TSTP Solution File: LCL157-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL157-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 12:50:02 EDT 2022
% Result : Unsatisfiable 0.61s 0.84s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 95
% Number of leaves : 282
% Syntax : Number of clauses : 1137 ( 561 unt; 0 nHn; 626 RR)
% Number of literals : 1978 (1977 equ; 844 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 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 : 1270 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
implies(truth,X) = X ).
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(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(x,falsehood) != 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( $equal(and(X,Y),and(Y,X)) )],[and_commutativity,refute_0_3]) ).
cnf(refute_0_5,plain,
and(x,falsehood) = and(falsehood,x),
inference(subst,[],[refute_0_4:[bind(X,$fot(falsehood)),bind(Y,$fot(x))]]) ).
cnf(refute_0_6,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$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( $equal(and_star(X,Y),not(or(not(X),not(Y)))) )],[and_star_definition,refute_0_9]) ).
cnf(refute_0_11,plain,
and_star(x,falsehood) = and(x,falsehood),
inference(subst,[],[refute_0_10:[bind(X,$fot(x)),bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_12,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_13,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_12]) ).
cnf(refute_0_14,plain,
( and(x,falsehood) != and(falsehood,x)
| and_star(x,falsehood) != and(x,falsehood)
| and_star(x,falsehood) = and(falsehood,x) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and_star(x,falsehood))),bind(Y0,$fot(and(x,falsehood))),bind(Z0,$fot(and(falsehood,x)))]]) ).
cnf(refute_0_15,plain,
( and(x,falsehood) != and(falsehood,x)
| and_star(x,falsehood) = and(falsehood,x) ),
inference(resolve,[$cnf( $equal(and_star(x,falsehood),and(x,falsehood)) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
and_star(x,falsehood) = and(falsehood,x),
inference(resolve,[$cnf( $equal(and(x,falsehood),and(falsehood,x)) )],[refute_0_5,refute_0_15]) ).
cnf(refute_0_17,plain,
( and(falsehood,x) != falsehood
| and_star(x,falsehood) != and(falsehood,x)
| and_star(x,falsehood) = falsehood ),
introduced(tautology,[equality,[$cnf( $equal(and_star(x,falsehood),and(falsehood,x)) ),[1],$fot(falsehood)]]) ).
cnf(refute_0_18,plain,
( and(falsehood,x) != falsehood
| and_star(x,falsehood) = falsehood ),
inference(resolve,[$cnf( $equal(and_star(x,falsehood),and(falsehood,x)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
and(falsehood,x) != falsehood,
inference(resolve,[$cnf( $equal(and_star(x,falsehood),falsehood) )],[refute_0_18,prove_alternative_wajsberg_axiom]) ).
cnf(refute_0_20,plain,
implies(implies(not(not(Y)),Y),Y) = implies(implies(Y,not(not(Y))),not(not(Y))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_21,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_22,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[or_definition,refute_0_21]) ).
cnf(refute_0_23,plain,
implies(not(X),not(Y)) = or(X,not(Y)),
inference(subst,[],[refute_0_22:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_24,plain,
implies(implies(not(X),not(Y)),implies(Y,X)) = implies(implies(not(X),not(Y)),implies(Y,X)),
introduced(tautology,[refl,[$fot(implies(implies(not(X),not(Y)),implies(Y,X)))]]) ).
cnf(refute_0_25,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != implies(implies(not(X),not(Y)),implies(Y,X))
| implies(not(X),not(Y)) != or(X,not(Y))
| implies(implies(not(X),not(Y)),implies(Y,X)) = implies(or(X,not(Y)),implies(Y,X)) ),
introduced(tautology,[equality,[$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_26,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( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(not(X),not(Y)),implies(Y,X))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
implies(implies(not(X),not(Y)),implies(Y,X)) = implies(or(X,not(Y)),implies(Y,X)),
inference(resolve,[$cnf( $equal(implies(not(X),not(Y)),or(X,not(Y))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != implies(or(X,not(Y)),implies(Y,X))
| implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(or(X,not(Y)),implies(Y,X)) = truth ),
introduced(tautology,[equality,[$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_29,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(or(X,not(Y)),implies(Y,X)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(or(X,not(Y)),implies(Y,X))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
implies(or(X,not(Y)),implies(Y,X)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[wajsberg_4,refute_0_29]) ).
cnf(refute_0_31,plain,
implies(or(X_42,not(X_43)),implies(X_43,X_42)) = truth,
inference(subst,[],[refute_0_30:[bind(X,$fot(X_42)),bind(Y,$fot(X_43))]]) ).
cnf(refute_0_32,plain,
or(not(X_43),X_42) = or(X_42,not(X_43)),
inference(subst,[],[or_commutativity:[bind(X,$fot(not(X_43))),bind(Y,$fot(X_42))]]) ).
cnf(refute_0_33,plain,
( or(not(X_43),X_42) != or(X_42,not(X_43))
| or(X_42,not(X_43)) = or(not(X_43),X_42) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(not(X_43),X_42))),bind(Y0,$fot(or(X_42,not(X_43))))]]) ).
cnf(refute_0_34,plain,
or(X_42,not(X_43)) = or(not(X_43),X_42),
inference(resolve,[$cnf( $equal(or(not(X_43),X_42),or(X_42,not(X_43))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( implies(or(X_42,not(X_43)),implies(X_43,X_42)) != truth
| or(X_42,not(X_43)) != or(not(X_43),X_42)
| implies(or(not(X_43),X_42),implies(X_43,X_42)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_42,not(X_43)),implies(X_43,X_42)),truth) ),[0,0],$fot(or(not(X_43),X_42))]]) ).
cnf(refute_0_36,plain,
( implies(or(X_42,not(X_43)),implies(X_43,X_42)) != truth
| implies(or(not(X_43),X_42),implies(X_43,X_42)) = truth ),
inference(resolve,[$cnf( $equal(or(X_42,not(X_43)),or(not(X_43),X_42)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
implies(or(not(X_43),X_42),implies(X_43,X_42)) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_42,not(X_43)),implies(X_43,X_42)),truth) )],[refute_0_31,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(or(not(X_53),not(not(X_53))),implies(X_53,not(not(X_53)))) = truth,
inference(subst,[],[refute_0_37:[bind(X_42,$fot(not(not(X_53)))),bind(X_43,$fot(X_53))]]) ).
cnf(refute_0_39,plain,
implies(or(falsehood,not(Y)),implies(Y,falsehood)) = truth,
inference(subst,[],[refute_0_30:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_40,plain,
or(falsehood,Y) = implies(not(falsehood),Y),
inference(subst,[],[or_definition:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_41,plain,
implies(or(X_42,not(truth)),implies(truth,X_42)) = truth,
inference(subst,[],[refute_0_30:[bind(X,$fot(X_42)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_42,plain,
implies(truth,X_42) = X_42,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_42))]]) ).
cnf(refute_0_43,plain,
( implies(or(X_42,not(truth)),implies(truth,X_42)) != truth
| implies(truth,X_42) != X_42
| implies(or(X_42,not(truth)),X_42) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_42,not(truth)),implies(truth,X_42)),truth) ),[0,1],$fot(X_42)]]) ).
cnf(refute_0_44,plain,
( implies(or(X_42,not(truth)),implies(truth,X_42)) != truth
| implies(or(X_42,not(truth)),X_42) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_42),X_42) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
implies(or(X_42,not(truth)),X_42) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_42,not(truth)),implies(truth,X_42)),truth) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
or(X_42,not(truth)) = or(X_42,not(truth)),
introduced(tautology,[refl,[$fot(or(X_42,not(truth)))]]) ).
cnf(refute_0_47,plain,
( not(truth) != falsehood
| or(X_42,not(truth)) != or(X_42,not(truth))
| or(X_42,not(truth)) = or(X_42,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_42,not(truth)),or(X_42,not(truth))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_48,plain,
( not(truth) != falsehood
| or(X_42,not(truth)) = or(X_42,falsehood) ),
inference(resolve,[$cnf( $equal(or(X_42,not(truth)),or(X_42,not(truth))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
or(X_42,not(truth)) = or(X_42,falsehood),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_48]) ).
cnf(refute_0_50,plain,
implies(or(X_42,not(truth)),X_42) = implies(or(X_42,not(truth)),X_42),
introduced(tautology,[refl,[$fot(implies(or(X_42,not(truth)),X_42))]]) ).
cnf(refute_0_51,plain,
( implies(or(X_42,not(truth)),X_42) != implies(or(X_42,not(truth)),X_42)
| or(X_42,not(truth)) != or(X_42,falsehood)
| implies(or(X_42,not(truth)),X_42) = implies(or(X_42,falsehood),X_42) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_42,not(truth)),X_42),implies(or(X_42,not(truth)),X_42)) ),[1,0],$fot(or(X_42,falsehood))]]) ).
cnf(refute_0_52,plain,
( or(X_42,not(truth)) != or(X_42,falsehood)
| implies(or(X_42,not(truth)),X_42) = implies(or(X_42,falsehood),X_42) ),
inference(resolve,[$cnf( $equal(implies(or(X_42,not(truth)),X_42),implies(or(X_42,not(truth)),X_42)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
implies(or(X_42,not(truth)),X_42) = implies(or(X_42,falsehood),X_42),
inference(resolve,[$cnf( $equal(or(X_42,not(truth)),or(X_42,falsehood)) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
( implies(or(X_42,not(truth)),X_42) != implies(or(X_42,falsehood),X_42)
| implies(or(X_42,not(truth)),X_42) != truth
| implies(or(X_42,falsehood),X_42) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_42,not(truth)),X_42),truth) ),[0],$fot(implies(or(X_42,falsehood),X_42))]]) ).
cnf(refute_0_55,plain,
( implies(or(X_42,not(truth)),X_42) != truth
| implies(or(X_42,falsehood),X_42) = truth ),
inference(resolve,[$cnf( $equal(implies(or(X_42,not(truth)),X_42),implies(or(X_42,falsehood),X_42)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
implies(or(X_42,falsehood),X_42) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_42,not(truth)),X_42),truth) )],[refute_0_45,refute_0_55]) ).
cnf(refute_0_57,plain,
implies(or(X_44,falsehood),X_44) = truth,
inference(subst,[],[refute_0_56:[bind(X_42,$fot(X_44))]]) ).
cnf(refute_0_58,plain,
or(falsehood,X_44) = or(X_44,falsehood),
inference(subst,[],[or_commutativity:[bind(X,$fot(falsehood)),bind(Y,$fot(X_44))]]) ).
cnf(refute_0_59,plain,
( or(falsehood,X_44) != or(X_44,falsehood)
| or(X_44,falsehood) = or(falsehood,X_44) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(falsehood,X_44))),bind(Y0,$fot(or(X_44,falsehood)))]]) ).
cnf(refute_0_60,plain,
or(X_44,falsehood) = or(falsehood,X_44),
inference(resolve,[$cnf( $equal(or(falsehood,X_44),or(X_44,falsehood)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( implies(or(X_44,falsehood),X_44) != truth
| or(X_44,falsehood) != or(falsehood,X_44)
| implies(or(falsehood,X_44),X_44) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_44,falsehood),X_44),truth) ),[0,0],$fot(or(falsehood,X_44))]]) ).
cnf(refute_0_62,plain,
( implies(or(X_44,falsehood),X_44) != truth
| implies(or(falsehood,X_44),X_44) = truth ),
inference(resolve,[$cnf( $equal(or(X_44,falsehood),or(falsehood,X_44)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
implies(or(falsehood,X_44),X_44) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_44,falsehood),X_44),truth) )],[refute_0_57,refute_0_62]) ).
cnf(refute_0_64,plain,
implies(or(falsehood,not(falsehood)),not(falsehood)) = truth,
inference(subst,[],[refute_0_63:[bind(X_44,$fot(not(falsehood)))]]) ).
cnf(refute_0_65,plain,
implies(or(truth,falsehood),truth) = truth,
inference(subst,[],[refute_0_56:[bind(X_42,$fot(truth))]]) ).
cnf(refute_0_66,plain,
or(truth,X_8) = implies(not(truth),X_8),
inference(subst,[],[or_definition:[bind(X,$fot(truth)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_67,plain,
( not(truth) != falsehood
| or(truth,X_8) != implies(not(truth),X_8)
| or(truth,X_8) = implies(falsehood,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(truth,X_8),implies(not(truth),X_8)) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_68,plain,
( or(truth,X_8) != implies(not(truth),X_8)
| or(truth,X_8) = implies(falsehood,X_8) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_67]) ).
cnf(refute_0_69,plain,
or(truth,X_8) = implies(falsehood,X_8),
inference(resolve,[$cnf( $equal(or(truth,X_8),implies(not(truth),X_8)) )],[refute_0_66,refute_0_68]) ).
cnf(refute_0_70,plain,
or(truth,falsehood) = implies(falsehood,falsehood),
inference(subst,[],[refute_0_69:[bind(X_8,$fot(falsehood))]]) ).
cnf(refute_0_71,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_72,plain,
( implies(or(truth,falsehood),truth) != truth
| implies(implies(falsehood,falsehood),truth) = truth ),
inference(resolve,[$cnf( $equal(or(truth,falsehood),implies(falsehood,falsehood)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
implies(implies(falsehood,falsehood),truth) = truth,
inference(resolve,[$cnf( $equal(implies(or(truth,falsehood),truth),truth) )],[refute_0_65,refute_0_72]) ).
cnf(refute_0_74,plain,
or(X,not(X)) = implies(not(X),not(X)),
inference(subst,[],[or_definition:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_75,plain,
implies(implies(truth,X_23),X_23) = implies(implies(X_23,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_23))]]) ).
cnf(refute_0_76,plain,
implies(truth,X_23) = X_23,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_23))]]) ).
cnf(refute_0_77,plain,
( implies(implies(truth,X_23),X_23) != implies(implies(X_23,truth),truth)
| implies(truth,X_23) != X_23
| implies(X_23,X_23) = implies(implies(X_23,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_23),X_23),implies(implies(X_23,truth),truth)) ),[0,0],$fot(X_23)]]) ).
cnf(refute_0_78,plain,
( implies(implies(truth,X_23),X_23) != implies(implies(X_23,truth),truth)
| implies(X_23,X_23) = implies(implies(X_23,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(truth,X_23),X_23) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
implies(X_23,X_23) = implies(implies(X_23,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_23),X_23),implies(implies(X_23,truth),truth)) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
implies(not(X),not(X)) = implies(implies(not(X),truth),truth),
inference(subst,[],[refute_0_79:[bind(X_23,$fot(not(X)))]]) ).
cnf(refute_0_81,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_82,plain,
( or(X,not(X)) != implies(not(X),not(X))
| or(X,not(X)) = implies(implies(not(X),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X)),implies(implies(not(X),truth),truth)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
or(X,not(X)) = implies(implies(not(X),truth),truth),
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(not(X),not(X))) )],[refute_0_74,refute_0_82]) ).
cnf(refute_0_84,plain,
or(truth,X_8) = or(X_8,truth),
inference(subst,[],[or_commutativity:[bind(X,$fot(truth)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_85,plain,
( or(truth,X_8) != implies(falsehood,X_8)
| or(truth,X_8) != or(X_8,truth)
| or(X_8,truth) = implies(falsehood,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(truth,X_8),implies(falsehood,X_8)) ),[0],$fot(or(X_8,truth))]]) ).
cnf(refute_0_86,plain,
( or(truth,X_8) != implies(falsehood,X_8)
| or(X_8,truth) = implies(falsehood,X_8) ),
inference(resolve,[$cnf( $equal(or(truth,X_8),or(X_8,truth)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
or(X_8,truth) = implies(falsehood,X_8),
inference(resolve,[$cnf( $equal(or(truth,X_8),implies(falsehood,X_8)) )],[refute_0_69,refute_0_86]) ).
cnf(refute_0_88,plain,
or(X,truth) = implies(falsehood,X),
inference(subst,[],[refute_0_87:[bind(X_8,$fot(X))]]) ).
cnf(refute_0_89,plain,
implies(not(X),truth) = or(X,truth),
inference(subst,[],[refute_0_22:[bind(Y,$fot(truth))]]) ).
cnf(refute_0_90,plain,
( implies(not(X),truth) != or(X,truth)
| or(X,truth) != implies(falsehood,X)
| implies(not(X),truth) = implies(falsehood,X) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(not(X),truth))),bind(Y0,$fot(or(X,truth))),bind(Z0,$fot(implies(falsehood,X)))]]) ).
cnf(refute_0_91,plain,
( or(X,truth) != implies(falsehood,X)
| implies(not(X),truth) = implies(falsehood,X) ),
inference(resolve,[$cnf( $equal(implies(not(X),truth),or(X,truth)) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
implies(not(X),truth) = implies(falsehood,X),
inference(resolve,[$cnf( $equal(or(X,truth),implies(falsehood,X)) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
implies(implies(not(X),truth),truth) = implies(implies(not(X),truth),truth),
introduced(tautology,[refl,[$fot(implies(implies(not(X),truth),truth))]]) ).
cnf(refute_0_94,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_95,plain,
( implies(not(X),truth) != implies(falsehood,X)
| implies(implies(not(X),truth),truth) = implies(implies(falsehood,X),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),truth),implies(implies(not(X),truth),truth)) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
implies(implies(not(X),truth),truth) = implies(implies(falsehood,X),truth),
inference(resolve,[$cnf( $equal(implies(not(X),truth),implies(falsehood,X)) )],[refute_0_92,refute_0_95]) ).
cnf(refute_0_97,plain,
( implies(implies(not(X),truth),truth) != implies(implies(falsehood,X),truth)
| or(X,not(X)) != implies(implies(not(X),truth),truth)
| or(X,not(X)) = implies(implies(falsehood,X),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(X)),implies(implies(not(X),truth),truth)) ),[1],$fot(implies(implies(falsehood,X),truth))]]) ).
cnf(refute_0_98,plain,
( or(X,not(X)) != implies(implies(not(X),truth),truth)
| or(X,not(X)) = implies(implies(falsehood,X),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),truth),implies(implies(falsehood,X),truth)) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
or(X,not(X)) = implies(implies(falsehood,X),truth),
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(implies(not(X),truth),truth)) )],[refute_0_83,refute_0_98]) ).
cnf(refute_0_100,plain,
( or(X,not(X)) != implies(implies(falsehood,X),truth)
| implies(implies(falsehood,X),truth) = or(X,not(X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,not(X)))),bind(Y0,$fot(implies(implies(falsehood,X),truth)))]]) ).
cnf(refute_0_101,plain,
implies(implies(falsehood,X),truth) = or(X,not(X)),
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(implies(falsehood,X),truth)) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
implies(implies(falsehood,falsehood),truth) = or(falsehood,not(falsehood)),
inference(subst,[],[refute_0_101:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_103,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_104,plain,
( implies(implies(falsehood,falsehood),truth) != truth
| or(falsehood,not(falsehood)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,falsehood),truth),or(falsehood,not(falsehood))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
or(falsehood,not(falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,falsehood),truth),truth) )],[refute_0_73,refute_0_104]) ).
cnf(refute_0_106,plain,
( implies(or(falsehood,not(falsehood)),not(falsehood)) != truth
| or(falsehood,not(falsehood)) != truth
| implies(truth,not(falsehood)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,not(falsehood)),not(falsehood)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_107,plain,
( implies(or(falsehood,not(falsehood)),not(falsehood)) != truth
| implies(truth,not(falsehood)) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,not(falsehood)),truth) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
implies(truth,not(falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,not(falsehood)),not(falsehood)),truth) )],[refute_0_64,refute_0_107]) ).
cnf(refute_0_109,plain,
implies(truth,not(falsehood)) = not(falsehood),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(falsehood)))]]) ).
cnf(refute_0_110,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_111,plain,
( implies(truth,not(falsehood)) != truth
| not(falsehood) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,not(falsehood)),not(falsehood)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
not(falsehood) = truth,
inference(resolve,[$cnf( $equal(implies(truth,not(falsehood)),truth) )],[refute_0_108,refute_0_111]) ).
cnf(refute_0_113,plain,
( not(falsehood) != truth
| or(falsehood,Y) != implies(not(falsehood),Y)
| or(falsehood,Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,Y),implies(not(falsehood),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_114,plain,
( or(falsehood,Y) != implies(not(falsehood),Y)
| or(falsehood,Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
or(falsehood,Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(or(falsehood,Y),implies(not(falsehood),Y)) )],[refute_0_40,refute_0_114]) ).
cnf(refute_0_116,plain,
implies(truth,Y) = Y,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_117,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_118,plain,
( or(falsehood,Y) != implies(truth,Y)
| or(falsehood,Y) = Y ),
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
or(falsehood,Y) = Y,
inference(resolve,[$cnf( $equal(or(falsehood,Y),implies(truth,Y)) )],[refute_0_115,refute_0_118]) ).
cnf(refute_0_120,plain,
or(falsehood,not(Y)) = not(Y),
inference(subst,[],[refute_0_119:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_121,plain,
( implies(or(falsehood,not(Y)),implies(Y,falsehood)) != truth
| or(falsehood,not(Y)) != not(Y)
| implies(not(Y),implies(Y,falsehood)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,not(Y)),implies(Y,falsehood)),truth) ),[0,0],$fot(not(Y))]]) ).
cnf(refute_0_122,plain,
( implies(or(falsehood,not(Y)),implies(Y,falsehood)) != truth
| implies(not(Y),implies(Y,falsehood)) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,not(Y)),not(Y)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
implies(not(Y),implies(Y,falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,not(Y)),implies(Y,falsehood)),truth) )],[refute_0_39,refute_0_122]) ).
cnf(refute_0_124,plain,
implies(not(Y),implies(Y,falsehood)) = or(Y,implies(Y,falsehood)),
inference(subst,[],[refute_0_22:[bind(X,$fot(Y)),bind(Y,$fot(implies(Y,falsehood)))]]) ).
cnf(refute_0_125,plain,
( implies(not(Y),implies(Y,falsehood)) != or(Y,implies(Y,falsehood))
| implies(not(Y),implies(Y,falsehood)) != truth
| or(Y,implies(Y,falsehood)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(Y),implies(Y,falsehood)),truth) ),[0],$fot(or(Y,implies(Y,falsehood)))]]) ).
cnf(refute_0_126,plain,
( implies(not(Y),implies(Y,falsehood)) != truth
| or(Y,implies(Y,falsehood)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(Y),implies(Y,falsehood)),or(Y,implies(Y,falsehood))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
or(Y,implies(Y,falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(not(Y),implies(Y,falsehood)),truth) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
or(not(X),implies(not(X),falsehood)) = truth,
inference(subst,[],[refute_0_127:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_129,plain,
or(X,falsehood) = implies(not(X),falsehood),
inference(subst,[],[or_definition:[bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_130,plain,
( or(X,falsehood) != implies(not(X),falsehood)
| implies(not(X),falsehood) = or(X,falsehood) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,falsehood))),bind(Y0,$fot(implies(not(X),falsehood)))]]) ).
cnf(refute_0_131,plain,
implies(not(X),falsehood) = or(X,falsehood),
inference(resolve,[$cnf( $equal(or(X,falsehood),implies(not(X),falsehood)) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
( implies(not(X),falsehood) != or(X,falsehood)
| or(not(X),implies(not(X),falsehood)) != truth
| or(not(X),or(X,falsehood)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X),implies(not(X),falsehood)),truth) ),[0,1],$fot(or(X,falsehood))]]) ).
cnf(refute_0_133,plain,
( or(not(X),implies(not(X),falsehood)) != truth
| or(not(X),or(X,falsehood)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X),falsehood),or(X,falsehood)) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
or(not(X),or(X,falsehood)) = truth,
inference(resolve,[$cnf( $equal(or(not(X),implies(not(X),falsehood)),truth) )],[refute_0_128,refute_0_133]) ).
cnf(refute_0_135,plain,
or(X_36,not(X_35)) = or(not(X_35),X_36),
inference(subst,[],[or_commutativity:[bind(X,$fot(X_36)),bind(Y,$fot(not(X_35)))]]) ).
cnf(refute_0_136,plain,
( or(X_36,not(X_35)) != or(not(X_35),X_36)
| or(not(X_35),X_36) = or(X_36,not(X_35)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X_36,not(X_35)))),bind(Y0,$fot(or(not(X_35),X_36)))]]) ).
cnf(refute_0_137,plain,
or(not(X_35),X_36) = or(X_36,not(X_35)),
inference(resolve,[$cnf( $equal(or(X_36,not(X_35)),or(not(X_35),X_36)) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
or(not(X),X) = or(X,not(X)),
inference(subst,[],[refute_0_137:[bind(X_35,$fot(X)),bind(X_36,$fot(X))]]) ).
cnf(refute_0_139,plain,
or(or(falsehood,falsehood),X_8) = implies(not(or(falsehood,falsehood)),X_8),
inference(subst,[],[or_definition:[bind(X,$fot(or(falsehood,falsehood))),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_140,plain,
and(X_1,truth) = not(or(not(X_1),not(truth))),
inference(subst,[],[and_definition:[bind(X,$fot(X_1)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_141,plain,
( and(X_1,truth) != not(or(not(X_1),not(truth)))
| not(truth) != falsehood
| and(X_1,truth) = not(or(not(X_1),falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_1,truth),not(or(not(X_1),not(truth)))) ),[1,0,1],$fot(falsehood)]]) ).
cnf(refute_0_142,plain,
( and(X_1,truth) != not(or(not(X_1),not(truth)))
| and(X_1,truth) = not(or(not(X_1),falsehood)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_141]) ).
cnf(refute_0_143,plain,
and(X_1,truth) = not(or(not(X_1),falsehood)),
inference(resolve,[$cnf( $equal(and(X_1,truth),not(or(not(X_1),not(truth)))) )],[refute_0_140,refute_0_142]) ).
cnf(refute_0_144,plain,
( or(X,Y) != or(Y,X)
| or(Y,X) = or(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(or(Y,X)))]]) ).
cnf(refute_0_145,plain,
or(Y,X) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),or(Y,X)) )],[or_commutativity,refute_0_144]) ).
cnf(refute_0_146,plain,
or(not(X_1),falsehood) = or(falsehood,not(X_1)),
inference(subst,[],[refute_0_145:[bind(X,$fot(falsehood)),bind(Y,$fot(not(X_1)))]]) ).
cnf(refute_0_147,plain,
not(or(not(X_1),falsehood)) = not(or(not(X_1),falsehood)),
introduced(tautology,[refl,[$fot(not(or(not(X_1),falsehood)))]]) ).
cnf(refute_0_148,plain,
( not(or(not(X_1),falsehood)) != not(or(not(X_1),falsehood))
| or(not(X_1),falsehood) != or(falsehood,not(X_1))
| not(or(not(X_1),falsehood)) = not(or(falsehood,not(X_1))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X_1),falsehood)),not(or(not(X_1),falsehood))) ),[1,0],$fot(or(falsehood,not(X_1)))]]) ).
cnf(refute_0_149,plain,
( or(not(X_1),falsehood) != or(falsehood,not(X_1))
| not(or(not(X_1),falsehood)) = not(or(falsehood,not(X_1))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_1),falsehood)),not(or(not(X_1),falsehood))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
not(or(not(X_1),falsehood)) = not(or(falsehood,not(X_1))),
inference(resolve,[$cnf( $equal(or(not(X_1),falsehood),or(falsehood,not(X_1))) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
( and(X_1,truth) != not(or(not(X_1),falsehood))
| not(or(not(X_1),falsehood)) != not(or(falsehood,not(X_1)))
| and(X_1,truth) = not(or(falsehood,not(X_1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_1,truth),not(or(falsehood,not(X_1)))) ),[0],$fot(not(or(not(X_1),falsehood)))]]) ).
cnf(refute_0_152,plain,
( and(X_1,truth) != not(or(not(X_1),falsehood))
| and(X_1,truth) = not(or(falsehood,not(X_1))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_1),falsehood)),not(or(falsehood,not(X_1)))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
and(X_1,truth) = not(or(falsehood,not(X_1))),
inference(resolve,[$cnf( $equal(and(X_1,truth),not(or(not(X_1),falsehood))) )],[refute_0_143,refute_0_152]) ).
cnf(refute_0_154,plain,
and(truth,truth) = not(or(falsehood,not(truth))),
inference(subst,[],[refute_0_153:[bind(X_1,$fot(truth))]]) ).
cnf(refute_0_155,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_156,plain,
( and(truth,truth) != not(or(falsehood,not(truth)))
| and(truth,truth) = not(or(falsehood,falsehood)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_155]) ).
cnf(refute_0_157,plain,
and(truth,truth) = not(or(falsehood,falsehood)),
inference(resolve,[$cnf( $equal(and(truth,truth),not(or(falsehood,not(truth)))) )],[refute_0_154,refute_0_156]) ).
cnf(refute_0_158,plain,
( and(truth,truth) != not(or(falsehood,falsehood))
| not(or(falsehood,falsehood)) = and(truth,truth) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,truth))),bind(Y0,$fot(not(or(falsehood,falsehood))))]]) ).
cnf(refute_0_159,plain,
not(or(falsehood,falsehood)) = and(truth,truth),
inference(resolve,[$cnf( $equal(and(truth,truth),not(or(falsehood,falsehood))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
( not(or(falsehood,falsehood)) != and(truth,truth)
| or(or(falsehood,falsehood),X_8) != implies(not(or(falsehood,falsehood)),X_8)
| or(or(falsehood,falsehood),X_8) = implies(and(truth,truth),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(falsehood,falsehood),X_8),implies(not(or(falsehood,falsehood)),X_8)) ),[1,0],$fot(and(truth,truth))]]) ).
cnf(refute_0_161,plain,
( or(or(falsehood,falsehood),X_8) != implies(not(or(falsehood,falsehood)),X_8)
| or(or(falsehood,falsehood),X_8) = implies(and(truth,truth),X_8) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,falsehood)),and(truth,truth)) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
or(or(falsehood,falsehood),X_8) = implies(and(truth,truth),X_8),
inference(resolve,[$cnf( $equal(or(or(falsehood,falsehood),X_8),implies(not(or(falsehood,falsehood)),X_8)) )],[refute_0_139,refute_0_161]) ).
cnf(refute_0_163,plain,
or(or(falsehood,falsehood),X_8) = or(falsehood,or(falsehood,X_8)),
inference(subst,[],[or_associativity:[bind(X,$fot(falsehood)),bind(Y,$fot(falsehood)),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_164,plain,
( or(or(falsehood,falsehood),X_8) != implies(and(truth,truth),X_8)
| or(or(falsehood,falsehood),X_8) != or(falsehood,or(falsehood,X_8))
| or(falsehood,or(falsehood,X_8)) = implies(and(truth,truth),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(falsehood,falsehood),X_8),implies(and(truth,truth),X_8)) ),[0],$fot(or(falsehood,or(falsehood,X_8)))]]) ).
cnf(refute_0_165,plain,
( or(or(falsehood,falsehood),X_8) != implies(and(truth,truth),X_8)
| or(falsehood,or(falsehood,X_8)) = implies(and(truth,truth),X_8) ),
inference(resolve,[$cnf( $equal(or(or(falsehood,falsehood),X_8),or(falsehood,or(falsehood,X_8))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
or(falsehood,or(falsehood,X_8)) = implies(and(truth,truth),X_8),
inference(resolve,[$cnf( $equal(or(or(falsehood,falsehood),X_8),implies(and(truth,truth),X_8)) )],[refute_0_162,refute_0_165]) ).
cnf(refute_0_167,plain,
or(falsehood,X_8) = or(X_8,falsehood),
inference(subst,[],[or_commutativity:[bind(X,$fot(falsehood)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_168,plain,
( or(falsehood,X_8) != or(X_8,falsehood)
| or(falsehood,or(falsehood,X_8)) != implies(and(truth,truth),X_8)
| or(falsehood,or(X_8,falsehood)) = implies(and(truth,truth),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(falsehood,X_8)),implies(and(truth,truth),X_8)) ),[0,1],$fot(or(X_8,falsehood))]]) ).
cnf(refute_0_169,plain,
( or(falsehood,or(falsehood,X_8)) != implies(and(truth,truth),X_8)
| or(falsehood,or(X_8,falsehood)) = implies(and(truth,truth),X_8) ),
inference(resolve,[$cnf( $equal(or(falsehood,X_8),or(X_8,falsehood)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
or(falsehood,or(X_8,falsehood)) = implies(and(truth,truth),X_8),
inference(resolve,[$cnf( $equal(or(falsehood,or(falsehood,X_8)),implies(and(truth,truth),X_8)) )],[refute_0_166,refute_0_169]) ).
cnf(refute_0_171,plain,
or(falsehood,or(X_8,falsehood)) = or(X_8,falsehood),
inference(subst,[],[refute_0_119:[bind(Y,$fot(or(X_8,falsehood)))]]) ).
cnf(refute_0_172,plain,
( or(falsehood,or(X_8,falsehood)) != implies(and(truth,truth),X_8)
| or(falsehood,or(X_8,falsehood)) != or(X_8,falsehood)
| or(X_8,falsehood) = implies(and(truth,truth),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(X_8,falsehood)),implies(and(truth,truth),X_8)) ),[0],$fot(or(X_8,falsehood))]]) ).
cnf(refute_0_173,plain,
( or(falsehood,or(X_8,falsehood)) != implies(and(truth,truth),X_8)
| or(X_8,falsehood) = implies(and(truth,truth),X_8) ),
inference(resolve,[$cnf( $equal(or(falsehood,or(X_8,falsehood)),or(X_8,falsehood)) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
implies(truth,X_8) = X_8,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_8))]]) ).
cnf(refute_0_175,plain,
not(not(truth)) = not(not(truth)),
introduced(tautology,[refl,[$fot(not(not(truth)))]]) ).
cnf(refute_0_176,plain,
( not(not(truth)) != not(not(truth))
| not(truth) != falsehood
| not(not(truth)) = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(truth)),not(not(truth))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_177,plain,
( not(truth) != falsehood
| not(not(truth)) = not(falsehood) ),
inference(resolve,[$cnf( $equal(not(not(truth)),not(not(truth))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
not(not(truth)) = not(falsehood),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_177]) ).
cnf(refute_0_179,plain,
( not(falsehood) != truth
| not(not(truth)) != not(falsehood)
| not(not(truth)) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(not(truth)))),bind(Y0,$fot(not(falsehood))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_180,plain,
( not(falsehood) != truth
| not(not(truth)) = truth ),
inference(resolve,[$cnf( $equal(not(not(truth)),not(falsehood)) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
not(not(truth)) = truth,
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_112,refute_0_180]) ).
cnf(refute_0_182,plain,
or(falsehood,not(X_1)) = not(X_1),
inference(subst,[],[refute_0_119:[bind(Y,$fot(not(X_1)))]]) ).
cnf(refute_0_183,plain,
not(or(falsehood,not(X_1))) = not(or(falsehood,not(X_1))),
introduced(tautology,[refl,[$fot(not(or(falsehood,not(X_1))))]]) ).
cnf(refute_0_184,plain,
( not(or(falsehood,not(X_1))) != not(or(falsehood,not(X_1)))
| or(falsehood,not(X_1)) != not(X_1)
| not(or(falsehood,not(X_1))) = not(not(X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,not(X_1))),not(or(falsehood,not(X_1)))) ),[1,0],$fot(not(X_1))]]) ).
cnf(refute_0_185,plain,
( or(falsehood,not(X_1)) != not(X_1)
| not(or(falsehood,not(X_1))) = not(not(X_1)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_1))),not(or(falsehood,not(X_1)))) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
not(or(falsehood,not(X_1))) = not(not(X_1)),
inference(resolve,[$cnf( $equal(or(falsehood,not(X_1)),not(X_1)) )],[refute_0_182,refute_0_185]) ).
cnf(refute_0_187,plain,
( and(X_1,truth) != not(or(falsehood,not(X_1)))
| not(or(falsehood,not(X_1))) != not(not(X_1))
| and(X_1,truth) = not(not(X_1)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_1,truth),not(not(X_1))) ),[0],$fot(not(or(falsehood,not(X_1))))]]) ).
cnf(refute_0_188,plain,
( and(X_1,truth) != not(or(falsehood,not(X_1)))
| and(X_1,truth) = not(not(X_1)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_1))),not(not(X_1))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
and(X_1,truth) = not(not(X_1)),
inference(resolve,[$cnf( $equal(and(X_1,truth),not(or(falsehood,not(X_1)))) )],[refute_0_153,refute_0_188]) ).
cnf(refute_0_190,plain,
and(truth,truth) = not(not(truth)),
inference(subst,[],[refute_0_189:[bind(X_1,$fot(truth))]]) ).
cnf(refute_0_191,plain,
( and(truth,truth) != not(not(truth))
| not(not(truth)) != truth
| and(truth,truth) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(truth,truth))),bind(Y0,$fot(not(not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_192,plain,
( not(not(truth)) != truth
| and(truth,truth) = truth ),
inference(resolve,[$cnf( $equal(and(truth,truth),not(not(truth))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
and(truth,truth) = truth,
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_181,refute_0_192]) ).
cnf(refute_0_194,plain,
implies(and(truth,truth),X_8) = implies(and(truth,truth),X_8),
introduced(tautology,[refl,[$fot(implies(and(truth,truth),X_8))]]) ).
cnf(refute_0_195,plain,
( and(truth,truth) != truth
| implies(and(truth,truth),X_8) != implies(and(truth,truth),X_8)
| implies(and(truth,truth),X_8) = implies(truth,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(truth,truth),X_8),implies(and(truth,truth),X_8)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_196,plain,
( and(truth,truth) != truth
| implies(and(truth,truth),X_8) = implies(truth,X_8) ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),X_8),implies(and(truth,truth),X_8)) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
implies(and(truth,truth),X_8) = implies(truth,X_8),
inference(resolve,[$cnf( $equal(and(truth,truth),truth) )],[refute_0_193,refute_0_196]) ).
cnf(refute_0_198,plain,
( implies(and(truth,truth),X_8) != implies(truth,X_8)
| implies(truth,X_8) != X_8
| implies(and(truth,truth),X_8) = X_8 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(and(truth,truth),X_8))),bind(Y0,$fot(implies(truth,X_8))),bind(Z0,$fot(X_8))]]) ).
