TSTP Solution File: LCL153-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL153-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 12:50:00 EDT 2022
% Result : Unsatisfiable 0.47s 0.65s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 110
% Number of leaves : 212
% Syntax : Number of clauses : 793 ( 405 unt; 0 nHn; 414 RR)
% Number of literals : 1361 (1360 equ; 572 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 985 ( 49 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
implies(truth,X) = X ).
cnf(wajsberg_2,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ).
cnf(wajsberg_3,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth ).
cnf(or_definition,axiom,
or(X,Y) = implies(not(X),Y) ).
cnf(or_associativity,axiom,
or(or(X,Y),Z) = or(X,or(Y,Z)) ).
cnf(or_commutativity,axiom,
or(X,Y) = or(Y,X) ).
cnf(and_definition,axiom,
and(X,Y) = not(or(not(X),not(Y))) ).
cnf(and_associativity,axiom,
and(and(X,Y),Z) = and(X,and(Y,Z)) ).
cnf(and_commutativity,axiom,
and(X,Y) = and(Y,X) ).
cnf(xor_definition,axiom,
xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ).
cnf(xor_commutativity,axiom,
xor(X,Y) = xor(Y,X) ).
cnf(false_definition,axiom,
not(truth) = falsehood ).
cnf(prove_alternative_wajsberg_axiom,negated_conjecture,
not(x) != xor(x,truth) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( xor(X,Y) != xor(Y,X)
| xor(Y,X) = xor(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(X,Y))),bind(Y0,$fot(xor(Y,X)))]]) ).
cnf(refute_0_4,plain,
xor(Y,X) = xor(X,Y),
inference(resolve,[$cnf( $equal(xor(X,Y),xor(Y,X)) )],[xor_commutativity,refute_0_3]) ).
cnf(refute_0_5,plain,
xor(x,truth) = xor(truth,x),
inference(subst,[],[refute_0_4:[bind(X,$fot(truth)),bind(Y,$fot(x))]]) ).
cnf(refute_0_6,plain,
( not(x) != xor(truth,x)
| xor(x,truth) != xor(truth,x)
| not(x) = xor(x,truth) ),
introduced(tautology,[equality,[$cnf( ~ $equal(not(x),xor(x,truth)) ),[1],$fot(xor(truth,x))]]) ).
cnf(refute_0_7,plain,
( not(x) != xor(truth,x)
| not(x) = xor(x,truth) ),
inference(resolve,[$cnf( $equal(xor(x,truth),xor(truth,x)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
not(x) != xor(truth,x),
inference(resolve,[$cnf( $equal(not(x),xor(x,truth)) )],[refute_0_7,prove_alternative_wajsberg_axiom]) ).
cnf(refute_0_9,plain,
xor(truth,X_8) = or(and(truth,not(X_8)),and(not(truth),X_8)),
inference(subst,[],[xor_definition:[bind(X,$fot(truth)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_10,plain,
( not(truth) != falsehood
| xor(truth,X_8) != or(and(truth,not(X_8)),and(not(truth),X_8))
| xor(truth,X_8) = or(and(truth,not(X_8)),and(falsehood,X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_8),or(and(truth,not(X_8)),and(not(truth),X_8))) ),[1,1,0],$fot(falsehood)]]) ).
cnf(refute_0_11,plain,
( xor(truth,X_8) != or(and(truth,not(X_8)),and(not(truth),X_8))
| xor(truth,X_8) = or(and(truth,not(X_8)),and(falsehood,X_8)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_10]) ).
cnf(refute_0_12,plain,
xor(truth,X_8) = or(and(truth,not(X_8)),and(falsehood,X_8)),
inference(resolve,[$cnf( $equal(xor(truth,X_8),or(and(truth,not(X_8)),and(not(truth),X_8))) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( or(X,Y) != or(Y,X)
| or(Y,X) = or(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(or(Y,X)))]]) ).
cnf(refute_0_14,plain,
or(Y,X) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),or(Y,X)) )],[or_commutativity,refute_0_13]) ).
cnf(refute_0_15,plain,
or(and(truth,not(X_8)),and(falsehood,X_8)) = or(and(falsehood,X_8),and(truth,not(X_8))),
inference(subst,[],[refute_0_14:[bind(X,$fot(and(falsehood,X_8))),bind(Y,$fot(and(truth,not(X_8))))]]) ).
cnf(refute_0_16,plain,
( or(and(truth,not(X_8)),and(falsehood,X_8)) != or(and(falsehood,X_8),and(truth,not(X_8)))
| xor(truth,X_8) != or(and(truth,not(X_8)),and(falsehood,X_8))
| xor(truth,X_8) = or(and(falsehood,X_8),and(truth,not(X_8))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_8),or(and(truth,not(X_8)),and(falsehood,X_8))) ),[1],$fot(or(and(falsehood,X_8),and(truth,not(X_8))))]]) ).
cnf(refute_0_17,plain,
( xor(truth,X_8) != or(and(truth,not(X_8)),and(falsehood,X_8))
| xor(truth,X_8) = or(and(falsehood,X_8),and(truth,not(X_8))) ),
inference(resolve,[$cnf( $equal(or(and(truth,not(X_8)),and(falsehood,X_8)),or(and(falsehood,X_8),and(truth,not(X_8)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
xor(truth,X_8) = or(and(falsehood,X_8),and(truth,not(X_8))),
inference(resolve,[$cnf( $equal(xor(truth,X_8),or(and(truth,not(X_8)),and(falsehood,X_8))) )],[refute_0_12,refute_0_17]) ).
cnf(refute_0_19,plain,
and(X_21,truth) = not(or(not(X_21),not(truth))),
inference(subst,[],[and_definition:[bind(X,$fot(X_21)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_20,plain,
( and(X_21,truth) != not(or(not(X_21),not(truth)))
| not(truth) != falsehood
| and(X_21,truth) = not(or(not(X_21),falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_21,truth),not(or(not(X_21),not(truth)))) ),[1,0,1],$fot(falsehood)]]) ).
cnf(refute_0_21,plain,
( and(X_21,truth) != not(or(not(X_21),not(truth)))
| and(X_21,truth) = not(or(not(X_21),falsehood)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_20]) ).
cnf(refute_0_22,plain,
and(X_21,truth) = not(or(not(X_21),falsehood)),
inference(resolve,[$cnf( $equal(and(X_21,truth),not(or(not(X_21),not(truth)))) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
or(not(X_21),falsehood) = or(falsehood,not(X_21)),
inference(subst,[],[refute_0_14:[bind(X,$fot(falsehood)),bind(Y,$fot(not(X_21)))]]) ).
cnf(refute_0_24,plain,
not(or(not(X_21),falsehood)) = not(or(not(X_21),falsehood)),
introduced(tautology,[refl,[$fot(not(or(not(X_21),falsehood)))]]) ).
cnf(refute_0_25,plain,
( not(or(not(X_21),falsehood)) != not(or(not(X_21),falsehood))
| or(not(X_21),falsehood) != or(falsehood,not(X_21))
| not(or(not(X_21),falsehood)) = not(or(falsehood,not(X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X_21),falsehood)),not(or(not(X_21),falsehood))) ),[1,0],$fot(or(falsehood,not(X_21)))]]) ).
