not(falsehood),not(Y))),
inference(subst,[],[and_definition:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_243,plain,
( and(falsehood,Y) != not(or(not(falsehood),not(Y)))
| not(falsehood) != truth
| and(falsehood,Y) = not(or(truth,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(falsehood,Y),not(or(not(falsehood),not(Y)))) ),[1,0,0],$fot(truth)]]) ).
cnf(refute_0_244,plain,
( and(falsehood,Y) != not(or(not(falsehood),not(Y)))
| and(falsehood,Y) = not(or(truth,not(Y))) ),
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_105,refute_0_243]) ).
cnf(refute_0_245,plain,
and(falsehood,Y) = not(or(truth,not(Y))),
inference(resolve,[$cnf( $equal(and(falsehood,Y),not(or(not(falsehood),not(Y)))) )],[refute_0_242,refute_0_244]) ).
cnf(refute_0_246,plain,
or(truth,not(Y)) = implies(falsehood,not(Y)),
inference(subst,[],[refute_0_63:[bind(X_8,$fot(not(Y)))]]) ).
cnf(refute_0_247,plain,
not(or(truth,not(Y))) = not(or(truth,not(Y))),
introduced(tautology,[refl,[$fot(not(or(truth,not(Y))))]]) ).
cnf(refute_0_248,plain,
( not(or(truth,not(Y))) != not(or(truth,not(Y)))
| or(truth,not(Y)) != implies(falsehood,not(Y))
| not(or(truth,not(Y))) = not(implies(falsehood,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(truth,not(Y))),not(or(truth,not(Y)))) ),[1,0],$fot(implies(falsehood,not(Y)))]]) ).
cnf(refute_0_249,plain,
( or(truth,not(Y)) != implies(falsehood,not(Y))
| not(or(truth,not(Y))) = not(implies(falsehood,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(truth,not(Y))),not(or(truth,not(Y)))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
not(or(truth,not(Y))) = not(implies(falsehood,not(Y))),
inference(resolve,[$cnf( $equal(or(truth,not(Y)),implies(falsehood,not(Y))) )],[refute_0_246,refute_0_249]) ).
cnf(refute_0_251,plain,
( and(falsehood,Y) != not(or(truth,not(Y)))
| not(or(truth,not(Y))) != not(implies(falsehood,not(Y)))
| and(falsehood,Y) = not(implies(falsehood,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(falsehood,Y),not(implies(falsehood,not(Y)))) ),[0],$fot(not(or(truth,not(Y))))]]) ).
cnf(refute_0_252,plain,
( and(falsehood,Y) != not(or(truth,not(Y)))
| and(falsehood,Y) = not(implies(falsehood,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(truth,not(Y))),not(implies(falsehood,not(Y)))) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
and(falsehood,Y) = not(implies(falsehood,not(Y))),
inference(resolve,[$cnf( $equal(and(falsehood,Y),not(or(truth,not(Y)))) )],[refute_0_245,refute_0_252]) ).
cnf(refute_0_254,plain,
implies(falsehood,not(Y)) = truth,
inference(subst,[],[refute_0_197:[bind(X_61,$fot(not(Y)))]]) ).
cnf(refute_0_255,plain,
not(implies(falsehood,not(Y))) = not(implies(falsehood,not(Y))),
introduced(tautology,[refl,[$fot(not(implies(falsehood,not(Y))))]]) ).
cnf(refute_0_256,plain,
( implies(falsehood,not(Y)) != truth
| not(implies(falsehood,not(Y))) != not(implies(falsehood,not(Y)))
| not(implies(falsehood,not(Y))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(falsehood,not(Y))),not(implies(falsehood,not(Y)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_257,plain,
( implies(falsehood,not(Y)) != truth
| not(implies(falsehood,not(Y))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(implies(falsehood,not(Y))),not(implies(falsehood,not(Y)))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
not(implies(falsehood,not(Y))) = not(truth),
inference(resolve,[$cnf( $equal(implies(falsehood,not(Y)),truth) )],[refute_0_254,refute_0_257]) ).
cnf(refute_0_259,plain,
( not(implies(falsehood,not(Y))) != not(truth)
| not(truth) != falsehood
| not(implies(falsehood,not(Y))) = falsehood ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(implies(falsehood,not(Y))))),bind(Y0,$fot(not(truth))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_260,plain,
( not(truth) != falsehood
| not(implies(falsehood,not(Y))) = falsehood ),
inference(resolve,[$cnf( $equal(not(implies(falsehood,not(Y))),not(truth)) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
not(implies(falsehood,not(Y))) = falsehood,
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_260]) ).
cnf(refute_0_262,plain,
( and(falsehood,Y) != not(implies(falsehood,not(Y)))
| not(implies(falsehood,not(Y))) != falsehood
| and(falsehood,Y) = falsehood ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(falsehood,Y),falsehood) ),[0],$fot(not(implies(falsehood,not(Y))))]]) ).
cnf(refute_0_263,plain,
( and(falsehood,Y) != not(implies(falsehood,not(Y)))
| and(falsehood,Y) = falsehood ),
inference(resolve,[$cnf( $equal(not(implies(falsehood,not(Y))),falsehood) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
and(falsehood,Y) = falsehood,
inference(resolve,[$cnf( $equal(and(falsehood,Y),not(implies(falsehood,not(Y)))) )],[refute_0_253,refute_0_263]) ).
cnf(refute_0_265,plain,
and(falsehood,X_85) = falsehood,
inference(subst,[],[refute_0_264:[bind(Y,$fot(X_85))]]) ).
cnf(refute_0_266,plain,
implies(X_85,and(falsehood,X_85)) = implies(X_85,and(falsehood,X_85)),
introduced(tautology,[refl,[$fot(implies(X_85,and(falsehood,X_85)))]]) ).
cnf(refute_0_267,plain,
( and(falsehood,X_85) != falsehood
| implies(X_85,and(falsehood,X_85)) != implies(X_85,and(falsehood,X_85))
| implies(X_85,and(falsehood,X_85)) = implies(X_85,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_85,and(falsehood,X_85)),implies(X_85,and(falsehood,X_85))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_268,plain,
( and(falsehood,X_85) != falsehood
| implies(X_85,and(falsehood,X_85)) = implies(X_85,falsehood) ),
inference(resolve,[$cnf( $equal(implies(X_85,and(falsehood,X_85)),implies(X_85,and(falsehood,X_85))) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
implies(X_85,and(falsehood,X_85)) = implies(X_85,falsehood),
inference(resolve,[$cnf( $equal(and(falsehood,X_85),falsehood) )],[refute_0_265,refute_0_268]) ).
cnf(refute_0_270,plain,
implies(truth,X_85) = X_85,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_85))]]) ).
cnf(refute_0_271,plain,
implies(implies(truth,X_85),and(falsehood,X_85)) = implies(implies(truth,X_85),and(falsehood,X_85)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_85),and(falsehood,X_85)))]]) ).
cnf(refute_0_272,plain,
( implies(implies(truth,X_85),and(falsehood,X_85)) != implies(implies(truth,X_85),and(falsehood,X_85))
| implies(truth,X_85) != X_85
| implies(implies(truth,X_85),and(falsehood,X_85)) = implies(X_85,and(falsehood,X_85)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_85),and(falsehood,X_85)),implies(implies(truth,X_85),and(falsehood,X_85))) ),[1,0],$fot(X_85)]]) ).
cnf(refute_0_273,plain,
( implies(truth,X_85) != X_85
| implies(implies(truth,X_85),and(falsehood,X_85)) = implies(X_85,and(falsehood,X_85)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_85),and(falsehood,X_85)),implies(implies(truth,X_85),and(falsehood,X_85))) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
implies(implies(truth,X_85),and(falsehood,X_85)) = implies(X_85,and(falsehood,X_85)),
inference(resolve,[$cnf( $equal(implies(truth,X_85),X_85) )],[refute_0_270,refute_0_273]) ).
cnf(refute_0_275,plain,
( implies(X_85,and(falsehood,X_85)) != implies(X_85,falsehood)
| implies(implies(truth,X_85),and(falsehood,X_85)) != implies(X_85,and(falsehood,X_85))
| implies(implies(truth,X_85),and(falsehood,X_85)) = implies(X_85,falsehood) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(implies(truth,X_85),and(falsehood,X_85)))),bind(Y0,$fot(implies(X_85,and(falsehood,X_85)))),bind(Z0,$fot(implies(X_85,falsehood)))]]) ).
cnf(refute_0_276,plain,
( implies(X_85,and(falsehood,X_85)) != implies(X_85,falsehood)
| implies(implies(truth,X_85),and(falsehood,X_85)) = implies(X_85,falsehood) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_85),and(falsehood,X_85)),implies(X_85,and(falsehood,X_85))) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
implies(implies(truth,X_85),and(falsehood,X_85)) = implies(X_85,falsehood),
inference(resolve,[$cnf( $equal(implies(X_85,and(falsehood,X_85)),implies(X_85,falsehood)) )],[refute_0_269,refute_0_276]) ).