cnf(refute_0_199,plain,
( implies(truth,X_8) != X_8
| implies(and(truth,truth),X_8) = X_8 ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),X_8),implies(truth,X_8)) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
implies(and(truth,truth),X_8) = X_8,
inference(resolve,[$cnf( $equal(implies(truth,X_8),X_8) )],[refute_0_174,refute_0_199]) ).
cnf(refute_0_201,plain,
( implies(and(truth,truth),X_8) != X_8
| or(X_8,falsehood) != implies(and(truth,truth),X_8)
| or(X_8,falsehood) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(or(X_8,falsehood),implies(and(truth,truth),X_8)) ),[1],$fot(X_8)]]) ).
cnf(refute_0_202,plain,
( or(X_8,falsehood) != implies(and(truth,truth),X_8)
| or(X_8,falsehood) = X_8 ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),X_8),X_8) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
( or(falsehood,or(X_8,falsehood)) != implies(and(truth,truth),X_8)
| or(X_8,falsehood) = X_8 ),
inference(resolve,[$cnf( $equal(or(X_8,falsehood),implies(and(truth,truth),X_8)) )],[refute_0_173,refute_0_202]) ).
cnf(refute_0_204,plain,
or(X_8,falsehood) = X_8,
inference(resolve,[$cnf( $equal(or(falsehood,or(X_8,falsehood)),implies(and(truth,truth),X_8)) )],[refute_0_170,refute_0_203]) ).
cnf(refute_0_205,plain,
or(X,falsehood) = X,
inference(subst,[],[refute_0_204:[bind(X_8,$fot(X))]]) ).
cnf(refute_0_206,plain,
or(not(X),or(X,falsehood)) = or(not(X),or(X,falsehood)),
introduced(tautology,[refl,[$fot(or(not(X),or(X,falsehood)))]]) ).
cnf(refute_0_207,plain,
( or(X,falsehood) != X
| or(not(X),or(X,falsehood)) != or(not(X),or(X,falsehood))
| or(not(X),or(X,falsehood)) = or(not(X),X) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X),or(X,falsehood)),or(not(X),or(X,falsehood))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_208,plain,
( or(X,falsehood) != X
| or(not(X),or(X,falsehood)) = or(not(X),X) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X,falsehood)),or(not(X),or(X,falsehood))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
or(not(X),or(X,falsehood)) = or(not(X),X),
inference(resolve,[$cnf( $equal(or(X,falsehood),X) )],[refute_0_205,refute_0_208]) ).
cnf(refute_0_210,plain,
( or(not(X),X) != or(X,not(X))
| or(not(X),or(X,falsehood)) != or(not(X),X)
| or(not(X),or(X,falsehood)) = or(X,not(X)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(not(X),or(X,falsehood)))),bind(Y0,$fot(or(not(X),X))),bind(Z0,$fot(or(X,not(X))))]]) ).
cnf(refute_0_211,plain,
( or(not(X),X) != or(X,not(X))
| or(not(X),or(X,falsehood)) = or(X,not(X)) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X,falsehood)),or(not(X),X)) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
or(not(X),or(X,falsehood)) = or(X,not(X)),
inference(resolve,[$cnf( $equal(or(not(X),X),or(X,not(X))) )],[refute_0_138,refute_0_211]) ).
cnf(refute_0_213,plain,
( or(not(X),or(X,falsehood)) != or(X,not(X))
| or(not(X),or(X,falsehood)) != truth
| or(X,not(X)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X),or(X,falsehood)),truth) ),[0],$fot(or(X,not(X)))]]) ).
cnf(refute_0_214,plain,
( or(not(X),or(X,falsehood)) != truth
| or(X,not(X)) = truth ),
inference(resolve,[$cnf( $equal(or(not(X),or(X,falsehood)),or(X,not(X))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
or(X,not(X)) = truth,
inference(resolve,[$cnf( $equal(or(not(X),or(X,falsehood)),truth) )],[refute_0_134,refute_0_214]) ).
cnf(refute_0_216,plain,
or(not(X_53),not(not(X_53))) = truth,
inference(subst,[],[refute_0_215:[bind(X,$fot(not(X_53)))]]) ).
cnf(refute_0_217,plain,
( implies(or(not(X_53),not(not(X_53))),implies(X_53,not(not(X_53)))) != truth
| or(not(X_53),not(not(X_53))) != truth
| implies(truth,implies(X_53,not(not(X_53)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X_53),not(not(X_53))),implies(X_53,not(not(X_53)))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_218,plain,
( implies(or(not(X_53),not(not(X_53))),implies(X_53,not(not(X_53)))) != truth
| implies(truth,implies(X_53,not(not(X_53)))) = truth ),
inference(resolve,[$cnf( $equal(or(not(X_53),not(not(X_53))),truth) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
implies(truth,implies(X_53,not(not(X_53)))) = truth,
inference(resolve,[$cnf( $equal(implies(or(not(X_53),not(not(X_53))),implies(X_53,not(not(X_53)))),truth) )],[refute_0_38,refute_0_218]) ).
cnf(refute_0_220,plain,
implies(truth,implies(X_53,not(not(X_53)))) = implies(X_53,not(not(X_53))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_53,not(not(X_53)))))]]) ).
cnf(refute_0_221,plain,
( implies(truth,implies(X_53,not(not(X_53)))) != implies(X_53,not(not(X_53)))
| implies(truth,implies(X_53,not(not(X_53)))) != truth
| implies(X_53,not(not(X_53))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(X_53,not(not(X_53)))),truth) ),[0],$fot(implies(X_53,not(not(X_53))))]]) ).
cnf(refute_0_222,plain,
( implies(truth,implies(X_53,not(not(X_53)))) != truth
| implies(X_53,not(not(X_53))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_53,not(not(X_53)))),implies(X_53,not(not(X_53)))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
implies(X_53,not(not(X_53))) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(X_53,not(not(X_53)))),truth) )],[refute_0_219,refute_0_222]) ).
cnf(refute_0_224,plain,
implies(Y,not(not(Y))) = truth,
inference(subst,[],[refute_0_223:[bind(X_53,$fot(Y))]]) ).
cnf(refute_0_225,plain,
( implies(Y,not(not(Y))) != truth
| implies(implies(not(not(Y)),Y),Y) != implies(implies(Y,not(not(Y))),not(not(Y)))
| implies(implies(not(not(Y)),Y),Y) = implies(truth,not(not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(Y,not(not(Y))),not(not(Y)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_226,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(implies(Y,not(not(Y))),not(not(Y)))
| implies(implies(not(not(Y)),Y),Y) = implies(truth,not(not(Y))) ),
inference(resolve,[$cnf( $equal(implies(Y,not(not(Y))),truth) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
implies(implies(not(not(Y)),Y),Y) = implies(truth,not(not(Y))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(Y,not(not(Y))),not(not(Y)))) )],[refute_0_20,refute_0_226]) ).
cnf(refute_0_228,plain,
or(Y,not(Y)) = truth,
inference(subst,[],[refute_0_215:[bind(X,$fot(Y))]]) ).
cnf(refute_0_229,plain,
or(not(Y),Y) = or(Y,not(Y)),
inference(subst,[],[refute_0_137:[bind(X_35,$fot(Y)),bind(X_36,$fot(Y))]]) ).
cnf(refute_0_230,plain,
( or(Y,not(Y)) != truth
| or(not(Y),Y) != or(Y,not(Y))
| or(not(Y),Y) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(not(Y),Y))),bind(Y0,$fot(or(Y,not(Y)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_231,plain,
( or(Y,not(Y)) != truth
| or(not(Y),Y) = truth ),
inference(resolve,[$cnf( $equal(or(not(Y),Y),or(Y,not(Y))) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
or(not(Y),Y) = truth,
inference(resolve,[$cnf( $equal(or(Y,not(Y)),truth) )],[refute_0_228,refute_0_231]) ).
cnf(refute_0_233,plain,
implies(not(not(Y)),Y) = or(not(Y),Y),
inference(subst,[],[refute_0_22:[bind(X,$fot(not(Y)))]]) ).
cnf(refute_0_234,plain,
( implies(not(not(Y)),Y) != or(not(Y),Y)
| or(not(Y),Y) != truth
| implies(not(not(Y)),Y) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(not(not(Y)),Y))),bind(Y0,$fot(or(not(Y),Y))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_235,plain,
( or(not(Y),Y) != truth
| implies(not(not(Y)),Y) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),Y),or(not(Y),Y)) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
implies(not(not(Y)),Y) = truth,
inference(resolve,[$cnf( $equal(or(not(Y),Y),truth) )],[refute_0_232,refute_0_235]) ).
cnf(refute_0_237,plain,
implies(implies(not(not(Y)),Y),Y) = implies(implies(not(not(Y)),Y),Y),
introduced(tautology,[refl,[$fot(implies(implies(not(not(Y)),Y),Y))]]) ).
cnf(refute_0_238,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(implies(not(not(Y)),Y),Y)
| implies(not(not(Y)),Y) != truth
| implies(implies(not(not(Y)),Y),Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(not(not(Y)),Y),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_239,plain,
( implies(not(not(Y)),Y) != truth
| implies(implies(not(not(Y)),Y),Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(not(not(Y)),Y),Y)) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
implies(implies(not(not(Y)),Y),Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),Y),truth) )],[refute_0_236,refute_0_239]) ).
cnf(refute_0_241,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(truth,Y)
| implies(truth,Y) != Y
| implies(implies(not(not(Y)),Y),Y) = Y ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(implies(not(not(Y)),Y),Y))),bind(Y0,$fot(implies(truth,Y))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_242,plain,
( implies(truth,Y) != Y
| implies(implies(not(not(Y)),Y),Y) = Y ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,Y)) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
implies(implies(not(not(Y)),Y),Y) = Y,
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_116,refute_0_242]) ).
cnf(refute_0_244,plain,
( implies(implies(not(not(Y)),Y),Y) != Y
| implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
| Y = implies(truth,not(not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,not(not(Y)))) ),[0],$fot(Y)]]) ).
cnf(refute_0_245,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
| Y = implies(truth,not(not(Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),Y) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
implies(truth,not(not(Y))) = not(not(Y)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_247,plain,
( Y != implies(truth,not(not(Y)))
| implies(truth,not(not(Y))) != not(not(Y))
| Y = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(Y,not(not(Y))) ),[0],$fot(implies(truth,not(not(Y))))]]) ).
cnf(refute_0_248,plain,
( Y != implies(truth,not(not(Y)))
| Y = not(not(Y)) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(Y))),not(not(Y))) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
| Y = not(not(Y)) ),
inference(resolve,[$cnf( $equal(Y,implies(truth,not(not(Y)))) )],[refute_0_245,refute_0_248]) ).
cnf(refute_0_250,plain,
Y = not(not(Y)),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,not(not(Y)))) )],[refute_0_227,refute_0_249]) ).
cnf(refute_0_251,plain,
and(falsehood,X_61) = not(not(and(falsehood,X_61))),
inference(subst,[],[refute_0_250:[bind(Y,$fot(and(falsehood,X_61)))]]) ).
cnf(refute_0_252,plain,
or(or(falsehood,not(X_1)),X_8) = implies(not(or(falsehood,not(X_1))),X_8),
inference(subst,[],[or_definition:[bind(X,$fot(or(falsehood,not(X_1)))),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_253,plain,
( and(X_1,truth) != not(or(falsehood,not(X_1)))
| not(or(falsehood,not(X_1))) = and(X_1,truth) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_1,truth))),bind(Y0,$fot(not(or(falsehood,not(X_1)))))]]) ).
cnf(refute_0_254,plain,
not(or(falsehood,not(X_1))) = and(X_1,truth),
inference(resolve,[$cnf( $equal(and(X_1,truth),not(or(falsehood,not(X_1)))) )],[refute_0_153,refute_0_253]) ).
cnf(refute_0_255,plain,
( not(or(falsehood,not(X_1))) != and(X_1,truth)
| or(or(falsehood,not(X_1)),X_8) != implies(not(or(falsehood,not(X_1))),X_8)
| or(or(falsehood,not(X_1)),X_8) = implies(and(X_1,truth),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(falsehood,not(X_1)),X_8),implies(not(or(falsehood,not(X_1))),X_8)) ),[1,0],$fot(and(X_1,truth))]]) ).
cnf(refute_0_256,plain,
( or(or(falsehood,not(X_1)),X_8) != implies(not(or(falsehood,not(X_1))),X_8)
| or(or(falsehood,not(X_1)),X_8) = implies(and(X_1,truth),X_8) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_1))),and(X_1,truth)) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
or(or(falsehood,not(X_1)),X_8) = implies(and(X_1,truth),X_8),
inference(resolve,[$cnf( $equal(or(or(falsehood,not(X_1)),X_8),implies(not(or(falsehood,not(X_1))),X_8)) )],[refute_0_252,refute_0_256]) ).
cnf(refute_0_258,plain,
or(or(falsehood,not(X_1)),X_8) = or(falsehood,or(not(X_1),X_8)),
inference(subst,[],[or_associativity:[bind(X,$fot(falsehood)),bind(Y,$fot(not(X_1))),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_259,plain,
( or(or(falsehood,not(X_1)),X_8) != implies(and(X_1,truth),X_8)
| or(or(falsehood,not(X_1)),X_8) != or(falsehood,or(not(X_1),X_8))
| or(falsehood,or(not(X_1),X_8)) = implies(and(X_1,truth),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(falsehood,not(X_1)),X_8),implies(and(X_1,truth),X_8)) ),[0],$fot(or(falsehood,or(not(X_1),X_8)))]]) ).
cnf(refute_0_260,plain,
( or(or(falsehood,not(X_1)),X_8) != implies(and(X_1,truth),X_8)
| or(falsehood,or(not(X_1),X_8)) = implies(and(X_1,truth),X_8) ),
inference(resolve,[$cnf( $equal(or(or(falsehood,not(X_1)),X_8),or(falsehood,or(not(X_1),X_8))) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
or(falsehood,or(not(X_1),X_8)) = implies(and(X_1,truth),X_8),
inference(resolve,[$cnf( $equal(or(or(falsehood,not(X_1)),X_8),implies(and(X_1,truth),X_8)) )],[refute_0_257,refute_0_260]) ).
cnf(refute_0_262,plain,
or(falsehood,or(not(X_35),truth)) = implies(and(X_35,truth),truth),
inference(subst,[],[refute_0_261:[bind(X_1,$fot(X_35)),bind(X_8,$fot(truth))]]) ).
cnf(refute_0_263,plain,
or(not(X_35),truth) = implies(falsehood,not(X_35)),
inference(subst,[],[refute_0_87:[bind(X_8,$fot(not(X_35)))]]) ).
cnf(refute_0_264,plain,
( or(falsehood,or(not(X_35),truth)) != implies(and(X_35,truth),truth)
| or(not(X_35),truth) != implies(falsehood,not(X_35))
| or(falsehood,implies(falsehood,not(X_35))) = implies(and(X_35,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(not(X_35),truth)),implies(and(X_35,truth),truth)) ),[0,1],$fot(implies(falsehood,not(X_35)))]]) ).
cnf(refute_0_265,plain,
( or(falsehood,or(not(X_35),truth)) != implies(and(X_35,truth),truth)
| or(falsehood,implies(falsehood,not(X_35))) = implies(and(X_35,truth),truth) ),
inference(resolve,[$cnf( $equal(or(not(X_35),truth),implies(falsehood,not(X_35))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
or(falsehood,implies(falsehood,not(X_35))) = implies(and(X_35,truth),truth),
inference(resolve,[$cnf( $equal(or(falsehood,or(not(X_35),truth)),implies(and(X_35,truth),truth)) )],[refute_0_262,refute_0_265]) ).
cnf(refute_0_267,plain,
or(not(X),not(Y)) = not(not(or(not(X),not(Y)))),
inference(subst,[],[refute_0_250:[bind(Y,$fot(or(not(X),not(Y))))]]) ).
cnf(refute_0_268,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_269,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( $equal(not(or(not(X),not(Y))),and(X,Y)) )],[refute_0_7,refute_0_268]) ).
cnf(refute_0_270,plain,
or(not(X),not(Y)) = not(and(X,Y)),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),not(not(or(not(X),not(Y))))) )],[refute_0_267,refute_0_269]) ).
cnf(refute_0_271,plain,
or(not(X_56),Y) = implies(not(not(X_56)),Y),
inference(subst,[],[or_definition:[bind(X,$fot(not(X_56)))]]) ).
cnf(refute_0_272,plain,
X_56 = not(not(X_56)),
inference(subst,[],[refute_0_250:[bind(Y,$fot(X_56))]]) ).
cnf(refute_0_273,plain,
( X_56 != not(not(X_56))
| not(not(X_56)) = X_56 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_56)),bind(Y0,$fot(not(not(X_56))))]]) ).
cnf(refute_0_274,plain,
not(not(X_56)) = X_56,
inference(resolve,[$cnf( $equal(X_56,not(not(X_56))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
( not(not(X_56)) != X_56
| or(not(X_56),Y) != implies(not(not(X_56)),Y)
| or(not(X_56),Y) = implies(X_56,Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X_56),Y),implies(not(not(X_56)),Y)) ),[1,0],$fot(X_56)]]) ).
cnf(refute_0_276,plain,
( or(not(X_56),Y) != implies(not(not(X_56)),Y)
| or(not(X_56),Y) = implies(X_56,Y) ),
inference(resolve,[$cnf( $equal(not(not(X_56)),X_56) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
or(not(X_56),Y) = implies(X_56,Y),
inference(resolve,[$cnf( $equal(or(not(X_56),Y),implies(not(not(X_56)),Y)) )],[refute_0_271,refute_0_276]) ).
cnf(refute_0_278,plain,
or(not(X),not(Y)) = implies(X,not(Y)),
inference(subst,[],[refute_0_277:[bind(Y,$fot(not(Y))),bind(X_56,$fot(X))]]) ).
cnf(refute_0_279,plain,
( or(not(X),not(Y)) != implies(X,not(Y))
| or(not(X),not(Y)) != not(and(X,Y))
| implies(X,not(Y)) = not(and(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X),not(Y)),not(and(X,Y))) ),[0],$fot(implies(X,not(Y)))]]) ).
cnf(refute_0_280,plain,
( or(not(X),not(Y)) != not(and(X,Y))
| implies(X,not(Y)) = not(and(X,Y)) ),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),implies(X,not(Y))) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
implies(X,not(Y)) = not(and(X,Y)),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),not(and(X,Y))) )],[refute_0_270,refute_0_280]) ).
cnf(refute_0_282,plain,
implies(falsehood,not(X_35)) = not(and(falsehood,X_35)),
inference(subst,[],[refute_0_281:[bind(X,$fot(falsehood)),bind(Y,$fot(X_35))]]) ).
cnf(refute_0_283,plain,
or(falsehood,implies(falsehood,not(X_35))) = implies(falsehood,not(X_35)),
inference(subst,[],[refute_0_119:[bind(Y,$fot(implies(falsehood,not(X_35))))]]) ).
cnf(refute_0_284,plain,
( implies(falsehood,not(X_35)) != not(and(falsehood,X_35))
| or(falsehood,implies(falsehood,not(X_35))) != implies(falsehood,not(X_35))
| or(falsehood,implies(falsehood,not(X_35))) = not(and(falsehood,X_35)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(falsehood,implies(falsehood,not(X_35))))),bind(Y0,$fot(implies(falsehood,not(X_35)))),bind(Z0,$fot(not(and(falsehood,X_35))))]]) ).
cnf(refute_0_285,plain,
( implies(falsehood,not(X_35)) != not(and(falsehood,X_35))
| or(falsehood,implies(falsehood,not(X_35))) = not(and(falsehood,X_35)) ),
inference(resolve,[$cnf( $equal(or(falsehood,implies(falsehood,not(X_35))),implies(falsehood,not(X_35))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
or(falsehood,implies(falsehood,not(X_35))) = not(and(falsehood,X_35)),
inference(resolve,[$cnf( $equal(implies(falsehood,not(X_35)),not(and(falsehood,X_35))) )],[refute_0_282,refute_0_285]) ).
cnf(refute_0_287,plain,
( or(falsehood,implies(falsehood,not(X_35))) != implies(and(X_35,truth),truth)
| or(falsehood,implies(falsehood,not(X_35))) != not(and(falsehood,X_35))
| not(and(falsehood,X_35)) = implies(and(X_35,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,implies(falsehood,not(X_35))),implies(and(X_35,truth),truth)) ),[0],$fot(not(and(falsehood,X_35)))]]) ).
cnf(refute_0_288,plain,
( or(falsehood,implies(falsehood,not(X_35))) != implies(and(X_35,truth),truth)
| not(and(falsehood,X_35)) = implies(and(X_35,truth),truth) ),
inference(resolve,[$cnf( $equal(or(falsehood,implies(falsehood,not(X_35))),not(and(falsehood,X_35))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(falsehood,X_14))) = truth,
inference(subst,[],[refute_0_30:[bind(X,$fot(or(falsehood,X_14))),bind(Y,$fot(and(truth,truth)))]]) ).
cnf(refute_0_290,plain,
or(falsehood,or(falsehood,or(X_14,falsehood))) = implies(and(truth,truth),or(X_14,falsehood)),
inference(subst,[],[refute_0_166:[bind(X_8,$fot(or(X_14,falsehood)))]]) ).
cnf(refute_0_291,plain,
or(falsehood,or(X_14,falsehood)) = implies(and(truth,truth),X_14),
inference(subst,[],[refute_0_170:[bind(X_8,$fot(X_14))]]) ).
cnf(refute_0_292,plain,
( or(falsehood,or(X_14,falsehood)) != implies(and(truth,truth),X_14)
| or(falsehood,or(falsehood,or(X_14,falsehood))) != implies(and(truth,truth),or(X_14,falsehood))
| or(falsehood,implies(and(truth,truth),X_14)) = implies(and(truth,truth),or(X_14,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(falsehood,or(X_14,falsehood))),implies(and(truth,truth),or(X_14,falsehood))) ),[0,1],$fot(implies(and(truth,truth),X_14))]]) ).
cnf(refute_0_293,plain,
( or(falsehood,or(falsehood,or(X_14,falsehood))) != implies(and(truth,truth),or(X_14,falsehood))
| or(falsehood,implies(and(truth,truth),X_14)) = implies(and(truth,truth),or(X_14,falsehood)) ),
inference(resolve,[$cnf( $equal(or(falsehood,or(X_14,falsehood)),implies(and(truth,truth),X_14)) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
or(falsehood,implies(and(truth,truth),X_14)) = implies(and(truth,truth),or(X_14,falsehood)),
inference(resolve,[$cnf( $equal(or(falsehood,or(falsehood,or(X_14,falsehood))),implies(and(truth,truth),or(X_14,falsehood))) )],[refute_0_290,refute_0_293]) ).
cnf(refute_0_295,plain,
or(falsehood,or(falsehood,or(falsehood,X_10))) = implies(and(truth,truth),or(falsehood,X_10)),
inference(subst,[],[refute_0_166:[bind(X_8,$fot(or(falsehood,X_10)))]]) ).
cnf(refute_0_296,plain,
or(falsehood,or(falsehood,X_10)) = implies(and(truth,truth),X_10),
inference(subst,[],[refute_0_166:[bind(X_8,$fot(X_10))]]) ).
cnf(refute_0_297,plain,
( or(falsehood,or(falsehood,X_10)) != implies(and(truth,truth),X_10)
| or(falsehood,or(falsehood,or(falsehood,X_10))) != implies(and(truth,truth),or(falsehood,X_10))
| or(falsehood,implies(and(truth,truth),X_10)) = implies(and(truth,truth),or(falsehood,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(falsehood,or(falsehood,X_10))),implies(and(truth,truth),or(falsehood,X_10))) ),[0,1],$fot(implies(and(truth,truth),X_10))]]) ).
cnf(refute_0_298,plain,
( or(falsehood,or(falsehood,or(falsehood,X_10))) != implies(and(truth,truth),or(falsehood,X_10))
| or(falsehood,implies(and(truth,truth),X_10)) = implies(and(truth,truth),or(falsehood,X_10)) ),
inference(resolve,[$cnf( $equal(or(falsehood,or(falsehood,X_10)),implies(and(truth,truth),X_10)) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
or(falsehood,implies(and(truth,truth),X_10)) = implies(and(truth,truth),or(falsehood,X_10)),
inference(resolve,[$cnf( $equal(or(falsehood,or(falsehood,or(falsehood,X_10))),implies(and(truth,truth),or(falsehood,X_10))) )],[refute_0_295,refute_0_298]) ).
cnf(refute_0_300,plain,
or(falsehood,implies(and(truth,truth),X_14)) = implies(and(truth,truth),or(falsehood,X_14)),
inference(subst,[],[refute_0_299:[bind(X_10,$fot(X_14))]]) ).
cnf(refute_0_301,plain,
( or(falsehood,implies(and(truth,truth),X_14)) != implies(and(truth,truth),or(X_14,falsehood))
| or(falsehood,implies(and(truth,truth),X_14)) != implies(and(truth,truth),or(falsehood,X_14))
| implies(and(truth,truth),or(falsehood,X_14)) = implies(and(truth,truth),or(X_14,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,implies(and(truth,truth),X_14)),implies(and(truth,truth),or(X_14,falsehood))) ),[0],$fot(implies(and(truth,truth),or(falsehood,X_14)))]]) ).
cnf(refute_0_302,plain,
( or(falsehood,implies(and(truth,truth),X_14)) != implies(and(truth,truth),or(X_14,falsehood))
| implies(and(truth,truth),or(falsehood,X_14)) = implies(and(truth,truth),or(X_14,falsehood)) ),
inference(resolve,[$cnf( $equal(or(falsehood,implies(and(truth,truth),X_14)),implies(and(truth,truth),or(falsehood,X_14))) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
implies(and(truth,truth),or(falsehood,X_14)) = implies(and(truth,truth),or(X_14,falsehood)),
inference(resolve,[$cnf( $equal(or(falsehood,implies(and(truth,truth),X_14)),implies(and(truth,truth),or(X_14,falsehood))) )],[refute_0_294,refute_0_302]) ).
cnf(refute_0_304,plain,
( implies(and(truth,truth),or(falsehood,X_14)) != implies(and(truth,truth),or(X_14,falsehood))
| implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(falsehood,X_14))) != truth
| implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(falsehood,X_14))),truth) ),[0,1],$fot(implies(and(truth,truth),or(X_14,falsehood)))]]) ).
cnf(refute_0_305,plain,
( implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(falsehood,X_14))) != truth
| implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))) = truth ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),or(falsehood,X_14)),implies(and(truth,truth),or(X_14,falsehood))) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))) = truth,
inference(resolve,[$cnf( $equal(implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(falsehood,X_14))),truth) )],[refute_0_289,refute_0_305]) ).
cnf(refute_0_307,plain,
or(falsehood,or(not(X_35),X_36)) = implies(and(X_35,truth),X_36),
inference(subst,[],[refute_0_261:[bind(X_1,$fot(X_35)),bind(X_8,$fot(X_36))]]) ).
cnf(refute_0_308,plain,
and(truth,X_35) = and(X_35,truth),
inference(subst,[],[and_commutativity:[bind(X,$fot(truth)),bind(Y,$fot(X_35))]]) ).
cnf(refute_0_309,plain,
( and(truth,X_35) != and(X_35,truth)
| and(X_35,truth) = and(truth,X_35) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,X_35))),bind(Y0,$fot(and(X_35,truth)))]]) ).
cnf(refute_0_310,plain,
and(X_35,truth) = and(truth,X_35),
inference(resolve,[$cnf( $equal(and(truth,X_35),and(X_35,truth)) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
( and(X_35,truth) != and(truth,X_35)
| or(falsehood,or(not(X_35),X_36)) != implies(and(X_35,truth),X_36)
| or(falsehood,or(not(X_35),X_36)) = implies(and(truth,X_35),X_36) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(not(X_35),X_36)),implies(and(X_35,truth),X_36)) ),[1,0],$fot(and(truth,X_35))]]) ).
cnf(refute_0_312,plain,
( or(falsehood,or(not(X_35),X_36)) != implies(and(X_35,truth),X_36)
| or(falsehood,or(not(X_35),X_36)) = implies(and(truth,X_35),X_36) ),
inference(resolve,[$cnf( $equal(and(X_35,truth),and(truth,X_35)) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
or(falsehood,or(not(X_35),X_36)) = implies(and(truth,X_35),X_36),
inference(resolve,[$cnf( $equal(or(falsehood,or(not(X_35),X_36)),implies(and(X_35,truth),X_36)) )],[refute_0_307,refute_0_312]) ).
cnf(refute_0_314,plain,
( or(falsehood,or(not(X_35),X_36)) != implies(and(X_35,truth),X_36)
| or(falsehood,or(not(X_35),X_36)) != implies(and(truth,X_35),X_36)
| implies(and(X_35,truth),X_36) = implies(and(truth,X_35),X_36) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(not(X_35),X_36)),implies(and(truth,X_35),X_36)) ),[0],$fot(implies(and(X_35,truth),X_36))]]) ).
cnf(refute_0_315,plain,
( or(falsehood,or(not(X_35),X_36)) != implies(and(truth,X_35),X_36)
| implies(and(X_35,truth),X_36) = implies(and(truth,X_35),X_36) ),
inference(resolve,[$cnf( $equal(or(falsehood,or(not(X_35),X_36)),implies(and(X_35,truth),X_36)) )],[refute_0_307,refute_0_314]) ).
cnf(refute_0_316,plain,
implies(and(X_35,truth),X_36) = implies(and(truth,X_35),X_36),
inference(resolve,[$cnf( $equal(or(falsehood,or(not(X_35),X_36)),implies(and(truth,X_35),X_36)) )],[refute_0_313,refute_0_315]) ).
cnf(refute_0_317,plain,
implies(and(and(truth,truth),truth),X_14) = implies(and(truth,and(truth,truth)),X_14),
inference(subst,[],[refute_0_316:[bind(X_35,$fot(and(truth,truth))),bind(X_36,$fot(X_14))]]) ).
cnf(refute_0_318,plain,
( or(falsehood,or(not(X_35),X_36)) != implies(and(X_35,truth),X_36)
| or(not(X_35),X_36) != or(X_36,not(X_35))
| or(falsehood,or(X_36,not(X_35))) = implies(and(X_35,truth),X_36) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(not(X_35),X_36)),implies(and(X_35,truth),X_36)) ),[0,1],$fot(or(X_36,not(X_35)))]]) ).
cnf(refute_0_319,plain,
( or(falsehood,or(not(X_35),X_36)) != implies(and(X_35,truth),X_36)
| or(falsehood,or(X_36,not(X_35))) = implies(and(X_35,truth),X_36) ),
inference(resolve,[$cnf( $equal(or(not(X_35),X_36),or(X_36,not(X_35))) )],[refute_0_137,refute_0_318]) ).
cnf(refute_0_320,plain,
or(falsehood,or(X_36,not(X_35))) = implies(and(X_35,truth),X_36),
inference(resolve,[$cnf( $equal(or(falsehood,or(not(X_35),X_36)),implies(and(X_35,truth),X_36)) )],[refute_0_307,refute_0_319]) ).
cnf(refute_0_321,plain,
or(falsehood,or(X_14,not(and(truth,truth)))) = implies(and(and(truth,truth),truth),X_14),
inference(subst,[],[refute_0_320:[bind(X_35,$fot(and(truth,truth))),bind(X_36,$fot(X_14))]]) ).
cnf(refute_0_322,plain,
( implies(and(and(truth,truth),truth),X_14) != implies(and(truth,and(truth,truth)),X_14)
| or(falsehood,or(X_14,not(and(truth,truth)))) != implies(and(and(truth,truth),truth),X_14)
| or(falsehood,or(X_14,not(and(truth,truth)))) = implies(and(truth,and(truth,truth)),X_14) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(falsehood,or(X_14,not(and(truth,truth)))))),bind(Y0,$fot(implies(and(and(truth,truth),truth),X_14))),bind(Z0,$fot(implies(and(truth,and(truth,truth)),X_14)))]]) ).
cnf(refute_0_323,plain,
( implies(and(and(truth,truth),truth),X_14) != implies(and(truth,and(truth,truth)),X_14)
| or(falsehood,or(X_14,not(and(truth,truth)))) = implies(and(truth,and(truth,truth)),X_14) ),
inference(resolve,[$cnf( $equal(or(falsehood,or(X_14,not(and(truth,truth)))),implies(and(and(truth,truth),truth),X_14)) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
or(falsehood,or(X_14,not(and(truth,truth)))) = implies(and(truth,and(truth,truth)),X_14),
inference(resolve,[$cnf( $equal(implies(and(and(truth,truth),truth),X_14),implies(and(truth,and(truth,truth)),X_14)) )],[refute_0_317,refute_0_323]) ).
cnf(refute_0_325,plain,
or(or(falsehood,X_14),not(and(truth,truth))) = or(falsehood,or(X_14,not(and(truth,truth)))),
inference(subst,[],[or_associativity:[bind(X,$fot(falsehood)),bind(Y,$fot(X_14)),bind(Z,$fot(not(and(truth,truth))))]]) ).
cnf(refute_0_326,plain,
( or(falsehood,or(X_14,not(and(truth,truth)))) != implies(and(truth,and(truth,truth)),X_14)
| or(or(falsehood,X_14),not(and(truth,truth))) != or(falsehood,or(X_14,not(and(truth,truth))))
| or(or(falsehood,X_14),not(and(truth,truth))) = implies(and(truth,and(truth,truth)),X_14) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(or(falsehood,X_14),not(and(truth,truth))))),bind(Y0,$fot(or(falsehood,or(X_14,not(and(truth,truth)))))),bind(Z0,$fot(implies(and(truth,and(truth,truth)),X_14)))]]) ).
cnf(refute_0_327,plain,
( or(falsehood,or(X_14,not(and(truth,truth)))) != implies(and(truth,and(truth,truth)),X_14)
| or(or(falsehood,X_14),not(and(truth,truth))) = implies(and(truth,and(truth,truth)),X_14) ),
inference(resolve,[$cnf( $equal(or(or(falsehood,X_14),not(and(truth,truth))),or(falsehood,or(X_14,not(and(truth,truth))))) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
or(or(falsehood,X_14),not(and(truth,truth))) = implies(and(truth,and(truth,truth)),X_14),
inference(resolve,[$cnf( $equal(or(falsehood,or(X_14,not(and(truth,truth)))),implies(and(truth,and(truth,truth)),X_14)) )],[refute_0_324,refute_0_327]) ).
cnf(refute_0_329,plain,
implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))) = implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))),
introduced(tautology,[refl,[$fot(implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))))]]) ).
cnf(refute_0_330,plain,
( implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))) != implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood)))
| or(or(falsehood,X_14),not(and(truth,truth))) != implies(and(truth,and(truth,truth)),X_14)
| implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))) = implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))),implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood)))) ),[1,0],$fot(implies(and(truth,and(truth,truth)),X_14))]]) ).
cnf(refute_0_331,plain,
( or(or(falsehood,X_14),not(and(truth,truth))) != implies(and(truth,and(truth,truth)),X_14)
| implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))) = implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) ),
inference(resolve,[$cnf( $equal(implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))),implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood)))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))) = implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))),
inference(resolve,[$cnf( $equal(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,and(truth,truth)),X_14)) )],[refute_0_328,refute_0_331]) ).
cnf(refute_0_333,plain,
( implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))) != implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood)))
| implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))) != truth
| implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))),truth) ),[0],$fot(implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))))]]) ).
cnf(refute_0_334,plain,
( implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))) != truth
| implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) = truth ),
inference(resolve,[$cnf( $equal(implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))),implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood)))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) = truth,
inference(resolve,[$cnf( $equal(implies(or(or(falsehood,X_14),not(and(truth,truth))),implies(and(truth,truth),or(X_14,falsehood))),truth) )],[refute_0_306,refute_0_334]) ).
cnf(refute_0_336,plain,
implies(truth,X_14) = X_14,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_14))]]) ).
cnf(refute_0_337,plain,
or(X_14,falsehood) = X_14,
inference(subst,[],[refute_0_204:[bind(X_8,$fot(X_14))]]) ).
cnf(refute_0_338,plain,
implies(truth,or(X_14,falsehood)) = implies(truth,or(X_14,falsehood)),
introduced(tautology,[refl,[$fot(implies(truth,or(X_14,falsehood)))]]) ).
cnf(refute_0_339,plain,
( implies(truth,or(X_14,falsehood)) != implies(truth,or(X_14,falsehood))
| or(X_14,falsehood) != X_14
| implies(truth,or(X_14,falsehood)) = implies(truth,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,or(X_14,falsehood)),implies(truth,or(X_14,falsehood))) ),[1,1],$fot(X_14)]]) ).
cnf(refute_0_340,plain,
( or(X_14,falsehood) != X_14
| implies(truth,or(X_14,falsehood)) = implies(truth,X_14) ),
inference(resolve,[$cnf( $equal(implies(truth,or(X_14,falsehood)),implies(truth,or(X_14,falsehood))) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
implies(truth,or(X_14,falsehood)) = implies(truth,X_14),
inference(resolve,[$cnf( $equal(or(X_14,falsehood),X_14) )],[refute_0_337,refute_0_340]) ).
cnf(refute_0_342,plain,
implies(and(truth,truth),or(X_14,falsehood)) = implies(and(truth,truth),or(X_14,falsehood)),
introduced(tautology,[refl,[$fot(implies(and(truth,truth),or(X_14,falsehood)))]]) ).
cnf(refute_0_343,plain,
( and(truth,truth) != truth
| implies(and(truth,truth),or(X_14,falsehood)) != implies(and(truth,truth),or(X_14,falsehood))
| implies(and(truth,truth),or(X_14,falsehood)) = implies(truth,or(X_14,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(truth,truth),or(X_14,falsehood)),implies(and(truth,truth),or(X_14,falsehood))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_344,plain,
( and(truth,truth) != truth
| implies(and(truth,truth),or(X_14,falsehood)) = implies(truth,or(X_14,falsehood)) ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),or(X_14,falsehood)),implies(and(truth,truth),or(X_14,falsehood))) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
implies(and(truth,truth),or(X_14,falsehood)) = implies(truth,or(X_14,falsehood)),
inference(resolve,[$cnf( $equal(and(truth,truth),truth) )],[refute_0_193,refute_0_344]) ).