cnf(refute_0_26,plain,
( or(not(X_21),falsehood) != or(falsehood,not(X_21))
| not(or(not(X_21),falsehood)) = not(or(falsehood,not(X_21))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_21),falsehood)),not(or(not(X_21),falsehood))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
not(or(not(X_21),falsehood)) = not(or(falsehood,not(X_21))),
inference(resolve,[$cnf( $equal(or(not(X_21),falsehood),or(falsehood,not(X_21))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
( and(X_21,truth) != not(or(not(X_21),falsehood))
| not(or(not(X_21),falsehood)) != not(or(falsehood,not(X_21)))
| and(X_21,truth) = not(or(falsehood,not(X_21))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_21,truth),not(or(falsehood,not(X_21)))) ),[0],$fot(not(or(not(X_21),falsehood)))]]) ).
cnf(refute_0_29,plain,
( and(X_21,truth) != not(or(not(X_21),falsehood))
| and(X_21,truth) = not(or(falsehood,not(X_21))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_21),falsehood)),not(or(falsehood,not(X_21)))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
and(X_21,truth) = not(or(falsehood,not(X_21))),
inference(resolve,[$cnf( $equal(and(X_21,truth),not(or(not(X_21),falsehood))) )],[refute_0_22,refute_0_29]) ).
cnf(refute_0_31,plain,
and(or(falsehood,not(X_23)),truth) = not(or(falsehood,not(or(falsehood,not(X_23))))),
inference(subst,[],[refute_0_30:[bind(X_21,$fot(or(falsehood,not(X_23))))]]) ).
cnf(refute_0_32,plain,
and(X_23,truth) = not(or(falsehood,not(X_23))),
inference(subst,[],[refute_0_30:[bind(X_21,$fot(X_23))]]) ).
cnf(refute_0_33,plain,
( and(X_23,truth) != not(or(falsehood,not(X_23)))
| not(or(falsehood,not(X_23))) = and(X_23,truth) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_23,truth))),bind(Y0,$fot(not(or(falsehood,not(X_23)))))]]) ).
cnf(refute_0_34,plain,
not(or(falsehood,not(X_23))) = and(X_23,truth),
inference(resolve,[$cnf( $equal(and(X_23,truth),not(or(falsehood,not(X_23)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( and(or(falsehood,not(X_23)),truth) != not(or(falsehood,not(or(falsehood,not(X_23)))))
| not(or(falsehood,not(X_23))) != and(X_23,truth)
| and(or(falsehood,not(X_23)),truth) = not(or(falsehood,and(X_23,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,not(X_23)),truth),not(or(falsehood,not(or(falsehood,not(X_23)))))) ),[1,0,1],$fot(and(X_23,truth))]]) ).
cnf(refute_0_36,plain,
( and(or(falsehood,not(X_23)),truth) != not(or(falsehood,not(or(falsehood,not(X_23)))))
| and(or(falsehood,not(X_23)),truth) = not(or(falsehood,and(X_23,truth))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_23))),and(X_23,truth)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
and(or(falsehood,not(X_23)),truth) = not(or(falsehood,and(X_23,truth))),
inference(resolve,[$cnf( $equal(and(or(falsehood,not(X_23)),truth),not(or(falsehood,not(or(falsehood,not(X_23)))))) )],[refute_0_31,refute_0_36]) ).
cnf(refute_0_38,plain,
( and(X,Y) != and(Y,X)
| and(Y,X) = and(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(and(Y,X)))]]) ).
cnf(refute_0_39,plain,
and(Y,X) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),and(Y,X)) )],[and_commutativity,refute_0_38]) ).
cnf(refute_0_40,plain,
and(or(falsehood,not(X_23)),truth) = and(truth,or(falsehood,not(X_23))),
inference(subst,[],[refute_0_39:[bind(X,$fot(truth)),bind(Y,$fot(or(falsehood,not(X_23))))]]) ).
cnf(refute_0_41,plain,
( and(or(falsehood,not(X_23)),truth) != and(truth,or(falsehood,not(X_23)))
| and(or(falsehood,not(X_23)),truth) != not(or(falsehood,and(X_23,truth)))
| and(truth,or(falsehood,not(X_23))) = not(or(falsehood,and(X_23,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,not(X_23)),truth),not(or(falsehood,and(X_23,truth)))) ),[0],$fot(and(truth,or(falsehood,not(X_23))))]]) ).
cnf(refute_0_42,plain,
( and(or(falsehood,not(X_23)),truth) != not(or(falsehood,and(X_23,truth)))
| and(truth,or(falsehood,not(X_23))) = not(or(falsehood,and(X_23,truth))) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,not(X_23)),truth),and(truth,or(falsehood,not(X_23)))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
and(truth,or(falsehood,not(X_23))) = not(or(falsehood,and(X_23,truth))),
inference(resolve,[$cnf( $equal(and(or(falsehood,not(X_23)),truth),not(or(falsehood,and(X_23,truth)))) )],[refute_0_37,refute_0_42]) ).
cnf(refute_0_44,plain,
or(falsehood,Y) = implies(not(falsehood),Y),
inference(subst,[],[or_definition:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_45,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_46,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[or_definition,refute_0_45]) ).
cnf(refute_0_47,plain,
implies(not(X),not(Y)) = or(X,not(Y)),
inference(subst,[],[refute_0_46:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_48,plain,
implies(implies(not(X),not(Y)),implies(Y,X)) = implies(implies(not(X),not(Y)),implies(Y,X)),
introduced(tautology,[refl,[$fot(implies(implies(not(X),not(Y)),implies(Y,X)))]]) ).
cnf(refute_0_49,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != implies(implies(not(X),not(Y)),implies(Y,X))
| implies(not(X),not(Y)) != or(X,not(Y))
| implies(implies(not(X),not(Y)),implies(Y,X)) = implies(or(X,not(Y)),implies(Y,X)) ),
introduced(tautology,[equality,[$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_50,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( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(not(X),not(Y)),implies(Y,X))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
implies(implies(not(X),not(Y)),implies(Y,X)) = implies(or(X,not(Y)),implies(Y,X)),
inference(resolve,[$cnf( $equal(implies(not(X),not(Y)),or(X,not(Y))) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != implies(or(X,not(Y)),implies(Y,X))
| implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(or(X,not(Y)),implies(Y,X)) = truth ),
introduced(tautology,[equality,[$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_53,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(or(X,not(Y)),implies(Y,X)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(or(X,not(Y)),implies(Y,X))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
implies(or(X,not(Y)),implies(Y,X)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[wajsberg_4,refute_0_53]) ).
cnf(refute_0_55,plain,
implies(or(X_28,not(truth)),implies(truth,X_28)) = truth,
inference(subst,[],[refute_0_54:[bind(X,$fot(X_28)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_56,plain,
implies(truth,X_28) = X_28,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_28))]]) ).
cnf(refute_0_57,plain,
( implies(or(X_28,not(truth)),implies(truth,X_28)) != truth
| implies(truth,X_28) != X_28
| implies(or(X_28,not(truth)),X_28) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_28,not(truth)),implies(truth,X_28)),truth) ),[0,1],$fot(X_28)]]) ).
cnf(refute_0_58,plain,
( implies(or(X_28,not(truth)),implies(truth,X_28)) != truth
| implies(or(X_28,not(truth)),X_28) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_28),X_28) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
implies(or(X_28,not(truth)),X_28) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_28,not(truth)),implies(truth,X_28)),truth) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
or(X_28,not(truth)) = or(X_28,not(truth)),
introduced(tautology,[refl,[$fot(or(X_28,not(truth)))]]) ).