cnf(refute_0_278,plain,
( implies(implies(truth,X_85),and(falsehood,X_85)) != implies(X_85,falsehood)
| xor(truth,X_85) != implies(implies(truth,X_85),and(falsehood,X_85))
| xor(truth,X_85) = implies(X_85,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_85),implies(implies(truth,X_85),and(falsehood,X_85))) ),[1],$fot(implies(X_85,falsehood))]]) ).
cnf(refute_0_279,plain,
( xor(truth,X_85) != implies(implies(truth,X_85),and(falsehood,X_85))
| xor(truth,X_85) = implies(X_85,falsehood) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_85),and(falsehood,X_85)),implies(X_85,falsehood)) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
xor(truth,X_85) = implies(X_85,falsehood),
inference(resolve,[$cnf( $equal(xor(truth,X_85),implies(implies(truth,X_85),and(falsehood,X_85))) )],[refute_0_241,refute_0_279]) ).
cnf(refute_0_281,plain,
xor(truth,x) = implies(x,falsehood),
inference(subst,[],[refute_0_280:[bind(X_85,$fot(x))]]) ).
cnf(refute_0_282,plain,
and(x,xor(truth,x)) = and(x,xor(truth,x)),
introduced(tautology,[refl,[$fot(and(x,xor(truth,x)))]]) ).
cnf(refute_0_283,plain,
( and(x,xor(truth,x)) != and(x,xor(truth,x))
| xor(truth,x) != implies(x,falsehood)
| and(x,xor(truth,x)) = and(x,implies(x,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(x,xor(truth,x)),and(x,xor(truth,x))) ),[1,1],$fot(implies(x,falsehood))]]) ).
cnf(refute_0_284,plain,
( xor(truth,x) != implies(x,falsehood)
| and(x,xor(truth,x)) = and(x,implies(x,falsehood)) ),
inference(resolve,[$cnf( $equal(and(x,xor(truth,x)),and(x,xor(truth,x))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
and(x,xor(truth,x)) = and(x,implies(x,falsehood)),
inference(resolve,[$cnf( $equal(xor(truth,x),implies(x,falsehood)) )],[refute_0_281,refute_0_284]) ).
cnf(refute_0_286,plain,
( and(x,implies(x,falsehood)) != falsehood
| and(x,xor(truth,x)) != and(x,implies(x,falsehood))
| and(x,xor(truth,x)) = falsehood ),
introduced(tautology,[equality,[$cnf( $equal(and(x,xor(truth,x)),and(x,implies(x,falsehood))) ),[1],$fot(falsehood)]]) ).
cnf(refute_0_287,plain,
( and(x,implies(x,falsehood)) != falsehood
| and(x,xor(truth,x)) = falsehood ),
inference(resolve,[$cnf( $equal(and(x,xor(truth,x)),and(x,implies(x,falsehood))) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
and(x,implies(x,falsehood)) != falsehood,
inference(resolve,[$cnf( $equal(and(x,xor(truth,x)),falsehood) )],[refute_0_287,refute_0_19]) ).
cnf(refute_0_289,plain,
implies(x,x) = truth,
inference(subst,[],[refute_0_120:[bind(X_15,$fot(x))]]) ).
cnf(refute_0_290,plain,
not(implies(x,x)) = not(implies(x,x)),
introduced(tautology,[refl,[$fot(not(implies(x,x)))]]) ).
cnf(refute_0_291,plain,
( implies(x,x) != truth
| not(implies(x,x)) != not(implies(x,x))
| not(implies(x,x)) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(x,x)),not(implies(x,x))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_292,plain,
( implies(x,x) != truth
| not(implies(x,x)) = not(truth) ),
inference(resolve,[$cnf( $equal(not(implies(x,x)),not(implies(x,x))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
not(implies(x,x)) = not(truth),
inference(resolve,[$cnf( $equal(implies(x,x),truth) )],[refute_0_289,refute_0_292]) ).
cnf(refute_0_294,plain,
( not(implies(x,x)) != not(truth)
| not(truth) != falsehood
| not(implies(x,x)) = falsehood ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(implies(x,x)))),bind(Y0,$fot(not(truth))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_295,plain,
( not(truth) != falsehood
| not(implies(x,x)) = falsehood ),
inference(resolve,[$cnf( $equal(not(implies(x,x)),not(truth)) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
not(implies(x,x)) = falsehood,
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_295]) ).
cnf(refute_0_297,plain,
and(x,not(x)) = not(implies(x,x)),
inference(subst,[],[refute_0_226:[bind(X,$fot(x)),bind(X_81,$fot(x))]]) ).
cnf(refute_0_298,plain,
( and(x,not(x)) != not(implies(x,x))
| not(implies(x,x)) != falsehood
| and(x,not(x)) = falsehood ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(x,not(x)))),bind(Y0,$fot(not(implies(x,x)))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_299,plain,
( not(implies(x,x)) != falsehood
| and(x,not(x)) = falsehood ),
inference(resolve,[$cnf( $equal(and(x,not(x)),not(implies(x,x))) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
and(x,not(x)) = falsehood,
inference(resolve,[$cnf( $equal(not(implies(x,x)),falsehood) )],[refute_0_296,refute_0_299]) ).
cnf(refute_0_301,plain,
xor(truth,Y) = xor(Y,truth),
inference(subst,[],[xor_commutativity:[bind(X,$fot(truth))]]) ).
cnf(refute_0_302,plain,
xor(X_84,truth) = implies(implies(X_84,truth),and(not(X_84),truth)),
inference(subst,[],[refute_0_237:[bind(X,$fot(X_84)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_303,plain,
and(X_17,truth) = not(or(not(X_17),not(truth))),
inference(subst,[],[and_definition:[bind(X,$fot(X_17)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_304,plain,
( and(X_17,truth) != not(or(not(X_17),not(truth)))
| not(truth) != falsehood
| and(X_17,truth) = not(or(not(X_17),falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_17,truth),not(or(not(X_17),not(truth)))) ),[1,0,1],$fot(falsehood)]]) ).
cnf(refute_0_305,plain,
( and(X_17,truth) != not(or(not(X_17),not(truth)))
| and(X_17,truth) = not(or(not(X_17),falsehood)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_304]) ).
cnf(refute_0_306,plain,
and(X_17,truth) = not(or(not(X_17),falsehood)),
inference(resolve,[$cnf( $equal(and(X_17,truth),not(or(not(X_17),not(truth)))) )],[refute_0_303,refute_0_305]) ).
cnf(refute_0_307,plain,
( or(X,Y) != or(Y,X)
| or(Y,X) = or(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(or(Y,X)))]]) ).
cnf(refute_0_308,plain,
or(Y,X) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),or(Y,X)) )],[or_commutativity,refute_0_307]) ).
cnf(refute_0_309,plain,
or(not(X_17),falsehood) = or(falsehood,not(X_17)),
inference(subst,[],[refute_0_308:[bind(X,$fot(falsehood)),bind(Y,$fot(not(X_17)))]]) ).
cnf(refute_0_310,plain,
not(or(not(X_17),falsehood)) = not(or(not(X_17),falsehood)),
introduced(tautology,[refl,[$fot(not(or(not(X_17),falsehood)))]]) ).
cnf(refute_0_311,plain,
( not(or(not(X_17),falsehood)) != not(or(not(X_17),falsehood))
| or(not(X_17),falsehood) != or(falsehood,not(X_17))
| not(or(not(X_17),falsehood)) = not(or(falsehood,not(X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X_17),falsehood)),not(or(not(X_17),falsehood))) ),[1,0],$fot(or(falsehood,not(X_17)))]]) ).
cnf(refute_0_312,plain,
( or(not(X_17),falsehood) != or(falsehood,not(X_17))
| not(or(not(X_17),falsehood)) = not(or(falsehood,not(X_17))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_17),falsehood)),not(or(not(X_17),falsehood))) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
not(or(not(X_17),falsehood)) = not(or(falsehood,not(X_17))),
inference(resolve,[$cnf( $equal(or(not(X_17),falsehood),or(falsehood,not(X_17))) )],[refute_0_309,refute_0_312]) ).
cnf(refute_0_314,plain,
( and(X_17,truth) != not(or(not(X_17),falsehood))
| not(or(not(X_17),falsehood)) != not(or(falsehood,not(X_17)))
| and(X_17,truth) = not(or(falsehood,not(X_17))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_17,truth),not(or(falsehood,not(X_17)))) ),[0],$fot(not(or(not(X_17),falsehood)))]]) ).
cnf(refute_0_315,plain,
( and(X_17,truth) != not(or(not(X_17),falsehood))
| and(X_17,truth) = not(or(falsehood,not(X_17))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_17),falsehood)),not(or(falsehood,not(X_17)))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
and(X_17,truth) = not(or(falsehood,not(X_17))),
inference(resolve,[$cnf( $equal(and(X_17,truth),not(or(not(X_17),falsehood))) )],[refute_0_306,refute_0_315]) ).