cnf(refute_0_346,plain,
( implies(and(truth,truth),or(X_14,falsehood)) != implies(truth,or(X_14,falsehood))
| implies(truth,or(X_14,falsehood)) != implies(truth,X_14)
| implies(and(truth,truth),or(X_14,falsehood)) = implies(truth,X_14) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(and(truth,truth),or(X_14,falsehood)))),bind(Y0,$fot(implies(truth,or(X_14,falsehood)))),bind(Z0,$fot(implies(truth,X_14)))]]) ).
cnf(refute_0_347,plain,
( implies(truth,or(X_14,falsehood)) != implies(truth,X_14)
| implies(and(truth,truth),or(X_14,falsehood)) = implies(truth,X_14) ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),or(X_14,falsehood)),implies(truth,or(X_14,falsehood))) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
implies(and(truth,truth),or(X_14,falsehood)) = implies(truth,X_14),
inference(resolve,[$cnf( $equal(implies(truth,or(X_14,falsehood)),implies(truth,X_14)) )],[refute_0_341,refute_0_347]) ).
cnf(refute_0_349,plain,
( implies(and(truth,truth),or(X_14,falsehood)) != implies(truth,X_14)
| implies(truth,X_14) != X_14
| implies(and(truth,truth),or(X_14,falsehood)) = X_14 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(and(truth,truth),or(X_14,falsehood)))),bind(Y0,$fot(implies(truth,X_14))),bind(Z0,$fot(X_14))]]) ).
cnf(refute_0_350,plain,
( implies(truth,X_14) != X_14
| implies(and(truth,truth),or(X_14,falsehood)) = X_14 ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),or(X_14,falsehood)),implies(truth,X_14)) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
implies(and(truth,truth),or(X_14,falsehood)) = X_14,
inference(resolve,[$cnf( $equal(implies(truth,X_14),X_14) )],[refute_0_336,refute_0_350]) ).
cnf(refute_0_352,plain,
implies(X_14,implies(and(truth,truth),or(X_14,falsehood))) = implies(X_14,implies(and(truth,truth),or(X_14,falsehood))),
introduced(tautology,[refl,[$fot(implies(X_14,implies(and(truth,truth),or(X_14,falsehood))))]]) ).
cnf(refute_0_353,plain,
( implies(X_14,implies(and(truth,truth),or(X_14,falsehood))) != implies(X_14,implies(and(truth,truth),or(X_14,falsehood)))
| implies(and(truth,truth),or(X_14,falsehood)) != X_14
| implies(X_14,implies(and(truth,truth),or(X_14,falsehood))) = implies(X_14,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_14,implies(and(truth,truth),or(X_14,falsehood))),implies(X_14,implies(and(truth,truth),or(X_14,falsehood)))) ),[1,1],$fot(X_14)]]) ).
cnf(refute_0_354,plain,
( implies(and(truth,truth),or(X_14,falsehood)) != X_14
| implies(X_14,implies(and(truth,truth),or(X_14,falsehood))) = implies(X_14,X_14) ),
inference(resolve,[$cnf( $equal(implies(X_14,implies(and(truth,truth),or(X_14,falsehood))),implies(X_14,implies(and(truth,truth),or(X_14,falsehood)))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
implies(X_14,implies(and(truth,truth),or(X_14,falsehood))) = implies(X_14,X_14),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),or(X_14,falsehood)),X_14) )],[refute_0_351,refute_0_354]) ).
cnf(refute_0_356,plain,
not(and(truth,truth)) = not(and(truth,truth)),
introduced(tautology,[refl,[$fot(not(and(truth,truth)))]]) ).
cnf(refute_0_357,plain,
( and(truth,truth) != truth
| not(and(truth,truth)) != not(and(truth,truth))
| not(and(truth,truth)) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(truth,truth)),not(and(truth,truth))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_358,plain,
( and(truth,truth) != truth
| not(and(truth,truth)) = not(truth) ),
inference(resolve,[$cnf( $equal(not(and(truth,truth)),not(and(truth,truth))) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
not(and(truth,truth)) = not(truth),
inference(resolve,[$cnf( $equal(and(truth,truth),truth) )],[refute_0_193,refute_0_358]) ).
cnf(refute_0_360,plain,
( not(and(truth,truth)) != not(truth)
| not(truth) != falsehood
| not(and(truth,truth)) = falsehood ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(and(truth,truth)))),bind(Y0,$fot(not(truth))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_361,plain,
( not(truth) != falsehood
| not(and(truth,truth)) = falsehood ),
inference(resolve,[$cnf( $equal(not(and(truth,truth)),not(truth)) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
not(and(truth,truth)) = falsehood,
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_361]) ).
cnf(refute_0_363,plain,
not(not(and(truth,truth))) = not(not(and(truth,truth))),
introduced(tautology,[refl,[$fot(not(not(and(truth,truth))))]]) ).
cnf(refute_0_364,plain,
( not(and(truth,truth)) != falsehood
| not(not(and(truth,truth))) != not(not(and(truth,truth)))
| not(not(and(truth,truth))) = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(and(truth,truth))),not(not(and(truth,truth)))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_365,plain,
( not(and(truth,truth)) != falsehood
| not(not(and(truth,truth))) = not(falsehood) ),
inference(resolve,[$cnf( $equal(not(not(and(truth,truth))),not(not(and(truth,truth)))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
not(not(and(truth,truth))) = not(falsehood),
inference(resolve,[$cnf( $equal(not(and(truth,truth)),falsehood) )],[refute_0_362,refute_0_365]) ).
cnf(refute_0_367,plain,
( not(falsehood) != truth
| not(not(and(truth,truth))) != not(falsehood)
| not(not(and(truth,truth))) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(not(and(truth,truth))))),bind(Y0,$fot(not(falsehood))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_368,plain,
( not(falsehood) != truth
| not(not(and(truth,truth))) = truth ),
inference(resolve,[$cnf( $equal(not(not(and(truth,truth))),not(falsehood)) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
not(not(and(truth,truth))) = truth,
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_112,refute_0_368]) ).
cnf(refute_0_370,plain,
and(or(falsehood,and(truth,truth)),Y) = not(or(not(or(falsehood,and(truth,truth))),not(Y))),
inference(subst,[],[and_definition:[bind(X,$fot(or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_371,plain,
and(or(falsehood,falsehood),truth) = not(or(falsehood,not(or(falsehood,falsehood)))),
inference(subst,[],[refute_0_153:[bind(X_1,$fot(or(falsehood,falsehood)))]]) ).
cnf(refute_0_372,plain,
( and(or(falsehood,falsehood),truth) != not(or(falsehood,not(or(falsehood,falsehood))))
| not(or(falsehood,falsehood)) != and(truth,truth)
| and(or(falsehood,falsehood),truth) = not(or(falsehood,and(truth,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,not(or(falsehood,falsehood))))) ),[1,0,1],$fot(and(truth,truth))]]) ).
cnf(refute_0_373,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( $equal(not(or(falsehood,falsehood)),and(truth,truth)) )],[refute_0_159,refute_0_372]) ).
cnf(refute_0_374,plain,
and(or(falsehood,falsehood),truth) = not(or(falsehood,and(truth,truth))),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,not(or(falsehood,falsehood))))) )],[refute_0_371,refute_0_373]) ).
cnf(refute_0_375,plain,
and(truth,X_2) = not(or(not(truth),not(X_2))),
inference(subst,[],[and_definition:[bind(X,$fot(truth)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_376,plain,
( and(truth,X_2) != not(or(not(truth),not(X_2)))
| not(truth) != falsehood
| and(truth,X_2) = not(or(falsehood,not(X_2))) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,X_2),not(or(not(truth),not(X_2)))) ),[1,0,0],$fot(falsehood)]]) ).
cnf(refute_0_377,plain,
( and(truth,X_2) != not(or(not(truth),not(X_2)))
| and(truth,X_2) = not(or(falsehood,not(X_2))) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_376]) ).
cnf(refute_0_378,plain,
and(truth,X_2) = not(or(falsehood,not(X_2))),
inference(resolve,[$cnf( $equal(and(truth,X_2),not(or(not(truth),not(X_2)))) )],[refute_0_375,refute_0_377]) ).
cnf(refute_0_379,plain,
not(or(falsehood,not(X_2))) = and(X_2,truth),
inference(subst,[],[refute_0_254:[bind(X_1,$fot(X_2))]]) ).
cnf(refute_0_380,plain,
( and(truth,X_2) != not(or(falsehood,not(X_2)))
| not(or(falsehood,not(X_2))) != and(X_2,truth)
| and(truth,X_2) = and(X_2,truth) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(truth,X_2),and(X_2,truth)) ),[0],$fot(not(or(falsehood,not(X_2))))]]) ).
cnf(refute_0_381,plain,
( and(truth,X_2) != not(or(falsehood,not(X_2)))
| and(truth,X_2) = and(X_2,truth) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_2))),and(X_2,truth)) )],[refute_0_379,refute_0_380]) ).
cnf(refute_0_382,plain,
and(truth,X_2) = and(X_2,truth),
inference(resolve,[$cnf( $equal(and(truth,X_2),not(or(falsehood,not(X_2)))) )],[refute_0_378,refute_0_381]) ).
cnf(refute_0_383,plain,
( and(truth,X_2) != and(X_2,truth)
| and(X_2,truth) = and(truth,X_2) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,X_2))),bind(Y0,$fot(and(X_2,truth)))]]) ).
cnf(refute_0_384,plain,
and(X_2,truth) = and(truth,X_2),
inference(resolve,[$cnf( $equal(and(truth,X_2),and(X_2,truth)) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
and(or(falsehood,falsehood),truth) = and(truth,or(falsehood,falsehood)),
inference(subst,[],[refute_0_384:[bind(X_2,$fot(or(falsehood,falsehood)))]]) ).
cnf(refute_0_386,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_387,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( $equal(and(or(falsehood,falsehood),truth),and(truth,or(falsehood,falsehood))) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
and(truth,or(falsehood,falsehood)) = not(or(falsehood,and(truth,truth))),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,and(truth,truth)))) )],[refute_0_374,refute_0_387]) ).
cnf(refute_0_389,plain,
( and(truth,or(falsehood,falsehood)) != not(or(falsehood,and(truth,truth)))
| not(or(falsehood,and(truth,truth))) = and(truth,or(falsehood,falsehood)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,or(falsehood,falsehood)))),bind(Y0,$fot(not(or(falsehood,and(truth,truth)))))]]) ).
cnf(refute_0_390,plain,
not(or(falsehood,and(truth,truth))) = and(truth,or(falsehood,falsehood)),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),not(or(falsehood,and(truth,truth)))) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
( and(or(falsehood,and(truth,truth)),Y) != not(or(not(or(falsehood,and(truth,truth))),not(Y)))
| not(or(falsehood,and(truth,truth))) != and(truth,or(falsehood,falsehood))
| and(or(falsehood,and(truth,truth)),Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))) ),
introduced(tautology,[equality,[$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_392,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( $equal(not(or(falsehood,and(truth,truth))),and(truth,or(falsehood,falsehood))) )],[refute_0_390,refute_0_391]) ).
cnf(refute_0_393,plain,
and(or(falsehood,and(truth,truth)),Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),not(or(not(or(falsehood,and(truth,truth))),not(Y)))) )],[refute_0_370,refute_0_392]) ).
cnf(refute_0_394,plain,
or(falsehood,and(truth,truth)) = and(truth,truth),
inference(subst,[],[refute_0_119:[bind(Y,$fot(and(truth,truth)))]]) ).
cnf(refute_0_395,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,$fot(not(not(truth))))]]) ).
cnf(refute_0_396,plain,
( and(truth,truth) != not(not(truth))
| or(falsehood,and(truth,truth)) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),and(truth,truth)) )],[refute_0_394,refute_0_395]) ).
cnf(refute_0_397,plain,
or(falsehood,and(truth,truth)) = not(not(truth)),
inference(resolve,[$cnf( $equal(and(truth,truth),not(not(truth))) )],[refute_0_190,refute_0_396]) ).
cnf(refute_0_398,plain,
( not(not(truth)) != truth
| or(falsehood,and(truth,truth)) != not(not(truth))
| or(falsehood,and(truth,truth)) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(falsehood,and(truth,truth)))),bind(Y0,$fot(not(not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_399,plain,
( not(not(truth)) != truth
| or(falsehood,and(truth,truth)) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),not(not(truth))) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
or(falsehood,and(truth,truth)) = truth,
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_181,refute_0_399]) ).
cnf(refute_0_401,plain,
and(or(falsehood,and(truth,truth)),Y) = and(or(falsehood,and(truth,truth)),Y),
introduced(tautology,[refl,[$fot(and(or(falsehood,and(truth,truth)),Y))]]) ).
cnf(refute_0_402,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_403,plain,
( or(falsehood,and(truth,truth)) != truth
| and(or(falsehood,and(truth,truth)),Y) = and(truth,Y) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),and(or(falsehood,and(truth,truth)),Y)) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
and(or(falsehood,and(truth,truth)),Y) = and(truth,Y),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),truth) )],[refute_0_400,refute_0_403]) ).
cnf(refute_0_405,plain,
( and(or(falsehood,and(truth,truth)),Y) != and(truth,Y)
| and(or(falsehood,and(truth,truth)),Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))) ),
introduced(tautology,[equality,[$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_406,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( $equal(and(or(falsehood,and(truth,truth)),Y),and(truth,Y)) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
and(falsehood,truth) = not(or(falsehood,not(falsehood))),
inference(subst,[],[refute_0_153:[bind(X_1,$fot(falsehood))]]) ).
cnf(refute_0_408,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_409,plain,
( and(falsehood,truth) != not(or(falsehood,not(falsehood)))
| and(falsehood,truth) = not(truth) ),
inference(resolve,[$cnf( $equal(or(falsehood,not(falsehood)),truth) )],[refute_0_105,refute_0_408]) ).
cnf(refute_0_410,plain,
and(falsehood,truth) = not(truth),
inference(resolve,[$cnf( $equal(and(falsehood,truth),not(or(falsehood,not(falsehood)))) )],[refute_0_407,refute_0_409]) ).
cnf(refute_0_411,plain,
( and(falsehood,truth) != not(truth)
| not(truth) != falsehood
| and(falsehood,truth) = falsehood ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(falsehood,truth),falsehood) ),[0],$fot(not(truth))]]) ).
cnf(refute_0_412,plain,
( and(falsehood,truth) != not(truth)
| and(falsehood,truth) = falsehood ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_411]) ).
cnf(refute_0_413,plain,
and(falsehood,truth) = falsehood,
inference(resolve,[$cnf( $equal(and(falsehood,truth),not(truth)) )],[refute_0_410,refute_0_412]) ).
cnf(refute_0_414,plain,
and(truth,falsehood) = and(falsehood,truth),
inference(subst,[],[refute_0_4:[bind(X,$fot(falsehood)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_415,plain,
( and(falsehood,truth) != falsehood
| and(truth,falsehood) != and(falsehood,truth)
| and(truth,falsehood) = falsehood ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(truth,falsehood))),bind(Y0,$fot(and(falsehood,truth))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_416,plain,
( and(falsehood,truth) != falsehood
| and(truth,falsehood) = falsehood ),
inference(resolve,[$cnf( $equal(and(truth,falsehood),and(falsehood,truth)) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
and(truth,falsehood) = falsehood,
inference(resolve,[$cnf( $equal(and(falsehood,truth),falsehood) )],[refute_0_413,refute_0_416]) ).
cnf(refute_0_418,plain,
or(falsehood,falsehood) = falsehood,
inference(subst,[],[refute_0_119:[bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_419,plain,
and(truth,or(falsehood,falsehood)) = and(truth,or(falsehood,falsehood)),
introduced(tautology,[refl,[$fot(and(truth,or(falsehood,falsehood)))]]) ).
cnf(refute_0_420,plain,
( and(truth,or(falsehood,falsehood)) != and(truth,or(falsehood,falsehood))
| or(falsehood,falsehood) != falsehood
| and(truth,or(falsehood,falsehood)) = and(truth,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,or(falsehood,falsehood)),and(truth,or(falsehood,falsehood))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_421,plain,
( or(falsehood,falsehood) != falsehood
| and(truth,or(falsehood,falsehood)) = and(truth,falsehood) ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),and(truth,or(falsehood,falsehood))) )],[refute_0_419,refute_0_420]) ).
cnf(refute_0_422,plain,
and(truth,or(falsehood,falsehood)) = and(truth,falsehood),
inference(resolve,[$cnf( $equal(or(falsehood,falsehood),falsehood) )],[refute_0_418,refute_0_421]) ).
cnf(refute_0_423,plain,
( and(truth,falsehood) != falsehood
| and(truth,or(falsehood,falsehood)) != and(truth,falsehood)
| and(truth,or(falsehood,falsehood)) = falsehood ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(truth,or(falsehood,falsehood)))),bind(Y0,$fot(and(truth,falsehood))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_424,plain,
( and(truth,falsehood) != falsehood
| and(truth,or(falsehood,falsehood)) = falsehood ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),and(truth,falsehood)) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
and(truth,or(falsehood,falsehood)) = falsehood,
inference(resolve,[$cnf( $equal(and(truth,falsehood),falsehood) )],[refute_0_417,refute_0_424]) ).
cnf(refute_0_426,plain,
or(and(truth,or(falsehood,falsehood)),not(Y)) = or(and(truth,or(falsehood,falsehood)),not(Y)),
introduced(tautology,[refl,[$fot(or(and(truth,or(falsehood,falsehood)),not(Y)))]]) ).
cnf(refute_0_427,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_428,plain,
( and(truth,or(falsehood,falsehood)) != falsehood
| or(and(truth,or(falsehood,falsehood)),not(Y)) = or(falsehood,not(Y)) ),
inference(resolve,[$cnf( $equal(or(and(truth,or(falsehood,falsehood)),not(Y)),or(and(truth,or(falsehood,falsehood)),not(Y))) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
or(and(truth,or(falsehood,falsehood)),not(Y)) = or(falsehood,not(Y)),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),falsehood) )],[refute_0_425,refute_0_428]) ).
cnf(refute_0_430,plain,
( or(and(truth,or(falsehood,falsehood)),not(Y)) != or(falsehood,not(Y))
| or(falsehood,not(Y)) != not(Y)
| or(and(truth,or(falsehood,falsehood)),not(Y)) = not(Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(and(truth,or(falsehood,falsehood)),not(Y)))),bind(Y0,$fot(or(falsehood,not(Y)))),bind(Z0,$fot(not(Y)))]]) ).
cnf(refute_0_431,plain,
( or(falsehood,not(Y)) != not(Y)
| or(and(truth,or(falsehood,falsehood)),not(Y)) = not(Y) ),
inference(resolve,[$cnf( $equal(or(and(truth,or(falsehood,falsehood)),not(Y)),or(falsehood,not(Y))) )],[refute_0_429,refute_0_430]) ).
cnf(refute_0_432,plain,
or(and(truth,or(falsehood,falsehood)),not(Y)) = not(Y),
inference(resolve,[$cnf( $equal(or(falsehood,not(Y)),not(Y)) )],[refute_0_120,refute_0_431]) ).
cnf(refute_0_433,plain,
not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(or(and(truth,or(falsehood,falsehood)),not(Y))),
introduced(tautology,[refl,[$fot(not(or(and(truth,or(falsehood,falsehood)),not(Y))))]]) ).
cnf(refute_0_434,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_435,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( $equal(not(or(and(truth,or(falsehood,falsehood)),not(Y))),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) )],[refute_0_433,refute_0_434]) ).
cnf(refute_0_436,plain,
not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(not(Y)),
inference(resolve,[$cnf( $equal(or(and(truth,or(falsehood,falsehood)),not(Y)),not(Y)) )],[refute_0_432,refute_0_435]) ).
cnf(refute_0_437,plain,
( and(truth,Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) != not(not(Y))
| and(truth,Y) = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(truth,Y),not(not(Y))) ),[0],$fot(not(or(and(truth,or(falsehood,falsehood)),not(Y))))]]) ).
cnf(refute_0_438,plain,
( and(truth,Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(not(or(and(truth,or(falsehood,falsehood)),not(Y))),not(not(Y))) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
( and(or(falsehood,and(truth,truth)),Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(and(truth,Y),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) )],[refute_0_406,refute_0_438]) ).
cnf(refute_0_440,plain,
and(truth,Y) = not(not(Y)),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) )],[refute_0_393,refute_0_439]) ).
cnf(refute_0_441,plain,
and(truth,and(truth,truth)) = not(not(and(truth,truth))),
inference(subst,[],[refute_0_440:[bind(Y,$fot(and(truth,truth)))]]) ).
cnf(refute_0_442,plain,
( and(truth,and(truth,truth)) != not(not(and(truth,truth)))
| not(not(and(truth,truth))) != truth
| and(truth,and(truth,truth)) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(truth,and(truth,truth)))),bind(Y0,$fot(not(not(and(truth,truth))))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_443,plain,
( not(not(and(truth,truth))) != truth
| and(truth,and(truth,truth)) = truth ),
inference(resolve,[$cnf( $equal(and(truth,and(truth,truth)),not(not(and(truth,truth)))) )],[refute_0_441,refute_0_442]) ).
cnf(refute_0_444,plain,
and(truth,and(truth,truth)) = truth,
inference(resolve,[$cnf( $equal(not(not(and(truth,truth))),truth) )],[refute_0_369,refute_0_443]) ).
cnf(refute_0_445,plain,
implies(and(truth,and(truth,truth)),X_14) = implies(and(truth,and(truth,truth)),X_14),
introduced(tautology,[refl,[$fot(implies(and(truth,and(truth,truth)),X_14))]]) ).
cnf(refute_0_446,plain,
( and(truth,and(truth,truth)) != truth
| implies(and(truth,and(truth,truth)),X_14) != implies(and(truth,and(truth,truth)),X_14)
| implies(and(truth,and(truth,truth)),X_14) = implies(truth,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,and(truth,truth)),X_14)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_447,plain,
( and(truth,and(truth,truth)) != truth
| implies(and(truth,and(truth,truth)),X_14) = implies(truth,X_14) ),
inference(resolve,[$cnf( $equal(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,and(truth,truth)),X_14)) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
implies(and(truth,and(truth,truth)),X_14) = implies(truth,X_14),
inference(resolve,[$cnf( $equal(and(truth,and(truth,truth)),truth) )],[refute_0_444,refute_0_447]) ).
cnf(refute_0_449,plain,
( implies(and(truth,and(truth,truth)),X_14) != implies(truth,X_14)
| implies(truth,X_14) != X_14
| implies(and(truth,and(truth,truth)),X_14) = X_14 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(and(truth,and(truth,truth)),X_14))),bind(Y0,$fot(implies(truth,X_14))),bind(Z0,$fot(X_14))]]) ).
cnf(refute_0_450,plain,
( implies(truth,X_14) != X_14
| implies(and(truth,and(truth,truth)),X_14) = X_14 ),
inference(resolve,[$cnf( $equal(implies(and(truth,and(truth,truth)),X_14),implies(truth,X_14)) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
implies(and(truth,and(truth,truth)),X_14) = X_14,
inference(resolve,[$cnf( $equal(implies(truth,X_14),X_14) )],[refute_0_336,refute_0_450]) ).
cnf(refute_0_452,plain,
implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) = implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))),
introduced(tautology,[refl,[$fot(implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))))]]) ).
cnf(refute_0_453,plain,
( implies(and(truth,and(truth,truth)),X_14) != X_14
| implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) != implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood)))
| implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) = implies(X_14,implies(and(truth,truth),or(X_14,falsehood))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))),implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood)))) ),[1,0],$fot(X_14)]]) ).
cnf(refute_0_454,plain,
( implies(and(truth,and(truth,truth)),X_14) != X_14
| implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) = implies(X_14,implies(and(truth,truth),or(X_14,falsehood))) ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))),implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood)))) )],[refute_0_452,refute_0_453]) ).
cnf(refute_0_455,plain,
implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) = implies(X_14,implies(and(truth,truth),or(X_14,falsehood))),
inference(resolve,[$cnf( $equal(implies(and(truth,and(truth,truth)),X_14),X_14) )],[refute_0_451,refute_0_454]) ).
cnf(refute_0_456,plain,
( implies(X_14,implies(and(truth,truth),or(X_14,falsehood))) != implies(X_14,X_14)
| implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) != implies(X_14,implies(and(truth,truth),or(X_14,falsehood)))
| implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) = implies(X_14,X_14) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))))),bind(Y0,$fot(implies(X_14,implies(and(truth,truth),or(X_14,falsehood))))),bind(Z0,$fot(implies(X_14,X_14)))]]) ).
cnf(refute_0_457,plain,
( implies(X_14,implies(and(truth,truth),or(X_14,falsehood))) != implies(X_14,X_14)
| implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) = implies(X_14,X_14) ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))),implies(X_14,implies(and(truth,truth),or(X_14,falsehood)))) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) = implies(X_14,X_14),
inference(resolve,[$cnf( $equal(implies(X_14,implies(and(truth,truth),or(X_14,falsehood))),implies(X_14,X_14)) )],[refute_0_355,refute_0_457]) ).
cnf(refute_0_459,plain,
( implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) != implies(X_14,X_14)
| implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) != truth
| implies(X_14,X_14) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))),truth) ),[0],$fot(implies(X_14,X_14))]]) ).
cnf(refute_0_460,plain,
( implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))) != truth
| implies(X_14,X_14) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))),implies(X_14,X_14)) )],[refute_0_458,refute_0_459]) ).
cnf(refute_0_461,plain,
implies(X_14,X_14) = truth,
inference(resolve,[$cnf( $equal(implies(implies(and(truth,and(truth,truth)),X_14),implies(and(truth,truth),or(X_14,falsehood))),truth) )],[refute_0_335,refute_0_460]) ).
cnf(refute_0_462,plain,
implies(truth,truth) = truth,
inference(subst,[],[refute_0_461:[bind(X_14,$fot(truth))]]) ).
cnf(refute_0_463,plain,
implies(X_35,implies(truth,truth)) = implies(X_35,implies(truth,truth)),
introduced(tautology,[refl,[$fot(implies(X_35,implies(truth,truth)))]]) ).
cnf(refute_0_464,plain,
( implies(X_35,implies(truth,truth)) != implies(X_35,implies(truth,truth))
| implies(truth,truth) != truth
| implies(X_35,implies(truth,truth)) = implies(X_35,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_35,implies(truth,truth)),implies(X_35,implies(truth,truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_465,plain,
( implies(truth,truth) != truth
| implies(X_35,implies(truth,truth)) = implies(X_35,truth) ),
inference(resolve,[$cnf( $equal(implies(X_35,implies(truth,truth)),implies(X_35,implies(truth,truth))) )],[refute_0_463,refute_0_464]) ).
cnf(refute_0_466,plain,
implies(X_35,implies(truth,truth)) = implies(X_35,truth),
inference(resolve,[$cnf( $equal(implies(truth,truth),truth) )],[refute_0_462,refute_0_465]) ).
cnf(refute_0_467,plain,
or(or(not(X),not(Y)),X_8) = implies(not(or(not(X),not(Y))),X_8),
inference(subst,[],[or_definition:[bind(X,$fot(or(not(X),not(Y)))),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_468,plain,
( not(or(not(X),not(Y))) != and(X,Y)
| or(or(not(X),not(Y)),X_8) != implies(not(or(not(X),not(Y))),X_8)
| or(or(not(X),not(Y)),X_8) = implies(and(X,Y),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(not(X),not(Y)),X_8),implies(not(or(not(X),not(Y))),X_8)) ),[1,0],$fot(and(X,Y))]]) ).
cnf(refute_0_469,plain,
( or(or(not(X),not(Y)),X_8) != implies(not(or(not(X),not(Y))),X_8)
| or(or(not(X),not(Y)),X_8) = implies(and(X,Y),X_8) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),and(X,Y)) )],[refute_0_7,refute_0_468]) ).
cnf(refute_0_470,plain,
or(or(not(X),not(Y)),X_8) = implies(and(X,Y),X_8),
inference(resolve,[$cnf( $equal(or(or(not(X),not(Y)),X_8),implies(not(or(not(X),not(Y))),X_8)) )],[refute_0_467,refute_0_469]) ).
cnf(refute_0_471,plain,
or(or(not(X),not(Y)),X_8) = or(not(X),or(not(Y),X_8)),
inference(subst,[],[or_associativity:[bind(X,$fot(not(X))),bind(Y,$fot(not(Y))),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_472,plain,
( or(or(not(X),not(Y)),X_8) != implies(and(X,Y),X_8)
| or(or(not(X),not(Y)),X_8) != or(not(X),or(not(Y),X_8))
| or(not(X),or(not(Y),X_8)) = implies(and(X,Y),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(not(X),not(Y)),X_8),implies(and(X,Y),X_8)) ),[0],$fot(or(not(X),or(not(Y),X_8)))]]) ).
cnf(refute_0_473,plain,
( or(or(not(X),not(Y)),X_8) != implies(and(X,Y),X_8)
| or(not(X),or(not(Y),X_8)) = implies(and(X,Y),X_8) ),
inference(resolve,[$cnf( $equal(or(or(not(X),not(Y)),X_8),or(not(X),or(not(Y),X_8))) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
or(not(X),or(not(Y),X_8)) = implies(and(X,Y),X_8),
inference(resolve,[$cnf( $equal(or(or(not(X),not(Y)),X_8),implies(and(X,Y),X_8)) )],[refute_0_470,refute_0_473]) ).
cnf(refute_0_475,plain,
or(not(Y),X_8) = implies(Y,X_8),
inference(subst,[],[refute_0_277:[bind(Y,$fot(X_8)),bind(X_56,$fot(Y))]]) ).
cnf(refute_0_476,plain,
implies(X,or(not(Y),X_8)) = implies(X,or(not(Y),X_8)),
introduced(tautology,[refl,[$fot(implies(X,or(not(Y),X_8)))]]) ).
cnf(refute_0_477,plain,
( implies(X,or(not(Y),X_8)) != implies(X,or(not(Y),X_8))
| or(not(Y),X_8) != implies(Y,X_8)
| implies(X,or(not(Y),X_8)) = implies(X,implies(Y,X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,or(not(Y),X_8)),implies(X,or(not(Y),X_8))) ),[1,1],$fot(implies(Y,X_8))]]) ).
cnf(refute_0_478,plain,
( or(not(Y),X_8) != implies(Y,X_8)
| implies(X,or(not(Y),X_8)) = implies(X,implies(Y,X_8)) ),
inference(resolve,[$cnf( $equal(implies(X,or(not(Y),X_8)),implies(X,or(not(Y),X_8))) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
implies(X,or(not(Y),X_8)) = implies(X,implies(Y,X_8)),
inference(resolve,[$cnf( $equal(or(not(Y),X_8),implies(Y,X_8)) )],[refute_0_475,refute_0_478]) ).
cnf(refute_0_480,plain,
or(not(X),or(not(Y),X_8)) = implies(X,or(not(Y),X_8)),
inference(subst,[],[refute_0_277:[bind(Y,$fot(or(not(Y),X_8))),bind(X_56,$fot(X))]]) ).
cnf(refute_0_481,plain,
( implies(X,or(not(Y),X_8)) != implies(X,implies(Y,X_8))
| or(not(X),or(not(Y),X_8)) != implies(X,or(not(Y),X_8))
| or(not(X),or(not(Y),X_8)) = implies(X,implies(Y,X_8)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(not(X),or(not(Y),X_8)))),bind(Y0,$fot(implies(X,or(not(Y),X_8)))),bind(Z0,$fot(implies(X,implies(Y,X_8))))]]) ).
cnf(refute_0_482,plain,
( implies(X,or(not(Y),X_8)) != implies(X,implies(Y,X_8))
| or(not(X),or(not(Y),X_8)) = implies(X,implies(Y,X_8)) ),
inference(resolve,[$cnf( $equal(or(not(X),or(not(Y),X_8)),implies(X,or(not(Y),X_8))) )],[refute_0_480,refute_0_481]) ).
cnf(refute_0_483,plain,
or(not(X),or(not(Y),X_8)) = implies(X,implies(Y,X_8)),
inference(resolve,[$cnf( $equal(implies(X,or(not(Y),X_8)),implies(X,implies(Y,X_8))) )],[refute_0_479,refute_0_482]) ).
cnf(refute_0_484,plain,
( or(not(X),or(not(Y),X_8)) != implies(X,implies(Y,X_8))
| or(not(X),or(not(Y),X_8)) != implies(and(X,Y),X_8)
| implies(X,implies(Y,X_8)) = implies(and(X,Y),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X),or(not(Y),X_8)),implies(and(X,Y),X_8)) ),[0],$fot(implies(X,implies(Y,X_8)))]]) ).
cnf(refute_0_485,plain,
( or(not(X),or(not(Y),X_8)) != implies(and(X,Y),X_8)
| implies(X,implies(Y,X_8)) = implies(and(X,Y),X_8) ),
inference(resolve,[$cnf( $equal(or(not(X),or(not(Y),X_8)),implies(X,implies(Y,X_8))) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
implies(X,implies(Y,X_8)) = implies(and(X,Y),X_8),
inference(resolve,[$cnf( $equal(or(not(X),or(not(Y),X_8)),implies(and(X,Y),X_8)) )],[refute_0_474,refute_0_485]) ).
cnf(refute_0_487,plain,
( implies(X,implies(Y,X_8)) != implies(and(X,Y),X_8)
| implies(and(X,Y),X_8) = implies(X,implies(Y,X_8)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,implies(Y,X_8)))),bind(Y0,$fot(implies(and(X,Y),X_8)))]]) ).
cnf(refute_0_488,plain,
implies(and(X,Y),X_8) = implies(X,implies(Y,X_8)),
inference(resolve,[$cnf( $equal(implies(X,implies(Y,X_8)),implies(and(X,Y),X_8)) )],[refute_0_486,refute_0_487]) ).
cnf(refute_0_489,plain,
implies(and(X_35,truth),truth) = implies(X_35,implies(truth,truth)),
inference(subst,[],[refute_0_488:[bind(X,$fot(X_35)),bind(Y,$fot(truth)),bind(X_8,$fot(truth))]]) ).
cnf(refute_0_490,plain,
( implies(X_35,implies(truth,truth)) != implies(X_35,truth)
| implies(and(X_35,truth),truth) != implies(X_35,implies(truth,truth))
| implies(and(X_35,truth),truth) = implies(X_35,truth) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(and(X_35,truth),truth))),bind(Y0,$fot(implies(X_35,implies(truth,truth)))),bind(Z0,$fot(implies(X_35,truth)))]]) ).
cnf(refute_0_491,plain,
( implies(X_35,implies(truth,truth)) != implies(X_35,truth)
| implies(and(X_35,truth),truth) = implies(X_35,truth) ),
inference(resolve,[$cnf( $equal(implies(and(X_35,truth),truth),implies(X_35,implies(truth,truth))) )],[refute_0_489,refute_0_490]) ).
cnf(refute_0_492,plain,
implies(and(X_35,truth),truth) = implies(X_35,truth),
inference(resolve,[$cnf( $equal(implies(X_35,implies(truth,truth)),implies(X_35,truth)) )],[refute_0_466,refute_0_491]) ).
cnf(refute_0_493,plain,
( implies(and(X_35,truth),truth) != implies(X_35,truth)
| not(and(falsehood,X_35)) != implies(and(X_35,truth),truth)
| not(and(falsehood,X_35)) = implies(X_35,truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(falsehood,X_35)),implies(and(X_35,truth),truth)) ),[1],$fot(implies(X_35,truth))]]) ).
cnf(refute_0_494,plain,
( not(and(falsehood,X_35)) != implies(and(X_35,truth),truth)
| not(and(falsehood,X_35)) = implies(X_35,truth) ),
inference(resolve,[$cnf( $equal(implies(and(X_35,truth),truth),implies(X_35,truth)) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
( or(falsehood,implies(falsehood,not(X_35))) != implies(and(X_35,truth),truth)
| not(and(falsehood,X_35)) = implies(X_35,truth) ),
inference(resolve,[$cnf( $equal(not(and(falsehood,X_35)),implies(and(X_35,truth),truth)) )],[refute_0_288,refute_0_494]) ).
cnf(refute_0_496,plain,
not(and(falsehood,X_35)) = implies(X_35,truth),
inference(resolve,[$cnf( $equal(or(falsehood,implies(falsehood,not(X_35))),implies(and(X_35,truth),truth)) )],[refute_0_266,refute_0_495]) ).
cnf(refute_0_497,plain,
not(and(falsehood,X_61)) = implies(X_61,truth),
inference(subst,[],[refute_0_496:[bind(X_35,$fot(X_61))]]) ).
cnf(refute_0_498,plain,
( and(falsehood,X_61) != not(not(and(falsehood,X_61)))
| not(and(falsehood,X_61)) != implies(X_61,truth)
| and(falsehood,X_61) = not(implies(X_61,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(and(falsehood,X_61),not(not(and(falsehood,X_61)))) ),[1,0],$fot(implies(X_61,truth))]]) ).
cnf(refute_0_499,plain,
( and(falsehood,X_61) != not(not(and(falsehood,X_61)))
| and(falsehood,X_61) = not(implies(X_61,truth)) ),
inference(resolve,[$cnf( $equal(not(and(falsehood,X_61)),implies(X_61,truth)) )],[refute_0_497,refute_0_498]) ).
cnf(refute_0_500,plain,
and(falsehood,X_61) = not(implies(X_61,truth)),
inference(resolve,[$cnf( $equal(and(falsehood,X_61),not(not(and(falsehood,X_61)))) )],[refute_0_251,refute_0_499]) ).