cnf(refute_0_61,plain,
( not(truth) != falsehood
| or(X_28,not(truth)) != or(X_28,not(truth))
| or(X_28,not(truth)) = or(X_28,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_28,not(truth)),or(X_28,not(truth))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_62,plain,
( not(truth) != falsehood
| or(X_28,not(truth)) = or(X_28,falsehood) ),
inference(resolve,[$cnf( $equal(or(X_28,not(truth)),or(X_28,not(truth))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
or(X_28,not(truth)) = or(X_28,falsehood),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_62]) ).
cnf(refute_0_64,plain,
implies(or(X_28,not(truth)),X_28) = implies(or(X_28,not(truth)),X_28),
introduced(tautology,[refl,[$fot(implies(or(X_28,not(truth)),X_28))]]) ).
cnf(refute_0_65,plain,
( implies(or(X_28,not(truth)),X_28) != implies(or(X_28,not(truth)),X_28)
| or(X_28,not(truth)) != or(X_28,falsehood)
| implies(or(X_28,not(truth)),X_28) = implies(or(X_28,falsehood),X_28) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_28,not(truth)),X_28),implies(or(X_28,not(truth)),X_28)) ),[1,0],$fot(or(X_28,falsehood))]]) ).
cnf(refute_0_66,plain,
( or(X_28,not(truth)) != or(X_28,falsehood)
| implies(or(X_28,not(truth)),X_28) = implies(or(X_28,falsehood),X_28) ),
inference(resolve,[$cnf( $equal(implies(or(X_28,not(truth)),X_28),implies(or(X_28,not(truth)),X_28)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
implies(or(X_28,not(truth)),X_28) = implies(or(X_28,falsehood),X_28),
inference(resolve,[$cnf( $equal(or(X_28,not(truth)),or(X_28,falsehood)) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
( implies(or(X_28,not(truth)),X_28) != implies(or(X_28,falsehood),X_28)
| implies(or(X_28,not(truth)),X_28) != truth
| implies(or(X_28,falsehood),X_28) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_28,not(truth)),X_28),truth) ),[0],$fot(implies(or(X_28,falsehood),X_28))]]) ).
cnf(refute_0_69,plain,
( implies(or(X_28,not(truth)),X_28) != truth
| implies(or(X_28,falsehood),X_28) = truth ),
inference(resolve,[$cnf( $equal(implies(or(X_28,not(truth)),X_28),implies(or(X_28,falsehood),X_28)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
implies(or(X_28,falsehood),X_28) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_28,not(truth)),X_28),truth) )],[refute_0_59,refute_0_69]) ).
cnf(refute_0_71,plain,
implies(or(X_30,falsehood),X_30) = truth,
inference(subst,[],[refute_0_70:[bind(X_28,$fot(X_30))]]) ).
cnf(refute_0_72,plain,
or(falsehood,X_30) = or(X_30,falsehood),
inference(subst,[],[or_commutativity:[bind(X,$fot(falsehood)),bind(Y,$fot(X_30))]]) ).
cnf(refute_0_73,plain,
( or(falsehood,X_30) != or(X_30,falsehood)
| or(X_30,falsehood) = or(falsehood,X_30) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(falsehood,X_30))),bind(Y0,$fot(or(X_30,falsehood)))]]) ).
cnf(refute_0_74,plain,
or(X_30,falsehood) = or(falsehood,X_30),
inference(resolve,[$cnf( $equal(or(falsehood,X_30),or(X_30,falsehood)) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( implies(or(X_30,falsehood),X_30) != truth
| or(X_30,falsehood) != or(falsehood,X_30)
| implies(or(falsehood,X_30),X_30) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_30,falsehood),X_30),truth) ),[0,0],$fot(or(falsehood,X_30))]]) ).
cnf(refute_0_76,plain,
( implies(or(X_30,falsehood),X_30) != truth
| implies(or(falsehood,X_30),X_30) = truth ),
inference(resolve,[$cnf( $equal(or(X_30,falsehood),or(falsehood,X_30)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
implies(or(falsehood,X_30),X_30) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_30,falsehood),X_30),truth) )],[refute_0_71,refute_0_76]) ).
cnf(refute_0_78,plain,
implies(or(falsehood,not(falsehood)),not(falsehood)) = truth,
inference(subst,[],[refute_0_77:[bind(X_30,$fot(not(falsehood)))]]) ).
cnf(refute_0_79,plain,
implies(or(truth,falsehood),truth) = truth,
inference(subst,[],[refute_0_70:[bind(X_28,$fot(truth))]]) ).
cnf(refute_0_80,plain,
or(truth,X_4) = implies(not(truth),X_4),
inference(subst,[],[or_definition:[bind(X,$fot(truth)),bind(Y,$fot(X_4))]]) ).
cnf(refute_0_81,plain,
( not(truth) != falsehood
| or(truth,X_4) != implies(not(truth),X_4)
| or(truth,X_4) = implies(falsehood,X_4) ),
introduced(tautology,[equality,[$cnf( $equal(or(truth,X_4),implies(not(truth),X_4)) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_82,plain,
( or(truth,X_4) != implies(not(truth),X_4)
| or(truth,X_4) = implies(falsehood,X_4) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_81]) ).
cnf(refute_0_83,plain,
or(truth,X_4) = implies(falsehood,X_4),
inference(resolve,[$cnf( $equal(or(truth,X_4),implies(not(truth),X_4)) )],[refute_0_80,refute_0_82]) ).
cnf(refute_0_84,plain,
or(truth,falsehood) = implies(falsehood,falsehood),
inference(subst,[],[refute_0_83:[bind(X_4,$fot(falsehood))]]) ).
cnf(refute_0_85,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_86,plain,
( implies(or(truth,falsehood),truth) != truth
| implies(implies(falsehood,falsehood),truth) = truth ),
inference(resolve,[$cnf( $equal(or(truth,falsehood),implies(falsehood,falsehood)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
implies(implies(falsehood,falsehood),truth) = truth,
inference(resolve,[$cnf( $equal(implies(or(truth,falsehood),truth),truth) )],[refute_0_79,refute_0_86]) ).
cnf(refute_0_88,plain,
or(X,not(X)) = implies(not(X),not(X)),
inference(subst,[],[or_definition:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_89,plain,
implies(implies(truth,X_25),X_25) = implies(implies(X_25,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_25))]]) ).
cnf(refute_0_90,plain,
implies(truth,X_25) = X_25,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_25))]]) ).
cnf(refute_0_91,plain,
( implies(implies(truth,X_25),X_25) != implies(implies(X_25,truth),truth)
| implies(truth,X_25) != X_25
| implies(X_25,X_25) = implies(implies(X_25,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_25),X_25),implies(implies(X_25,truth),truth)) ),[0,0],$fot(X_25)]]) ).
cnf(refute_0_92,plain,
( implies(implies(truth,X_25),X_25) != implies(implies(X_25,truth),truth)
| implies(X_25,X_25) = implies(implies(X_25,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(truth,X_25),X_25) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
implies(X_25,X_25) = implies(implies(X_25,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_25),X_25),implies(implies(X_25,truth),truth)) )],[refute_0_89,refute_0_92]) ).
cnf(refute_0_94,plain,
implies(not(X),not(X)) = implies(implies(not(X),truth),truth),
inference(subst,[],[refute_0_93:[bind(X_25,$fot(not(X)))]]) ).