cnf(refute_0_317,plain,
or(falsehood,not(X_17)) = not(X_17),
inference(subst,[],[refute_0_112:[bind(Y,$fot(not(X_17)))]]) ).
cnf(refute_0_318,plain,
not(or(falsehood,not(X_17))) = not(or(falsehood,not(X_17))),
introduced(tautology,[refl,[$fot(not(or(falsehood,not(X_17))))]]) ).
cnf(refute_0_319,plain,
( not(or(falsehood,not(X_17))) != not(or(falsehood,not(X_17)))
| or(falsehood,not(X_17)) != not(X_17)
| not(or(falsehood,not(X_17))) = not(not(X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,not(X_17))),not(or(falsehood,not(X_17)))) ),[1,0],$fot(not(X_17))]]) ).
cnf(refute_0_320,plain,
( or(falsehood,not(X_17)) != not(X_17)
| not(or(falsehood,not(X_17))) = not(not(X_17)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_17))),not(or(falsehood,not(X_17)))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
not(or(falsehood,not(X_17))) = not(not(X_17)),
inference(resolve,[$cnf( $equal(or(falsehood,not(X_17)),not(X_17)) )],[refute_0_317,refute_0_320]) ).
cnf(refute_0_322,plain,
( and(X_17,truth) != not(or(falsehood,not(X_17)))
| not(or(falsehood,not(X_17))) != not(not(X_17))
| and(X_17,truth) = not(not(X_17)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_17,truth),not(not(X_17))) ),[0],$fot(not(or(falsehood,not(X_17))))]]) ).
cnf(refute_0_323,plain,
( and(X_17,truth) != not(or(falsehood,not(X_17)))
| and(X_17,truth) = not(not(X_17)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_17))),not(not(X_17))) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
and(X_17,truth) = not(not(X_17)),
inference(resolve,[$cnf( $equal(and(X_17,truth),not(or(falsehood,not(X_17)))) )],[refute_0_316,refute_0_323]) ).
cnf(refute_0_325,plain,
( X_61 != not(not(X_61))
| not(not(X_61)) = X_61 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_61)),bind(Y0,$fot(not(not(X_61))))]]) ).
cnf(refute_0_326,plain,
not(not(X_61)) = X_61,
inference(resolve,[$cnf( $equal(X_61,not(not(X_61))) )],[refute_0_207,refute_0_325]) ).
cnf(refute_0_327,plain,
not(not(X_17)) = X_17,
inference(subst,[],[refute_0_326:[bind(X_61,$fot(X_17))]]) ).
cnf(refute_0_328,plain,
( and(X_17,truth) != not(not(X_17))
| not(not(X_17)) != X_17
| and(X_17,truth) = X_17 ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_17,truth),X_17) ),[0],$fot(not(not(X_17)))]]) ).
cnf(refute_0_329,plain,
( and(X_17,truth) != not(not(X_17))
| and(X_17,truth) = X_17 ),
inference(resolve,[$cnf( $equal(not(not(X_17)),X_17) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
and(X_17,truth) = X_17,
inference(resolve,[$cnf( $equal(and(X_17,truth),not(not(X_17))) )],[refute_0_324,refute_0_329]) ).
cnf(refute_0_331,plain,
and(not(X_84),truth) = not(X_84),
inference(subst,[],[refute_0_330:[bind(X_17,$fot(not(X_84)))]]) ).
cnf(refute_0_332,plain,
( and(not(X_84),truth) != not(X_84)
| xor(X_84,truth) != implies(implies(X_84,truth),and(not(X_84),truth))
| xor(X_84,truth) = implies(implies(X_84,truth),not(X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_84,truth),implies(implies(X_84,truth),and(not(X_84),truth))) ),[1,1],$fot(not(X_84))]]) ).
cnf(refute_0_333,plain,
( xor(X_84,truth) != implies(implies(X_84,truth),and(not(X_84),truth))
| xor(X_84,truth) = implies(implies(X_84,truth),not(X_84)) ),
inference(resolve,[$cnf( $equal(and(not(X_84),truth),not(X_84)) )],[refute_0_331,refute_0_332]) ).
cnf(refute_0_334,plain,
xor(X_84,truth) = implies(implies(X_84,truth),not(X_84)),
inference(resolve,[$cnf( $equal(xor(X_84,truth),implies(implies(X_84,truth),and(not(X_84),truth))) )],[refute_0_302,refute_0_333]) ).
cnf(refute_0_335,plain,
and(X_84,truth) = X_84,
inference(subst,[],[refute_0_330:[bind(X_17,$fot(X_84))]]) ).
cnf(refute_0_336,plain,
implies(or(truth,not(X_14)),implies(X_14,truth)) = truth,
inference(subst,[],[refute_0_33:[bind(X,$fot(truth)),bind(Y,$fot(X_14))]]) ).
cnf(refute_0_337,plain,
or(truth,not(X_14)) = implies(falsehood,not(X_14)),
inference(subst,[],[refute_0_63:[bind(X_8,$fot(not(X_14)))]]) ).
cnf(refute_0_338,plain,
( implies(or(truth,not(X_14)),implies(X_14,truth)) != truth
| or(truth,not(X_14)) != implies(falsehood,not(X_14))
| implies(implies(falsehood,not(X_14)),implies(X_14,truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(truth,not(X_14)),implies(X_14,truth)),truth) ),[0,0],$fot(implies(falsehood,not(X_14)))]]) ).
cnf(refute_0_339,plain,
( implies(or(truth,not(X_14)),implies(X_14,truth)) != truth
| implies(implies(falsehood,not(X_14)),implies(X_14,truth)) = truth ),
inference(resolve,[$cnf( $equal(or(truth,not(X_14)),implies(falsehood,not(X_14))) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
implies(implies(falsehood,not(X_14)),implies(X_14,truth)) = truth,
inference(resolve,[$cnf( $equal(implies(or(truth,not(X_14)),implies(X_14,truth)),truth) )],[refute_0_336,refute_0_339]) ).
cnf(refute_0_341,plain,
implies(truth,implies(X_14,truth)) = implies(X_14,truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_14,truth)))]]) ).
cnf(refute_0_342,plain,
implies(falsehood,not(X_14)) = truth,
inference(subst,[],[refute_0_197:[bind(X_61,$fot(not(X_14)))]]) ).
cnf(refute_0_343,plain,
implies(implies(falsehood,not(X_14)),implies(X_14,truth)) = implies(implies(falsehood,not(X_14)),implies(X_14,truth)),
introduced(tautology,[refl,[$fot(implies(implies(falsehood,not(X_14)),implies(X_14,truth)))]]) ).
cnf(refute_0_344,plain,
( implies(falsehood,not(X_14)) != truth
| implies(implies(falsehood,not(X_14)),implies(X_14,truth)) != implies(implies(falsehood,not(X_14)),implies(X_14,truth))
| implies(implies(falsehood,not(X_14)),implies(X_14,truth)) = implies(truth,implies(X_14,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,not(X_14)),implies(X_14,truth)),implies(implies(falsehood,not(X_14)),implies(X_14,truth))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_345,plain,
( implies(falsehood,not(X_14)) != truth
| implies(implies(falsehood,not(X_14)),implies(X_14,truth)) = implies(truth,implies(X_14,truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(X_14)),implies(X_14,truth)),implies(implies(falsehood,not(X_14)),implies(X_14,truth))) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
implies(implies(falsehood,not(X_14)),implies(X_14,truth)) = implies(truth,implies(X_14,truth)),
inference(resolve,[$cnf( $equal(implies(falsehood,not(X_14)),truth) )],[refute_0_342,refute_0_345]) ).
cnf(refute_0_347,plain,
( implies(implies(falsehood,not(X_14)),implies(X_14,truth)) != implies(truth,implies(X_14,truth))
| implies(truth,implies(X_14,truth)) != implies(X_14,truth)
| implies(implies(falsehood,not(X_14)),implies(X_14,truth)) = implies(X_14,truth) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(implies(falsehood,not(X_14)),implies(X_14,truth)))),bind(Y0,$fot(implies(truth,implies(X_14,truth)))),bind(Z0,$fot(implies(X_14,truth)))]]) ).
cnf(refute_0_348,plain,
( implies(truth,implies(X_14,truth)) != implies(X_14,truth)
| implies(implies(falsehood,not(X_14)),implies(X_14,truth)) = implies(X_14,truth) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(X_14)),implies(X_14,truth)),implies(truth,implies(X_14,truth))) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
implies(implies(falsehood,not(X_14)),implies(X_14,truth)) = implies(X_14,truth),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_14,truth)),implies(X_14,truth)) )],[refute_0_341,refute_0_348]) ).
cnf(refute_0_350,plain,
( implies(implies(falsehood,not(X_14)),implies(X_14,truth)) != implies(X_14,truth)
| implies(implies(falsehood,not(X_14)),implies(X_14,truth)) != truth
| implies(X_14,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,not(X_14)),implies(X_14,truth)),truth) ),[0],$fot(implies(X_14,truth))]]) ).