cnf(refute_0_501,plain,
implies(implies(X,implies(X_22,X)),implies(X_22,X)) = implies(implies(implies(X_22,X),X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(implies(X_22,X)))]]) ).
cnf(refute_0_502,plain,
implies(implies(X_22,X),X) = implies(implies(X,X_22),X_22),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_22)),bind(Y,$fot(X))]]) ).
cnf(refute_0_503,plain,
( implies(implies(X,implies(X_22,X)),implies(X_22,X)) != implies(implies(implies(X_22,X),X),X)
| implies(implies(X_22,X),X) != implies(implies(X,X_22),X_22)
| implies(implies(X,implies(X_22,X)),implies(X_22,X)) = implies(implies(implies(X,X_22),X_22),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_22,X)),implies(X_22,X)),implies(implies(implies(X_22,X),X),X)) ),[1,0],$fot(implies(implies(X,X_22),X_22))]]) ).
cnf(refute_0_504,plain,
( implies(implies(X,implies(X_22,X)),implies(X_22,X)) != implies(implies(implies(X_22,X),X),X)
| implies(implies(X,implies(X_22,X)),implies(X_22,X)) = implies(implies(implies(X,X_22),X_22),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X_22,X),X),implies(implies(X,X_22),X_22)) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
implies(implies(X,implies(X_22,X)),implies(X_22,X)) = implies(implies(implies(X,X_22),X_22),X),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_22,X)),implies(X_22,X)),implies(implies(implies(X_22,X),X),X)) )],[refute_0_501,refute_0_504]) ).
cnf(refute_0_506,plain,
( implies(implies(X,implies(X_22,X)),implies(X_22,X)) != implies(implies(implies(X,X_22),X_22),X)
| implies(implies(X,implies(X_22,X)),implies(X_22,X)) != implies(implies(implies(X_22,X),X),X)
| implies(implies(implies(X_22,X),X),X) = implies(implies(implies(X,X_22),X_22),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_22,X)),implies(X_22,X)),implies(implies(implies(X,X_22),X_22),X)) ),[0],$fot(implies(implies(implies(X_22,X),X),X))]]) ).
cnf(refute_0_507,plain,
( implies(implies(X,implies(X_22,X)),implies(X_22,X)) != implies(implies(implies(X,X_22),X_22),X)
| implies(implies(implies(X_22,X),X),X) = implies(implies(implies(X,X_22),X_22),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_22,X)),implies(X_22,X)),implies(implies(implies(X_22,X),X),X)) )],[refute_0_501,refute_0_506]) ).
cnf(refute_0_508,plain,
implies(implies(implies(X_22,X),X),X) = implies(implies(implies(X,X_22),X_22),X),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_22,X)),implies(X_22,X)),implies(implies(implies(X,X_22),X_22),X)) )],[refute_0_505,refute_0_507]) ).
cnf(refute_0_509,plain,
implies(implies(implies(falsehood,and(X_73,falsehood)),and(X_73,falsehood)),and(X_73,falsehood)) = implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)),
inference(subst,[],[refute_0_508:[bind(X,$fot(and(X_73,falsehood))),bind(X_22,$fot(falsehood))]]) ).
cnf(refute_0_510,plain,
implies(or(X_42,not(not(X))),implies(not(X),X_42)) = truth,
inference(subst,[],[refute_0_30:[bind(X,$fot(X_42)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_511,plain,
or(X,X_42) = implies(not(X),X_42),
inference(subst,[],[or_definition:[bind(Y,$fot(X_42))]]) ).
cnf(refute_0_512,plain,
( or(X,X_42) != implies(not(X),X_42)
| implies(not(X),X_42) = or(X,X_42) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,X_42))),bind(Y0,$fot(implies(not(X),X_42)))]]) ).
cnf(refute_0_513,plain,
implies(not(X),X_42) = or(X,X_42),
inference(resolve,[$cnf( $equal(or(X,X_42),implies(not(X),X_42)) )],[refute_0_511,refute_0_512]) ).
cnf(refute_0_514,plain,
( implies(not(X),X_42) != or(X,X_42)
| implies(or(X_42,not(not(X))),implies(not(X),X_42)) != truth
| implies(or(X_42,not(not(X))),or(X,X_42)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_42,not(not(X))),implies(not(X),X_42)),truth) ),[0,1],$fot(or(X,X_42))]]) ).
cnf(refute_0_515,plain,
( implies(or(X_42,not(not(X))),implies(not(X),X_42)) != truth
| implies(or(X_42,not(not(X))),or(X,X_42)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X),X_42),or(X,X_42)) )],[refute_0_513,refute_0_514]) ).
cnf(refute_0_516,plain,
implies(or(X_42,not(not(X))),or(X,X_42)) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_42,not(not(X))),implies(not(X),X_42)),truth) )],[refute_0_510,refute_0_515]) ).
cnf(refute_0_517,plain,
( Y != not(not(Y))
| not(not(Y)) = Y ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(Y)),bind(Y0,$fot(not(not(Y))))]]) ).
cnf(refute_0_518,plain,
not(not(Y)) = Y,
inference(resolve,[$cnf( $equal(Y,not(not(Y))) )],[refute_0_250,refute_0_517]) ).
cnf(refute_0_519,plain,
not(not(X)) = X,
inference(subst,[],[refute_0_518:[bind(Y,$fot(X))]]) ).
cnf(refute_0_520,plain,
or(X_42,not(not(X))) = or(X_42,not(not(X))),
introduced(tautology,[refl,[$fot(or(X_42,not(not(X))))]]) ).
cnf(refute_0_521,plain,
( not(not(X)) != X
| or(X_42,not(not(X))) != or(X_42,not(not(X)))
| or(X_42,not(not(X))) = or(X_42,X) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_42,not(not(X))),or(X_42,not(not(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_522,plain,
( not(not(X)) != X
| or(X_42,not(not(X))) = or(X_42,X) ),
inference(resolve,[$cnf( $equal(or(X_42,not(not(X))),or(X_42,not(not(X)))) )],[refute_0_520,refute_0_521]) ).
cnf(refute_0_523,plain,
or(X_42,not(not(X))) = or(X_42,X),
inference(resolve,[$cnf( $equal(not(not(X)),X) )],[refute_0_519,refute_0_522]) ).
cnf(refute_0_524,plain,
implies(or(X_42,not(not(X))),or(X,X_42)) = implies(or(X_42,not(not(X))),or(X,X_42)),
introduced(tautology,[refl,[$fot(implies(or(X_42,not(not(X))),or(X,X_42)))]]) ).
cnf(refute_0_525,plain,
( implies(or(X_42,not(not(X))),or(X,X_42)) != implies(or(X_42,not(not(X))),or(X,X_42))
| or(X_42,not(not(X))) != or(X_42,X)
| implies(or(X_42,not(not(X))),or(X,X_42)) = implies(or(X_42,X),or(X,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_42,not(not(X))),or(X,X_42)),implies(or(X_42,not(not(X))),or(X,X_42))) ),[1,0],$fot(or(X_42,X))]]) ).
cnf(refute_0_526,plain,
( or(X_42,not(not(X))) != or(X_42,X)
| implies(or(X_42,not(not(X))),or(X,X_42)) = implies(or(X_42,X),or(X,X_42)) ),
inference(resolve,[$cnf( $equal(implies(or(X_42,not(not(X))),or(X,X_42)),implies(or(X_42,not(not(X))),or(X,X_42))) )],[refute_0_524,refute_0_525]) ).
cnf(refute_0_527,plain,
implies(or(X_42,not(not(X))),or(X,X_42)) = implies(or(X_42,X),or(X,X_42)),
inference(resolve,[$cnf( $equal(or(X_42,not(not(X))),or(X_42,X)) )],[refute_0_523,refute_0_526]) ).
cnf(refute_0_528,plain,
( implies(or(X_42,not(not(X))),or(X,X_42)) != implies(or(X_42,X),or(X,X_42))
| implies(or(X_42,not(not(X))),or(X,X_42)) != truth
| implies(or(X_42,X),or(X,X_42)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_42,not(not(X))),or(X,X_42)),truth) ),[0],$fot(implies(or(X_42,X),or(X,X_42)))]]) ).
cnf(refute_0_529,plain,
( implies(or(X_42,not(not(X))),or(X,X_42)) != truth
| implies(or(X_42,X),or(X,X_42)) = truth ),
inference(resolve,[$cnf( $equal(implies(or(X_42,not(not(X))),or(X,X_42)),implies(or(X_42,X),or(X,X_42))) )],[refute_0_527,refute_0_528]) ).
cnf(refute_0_530,plain,
implies(or(X_42,X),or(X,X_42)) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_42,not(not(X))),or(X,X_42)),truth) )],[refute_0_516,refute_0_529]) ).
cnf(refute_0_531,plain,
implies(or(falsehood,X_71),or(X_71,falsehood)) = truth,
inference(subst,[],[refute_0_530:[bind(X,$fot(X_71)),bind(X_42,$fot(falsehood))]]) ).
cnf(refute_0_532,plain,
or(X_71,falsehood) = X_71,
inference(subst,[],[refute_0_204:[bind(X_8,$fot(X_71))]]) ).
cnf(refute_0_533,plain,
( implies(or(falsehood,X_71),or(X_71,falsehood)) != truth
| or(X_71,falsehood) != X_71
| implies(or(falsehood,X_71),X_71) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,X_71),or(X_71,falsehood)),truth) ),[0,1],$fot(X_71)]]) ).
cnf(refute_0_534,plain,
( implies(or(falsehood,X_71),or(X_71,falsehood)) != truth
| implies(or(falsehood,X_71),X_71) = truth ),
inference(resolve,[$cnf( $equal(or(X_71,falsehood),X_71) )],[refute_0_532,refute_0_533]) ).
cnf(refute_0_535,plain,
implies(or(falsehood,X_71),X_71) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,X_71),or(X_71,falsehood)),truth) )],[refute_0_531,refute_0_534]) ).
cnf(refute_0_536,plain,
implies(implies(not(X),X_23),X_23) = implies(implies(X_23,not(X)),not(X)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(X))),bind(Y,$fot(X_23))]]) ).
cnf(refute_0_537,plain,
or(X,X_23) = implies(not(X),X_23),
inference(subst,[],[or_definition:[bind(Y,$fot(X_23))]]) ).
cnf(refute_0_538,plain,
( or(X,X_23) != implies(not(X),X_23)
| implies(not(X),X_23) = or(X,X_23) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,X_23))),bind(Y0,$fot(implies(not(X),X_23)))]]) ).
cnf(refute_0_539,plain,
implies(not(X),X_23) = or(X,X_23),
inference(resolve,[$cnf( $equal(or(X,X_23),implies(not(X),X_23)) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
( implies(implies(not(X),X_23),X_23) != implies(implies(X_23,not(X)),not(X))
| implies(not(X),X_23) != or(X,X_23)
| implies(or(X,X_23),X_23) = implies(implies(X_23,not(X)),not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),X_23),X_23),implies(implies(X_23,not(X)),not(X))) ),[0,0],$fot(or(X,X_23))]]) ).
cnf(refute_0_541,plain,
( implies(implies(not(X),X_23),X_23) != implies(implies(X_23,not(X)),not(X))
| implies(or(X,X_23),X_23) = implies(implies(X_23,not(X)),not(X)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_23),or(X,X_23)) )],[refute_0_539,refute_0_540]) ).
cnf(refute_0_542,plain,
implies(or(X,X_23),X_23) = implies(implies(X_23,not(X)),not(X)),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_23),X_23),implies(implies(X_23,not(X)),not(X))) )],[refute_0_536,refute_0_541]) ).
cnf(refute_0_543,plain,
not(not(implies(X,and(X_23,X)))) = implies(X,and(X_23,X)),
inference(subst,[],[refute_0_518:[bind(Y,$fot(implies(X,and(X_23,X))))]]) ).
cnf(refute_0_544,plain,
and(X,not(X_56)) = not(or(not(X),not(not(X_56)))),
inference(subst,[],[and_definition:[bind(Y,$fot(not(X_56)))]]) ).
cnf(refute_0_545,plain,
( and(X,not(X_56)) != not(or(not(X),not(not(X_56))))
| not(not(X_56)) != X_56
| and(X,not(X_56)) = not(or(not(X),X_56)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,not(X_56)),not(or(not(X),not(not(X_56))))) ),[1,0,1],$fot(X_56)]]) ).
cnf(refute_0_546,plain,
( and(X,not(X_56)) != not(or(not(X),not(not(X_56))))
| and(X,not(X_56)) = not(or(not(X),X_56)) ),
inference(resolve,[$cnf( $equal(not(not(X_56)),X_56) )],[refute_0_274,refute_0_545]) ).
cnf(refute_0_547,plain,
and(X,not(X_56)) = not(or(not(X),X_56)),
inference(resolve,[$cnf( $equal(and(X,not(X_56)),not(or(not(X),not(not(X_56))))) )],[refute_0_544,refute_0_546]) ).
cnf(refute_0_548,plain,
or(not(X),X_56) = implies(X,X_56),
inference(subst,[],[refute_0_277:[bind(Y,$fot(X_56)),bind(X_56,$fot(X))]]) ).
cnf(refute_0_549,plain,
not(or(not(X),X_56)) = not(or(not(X),X_56)),
introduced(tautology,[refl,[$fot(not(or(not(X),X_56)))]]) ).
cnf(refute_0_550,plain,
( not(or(not(X),X_56)) != not(or(not(X),X_56))
| or(not(X),X_56) != implies(X,X_56)
| not(or(not(X),X_56)) = not(implies(X,X_56)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),X_56)),not(or(not(X),X_56))) ),[1,0],$fot(implies(X,X_56))]]) ).
cnf(refute_0_551,plain,
( or(not(X),X_56) != implies(X,X_56)
| not(or(not(X),X_56)) = not(implies(X,X_56)) ),
inference(resolve,[$cnf( $equal(not(or(not(X),X_56)),not(or(not(X),X_56))) )],[refute_0_549,refute_0_550]) ).
cnf(refute_0_552,plain,
not(or(not(X),X_56)) = not(implies(X,X_56)),
inference(resolve,[$cnf( $equal(or(not(X),X_56),implies(X,X_56)) )],[refute_0_548,refute_0_551]) ).
cnf(refute_0_553,plain,
( and(X,not(X_56)) != not(or(not(X),X_56))
| not(or(not(X),X_56)) != not(implies(X,X_56))
| and(X,not(X_56)) = not(implies(X,X_56)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,not(X_56)),not(implies(X,X_56))) ),[0],$fot(not(or(not(X),X_56)))]]) ).
cnf(refute_0_554,plain,
( and(X,not(X_56)) != not(or(not(X),X_56))
| and(X,not(X_56)) = not(implies(X,X_56)) ),
inference(resolve,[$cnf( $equal(not(or(not(X),X_56)),not(implies(X,X_56))) )],[refute_0_552,refute_0_553]) ).
cnf(refute_0_555,plain,
and(X,not(X_56)) = not(implies(X,X_56)),
inference(resolve,[$cnf( $equal(and(X,not(X_56)),not(or(not(X),X_56))) )],[refute_0_547,refute_0_554]) ).
cnf(refute_0_556,plain,
and(X,not(and(X_23,X))) = not(implies(X,and(X_23,X))),
inference(subst,[],[refute_0_555:[bind(X_56,$fot(and(X_23,X)))]]) ).
cnf(refute_0_557,plain,
implies(X_23,not(X)) = not(and(X_23,X)),
inference(subst,[],[refute_0_281:[bind(X,$fot(X_23)),bind(Y,$fot(X))]]) ).
cnf(refute_0_558,plain,
and(X,implies(X_23,not(X))) = and(X,implies(X_23,not(X))),
introduced(tautology,[refl,[$fot(and(X,implies(X_23,not(X))))]]) ).
cnf(refute_0_559,plain,
( and(X,implies(X_23,not(X))) != and(X,implies(X_23,not(X)))
| implies(X_23,not(X)) != not(and(X_23,X))
| and(X,implies(X_23,not(X))) = and(X,not(and(X_23,X))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,implies(X_23,not(X))),and(X,implies(X_23,not(X)))) ),[1,1],$fot(not(and(X_23,X)))]]) ).
cnf(refute_0_560,plain,
( implies(X_23,not(X)) != not(and(X_23,X))
| and(X,implies(X_23,not(X))) = and(X,not(and(X_23,X))) ),
inference(resolve,[$cnf( $equal(and(X,implies(X_23,not(X))),and(X,implies(X_23,not(X)))) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
and(X,implies(X_23,not(X))) = and(X,not(and(X_23,X))),
inference(resolve,[$cnf( $equal(implies(X_23,not(X)),not(and(X_23,X))) )],[refute_0_557,refute_0_560]) ).
cnf(refute_0_562,plain,
( and(X,implies(X_23,not(X))) != and(X,not(and(X_23,X)))
| and(X,not(and(X_23,X))) != not(implies(X,and(X_23,X)))
| and(X,implies(X_23,not(X))) = not(implies(X,and(X_23,X))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(X,implies(X_23,not(X))))),bind(Y0,$fot(and(X,not(and(X_23,X))))),bind(Z0,$fot(not(implies(X,and(X_23,X)))))]]) ).
cnf(refute_0_563,plain,
( and(X,not(and(X_23,X))) != not(implies(X,and(X_23,X)))
| and(X,implies(X_23,not(X))) = not(implies(X,and(X_23,X))) ),
inference(resolve,[$cnf( $equal(and(X,implies(X_23,not(X))),and(X,not(and(X_23,X)))) )],[refute_0_561,refute_0_562]) ).
cnf(refute_0_564,plain,
and(X,implies(X_23,not(X))) = not(implies(X,and(X_23,X))),
inference(resolve,[$cnf( $equal(and(X,not(and(X_23,X))),not(implies(X,and(X_23,X)))) )],[refute_0_556,refute_0_563]) ).
cnf(refute_0_565,plain,
and(and(X_34,truth),Y) = and(Y,and(X_34,truth)),
inference(subst,[],[and_commutativity:[bind(X,$fot(and(X_34,truth)))]]) ).
cnf(refute_0_566,plain,
and(and(X_19,truth),X_21) = and(X_19,and(truth,X_21)),
inference(subst,[],[and_associativity:[bind(X,$fot(X_19)),bind(Y,$fot(truth)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_567,plain,
and(truth,X_21) = and(X_21,truth),
inference(subst,[],[refute_0_382:[bind(X_2,$fot(X_21))]]) ).
cnf(refute_0_568,plain,
( and(and(X_19,truth),X_21) != and(X_19,and(truth,X_21))
| and(truth,X_21) != and(X_21,truth)
| and(and(X_19,truth),X_21) = and(X_19,and(X_21,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(X_19,truth),X_21),and(X_19,and(truth,X_21))) ),[1,1],$fot(and(X_21,truth))]]) ).
cnf(refute_0_569,plain,
( and(and(X_19,truth),X_21) != and(X_19,and(truth,X_21))
| and(and(X_19,truth),X_21) = and(X_19,and(X_21,truth)) ),
inference(resolve,[$cnf( $equal(and(truth,X_21),and(X_21,truth)) )],[refute_0_567,refute_0_568]) ).
cnf(refute_0_570,plain,
and(and(X_19,truth),X_21) = and(X_19,and(X_21,truth)),
inference(resolve,[$cnf( $equal(and(and(X_19,truth),X_21),and(X_19,and(truth,X_21))) )],[refute_0_566,refute_0_569]) ).
cnf(refute_0_571,plain,
( and(and(X_19,truth),X_21) != and(X_19,and(X_21,truth))
| and(and(X_19,truth),X_21) != and(X_19,and(truth,X_21))
| and(X_19,and(truth,X_21)) = and(X_19,and(X_21,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(X_19,truth),X_21),and(X_19,and(X_21,truth))) ),[0],$fot(and(X_19,and(truth,X_21)))]]) ).
cnf(refute_0_572,plain,
( and(and(X_19,truth),X_21) != and(X_19,and(X_21,truth))
| and(X_19,and(truth,X_21)) = and(X_19,and(X_21,truth)) ),
inference(resolve,[$cnf( $equal(and(and(X_19,truth),X_21),and(X_19,and(truth,X_21))) )],[refute_0_566,refute_0_571]) ).
cnf(refute_0_573,plain,
and(X_19,and(truth,X_21)) = and(X_19,and(X_21,truth)),
inference(resolve,[$cnf( $equal(and(and(X_19,truth),X_21),and(X_19,and(X_21,truth))) )],[refute_0_570,refute_0_572]) ).
cnf(refute_0_574,plain,
and(Y,and(truth,X_34)) = and(Y,and(X_34,truth)),
inference(subst,[],[refute_0_573:[bind(X_19,$fot(Y)),bind(X_21,$fot(X_34))]]) ).
cnf(refute_0_575,plain,
( and(Y,and(truth,X_34)) != and(Y,and(X_34,truth))
| and(Y,and(X_34,truth)) = and(Y,and(truth,X_34)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(Y,and(truth,X_34)))),bind(Y0,$fot(and(Y,and(X_34,truth))))]]) ).
cnf(refute_0_576,plain,
and(Y,and(X_34,truth)) = and(Y,and(truth,X_34)),
inference(resolve,[$cnf( $equal(and(Y,and(truth,X_34)),and(Y,and(X_34,truth))) )],[refute_0_574,refute_0_575]) ).
cnf(refute_0_577,plain,
( and(Y,and(X_34,truth)) != and(Y,and(truth,X_34))
| and(and(X_34,truth),Y) != and(Y,and(X_34,truth))
| and(and(X_34,truth),Y) = and(Y,and(truth,X_34)) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(X_34,truth),Y),and(Y,and(X_34,truth))) ),[1],$fot(and(Y,and(truth,X_34)))]]) ).
cnf(refute_0_578,plain,
( and(and(X_34,truth),Y) != and(Y,and(X_34,truth))
| and(and(X_34,truth),Y) = and(Y,and(truth,X_34)) ),
inference(resolve,[$cnf( $equal(and(Y,and(X_34,truth)),and(Y,and(truth,X_34))) )],[refute_0_576,refute_0_577]) ).
cnf(refute_0_579,plain,
and(and(X_34,truth),Y) = and(Y,and(truth,X_34)),
inference(resolve,[$cnf( $equal(and(and(X_34,truth),Y),and(Y,and(X_34,truth))) )],[refute_0_565,refute_0_578]) ).
cnf(refute_0_580,plain,
and(and(X_34,truth),Y) = and(X_34,and(truth,Y)),
inference(subst,[],[and_associativity:[bind(X,$fot(X_34)),bind(Y,$fot(truth)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_581,plain,
( and(and(X_34,truth),Y) != and(Y,and(truth,X_34))
| and(and(X_34,truth),Y) != and(X_34,and(truth,Y))
| and(X_34,and(truth,Y)) = and(Y,and(truth,X_34)) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(X_34,truth),Y),and(Y,and(truth,X_34))) ),[0],$fot(and(X_34,and(truth,Y)))]]) ).
cnf(refute_0_582,plain,
( and(and(X_34,truth),Y) != and(Y,and(truth,X_34))
| and(X_34,and(truth,Y)) = and(Y,and(truth,X_34)) ),
inference(resolve,[$cnf( $equal(and(and(X_34,truth),Y),and(X_34,and(truth,Y))) )],[refute_0_580,refute_0_581]) ).
cnf(refute_0_583,plain,
and(X_34,and(truth,Y)) = and(Y,and(truth,X_34)),
inference(resolve,[$cnf( $equal(and(and(X_34,truth),Y),and(Y,and(truth,X_34))) )],[refute_0_579,refute_0_582]) ).
cnf(refute_0_584,plain,
and(truth,and(X_19,X_20)) = and(and(X_19,X_20),truth),
inference(subst,[],[refute_0_382:[bind(X_2,$fot(and(X_19,X_20)))]]) ).
cnf(refute_0_585,plain,
and(and(X_19,X_20),truth) = and(X_19,and(X_20,truth)),
inference(subst,[],[and_associativity:[bind(X,$fot(X_19)),bind(Y,$fot(X_20)),bind(Z,$fot(truth))]]) ).
cnf(refute_0_586,plain,
( and(and(X_19,X_20),truth) != and(X_19,and(X_20,truth))
| and(truth,and(X_19,X_20)) != and(and(X_19,X_20),truth)
| and(truth,and(X_19,X_20)) = and(X_19,and(X_20,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,and(X_19,X_20)),and(and(X_19,X_20),truth)) ),[1],$fot(and(X_19,and(X_20,truth)))]]) ).
cnf(refute_0_587,plain,
( and(truth,and(X_19,X_20)) != and(and(X_19,X_20),truth)
| and(truth,and(X_19,X_20)) = and(X_19,and(X_20,truth)) ),
inference(resolve,[$cnf( $equal(and(and(X_19,X_20),truth),and(X_19,and(X_20,truth))) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
and(truth,and(X_19,X_20)) = and(X_19,and(X_20,truth)),
inference(resolve,[$cnf( $equal(and(truth,and(X_19,X_20)),and(and(X_19,X_20),truth)) )],[refute_0_584,refute_0_587]) ).
cnf(refute_0_589,plain,
and(truth,and(X_19,X_20)) = not(not(and(X_19,X_20))),
inference(subst,[],[refute_0_440:[bind(Y,$fot(and(X_19,X_20)))]]) ).
cnf(refute_0_590,plain,
( and(truth,and(X_19,X_20)) != and(X_19,and(X_20,truth))
| and(truth,and(X_19,X_20)) != not(not(and(X_19,X_20)))
| not(not(and(X_19,X_20))) = and(X_19,and(X_20,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,and(X_19,X_20)),and(X_19,and(X_20,truth))) ),[0],$fot(not(not(and(X_19,X_20))))]]) ).
cnf(refute_0_591,plain,
( and(truth,and(X_19,X_20)) != and(X_19,and(X_20,truth))
| not(not(and(X_19,X_20))) = and(X_19,and(X_20,truth)) ),
inference(resolve,[$cnf( $equal(and(truth,and(X_19,X_20)),not(not(and(X_19,X_20)))) )],[refute_0_589,refute_0_590]) ).
cnf(refute_0_592,plain,
and(X_20,truth) = not(not(X_20)),
inference(subst,[],[refute_0_189:[bind(X_1,$fot(X_20))]]) ).
cnf(refute_0_593,plain,
and(X_19,and(X_20,truth)) = and(X_19,and(X_20,truth)),
introduced(tautology,[refl,[$fot(and(X_19,and(X_20,truth)))]]) ).
cnf(refute_0_594,plain,
( and(X_19,and(X_20,truth)) != and(X_19,and(X_20,truth))
| and(X_20,truth) != not(not(X_20))
| and(X_19,and(X_20,truth)) = and(X_19,not(not(X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_19,and(X_20,truth)),and(X_19,and(X_20,truth))) ),[1,1],$fot(not(not(X_20)))]]) ).
cnf(refute_0_595,plain,
( and(X_20,truth) != not(not(X_20))
| and(X_19,and(X_20,truth)) = and(X_19,not(not(X_20))) ),
inference(resolve,[$cnf( $equal(and(X_19,and(X_20,truth)),and(X_19,and(X_20,truth))) )],[refute_0_593,refute_0_594]) ).
cnf(refute_0_596,plain,
and(X_19,and(X_20,truth)) = and(X_19,not(not(X_20))),
inference(resolve,[$cnf( $equal(and(X_20,truth),not(not(X_20))) )],[refute_0_592,refute_0_595]) ).
cnf(refute_0_597,plain,
( and(X_19,and(X_20,truth)) != and(X_19,not(not(X_20)))
| not(not(and(X_19,X_20))) != and(X_19,and(X_20,truth))
| not(not(and(X_19,X_20))) = and(X_19,not(not(X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(and(X_19,X_20))),and(X_19,and(X_20,truth))) ),[1],$fot(and(X_19,not(not(X_20))))]]) ).
cnf(refute_0_598,plain,
( not(not(and(X_19,X_20))) != and(X_19,and(X_20,truth))
| not(not(and(X_19,X_20))) = and(X_19,not(not(X_20))) ),
inference(resolve,[$cnf( $equal(and(X_19,and(X_20,truth)),and(X_19,not(not(X_20)))) )],[refute_0_596,refute_0_597]) ).
cnf(refute_0_599,plain,
( and(truth,and(X_19,X_20)) != and(X_19,and(X_20,truth))
| not(not(and(X_19,X_20))) = and(X_19,not(not(X_20))) ),
inference(resolve,[$cnf( $equal(not(not(and(X_19,X_20))),and(X_19,and(X_20,truth))) )],[refute_0_591,refute_0_598]) ).
cnf(refute_0_600,plain,
not(not(and(X_19,X_20))) = and(X_19,not(not(X_20))),
inference(resolve,[$cnf( $equal(and(truth,and(X_19,X_20)),and(X_19,and(X_20,truth))) )],[refute_0_588,refute_0_599]) ).
cnf(refute_0_601,plain,
( not(not(and(X_19,X_20))) != and(X_19,not(not(X_20)))
| and(X_19,not(not(X_20))) = not(not(and(X_19,X_20))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(not(not(and(X_19,X_20))))),bind(Y0,$fot(and(X_19,not(not(X_20)))))]]) ).
cnf(refute_0_602,plain,
and(X_19,not(not(X_20))) = not(not(and(X_19,X_20))),
inference(resolve,[$cnf( $equal(not(not(and(X_19,X_20))),and(X_19,not(not(X_20)))) )],[refute_0_600,refute_0_601]) ).
cnf(refute_0_603,plain,
and(X_34,not(not(Y))) = not(not(and(X_34,Y))),
inference(subst,[],[refute_0_602:[bind(X_19,$fot(X_34)),bind(X_20,$fot(Y))]]) ).
cnf(refute_0_604,plain,
and(X_34,and(truth,Y)) = and(X_34,and(truth,Y)),
introduced(tautology,[refl,[$fot(and(X_34,and(truth,Y)))]]) ).
cnf(refute_0_605,plain,
( and(X_34,and(truth,Y)) != and(X_34,and(truth,Y))
| and(truth,Y) != not(not(Y))
| and(X_34,and(truth,Y)) = and(X_34,not(not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_34,and(truth,Y)),and(X_34,and(truth,Y))) ),[1,1],$fot(not(not(Y)))]]) ).
cnf(refute_0_606,plain,
( and(truth,Y) != not(not(Y))
| and(X_34,and(truth,Y)) = and(X_34,not(not(Y))) ),
inference(resolve,[$cnf( $equal(and(X_34,and(truth,Y)),and(X_34,and(truth,Y))) )],[refute_0_604,refute_0_605]) ).
cnf(refute_0_607,plain,
and(X_34,and(truth,Y)) = and(X_34,not(not(Y))),
inference(resolve,[$cnf( $equal(and(truth,Y),not(not(Y))) )],[refute_0_440,refute_0_606]) ).
cnf(refute_0_608,plain,
( and(X_34,and(truth,Y)) != and(X_34,not(not(Y)))
| and(X_34,not(not(Y))) != not(not(and(X_34,Y)))
| and(X_34,and(truth,Y)) = not(not(and(X_34,Y))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(X_34,and(truth,Y)))),bind(Y0,$fot(and(X_34,not(not(Y))))),bind(Z0,$fot(not(not(and(X_34,Y)))))]]) ).
cnf(refute_0_609,plain,
( and(X_34,not(not(Y))) != not(not(and(X_34,Y)))
| and(X_34,and(truth,Y)) = not(not(and(X_34,Y))) ),
inference(resolve,[$cnf( $equal(and(X_34,and(truth,Y)),and(X_34,not(not(Y)))) )],[refute_0_607,refute_0_608]) ).
cnf(refute_0_610,plain,
and(X_34,and(truth,Y)) = not(not(and(X_34,Y))),
inference(resolve,[$cnf( $equal(and(X_34,not(not(Y))),not(not(and(X_34,Y)))) )],[refute_0_603,refute_0_609]) ).
cnf(refute_0_611,plain,
( and(X_34,and(truth,Y)) != and(Y,and(truth,X_34))
| and(X_34,and(truth,Y)) != not(not(and(X_34,Y)))
| not(not(and(X_34,Y))) = and(Y,and(truth,X_34)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_34,and(truth,Y)),and(Y,and(truth,X_34))) ),[0],$fot(not(not(and(X_34,Y))))]]) ).
cnf(refute_0_612,plain,
( and(X_34,and(truth,Y)) != and(Y,and(truth,X_34))
| not(not(and(X_34,Y))) = and(Y,and(truth,X_34)) ),
inference(resolve,[$cnf( $equal(and(X_34,and(truth,Y)),not(not(and(X_34,Y)))) )],[refute_0_610,refute_0_611]) ).
cnf(refute_0_613,plain,
and(Y,not(not(X_34))) = not(not(and(Y,X_34))),
inference(subst,[],[refute_0_602:[bind(X_19,$fot(Y)),bind(X_20,$fot(X_34))]]) ).
cnf(refute_0_614,plain,
and(truth,X_34) = not(not(X_34)),
inference(subst,[],[refute_0_440:[bind(Y,$fot(X_34))]]) ).
cnf(refute_0_615,plain,
and(Y,and(truth,X_34)) = and(Y,and(truth,X_34)),
introduced(tautology,[refl,[$fot(and(Y,and(truth,X_34)))]]) ).
cnf(refute_0_616,plain,
( and(Y,and(truth,X_34)) != and(Y,and(truth,X_34))
| and(truth,X_34) != not(not(X_34))
| and(Y,and(truth,X_34)) = and(Y,not(not(X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(and(Y,and(truth,X_34)),and(Y,and(truth,X_34))) ),[1,1],$fot(not(not(X_34)))]]) ).
cnf(refute_0_617,plain,
( and(truth,X_34) != not(not(X_34))
| and(Y,and(truth,X_34)) = and(Y,not(not(X_34))) ),
inference(resolve,[$cnf( $equal(and(Y,and(truth,X_34)),and(Y,and(truth,X_34))) )],[refute_0_615,refute_0_616]) ).
cnf(refute_0_618,plain,
and(Y,and(truth,X_34)) = and(Y,not(not(X_34))),
inference(resolve,[$cnf( $equal(and(truth,X_34),not(not(X_34))) )],[refute_0_614,refute_0_617]) ).
cnf(refute_0_619,plain,
( and(Y,and(truth,X_34)) != and(Y,not(not(X_34)))
| and(Y,not(not(X_34))) != not(not(and(Y,X_34)))
| and(Y,and(truth,X_34)) = not(not(and(Y,X_34))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(Y,and(truth,X_34)))),bind(Y0,$fot(and(Y,not(not(X_34))))),bind(Z0,$fot(not(not(and(Y,X_34)))))]]) ).
cnf(refute_0_620,plain,
( and(Y,not(not(X_34))) != not(not(and(Y,X_34)))
| and(Y,and(truth,X_34)) = not(not(and(Y,X_34))) ),
inference(resolve,[$cnf( $equal(and(Y,and(truth,X_34)),and(Y,not(not(X_34)))) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
and(Y,and(truth,X_34)) = not(not(and(Y,X_34))),
inference(resolve,[$cnf( $equal(and(Y,not(not(X_34))),not(not(and(Y,X_34)))) )],[refute_0_613,refute_0_620]) ).
cnf(refute_0_622,plain,
( and(Y,and(truth,X_34)) != not(not(and(Y,X_34)))
| not(not(and(X_34,Y))) != and(Y,and(truth,X_34))
| not(not(and(X_34,Y))) = not(not(and(Y,X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(and(X_34,Y))),and(Y,and(truth,X_34))) ),[1],$fot(not(not(and(Y,X_34))))]]) ).
cnf(refute_0_623,plain,
( not(not(and(X_34,Y))) != and(Y,and(truth,X_34))
| not(not(and(X_34,Y))) = not(not(and(Y,X_34))) ),
inference(resolve,[$cnf( $equal(and(Y,and(truth,X_34)),not(not(and(Y,X_34)))) )],[refute_0_621,refute_0_622]) ).
cnf(refute_0_624,plain,
( and(X_34,and(truth,Y)) != and(Y,and(truth,X_34))
| not(not(and(X_34,Y))) = not(not(and(Y,X_34))) ),
inference(resolve,[$cnf( $equal(not(not(and(X_34,Y))),and(Y,and(truth,X_34))) )],[refute_0_612,refute_0_623]) ).
cnf(refute_0_625,plain,
not(not(and(X_34,Y))) = not(not(and(Y,X_34))),
inference(resolve,[$cnf( $equal(and(X_34,and(truth,Y)),and(Y,and(truth,X_34))) )],[refute_0_583,refute_0_624]) ).
cnf(refute_0_626,plain,
not(not(and(X_34,Y))) = and(X_34,Y),
inference(subst,[],[refute_0_518:[bind(Y,$fot(and(X_34,Y)))]]) ).
cnf(refute_0_627,plain,
( not(not(and(X_34,Y))) != and(X_34,Y)
| not(not(and(X_34,Y))) != not(not(and(Y,X_34)))
| and(X_34,Y) = not(not(and(Y,X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(and(X_34,Y))),not(not(and(Y,X_34)))) ),[0],$fot(and(X_34,Y))]]) ).
cnf(refute_0_628,plain,
( not(not(and(X_34,Y))) != not(not(and(Y,X_34)))
| and(X_34,Y) = not(not(and(Y,X_34))) ),
inference(resolve,[$cnf( $equal(not(not(and(X_34,Y))),and(X_34,Y)) )],[refute_0_626,refute_0_627]) ).
cnf(refute_0_629,plain,
not(not(and(Y,X_34))) = and(Y,X_34),
inference(subst,[],[refute_0_518:[bind(Y,$fot(and(Y,X_34)))]]) ).
cnf(refute_0_630,plain,
( and(X_34,Y) != not(not(and(Y,X_34)))
| not(not(and(Y,X_34))) != and(Y,X_34)
| and(X_34,Y) = and(Y,X_34) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_34,Y),and(Y,X_34)) ),[0],$fot(not(not(and(Y,X_34))))]]) ).
cnf(refute_0_631,plain,
( and(X_34,Y) != not(not(and(Y,X_34)))
| and(X_34,Y) = and(Y,X_34) ),
inference(resolve,[$cnf( $equal(not(not(and(Y,X_34))),and(Y,X_34)) )],[refute_0_629,refute_0_630]) ).