cnf(refute_0_95,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_96,plain,
( or(X,not(X)) != implies(not(X),not(X))
| or(X,not(X)) = implies(implies(not(X),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X)),implies(implies(not(X),truth),truth)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
or(X,not(X)) = implies(implies(not(X),truth),truth),
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(not(X),not(X))) )],[refute_0_88,refute_0_96]) ).
cnf(refute_0_98,plain,
or(X,truth) = or(truth,X),
inference(subst,[],[or_commutativity:[bind(Y,$fot(truth))]]) ).
cnf(refute_0_99,plain,
or(truth,X) = implies(falsehood,X),
inference(subst,[],[refute_0_83:[bind(X_4,$fot(X))]]) ).
cnf(refute_0_100,plain,
( or(X,truth) != or(truth,X)
| or(truth,X) != implies(falsehood,X)
| or(X,truth) = implies(falsehood,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(or(X,truth),implies(falsehood,X)) ),[0],$fot(or(truth,X))]]) ).
cnf(refute_0_101,plain,
( or(X,truth) != or(truth,X)
| or(X,truth) = implies(falsehood,X) ),
inference(resolve,[$cnf( $equal(or(truth,X),implies(falsehood,X)) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
or(X,truth) = implies(falsehood,X),
inference(resolve,[$cnf( $equal(or(X,truth),or(truth,X)) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
implies(not(X),truth) = or(X,truth),
inference(subst,[],[refute_0_46:[bind(Y,$fot(truth))]]) ).
cnf(refute_0_104,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_105,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_104]) ).
cnf(refute_0_106,plain,
( implies(not(X),truth) != or(X,truth)
| or(X,truth) != implies(falsehood,X)
| implies(not(X),truth) = implies(falsehood,X) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(implies(not(X),truth))),bind(Y0,$fot(or(X,truth))),bind(Z0,$fot(implies(falsehood,X)))]]) ).
cnf(refute_0_107,plain,
( or(X,truth) != implies(falsehood,X)
| implies(not(X),truth) = implies(falsehood,X) ),
inference(resolve,[$cnf( $equal(implies(not(X),truth),or(X,truth)) )],[refute_0_103,refute_0_106]) ).
cnf(refute_0_108,plain,
implies(not(X),truth) = implies(falsehood,X),
inference(resolve,[$cnf( $equal(or(X,truth),implies(falsehood,X)) )],[refute_0_102,refute_0_107]) ).
cnf(refute_0_109,plain,
implies(implies(not(X),truth),truth) = implies(implies(not(X),truth),truth),
introduced(tautology,[refl,[$fot(implies(implies(not(X),truth),truth))]]) ).
cnf(refute_0_110,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_111,plain,
( implies(not(X),truth) != implies(falsehood,X)
| implies(implies(not(X),truth),truth) = implies(implies(falsehood,X),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),truth),implies(implies(not(X),truth),truth)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
implies(implies(not(X),truth),truth) = implies(implies(falsehood,X),truth),
inference(resolve,[$cnf( $equal(implies(not(X),truth),implies(falsehood,X)) )],[refute_0_108,refute_0_111]) ).
cnf(refute_0_113,plain,
( implies(implies(not(X),truth),truth) != implies(implies(falsehood,X),truth)
| or(X,not(X)) != implies(implies(not(X),truth),truth)
| or(X,not(X)) = implies(implies(falsehood,X),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(X)),implies(implies(not(X),truth),truth)) ),[1],$fot(implies(implies(falsehood,X),truth))]]) ).
cnf(refute_0_114,plain,
( or(X,not(X)) != implies(implies(not(X),truth),truth)
| or(X,not(X)) = implies(implies(falsehood,X),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),truth),implies(implies(falsehood,X),truth)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
or(X,not(X)) = implies(implies(falsehood,X),truth),
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(implies(not(X),truth),truth)) )],[refute_0_97,refute_0_114]) ).
cnf(refute_0_116,plain,
( or(X,not(X)) != implies(implies(falsehood,X),truth)
| implies(implies(falsehood,X),truth) = or(X,not(X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,not(X)))),bind(Y0,$fot(implies(implies(falsehood,X),truth)))]]) ).
cnf(refute_0_117,plain,
implies(implies(falsehood,X),truth) = or(X,not(X)),
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(implies(falsehood,X),truth)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
implies(implies(falsehood,falsehood),truth) = or(falsehood,not(falsehood)),
inference(subst,[],[refute_0_117:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_119,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_120,plain,
( implies(implies(falsehood,falsehood),truth) != truth
| or(falsehood,not(falsehood)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,falsehood),truth),or(falsehood,not(falsehood))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
or(falsehood,not(falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,falsehood),truth),truth) )],[refute_0_87,refute_0_120]) ).
cnf(refute_0_122,plain,
( implies(or(falsehood,not(falsehood)),not(falsehood)) != truth
| or(falsehood,not(falsehood)) != truth
| implies(truth,not(falsehood)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,not(falsehood)),not(falsehood)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_123,plain,
( implies(or(falsehood,not(falsehood)),not(falsehood)) != truth
| implies(truth,not(falsehood)) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,not(falsehood)),truth) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
implies(truth,not(falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,not(falsehood)),not(falsehood)),truth) )],[refute_0_78,refute_0_123]) ).
cnf(refute_0_125,plain,
implies(truth,not(falsehood)) = not(falsehood),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(falsehood)))]]) ).
cnf(refute_0_126,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_127,plain,
( implies(truth,not(falsehood)) != truth
| not(falsehood) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,not(falsehood)),not(falsehood)) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
not(falsehood) = truth,
inference(resolve,[$cnf( $equal(implies(truth,not(falsehood)),truth) )],[refute_0_124,refute_0_127]) ).
cnf(refute_0_129,plain,
( not(falsehood) != truth
| or(falsehood,Y) != implies(not(falsehood),Y)
| or(falsehood,Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,Y),implies(not(falsehood),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_130,plain,
( or(falsehood,Y) != implies(not(falsehood),Y)
| or(falsehood,Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
or(falsehood,Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(or(falsehood,Y),implies(not(falsehood),Y)) )],[refute_0_44,refute_0_130]) ).
cnf(refute_0_132,plain,
implies(truth,Y) = Y,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_133,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_134,plain,
( or(falsehood,Y) != implies(truth,Y)
| or(falsehood,Y) = Y ),
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
or(falsehood,Y) = Y,
inference(resolve,[$cnf( $equal(or(falsehood,Y),implies(truth,Y)) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
or(falsehood,not(X_23)) = not(X_23),
inference(subst,[],[refute_0_135:[bind(Y,$fot(not(X_23)))]]) ).
cnf(refute_0_137,plain,
and(truth,or(falsehood,not(X_23))) = and(truth,or(falsehood,not(X_23))),
introduced(tautology,[refl,[$fot(and(truth,or(falsehood,not(X_23))))]]) ).
cnf(refute_0_138,plain,
( and(truth,or(falsehood,not(X_23))) != and(truth,or(falsehood,not(X_23)))
| or(falsehood,not(X_23)) != not(X_23)
| and(truth,or(falsehood,not(X_23))) = and(truth,not(X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,or(falsehood,not(X_23))),and(truth,or(falsehood,not(X_23)))) ),[1,1],$fot(not(X_23))]]) ).
cnf(refute_0_139,plain,
( or(falsehood,not(X_23)) != not(X_23)
| and(truth,or(falsehood,not(X_23))) = and(truth,not(X_23)) ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,not(X_23))),and(truth,or(falsehood,not(X_23)))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
and(truth,or(falsehood,not(X_23))) = and(truth,not(X_23)),
inference(resolve,[$cnf( $equal(or(falsehood,not(X_23)),not(X_23)) )],[refute_0_136,refute_0_139]) ).