cnf(refute_0_351,plain,
( implies(implies(falsehood,not(X_14)),implies(X_14,truth)) != truth
| implies(X_14,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(X_14)),implies(X_14,truth)),implies(X_14,truth)) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
implies(X_14,truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(X_14)),implies(X_14,truth)),truth) )],[refute_0_340,refute_0_351]) ).
cnf(refute_0_353,plain,
implies(X_84,truth) = truth,
inference(subst,[],[refute_0_352:[bind(X_14,$fot(X_84))]]) ).
cnf(refute_0_354,plain,
and(X_84,implies(X_84,truth)) = and(X_84,implies(X_84,truth)),
introduced(tautology,[refl,[$fot(and(X_84,implies(X_84,truth)))]]) ).
cnf(refute_0_355,plain,
( and(X_84,implies(X_84,truth)) != and(X_84,implies(X_84,truth))
| implies(X_84,truth) != truth
| and(X_84,implies(X_84,truth)) = and(X_84,truth) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_84,implies(X_84,truth)),and(X_84,implies(X_84,truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_356,plain,
( implies(X_84,truth) != truth
| and(X_84,implies(X_84,truth)) = and(X_84,truth) ),
inference(resolve,[$cnf( $equal(and(X_84,implies(X_84,truth)),and(X_84,implies(X_84,truth))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
and(X_84,implies(X_84,truth)) = and(X_84,truth),
inference(resolve,[$cnf( $equal(implies(X_84,truth),truth) )],[refute_0_353,refute_0_356]) ).
cnf(refute_0_358,plain,
( and(X_84,implies(X_84,truth)) != and(X_84,truth)
| and(X_84,truth) != X_84
| and(X_84,implies(X_84,truth)) = X_84 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(X_84,implies(X_84,truth)))),bind(Y0,$fot(and(X_84,truth))),bind(Z0,$fot(X_84))]]) ).
cnf(refute_0_359,plain,
( and(X_84,truth) != X_84
| and(X_84,implies(X_84,truth)) = X_84 ),
inference(resolve,[$cnf( $equal(and(X_84,implies(X_84,truth)),and(X_84,truth)) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
and(X_84,implies(X_84,truth)) = X_84,
inference(resolve,[$cnf( $equal(and(X_84,truth),X_84) )],[refute_0_335,refute_0_359]) ).
cnf(refute_0_361,plain,
and(X,not(not(X_55))) = and(not(not(X_55)),X),
inference(subst,[],[and_commutativity:[bind(Y,$fot(not(not(X_55))))]]) ).
cnf(refute_0_362,plain,
and(and(X_40,truth),X_42) = and(X_40,and(truth,X_42)),
inference(subst,[],[and_associativity:[bind(X,$fot(X_40)),bind(Y,$fot(truth)),bind(Z,$fot(X_42))]]) ).
cnf(refute_0_363,plain,
and(X_40,truth) = not(not(X_40)),
inference(subst,[],[refute_0_324:[bind(X_17,$fot(X_40))]]) ).
cnf(refute_0_364,plain,
( and(X_40,truth) != not(not(X_40))
| and(and(X_40,truth),X_42) != and(X_40,and(truth,X_42))
| and(not(not(X_40)),X_42) = and(X_40,and(truth,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(X_40,truth),X_42),and(X_40,and(truth,X_42))) ),[0,0],$fot(not(not(X_40)))]]) ).
cnf(refute_0_365,plain,
( and(and(X_40,truth),X_42) != and(X_40,and(truth,X_42))
| and(not(not(X_40)),X_42) = and(X_40,and(truth,X_42)) ),
inference(resolve,[$cnf( $equal(and(X_40,truth),not(not(X_40))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
and(not(not(X_40)),X_42) = and(X_40,and(truth,X_42)),
inference(resolve,[$cnf( $equal(and(and(X_40,truth),X_42),and(X_40,and(truth,X_42))) )],[refute_0_362,refute_0_365]) ).
cnf(refute_0_367,plain,
and(and(X_40,X_41),truth) = not(not(and(X_40,X_41))),
inference(subst,[],[refute_0_324:[bind(X_17,$fot(and(X_40,X_41)))]]) ).
cnf(refute_0_368,plain,
and(and(X_40,X_41),truth) = and(X_40,and(X_41,truth)),
inference(subst,[],[and_associativity:[bind(X,$fot(X_40)),bind(Y,$fot(X_41)),bind(Z,$fot(truth))]]) ).
cnf(refute_0_369,plain,
( and(and(X_40,X_41),truth) != and(X_40,and(X_41,truth))
| and(and(X_40,X_41),truth) != not(not(and(X_40,X_41)))
| and(X_40,and(X_41,truth)) = not(not(and(X_40,X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(X_40,X_41),truth),not(not(and(X_40,X_41)))) ),[0],$fot(and(X_40,and(X_41,truth)))]]) ).
cnf(refute_0_370,plain,
( and(and(X_40,X_41),truth) != not(not(and(X_40,X_41)))
| and(X_40,and(X_41,truth)) = not(not(and(X_40,X_41))) ),
inference(resolve,[$cnf( $equal(and(and(X_40,X_41),truth),and(X_40,and(X_41,truth))) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
and(X_40,and(X_41,truth)) = not(not(and(X_40,X_41))),
inference(resolve,[$cnf( $equal(and(and(X_40,X_41),truth),not(not(and(X_40,X_41)))) )],[refute_0_367,refute_0_370]) ).
cnf(refute_0_372,plain,
and(X_41,truth) = not(not(X_41)),
inference(subst,[],[refute_0_324:[bind(X_17,$fot(X_41))]]) ).
cnf(refute_0_373,plain,
and(X_40,and(X_41,truth)) = and(X_40,and(X_41,truth)),
introduced(tautology,[refl,[$fot(and(X_40,and(X_41,truth)))]]) ).
cnf(refute_0_374,plain,
( and(X_40,and(X_41,truth)) != and(X_40,and(X_41,truth))
| and(X_41,truth) != not(not(X_41))
| and(X_40,and(X_41,truth)) = and(X_40,not(not(X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_40,and(X_41,truth)),and(X_40,and(X_41,truth))) ),[1,1],$fot(not(not(X_41)))]]) ).
cnf(refute_0_375,plain,
( and(X_41,truth) != not(not(X_41))
| and(X_40,and(X_41,truth)) = and(X_40,not(not(X_41))) ),
inference(resolve,[$cnf( $equal(and(X_40,and(X_41,truth)),and(X_40,and(X_41,truth))) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
and(X_40,and(X_41,truth)) = and(X_40,not(not(X_41))),
inference(resolve,[$cnf( $equal(and(X_41,truth),not(not(X_41))) )],[refute_0_372,refute_0_375]) ).
cnf(refute_0_377,plain,
( and(X_40,and(X_41,truth)) != and(X_40,not(not(X_41)))
| and(X_40,and(X_41,truth)) != not(not(and(X_40,X_41)))
| and(X_40,not(not(X_41))) = not(not(and(X_40,X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_40,and(X_41,truth)),not(not(and(X_40,X_41)))) ),[0],$fot(and(X_40,not(not(X_41))))]]) ).
cnf(refute_0_378,plain,
( and(X_40,and(X_41,truth)) != not(not(and(X_40,X_41)))
| and(X_40,not(not(X_41))) = not(not(and(X_40,X_41))) ),
inference(resolve,[$cnf( $equal(and(X_40,and(X_41,truth)),and(X_40,not(not(X_41)))) )],[refute_0_376,refute_0_377]) ).
cnf(refute_0_379,plain,
and(X_40,not(not(X_41))) = not(not(and(X_40,X_41))),
inference(resolve,[$cnf( $equal(and(X_40,and(X_41,truth)),not(not(and(X_40,X_41)))) )],[refute_0_371,refute_0_378]) ).
cnf(refute_0_380,plain,
and(X_40,not(not(X_42))) = not(not(and(X_40,X_42))),
inference(subst,[],[refute_0_379:[bind(X_41,$fot(X_42))]]) ).
cnf(refute_0_381,plain,
and(or(falsehood,and(truth,truth)),Y) = not(or(not(or(falsehood,and(truth,truth))),not(Y))),
inference(subst,[],[and_definition:[bind(X,$fot(or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_382,plain,
and(or(falsehood,falsehood),truth) = not(or(falsehood,not(or(falsehood,falsehood)))),
inference(subst,[],[refute_0_316:[bind(X_17,$fot(or(falsehood,falsehood)))]]) ).
cnf(refute_0_383,plain,
and(truth,truth) = not(or(falsehood,not(truth))),
inference(subst,[],[refute_0_316:[bind(X_17,$fot(truth))]]) ).
cnf(refute_0_384,plain,
( and(truth,truth) != not(or(falsehood,not(truth)))
| not(truth) != falsehood
| and(truth,truth) = not(or(falsehood,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,truth),not(or(falsehood,not(truth)))) ),[1,0,1],$fot(falsehood)]]) ).