cnf(refute_0_632,plain,
( not(not(and(X_34,Y))) != not(not(and(Y,X_34)))
| and(X_34,Y) = and(Y,X_34) ),
inference(resolve,[$cnf( $equal(and(X_34,Y),not(not(and(Y,X_34)))) )],[refute_0_628,refute_0_631]) ).
cnf(refute_0_633,plain,
and(X_34,Y) = and(Y,X_34),
inference(resolve,[$cnf( $equal(not(not(and(X_34,Y))),not(not(and(Y,X_34)))) )],[refute_0_625,refute_0_632]) ).
cnf(refute_0_634,plain,
( and(X_34,Y) != and(Y,X_34)
| and(Y,X_34) = and(X_34,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_34,Y))),bind(Y0,$fot(and(Y,X_34)))]]) ).
cnf(refute_0_635,plain,
and(Y,X_34) = and(X_34,Y),
inference(resolve,[$cnf( $equal(and(X_34,Y),and(Y,X_34)) )],[refute_0_633,refute_0_634]) ).
cnf(refute_0_636,plain,
and(implies(X_23,not(X)),X) = and(X,implies(X_23,not(X))),
inference(subst,[],[refute_0_635:[bind(Y,$fot(implies(X_23,not(X)))),bind(X_34,$fot(X))]]) ).
cnf(refute_0_637,plain,
( and(X,implies(X_23,not(X))) != not(implies(X,and(X_23,X)))
| and(implies(X_23,not(X)),X) != and(X,implies(X_23,not(X)))
| and(implies(X_23,not(X)),X) = not(implies(X,and(X_23,X))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(implies(X_23,not(X)),X))),bind(Y0,$fot(and(X,implies(X_23,not(X))))),bind(Z0,$fot(not(implies(X,and(X_23,X)))))]]) ).
cnf(refute_0_638,plain,
( and(X,implies(X_23,not(X))) != not(implies(X,and(X_23,X)))
| and(implies(X_23,not(X)),X) = not(implies(X,and(X_23,X))) ),
inference(resolve,[$cnf( $equal(and(implies(X_23,not(X)),X),and(X,implies(X_23,not(X)))) )],[refute_0_636,refute_0_637]) ).
cnf(refute_0_639,plain,
and(implies(X_23,not(X)),X) = not(implies(X,and(X_23,X))),
inference(resolve,[$cnf( $equal(and(X,implies(X_23,not(X))),not(implies(X,and(X_23,X)))) )],[refute_0_564,refute_0_638]) ).
cnf(refute_0_640,plain,
not(and(implies(X_23,not(X)),X)) = not(and(implies(X_23,not(X)),X)),
introduced(tautology,[refl,[$fot(not(and(implies(X_23,not(X)),X)))]]) ).
cnf(refute_0_641,plain,
( and(implies(X_23,not(X)),X) != not(implies(X,and(X_23,X)))
| not(and(implies(X_23,not(X)),X)) != not(and(implies(X_23,not(X)),X))
| not(and(implies(X_23,not(X)),X)) = not(not(implies(X,and(X_23,X)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(implies(X_23,not(X)),X)),not(and(implies(X_23,not(X)),X))) ),[1,0],$fot(not(implies(X,and(X_23,X))))]]) ).
cnf(refute_0_642,plain,
( and(implies(X_23,not(X)),X) != not(implies(X,and(X_23,X)))
| not(and(implies(X_23,not(X)),X)) = not(not(implies(X,and(X_23,X)))) ),
inference(resolve,[$cnf( $equal(not(and(implies(X_23,not(X)),X)),not(and(implies(X_23,not(X)),X))) )],[refute_0_640,refute_0_641]) ).
cnf(refute_0_643,plain,
not(and(implies(X_23,not(X)),X)) = not(not(implies(X,and(X_23,X)))),
inference(resolve,[$cnf( $equal(and(implies(X_23,not(X)),X),not(implies(X,and(X_23,X)))) )],[refute_0_639,refute_0_642]) ).
cnf(refute_0_644,plain,
( not(and(implies(X_23,not(X)),X)) != not(not(implies(X,and(X_23,X))))
| not(not(implies(X,and(X_23,X)))) != implies(X,and(X_23,X))
| not(and(implies(X_23,not(X)),X)) = implies(X,and(X_23,X)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(and(implies(X_23,not(X)),X)))),bind(Y0,$fot(not(not(implies(X,and(X_23,X)))))),bind(Z0,$fot(implies(X,and(X_23,X))))]]) ).
cnf(refute_0_645,plain,
( not(not(implies(X,and(X_23,X)))) != implies(X,and(X_23,X))
| not(and(implies(X_23,not(X)),X)) = implies(X,and(X_23,X)) ),
inference(resolve,[$cnf( $equal(not(and(implies(X_23,not(X)),X)),not(not(implies(X,and(X_23,X))))) )],[refute_0_643,refute_0_644]) ).
cnf(refute_0_646,plain,
not(and(implies(X_23,not(X)),X)) = implies(X,and(X_23,X)),
inference(resolve,[$cnf( $equal(not(not(implies(X,and(X_23,X)))),implies(X,and(X_23,X))) )],[refute_0_543,refute_0_645]) ).
cnf(refute_0_647,plain,
implies(implies(X_23,not(X)),not(X)) = not(and(implies(X_23,not(X)),X)),
inference(subst,[],[refute_0_281:[bind(X,$fot(implies(X_23,not(X)))),bind(Y,$fot(X))]]) ).
cnf(refute_0_648,plain,
( implies(implies(X_23,not(X)),not(X)) != not(and(implies(X_23,not(X)),X))
| not(and(implies(X_23,not(X)),X)) != implies(X,and(X_23,X))
| implies(implies(X_23,not(X)),not(X)) = implies(X,and(X_23,X)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(implies(X_23,not(X)),not(X)))),bind(Y0,$fot(not(and(implies(X_23,not(X)),X)))),bind(Z0,$fot(implies(X,and(X_23,X))))]]) ).
cnf(refute_0_649,plain,
( not(and(implies(X_23,not(X)),X)) != implies(X,and(X_23,X))
| implies(implies(X_23,not(X)),not(X)) = implies(X,and(X_23,X)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_23,not(X)),not(X)),not(and(implies(X_23,not(X)),X))) )],[refute_0_647,refute_0_648]) ).
cnf(refute_0_650,plain,
implies(implies(X_23,not(X)),not(X)) = implies(X,and(X_23,X)),
inference(resolve,[$cnf( $equal(not(and(implies(X_23,not(X)),X)),implies(X,and(X_23,X))) )],[refute_0_646,refute_0_649]) ).
cnf(refute_0_651,plain,
( implies(implies(X_23,not(X)),not(X)) != implies(X,and(X_23,X))
| implies(or(X,X_23),X_23) != implies(implies(X_23,not(X)),not(X))
| implies(or(X,X_23),X_23) = implies(X,and(X_23,X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X,X_23),X_23),implies(implies(X_23,not(X)),not(X))) ),[1],$fot(implies(X,and(X_23,X)))]]) ).
cnf(refute_0_652,plain,
( implies(or(X,X_23),X_23) != implies(implies(X_23,not(X)),not(X))
| implies(or(X,X_23),X_23) = implies(X,and(X_23,X)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_23,not(X)),not(X)),implies(X,and(X_23,X))) )],[refute_0_650,refute_0_651]) ).
cnf(refute_0_653,plain,
implies(or(X,X_23),X_23) = implies(X,and(X_23,X)),
inference(resolve,[$cnf( $equal(implies(or(X,X_23),X_23),implies(implies(X_23,not(X)),not(X))) )],[refute_0_542,refute_0_652]) ).
cnf(refute_0_654,plain,
implies(or(falsehood,X_71),X_71) = implies(falsehood,and(X_71,falsehood)),
inference(subst,[],[refute_0_653:[bind(X,$fot(falsehood)),bind(X_23,$fot(X_71))]]) ).
cnf(refute_0_655,plain,
( implies(or(falsehood,X_71),X_71) != implies(falsehood,and(X_71,falsehood))
| implies(or(falsehood,X_71),X_71) != truth
| implies(falsehood,and(X_71,falsehood)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,X_71),X_71),truth) ),[0],$fot(implies(falsehood,and(X_71,falsehood)))]]) ).
cnf(refute_0_656,plain,
( implies(or(falsehood,X_71),X_71) != truth
| implies(falsehood,and(X_71,falsehood)) = truth ),
inference(resolve,[$cnf( $equal(implies(or(falsehood,X_71),X_71),implies(falsehood,and(X_71,falsehood))) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
implies(falsehood,and(X_71,falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,X_71),X_71),truth) )],[refute_0_535,refute_0_656]) ).
cnf(refute_0_658,plain,
implies(falsehood,and(X_73,falsehood)) = truth,
inference(subst,[],[refute_0_657:[bind(X_71,$fot(X_73))]]) ).
cnf(refute_0_659,plain,
( implies(falsehood,and(X_73,falsehood)) != truth
| implies(implies(implies(falsehood,and(X_73,falsehood)),and(X_73,falsehood)),and(X_73,falsehood)) != implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood))
| implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)) = implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(falsehood,and(X_73,falsehood)),and(X_73,falsehood)),and(X_73,falsehood)),implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood))) ),[0,0,0],$fot(truth)]]) ).
cnf(refute_0_660,plain,
( implies(implies(implies(falsehood,and(X_73,falsehood)),and(X_73,falsehood)),and(X_73,falsehood)) != implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood))
| implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)) = implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)) ),
inference(resolve,[$cnf( $equal(implies(falsehood,and(X_73,falsehood)),truth) )],[refute_0_658,refute_0_659]) ).
cnf(refute_0_661,plain,
implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)) = implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)),
inference(resolve,[$cnf( $equal(implies(implies(implies(falsehood,and(X_73,falsehood)),and(X_73,falsehood)),and(X_73,falsehood)),implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood))) )],[refute_0_509,refute_0_660]) ).
cnf(refute_0_662,plain,
implies(X_23,X_23) = truth,
inference(subst,[],[refute_0_461:[bind(X_14,$fot(X_23))]]) ).
cnf(refute_0_663,plain,
( implies(X_23,X_23) != implies(implies(X_23,truth),truth)
| implies(X_23,X_23) != truth
| truth = implies(implies(X_23,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_23,X_23),implies(implies(X_23,truth),truth)) ),[0],$fot(truth)]]) ).
cnf(refute_0_664,plain,
( implies(X_23,X_23) != implies(implies(X_23,truth),truth)
| truth = implies(implies(X_23,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(X_23,X_23),truth) )],[refute_0_662,refute_0_663]) ).
cnf(refute_0_665,plain,
truth = implies(implies(X_23,truth),truth),
inference(resolve,[$cnf( $equal(implies(X_23,X_23),implies(implies(X_23,truth),truth)) )],[refute_0_79,refute_0_664]) ).
cnf(refute_0_666,plain,
( truth != implies(implies(X_23,truth),truth)
| implies(implies(X_23,truth),truth) = truth ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(implies(X_23,truth),truth)))]]) ).
cnf(refute_0_667,plain,
implies(implies(X_23,truth),truth) = truth,
inference(resolve,[$cnf( $equal(truth,implies(implies(X_23,truth),truth)) )],[refute_0_665,refute_0_666]) ).
cnf(refute_0_668,plain,
implies(implies(and(X_73,falsehood),truth),truth) = truth,
inference(subst,[],[refute_0_667:[bind(X_23,$fot(and(X_73,falsehood)))]]) ).
cnf(refute_0_669,plain,
( implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| implies(implies(Y,X),X) = implies(implies(X,Y),Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(X,Y),Y))),bind(Y0,$fot(implies(implies(Y,X),X)))]]) ).
cnf(refute_0_670,plain,
implies(implies(Y,X),X) = implies(implies(X,Y),Y),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),Y),implies(implies(Y,X),X)) )],[wajsberg_3,refute_0_669]) ).
cnf(refute_0_671,plain,
implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)) = implies(implies(and(X_73,falsehood),truth),truth),
inference(subst,[],[refute_0_670:[bind(X,$fot(and(X_73,falsehood))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_672,plain,
( implies(implies(and(X_73,falsehood),truth),truth) != truth
| implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)) != implies(implies(and(X_73,falsehood),truth),truth)
| implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)))),bind(Y0,$fot(implies(implies(and(X_73,falsehood),truth),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_673,plain,
( implies(implies(and(X_73,falsehood),truth),truth) != truth
| implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)),implies(implies(and(X_73,falsehood),truth),truth)) )],[refute_0_671,refute_0_672]) ).
cnf(refute_0_674,plain,
implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(and(X_73,falsehood),truth),truth),truth) )],[refute_0_668,refute_0_673]) ).
cnf(refute_0_675,plain,
( implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)) != implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood))
| implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)) != truth
| truth = implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)),implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood))) ),[0],$fot(truth)]]) ).
cnf(refute_0_676,plain,
( implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)) != implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood))
| truth = implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)),truth) )],[refute_0_674,refute_0_675]) ).
cnf(refute_0_677,plain,
xor(X_37,truth) = or(and(X_37,not(truth)),and(not(X_37),truth)),
inference(subst,[],[xor_definition:[bind(X,$fot(X_37)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_678,plain,
and(truth,not(X_37)) = and(not(X_37),truth),
inference(subst,[],[refute_0_382:[bind(X_2,$fot(not(X_37)))]]) ).
cnf(refute_0_679,plain,
( and(truth,not(X_37)) != and(not(X_37),truth)
| and(not(X_37),truth) = and(truth,not(X_37)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,not(X_37)))),bind(Y0,$fot(and(not(X_37),truth)))]]) ).
cnf(refute_0_680,plain,
and(not(X_37),truth) = and(truth,not(X_37)),
inference(resolve,[$cnf( $equal(and(truth,not(X_37)),and(not(X_37),truth)) )],[refute_0_678,refute_0_679]) ).
cnf(refute_0_681,plain,
( and(not(X_37),truth) != and(truth,not(X_37))
| xor(X_37,truth) != or(and(X_37,not(truth)),and(not(X_37),truth))
| xor(X_37,truth) = or(and(X_37,not(truth)),and(truth,not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_37,truth),or(and(X_37,not(truth)),and(not(X_37),truth))) ),[1,1],$fot(and(truth,not(X_37)))]]) ).
cnf(refute_0_682,plain,
( xor(X_37,truth) != or(and(X_37,not(truth)),and(not(X_37),truth))
| xor(X_37,truth) = or(and(X_37,not(truth)),and(truth,not(X_37))) ),
inference(resolve,[$cnf( $equal(and(not(X_37),truth),and(truth,not(X_37))) )],[refute_0_680,refute_0_681]) ).
cnf(refute_0_683,plain,
xor(X_37,truth) = or(and(X_37,not(truth)),and(truth,not(X_37))),
inference(resolve,[$cnf( $equal(xor(X_37,truth),or(and(X_37,not(truth)),and(not(X_37),truth))) )],[refute_0_677,refute_0_682]) ).
cnf(refute_0_684,plain,
and(X_37,not(truth)) = and(X_37,not(truth)),
introduced(tautology,[refl,[$fot(and(X_37,not(truth)))]]) ).
cnf(refute_0_685,plain,
( and(X_37,not(truth)) != and(X_37,not(truth))
| not(truth) != falsehood
| and(X_37,not(truth)) = and(X_37,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_37,not(truth)),and(X_37,not(truth))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_686,plain,
( not(truth) != falsehood
| and(X_37,not(truth)) = and(X_37,falsehood) ),
inference(resolve,[$cnf( $equal(and(X_37,not(truth)),and(X_37,not(truth))) )],[refute_0_684,refute_0_685]) ).
cnf(refute_0_687,plain,
and(X_37,not(truth)) = and(X_37,falsehood),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_686]) ).
cnf(refute_0_688,plain,
or(and(X_37,not(truth)),and(truth,not(X_37))) = or(and(X_37,not(truth)),and(truth,not(X_37))),
introduced(tautology,[refl,[$fot(or(and(X_37,not(truth)),and(truth,not(X_37))))]]) ).
cnf(refute_0_689,plain,
( and(X_37,not(truth)) != and(X_37,falsehood)
| or(and(X_37,not(truth)),and(truth,not(X_37))) != or(and(X_37,not(truth)),and(truth,not(X_37)))
| or(and(X_37,not(truth)),and(truth,not(X_37))) = or(and(X_37,falsehood),and(truth,not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_37,not(truth)),and(truth,not(X_37))),or(and(X_37,not(truth)),and(truth,not(X_37)))) ),[1,0],$fot(and(X_37,falsehood))]]) ).
cnf(refute_0_690,plain,
( and(X_37,not(truth)) != and(X_37,falsehood)
| or(and(X_37,not(truth)),and(truth,not(X_37))) = or(and(X_37,falsehood),and(truth,not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(X_37,not(truth)),and(truth,not(X_37))),or(and(X_37,not(truth)),and(truth,not(X_37)))) )],[refute_0_688,refute_0_689]) ).
cnf(refute_0_691,plain,
or(and(X_37,not(truth)),and(truth,not(X_37))) = or(and(X_37,falsehood),and(truth,not(X_37))),
inference(resolve,[$cnf( $equal(and(X_37,not(truth)),and(X_37,falsehood)) )],[refute_0_687,refute_0_690]) ).
cnf(refute_0_692,plain,
( or(and(X_37,not(truth)),and(truth,not(X_37))) != or(and(X_37,falsehood),and(truth,not(X_37)))
| xor(X_37,truth) != or(and(X_37,not(truth)),and(truth,not(X_37)))
| xor(X_37,truth) = or(and(X_37,falsehood),and(truth,not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_37,truth),or(and(X_37,not(truth)),and(truth,not(X_37)))) ),[1],$fot(or(and(X_37,falsehood),and(truth,not(X_37))))]]) ).
cnf(refute_0_693,plain,
( xor(X_37,truth) != or(and(X_37,not(truth)),and(truth,not(X_37)))
| xor(X_37,truth) = or(and(X_37,falsehood),and(truth,not(X_37))) ),
inference(resolve,[$cnf( $equal(or(and(X_37,not(truth)),and(truth,not(X_37))),or(and(X_37,falsehood),and(truth,not(X_37)))) )],[refute_0_691,refute_0_692]) ).
cnf(refute_0_694,plain,
xor(X_37,truth) = or(and(X_37,falsehood),and(truth,not(X_37))),
inference(resolve,[$cnf( $equal(xor(X_37,truth),or(and(X_37,not(truth)),and(truth,not(X_37)))) )],[refute_0_683,refute_0_693]) ).
cnf(refute_0_695,plain,
and(truth,not(X_37)) = not(not(not(X_37))),
inference(subst,[],[refute_0_440:[bind(Y,$fot(not(X_37)))]]) ).
cnf(refute_0_696,plain,
or(and(X_37,falsehood),and(truth,not(X_37))) = or(and(X_37,falsehood),and(truth,not(X_37))),
introduced(tautology,[refl,[$fot(or(and(X_37,falsehood),and(truth,not(X_37))))]]) ).
cnf(refute_0_697,plain,
( and(truth,not(X_37)) != not(not(not(X_37)))
| or(and(X_37,falsehood),and(truth,not(X_37))) != or(and(X_37,falsehood),and(truth,not(X_37)))
| or(and(X_37,falsehood),and(truth,not(X_37))) = or(and(X_37,falsehood),not(not(not(X_37)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_37,falsehood),and(truth,not(X_37))),or(and(X_37,falsehood),and(truth,not(X_37)))) ),[1,1],$fot(not(not(not(X_37))))]]) ).
cnf(refute_0_698,plain,
( and(truth,not(X_37)) != not(not(not(X_37)))
| or(and(X_37,falsehood),and(truth,not(X_37))) = or(and(X_37,falsehood),not(not(not(X_37)))) ),
inference(resolve,[$cnf( $equal(or(and(X_37,falsehood),and(truth,not(X_37))),or(and(X_37,falsehood),and(truth,not(X_37)))) )],[refute_0_696,refute_0_697]) ).
cnf(refute_0_699,plain,
or(and(X_37,falsehood),and(truth,not(X_37))) = or(and(X_37,falsehood),not(not(not(X_37)))),
inference(resolve,[$cnf( $equal(and(truth,not(X_37)),not(not(not(X_37)))) )],[refute_0_695,refute_0_698]) ).
cnf(refute_0_700,plain,
( or(and(X_37,falsehood),and(truth,not(X_37))) != or(and(X_37,falsehood),not(not(not(X_37))))
| xor(X_37,truth) != or(and(X_37,falsehood),and(truth,not(X_37)))
| xor(X_37,truth) = or(and(X_37,falsehood),not(not(not(X_37)))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_37,truth),or(and(X_37,falsehood),and(truth,not(X_37)))) ),[1],$fot(or(and(X_37,falsehood),not(not(not(X_37)))))]]) ).
cnf(refute_0_701,plain,
( xor(X_37,truth) != or(and(X_37,falsehood),and(truth,not(X_37)))
| xor(X_37,truth) = or(and(X_37,falsehood),not(not(not(X_37)))) ),
inference(resolve,[$cnf( $equal(or(and(X_37,falsehood),and(truth,not(X_37))),or(and(X_37,falsehood),not(not(not(X_37))))) )],[refute_0_699,refute_0_700]) ).
cnf(refute_0_702,plain,
xor(X_37,truth) = or(and(X_37,falsehood),not(not(not(X_37)))),
inference(resolve,[$cnf( $equal(xor(X_37,truth),or(and(X_37,falsehood),and(truth,not(X_37)))) )],[refute_0_694,refute_0_701]) ).
cnf(refute_0_703,plain,
or(and(X_37,falsehood),not(X_37)) = or(not(X_37),and(X_37,falsehood)),
inference(subst,[],[refute_0_135:[bind(X_35,$fot(X_37)),bind(X_36,$fot(and(X_37,falsehood)))]]) ).
cnf(refute_0_704,plain,
not(not(not(X_37))) = not(X_37),
inference(subst,[],[refute_0_518:[bind(Y,$fot(not(X_37)))]]) ).
cnf(refute_0_705,plain,
or(and(X_37,falsehood),not(not(not(X_37)))) = or(and(X_37,falsehood),not(not(not(X_37)))),
introduced(tautology,[refl,[$fot(or(and(X_37,falsehood),not(not(not(X_37)))))]]) ).
cnf(refute_0_706,plain,
( not(not(not(X_37))) != not(X_37)
| or(and(X_37,falsehood),not(not(not(X_37)))) != or(and(X_37,falsehood),not(not(not(X_37))))
| or(and(X_37,falsehood),not(not(not(X_37)))) = or(and(X_37,falsehood),not(X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_37,falsehood),not(not(not(X_37)))),or(and(X_37,falsehood),not(not(not(X_37))))) ),[1,1],$fot(not(X_37))]]) ).
cnf(refute_0_707,plain,
( not(not(not(X_37))) != not(X_37)
| or(and(X_37,falsehood),not(not(not(X_37)))) = or(and(X_37,falsehood),not(X_37)) ),
inference(resolve,[$cnf( $equal(or(and(X_37,falsehood),not(not(not(X_37)))),or(and(X_37,falsehood),not(not(not(X_37))))) )],[refute_0_705,refute_0_706]) ).
cnf(refute_0_708,plain,
or(and(X_37,falsehood),not(not(not(X_37)))) = or(and(X_37,falsehood),not(X_37)),
inference(resolve,[$cnf( $equal(not(not(not(X_37))),not(X_37)) )],[refute_0_704,refute_0_707]) ).
cnf(refute_0_709,plain,
( or(and(X_37,falsehood),not(X_37)) != or(not(X_37),and(X_37,falsehood))
| or(and(X_37,falsehood),not(not(not(X_37)))) != or(and(X_37,falsehood),not(X_37))
| or(and(X_37,falsehood),not(not(not(X_37)))) = or(not(X_37),and(X_37,falsehood)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(and(X_37,falsehood),not(not(not(X_37)))))),bind(Y0,$fot(or(and(X_37,falsehood),not(X_37)))),bind(Z0,$fot(or(not(X_37),and(X_37,falsehood))))]]) ).
cnf(refute_0_710,plain,
( or(and(X_37,falsehood),not(X_37)) != or(not(X_37),and(X_37,falsehood))
| or(and(X_37,falsehood),not(not(not(X_37)))) = or(not(X_37),and(X_37,falsehood)) ),
inference(resolve,[$cnf( $equal(or(and(X_37,falsehood),not(not(not(X_37)))),or(and(X_37,falsehood),not(X_37))) )],[refute_0_708,refute_0_709]) ).
cnf(refute_0_711,plain,
or(and(X_37,falsehood),not(not(not(X_37)))) = or(not(X_37),and(X_37,falsehood)),
inference(resolve,[$cnf( $equal(or(and(X_37,falsehood),not(X_37)),or(not(X_37),and(X_37,falsehood))) )],[refute_0_703,refute_0_710]) ).
cnf(refute_0_712,plain,
( or(and(X_37,falsehood),not(not(not(X_37)))) != or(not(X_37),and(X_37,falsehood))
| xor(X_37,truth) != or(and(X_37,falsehood),not(not(not(X_37))))
| xor(X_37,truth) = or(not(X_37),and(X_37,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_37,truth),or(and(X_37,falsehood),not(not(not(X_37))))) ),[1],$fot(or(not(X_37),and(X_37,falsehood)))]]) ).
cnf(refute_0_713,plain,
( xor(X_37,truth) != or(and(X_37,falsehood),not(not(not(X_37))))
| xor(X_37,truth) = or(not(X_37),and(X_37,falsehood)) ),
inference(resolve,[$cnf( $equal(or(and(X_37,falsehood),not(not(not(X_37)))),or(not(X_37),and(X_37,falsehood))) )],[refute_0_711,refute_0_712]) ).
cnf(refute_0_714,plain,
xor(X_37,truth) = or(not(X_37),and(X_37,falsehood)),
inference(resolve,[$cnf( $equal(xor(X_37,truth),or(and(X_37,falsehood),not(not(not(X_37))))) )],[refute_0_702,refute_0_713]) ).
cnf(refute_0_715,plain,
or(not(X_37),and(X_37,falsehood)) = implies(X_37,and(X_37,falsehood)),
inference(subst,[],[refute_0_277:[bind(Y,$fot(and(X_37,falsehood))),bind(X_56,$fot(X_37))]]) ).
cnf(refute_0_716,plain,
( or(not(X_37),and(X_37,falsehood)) != implies(X_37,and(X_37,falsehood))
| xor(X_37,truth) != or(not(X_37),and(X_37,falsehood))
| xor(X_37,truth) = implies(X_37,and(X_37,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_37,truth),or(not(X_37),and(X_37,falsehood))) ),[1],$fot(implies(X_37,and(X_37,falsehood)))]]) ).
cnf(refute_0_717,plain,
( xor(X_37,truth) != or(not(X_37),and(X_37,falsehood))
| xor(X_37,truth) = implies(X_37,and(X_37,falsehood)) ),
inference(resolve,[$cnf( $equal(or(not(X_37),and(X_37,falsehood)),implies(X_37,and(X_37,falsehood))) )],[refute_0_715,refute_0_716]) ).
cnf(refute_0_718,plain,
xor(X_37,truth) = implies(X_37,and(X_37,falsehood)),
inference(resolve,[$cnf( $equal(xor(X_37,truth),or(not(X_37),and(X_37,falsehood))) )],[refute_0_714,refute_0_717]) ).
cnf(refute_0_719,plain,
( xor(X_37,truth) != implies(X_37,and(X_37,falsehood))
| implies(X_37,and(X_37,falsehood)) = xor(X_37,truth) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(X_37,truth))),bind(Y0,$fot(implies(X_37,and(X_37,falsehood))))]]) ).
cnf(refute_0_720,plain,
implies(X_37,and(X_37,falsehood)) = xor(X_37,truth),
inference(resolve,[$cnf( $equal(xor(X_37,truth),implies(X_37,and(X_37,falsehood))) )],[refute_0_718,refute_0_719]) ).
cnf(refute_0_721,plain,
implies(X_73,and(X_73,falsehood)) = xor(X_73,truth),
inference(subst,[],[refute_0_720:[bind(X_37,$fot(X_73))]]) ).
cnf(refute_0_722,plain,
implies(falsehood,implies(X_73,and(X_73,falsehood))) = implies(falsehood,implies(X_73,and(X_73,falsehood))),
introduced(tautology,[refl,[$fot(implies(falsehood,implies(X_73,and(X_73,falsehood))))]]) ).
cnf(refute_0_723,plain,
( implies(X_73,and(X_73,falsehood)) != xor(X_73,truth)
| implies(falsehood,implies(X_73,and(X_73,falsehood))) != implies(falsehood,implies(X_73,and(X_73,falsehood)))
| implies(falsehood,implies(X_73,and(X_73,falsehood))) = implies(falsehood,xor(X_73,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(falsehood,implies(X_73,and(X_73,falsehood))),implies(falsehood,implies(X_73,and(X_73,falsehood)))) ),[1,1],$fot(xor(X_73,truth))]]) ).
cnf(refute_0_724,plain,
( implies(X_73,and(X_73,falsehood)) != xor(X_73,truth)
| implies(falsehood,implies(X_73,and(X_73,falsehood))) = implies(falsehood,xor(X_73,truth)) ),
inference(resolve,[$cnf( $equal(implies(falsehood,implies(X_73,and(X_73,falsehood))),implies(falsehood,implies(X_73,and(X_73,falsehood)))) )],[refute_0_722,refute_0_723]) ).
cnf(refute_0_725,plain,
implies(falsehood,implies(X_73,and(X_73,falsehood))) = implies(falsehood,xor(X_73,truth)),
inference(resolve,[$cnf( $equal(implies(X_73,and(X_73,falsehood)),xor(X_73,truth)) )],[refute_0_721,refute_0_724]) ).
cnf(refute_0_726,plain,
implies(and(falsehood,X_73),and(X_73,falsehood)) = implies(falsehood,implies(X_73,and(X_73,falsehood))),
inference(subst,[],[refute_0_488:[bind(X,$fot(falsehood)),bind(Y,$fot(X_73)),bind(X_8,$fot(and(X_73,falsehood)))]]) ).
cnf(refute_0_727,plain,
( implies(and(falsehood,X_73),and(X_73,falsehood)) != implies(falsehood,implies(X_73,and(X_73,falsehood)))
| implies(falsehood,implies(X_73,and(X_73,falsehood))) != implies(falsehood,xor(X_73,truth))
| implies(and(falsehood,X_73),and(X_73,falsehood)) = implies(falsehood,xor(X_73,truth)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(and(falsehood,X_73),and(X_73,falsehood)))),bind(Y0,$fot(implies(falsehood,implies(X_73,and(X_73,falsehood))))),bind(Z0,$fot(implies(falsehood,xor(X_73,truth))))]]) ).
cnf(refute_0_728,plain,
( implies(falsehood,implies(X_73,and(X_73,falsehood))) != implies(falsehood,xor(X_73,truth))
| implies(and(falsehood,X_73),and(X_73,falsehood)) = implies(falsehood,xor(X_73,truth)) ),
inference(resolve,[$cnf( $equal(implies(and(falsehood,X_73),and(X_73,falsehood)),implies(falsehood,implies(X_73,and(X_73,falsehood)))) )],[refute_0_726,refute_0_727]) ).
cnf(refute_0_729,plain,
implies(and(falsehood,X_73),and(X_73,falsehood)) = implies(falsehood,xor(X_73,truth)),
inference(resolve,[$cnf( $equal(implies(falsehood,implies(X_73,and(X_73,falsehood))),implies(falsehood,xor(X_73,truth))) )],[refute_0_725,refute_0_728]) ).
cnf(refute_0_730,plain,
( and(falsehood,X_61) != not(implies(X_61,truth))
| not(implies(X_61,truth)) = and(falsehood,X_61) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(falsehood,X_61))),bind(Y0,$fot(not(implies(X_61,truth))))]]) ).
cnf(refute_0_731,plain,
not(implies(X_61,truth)) = and(falsehood,X_61),
inference(resolve,[$cnf( $equal(and(falsehood,X_61),not(implies(X_61,truth))) )],[refute_0_500,refute_0_730]) ).
cnf(refute_0_732,plain,
not(implies(X_73,truth)) = and(falsehood,X_73),
inference(subst,[],[refute_0_731:[bind(X_61,$fot(X_73))]]) ).
cnf(refute_0_733,plain,
and(X_61,falsehood) = and(falsehood,X_61),
inference(subst,[],[and_commutativity:[bind(X,$fot(X_61)),bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_734,plain,
( and(X_61,falsehood) != and(falsehood,X_61)
| and(falsehood,X_61) = and(X_61,falsehood) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_61,falsehood))),bind(Y0,$fot(and(falsehood,X_61)))]]) ).
cnf(refute_0_735,plain,
and(falsehood,X_61) = and(X_61,falsehood),
inference(resolve,[$cnf( $equal(and(X_61,falsehood),and(falsehood,X_61)) )],[refute_0_733,refute_0_734]) ).
cnf(refute_0_736,plain,
( and(falsehood,X_61) != and(X_61,falsehood)
| not(and(falsehood,X_61)) != implies(X_61,truth)
| not(and(X_61,falsehood)) = implies(X_61,truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(falsehood,X_61)),implies(X_61,truth)) ),[0,0],$fot(and(X_61,falsehood))]]) ).
cnf(refute_0_737,plain,
( not(and(falsehood,X_61)) != implies(X_61,truth)
| not(and(X_61,falsehood)) = implies(X_61,truth) ),
inference(resolve,[$cnf( $equal(and(falsehood,X_61),and(X_61,falsehood)) )],[refute_0_735,refute_0_736]) ).
cnf(refute_0_738,plain,
not(and(X_61,falsehood)) = implies(X_61,truth),
inference(resolve,[$cnf( $equal(not(and(falsehood,X_61)),implies(X_61,truth)) )],[refute_0_497,refute_0_737]) ).
cnf(refute_0_739,plain,
not(and(X_73,falsehood)) = implies(X_73,truth),
inference(subst,[],[refute_0_738:[bind(X_61,$fot(X_73))]]) ).
cnf(refute_0_740,plain,
or(falsehood,or(not(X_35),falsehood)) = implies(and(truth,truth),not(X_35)),
inference(subst,[],[refute_0_170:[bind(X_8,$fot(not(X_35)))]]) ).
cnf(refute_0_741,plain,
or(falsehood,or(not(X_35),falsehood)) = implies(and(X_35,truth),falsehood),
inference(subst,[],[refute_0_261:[bind(X_1,$fot(X_35)),bind(X_8,$fot(falsehood))]]) ).
cnf(refute_0_742,plain,
( or(falsehood,or(not(X_35),falsehood)) != implies(and(X_35,truth),falsehood)
| or(falsehood,or(not(X_35),falsehood)) != implies(and(truth,truth),not(X_35))
| implies(and(X_35,truth),falsehood) = implies(and(truth,truth),not(X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(not(X_35),falsehood)),implies(and(truth,truth),not(X_35))) ),[0],$fot(implies(and(X_35,truth),falsehood))]]) ).
cnf(refute_0_743,plain,
( or(falsehood,or(not(X_35),falsehood)) != implies(and(truth,truth),not(X_35))
| implies(and(X_35,truth),falsehood) = implies(and(truth,truth),not(X_35)) ),
inference(resolve,[$cnf( $equal(or(falsehood,or(not(X_35),falsehood)),implies(and(X_35,truth),falsehood)) )],[refute_0_741,refute_0_742]) ).
cnf(refute_0_744,plain,
implies(and(X_35,truth),falsehood) = implies(and(truth,truth),not(X_35)),
inference(resolve,[$cnf( $equal(or(falsehood,or(not(X_35),falsehood)),implies(and(truth,truth),not(X_35))) )],[refute_0_740,refute_0_743]) ).
cnf(refute_0_745,plain,
implies(truth,falsehood) = falsehood,
inference(subst,[],[wajsberg_1:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_746,plain,
implies(X_35,implies(truth,falsehood)) = implies(X_35,implies(truth,falsehood)),
introduced(tautology,[refl,[$fot(implies(X_35,implies(truth,falsehood)))]]) ).
cnf(refute_0_747,plain,
( implies(X_35,implies(truth,falsehood)) != implies(X_35,implies(truth,falsehood))
| implies(truth,falsehood) != falsehood
| implies(X_35,implies(truth,falsehood)) = implies(X_35,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_35,implies(truth,falsehood)),implies(X_35,implies(truth,falsehood))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_748,plain,
( implies(truth,falsehood) != falsehood
| implies(X_35,implies(truth,falsehood)) = implies(X_35,falsehood) ),
inference(resolve,[$cnf( $equal(implies(X_35,implies(truth,falsehood)),implies(X_35,implies(truth,falsehood))) )],[refute_0_746,refute_0_747]) ).
cnf(refute_0_749,plain,
implies(X_35,implies(truth,falsehood)) = implies(X_35,falsehood),
inference(resolve,[$cnf( $equal(implies(truth,falsehood),falsehood) )],[refute_0_745,refute_0_748]) ).
cnf(refute_0_750,plain,
implies(and(X_35,truth),falsehood) = implies(X_35,implies(truth,falsehood)),
inference(subst,[],[refute_0_488:[bind(X,$fot(X_35)),bind(Y,$fot(truth)),bind(X_8,$fot(falsehood))]]) ).
cnf(refute_0_751,plain,
( implies(X_35,implies(truth,falsehood)) != implies(X_35,falsehood)
| implies(and(X_35,truth),falsehood) != implies(X_35,implies(truth,falsehood))
| implies(and(X_35,truth),falsehood) = implies(X_35,falsehood) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(and(X_35,truth),falsehood))),bind(Y0,$fot(implies(X_35,implies(truth,falsehood)))),bind(Z0,$fot(implies(X_35,falsehood)))]]) ).