cnf(refute_0_141,plain,
( and(truth,or(falsehood,not(X_23))) != and(truth,not(X_23))
| and(truth,or(falsehood,not(X_23))) != not(or(falsehood,and(X_23,truth)))
| and(truth,not(X_23)) = not(or(falsehood,and(X_23,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,or(falsehood,not(X_23))),not(or(falsehood,and(X_23,truth)))) ),[0],$fot(and(truth,not(X_23)))]]) ).
cnf(refute_0_142,plain,
( and(truth,or(falsehood,not(X_23))) != not(or(falsehood,and(X_23,truth)))
| and(truth,not(X_23)) = not(or(falsehood,and(X_23,truth))) ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,not(X_23))),and(truth,not(X_23))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
or(falsehood,not(X_21)) = not(X_21),
inference(subst,[],[refute_0_135:[bind(Y,$fot(not(X_21)))]]) ).
cnf(refute_0_144,plain,
not(or(falsehood,not(X_21))) = not(or(falsehood,not(X_21))),
introduced(tautology,[refl,[$fot(not(or(falsehood,not(X_21))))]]) ).
cnf(refute_0_145,plain,
( not(or(falsehood,not(X_21))) != not(or(falsehood,not(X_21)))
| or(falsehood,not(X_21)) != not(X_21)
| not(or(falsehood,not(X_21))) = not(not(X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,not(X_21))),not(or(falsehood,not(X_21)))) ),[1,0],$fot(not(X_21))]]) ).
cnf(refute_0_146,plain,
( or(falsehood,not(X_21)) != not(X_21)
| not(or(falsehood,not(X_21))) = not(not(X_21)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_21))),not(or(falsehood,not(X_21)))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
not(or(falsehood,not(X_21))) = not(not(X_21)),
inference(resolve,[$cnf( $equal(or(falsehood,not(X_21)),not(X_21)) )],[refute_0_143,refute_0_146]) ).
cnf(refute_0_148,plain,
( and(X_21,truth) != not(or(falsehood,not(X_21)))
| not(or(falsehood,not(X_21))) != not(not(X_21))
| and(X_21,truth) = not(not(X_21)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_21,truth),not(not(X_21))) ),[0],$fot(not(or(falsehood,not(X_21))))]]) ).
cnf(refute_0_149,plain,
( and(X_21,truth) != not(or(falsehood,not(X_21)))
| and(X_21,truth) = not(not(X_21)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_21))),not(not(X_21))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
and(X_21,truth) = not(not(X_21)),
inference(resolve,[$cnf( $equal(and(X_21,truth),not(or(falsehood,not(X_21)))) )],[refute_0_30,refute_0_149]) ).
cnf(refute_0_151,plain,
and(X_23,truth) = not(not(X_23)),
inference(subst,[],[refute_0_150:[bind(X_21,$fot(X_23))]]) ).
cnf(refute_0_152,plain,
or(falsehood,and(X_23,truth)) = and(X_23,truth),
inference(subst,[],[refute_0_135:[bind(Y,$fot(and(X_23,truth)))]]) ).
cnf(refute_0_153,plain,
( and(X_23,truth) != not(not(X_23))
| or(falsehood,and(X_23,truth)) != and(X_23,truth)
| or(falsehood,and(X_23,truth)) = not(not(X_23)) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(or(falsehood,and(X_23,truth)))),bind(Y0,$fot(and(X_23,truth))),bind(Z0,$fot(not(not(X_23))))]]) ).
cnf(refute_0_154,plain,
( and(X_23,truth) != not(not(X_23))
| or(falsehood,and(X_23,truth)) = not(not(X_23)) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(X_23,truth)),and(X_23,truth)) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
or(falsehood,and(X_23,truth)) = not(not(X_23)),
inference(resolve,[$cnf( $equal(and(X_23,truth),not(not(X_23))) )],[refute_0_151,refute_0_154]) ).
cnf(refute_0_156,plain,
not(or(falsehood,and(X_23,truth))) = not(or(falsehood,and(X_23,truth))),
introduced(tautology,[refl,[$fot(not(or(falsehood,and(X_23,truth))))]]) ).
cnf(refute_0_157,plain,
( not(or(falsehood,and(X_23,truth))) != not(or(falsehood,and(X_23,truth)))
| or(falsehood,and(X_23,truth)) != not(not(X_23))
| not(or(falsehood,and(X_23,truth))) = not(not(not(X_23))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,and(X_23,truth))),not(or(falsehood,and(X_23,truth)))) ),[1,0],$fot(not(not(X_23)))]]) ).
cnf(refute_0_158,plain,
( or(falsehood,and(X_23,truth)) != not(not(X_23))
| not(or(falsehood,and(X_23,truth))) = not(not(not(X_23))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(X_23,truth))),not(or(falsehood,and(X_23,truth)))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
not(or(falsehood,and(X_23,truth))) = not(not(not(X_23))),
inference(resolve,[$cnf( $equal(or(falsehood,and(X_23,truth)),not(not(X_23))) )],[refute_0_155,refute_0_158]) ).
cnf(refute_0_160,plain,
( and(truth,not(X_23)) != not(or(falsehood,and(X_23,truth)))
| not(or(falsehood,and(X_23,truth))) != not(not(not(X_23)))
| and(truth,not(X_23)) = not(not(not(X_23))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(truth,not(X_23)),not(not(not(X_23)))) ),[0],$fot(not(or(falsehood,and(X_23,truth))))]]) ).
cnf(refute_0_161,plain,
( and(truth,not(X_23)) != not(or(falsehood,and(X_23,truth)))
| and(truth,not(X_23)) = not(not(not(X_23))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(X_23,truth))),not(not(not(X_23)))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
( and(truth,or(falsehood,not(X_23))) != not(or(falsehood,and(X_23,truth)))
| and(truth,not(X_23)) = not(not(not(X_23))) ),
inference(resolve,[$cnf( $equal(and(truth,not(X_23)),not(or(falsehood,and(X_23,truth)))) )],[refute_0_142,refute_0_161]) ).
cnf(refute_0_163,plain,
and(truth,not(X_23)) = not(not(not(X_23))),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,not(X_23))),not(or(falsehood,and(X_23,truth)))) )],[refute_0_43,refute_0_162]) ).
cnf(refute_0_164,plain,
and(truth,not(X_8)) = not(not(not(X_8))),
inference(subst,[],[refute_0_163:[bind(X_23,$fot(X_8))]]) ).
cnf(refute_0_165,plain,
or(and(falsehood,X_8),and(truth,not(X_8))) = or(and(falsehood,X_8),and(truth,not(X_8))),
introduced(tautology,[refl,[$fot(or(and(falsehood,X_8),and(truth,not(X_8))))]]) ).
cnf(refute_0_166,plain,
( and(truth,not(X_8)) != not(not(not(X_8)))
| or(and(falsehood,X_8),and(truth,not(X_8))) != or(and(falsehood,X_8),and(truth,not(X_8)))
| or(and(falsehood,X_8),and(truth,not(X_8))) = or(and(falsehood,X_8),not(not(not(X_8)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(falsehood,X_8),and(truth,not(X_8))),or(and(falsehood,X_8),and(truth,not(X_8)))) ),[1,1],$fot(not(not(not(X_8))))]]) ).