cnf(refute_0_385,plain,
( and(truth,truth) != not(or(falsehood,not(truth)))
| and(truth,truth) = not(or(falsehood,falsehood)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_384]) ).
cnf(refute_0_386,plain,
and(truth,truth) = not(or(falsehood,falsehood)),
inference(resolve,[$cnf( $equal(and(truth,truth),not(or(falsehood,not(truth)))) )],[refute_0_383,refute_0_385]) ).
cnf(refute_0_387,plain,
( and(truth,truth) != not(or(falsehood,falsehood))
| not(or(falsehood,falsehood)) = and(truth,truth) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,truth))),bind(Y0,$fot(not(or(falsehood,falsehood))))]]) ).
cnf(refute_0_388,plain,
not(or(falsehood,falsehood)) = and(truth,truth),
inference(resolve,[$cnf( $equal(and(truth,truth),not(or(falsehood,falsehood))) )],[refute_0_386,refute_0_387]) ).
cnf(refute_0_389,plain,
( and(or(falsehood,falsehood),truth) != not(or(falsehood,not(or(falsehood,falsehood))))
| not(or(falsehood,falsehood)) != and(truth,truth)
| and(or(falsehood,falsehood),truth) = not(or(falsehood,and(truth,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,not(or(falsehood,falsehood))))) ),[1,0,1],$fot(and(truth,truth))]]) ).
cnf(refute_0_390,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( $equal(not(or(falsehood,falsehood)),and(truth,truth)) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
and(or(falsehood,falsehood),truth) = not(or(falsehood,and(truth,truth))),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,not(or(falsehood,falsehood))))) )],[refute_0_382,refute_0_390]) ).
cnf(refute_0_392,plain,
and(or(falsehood,falsehood),truth) = and(truth,or(falsehood,falsehood)),
inference(subst,[],[refute_0_4:[bind(X,$fot(truth)),bind(Y,$fot(or(falsehood,falsehood)))]]) ).
cnf(refute_0_393,plain,
( and(or(falsehood,falsehood),truth) != and(truth,or(falsehood,falsehood))
| and(or(falsehood,falsehood),truth) != not(or(falsehood,and(truth,truth)))
| and(truth,or(falsehood,falsehood)) = not(or(falsehood,and(truth,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,and(truth,truth)))) ),[0],$fot(and(truth,or(falsehood,falsehood)))]]) ).
cnf(refute_0_394,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( $equal(and(or(falsehood,falsehood),truth),and(truth,or(falsehood,falsehood))) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
and(truth,or(falsehood,falsehood)) = not(or(falsehood,and(truth,truth))),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,and(truth,truth)))) )],[refute_0_391,refute_0_394]) ).
cnf(refute_0_396,plain,
( and(truth,or(falsehood,falsehood)) != not(or(falsehood,and(truth,truth)))
| not(or(falsehood,and(truth,truth))) = and(truth,or(falsehood,falsehood)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,or(falsehood,falsehood)))),bind(Y0,$fot(not(or(falsehood,and(truth,truth)))))]]) ).
cnf(refute_0_397,plain,
not(or(falsehood,and(truth,truth))) = and(truth,or(falsehood,falsehood)),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),not(or(falsehood,and(truth,truth)))) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
( and(or(falsehood,and(truth,truth)),Y) != not(or(not(or(falsehood,and(truth,truth))),not(Y)))
| not(or(falsehood,and(truth,truth))) != and(truth,or(falsehood,falsehood))
| and(or(falsehood,and(truth,truth)),Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))) ),
introduced(tautology,[equality,[$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_399,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( $equal(not(or(falsehood,and(truth,truth))),and(truth,or(falsehood,falsehood))) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
and(or(falsehood,and(truth,truth)),Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),not(or(not(or(falsehood,and(truth,truth))),not(Y)))) )],[refute_0_381,refute_0_399]) ).
cnf(refute_0_401,plain,
not(not(truth)) = not(not(truth)),
introduced(tautology,[refl,[$fot(not(not(truth)))]]) ).
cnf(refute_0_402,plain,
( not(not(truth)) != not(not(truth))
| not(truth) != falsehood
| not(not(truth)) = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(truth)),not(not(truth))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_403,plain,
( not(truth) != falsehood
| not(not(truth)) = not(falsehood) ),
inference(resolve,[$cnf( $equal(not(not(truth)),not(not(truth))) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
not(not(truth)) = not(falsehood),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_403]) ).
cnf(refute_0_405,plain,
( not(falsehood) != truth
| not(not(truth)) != not(falsehood)
| not(not(truth)) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(not(truth)))),bind(Y0,$fot(not(falsehood))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_406,plain,
( not(falsehood) != truth
| not(not(truth)) = truth ),
inference(resolve,[$cnf( $equal(not(not(truth)),not(falsehood)) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
not(not(truth)) = truth,
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_105,refute_0_406]) ).
cnf(refute_0_408,plain,
and(truth,truth) = not(not(truth)),
inference(subst,[],[refute_0_324:[bind(X_17,$fot(truth))]]) ).
cnf(refute_0_409,plain,
or(falsehood,and(truth,truth)) = and(truth,truth),
inference(subst,[],[refute_0_112:[bind(Y,$fot(and(truth,truth)))]]) ).
cnf(refute_0_410,plain,
( and(truth,truth) != not(not(truth))
| or(falsehood,and(truth,truth)) != and(truth,truth)
| or(falsehood,and(truth,truth)) = not(not(truth)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(falsehood,and(truth,truth)))),bind(Y0,$fot(and(truth,truth))),bind(Z0,$fot(not(not(truth))))]]) ).
cnf(refute_0_411,plain,
( and(truth,truth) != not(not(truth))
| or(falsehood,and(truth,truth)) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),and(truth,truth)) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
or(falsehood,and(truth,truth)) = not(not(truth)),
inference(resolve,[$cnf( $equal(and(truth,truth),not(not(truth))) )],[refute_0_408,refute_0_411]) ).
cnf(refute_0_413,plain,
( not(not(truth)) != truth
| or(falsehood,and(truth,truth)) != not(not(truth))
| or(falsehood,and(truth,truth)) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(falsehood,and(truth,truth)))),bind(Y0,$fot(not(not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_414,plain,
( not(not(truth)) != truth
| or(falsehood,and(truth,truth)) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),not(not(truth))) )],[refute_0_412,refute_0_413]) ).
cnf(refute_0_415,plain,
or(falsehood,and(truth,truth)) = truth,
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_407,refute_0_414]) ).
cnf(refute_0_416,plain,
and(or(falsehood,and(truth,truth)),Y) = and(or(falsehood,and(truth,truth)),Y),
introduced(tautology,[refl,[$fot(and(or(falsehood,and(truth,truth)),Y))]]) ).
cnf(refute_0_417,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_418,plain,
( or(falsehood,and(truth,truth)) != truth
| and(or(falsehood,and(truth,truth)),Y) = and(truth,Y) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),and(or(falsehood,and(truth,truth)),Y)) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
and(or(falsehood,and(truth,truth)),Y) = and(truth,Y),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),truth) )],[refute_0_415,refute_0_418]) ).
cnf(refute_0_420,plain,
( and(or(falsehood,and(truth,truth)),Y) != and(truth,Y)
| and(or(falsehood,and(truth,truth)),Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))) ),
introduced(tautology,[equality,[$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_421,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( $equal(and(or(falsehood,and(truth,truth)),Y),and(truth,Y)) )],[refute_0_419,refute_0_420]) ).
cnf(refute_0_422,plain,
or(falsehood,not(Y)) = not(Y),
inference(subst,[],[refute_0_112:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_423,plain,
and(falsehood,truth) = not(or(falsehood,not(falsehood))),
inference(subst,[],[refute_0_316:[bind(X_17,$fot(falsehood))]]) ).
cnf(refute_0_424,plain,
( and(falsehood,truth) != not(or(falsehood,not(falsehood)))
| or(falsehood,not(falsehood)) != truth
| and(falsehood,truth) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(and(falsehood,truth),not(or(falsehood,not(falsehood)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_425,plain,
( and(falsehood,truth) != not(or(falsehood,not(falsehood)))
| and(falsehood,truth) = not(truth) ),
inference(resolve,[$cnf( $equal(or(falsehood,not(falsehood)),truth) )],[refute_0_98,refute_0_424]) ).
cnf(refute_0_426,plain,
and(falsehood,truth) = not(truth),
inference(resolve,[$cnf( $equal(and(falsehood,truth),not(or(falsehood,not(falsehood)))) )],[refute_0_423,refute_0_425]) ).
cnf(refute_0_427,plain,
( and(falsehood,truth) != not(truth)
| not(truth) != falsehood
| and(falsehood,truth) = falsehood ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(falsehood,truth),falsehood) ),[0],$fot(not(truth))]]) ).
cnf(refute_0_428,plain,
( and(falsehood,truth) != not(truth)
| and(falsehood,truth) = falsehood ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_427]) ).