cnf(refute_0_752,plain,
( implies(X_35,implies(truth,falsehood)) != implies(X_35,falsehood)
| implies(and(X_35,truth),falsehood) = implies(X_35,falsehood) ),
inference(resolve,[$cnf( $equal(implies(and(X_35,truth),falsehood),implies(X_35,implies(truth,falsehood))) )],[refute_0_750,refute_0_751]) ).
cnf(refute_0_753,plain,
implies(and(X_35,truth),falsehood) = implies(X_35,falsehood),
inference(resolve,[$cnf( $equal(implies(X_35,implies(truth,falsehood)),implies(X_35,falsehood)) )],[refute_0_749,refute_0_752]) ).
cnf(refute_0_754,plain,
( implies(and(X_35,truth),falsehood) != implies(X_35,falsehood)
| implies(and(X_35,truth),falsehood) != implies(and(truth,truth),not(X_35))
| implies(X_35,falsehood) = implies(and(truth,truth),not(X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(X_35,truth),falsehood),implies(and(truth,truth),not(X_35))) ),[0],$fot(implies(X_35,falsehood))]]) ).
cnf(refute_0_755,plain,
( implies(and(X_35,truth),falsehood) != implies(and(truth,truth),not(X_35))
| implies(X_35,falsehood) = implies(and(truth,truth),not(X_35)) ),
inference(resolve,[$cnf( $equal(implies(and(X_35,truth),falsehood),implies(X_35,falsehood)) )],[refute_0_753,refute_0_754]) ).
cnf(refute_0_756,plain,
( and(truth,Y) != not(not(Y))
| not(not(Y)) != Y
| and(truth,Y) = Y ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(truth,Y),Y) ),[0],$fot(not(not(Y)))]]) ).
cnf(refute_0_757,plain,
( and(truth,Y) != not(not(Y))
| and(truth,Y) = Y ),
inference(resolve,[$cnf( $equal(not(not(Y)),Y) )],[refute_0_518,refute_0_756]) ).
cnf(refute_0_758,plain,
and(truth,Y) = Y,
inference(resolve,[$cnf( $equal(and(truth,Y),not(not(Y))) )],[refute_0_440,refute_0_757]) ).
cnf(refute_0_759,plain,
and(truth,X_35) = X_35,
inference(subst,[],[refute_0_758:[bind(Y,$fot(X_35))]]) ).
cnf(refute_0_760,plain,
and(truth,and(truth,X_35)) = and(truth,X_35),
inference(subst,[],[refute_0_758:[bind(Y,$fot(and(truth,X_35)))]]) ).
cnf(refute_0_761,plain,
( and(truth,X_35) != X_35
| and(truth,and(truth,X_35)) != and(truth,X_35)
| and(truth,and(truth,X_35)) = X_35 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(truth,and(truth,X_35)))),bind(Y0,$fot(and(truth,X_35))),bind(Z0,$fot(X_35))]]) ).
cnf(refute_0_762,plain,
( and(truth,X_35) != X_35
| and(truth,and(truth,X_35)) = X_35 ),
inference(resolve,[$cnf( $equal(and(truth,and(truth,X_35)),and(truth,X_35)) )],[refute_0_760,refute_0_761]) ).
cnf(refute_0_763,plain,
and(truth,and(truth,X_35)) = X_35,
inference(resolve,[$cnf( $equal(and(truth,X_35),X_35) )],[refute_0_759,refute_0_762]) ).
cnf(refute_0_764,plain,
and(and(truth,truth),X_35) = and(truth,and(truth,X_35)),
inference(subst,[],[and_associativity:[bind(X,$fot(truth)),bind(Y,$fot(truth)),bind(Z,$fot(X_35))]]) ).
cnf(refute_0_765,plain,
( and(and(truth,truth),X_35) != and(truth,and(truth,X_35))
| and(truth,and(truth,X_35)) != X_35
| and(and(truth,truth),X_35) = X_35 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(and(truth,truth),X_35))),bind(Y0,$fot(and(truth,and(truth,X_35)))),bind(Z0,$fot(X_35))]]) ).
cnf(refute_0_766,plain,
( and(truth,and(truth,X_35)) != X_35
| and(and(truth,truth),X_35) = X_35 ),
inference(resolve,[$cnf( $equal(and(and(truth,truth),X_35),and(truth,and(truth,X_35))) )],[refute_0_764,refute_0_765]) ).
cnf(refute_0_767,plain,
and(and(truth,truth),X_35) = X_35,
inference(resolve,[$cnf( $equal(and(truth,and(truth,X_35)),X_35) )],[refute_0_763,refute_0_766]) ).
cnf(refute_0_768,plain,
not(and(and(truth,truth),X_35)) = not(and(and(truth,truth),X_35)),
introduced(tautology,[refl,[$fot(not(and(and(truth,truth),X_35)))]]) ).
cnf(refute_0_769,plain,
( and(and(truth,truth),X_35) != X_35
| not(and(and(truth,truth),X_35)) != not(and(and(truth,truth),X_35))
| not(and(and(truth,truth),X_35)) = not(X_35) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(and(truth,truth),X_35)),not(and(and(truth,truth),X_35))) ),[1,0],$fot(X_35)]]) ).
cnf(refute_0_770,plain,
( and(and(truth,truth),X_35) != X_35
| not(and(and(truth,truth),X_35)) = not(X_35) ),
inference(resolve,[$cnf( $equal(not(and(and(truth,truth),X_35)),not(and(and(truth,truth),X_35))) )],[refute_0_768,refute_0_769]) ).
cnf(refute_0_771,plain,
not(and(and(truth,truth),X_35)) = not(X_35),
inference(resolve,[$cnf( $equal(and(and(truth,truth),X_35),X_35) )],[refute_0_767,refute_0_770]) ).
cnf(refute_0_772,plain,
implies(and(truth,truth),not(X_35)) = not(and(and(truth,truth),X_35)),
inference(subst,[],[refute_0_281:[bind(X,$fot(and(truth,truth))),bind(Y,$fot(X_35))]]) ).
cnf(refute_0_773,plain,
( implies(and(truth,truth),not(X_35)) != not(and(and(truth,truth),X_35))
| not(and(and(truth,truth),X_35)) != not(X_35)
| implies(and(truth,truth),not(X_35)) = not(X_35) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(and(truth,truth),not(X_35)))),bind(Y0,$fot(not(and(and(truth,truth),X_35)))),bind(Z0,$fot(not(X_35)))]]) ).
cnf(refute_0_774,plain,
( not(and(and(truth,truth),X_35)) != not(X_35)
| implies(and(truth,truth),not(X_35)) = not(X_35) ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),not(X_35)),not(and(and(truth,truth),X_35))) )],[refute_0_772,refute_0_773]) ).
cnf(refute_0_775,plain,
implies(and(truth,truth),not(X_35)) = not(X_35),
inference(resolve,[$cnf( $equal(not(and(and(truth,truth),X_35)),not(X_35)) )],[refute_0_771,refute_0_774]) ).
cnf(refute_0_776,plain,
( implies(X_35,falsehood) != implies(and(truth,truth),not(X_35))
| implies(and(truth,truth),not(X_35)) != not(X_35)
| implies(X_35,falsehood) = not(X_35) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_35,falsehood),not(X_35)) ),[0],$fot(implies(and(truth,truth),not(X_35)))]]) ).
cnf(refute_0_777,plain,
( implies(X_35,falsehood) != implies(and(truth,truth),not(X_35))
| implies(X_35,falsehood) = not(X_35) ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),not(X_35)),not(X_35)) )],[refute_0_775,refute_0_776]) ).
cnf(refute_0_778,plain,
( implies(and(X_35,truth),falsehood) != implies(and(truth,truth),not(X_35))
| implies(X_35,falsehood) = not(X_35) ),
inference(resolve,[$cnf( $equal(implies(X_35,falsehood),implies(and(truth,truth),not(X_35))) )],[refute_0_755,refute_0_777]) ).
cnf(refute_0_779,plain,
implies(X_35,falsehood) = not(X_35),
inference(resolve,[$cnf( $equal(implies(and(X_35,truth),falsehood),implies(and(truth,truth),not(X_35))) )],[refute_0_744,refute_0_778]) ).
cnf(refute_0_780,plain,
implies(and(X_73,falsehood),falsehood) = not(and(X_73,falsehood)),
inference(subst,[],[refute_0_779:[bind(X_35,$fot(and(X_73,falsehood)))]]) ).
cnf(refute_0_781,plain,
( implies(and(X_73,falsehood),falsehood) != not(and(X_73,falsehood))
| not(and(X_73,falsehood)) != implies(X_73,truth)
| implies(and(X_73,falsehood),falsehood) = implies(X_73,truth) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(and(X_73,falsehood),falsehood))),bind(Y0,$fot(not(and(X_73,falsehood)))),bind(Z0,$fot(implies(X_73,truth)))]]) ).
cnf(refute_0_782,plain,
( not(and(X_73,falsehood)) != implies(X_73,truth)
| implies(and(X_73,falsehood),falsehood) = implies(X_73,truth) ),
inference(resolve,[$cnf( $equal(implies(and(X_73,falsehood),falsehood),not(and(X_73,falsehood))) )],[refute_0_780,refute_0_781]) ).
cnf(refute_0_783,plain,
implies(and(X_73,falsehood),falsehood) = implies(X_73,truth),
inference(resolve,[$cnf( $equal(not(and(X_73,falsehood)),implies(X_73,truth)) )],[refute_0_739,refute_0_782]) ).
cnf(refute_0_784,plain,
not(implies(and(X_73,falsehood),falsehood)) = not(implies(and(X_73,falsehood),falsehood)),
introduced(tautology,[refl,[$fot(not(implies(and(X_73,falsehood),falsehood)))]]) ).
cnf(refute_0_785,plain,
( implies(and(X_73,falsehood),falsehood) != implies(X_73,truth)
| not(implies(and(X_73,falsehood),falsehood)) != not(implies(and(X_73,falsehood),falsehood))
| not(implies(and(X_73,falsehood),falsehood)) = not(implies(X_73,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(and(X_73,falsehood),falsehood)),not(implies(and(X_73,falsehood),falsehood))) ),[1,0],$fot(implies(X_73,truth))]]) ).
cnf(refute_0_786,plain,
( implies(and(X_73,falsehood),falsehood) != implies(X_73,truth)
| not(implies(and(X_73,falsehood),falsehood)) = not(implies(X_73,truth)) ),
inference(resolve,[$cnf( $equal(not(implies(and(X_73,falsehood),falsehood)),not(implies(and(X_73,falsehood),falsehood))) )],[refute_0_784,refute_0_785]) ).
cnf(refute_0_787,plain,
not(implies(and(X_73,falsehood),falsehood)) = not(implies(X_73,truth)),
inference(resolve,[$cnf( $equal(implies(and(X_73,falsehood),falsehood),implies(X_73,truth)) )],[refute_0_783,refute_0_786]) ).
cnf(refute_0_788,plain,
( not(implies(X_73,truth)) != and(falsehood,X_73)
| not(implies(and(X_73,falsehood),falsehood)) != not(implies(X_73,truth))
| not(implies(and(X_73,falsehood),falsehood)) = and(falsehood,X_73) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(implies(and(X_73,falsehood),falsehood)))),bind(Y0,$fot(not(implies(X_73,truth)))),bind(Z0,$fot(and(falsehood,X_73)))]]) ).
cnf(refute_0_789,plain,
( not(implies(X_73,truth)) != and(falsehood,X_73)
| not(implies(and(X_73,falsehood),falsehood)) = and(falsehood,X_73) ),
inference(resolve,[$cnf( $equal(not(implies(and(X_73,falsehood),falsehood)),not(implies(X_73,truth))) )],[refute_0_787,refute_0_788]) ).
cnf(refute_0_790,plain,
not(implies(and(X_73,falsehood),falsehood)) = and(falsehood,X_73),
inference(resolve,[$cnf( $equal(not(implies(X_73,truth)),and(falsehood,X_73)) )],[refute_0_732,refute_0_789]) ).
cnf(refute_0_791,plain,
implies(implies(and(X_73,falsehood),falsehood),falsehood) = not(implies(and(X_73,falsehood),falsehood)),
inference(subst,[],[refute_0_779:[bind(X_35,$fot(implies(and(X_73,falsehood),falsehood)))]]) ).
cnf(refute_0_792,plain,
( implies(implies(and(X_73,falsehood),falsehood),falsehood) != not(implies(and(X_73,falsehood),falsehood))
| not(implies(and(X_73,falsehood),falsehood)) != and(falsehood,X_73)
| implies(implies(and(X_73,falsehood),falsehood),falsehood) = and(falsehood,X_73) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(implies(and(X_73,falsehood),falsehood),falsehood))),bind(Y0,$fot(not(implies(and(X_73,falsehood),falsehood)))),bind(Z0,$fot(and(falsehood,X_73)))]]) ).
cnf(refute_0_793,plain,
( not(implies(and(X_73,falsehood),falsehood)) != and(falsehood,X_73)
| implies(implies(and(X_73,falsehood),falsehood),falsehood) = and(falsehood,X_73) ),
inference(resolve,[$cnf( $equal(implies(implies(and(X_73,falsehood),falsehood),falsehood),not(implies(and(X_73,falsehood),falsehood))) )],[refute_0_791,refute_0_792]) ).
cnf(refute_0_794,plain,
implies(implies(and(X_73,falsehood),falsehood),falsehood) = and(falsehood,X_73),
inference(resolve,[$cnf( $equal(not(implies(and(X_73,falsehood),falsehood)),and(falsehood,X_73)) )],[refute_0_790,refute_0_793]) ).
cnf(refute_0_795,plain,
implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)) = implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)),
introduced(tautology,[refl,[$fot(implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)))]]) ).
cnf(refute_0_796,plain,
( implies(implies(and(X_73,falsehood),falsehood),falsehood) != and(falsehood,X_73)
| implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)) != implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood))
| implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)) = implies(and(falsehood,X_73),and(X_73,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)),implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood))) ),[1,0],$fot(and(falsehood,X_73))]]) ).
cnf(refute_0_797,plain,
( implies(implies(and(X_73,falsehood),falsehood),falsehood) != and(falsehood,X_73)
| implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)) = implies(and(falsehood,X_73),and(X_73,falsehood)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)),implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood))) )],[refute_0_795,refute_0_796]) ).
cnf(refute_0_798,plain,
implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)) = implies(and(falsehood,X_73),and(X_73,falsehood)),
inference(resolve,[$cnf( $equal(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(falsehood,X_73)) )],[refute_0_794,refute_0_797]) ).
cnf(refute_0_799,plain,
( implies(and(falsehood,X_73),and(X_73,falsehood)) != implies(falsehood,xor(X_73,truth))
| implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)) != implies(and(falsehood,X_73),and(X_73,falsehood))
| implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)) = implies(falsehood,xor(X_73,truth)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)))),bind(Y0,$fot(implies(and(falsehood,X_73),and(X_73,falsehood)))),bind(Z0,$fot(implies(falsehood,xor(X_73,truth))))]]) ).
cnf(refute_0_800,plain,
( implies(and(falsehood,X_73),and(X_73,falsehood)) != implies(falsehood,xor(X_73,truth))
| implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)) = implies(falsehood,xor(X_73,truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)),implies(and(falsehood,X_73),and(X_73,falsehood))) )],[refute_0_798,refute_0_799]) ).
cnf(refute_0_801,plain,
implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)) = implies(falsehood,xor(X_73,truth)),
inference(resolve,[$cnf( $equal(implies(and(falsehood,X_73),and(X_73,falsehood)),implies(falsehood,xor(X_73,truth))) )],[refute_0_729,refute_0_800]) ).
cnf(refute_0_802,plain,
( implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)) != implies(falsehood,xor(X_73,truth))
| truth != implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood))
| truth = implies(falsehood,xor(X_73,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(truth,implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood))) ),[1],$fot(implies(falsehood,xor(X_73,truth)))]]) ).
cnf(refute_0_803,plain,
( truth != implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood))
| truth = implies(falsehood,xor(X_73,truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood)),implies(falsehood,xor(X_73,truth))) )],[refute_0_801,refute_0_802]) ).
cnf(refute_0_804,plain,
( implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)) != implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood))
| truth = implies(falsehood,xor(X_73,truth)) ),
inference(resolve,[$cnf( $equal(truth,implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood))) )],[refute_0_676,refute_0_803]) ).
cnf(refute_0_805,plain,
truth = implies(falsehood,xor(X_73,truth)),
inference(resolve,[$cnf( $equal(implies(implies(truth,and(X_73,falsehood)),and(X_73,falsehood)),implies(implies(implies(and(X_73,falsehood),falsehood),falsehood),and(X_73,falsehood))) )],[refute_0_661,refute_0_804]) ).
cnf(refute_0_806,plain,
not(and(falsehood,X_73)) = implies(X_73,truth),
inference(subst,[],[refute_0_496:[bind(X_35,$fot(X_73))]]) ).
cnf(refute_0_807,plain,
implies(falsehood,not(X_73)) = not(and(falsehood,X_73)),
inference(subst,[],[refute_0_281:[bind(X,$fot(falsehood)),bind(Y,$fot(X_73))]]) ).
cnf(refute_0_808,plain,
( implies(falsehood,not(X_73)) != not(and(falsehood,X_73))
| not(and(falsehood,X_73)) != implies(X_73,truth)
| implies(falsehood,not(X_73)) = implies(X_73,truth) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(falsehood,not(X_73)))),bind(Y0,$fot(not(and(falsehood,X_73)))),bind(Z0,$fot(implies(X_73,truth)))]]) ).
cnf(refute_0_809,plain,
( not(and(falsehood,X_73)) != implies(X_73,truth)
| implies(falsehood,not(X_73)) = implies(X_73,truth) ),
inference(resolve,[$cnf( $equal(implies(falsehood,not(X_73)),not(and(falsehood,X_73))) )],[refute_0_807,refute_0_808]) ).
cnf(refute_0_810,plain,
implies(falsehood,not(X_73)) = implies(X_73,truth),
inference(resolve,[$cnf( $equal(not(and(falsehood,X_73)),implies(X_73,truth)) )],[refute_0_806,refute_0_809]) ).
cnf(refute_0_811,plain,
xor(truth,X_38) = or(and(truth,not(X_38)),and(not(truth),X_38)),
inference(subst,[],[xor_definition:[bind(X,$fot(truth)),bind(Y,$fot(X_38))]]) ).
cnf(refute_0_812,plain,
( not(truth) != falsehood
| xor(truth,X_38) != or(and(truth,not(X_38)),and(not(truth),X_38))
| xor(truth,X_38) = or(and(truth,not(X_38)),and(falsehood,X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_38),or(and(truth,not(X_38)),and(not(truth),X_38))) ),[1,1,0],$fot(falsehood)]]) ).
cnf(refute_0_813,plain,
( xor(truth,X_38) != or(and(truth,not(X_38)),and(not(truth),X_38))
| xor(truth,X_38) = or(and(truth,not(X_38)),and(falsehood,X_38)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_812]) ).
cnf(refute_0_814,plain,
xor(truth,X_38) = or(and(truth,not(X_38)),and(falsehood,X_38)),
inference(resolve,[$cnf( $equal(xor(truth,X_38),or(and(truth,not(X_38)),and(not(truth),X_38))) )],[refute_0_811,refute_0_813]) ).
cnf(refute_0_815,plain,
or(and(truth,not(X_38)),and(falsehood,X_38)) = or(and(falsehood,X_38),and(truth,not(X_38))),
inference(subst,[],[refute_0_145:[bind(X,$fot(and(falsehood,X_38))),bind(Y,$fot(and(truth,not(X_38))))]]) ).
cnf(refute_0_816,plain,
( or(and(truth,not(X_38)),and(falsehood,X_38)) != or(and(falsehood,X_38),and(truth,not(X_38)))
| xor(truth,X_38) != or(and(truth,not(X_38)),and(falsehood,X_38))
| xor(truth,X_38) = or(and(falsehood,X_38),and(truth,not(X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_38),or(and(truth,not(X_38)),and(falsehood,X_38))) ),[1],$fot(or(and(falsehood,X_38),and(truth,not(X_38))))]]) ).
cnf(refute_0_817,plain,
( xor(truth,X_38) != or(and(truth,not(X_38)),and(falsehood,X_38))
| xor(truth,X_38) = or(and(falsehood,X_38),and(truth,not(X_38))) ),
inference(resolve,[$cnf( $equal(or(and(truth,not(X_38)),and(falsehood,X_38)),or(and(falsehood,X_38),and(truth,not(X_38)))) )],[refute_0_815,refute_0_816]) ).
cnf(refute_0_818,plain,
xor(truth,X_38) = or(and(falsehood,X_38),and(truth,not(X_38))),
inference(resolve,[$cnf( $equal(xor(truth,X_38),or(and(truth,not(X_38)),and(falsehood,X_38))) )],[refute_0_814,refute_0_817]) ).
cnf(refute_0_819,plain,
xor(truth,and(truth,X_21)) = or(and(falsehood,and(truth,X_21)),and(truth,not(and(truth,X_21)))),
inference(subst,[],[refute_0_818:[bind(X_38,$fot(and(truth,X_21)))]]) ).
cnf(refute_0_820,plain,
and(falsehood,and(truth,X_21)) = and(falsehood,and(X_21,truth)),
inference(subst,[],[refute_0_573:[bind(X_19,$fot(falsehood))]]) ).
cnf(refute_0_821,plain,
( and(falsehood,and(truth,X_21)) != and(falsehood,and(X_21,truth))
| xor(truth,and(truth,X_21)) != or(and(falsehood,and(truth,X_21)),and(truth,not(and(truth,X_21))))
| xor(truth,and(truth,X_21)) = or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21)))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,and(truth,X_21)),or(and(falsehood,and(truth,X_21)),and(truth,not(and(truth,X_21))))) ),[1,0],$fot(and(falsehood,and(X_21,truth)))]]) ).
cnf(refute_0_822,plain,
( xor(truth,and(truth,X_21)) != or(and(falsehood,and(truth,X_21)),and(truth,not(and(truth,X_21))))
| xor(truth,and(truth,X_21)) = or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21)))) ),
inference(resolve,[$cnf( $equal(and(falsehood,and(truth,X_21)),and(falsehood,and(X_21,truth))) )],[refute_0_820,refute_0_821]) ).
cnf(refute_0_823,plain,
xor(truth,and(truth,X_21)) = or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21)))),
inference(resolve,[$cnf( $equal(xor(truth,and(truth,X_21)),or(and(falsehood,and(truth,X_21)),and(truth,not(and(truth,X_21))))) )],[refute_0_819,refute_0_822]) ).
cnf(refute_0_824,plain,
and(and(X,falsehood),truth) = and(X,and(falsehood,truth)),
inference(subst,[],[and_associativity:[bind(Y,$fot(falsehood)),bind(Z,$fot(truth))]]) ).
cnf(refute_0_825,plain,
( and(and(X,falsehood),truth) != and(X,and(falsehood,truth))
| and(falsehood,truth) != falsehood
| and(and(X,falsehood),truth) = and(X,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(X,falsehood),truth),and(X,and(falsehood,truth))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_826,plain,
( and(and(X,falsehood),truth) != and(X,and(falsehood,truth))
| and(and(X,falsehood),truth) = and(X,falsehood) ),
inference(resolve,[$cnf( $equal(and(falsehood,truth),falsehood) )],[refute_0_413,refute_0_825]) ).
cnf(refute_0_827,plain,
and(and(X,falsehood),truth) = and(X,falsehood),
inference(resolve,[$cnf( $equal(and(and(X,falsehood),truth),and(X,and(falsehood,truth))) )],[refute_0_824,refute_0_826]) ).
cnf(refute_0_828,plain,
and(and(truth,X_34),Y) = and(Y,and(truth,X_34)),
inference(subst,[],[and_commutativity:[bind(X,$fot(and(truth,X_34)))]]) ).
cnf(refute_0_829,plain,
( and(Y,and(truth,X_34)) != and(Y,and(X_34,truth))
| and(and(truth,X_34),Y) != and(Y,and(truth,X_34))
| and(and(truth,X_34),Y) = and(Y,and(X_34,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(truth,X_34),Y),and(Y,and(truth,X_34))) ),[1],$fot(and(Y,and(X_34,truth)))]]) ).
cnf(refute_0_830,plain,
( and(and(truth,X_34),Y) != and(Y,and(truth,X_34))
| and(and(truth,X_34),Y) = and(Y,and(X_34,truth)) ),
inference(resolve,[$cnf( $equal(and(Y,and(truth,X_34)),and(Y,and(X_34,truth))) )],[refute_0_574,refute_0_829]) ).
cnf(refute_0_831,plain,
and(and(truth,X_34),Y) = and(Y,and(X_34,truth)),
inference(resolve,[$cnf( $equal(and(and(truth,X_34),Y),and(Y,and(truth,X_34))) )],[refute_0_828,refute_0_830]) ).
cnf(refute_0_832,plain,
and(and(truth,X_34),Y) = and(truth,and(X_34,Y)),
inference(subst,[],[and_associativity:[bind(X,$fot(truth)),bind(Y,$fot(X_34)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_833,plain,
( and(and(truth,X_34),Y) != and(Y,and(X_34,truth))
| and(and(truth,X_34),Y) != and(truth,and(X_34,Y))
| and(truth,and(X_34,Y)) = and(Y,and(X_34,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(truth,X_34),Y),and(Y,and(X_34,truth))) ),[0],$fot(and(truth,and(X_34,Y)))]]) ).
cnf(refute_0_834,plain,
( and(and(truth,X_34),Y) != and(Y,and(X_34,truth))
| and(truth,and(X_34,Y)) = and(Y,and(X_34,truth)) ),
inference(resolve,[$cnf( $equal(and(and(truth,X_34),Y),and(truth,and(X_34,Y))) )],[refute_0_832,refute_0_833]) ).
cnf(refute_0_835,plain,
and(truth,and(X_34,Y)) = and(Y,and(X_34,truth)),
inference(resolve,[$cnf( $equal(and(and(truth,X_34),Y),and(Y,and(X_34,truth))) )],[refute_0_831,refute_0_834]) ).
cnf(refute_0_836,plain,
and(truth,and(X,falsehood)) = and(falsehood,and(X,truth)),
inference(subst,[],[refute_0_835:[bind(Y,$fot(falsehood)),bind(X_34,$fot(X))]]) ).
cnf(refute_0_837,plain,
and(and(X,falsehood),truth) = and(truth,and(X,falsehood)),
inference(subst,[],[refute_0_4:[bind(X,$fot(truth)),bind(Y,$fot(and(X,falsehood)))]]) ).
cnf(refute_0_838,plain,
( and(and(X,falsehood),truth) != and(truth,and(X,falsehood))
| and(truth,and(X,falsehood)) != and(falsehood,and(X,truth))
| and(and(X,falsehood),truth) = and(falsehood,and(X,truth)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(and(X,falsehood),truth))),bind(Y0,$fot(and(truth,and(X,falsehood)))),bind(Z0,$fot(and(falsehood,and(X,truth))))]]) ).
cnf(refute_0_839,plain,
( and(truth,and(X,falsehood)) != and(falsehood,and(X,truth))
| and(and(X,falsehood),truth) = and(falsehood,and(X,truth)) ),
inference(resolve,[$cnf( $equal(and(and(X,falsehood),truth),and(truth,and(X,falsehood))) )],[refute_0_837,refute_0_838]) ).
cnf(refute_0_840,plain,
and(and(X,falsehood),truth) = and(falsehood,and(X,truth)),
inference(resolve,[$cnf( $equal(and(truth,and(X,falsehood)),and(falsehood,and(X,truth))) )],[refute_0_836,refute_0_839]) ).
cnf(refute_0_841,plain,
( and(and(X,falsehood),truth) != and(X,falsehood)
| and(and(X,falsehood),truth) != and(falsehood,and(X,truth))
| and(falsehood,and(X,truth)) = and(X,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(X,falsehood),truth),and(X,falsehood)) ),[0],$fot(and(falsehood,and(X,truth)))]]) ).
cnf(refute_0_842,plain,
( and(and(X,falsehood),truth) != and(X,falsehood)
| and(falsehood,and(X,truth)) = and(X,falsehood) ),
inference(resolve,[$cnf( $equal(and(and(X,falsehood),truth),and(falsehood,and(X,truth))) )],[refute_0_840,refute_0_841]) ).
cnf(refute_0_843,plain,
and(falsehood,and(X,truth)) = and(X,falsehood),
inference(resolve,[$cnf( $equal(and(and(X,falsehood),truth),and(X,falsehood)) )],[refute_0_827,refute_0_842]) ).
cnf(refute_0_844,plain,
and(falsehood,and(X_21,truth)) = and(X_21,falsehood),
inference(subst,[],[refute_0_843:[bind(X,$fot(X_21))]]) ).
cnf(refute_0_845,plain,
or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21)))) = or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21)))),
introduced(tautology,[refl,[$fot(or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21)))))]]) ).
cnf(refute_0_846,plain,
( and(falsehood,and(X_21,truth)) != and(X_21,falsehood)
| or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21)))) != or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21))))
| or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21)))) = or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21)))),or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21))))) ),[1,0],$fot(and(X_21,falsehood))]]) ).
cnf(refute_0_847,plain,
( and(falsehood,and(X_21,truth)) != and(X_21,falsehood)
| or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21)))) = or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21)))),or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21))))) )],[refute_0_845,refute_0_846]) ).
cnf(refute_0_848,plain,
or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21)))) = or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))),
inference(resolve,[$cnf( $equal(and(falsehood,and(X_21,truth)),and(X_21,falsehood)) )],[refute_0_844,refute_0_847]) ).
cnf(refute_0_849,plain,
( or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21)))) != or(and(X_21,falsehood),and(truth,not(and(truth,X_21))))
| xor(truth,and(truth,X_21)) != or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21))))
| xor(truth,and(truth,X_21)) = or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,and(truth,X_21)),or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21))))) ),[1],$fot(or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))))]]) ).
cnf(refute_0_850,plain,
( xor(truth,and(truth,X_21)) != or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21))))
| xor(truth,and(truth,X_21)) = or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21)))),or(and(X_21,falsehood),and(truth,not(and(truth,X_21))))) )],[refute_0_848,refute_0_849]) ).
cnf(refute_0_851,plain,
xor(truth,and(truth,X_21)) = or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))),
inference(resolve,[$cnf( $equal(xor(truth,and(truth,X_21)),or(and(falsehood,and(X_21,truth)),and(truth,not(and(truth,X_21))))) )],[refute_0_823,refute_0_850]) ).
cnf(refute_0_852,plain,
xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) = or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(not(or(falsehood,and(truth,or(falsehood,falsehood)))),X_38)),
inference(subst,[],[xor_definition:[bind(X,$fot(or(falsehood,and(truth,or(falsehood,falsehood))))),bind(Y,$fot(X_38))]]) ).
cnf(refute_0_853,plain,
and(or(falsehood,and(truth,truth)),truth) = not(or(falsehood,not(or(falsehood,and(truth,truth))))),
inference(subst,[],[refute_0_153:[bind(X_1,$fot(or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_854,plain,
( and(or(falsehood,and(truth,truth)),truth) != not(or(falsehood,not(or(falsehood,and(truth,truth)))))
| not(or(falsehood,and(truth,truth))) != and(truth,or(falsehood,falsehood))
| and(or(falsehood,and(truth,truth)),truth) = not(or(falsehood,and(truth,or(falsehood,falsehood)))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,truth)),truth),not(or(falsehood,not(or(falsehood,and(truth,truth)))))) ),[1,0,1],$fot(and(truth,or(falsehood,falsehood)))]]) ).
cnf(refute_0_855,plain,
( and(or(falsehood,and(truth,truth)),truth) != not(or(falsehood,not(or(falsehood,and(truth,truth)))))
| and(or(falsehood,and(truth,truth)),truth) = not(or(falsehood,and(truth,or(falsehood,falsehood)))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,truth))),and(truth,or(falsehood,falsehood))) )],[refute_0_390,refute_0_854]) ).
cnf(refute_0_856,plain,
and(or(falsehood,and(truth,truth)),truth) = not(or(falsehood,and(truth,or(falsehood,falsehood)))),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),truth),not(or(falsehood,not(or(falsehood,and(truth,truth)))))) )],[refute_0_853,refute_0_855]) ).
cnf(refute_0_857,plain,
and(or(falsehood,and(truth,truth)),truth) = and(truth,or(falsehood,and(truth,truth))),
inference(subst,[],[refute_0_384:[bind(X_2,$fot(or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_858,plain,
( and(or(falsehood,and(truth,truth)),truth) != and(truth,or(falsehood,and(truth,truth)))
| and(or(falsehood,and(truth,truth)),truth) != not(or(falsehood,and(truth,or(falsehood,falsehood))))
| and(truth,or(falsehood,and(truth,truth))) = not(or(falsehood,and(truth,or(falsehood,falsehood)))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,truth)),truth),not(or(falsehood,and(truth,or(falsehood,falsehood))))) ),[0],$fot(and(truth,or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_859,plain,
( and(or(falsehood,and(truth,truth)),truth) != not(or(falsehood,and(truth,or(falsehood,falsehood))))
| and(truth,or(falsehood,and(truth,truth))) = not(or(falsehood,and(truth,or(falsehood,falsehood)))) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),truth),and(truth,or(falsehood,and(truth,truth)))) )],[refute_0_857,refute_0_858]) ).
cnf(refute_0_860,plain,
and(truth,or(falsehood,and(truth,truth))) = not(or(falsehood,and(truth,or(falsehood,falsehood)))),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),truth),not(or(falsehood,and(truth,or(falsehood,falsehood))))) )],[refute_0_856,refute_0_859]) ).
cnf(refute_0_861,plain,
( and(truth,or(falsehood,and(truth,truth))) != not(or(falsehood,and(truth,or(falsehood,falsehood))))
| not(or(falsehood,and(truth,or(falsehood,falsehood)))) = and(truth,or(falsehood,and(truth,truth))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,or(falsehood,and(truth,truth))))),bind(Y0,$fot(not(or(falsehood,and(truth,or(falsehood,falsehood))))))]]) ).
cnf(refute_0_862,plain,
not(or(falsehood,and(truth,or(falsehood,falsehood)))) = and(truth,or(falsehood,and(truth,truth))),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,and(truth,truth))),not(or(falsehood,and(truth,or(falsehood,falsehood))))) )],[refute_0_860,refute_0_861]) ).
cnf(refute_0_863,plain,
( not(or(falsehood,and(truth,or(falsehood,falsehood)))) != and(truth,or(falsehood,and(truth,truth)))
| xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) != or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(not(or(falsehood,and(truth,or(falsehood,falsehood)))),X_38))
| xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) = or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(and(truth,or(falsehood,and(truth,truth))),X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38),or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(not(or(falsehood,and(truth,or(falsehood,falsehood)))),X_38))) ),[1,1,0],$fot(and(truth,or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_864,plain,
( xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) != or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(not(or(falsehood,and(truth,or(falsehood,falsehood)))),X_38))
| xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) = or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(and(truth,or(falsehood,and(truth,truth))),X_38)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,or(falsehood,falsehood)))),and(truth,or(falsehood,and(truth,truth)))) )],[refute_0_862,refute_0_863]) ).
cnf(refute_0_865,plain,
xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) = or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(and(truth,or(falsehood,and(truth,truth))),X_38)),
inference(resolve,[$cnf( $equal(xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38),or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(not(or(falsehood,and(truth,or(falsehood,falsehood)))),X_38))) )],[refute_0_852,refute_0_864]) ).
cnf(refute_0_866,plain,
and(and(truth,or(falsehood,and(truth,truth))),X_38) = and(truth,and(or(falsehood,and(truth,truth)),X_38)),
inference(subst,[],[and_associativity:[bind(X,$fot(truth)),bind(Y,$fot(or(falsehood,and(truth,truth)))),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_867,plain,
or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),
introduced(tautology,[refl,[$fot(or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))))]]) ).
cnf(refute_0_868,plain,
( and(and(truth,or(falsehood,and(truth,truth))),X_38) != and(truth,and(or(falsehood,and(truth,truth)),X_38))
| or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) != or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))
| or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))) ),[1,0],$fot(and(truth,and(or(falsehood,and(truth,truth)),X_38)))]]) ).
cnf(refute_0_869,plain,
( and(and(truth,or(falsehood,and(truth,truth))),X_38) != and(truth,and(or(falsehood,and(truth,truth)),X_38))
| or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) ),
inference(resolve,[$cnf( $equal(or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))) )],[refute_0_867,refute_0_868]) ).
cnf(refute_0_870,plain,
or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),
inference(resolve,[$cnf( $equal(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(truth,and(or(falsehood,and(truth,truth)),X_38))) )],[refute_0_866,refute_0_869]) ).
cnf(refute_0_871,plain,
or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(and(truth,or(falsehood,and(truth,truth))),X_38)) = or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),
inference(subst,[],[refute_0_145:[bind(X,$fot(and(and(truth,or(falsehood,and(truth,truth))),X_38))),bind(Y,$fot(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))))]]) ).
cnf(refute_0_872,plain,
( or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) != or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))
| or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(and(truth,or(falsehood,and(truth,truth))),X_38)) != or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))
| or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(and(truth,or(falsehood,and(truth,truth))),X_38)) = or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(and(truth,or(falsehood,and(truth,truth))),X_38)))),bind(Y0,$fot(or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))))),bind(Z0,$fot(or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))))]]) ).
cnf(refute_0_873,plain,
( or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) != or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))
| or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(and(truth,or(falsehood,and(truth,truth))),X_38)) = or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) ),
inference(resolve,[$cnf( $equal(or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(and(truth,or(falsehood,and(truth,truth))),X_38)),or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))) )],[refute_0_871,refute_0_872]) ).
cnf(refute_0_874,plain,
or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(and(truth,or(falsehood,and(truth,truth))),X_38)) = or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),
inference(resolve,[$cnf( $equal(or(and(and(truth,or(falsehood,and(truth,truth))),X_38),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))) )],[refute_0_870,refute_0_873]) ).