cnf(refute_0_167,plain,
( and(truth,not(X_8)) != not(not(not(X_8)))
| or(and(falsehood,X_8),and(truth,not(X_8))) = or(and(falsehood,X_8),not(not(not(X_8)))) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,X_8),and(truth,not(X_8))),or(and(falsehood,X_8),and(truth,not(X_8)))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
or(and(falsehood,X_8),and(truth,not(X_8))) = or(and(falsehood,X_8),not(not(not(X_8)))),
inference(resolve,[$cnf( $equal(and(truth,not(X_8)),not(not(not(X_8)))) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
( or(and(falsehood,X_8),and(truth,not(X_8))) != or(and(falsehood,X_8),not(not(not(X_8))))
| xor(truth,X_8) != or(and(falsehood,X_8),and(truth,not(X_8)))
| xor(truth,X_8) = or(and(falsehood,X_8),not(not(not(X_8)))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_8),or(and(falsehood,X_8),and(truth,not(X_8)))) ),[1],$fot(or(and(falsehood,X_8),not(not(not(X_8)))))]]) ).
cnf(refute_0_170,plain,
( xor(truth,X_8) != or(and(falsehood,X_8),and(truth,not(X_8)))
| xor(truth,X_8) = or(and(falsehood,X_8),not(not(not(X_8)))) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,X_8),and(truth,not(X_8))),or(and(falsehood,X_8),not(not(not(X_8))))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
xor(truth,X_8) = or(and(falsehood,X_8),not(not(not(X_8)))),
inference(resolve,[$cnf( $equal(xor(truth,X_8),or(and(falsehood,X_8),and(truth,not(X_8)))) )],[refute_0_18,refute_0_170]) ).
cnf(refute_0_172,plain,
or(and(falsehood,X_8),not(X_8)) = or(not(X_8),and(falsehood,X_8)),
inference(subst,[],[refute_0_14:[bind(X,$fot(not(X_8))),bind(Y,$fot(and(falsehood,X_8)))]]) ).
cnf(refute_0_173,plain,
implies(implies(not(not(Y)),Y),Y) = implies(implies(Y,not(not(Y))),not(not(Y))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_174,plain,
implies(or(X_28,not(X_29)),implies(X_29,X_28)) = truth,
inference(subst,[],[refute_0_54:[bind(X,$fot(X_28)),bind(Y,$fot(X_29))]]) ).
cnf(refute_0_175,plain,
or(not(X_29),X_28) = or(X_28,not(X_29)),
inference(subst,[],[or_commutativity:[bind(X,$fot(not(X_29))),bind(Y,$fot(X_28))]]) ).
cnf(refute_0_176,plain,
( or(not(X_29),X_28) != or(X_28,not(X_29))
| or(X_28,not(X_29)) = or(not(X_29),X_28) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(not(X_29),X_28))),bind(Y0,$fot(or(X_28,not(X_29))))]]) ).
cnf(refute_0_177,plain,
or(X_28,not(X_29)) = or(not(X_29),X_28),
inference(resolve,[$cnf( $equal(or(not(X_29),X_28),or(X_28,not(X_29))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
( implies(or(X_28,not(X_29)),implies(X_29,X_28)) != truth
| or(X_28,not(X_29)) != or(not(X_29),X_28)
| implies(or(not(X_29),X_28),implies(X_29,X_28)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_28,not(X_29)),implies(X_29,X_28)),truth) ),[0,0],$fot(or(not(X_29),X_28))]]) ).
cnf(refute_0_179,plain,
( implies(or(X_28,not(X_29)),implies(X_29,X_28)) != truth
| implies(or(not(X_29),X_28),implies(X_29,X_28)) = truth ),
inference(resolve,[$cnf( $equal(or(X_28,not(X_29)),or(not(X_29),X_28)) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
implies(or(not(X_29),X_28),implies(X_29,X_28)) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_28,not(X_29)),implies(X_29,X_28)),truth) )],[refute_0_174,refute_0_179]) ).
cnf(refute_0_181,plain,
implies(or(not(X_43),not(not(X_43))),implies(X_43,not(not(X_43)))) = truth,
inference(subst,[],[refute_0_180:[bind(X_28,$fot(not(not(X_43)))),bind(X_29,$fot(X_43))]]) ).
cnf(refute_0_182,plain,
or(falsehood,X_30) = X_30,
inference(subst,[],[refute_0_135:[bind(Y,$fot(X_30))]]) ).
cnf(refute_0_183,plain,
implies(or(falsehood,X_30),X_30) = implies(or(falsehood,X_30),X_30),
introduced(tautology,[refl,[$fot(implies(or(falsehood,X_30),X_30))]]) ).
cnf(refute_0_184,plain,
( implies(or(falsehood,X_30),X_30) != implies(or(falsehood,X_30),X_30)
| or(falsehood,X_30) != X_30
| implies(or(falsehood,X_30),X_30) = implies(X_30,X_30) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,X_30),X_30),implies(or(falsehood,X_30),X_30)) ),[1,0],$fot(X_30)]]) ).
cnf(refute_0_185,plain,
( or(falsehood,X_30) != X_30
| implies(or(falsehood,X_30),X_30) = implies(X_30,X_30) ),
inference(resolve,[$cnf( $equal(implies(or(falsehood,X_30),X_30),implies(or(falsehood,X_30),X_30)) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
implies(or(falsehood,X_30),X_30) = implies(X_30,X_30),
inference(resolve,[$cnf( $equal(or(falsehood,X_30),X_30) )],[refute_0_182,refute_0_185]) ).
cnf(refute_0_187,plain,
( implies(or(falsehood,X_30),X_30) != implies(X_30,X_30)
| implies(or(falsehood,X_30),X_30) != truth
| implies(X_30,X_30) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,X_30),X_30),truth) ),[0],$fot(implies(X_30,X_30))]]) ).
cnf(refute_0_188,plain,
( implies(or(falsehood,X_30),X_30) != truth
| implies(X_30,X_30) = truth ),
inference(resolve,[$cnf( $equal(implies(or(falsehood,X_30),X_30),implies(X_30,X_30)) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
implies(X_30,X_30) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,X_30),X_30),truth) )],[refute_0_77,refute_0_188]) ).
cnf(refute_0_190,plain,
implies(not(X),not(X)) = truth,
inference(subst,[],[refute_0_189:[bind(X_30,$fot(not(X)))]]) ).
cnf(refute_0_191,plain,
( implies(not(X),not(X)) != truth
| or(X,not(X)) != implies(not(X),not(X))
| or(X,not(X)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(X)),implies(not(X),not(X))) ),[1],$fot(truth)]]) ).
cnf(refute_0_192,plain,
( or(X,not(X)) != implies(not(X),not(X))
| or(X,not(X)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X)),truth) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
or(X,not(X)) = truth,
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(not(X),not(X))) )],[refute_0_88,refute_0_192]) ).
cnf(refute_0_194,plain,
or(not(X_43),not(not(X_43))) = truth,
inference(subst,[],[refute_0_193:[bind(X,$fot(not(X_43)))]]) ).
cnf(refute_0_195,plain,
( implies(or(not(X_43),not(not(X_43))),implies(X_43,not(not(X_43)))) != truth
| or(not(X_43),not(not(X_43))) != truth
| implies(truth,implies(X_43,not(not(X_43)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X_43),not(not(X_43))),implies(X_43,not(not(X_43)))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_196,plain,
( implies(or(not(X_43),not(not(X_43))),implies(X_43,not(not(X_43)))) != truth
| implies(truth,implies(X_43,not(not(X_43)))) = truth ),
inference(resolve,[$cnf( $equal(or(not(X_43),not(not(X_43))),truth) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
implies(truth,implies(X_43,not(not(X_43)))) = truth,
inference(resolve,[$cnf( $equal(implies(or(not(X_43),not(not(X_43))),implies(X_43,not(not(X_43)))),truth) )],[refute_0_181,refute_0_196]) ).