cnf(refute_0_429,plain,
and(falsehood,truth) = falsehood,
inference(resolve,[$cnf( $equal(and(falsehood,truth),not(truth)) )],[refute_0_426,refute_0_428]) ).
cnf(refute_0_430,plain,
and(truth,falsehood) = and(falsehood,truth),
inference(subst,[],[refute_0_4:[bind(X,$fot(falsehood)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_431,plain,
( and(falsehood,truth) != falsehood
| and(truth,falsehood) != and(falsehood,truth)
| and(truth,falsehood) = falsehood ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(truth,falsehood))),bind(Y0,$fot(and(falsehood,truth))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_432,plain,
( and(falsehood,truth) != falsehood
| and(truth,falsehood) = falsehood ),
inference(resolve,[$cnf( $equal(and(truth,falsehood),and(falsehood,truth)) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
and(truth,falsehood) = falsehood,
inference(resolve,[$cnf( $equal(and(falsehood,truth),falsehood) )],[refute_0_429,refute_0_432]) ).
cnf(refute_0_434,plain,
or(falsehood,falsehood) = falsehood,
inference(subst,[],[refute_0_112:[bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_435,plain,
and(truth,or(falsehood,falsehood)) = and(truth,or(falsehood,falsehood)),
introduced(tautology,[refl,[$fot(and(truth,or(falsehood,falsehood)))]]) ).
cnf(refute_0_436,plain,
( and(truth,or(falsehood,falsehood)) != and(truth,or(falsehood,falsehood))
| or(falsehood,falsehood) != falsehood
| and(truth,or(falsehood,falsehood)) = and(truth,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,or(falsehood,falsehood)),and(truth,or(falsehood,falsehood))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_437,plain,
( or(falsehood,falsehood) != falsehood
| and(truth,or(falsehood,falsehood)) = and(truth,falsehood) ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),and(truth,or(falsehood,falsehood))) )],[refute_0_435,refute_0_436]) ).
cnf(refute_0_438,plain,
and(truth,or(falsehood,falsehood)) = and(truth,falsehood),
inference(resolve,[$cnf( $equal(or(falsehood,falsehood),falsehood) )],[refute_0_434,refute_0_437]) ).
cnf(refute_0_439,plain,
( and(truth,falsehood) != falsehood
| and(truth,or(falsehood,falsehood)) != and(truth,falsehood)
| and(truth,or(falsehood,falsehood)) = falsehood ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(truth,or(falsehood,falsehood)))),bind(Y0,$fot(and(truth,falsehood))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_440,plain,
( and(truth,falsehood) != falsehood
| and(truth,or(falsehood,falsehood)) = falsehood ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),and(truth,falsehood)) )],[refute_0_438,refute_0_439]) ).
cnf(refute_0_441,plain,
and(truth,or(falsehood,falsehood)) = falsehood,
inference(resolve,[$cnf( $equal(and(truth,falsehood),falsehood) )],[refute_0_433,refute_0_440]) ).
cnf(refute_0_442,plain,
or(and(truth,or(falsehood,falsehood)),not(Y)) = or(and(truth,or(falsehood,falsehood)),not(Y)),
introduced(tautology,[refl,[$fot(or(and(truth,or(falsehood,falsehood)),not(Y)))]]) ).
cnf(refute_0_443,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_444,plain,
( and(truth,or(falsehood,falsehood)) != falsehood
| or(and(truth,or(falsehood,falsehood)),not(Y)) = or(falsehood,not(Y)) ),
inference(resolve,[$cnf( $equal(or(and(truth,or(falsehood,falsehood)),not(Y)),or(and(truth,or(falsehood,falsehood)),not(Y))) )],[refute_0_442,refute_0_443]) ).
cnf(refute_0_445,plain,
or(and(truth,or(falsehood,falsehood)),not(Y)) = or(falsehood,not(Y)),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),falsehood) )],[refute_0_441,refute_0_444]) ).
cnf(refute_0_446,plain,
( or(and(truth,or(falsehood,falsehood)),not(Y)) != or(falsehood,not(Y))
| or(falsehood,not(Y)) != not(Y)
| or(and(truth,or(falsehood,falsehood)),not(Y)) = not(Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(and(truth,or(falsehood,falsehood)),not(Y)))),bind(Y0,$fot(or(falsehood,not(Y)))),bind(Z0,$fot(not(Y)))]]) ).
cnf(refute_0_447,plain,
( or(falsehood,not(Y)) != not(Y)
| or(and(truth,or(falsehood,falsehood)),not(Y)) = not(Y) ),
inference(resolve,[$cnf( $equal(or(and(truth,or(falsehood,falsehood)),not(Y)),or(falsehood,not(Y))) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
or(and(truth,or(falsehood,falsehood)),not(Y)) = not(Y),
inference(resolve,[$cnf( $equal(or(falsehood,not(Y)),not(Y)) )],[refute_0_422,refute_0_447]) ).
cnf(refute_0_449,plain,
not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(or(and(truth,or(falsehood,falsehood)),not(Y))),
introduced(tautology,[refl,[$fot(not(or(and(truth,or(falsehood,falsehood)),not(Y))))]]) ).
cnf(refute_0_450,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)) != not(Y)
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(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(not(Y))]]) ).
cnf(refute_0_451,plain,
( or(and(truth,or(falsehood,falsehood)),not(Y)) != not(Y)
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(not(or(and(truth,or(falsehood,falsehood)),not(Y))),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) )],[refute_0_449,refute_0_450]) ).
cnf(refute_0_452,plain,
not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(not(Y)),
inference(resolve,[$cnf( $equal(or(and(truth,or(falsehood,falsehood)),not(Y)),not(Y)) )],[refute_0_448,refute_0_451]) ).
cnf(refute_0_453,plain,
( and(truth,Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) != not(not(Y))
| and(truth,Y) = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(truth,Y),not(not(Y))) ),[0],$fot(not(or(and(truth,or(falsehood,falsehood)),not(Y))))]]) ).
cnf(refute_0_454,plain,
( and(truth,Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(not(or(and(truth,or(falsehood,falsehood)),not(Y))),not(not(Y))) )],[refute_0_452,refute_0_453]) ).
cnf(refute_0_455,plain,
( and(or(falsehood,and(truth,truth)),Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(and(truth,Y),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) )],[refute_0_421,refute_0_454]) ).
cnf(refute_0_456,plain,
and(truth,Y) = not(not(Y)),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) )],[refute_0_400,refute_0_455]) ).
cnf(refute_0_457,plain,
and(truth,X_42) = not(not(X_42)),
inference(subst,[],[refute_0_456:[bind(Y,$fot(X_42))]]) ).
cnf(refute_0_458,plain,
and(X_40,and(truth,X_42)) = and(X_40,and(truth,X_42)),
introduced(tautology,[refl,[$fot(and(X_40,and(truth,X_42)))]]) ).
cnf(refute_0_459,plain,
( and(X_40,and(truth,X_42)) != and(X_40,and(truth,X_42))
| and(truth,X_42) != not(not(X_42))
| and(X_40,and(truth,X_42)) = and(X_40,not(not(X_42))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_40,and(truth,X_42)),and(X_40,and(truth,X_42))) ),[1,1],$fot(not(not(X_42)))]]) ).
cnf(refute_0_460,plain,
( and(truth,X_42) != not(not(X_42))
| and(X_40,and(truth,X_42)) = and(X_40,not(not(X_42))) ),
inference(resolve,[$cnf( $equal(and(X_40,and(truth,X_42)),and(X_40,and(truth,X_42))) )],[refute_0_458,refute_0_459]) ).
cnf(refute_0_461,plain,
and(X_40,and(truth,X_42)) = and(X_40,not(not(X_42))),
inference(resolve,[$cnf( $equal(and(truth,X_42),not(not(X_42))) )],[refute_0_457,refute_0_460]) ).
cnf(refute_0_462,plain,
( and(X_40,and(truth,X_42)) != and(X_40,not(not(X_42)))
| and(X_40,not(not(X_42))) != not(not(and(X_40,X_42)))
| and(X_40,and(truth,X_42)) = not(not(and(X_40,X_42))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(X_40,and(truth,X_42)))),bind(Y0,$fot(and(X_40,not(not(X_42))))),bind(Z0,$fot(not(not(and(X_40,X_42)))))]]) ).
cnf(refute_0_463,plain,
( and(X_40,not(not(X_42))) != not(not(and(X_40,X_42)))
| and(X_40,and(truth,X_42)) = not(not(and(X_40,X_42))) ),
inference(resolve,[$cnf( $equal(and(X_40,and(truth,X_42)),and(X_40,not(not(X_42)))) )],[refute_0_461,refute_0_462]) ).
cnf(refute_0_464,plain,
and(X_40,and(truth,X_42)) = not(not(and(X_40,X_42))),
inference(resolve,[$cnf( $equal(and(X_40,not(not(X_42))),not(not(and(X_40,X_42)))) )],[refute_0_380,refute_0_463]) ).