cnf(refute_0_875,plain,
( or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(and(truth,or(falsehood,and(truth,truth))),X_38)) != or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))
| xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) != or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(and(truth,or(falsehood,and(truth,truth))),X_38))
| xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) = or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38),or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(and(truth,or(falsehood,and(truth,truth))),X_38))) ),[1],$fot(or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))))]]) ).
cnf(refute_0_876,plain,
( xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) != or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(and(truth,or(falsehood,and(truth,truth))),X_38))
| xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) = or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) ),
inference(resolve,[$cnf( $equal(or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(and(truth,or(falsehood,and(truth,truth))),X_38)),or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))) )],[refute_0_874,refute_0_875]) ).
cnf(refute_0_877,plain,
xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) = or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),
inference(resolve,[$cnf( $equal(xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38),or(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(and(truth,or(falsehood,and(truth,truth))),X_38))) )],[refute_0_865,refute_0_876]) ).
cnf(refute_0_878,plain,
not(or(falsehood,falsehood)) = not(or(falsehood,falsehood)),
introduced(tautology,[refl,[$fot(not(or(falsehood,falsehood)))]]) ).
cnf(refute_0_879,plain,
( not(or(falsehood,falsehood)) != not(or(falsehood,falsehood))
| or(falsehood,falsehood) != falsehood
| not(or(falsehood,falsehood)) = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,falsehood)),not(or(falsehood,falsehood))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_880,plain,
( or(falsehood,falsehood) != falsehood
| not(or(falsehood,falsehood)) = not(falsehood) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,falsehood)),not(or(falsehood,falsehood))) )],[refute_0_878,refute_0_879]) ).
cnf(refute_0_881,plain,
not(or(falsehood,falsehood)) = not(falsehood),
inference(resolve,[$cnf( $equal(or(falsehood,falsehood),falsehood) )],[refute_0_418,refute_0_880]) ).
cnf(refute_0_882,plain,
( not(falsehood) != truth
| not(or(falsehood,falsehood)) != not(falsehood)
| not(or(falsehood,falsehood)) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(or(falsehood,falsehood)))),bind(Y0,$fot(not(falsehood))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_883,plain,
( not(falsehood) != truth
| not(or(falsehood,falsehood)) = truth ),
inference(resolve,[$cnf( $equal(not(or(falsehood,falsehood)),not(falsehood)) )],[refute_0_881,refute_0_882]) ).
cnf(refute_0_884,plain,
not(or(falsehood,falsehood)) = truth,
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_112,refute_0_883]) ).
cnf(refute_0_885,plain,
not(not(or(falsehood,falsehood))) = not(not(or(falsehood,falsehood))),
introduced(tautology,[refl,[$fot(not(not(or(falsehood,falsehood))))]]) ).
cnf(refute_0_886,plain,
( not(not(or(falsehood,falsehood))) != not(not(or(falsehood,falsehood)))
| not(or(falsehood,falsehood)) != truth
| not(not(or(falsehood,falsehood))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(or(falsehood,falsehood))),not(not(or(falsehood,falsehood)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_887,plain,
( not(or(falsehood,falsehood)) != truth
| not(not(or(falsehood,falsehood))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(not(or(falsehood,falsehood))),not(not(or(falsehood,falsehood)))) )],[refute_0_885,refute_0_886]) ).
cnf(refute_0_888,plain,
not(not(or(falsehood,falsehood))) = not(truth),
inference(resolve,[$cnf( $equal(not(or(falsehood,falsehood)),truth) )],[refute_0_884,refute_0_887]) ).
cnf(refute_0_889,plain,
( not(not(or(falsehood,falsehood))) != not(truth)
| not(truth) != falsehood
| not(not(or(falsehood,falsehood))) = falsehood ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(not(or(falsehood,falsehood))))),bind(Y0,$fot(not(truth))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_890,plain,
( not(truth) != falsehood
| not(not(or(falsehood,falsehood))) = falsehood ),
inference(resolve,[$cnf( $equal(not(not(or(falsehood,falsehood))),not(truth)) )],[refute_0_888,refute_0_889]) ).
cnf(refute_0_891,plain,
not(not(or(falsehood,falsehood))) = falsehood,
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_890]) ).
cnf(refute_0_892,plain,
and(truth,or(falsehood,falsehood)) = not(not(or(falsehood,falsehood))),
inference(subst,[],[refute_0_440:[bind(Y,$fot(or(falsehood,falsehood)))]]) ).
cnf(refute_0_893,plain,
or(falsehood,and(truth,or(falsehood,falsehood))) = and(truth,or(falsehood,falsehood)),
inference(subst,[],[refute_0_119:[bind(Y,$fot(and(truth,or(falsehood,falsehood))))]]) ).
cnf(refute_0_894,plain,
( and(truth,or(falsehood,falsehood)) != not(not(or(falsehood,falsehood)))
| or(falsehood,and(truth,or(falsehood,falsehood))) != and(truth,or(falsehood,falsehood))
| or(falsehood,and(truth,or(falsehood,falsehood))) = not(not(or(falsehood,falsehood))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(falsehood,and(truth,or(falsehood,falsehood))))),bind(Y0,$fot(and(truth,or(falsehood,falsehood)))),bind(Z0,$fot(not(not(or(falsehood,falsehood)))))]]) ).
cnf(refute_0_895,plain,
( and(truth,or(falsehood,falsehood)) != not(not(or(falsehood,falsehood)))
| or(falsehood,and(truth,or(falsehood,falsehood))) = not(not(or(falsehood,falsehood))) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,falsehood))),and(truth,or(falsehood,falsehood))) )],[refute_0_893,refute_0_894]) ).
cnf(refute_0_896,plain,
or(falsehood,and(truth,or(falsehood,falsehood))) = not(not(or(falsehood,falsehood))),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),not(not(or(falsehood,falsehood)))) )],[refute_0_892,refute_0_895]) ).
cnf(refute_0_897,plain,
( not(not(or(falsehood,falsehood))) != falsehood
| or(falsehood,and(truth,or(falsehood,falsehood))) != not(not(or(falsehood,falsehood)))
| or(falsehood,and(truth,or(falsehood,falsehood))) = falsehood ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(falsehood,and(truth,or(falsehood,falsehood))))),bind(Y0,$fot(not(not(or(falsehood,falsehood))))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_898,plain,
( not(not(or(falsehood,falsehood))) != falsehood
| or(falsehood,and(truth,or(falsehood,falsehood))) = falsehood ),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,falsehood))),not(not(or(falsehood,falsehood)))) )],[refute_0_896,refute_0_897]) ).
cnf(refute_0_899,plain,
or(falsehood,and(truth,or(falsehood,falsehood))) = falsehood,
inference(resolve,[$cnf( $equal(not(not(or(falsehood,falsehood))),falsehood) )],[refute_0_891,refute_0_898]) ).
cnf(refute_0_900,plain,
xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) = xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38),
introduced(tautology,[refl,[$fot(xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38))]]) ).
cnf(refute_0_901,plain,
( or(falsehood,and(truth,or(falsehood,falsehood))) != falsehood
| xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) != xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38)
| xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) = xor(falsehood,X_38) ),
introduced(tautology,[equality,[$cnf( $equal(xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38),xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38)) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_902,plain,
( or(falsehood,and(truth,or(falsehood,falsehood))) != falsehood
| xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) = xor(falsehood,X_38) ),
inference(resolve,[$cnf( $equal(xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38),xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38)) )],[refute_0_900,refute_0_901]) ).
cnf(refute_0_903,plain,
xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) = xor(falsehood,X_38),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,falsehood))),falsehood) )],[refute_0_899,refute_0_902]) ).
cnf(refute_0_904,plain,
( xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) != or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))
| xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) != xor(falsehood,X_38)
| xor(falsehood,X_38) = or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38),or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))) ),[0],$fot(xor(falsehood,X_38))]]) ).
cnf(refute_0_905,plain,
( xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) != or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))
| xor(falsehood,X_38) = or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) ),
inference(resolve,[$cnf( $equal(xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38),xor(falsehood,X_38)) )],[refute_0_903,refute_0_904]) ).
cnf(refute_0_906,plain,
or(not(not(not(not(X_38)))),and(falsehood,not(X_38))) = or(and(falsehood,not(X_38)),not(not(not(not(X_38))))),
inference(subst,[],[refute_0_137:[bind(X_35,$fot(not(not(not(X_38))))),bind(X_36,$fot(and(falsehood,not(X_38))))]]) ).
cnf(refute_0_907,plain,
and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)) = and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),
introduced(tautology,[refl,[$fot(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))]]) ).
cnf(refute_0_908,plain,
( and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)) != and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))
| or(falsehood,and(truth,or(falsehood,falsehood))) != falsehood
| and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)) = and(falsehood,not(X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_909,plain,
( or(falsehood,and(truth,or(falsehood,falsehood))) != falsehood
| and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)) = and(falsehood,not(X_38)) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) )],[refute_0_907,refute_0_908]) ).
cnf(refute_0_910,plain,
and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)) = and(falsehood,not(X_38)),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,or(falsehood,falsehood))),falsehood) )],[refute_0_899,refute_0_909]) ).
cnf(refute_0_911,plain,
or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),
introduced(tautology,[refl,[$fot(or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))))]]) ).
cnf(refute_0_912,plain,
( and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)) != and(falsehood,not(X_38))
| or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) != or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))
| or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(not(not(not(not(X_38)))),and(falsehood,not(X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))) ),[1,1],$fot(and(falsehood,not(X_38)))]]) ).
cnf(refute_0_913,plain,
( and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)) != and(falsehood,not(X_38))
| or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(not(not(not(not(X_38)))),and(falsehood,not(X_38))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))) )],[refute_0_911,refute_0_912]) ).
cnf(refute_0_914,plain,
or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(not(not(not(not(X_38)))),and(falsehood,not(X_38))),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)),and(falsehood,not(X_38))) )],[refute_0_910,refute_0_913]) ).
cnf(refute_0_915,plain,
and(truth,X_38) = not(not(X_38)),
inference(subst,[],[refute_0_440:[bind(Y,$fot(X_38))]]) ).
cnf(refute_0_916,plain,
and(or(falsehood,and(truth,truth)),X_38) = and(or(falsehood,and(truth,truth)),X_38),
introduced(tautology,[refl,[$fot(and(or(falsehood,and(truth,truth)),X_38))]]) ).
cnf(refute_0_917,plain,
( and(or(falsehood,and(truth,truth)),X_38) != and(or(falsehood,and(truth,truth)),X_38)
| or(falsehood,and(truth,truth)) != truth
| and(or(falsehood,and(truth,truth)),X_38) = and(truth,X_38) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,truth)),X_38),and(or(falsehood,and(truth,truth)),X_38)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_918,plain,
( or(falsehood,and(truth,truth)) != truth
| and(or(falsehood,and(truth,truth)),X_38) = and(truth,X_38) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),X_38),and(or(falsehood,and(truth,truth)),X_38)) )],[refute_0_916,refute_0_917]) ).
cnf(refute_0_919,plain,
and(or(falsehood,and(truth,truth)),X_38) = and(truth,X_38),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),truth) )],[refute_0_400,refute_0_918]) ).
cnf(refute_0_920,plain,
( and(or(falsehood,and(truth,truth)),X_38) != and(truth,X_38)
| and(truth,X_38) != not(not(X_38))
| and(or(falsehood,and(truth,truth)),X_38) = not(not(X_38)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(or(falsehood,and(truth,truth)),X_38))),bind(Y0,$fot(and(truth,X_38))),bind(Z0,$fot(not(not(X_38))))]]) ).
cnf(refute_0_921,plain,
( and(truth,X_38) != not(not(X_38))
| and(or(falsehood,and(truth,truth)),X_38) = not(not(X_38)) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),X_38),and(truth,X_38)) )],[refute_0_919,refute_0_920]) ).
cnf(refute_0_922,plain,
and(or(falsehood,and(truth,truth)),X_38) = not(not(X_38)),
inference(resolve,[$cnf( $equal(and(truth,X_38),not(not(X_38))) )],[refute_0_915,refute_0_921]) ).
cnf(refute_0_923,plain,
not(and(or(falsehood,and(truth,truth)),X_38)) = not(and(or(falsehood,and(truth,truth)),X_38)),
introduced(tautology,[refl,[$fot(not(and(or(falsehood,and(truth,truth)),X_38)))]]) ).
cnf(refute_0_924,plain,
( and(or(falsehood,and(truth,truth)),X_38) != not(not(X_38))
| not(and(or(falsehood,and(truth,truth)),X_38)) != not(and(or(falsehood,and(truth,truth)),X_38))
| not(and(or(falsehood,and(truth,truth)),X_38)) = not(not(not(X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(or(falsehood,and(truth,truth)),X_38)),not(and(or(falsehood,and(truth,truth)),X_38))) ),[1,0],$fot(not(not(X_38)))]]) ).
cnf(refute_0_925,plain,
( and(or(falsehood,and(truth,truth)),X_38) != not(not(X_38))
| not(and(or(falsehood,and(truth,truth)),X_38)) = not(not(not(X_38))) ),
inference(resolve,[$cnf( $equal(not(and(or(falsehood,and(truth,truth)),X_38)),not(and(or(falsehood,and(truth,truth)),X_38))) )],[refute_0_923,refute_0_924]) ).
cnf(refute_0_926,plain,
not(and(or(falsehood,and(truth,truth)),X_38)) = not(not(not(X_38))),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),X_38),not(not(X_38))) )],[refute_0_922,refute_0_925]) ).
cnf(refute_0_927,plain,
not(not(and(or(falsehood,and(truth,truth)),X_38))) = not(not(and(or(falsehood,and(truth,truth)),X_38))),
introduced(tautology,[refl,[$fot(not(not(and(or(falsehood,and(truth,truth)),X_38))))]]) ).
cnf(refute_0_928,plain,
( not(and(or(falsehood,and(truth,truth)),X_38)) != not(not(not(X_38)))
| not(not(and(or(falsehood,and(truth,truth)),X_38))) != not(not(and(or(falsehood,and(truth,truth)),X_38)))
| not(not(and(or(falsehood,and(truth,truth)),X_38))) = not(not(not(not(X_38)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(and(or(falsehood,and(truth,truth)),X_38))),not(not(and(or(falsehood,and(truth,truth)),X_38)))) ),[1,0],$fot(not(not(not(X_38))))]]) ).
cnf(refute_0_929,plain,
( not(and(or(falsehood,and(truth,truth)),X_38)) != not(not(not(X_38)))
| not(not(and(or(falsehood,and(truth,truth)),X_38))) = not(not(not(not(X_38)))) ),
inference(resolve,[$cnf( $equal(not(not(and(or(falsehood,and(truth,truth)),X_38))),not(not(and(or(falsehood,and(truth,truth)),X_38)))) )],[refute_0_927,refute_0_928]) ).
cnf(refute_0_930,plain,
not(not(and(or(falsehood,and(truth,truth)),X_38))) = not(not(not(not(X_38)))),
inference(resolve,[$cnf( $equal(not(and(or(falsehood,and(truth,truth)),X_38)),not(not(not(X_38)))) )],[refute_0_926,refute_0_929]) ).
cnf(refute_0_931,plain,
and(truth,and(or(falsehood,and(truth,truth)),X_38)) = not(not(and(or(falsehood,and(truth,truth)),X_38))),
inference(subst,[],[refute_0_440:[bind(Y,$fot(and(or(falsehood,and(truth,truth)),X_38)))]]) ).
cnf(refute_0_932,plain,
( and(truth,and(or(falsehood,and(truth,truth)),X_38)) != not(not(and(or(falsehood,and(truth,truth)),X_38)))
| not(not(and(or(falsehood,and(truth,truth)),X_38))) != not(not(not(not(X_38))))
| and(truth,and(or(falsehood,and(truth,truth)),X_38)) = not(not(not(not(X_38)))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(truth,and(or(falsehood,and(truth,truth)),X_38)))),bind(Y0,$fot(not(not(and(or(falsehood,and(truth,truth)),X_38))))),bind(Z0,$fot(not(not(not(not(X_38))))))]]) ).
cnf(refute_0_933,plain,
( not(not(and(or(falsehood,and(truth,truth)),X_38))) != not(not(not(not(X_38))))
| and(truth,and(or(falsehood,and(truth,truth)),X_38)) = not(not(not(not(X_38)))) ),
inference(resolve,[$cnf( $equal(and(truth,and(or(falsehood,and(truth,truth)),X_38)),not(not(and(or(falsehood,and(truth,truth)),X_38)))) )],[refute_0_931,refute_0_932]) ).
cnf(refute_0_934,plain,
and(truth,and(or(falsehood,and(truth,truth)),X_38)) = not(not(not(not(X_38)))),
inference(resolve,[$cnf( $equal(not(not(and(or(falsehood,and(truth,truth)),X_38))),not(not(not(not(X_38))))) )],[refute_0_930,refute_0_933]) ).
cnf(refute_0_935,plain,
or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),
introduced(tautology,[refl,[$fot(or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))))]]) ).
cnf(refute_0_936,plain,
( and(truth,and(or(falsehood,and(truth,truth)),X_38)) != not(not(not(not(X_38))))
| or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) != or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))
| or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))) ),[1,0],$fot(not(not(not(not(X_38)))))]]) ).
cnf(refute_0_937,plain,
( and(truth,and(or(falsehood,and(truth,truth)),X_38)) != not(not(not(not(X_38))))
| or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) ),
inference(resolve,[$cnf( $equal(or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))) )],[refute_0_935,refute_0_936]) ).
cnf(refute_0_938,plain,
or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),
inference(resolve,[$cnf( $equal(and(truth,and(or(falsehood,and(truth,truth)),X_38)),not(not(not(not(X_38))))) )],[refute_0_934,refute_0_937]) ).
cnf(refute_0_939,plain,
( or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) != or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))
| or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) != or(not(not(not(not(X_38)))),and(falsehood,not(X_38)))
| or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(not(not(not(not(X_38)))),and(falsehood,not(X_38))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))))),bind(Y0,$fot(or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))))),bind(Z0,$fot(or(not(not(not(not(X_38)))),and(falsehood,not(X_38)))))]]) ).
cnf(refute_0_940,plain,
( or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) != or(not(not(not(not(X_38)))),and(falsehood,not(X_38)))
| or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(not(not(not(not(X_38)))),and(falsehood,not(X_38))) ),
inference(resolve,[$cnf( $equal(or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))) )],[refute_0_938,refute_0_939]) ).
cnf(refute_0_941,plain,
or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(not(not(not(not(X_38)))),and(falsehood,not(X_38))),
inference(resolve,[$cnf( $equal(or(not(not(not(not(X_38)))),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),or(not(not(not(not(X_38)))),and(falsehood,not(X_38)))) )],[refute_0_914,refute_0_940]) ).
cnf(refute_0_942,plain,
( or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) != or(not(not(not(not(X_38)))),and(falsehood,not(X_38)))
| or(not(not(not(not(X_38)))),and(falsehood,not(X_38))) != or(and(falsehood,not(X_38)),not(not(not(not(X_38)))))
| or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(and(falsehood,not(X_38)),not(not(not(not(X_38))))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))))),bind(Y0,$fot(or(not(not(not(not(X_38)))),and(falsehood,not(X_38))))),bind(Z0,$fot(or(and(falsehood,not(X_38)),not(not(not(not(X_38)))))))]]) ).
cnf(refute_0_943,plain,
( or(not(not(not(not(X_38)))),and(falsehood,not(X_38))) != or(and(falsehood,not(X_38)),not(not(not(not(X_38)))))
| or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(and(falsehood,not(X_38)),not(not(not(not(X_38))))) ),
inference(resolve,[$cnf( $equal(or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),or(not(not(not(not(X_38)))),and(falsehood,not(X_38)))) )],[refute_0_941,refute_0_942]) ).
cnf(refute_0_944,plain,
or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) = or(and(falsehood,not(X_38)),not(not(not(not(X_38))))),
inference(resolve,[$cnf( $equal(or(not(not(not(not(X_38)))),and(falsehood,not(X_38))),or(and(falsehood,not(X_38)),not(not(not(not(X_38)))))) )],[refute_0_906,refute_0_943]) ).
cnf(refute_0_945,plain,
( or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))) != or(and(falsehood,not(X_38)),not(not(not(not(X_38)))))
| xor(falsehood,X_38) != or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))
| xor(falsehood,X_38) = or(and(falsehood,not(X_38)),not(not(not(not(X_38))))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(falsehood,X_38),or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))) ),[1],$fot(or(and(falsehood,not(X_38)),not(not(not(not(X_38))))))]]) ).
cnf(refute_0_946,plain,
( xor(falsehood,X_38) != or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))
| xor(falsehood,X_38) = or(and(falsehood,not(X_38)),not(not(not(not(X_38))))) ),
inference(resolve,[$cnf( $equal(or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38))),or(and(falsehood,not(X_38)),not(not(not(not(X_38)))))) )],[refute_0_944,refute_0_945]) ).
cnf(refute_0_947,plain,
( xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38) != or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))
| xor(falsehood,X_38) = or(and(falsehood,not(X_38)),not(not(not(not(X_38))))) ),
inference(resolve,[$cnf( $equal(xor(falsehood,X_38),or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))) )],[refute_0_905,refute_0_946]) ).
cnf(refute_0_948,plain,
xor(falsehood,X_38) = or(and(falsehood,not(X_38)),not(not(not(not(X_38))))),
inference(resolve,[$cnf( $equal(xor(or(falsehood,and(truth,or(falsehood,falsehood))),X_38),or(and(truth,and(or(falsehood,and(truth,truth)),X_38)),and(or(falsehood,and(truth,or(falsehood,falsehood))),not(X_38)))) )],[refute_0_877,refute_0_947]) ).
cnf(refute_0_949,plain,
and(truth,not(X_38)) = not(not(not(X_38))),
inference(subst,[],[refute_0_440:[bind(Y,$fot(not(X_38)))]]) ).
cnf(refute_0_950,plain,
or(and(falsehood,X_38),and(truth,not(X_38))) = or(and(falsehood,X_38),and(truth,not(X_38))),
introduced(tautology,[refl,[$fot(or(and(falsehood,X_38),and(truth,not(X_38))))]]) ).
cnf(refute_0_951,plain,
( and(truth,not(X_38)) != not(not(not(X_38)))
| or(and(falsehood,X_38),and(truth,not(X_38))) != or(and(falsehood,X_38),and(truth,not(X_38)))
| or(and(falsehood,X_38),and(truth,not(X_38))) = or(and(falsehood,X_38),not(not(not(X_38)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(falsehood,X_38),and(truth,not(X_38))),or(and(falsehood,X_38),and(truth,not(X_38)))) ),[1,1],$fot(not(not(not(X_38))))]]) ).
cnf(refute_0_952,plain,
( and(truth,not(X_38)) != not(not(not(X_38)))
| or(and(falsehood,X_38),and(truth,not(X_38))) = or(and(falsehood,X_38),not(not(not(X_38)))) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,X_38),and(truth,not(X_38))),or(and(falsehood,X_38),and(truth,not(X_38)))) )],[refute_0_950,refute_0_951]) ).
cnf(refute_0_953,plain,
or(and(falsehood,X_38),and(truth,not(X_38))) = or(and(falsehood,X_38),not(not(not(X_38)))),
inference(resolve,[$cnf( $equal(and(truth,not(X_38)),not(not(not(X_38)))) )],[refute_0_949,refute_0_952]) ).
cnf(refute_0_954,plain,
( or(and(falsehood,X_38),and(truth,not(X_38))) != or(and(falsehood,X_38),not(not(not(X_38))))
| xor(truth,X_38) != or(and(falsehood,X_38),and(truth,not(X_38)))
| xor(truth,X_38) = or(and(falsehood,X_38),not(not(not(X_38)))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_38),or(and(falsehood,X_38),and(truth,not(X_38)))) ),[1],$fot(or(and(falsehood,X_38),not(not(not(X_38)))))]]) ).
cnf(refute_0_955,plain,
( xor(truth,X_38) != or(and(falsehood,X_38),and(truth,not(X_38)))
| xor(truth,X_38) = or(and(falsehood,X_38),not(not(not(X_38)))) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,X_38),and(truth,not(X_38))),or(and(falsehood,X_38),not(not(not(X_38))))) )],[refute_0_953,refute_0_954]) ).
cnf(refute_0_956,plain,
xor(truth,X_38) = or(and(falsehood,X_38),not(not(not(X_38)))),
inference(resolve,[$cnf( $equal(xor(truth,X_38),or(and(falsehood,X_38),and(truth,not(X_38)))) )],[refute_0_818,refute_0_955]) ).
cnf(refute_0_957,plain,
( xor(truth,X_38) != or(and(falsehood,X_38),not(not(not(X_38))))
| or(and(falsehood,X_38),not(not(not(X_38)))) = xor(truth,X_38) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(truth,X_38))),bind(Y0,$fot(or(and(falsehood,X_38),not(not(not(X_38))))))]]) ).
cnf(refute_0_958,plain,
or(and(falsehood,X_38),not(not(not(X_38)))) = xor(truth,X_38),
inference(resolve,[$cnf( $equal(xor(truth,X_38),or(and(falsehood,X_38),not(not(not(X_38))))) )],[refute_0_956,refute_0_957]) ).
cnf(refute_0_959,plain,
or(and(falsehood,not(X_38)),not(not(not(not(X_38))))) = xor(truth,not(X_38)),
inference(subst,[],[refute_0_958:[bind(X_38,$fot(not(X_38)))]]) ).
cnf(refute_0_960,plain,
( or(and(falsehood,not(X_38)),not(not(not(not(X_38))))) != xor(truth,not(X_38))
| xor(falsehood,X_38) != or(and(falsehood,not(X_38)),not(not(not(not(X_38)))))
| xor(falsehood,X_38) = xor(truth,not(X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(falsehood,X_38),or(and(falsehood,not(X_38)),not(not(not(not(X_38)))))) ),[1],$fot(xor(truth,not(X_38)))]]) ).
cnf(refute_0_961,plain,
( xor(falsehood,X_38) != or(and(falsehood,not(X_38)),not(not(not(not(X_38)))))
| xor(falsehood,X_38) = xor(truth,not(X_38)) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,not(X_38)),not(not(not(not(X_38))))),xor(truth,not(X_38))) )],[refute_0_959,refute_0_960]) ).
cnf(refute_0_962,plain,
xor(falsehood,X_38) = xor(truth,not(X_38)),
inference(resolve,[$cnf( $equal(xor(falsehood,X_38),or(and(falsehood,not(X_38)),not(not(not(not(X_38)))))) )],[refute_0_948,refute_0_961]) ).
cnf(refute_0_963,plain,
( xor(falsehood,X_38) != xor(truth,not(X_38))
| xor(truth,not(X_38)) = xor(falsehood,X_38) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(falsehood,X_38))),bind(Y0,$fot(xor(truth,not(X_38))))]]) ).
cnf(refute_0_964,plain,
xor(truth,not(X_38)) = xor(falsehood,X_38),
inference(resolve,[$cnf( $equal(xor(falsehood,X_38),xor(truth,not(X_38))) )],[refute_0_962,refute_0_963]) ).
cnf(refute_0_965,plain,
xor(truth,not(not(X_21))) = xor(falsehood,not(X_21)),
inference(subst,[],[refute_0_964:[bind(X_38,$fot(not(X_21)))]]) ).
cnf(refute_0_966,plain,
and(truth,X_21) = not(not(X_21)),
inference(subst,[],[refute_0_440:[bind(Y,$fot(X_21))]]) ).
cnf(refute_0_967,plain,
xor(truth,and(truth,X_21)) = xor(truth,and(truth,X_21)),
introduced(tautology,[refl,[$fot(xor(truth,and(truth,X_21)))]]) ).
cnf(refute_0_968,plain,
( and(truth,X_21) != not(not(X_21))
| xor(truth,and(truth,X_21)) != xor(truth,and(truth,X_21))
| xor(truth,and(truth,X_21)) = xor(truth,not(not(X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,and(truth,X_21)),xor(truth,and(truth,X_21))) ),[1,1],$fot(not(not(X_21)))]]) ).
cnf(refute_0_969,plain,
( and(truth,X_21) != not(not(X_21))
| xor(truth,and(truth,X_21)) = xor(truth,not(not(X_21))) ),
inference(resolve,[$cnf( $equal(xor(truth,and(truth,X_21)),xor(truth,and(truth,X_21))) )],[refute_0_967,refute_0_968]) ).
cnf(refute_0_970,plain,
xor(truth,and(truth,X_21)) = xor(truth,not(not(X_21))),
inference(resolve,[$cnf( $equal(and(truth,X_21),not(not(X_21))) )],[refute_0_966,refute_0_969]) ).
cnf(refute_0_971,plain,
( xor(truth,and(truth,X_21)) != xor(truth,not(not(X_21)))
| xor(truth,not(not(X_21))) != xor(falsehood,not(X_21))
| xor(truth,and(truth,X_21)) = xor(falsehood,not(X_21)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(xor(truth,and(truth,X_21)))),bind(Y0,$fot(xor(truth,not(not(X_21))))),bind(Z0,$fot(xor(falsehood,not(X_21))))]]) ).
cnf(refute_0_972,plain,
( xor(truth,not(not(X_21))) != xor(falsehood,not(X_21))
| xor(truth,and(truth,X_21)) = xor(falsehood,not(X_21)) ),
inference(resolve,[$cnf( $equal(xor(truth,and(truth,X_21)),xor(truth,not(not(X_21)))) )],[refute_0_970,refute_0_971]) ).
cnf(refute_0_973,plain,
xor(truth,and(truth,X_21)) = xor(falsehood,not(X_21)),
inference(resolve,[$cnf( $equal(xor(truth,not(not(X_21))),xor(falsehood,not(X_21))) )],[refute_0_965,refute_0_972]) ).
cnf(refute_0_974,plain,
( xor(truth,and(truth,X_21)) != or(and(X_21,falsehood),and(truth,not(and(truth,X_21))))
| xor(truth,and(truth,X_21)) != xor(falsehood,not(X_21))
| xor(falsehood,not(X_21)) = or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,and(truth,X_21)),or(and(X_21,falsehood),and(truth,not(and(truth,X_21))))) ),[0],$fot(xor(falsehood,not(X_21)))]]) ).
cnf(refute_0_975,plain,
( xor(truth,and(truth,X_21)) != or(and(X_21,falsehood),and(truth,not(and(truth,X_21))))
| xor(falsehood,not(X_21)) = or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))) ),
inference(resolve,[$cnf( $equal(xor(truth,and(truth,X_21)),xor(falsehood,not(X_21))) )],[refute_0_973,refute_0_974]) ).
cnf(refute_0_976,plain,
not(and(truth,X_21)) = not(and(truth,X_21)),
introduced(tautology,[refl,[$fot(not(and(truth,X_21)))]]) ).
cnf(refute_0_977,plain,
( and(truth,X_21) != not(not(X_21))
| not(and(truth,X_21)) != not(and(truth,X_21))
| not(and(truth,X_21)) = not(not(not(X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(truth,X_21)),not(and(truth,X_21))) ),[1,0],$fot(not(not(X_21)))]]) ).
cnf(refute_0_978,plain,
( and(truth,X_21) != not(not(X_21))
| not(and(truth,X_21)) = not(not(not(X_21))) ),
inference(resolve,[$cnf( $equal(not(and(truth,X_21)),not(and(truth,X_21))) )],[refute_0_976,refute_0_977]) ).
cnf(refute_0_979,plain,
not(and(truth,X_21)) = not(not(not(X_21))),
inference(resolve,[$cnf( $equal(and(truth,X_21),not(not(X_21))) )],[refute_0_966,refute_0_978]) ).
cnf(refute_0_980,plain,
not(not(and(truth,X_21))) = not(not(and(truth,X_21))),
introduced(tautology,[refl,[$fot(not(not(and(truth,X_21))))]]) ).
cnf(refute_0_981,plain,
( not(and(truth,X_21)) != not(not(not(X_21)))
| not(not(and(truth,X_21))) != not(not(and(truth,X_21)))
| not(not(and(truth,X_21))) = not(not(not(not(X_21)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(and(truth,X_21))),not(not(and(truth,X_21)))) ),[1,0],$fot(not(not(not(X_21))))]]) ).
cnf(refute_0_982,plain,
( not(and(truth,X_21)) != not(not(not(X_21)))
| not(not(and(truth,X_21))) = not(not(not(not(X_21)))) ),
inference(resolve,[$cnf( $equal(not(not(and(truth,X_21))),not(not(and(truth,X_21)))) )],[refute_0_980,refute_0_981]) ).
cnf(refute_0_983,plain,
not(not(and(truth,X_21))) = not(not(not(not(X_21)))),
inference(resolve,[$cnf( $equal(not(and(truth,X_21)),not(not(not(X_21)))) )],[refute_0_979,refute_0_982]) ).
cnf(refute_0_984,plain,
not(not(not(and(truth,X_21)))) = not(not(not(and(truth,X_21)))),
introduced(tautology,[refl,[$fot(not(not(not(and(truth,X_21)))))]]) ).
cnf(refute_0_985,plain,
( not(not(and(truth,X_21))) != not(not(not(not(X_21))))
| not(not(not(and(truth,X_21)))) != not(not(not(and(truth,X_21))))
| not(not(not(and(truth,X_21)))) = not(not(not(not(not(X_21))))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(not(and(truth,X_21)))),not(not(not(and(truth,X_21))))) ),[1,0],$fot(not(not(not(not(X_21)))))]]) ).
cnf(refute_0_986,plain,
( not(not(and(truth,X_21))) != not(not(not(not(X_21))))
| not(not(not(and(truth,X_21)))) = not(not(not(not(not(X_21))))) ),
inference(resolve,[$cnf( $equal(not(not(not(and(truth,X_21)))),not(not(not(and(truth,X_21))))) )],[refute_0_984,refute_0_985]) ).
cnf(refute_0_987,plain,
not(not(not(and(truth,X_21)))) = not(not(not(not(not(X_21))))),
inference(resolve,[$cnf( $equal(not(not(and(truth,X_21))),not(not(not(not(X_21))))) )],[refute_0_983,refute_0_986]) ).
cnf(refute_0_988,plain,
and(truth,not(and(truth,X_21))) = not(not(not(and(truth,X_21)))),
inference(subst,[],[refute_0_440:[bind(Y,$fot(not(and(truth,X_21))))]]) ).
cnf(refute_0_989,plain,
( and(truth,not(and(truth,X_21))) != not(not(not(and(truth,X_21))))
| not(not(not(and(truth,X_21)))) != not(not(not(not(not(X_21)))))
| and(truth,not(and(truth,X_21))) = not(not(not(not(not(X_21))))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(truth,not(and(truth,X_21))))),bind(Y0,$fot(not(not(not(and(truth,X_21)))))),bind(Z0,$fot(not(not(not(not(not(X_21)))))))]]) ).
cnf(refute_0_990,plain,
( not(not(not(and(truth,X_21)))) != not(not(not(not(not(X_21)))))
| and(truth,not(and(truth,X_21))) = not(not(not(not(not(X_21))))) ),
inference(resolve,[$cnf( $equal(and(truth,not(and(truth,X_21))),not(not(not(and(truth,X_21))))) )],[refute_0_988,refute_0_989]) ).
cnf(refute_0_991,plain,
and(truth,not(and(truth,X_21))) = not(not(not(not(not(X_21))))),
inference(resolve,[$cnf( $equal(not(not(not(and(truth,X_21)))),not(not(not(not(not(X_21)))))) )],[refute_0_987,refute_0_990]) ).
cnf(refute_0_992,plain,
or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))) = or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))),
introduced(tautology,[refl,[$fot(or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))))]]) ).
cnf(refute_0_993,plain,
( and(truth,not(and(truth,X_21))) != not(not(not(not(not(X_21)))))
| or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))) != or(and(X_21,falsehood),and(truth,not(and(truth,X_21))))
| or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))) = or(and(X_21,falsehood),not(not(not(not(not(X_21)))))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))),or(and(X_21,falsehood),and(truth,not(and(truth,X_21))))) ),[1,1],$fot(not(not(not(not(not(X_21))))))]]) ).
cnf(refute_0_994,plain,
( and(truth,not(and(truth,X_21))) != not(not(not(not(not(X_21)))))
| or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))) = or(and(X_21,falsehood),not(not(not(not(not(X_21)))))) ),
inference(resolve,[$cnf( $equal(or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))),or(and(X_21,falsehood),and(truth,not(and(truth,X_21))))) )],[refute_0_992,refute_0_993]) ).
cnf(refute_0_995,plain,
or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))) = or(and(X_21,falsehood),not(not(not(not(not(X_21)))))),
inference(resolve,[$cnf( $equal(and(truth,not(and(truth,X_21))),not(not(not(not(not(X_21)))))) )],[refute_0_991,refute_0_994]) ).
cnf(refute_0_996,plain,
( or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))) != or(and(X_21,falsehood),not(not(not(not(not(X_21))))))
| xor(falsehood,not(X_21)) != or(and(X_21,falsehood),and(truth,not(and(truth,X_21))))
| xor(falsehood,not(X_21)) = or(and(X_21,falsehood),not(not(not(not(not(X_21)))))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(falsehood,not(X_21)),or(and(X_21,falsehood),and(truth,not(and(truth,X_21))))) ),[1],$fot(or(and(X_21,falsehood),not(not(not(not(not(X_21)))))))]]) ).
cnf(refute_0_997,plain,
( xor(falsehood,not(X_21)) != or(and(X_21,falsehood),and(truth,not(and(truth,X_21))))
| xor(falsehood,not(X_21)) = or(and(X_21,falsehood),not(not(not(not(not(X_21)))))) ),
inference(resolve,[$cnf( $equal(or(and(X_21,falsehood),and(truth,not(and(truth,X_21)))),or(and(X_21,falsehood),not(not(not(not(not(X_21))))))) )],[refute_0_995,refute_0_996]) ).