cnf(refute_0_198,plain,
implies(truth,implies(X_43,not(not(X_43)))) = implies(X_43,not(not(X_43))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_43,not(not(X_43)))))]]) ).
cnf(refute_0_199,plain,
( implies(truth,implies(X_43,not(not(X_43)))) != implies(X_43,not(not(X_43)))
| implies(truth,implies(X_43,not(not(X_43)))) != truth
| implies(X_43,not(not(X_43))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(X_43,not(not(X_43)))),truth) ),[0],$fot(implies(X_43,not(not(X_43))))]]) ).
cnf(refute_0_200,plain,
( implies(truth,implies(X_43,not(not(X_43)))) != truth
| implies(X_43,not(not(X_43))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_43,not(not(X_43)))),implies(X_43,not(not(X_43)))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
implies(X_43,not(not(X_43))) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(X_43,not(not(X_43)))),truth) )],[refute_0_197,refute_0_200]) ).
cnf(refute_0_202,plain,
implies(Y,not(not(Y))) = truth,
inference(subst,[],[refute_0_201:[bind(X_43,$fot(Y))]]) ).
cnf(refute_0_203,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_204,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( $equal(implies(Y,not(not(Y))),truth) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
implies(implies(not(not(Y)),Y),Y) = implies(truth,not(not(Y))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(Y,not(not(Y))),not(not(Y)))) )],[refute_0_173,refute_0_204]) ).
cnf(refute_0_206,plain,
or(Y,not(Y)) = truth,
inference(subst,[],[refute_0_193:[bind(X,$fot(Y))]]) ).
cnf(refute_0_207,plain,
or(not(Y),Y) = or(Y,not(Y)),
inference(subst,[],[refute_0_14:[bind(X,$fot(Y)),bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_208,plain,
( or(Y,not(Y)) != truth
| or(not(Y),Y) != or(Y,not(Y))
| or(not(Y),Y) = truth ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(or(not(Y),Y))),bind(Y0,$fot(or(Y,not(Y)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_209,plain,
( or(Y,not(Y)) != truth
| or(not(Y),Y) = truth ),
inference(resolve,[$cnf( $equal(or(not(Y),Y),or(Y,not(Y))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
or(not(Y),Y) = truth,
inference(resolve,[$cnf( $equal(or(Y,not(Y)),truth) )],[refute_0_206,refute_0_209]) ).
cnf(refute_0_211,plain,
implies(not(not(Y)),Y) = or(not(Y),Y),
inference(subst,[],[refute_0_46:[bind(X,$fot(not(Y)))]]) ).
cnf(refute_0_212,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_105:[bind(X0,$fot(implies(not(not(Y)),Y))),bind(Y0,$fot(or(not(Y),Y))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_213,plain,
( or(not(Y),Y) != truth
| implies(not(not(Y)),Y) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),Y),or(not(Y),Y)) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
implies(not(not(Y)),Y) = truth,
inference(resolve,[$cnf( $equal(or(not(Y),Y),truth) )],[refute_0_210,refute_0_213]) ).
cnf(refute_0_215,plain,
implies(implies(not(not(Y)),Y),Y) = implies(implies(not(not(Y)),Y),Y),
introduced(tautology,[refl,[$fot(implies(implies(not(not(Y)),Y),Y))]]) ).
cnf(refute_0_216,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_217,plain,
( implies(not(not(Y)),Y) != truth
| implies(implies(not(not(Y)),Y),Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(not(not(Y)),Y),Y)) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
implies(implies(not(not(Y)),Y),Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),Y),truth) )],[refute_0_214,refute_0_217]) ).
cnf(refute_0_219,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(truth,Y)
| implies(truth,Y) != Y
| implies(implies(not(not(Y)),Y),Y) = Y ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(implies(implies(not(not(Y)),Y),Y))),bind(Y0,$fot(implies(truth,Y))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_220,plain,
( implies(truth,Y) != Y
| implies(implies(not(not(Y)),Y),Y) = Y ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,Y)) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
implies(implies(not(not(Y)),Y),Y) = Y,
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_132,refute_0_220]) ).
cnf(refute_0_222,plain,
( implies(implies(not(not(Y)),Y),Y) != Y
| implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
| Y = implies(truth,not(not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,not(not(Y)))) ),[0],$fot(Y)]]) ).
cnf(refute_0_223,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
| Y = implies(truth,not(not(Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),Y) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
implies(truth,not(not(Y))) = not(not(Y)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_225,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_226,plain,
( Y != implies(truth,not(not(Y)))
| Y = not(not(Y)) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(Y))),not(not(Y))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
| Y = not(not(Y)) ),
inference(resolve,[$cnf( $equal(Y,implies(truth,not(not(Y)))) )],[refute_0_223,refute_0_226]) ).
cnf(refute_0_228,plain,
Y = not(not(Y)),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,not(not(Y)))) )],[refute_0_205,refute_0_227]) ).
cnf(refute_0_229,plain,
( Y != not(not(Y))
| not(not(Y)) = Y ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(Y)),bind(Y0,$fot(not(not(Y))))]]) ).
cnf(refute_0_230,plain,
not(not(Y)) = Y,
inference(resolve,[$cnf( $equal(Y,not(not(Y))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
not(not(not(X_8))) = not(X_8),
inference(subst,[],[refute_0_230:[bind(Y,$fot(not(X_8)))]]) ).
cnf(refute_0_232,plain,
or(and(falsehood,X_8),not(not(not(X_8)))) = or(and(falsehood,X_8),not(not(not(X_8)))),
introduced(tautology,[refl,[$fot(or(and(falsehood,X_8),not(not(not(X_8)))))]]) ).
cnf(refute_0_233,plain,
( not(not(not(X_8))) != not(X_8)
| or(and(falsehood,X_8),not(not(not(X_8)))) != or(and(falsehood,X_8),not(not(not(X_8))))
| or(and(falsehood,X_8),not(not(not(X_8)))) = or(and(falsehood,X_8),not(X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(falsehood,X_8),not(not(not(X_8)))),or(and(falsehood,X_8),not(not(not(X_8))))) ),[1,1],$fot(not(X_8))]]) ).
cnf(refute_0_234,plain,
( not(not(not(X_8))) != not(X_8)
| or(and(falsehood,X_8),not(not(not(X_8)))) = or(and(falsehood,X_8),not(X_8)) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,X_8),not(not(not(X_8)))),or(and(falsehood,X_8),not(not(not(X_8))))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
or(and(falsehood,X_8),not(not(not(X_8)))) = or(and(falsehood,X_8),not(X_8)),
inference(resolve,[$cnf( $equal(not(not(not(X_8))),not(X_8)) )],[refute_0_231,refute_0_234]) ).
cnf(refute_0_236,plain,
( or(and(falsehood,X_8),not(X_8)) != or(not(X_8),and(falsehood,X_8))
| or(and(falsehood,X_8),not(not(not(X_8)))) != or(and(falsehood,X_8),not(X_8))
| or(and(falsehood,X_8),not(not(not(X_8)))) = or(not(X_8),and(falsehood,X_8)) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(or(and(falsehood,X_8),not(not(not(X_8)))))),bind(Y0,$fot(or(and(falsehood,X_8),not(X_8)))),bind(Z0,$fot(or(not(X_8),and(falsehood,X_8))))]]) ).