cnf(refute_0_465,plain,
( and(X_40,and(truth,X_42)) != not(not(and(X_40,X_42)))
| and(not(not(X_40)),X_42) != and(X_40,and(truth,X_42))
| and(not(not(X_40)),X_42) = not(not(and(X_40,X_42))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X_40)),X_42),and(X_40,and(truth,X_42))) ),[1],$fot(not(not(and(X_40,X_42))))]]) ).
cnf(refute_0_466,plain,
( and(not(not(X_40)),X_42) != and(X_40,and(truth,X_42))
| and(not(not(X_40)),X_42) = not(not(and(X_40,X_42))) ),
inference(resolve,[$cnf( $equal(and(X_40,and(truth,X_42)),not(not(and(X_40,X_42)))) )],[refute_0_464,refute_0_465]) ).
cnf(refute_0_467,plain,
and(not(not(X_40)),X_42) = not(not(and(X_40,X_42))),
inference(resolve,[$cnf( $equal(and(not(not(X_40)),X_42),and(X_40,and(truth,X_42))) )],[refute_0_366,refute_0_466]) ).
cnf(refute_0_468,plain,
and(not(not(X_55)),X) = not(not(and(X_55,X))),
inference(subst,[],[refute_0_467:[bind(X_40,$fot(X_55)),bind(X_42,$fot(X))]]) ).
cnf(refute_0_469,plain,
( and(X,not(not(X_55))) != and(not(not(X_55)),X)
| and(not(not(X_55)),X) != not(not(and(X_55,X)))
| and(X,not(not(X_55))) = not(not(and(X_55,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,not(not(X_55))),not(not(and(X_55,X)))) ),[0],$fot(and(not(not(X_55)),X))]]) ).
cnf(refute_0_470,plain,
( and(X,not(not(X_55))) != and(not(not(X_55)),X)
| and(X,not(not(X_55))) = not(not(and(X_55,X))) ),
inference(resolve,[$cnf( $equal(and(not(not(X_55)),X),not(not(and(X_55,X)))) )],[refute_0_468,refute_0_469]) ).
cnf(refute_0_471,plain,
and(X,not(not(X_55))) = not(not(and(X_55,X))),
inference(resolve,[$cnf( $equal(and(X,not(not(X_55))),and(not(not(X_55)),X)) )],[refute_0_361,refute_0_470]) ).
cnf(refute_0_472,plain,
and(X,not(not(X_55))) = not(not(and(X,X_55))),
inference(subst,[],[refute_0_379:[bind(X_40,$fot(X)),bind(X_41,$fot(X_55))]]) ).
cnf(refute_0_473,plain,
( and(X,not(not(X_55))) != not(not(and(X,X_55)))
| and(X,not(not(X_55))) != not(not(and(X_55,X)))
| not(not(and(X,X_55))) = not(not(and(X_55,X))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,not(not(X_55))),not(not(and(X_55,X)))) ),[0],$fot(not(not(and(X,X_55))))]]) ).
cnf(refute_0_474,plain,
( and(X,not(not(X_55))) != not(not(and(X_55,X)))
| not(not(and(X,X_55))) = not(not(and(X_55,X))) ),
inference(resolve,[$cnf( $equal(and(X,not(not(X_55))),not(not(and(X,X_55)))) )],[refute_0_472,refute_0_473]) ).
cnf(refute_0_475,plain,
not(not(and(X,X_55))) = not(not(and(X_55,X))),
inference(resolve,[$cnf( $equal(and(X,not(not(X_55))),not(not(and(X_55,X)))) )],[refute_0_471,refute_0_474]) ).
cnf(refute_0_476,plain,
not(not(and(X,X_55))) = and(X,X_55),
inference(subst,[],[refute_0_326:[bind(X_61,$fot(and(X,X_55)))]]) ).
cnf(refute_0_477,plain,
( not(not(and(X,X_55))) != and(X,X_55)
| not(not(and(X,X_55))) != not(not(and(X_55,X)))
| and(X,X_55) = not(not(and(X_55,X))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(and(X,X_55))),not(not(and(X_55,X)))) ),[0],$fot(and(X,X_55))]]) ).
cnf(refute_0_478,plain,
( not(not(and(X,X_55))) != not(not(and(X_55,X)))
| and(X,X_55) = not(not(and(X_55,X))) ),
inference(resolve,[$cnf( $equal(not(not(and(X,X_55))),and(X,X_55)) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
not(not(and(X_55,X))) = and(X_55,X),
inference(subst,[],[refute_0_326:[bind(X_61,$fot(and(X_55,X)))]]) ).
cnf(refute_0_480,plain,
( and(X,X_55) != not(not(and(X_55,X)))
| not(not(and(X_55,X))) != and(X_55,X)
| and(X,X_55) = and(X_55,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,X_55),and(X_55,X)) ),[0],$fot(not(not(and(X_55,X))))]]) ).
cnf(refute_0_481,plain,
( and(X,X_55) != not(not(and(X_55,X)))
| and(X,X_55) = and(X_55,X) ),
inference(resolve,[$cnf( $equal(not(not(and(X_55,X))),and(X_55,X)) )],[refute_0_479,refute_0_480]) ).
cnf(refute_0_482,plain,
( not(not(and(X,X_55))) != not(not(and(X_55,X)))
| and(X,X_55) = and(X_55,X) ),
inference(resolve,[$cnf( $equal(and(X,X_55),not(not(and(X_55,X)))) )],[refute_0_478,refute_0_481]) ).
cnf(refute_0_483,plain,
and(X,X_55) = and(X_55,X),
inference(resolve,[$cnf( $equal(not(not(and(X,X_55))),not(not(and(X_55,X)))) )],[refute_0_475,refute_0_482]) ).
cnf(refute_0_484,plain,
( and(X,X_55) != and(X_55,X)
| and(X_55,X) = and(X,X_55) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X,X_55))),bind(Y0,$fot(and(X_55,X)))]]) ).
cnf(refute_0_485,plain,
and(X_55,X) = and(X,X_55),
inference(resolve,[$cnf( $equal(and(X,X_55),and(X_55,X)) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
and(implies(X_84,truth),X_84) = and(X_84,implies(X_84,truth)),
inference(subst,[],[refute_0_485:[bind(X,$fot(X_84)),bind(X_55,$fot(implies(X_84,truth)))]]) ).
cnf(refute_0_487,plain,
( and(X_84,implies(X_84,truth)) != X_84
| and(implies(X_84,truth),X_84) != and(X_84,implies(X_84,truth))
| and(implies(X_84,truth),X_84) = X_84 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(implies(X_84,truth),X_84))),bind(Y0,$fot(and(X_84,implies(X_84,truth)))),bind(Z0,$fot(X_84))]]) ).
cnf(refute_0_488,plain,
( and(X_84,implies(X_84,truth)) != X_84
| and(implies(X_84,truth),X_84) = X_84 ),
inference(resolve,[$cnf( $equal(and(implies(X_84,truth),X_84),and(X_84,implies(X_84,truth))) )],[refute_0_486,refute_0_487]) ).
cnf(refute_0_489,plain,
and(implies(X_84,truth),X_84) = X_84,
inference(resolve,[$cnf( $equal(and(X_84,implies(X_84,truth)),X_84) )],[refute_0_360,refute_0_488]) ).
cnf(refute_0_490,plain,
not(and(implies(X_84,truth),X_84)) = not(and(implies(X_84,truth),X_84)),
introduced(tautology,[refl,[$fot(not(and(implies(X_84,truth),X_84)))]]) ).
cnf(refute_0_491,plain,
( and(implies(X_84,truth),X_84) != X_84
| not(and(implies(X_84,truth),X_84)) != not(and(implies(X_84,truth),X_84))
| not(and(implies(X_84,truth),X_84)) = not(X_84) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(implies(X_84,truth),X_84)),not(and(implies(X_84,truth),X_84))) ),[1,0],$fot(X_84)]]) ).
cnf(refute_0_492,plain,
( and(implies(X_84,truth),X_84) != X_84
| not(and(implies(X_84,truth),X_84)) = not(X_84) ),
inference(resolve,[$cnf( $equal(not(and(implies(X_84,truth),X_84)),not(and(implies(X_84,truth),X_84))) )],[refute_0_490,refute_0_491]) ).
cnf(refute_0_493,plain,
not(and(implies(X_84,truth),X_84)) = not(X_84),
inference(resolve,[$cnf( $equal(and(implies(X_84,truth),X_84),X_84) )],[refute_0_489,refute_0_492]) ).
cnf(refute_0_494,plain,
or(not(X),not(Y)) = not(not(or(not(X),not(Y)))),
inference(subst,[],[refute_0_207:[bind(X_61,$fot(or(not(X),not(Y))))]]) ).
cnf(refute_0_495,plain,
( not(or(not(X),not(Y))) != and(X,Y)
| or(not(X),not(Y)) != not(not(or(not(X),not(Y))))
| or(not(X),not(Y)) = not(and(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X),not(Y)),not(not(or(not(X),not(Y))))) ),[1,0],$fot(and(X,Y))]]) ).