cnf(refute_0_998,plain,
( xor(truth,and(truth,X_21)) != or(and(X_21,falsehood),and(truth,not(and(truth,X_21))))
| xor(falsehood,not(X_21)) = or(and(X_21,falsehood),not(not(not(not(not(X_21)))))) ),
inference(resolve,[$cnf( $equal(xor(falsehood,not(X_21)),or(and(X_21,falsehood),and(truth,not(and(truth,X_21))))) )],[refute_0_975,refute_0_997]) ).
cnf(refute_0_999,plain,
xor(falsehood,not(X_21)) = or(and(X_21,falsehood),not(not(not(not(not(X_21)))))),
inference(resolve,[$cnf( $equal(xor(truth,and(truth,X_21)),or(and(X_21,falsehood),and(truth,not(and(truth,X_21))))) )],[refute_0_851,refute_0_998]) ).
cnf(refute_0_1000,plain,
( xor(X_37,truth) != or(and(X_37,falsehood),not(not(not(X_37))))
| or(and(X_37,falsehood),not(not(not(X_37)))) = xor(X_37,truth) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(X_37,truth))),bind(Y0,$fot(or(and(X_37,falsehood),not(not(not(X_37))))))]]) ).
cnf(refute_0_1001,plain,
or(and(X_37,falsehood),not(not(not(X_37)))) = xor(X_37,truth),
inference(resolve,[$cnf( $equal(xor(X_37,truth),or(and(X_37,falsehood),not(not(not(X_37))))) )],[refute_0_702,refute_0_1000]) ).
cnf(refute_0_1002,plain,
or(and(X_21,falsehood),not(not(not(X_21)))) = xor(X_21,truth),
inference(subst,[],[refute_0_1001:[bind(X_37,$fot(X_21))]]) ).
cnf(refute_0_1003,plain,
and(truth,and(truth,X_20)) = and(truth,and(X_20,truth)),
inference(subst,[],[refute_0_588:[bind(X_19,$fot(truth))]]) ).
cnf(refute_0_1004,plain,
and(truth,and(X_20,truth)) = and(X_20,and(truth,truth)),
inference(subst,[],[refute_0_588:[bind(X_19,$fot(X_20)),bind(X_20,$fot(truth))]]) ).
cnf(refute_0_1005,plain,
( and(truth,and(X_20,truth)) != and(X_20,and(truth,truth))
| and(truth,and(truth,X_20)) != and(truth,and(X_20,truth))
| and(truth,and(truth,X_20)) = and(X_20,and(truth,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,and(truth,X_20)),and(truth,and(X_20,truth))) ),[1],$fot(and(X_20,and(truth,truth)))]]) ).
cnf(refute_0_1006,plain,
( and(truth,and(truth,X_20)) != and(truth,and(X_20,truth))
| and(truth,and(truth,X_20)) = and(X_20,and(truth,truth)) ),
inference(resolve,[$cnf( $equal(and(truth,and(X_20,truth)),and(X_20,and(truth,truth))) )],[refute_0_1004,refute_0_1005]) ).
cnf(refute_0_1007,plain,
and(truth,and(truth,X_20)) = and(X_20,and(truth,truth)),
inference(resolve,[$cnf( $equal(and(truth,and(truth,X_20)),and(truth,and(X_20,truth))) )],[refute_0_1003,refute_0_1006]) ).
cnf(refute_0_1008,plain,
and(truth,X_20) = not(not(X_20)),
inference(subst,[],[refute_0_440:[bind(Y,$fot(X_20))]]) ).
cnf(refute_0_1009,plain,
not(and(truth,X_20)) = not(and(truth,X_20)),
introduced(tautology,[refl,[$fot(not(and(truth,X_20)))]]) ).
cnf(refute_0_1010,plain,
( and(truth,X_20) != not(not(X_20))
| not(and(truth,X_20)) != not(and(truth,X_20))
| not(and(truth,X_20)) = not(not(not(X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(truth,X_20)),not(and(truth,X_20))) ),[1,0],$fot(not(not(X_20)))]]) ).
cnf(refute_0_1011,plain,
( and(truth,X_20) != not(not(X_20))
| not(and(truth,X_20)) = not(not(not(X_20))) ),
inference(resolve,[$cnf( $equal(not(and(truth,X_20)),not(and(truth,X_20))) )],[refute_0_1009,refute_0_1010]) ).
cnf(refute_0_1012,plain,
not(and(truth,X_20)) = not(not(not(X_20))),
inference(resolve,[$cnf( $equal(and(truth,X_20),not(not(X_20))) )],[refute_0_1008,refute_0_1011]) ).
cnf(refute_0_1013,plain,
not(not(and(truth,X_20))) = not(not(and(truth,X_20))),
introduced(tautology,[refl,[$fot(not(not(and(truth,X_20))))]]) ).
cnf(refute_0_1014,plain,
( not(and(truth,X_20)) != not(not(not(X_20)))
| not(not(and(truth,X_20))) != not(not(and(truth,X_20)))
| not(not(and(truth,X_20))) = not(not(not(not(X_20)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(and(truth,X_20))),not(not(and(truth,X_20)))) ),[1,0],$fot(not(not(not(X_20))))]]) ).
cnf(refute_0_1015,plain,
( not(and(truth,X_20)) != not(not(not(X_20)))
| not(not(and(truth,X_20))) = not(not(not(not(X_20)))) ),
inference(resolve,[$cnf( $equal(not(not(and(truth,X_20))),not(not(and(truth,X_20)))) )],[refute_0_1013,refute_0_1014]) ).
cnf(refute_0_1016,plain,
not(not(and(truth,X_20))) = not(not(not(not(X_20)))),
inference(resolve,[$cnf( $equal(not(and(truth,X_20)),not(not(not(X_20)))) )],[refute_0_1012,refute_0_1015]) ).
cnf(refute_0_1017,plain,
and(truth,and(truth,X_20)) = not(not(and(truth,X_20))),
inference(subst,[],[refute_0_440:[bind(Y,$fot(and(truth,X_20)))]]) ).
cnf(refute_0_1018,plain,
( and(truth,and(truth,X_20)) != not(not(and(truth,X_20)))
| not(not(and(truth,X_20))) != not(not(not(not(X_20))))
| and(truth,and(truth,X_20)) = not(not(not(not(X_20)))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(truth,and(truth,X_20)))),bind(Y0,$fot(not(not(and(truth,X_20))))),bind(Z0,$fot(not(not(not(not(X_20))))))]]) ).
cnf(refute_0_1019,plain,
( not(not(and(truth,X_20))) != not(not(not(not(X_20))))
| and(truth,and(truth,X_20)) = not(not(not(not(X_20)))) ),
inference(resolve,[$cnf( $equal(and(truth,and(truth,X_20)),not(not(and(truth,X_20)))) )],[refute_0_1017,refute_0_1018]) ).
cnf(refute_0_1020,plain,
and(truth,and(truth,X_20)) = not(not(not(not(X_20)))),
inference(resolve,[$cnf( $equal(not(not(and(truth,X_20))),not(not(not(not(X_20))))) )],[refute_0_1016,refute_0_1019]) ).
cnf(refute_0_1021,plain,
( and(truth,and(truth,X_20)) != and(X_20,and(truth,truth))
| and(truth,and(truth,X_20)) != not(not(not(not(X_20))))
| not(not(not(not(X_20)))) = and(X_20,and(truth,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,and(truth,X_20)),and(X_20,and(truth,truth))) ),[0],$fot(not(not(not(not(X_20)))))]]) ).
cnf(refute_0_1022,plain,
( and(truth,and(truth,X_20)) != and(X_20,and(truth,truth))
| not(not(not(not(X_20)))) = and(X_20,and(truth,truth)) ),
inference(resolve,[$cnf( $equal(and(truth,and(truth,X_20)),not(not(not(not(X_20))))) )],[refute_0_1020,refute_0_1021]) ).
cnf(refute_0_1023,plain,
and(X_20,and(truth,truth)) = and(X_20,and(truth,truth)),
introduced(tautology,[refl,[$fot(and(X_20,and(truth,truth)))]]) ).
cnf(refute_0_1024,plain,
( and(X_20,and(truth,truth)) != and(X_20,and(truth,truth))
| and(truth,truth) != truth
| and(X_20,and(truth,truth)) = and(X_20,truth) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_20,and(truth,truth)),and(X_20,and(truth,truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_1025,plain,
( and(truth,truth) != truth
| and(X_20,and(truth,truth)) = and(X_20,truth) ),
inference(resolve,[$cnf( $equal(and(X_20,and(truth,truth)),and(X_20,and(truth,truth))) )],[refute_0_1023,refute_0_1024]) ).
cnf(refute_0_1026,plain,
and(X_20,and(truth,truth)) = and(X_20,truth),
inference(resolve,[$cnf( $equal(and(truth,truth),truth) )],[refute_0_193,refute_0_1025]) ).
cnf(refute_0_1027,plain,
( and(X_20,and(truth,truth)) != and(X_20,truth)
| and(X_20,truth) != not(not(X_20))
| and(X_20,and(truth,truth)) = not(not(X_20)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(X_20,and(truth,truth)))),bind(Y0,$fot(and(X_20,truth))),bind(Z0,$fot(not(not(X_20))))]]) ).
cnf(refute_0_1028,plain,
( and(X_20,truth) != not(not(X_20))
| and(X_20,and(truth,truth)) = not(not(X_20)) ),
inference(resolve,[$cnf( $equal(and(X_20,and(truth,truth)),and(X_20,truth)) )],[refute_0_1026,refute_0_1027]) ).
cnf(refute_0_1029,plain,
and(X_20,and(truth,truth)) = not(not(X_20)),
inference(resolve,[$cnf( $equal(and(X_20,truth),not(not(X_20))) )],[refute_0_592,refute_0_1028]) ).
cnf(refute_0_1030,plain,
( and(X_20,and(truth,truth)) != not(not(X_20))
| not(not(not(not(X_20)))) != and(X_20,and(truth,truth))
| not(not(not(not(X_20)))) = not(not(X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(not(not(X_20)))),and(X_20,and(truth,truth))) ),[1],$fot(not(not(X_20)))]]) ).
cnf(refute_0_1031,plain,
( not(not(not(not(X_20)))) != and(X_20,and(truth,truth))
| not(not(not(not(X_20)))) = not(not(X_20)) ),
inference(resolve,[$cnf( $equal(and(X_20,and(truth,truth)),not(not(X_20))) )],[refute_0_1029,refute_0_1030]) ).
cnf(refute_0_1032,plain,
( and(truth,and(truth,X_20)) != and(X_20,and(truth,truth))
| not(not(not(not(X_20)))) = not(not(X_20)) ),
inference(resolve,[$cnf( $equal(not(not(not(not(X_20)))),and(X_20,and(truth,truth))) )],[refute_0_1022,refute_0_1031]) ).
cnf(refute_0_1033,plain,
not(not(not(not(X_20)))) = not(not(X_20)),
inference(resolve,[$cnf( $equal(and(truth,and(truth,X_20)),and(X_20,and(truth,truth))) )],[refute_0_1007,refute_0_1032]) ).
cnf(refute_0_1034,plain,
not(not(not(not(not(X_21))))) = not(not(not(X_21))),
inference(subst,[],[refute_0_1033:[bind(X_20,$fot(not(X_21)))]]) ).
cnf(refute_0_1035,plain,
or(and(X_21,falsehood),not(not(not(not(not(X_21)))))) = or(and(X_21,falsehood),not(not(not(not(not(X_21)))))),
introduced(tautology,[refl,[$fot(or(and(X_21,falsehood),not(not(not(not(not(X_21)))))))]]) ).
cnf(refute_0_1036,plain,
( not(not(not(not(not(X_21))))) != not(not(not(X_21)))
| or(and(X_21,falsehood),not(not(not(not(not(X_21)))))) != or(and(X_21,falsehood),not(not(not(not(not(X_21))))))
| or(and(X_21,falsehood),not(not(not(not(not(X_21)))))) = or(and(X_21,falsehood),not(not(not(X_21)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_21,falsehood),not(not(not(not(not(X_21)))))),or(and(X_21,falsehood),not(not(not(not(not(X_21))))))) ),[1,1],$fot(not(not(not(X_21))))]]) ).
cnf(refute_0_1037,plain,
( not(not(not(not(not(X_21))))) != not(not(not(X_21)))
| or(and(X_21,falsehood),not(not(not(not(not(X_21)))))) = or(and(X_21,falsehood),not(not(not(X_21)))) ),
inference(resolve,[$cnf( $equal(or(and(X_21,falsehood),not(not(not(not(not(X_21)))))),or(and(X_21,falsehood),not(not(not(not(not(X_21))))))) )],[refute_0_1035,refute_0_1036]) ).
cnf(refute_0_1038,plain,
or(and(X_21,falsehood),not(not(not(not(not(X_21)))))) = or(and(X_21,falsehood),not(not(not(X_21)))),
inference(resolve,[$cnf( $equal(not(not(not(not(not(X_21))))),not(not(not(X_21)))) )],[refute_0_1034,refute_0_1037]) ).
cnf(refute_0_1039,plain,
( or(and(X_21,falsehood),not(not(not(X_21)))) != xor(X_21,truth)
| or(and(X_21,falsehood),not(not(not(not(not(X_21)))))) != or(and(X_21,falsehood),not(not(not(X_21))))
| or(and(X_21,falsehood),not(not(not(not(not(X_21)))))) = xor(X_21,truth) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(and(X_21,falsehood),not(not(not(not(not(X_21)))))))),bind(Y0,$fot(or(and(X_21,falsehood),not(not(not(X_21)))))),bind(Z0,$fot(xor(X_21,truth)))]]) ).
cnf(refute_0_1040,plain,
( or(and(X_21,falsehood),not(not(not(X_21)))) != xor(X_21,truth)
| or(and(X_21,falsehood),not(not(not(not(not(X_21)))))) = xor(X_21,truth) ),
inference(resolve,[$cnf( $equal(or(and(X_21,falsehood),not(not(not(not(not(X_21)))))),or(and(X_21,falsehood),not(not(not(X_21))))) )],[refute_0_1038,refute_0_1039]) ).
cnf(refute_0_1041,plain,
or(and(X_21,falsehood),not(not(not(not(not(X_21)))))) = xor(X_21,truth),
inference(resolve,[$cnf( $equal(or(and(X_21,falsehood),not(not(not(X_21)))),xor(X_21,truth)) )],[refute_0_1002,refute_0_1040]) ).
cnf(refute_0_1042,plain,
( or(and(X_21,falsehood),not(not(not(not(not(X_21)))))) != xor(X_21,truth)
| xor(falsehood,not(X_21)) != or(and(X_21,falsehood),not(not(not(not(not(X_21))))))
| xor(falsehood,not(X_21)) = xor(X_21,truth) ),
introduced(tautology,[equality,[$cnf( $equal(xor(falsehood,not(X_21)),or(and(X_21,falsehood),not(not(not(not(not(X_21))))))) ),[1],$fot(xor(X_21,truth))]]) ).
cnf(refute_0_1043,plain,
( xor(falsehood,not(X_21)) != or(and(X_21,falsehood),not(not(not(not(not(X_21))))))
| xor(falsehood,not(X_21)) = xor(X_21,truth) ),
inference(resolve,[$cnf( $equal(or(and(X_21,falsehood),not(not(not(not(not(X_21)))))),xor(X_21,truth)) )],[refute_0_1041,refute_0_1042]) ).
cnf(refute_0_1044,plain,
xor(falsehood,not(X_21)) = xor(X_21,truth),
inference(resolve,[$cnf( $equal(xor(falsehood,not(X_21)),or(and(X_21,falsehood),not(not(not(not(not(X_21))))))) )],[refute_0_999,refute_0_1043]) ).
cnf(refute_0_1045,plain,
not(not(X_38)) = X_38,
inference(subst,[],[refute_0_518:[bind(Y,$fot(X_38))]]) ).
cnf(refute_0_1046,plain,
implies(or(X_98,falsehood),falsehood) = not(or(X_98,falsehood)),
inference(subst,[],[refute_0_779:[bind(X_35,$fot(or(X_98,falsehood)))]]) ).
cnf(refute_0_1047,plain,
implies(or(X_98,falsehood),falsehood) = implies(X_98,and(falsehood,X_98)),
inference(subst,[],[refute_0_653:[bind(X,$fot(X_98)),bind(X_23,$fot(falsehood))]]) ).
cnf(refute_0_1048,plain,
( implies(or(X_98,falsehood),falsehood) != implies(X_98,and(falsehood,X_98))
| implies(or(X_98,falsehood),falsehood) != not(or(X_98,falsehood))
| implies(X_98,and(falsehood,X_98)) = not(or(X_98,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_98,falsehood),falsehood),not(or(X_98,falsehood))) ),[0],$fot(implies(X_98,and(falsehood,X_98)))]]) ).
cnf(refute_0_1049,plain,
( implies(or(X_98,falsehood),falsehood) != not(or(X_98,falsehood))
| implies(X_98,and(falsehood,X_98)) = not(or(X_98,falsehood)) ),
inference(resolve,[$cnf( $equal(implies(or(X_98,falsehood),falsehood),implies(X_98,and(falsehood,X_98))) )],[refute_0_1047,refute_0_1048]) ).
cnf(refute_0_1050,plain,
implies(X_98,and(falsehood,X_98)) = not(or(X_98,falsehood)),
inference(resolve,[$cnf( $equal(implies(or(X_98,falsehood),falsehood),not(or(X_98,falsehood))) )],[refute_0_1046,refute_0_1049]) ).
cnf(refute_0_1051,plain,
or(and(falsehood,X_38),not(X_38)) = or(not(X_38),and(falsehood,X_38)),
inference(subst,[],[refute_0_135:[bind(X_35,$fot(X_38)),bind(X_36,$fot(and(falsehood,X_38)))]]) ).
cnf(refute_0_1052,plain,
not(not(not(X_38))) = not(X_38),
inference(subst,[],[refute_0_518:[bind(Y,$fot(not(X_38)))]]) ).
cnf(refute_0_1053,plain,
or(and(falsehood,X_38),not(not(not(X_38)))) = or(and(falsehood,X_38),not(not(not(X_38)))),
introduced(tautology,[refl,[$fot(or(and(falsehood,X_38),not(not(not(X_38)))))]]) ).
cnf(refute_0_1054,plain,
( not(not(not(X_38))) != not(X_38)
| or(and(falsehood,X_38),not(not(not(X_38)))) != or(and(falsehood,X_38),not(not(not(X_38))))
| or(and(falsehood,X_38),not(not(not(X_38)))) = or(and(falsehood,X_38),not(X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(falsehood,X_38),not(not(not(X_38)))),or(and(falsehood,X_38),not(not(not(X_38))))) ),[1,1],$fot(not(X_38))]]) ).
cnf(refute_0_1055,plain,
( not(not(not(X_38))) != not(X_38)
| or(and(falsehood,X_38),not(not(not(X_38)))) = or(and(falsehood,X_38),not(X_38)) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,X_38),not(not(not(X_38)))),or(and(falsehood,X_38),not(not(not(X_38))))) )],[refute_0_1053,refute_0_1054]) ).
cnf(refute_0_1056,plain,
or(and(falsehood,X_38),not(not(not(X_38)))) = or(and(falsehood,X_38),not(X_38)),
inference(resolve,[$cnf( $equal(not(not(not(X_38))),not(X_38)) )],[refute_0_1052,refute_0_1055]) ).
cnf(refute_0_1057,plain,
( or(and(falsehood,X_38),not(X_38)) != or(not(X_38),and(falsehood,X_38))
| or(and(falsehood,X_38),not(not(not(X_38)))) != or(and(falsehood,X_38),not(X_38))
| or(and(falsehood,X_38),not(not(not(X_38)))) = or(not(X_38),and(falsehood,X_38)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(and(falsehood,X_38),not(not(not(X_38)))))),bind(Y0,$fot(or(and(falsehood,X_38),not(X_38)))),bind(Z0,$fot(or(not(X_38),and(falsehood,X_38))))]]) ).
cnf(refute_0_1058,plain,
( or(and(falsehood,X_38),not(X_38)) != or(not(X_38),and(falsehood,X_38))
| or(and(falsehood,X_38),not(not(not(X_38)))) = or(not(X_38),and(falsehood,X_38)) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,X_38),not(not(not(X_38)))),or(and(falsehood,X_38),not(X_38))) )],[refute_0_1056,refute_0_1057]) ).
cnf(refute_0_1059,plain,
or(and(falsehood,X_38),not(not(not(X_38)))) = or(not(X_38),and(falsehood,X_38)),
inference(resolve,[$cnf( $equal(or(and(falsehood,X_38),not(X_38)),or(not(X_38),and(falsehood,X_38))) )],[refute_0_1051,refute_0_1058]) ).
cnf(refute_0_1060,plain,
( or(and(falsehood,X_38),not(not(not(X_38)))) != or(not(X_38),and(falsehood,X_38))
| xor(truth,X_38) != or(and(falsehood,X_38),not(not(not(X_38))))
| xor(truth,X_38) = or(not(X_38),and(falsehood,X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_38),or(and(falsehood,X_38),not(not(not(X_38))))) ),[1],$fot(or(not(X_38),and(falsehood,X_38)))]]) ).
cnf(refute_0_1061,plain,
( xor(truth,X_38) != or(and(falsehood,X_38),not(not(not(X_38))))
| xor(truth,X_38) = or(not(X_38),and(falsehood,X_38)) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,X_38),not(not(not(X_38)))),or(not(X_38),and(falsehood,X_38))) )],[refute_0_1059,refute_0_1060]) ).
cnf(refute_0_1062,plain,
xor(truth,X_38) = or(not(X_38),and(falsehood,X_38)),
inference(resolve,[$cnf( $equal(xor(truth,X_38),or(and(falsehood,X_38),not(not(not(X_38))))) )],[refute_0_956,refute_0_1061]) ).
cnf(refute_0_1063,plain,
or(not(X_38),and(falsehood,X_38)) = implies(X_38,and(falsehood,X_38)),
inference(subst,[],[refute_0_277:[bind(Y,$fot(and(falsehood,X_38))),bind(X_56,$fot(X_38))]]) ).
cnf(refute_0_1064,plain,
( or(not(X_38),and(falsehood,X_38)) != implies(X_38,and(falsehood,X_38))
| xor(truth,X_38) != or(not(X_38),and(falsehood,X_38))
| xor(truth,X_38) = implies(X_38,and(falsehood,X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_38),or(not(X_38),and(falsehood,X_38))) ),[1],$fot(implies(X_38,and(falsehood,X_38)))]]) ).
cnf(refute_0_1065,plain,
( xor(truth,X_38) != or(not(X_38),and(falsehood,X_38))
| xor(truth,X_38) = implies(X_38,and(falsehood,X_38)) ),
inference(resolve,[$cnf( $equal(or(not(X_38),and(falsehood,X_38)),implies(X_38,and(falsehood,X_38))) )],[refute_0_1063,refute_0_1064]) ).
cnf(refute_0_1066,plain,
xor(truth,X_38) = implies(X_38,and(falsehood,X_38)),
inference(resolve,[$cnf( $equal(xor(truth,X_38),or(not(X_38),and(falsehood,X_38))) )],[refute_0_1062,refute_0_1065]) ).
cnf(refute_0_1067,plain,
( xor(truth,X_38) != implies(X_38,and(falsehood,X_38))
| implies(X_38,and(falsehood,X_38)) = xor(truth,X_38) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(truth,X_38))),bind(Y0,$fot(implies(X_38,and(falsehood,X_38))))]]) ).
cnf(refute_0_1068,plain,
implies(X_38,and(falsehood,X_38)) = xor(truth,X_38),
inference(resolve,[$cnf( $equal(xor(truth,X_38),implies(X_38,and(falsehood,X_38))) )],[refute_0_1066,refute_0_1067]) ).
cnf(refute_0_1069,plain,
implies(X_98,and(falsehood,X_98)) = xor(truth,X_98),
inference(subst,[],[refute_0_1068:[bind(X_38,$fot(X_98))]]) ).
cnf(refute_0_1070,plain,
( implies(X_98,and(falsehood,X_98)) != not(or(X_98,falsehood))
| implies(X_98,and(falsehood,X_98)) != xor(truth,X_98)
| xor(truth,X_98) = not(or(X_98,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_98,and(falsehood,X_98)),not(or(X_98,falsehood))) ),[0],$fot(xor(truth,X_98))]]) ).
cnf(refute_0_1071,plain,
( implies(X_98,and(falsehood,X_98)) != not(or(X_98,falsehood))
| xor(truth,X_98) = not(or(X_98,falsehood)) ),
inference(resolve,[$cnf( $equal(implies(X_98,and(falsehood,X_98)),xor(truth,X_98)) )],[refute_0_1069,refute_0_1070]) ).
cnf(refute_0_1072,plain,
or(X_98,falsehood) = X_98,
inference(subst,[],[refute_0_204:[bind(X_8,$fot(X_98))]]) ).
cnf(refute_0_1073,plain,
not(or(X_98,falsehood)) = not(or(X_98,falsehood)),
introduced(tautology,[refl,[$fot(not(or(X_98,falsehood)))]]) ).
cnf(refute_0_1074,plain,
( not(or(X_98,falsehood)) != not(or(X_98,falsehood))
| or(X_98,falsehood) != X_98
| not(or(X_98,falsehood)) = not(X_98) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(X_98,falsehood)),not(or(X_98,falsehood))) ),[1,0],$fot(X_98)]]) ).
cnf(refute_0_1075,plain,
( or(X_98,falsehood) != X_98
| not(or(X_98,falsehood)) = not(X_98) ),
inference(resolve,[$cnf( $equal(not(or(X_98,falsehood)),not(or(X_98,falsehood))) )],[refute_0_1073,refute_0_1074]) ).
cnf(refute_0_1076,plain,
not(or(X_98,falsehood)) = not(X_98),
inference(resolve,[$cnf( $equal(or(X_98,falsehood),X_98) )],[refute_0_1072,refute_0_1075]) ).
cnf(refute_0_1077,plain,
( not(or(X_98,falsehood)) != not(X_98)
| xor(truth,X_98) != not(or(X_98,falsehood))
| xor(truth,X_98) = not(X_98) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_98),not(or(X_98,falsehood))) ),[1],$fot(not(X_98))]]) ).
cnf(refute_0_1078,plain,
( xor(truth,X_98) != not(or(X_98,falsehood))
| xor(truth,X_98) = not(X_98) ),
inference(resolve,[$cnf( $equal(not(or(X_98,falsehood)),not(X_98)) )],[refute_0_1076,refute_0_1077]) ).
cnf(refute_0_1079,plain,
( implies(X_98,and(falsehood,X_98)) != not(or(X_98,falsehood))
| xor(truth,X_98) = not(X_98) ),
inference(resolve,[$cnf( $equal(xor(truth,X_98),not(or(X_98,falsehood))) )],[refute_0_1071,refute_0_1078]) ).
cnf(refute_0_1080,plain,
xor(truth,X_98) = not(X_98),
inference(resolve,[$cnf( $equal(implies(X_98,and(falsehood,X_98)),not(or(X_98,falsehood))) )],[refute_0_1050,refute_0_1079]) ).
cnf(refute_0_1081,plain,
xor(truth,not(X_38)) = not(not(X_38)),
inference(subst,[],[refute_0_1080:[bind(X_98,$fot(not(X_38)))]]) ).
cnf(refute_0_1082,plain,
( not(not(X_38)) != X_38
| xor(truth,not(X_38)) != not(not(X_38))
| xor(truth,not(X_38)) = X_38 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(xor(truth,not(X_38)))),bind(Y0,$fot(not(not(X_38)))),bind(Z0,$fot(X_38))]]) ).
cnf(refute_0_1083,plain,
( not(not(X_38)) != X_38
| xor(truth,not(X_38)) = X_38 ),
inference(resolve,[$cnf( $equal(xor(truth,not(X_38)),not(not(X_38))) )],[refute_0_1081,refute_0_1082]) ).
cnf(refute_0_1084,plain,
xor(truth,not(X_38)) = X_38,
inference(resolve,[$cnf( $equal(not(not(X_38)),X_38) )],[refute_0_1045,refute_0_1083]) ).
cnf(refute_0_1085,plain,
( xor(falsehood,X_38) != xor(truth,not(X_38))
| xor(truth,not(X_38)) != X_38
| xor(falsehood,X_38) = X_38 ),
introduced(tautology,[equality,[$cnf( ~ $equal(xor(falsehood,X_38),X_38) ),[0],$fot(xor(truth,not(X_38)))]]) ).
cnf(refute_0_1086,plain,
( xor(falsehood,X_38) != xor(truth,not(X_38))
| xor(falsehood,X_38) = X_38 ),
inference(resolve,[$cnf( $equal(xor(truth,not(X_38)),X_38) )],[refute_0_1084,refute_0_1085]) ).
cnf(refute_0_1087,plain,
xor(falsehood,X_38) = X_38,
inference(resolve,[$cnf( $equal(xor(falsehood,X_38),xor(truth,not(X_38))) )],[refute_0_962,refute_0_1086]) ).
cnf(refute_0_1088,plain,
xor(falsehood,not(X_21)) = not(X_21),
inference(subst,[],[refute_0_1087:[bind(X_38,$fot(not(X_21)))]]) ).
cnf(refute_0_1089,plain,
( xor(falsehood,not(X_21)) != not(X_21)
| xor(falsehood,not(X_21)) != xor(X_21,truth)
| not(X_21) = xor(X_21,truth) ),
introduced(tautology,[equality,[$cnf( $equal(xor(falsehood,not(X_21)),xor(X_21,truth)) ),[0],$fot(not(X_21))]]) ).
cnf(refute_0_1090,plain,
( xor(falsehood,not(X_21)) != xor(X_21,truth)
| not(X_21) = xor(X_21,truth) ),
inference(resolve,[$cnf( $equal(xor(falsehood,not(X_21)),not(X_21)) )],[refute_0_1088,refute_0_1089]) ).
cnf(refute_0_1091,plain,
not(X_21) = xor(X_21,truth),
inference(resolve,[$cnf( $equal(xor(falsehood,not(X_21)),xor(X_21,truth)) )],[refute_0_1044,refute_0_1090]) ).
cnf(refute_0_1092,plain,
( not(X_21) != xor(X_21,truth)
| xor(X_21,truth) = not(X_21) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(not(X_21))),bind(Y0,$fot(xor(X_21,truth)))]]) ).
cnf(refute_0_1093,plain,
xor(X_21,truth) = not(X_21),
inference(resolve,[$cnf( $equal(not(X_21),xor(X_21,truth)) )],[refute_0_1091,refute_0_1092]) ).
cnf(refute_0_1094,plain,
xor(X_73,truth) = not(X_73),
inference(subst,[],[refute_0_1093:[bind(X_21,$fot(X_73))]]) ).
cnf(refute_0_1095,plain,
implies(falsehood,xor(X_73,truth)) = implies(falsehood,xor(X_73,truth)),
introduced(tautology,[refl,[$fot(implies(falsehood,xor(X_73,truth)))]]) ).
cnf(refute_0_1096,plain,
( implies(falsehood,xor(X_73,truth)) != implies(falsehood,xor(X_73,truth))
| xor(X_73,truth) != not(X_73)
| implies(falsehood,xor(X_73,truth)) = implies(falsehood,not(X_73)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(falsehood,xor(X_73,truth)),implies(falsehood,xor(X_73,truth))) ),[1,1],$fot(not(X_73))]]) ).
cnf(refute_0_1097,plain,
( xor(X_73,truth) != not(X_73)
| implies(falsehood,xor(X_73,truth)) = implies(falsehood,not(X_73)) ),
inference(resolve,[$cnf( $equal(implies(falsehood,xor(X_73,truth)),implies(falsehood,xor(X_73,truth))) )],[refute_0_1095,refute_0_1096]) ).
cnf(refute_0_1098,plain,
implies(falsehood,xor(X_73,truth)) = implies(falsehood,not(X_73)),
inference(resolve,[$cnf( $equal(xor(X_73,truth),not(X_73)) )],[refute_0_1094,refute_0_1097]) ).
cnf(refute_0_1099,plain,
( implies(falsehood,not(X_73)) != implies(X_73,truth)
| implies(falsehood,xor(X_73,truth)) != implies(falsehood,not(X_73))
| implies(falsehood,xor(X_73,truth)) = implies(X_73,truth) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(falsehood,xor(X_73,truth)))),bind(Y0,$fot(implies(falsehood,not(X_73)))),bind(Z0,$fot(implies(X_73,truth)))]]) ).
cnf(refute_0_1100,plain,
( implies(falsehood,not(X_73)) != implies(X_73,truth)
| implies(falsehood,xor(X_73,truth)) = implies(X_73,truth) ),
inference(resolve,[$cnf( $equal(implies(falsehood,xor(X_73,truth)),implies(falsehood,not(X_73))) )],[refute_0_1098,refute_0_1099]) ).
cnf(refute_0_1101,plain,
implies(falsehood,xor(X_73,truth)) = implies(X_73,truth),
inference(resolve,[$cnf( $equal(implies(falsehood,not(X_73)),implies(X_73,truth)) )],[refute_0_810,refute_0_1100]) ).
cnf(refute_0_1102,plain,
( implies(falsehood,xor(X_73,truth)) != implies(X_73,truth)
| truth != implies(falsehood,xor(X_73,truth))
| truth = implies(X_73,truth) ),
introduced(tautology,[equality,[$cnf( $equal(truth,implies(falsehood,xor(X_73,truth))) ),[1],$fot(implies(X_73,truth))]]) ).
cnf(refute_0_1103,plain,
( truth != implies(falsehood,xor(X_73,truth))
| truth = implies(X_73,truth) ),
inference(resolve,[$cnf( $equal(implies(falsehood,xor(X_73,truth)),implies(X_73,truth)) )],[refute_0_1101,refute_0_1102]) ).
cnf(refute_0_1104,plain,
truth = implies(X_73,truth),
inference(resolve,[$cnf( $equal(truth,implies(falsehood,xor(X_73,truth))) )],[refute_0_805,refute_0_1103]) ).
cnf(refute_0_1105,plain,
( truth != implies(X_73,truth)
| implies(X_73,truth) = truth ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(X_73,truth)))]]) ).
cnf(refute_0_1106,plain,
implies(X_73,truth) = truth,
inference(resolve,[$cnf( $equal(truth,implies(X_73,truth)) )],[refute_0_1104,refute_0_1105]) ).
cnf(refute_0_1107,plain,
implies(X_61,truth) = truth,
inference(subst,[],[refute_0_1106:[bind(X_73,$fot(X_61))]]) ).
cnf(refute_0_1108,plain,
not(implies(X_61,truth)) = not(implies(X_61,truth)),
introduced(tautology,[refl,[$fot(not(implies(X_61,truth)))]]) ).
cnf(refute_0_1109,plain,
( implies(X_61,truth) != truth
| not(implies(X_61,truth)) != not(implies(X_61,truth))
| not(implies(X_61,truth)) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_61,truth)),not(implies(X_61,truth))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_1110,plain,
( implies(X_61,truth) != truth
| not(implies(X_61,truth)) = not(truth) ),
inference(resolve,[$cnf( $equal(not(implies(X_61,truth)),not(implies(X_61,truth))) )],[refute_0_1108,refute_0_1109]) ).
cnf(refute_0_1111,plain,
not(implies(X_61,truth)) = not(truth),
inference(resolve,[$cnf( $equal(implies(X_61,truth),truth) )],[refute_0_1107,refute_0_1110]) ).
cnf(refute_0_1112,plain,
( not(implies(X_61,truth)) != not(truth)
| not(truth) != falsehood
| not(implies(X_61,truth)) = falsehood ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(implies(X_61,truth)))),bind(Y0,$fot(not(truth))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_1113,plain,
( not(truth) != falsehood
| not(implies(X_61,truth)) = falsehood ),
inference(resolve,[$cnf( $equal(not(implies(X_61,truth)),not(truth)) )],[refute_0_1111,refute_0_1112]) ).
cnf(refute_0_1114,plain,
not(implies(X_61,truth)) = falsehood,
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_1113]) ).
cnf(refute_0_1115,plain,
( and(falsehood,X_61) != not(implies(X_61,truth))
| not(implies(X_61,truth)) != falsehood
| and(falsehood,X_61) = falsehood ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(falsehood,X_61),falsehood) ),[0],$fot(not(implies(X_61,truth)))]]) ).
cnf(refute_0_1116,plain,
( and(falsehood,X_61) != not(implies(X_61,truth))
| and(falsehood,X_61) = falsehood ),
inference(resolve,[$cnf( $equal(not(implies(X_61,truth)),falsehood) )],[refute_0_1114,refute_0_1115]) ).
cnf(refute_0_1117,plain,
and(falsehood,X_61) = falsehood,
inference(resolve,[$cnf( $equal(and(falsehood,X_61),not(implies(X_61,truth))) )],[refute_0_500,refute_0_1116]) ).
cnf(refute_0_1118,plain,
and(falsehood,x) = falsehood,
inference(subst,[],[refute_0_1117:[bind(X_61,$fot(x))]]) ).
cnf(refute_0_1119,plain,
( and(falsehood,x) != falsehood
| falsehood != falsehood
| and(falsehood,x) = falsehood ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(falsehood,x),falsehood) ),[0],$fot(falsehood)]]) ).
cnf(refute_0_1120,plain,
( falsehood != falsehood
| and(falsehood,x) = falsehood ),
inference(resolve,[$cnf( $equal(and(falsehood,x),falsehood) )],[refute_0_1118,refute_0_1119]) ).
cnf(refute_0_1121,plain,
falsehood != falsehood,
inference(resolve,[$cnf( $equal(and(falsehood,x),falsehood) )],[refute_0_1120,refute_0_19]) ).
cnf(refute_0_1122,plain,
falsehood = falsehood,
introduced(tautology,[refl,[$fot(falsehood)]]) ).
cnf(refute_0_1123,plain,
$false,
inference(resolve,[$cnf( $equal(falsehood,falsehood) )],[refute_0_1122,refute_0_1121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL157-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 00:10:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.61/0.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.61/0.84
% 0.61/0.84 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.77/0.94
%------------------------------------------------------------------------------