cnf(refute_0_496,plain,
( or(not(X),not(Y)) != not(not(or(not(X),not(Y))))
| or(not(X),not(Y)) = not(and(X,Y)) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),and(X,Y)) )],[refute_0_7,refute_0_495]) ).
cnf(refute_0_497,plain,
or(not(X),not(Y)) = not(and(X,Y)),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),not(not(or(not(X),not(Y))))) )],[refute_0_494,refute_0_496]) ).
cnf(refute_0_498,plain,
or(not(X),not(Y)) = implies(X,not(Y)),
inference(subst,[],[refute_0_213:[bind(Y,$fot(not(Y))),bind(X_81,$fot(X))]]) ).
cnf(refute_0_499,plain,
( or(not(X),not(Y)) != implies(X,not(Y))
| or(not(X),not(Y)) != not(and(X,Y))
| implies(X,not(Y)) = not(and(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X),not(Y)),not(and(X,Y))) ),[0],$fot(implies(X,not(Y)))]]) ).
cnf(refute_0_500,plain,
( or(not(X),not(Y)) != not(and(X,Y))
| implies(X,not(Y)) = not(and(X,Y)) ),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),implies(X,not(Y))) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
implies(X,not(Y)) = not(and(X,Y)),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),not(and(X,Y))) )],[refute_0_497,refute_0_500]) ).
cnf(refute_0_502,plain,
implies(implies(X_84,truth),not(X_84)) = not(and(implies(X_84,truth),X_84)),
inference(subst,[],[refute_0_501:[bind(X,$fot(implies(X_84,truth))),bind(Y,$fot(X_84))]]) ).
cnf(refute_0_503,plain,
( implies(implies(X_84,truth),not(X_84)) != not(and(implies(X_84,truth),X_84))
| not(and(implies(X_84,truth),X_84)) != not(X_84)
| implies(implies(X_84,truth),not(X_84)) = not(X_84) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(implies(X_84,truth),not(X_84)))),bind(Y0,$fot(not(and(implies(X_84,truth),X_84)))),bind(Z0,$fot(not(X_84)))]]) ).
cnf(refute_0_504,plain,
( not(and(implies(X_84,truth),X_84)) != not(X_84)
| implies(implies(X_84,truth),not(X_84)) = not(X_84) ),
inference(resolve,[$cnf( $equal(implies(implies(X_84,truth),not(X_84)),not(and(implies(X_84,truth),X_84))) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
implies(implies(X_84,truth),not(X_84)) = not(X_84),
inference(resolve,[$cnf( $equal(not(and(implies(X_84,truth),X_84)),not(X_84)) )],[refute_0_493,refute_0_504]) ).
cnf(refute_0_506,plain,
( implies(implies(X_84,truth),not(X_84)) != not(X_84)
| xor(X_84,truth) != implies(implies(X_84,truth),not(X_84))
| xor(X_84,truth) = not(X_84) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_84,truth),implies(implies(X_84,truth),not(X_84))) ),[1],$fot(not(X_84))]]) ).
cnf(refute_0_507,plain,
( xor(X_84,truth) != implies(implies(X_84,truth),not(X_84))
| xor(X_84,truth) = not(X_84) ),
inference(resolve,[$cnf( $equal(implies(implies(X_84,truth),not(X_84)),not(X_84)) )],[refute_0_505,refute_0_506]) ).
cnf(refute_0_508,plain,
xor(X_84,truth) = not(X_84),
inference(resolve,[$cnf( $equal(xor(X_84,truth),implies(implies(X_84,truth),not(X_84))) )],[refute_0_334,refute_0_507]) ).
cnf(refute_0_509,plain,
xor(Y,truth) = not(Y),
inference(subst,[],[refute_0_508:[bind(X_84,$fot(Y))]]) ).
cnf(refute_0_510,plain,
( xor(Y,truth) != not(Y)
| xor(truth,Y) != xor(Y,truth)
| xor(truth,Y) = not(Y) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,Y),xor(Y,truth)) ),[1],$fot(not(Y))]]) ).
cnf(refute_0_511,plain,
( xor(truth,Y) != xor(Y,truth)
| xor(truth,Y) = not(Y) ),
inference(resolve,[$cnf( $equal(xor(Y,truth),not(Y)) )],[refute_0_509,refute_0_510]) ).
cnf(refute_0_512,plain,
xor(truth,Y) = not(Y),
inference(resolve,[$cnf( $equal(xor(truth,Y),xor(Y,truth)) )],[refute_0_301,refute_0_511]) ).
cnf(refute_0_513,plain,
xor(truth,Y) = implies(Y,falsehood),
inference(subst,[],[refute_0_280:[bind(X_85,$fot(Y))]]) ).
cnf(refute_0_514,plain,
( xor(truth,Y) != implies(Y,falsehood)
| xor(truth,Y) != not(Y)
| implies(Y,falsehood) = not(Y) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,Y),not(Y)) ),[0],$fot(implies(Y,falsehood))]]) ).
cnf(refute_0_515,plain,
( xor(truth,Y) != not(Y)
| implies(Y,falsehood) = not(Y) ),
inference(resolve,[$cnf( $equal(xor(truth,Y),implies(Y,falsehood)) )],[refute_0_513,refute_0_514]) ).
cnf(refute_0_516,plain,
implies(Y,falsehood) = not(Y),
inference(resolve,[$cnf( $equal(xor(truth,Y),not(Y)) )],[refute_0_512,refute_0_515]) ).
cnf(refute_0_517,plain,
implies(x,falsehood) = not(x),
inference(subst,[],[refute_0_516:[bind(Y,$fot(x))]]) ).
cnf(refute_0_518,plain,
and(x,implies(x,falsehood)) = and(x,implies(x,falsehood)),
introduced(tautology,[refl,[$fot(and(x,implies(x,falsehood)))]]) ).
cnf(refute_0_519,plain,
( and(x,implies(x,falsehood)) != and(x,implies(x,falsehood))
| implies(x,falsehood) != not(x)
| and(x,implies(x,falsehood)) = and(x,not(x)) ),
introduced(tautology,[equality,[$cnf( $equal(and(x,implies(x,falsehood)),and(x,implies(x,falsehood))) ),[1,1],$fot(not(x))]]) ).
cnf(refute_0_520,plain,
( implies(x,falsehood) != not(x)
| and(x,implies(x,falsehood)) = and(x,not(x)) ),
inference(resolve,[$cnf( $equal(and(x,implies(x,falsehood)),and(x,implies(x,falsehood))) )],[refute_0_518,refute_0_519]) ).
cnf(refute_0_521,plain,
and(x,implies(x,falsehood)) = and(x,not(x)),
inference(resolve,[$cnf( $equal(implies(x,falsehood),not(x)) )],[refute_0_517,refute_0_520]) ).
cnf(refute_0_522,plain,
( and(x,implies(x,falsehood)) != and(x,not(x))
| and(x,not(x)) != falsehood
| and(x,implies(x,falsehood)) = falsehood ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(x,implies(x,falsehood)))),bind(Y0,$fot(and(x,not(x)))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_523,plain,
( and(x,not(x)) != falsehood
| and(x,implies(x,falsehood)) = falsehood ),
inference(resolve,[$cnf( $equal(and(x,implies(x,falsehood)),and(x,not(x))) )],[refute_0_521,refute_0_522]) ).
cnf(refute_0_524,plain,
and(x,implies(x,falsehood)) = falsehood,
inference(resolve,[$cnf( $equal(and(x,not(x)),falsehood) )],[refute_0_300,refute_0_523]) ).
cnf(refute_0_525,plain,
( and(x,implies(x,falsehood)) != falsehood
| falsehood != falsehood
| and(x,implies(x,falsehood)) = falsehood ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(x,implies(x,falsehood)),falsehood) ),[0],$fot(falsehood)]]) ).
cnf(refute_0_526,plain,
( falsehood != falsehood
| and(x,implies(x,falsehood)) = falsehood ),
inference(resolve,[$cnf( $equal(and(x,implies(x,falsehood)),falsehood) )],[refute_0_524,refute_0_525]) ).
cnf(refute_0_527,plain,
falsehood != falsehood,
inference(resolve,[$cnf( $equal(and(x,implies(x,falsehood)),falsehood) )],[refute_0_526,refute_0_288]) ).
cnf(refute_0_528,plain,
falsehood = falsehood,
introduced(tautology,[refl,[$fot(falsehood)]]) ).
cnf(refute_0_529,plain,
$false,
inference(resolve,[$cnf( $equal(falsehood,falsehood) )],[refute_0_528,refute_0_527]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL158-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.11 % Command : metis --show proof --show saturation %s
% 0.10/0.32 % Computer : n023.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 600
% 0.10/0.32 % DateTime : Sat Jul 2 19:59:43 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.18/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.56 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.56
% 0.18/0.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.45/0.61
%------------------------------------------------------------------------------