cnf(refute_0_237,plain,
( or(and(falsehood,X_8),not(X_8)) != or(not(X_8),and(falsehood,X_8))
| or(and(falsehood,X_8),not(not(not(X_8)))) = or(not(X_8),and(falsehood,X_8)) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,X_8),not(not(not(X_8)))),or(and(falsehood,X_8),not(X_8))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
or(and(falsehood,X_8),not(not(not(X_8)))) = or(not(X_8),and(falsehood,X_8)),
inference(resolve,[$cnf( $equal(or(and(falsehood,X_8),not(X_8)),or(not(X_8),and(falsehood,X_8))) )],[refute_0_172,refute_0_237]) ).
cnf(refute_0_239,plain,
( or(and(falsehood,X_8),not(not(not(X_8)))) != or(not(X_8),and(falsehood,X_8))
| xor(truth,X_8) != or(and(falsehood,X_8),not(not(not(X_8))))
| xor(truth,X_8) = or(not(X_8),and(falsehood,X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_8),or(and(falsehood,X_8),not(not(not(X_8))))) ),[1],$fot(or(not(X_8),and(falsehood,X_8)))]]) ).
cnf(refute_0_240,plain,
( xor(truth,X_8) != or(and(falsehood,X_8),not(not(not(X_8))))
| xor(truth,X_8) = or(not(X_8),and(falsehood,X_8)) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,X_8),not(not(not(X_8)))),or(not(X_8),and(falsehood,X_8))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
xor(truth,X_8) = or(not(X_8),and(falsehood,X_8)),
inference(resolve,[$cnf( $equal(xor(truth,X_8),or(and(falsehood,X_8),not(not(not(X_8))))) )],[refute_0_171,refute_0_240]) ).
cnf(refute_0_242,plain,
or(not(X_45),Y) = implies(not(not(X_45)),Y),
inference(subst,[],[or_definition:[bind(X,$fot(not(X_45)))]]) ).
cnf(refute_0_243,plain,
X_45 = not(not(X_45)),
inference(subst,[],[refute_0_228:[bind(Y,$fot(X_45))]]) ).
cnf(refute_0_244,plain,
( X_45 != not(not(X_45))
| not(not(X_45)) = X_45 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_45)),bind(Y0,$fot(not(not(X_45))))]]) ).
cnf(refute_0_245,plain,
not(not(X_45)) = X_45,
inference(resolve,[$cnf( $equal(X_45,not(not(X_45))) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
( not(not(X_45)) != X_45
| or(not(X_45),Y) != implies(not(not(X_45)),Y)
| or(not(X_45),Y) = implies(X_45,Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X_45),Y),implies(not(not(X_45)),Y)) ),[1,0],$fot(X_45)]]) ).
cnf(refute_0_247,plain,
( or(not(X_45),Y) != implies(not(not(X_45)),Y)
| or(not(X_45),Y) = implies(X_45,Y) ),
inference(resolve,[$cnf( $equal(not(not(X_45)),X_45) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
or(not(X_45),Y) = implies(X_45,Y),
inference(resolve,[$cnf( $equal(or(not(X_45),Y),implies(not(not(X_45)),Y)) )],[refute_0_242,refute_0_247]) ).
cnf(refute_0_249,plain,
or(not(X_8),and(falsehood,X_8)) = implies(X_8,and(falsehood,X_8)),
inference(subst,[],[refute_0_248:[bind(Y,$fot(and(falsehood,X_8))),bind(X_45,$fot(X_8))]]) ).
cnf(refute_0_250,plain,
( or(not(X_8),and(falsehood,X_8)) != implies(X_8,and(falsehood,X_8))
| xor(truth,X_8) != or(not(X_8),and(falsehood,X_8))
| xor(truth,X_8) = implies(X_8,and(falsehood,X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_8),or(not(X_8),and(falsehood,X_8))) ),[1],$fot(implies(X_8,and(falsehood,X_8)))]]) ).
cnf(refute_0_251,plain,
( xor(truth,X_8) != or(not(X_8),and(falsehood,X_8))
| xor(truth,X_8) = implies(X_8,and(falsehood,X_8)) ),
inference(resolve,[$cnf( $equal(or(not(X_8),and(falsehood,X_8)),implies(X_8,and(falsehood,X_8))) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
xor(truth,X_8) = implies(X_8,and(falsehood,X_8)),
inference(resolve,[$cnf( $equal(xor(truth,X_8),or(not(X_8),and(falsehood,X_8))) )],[refute_0_241,refute_0_251]) ).
cnf(refute_0_253,plain,
and(and(falsehood,falsehood),Z) = and(falsehood,and(falsehood,Z)),
inference(subst,[],[and_associativity:[bind(X,$fot(falsehood)),bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_254,plain,
and(falsehood,and(falsehood,implies(falsehood,truth))) = not(not(and(falsehood,and(falsehood,implies(falsehood,truth))))),
inference(subst,[],[refute_0_228:[bind(Y,$fot(and(falsehood,and(falsehood,implies(falsehood,truth)))))]]) ).
cnf(refute_0_255,plain,
or(implies(falsehood,X_47),not(implies(falsehood,X_47))) = truth,
inference(subst,[],[refute_0_193:[bind(X,$fot(implies(falsehood,X_47)))]]) ).
cnf(refute_0_256,plain,
or(or(truth,X_19),X_20) = or(truth,or(X_19,X_20)),
inference(subst,[],[or_associativity:[bind(X,$fot(truth)),bind(Y,$fot(X_19)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_257,plain,
or(truth,X_19) = implies(falsehood,X_19),
inference(subst,[],[refute_0_83:[bind(X_4,$fot(X_19))]]) ).
cnf(refute_0_258,plain,
( or(or(truth,X_19),X_20) != or(truth,or(X_19,X_20))
| or(truth,X_19) != implies(falsehood,X_19)
| or(implies(falsehood,X_19),X_20) = or(truth,or(X_19,X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(truth,X_19),X_20),or(truth,or(X_19,X_20))) ),[0,0],$fot(implies(falsehood,X_19))]]) ).
cnf(refute_0_259,plain,
( or(or(truth,X_19),X_20) != or(truth,or(X_19,X_20))
| or(implies(falsehood,X_19),X_20) = or(truth,or(X_19,X_20)) ),
inference(resolve,[$cnf( $equal(or(truth,X_19),implies(falsehood,X_19)) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
or(implies(falsehood,X_19),X_20) = or(truth,or(X_19,X_20)),
inference(resolve,[$cnf( $equal(or(or(truth,X_19),X_20),or(truth,or(X_19,X_20))) )],[refute_0_256,refute_0_259]) ).
cnf(refute_0_261,plain,
or(truth,or(X_19,X_20)) = implies(falsehood,or(X_19,X_20)),
inference(subst,[],[refute_0_83:[bind(X_4,$fot(or(X_19,X_20)))]]) ).
cnf(refute_0_262,plain,
( or(implies(falsehood,X_19),X_20) != or(truth,or(X_19,X_20))
| or(truth,or(X_19,X_20)) != implies(falsehood,or(X_19,X_20))
| or(implies(falsehood,X_19),X_20) = implies(falsehood,or(X_19,X_20)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(or(implies(falsehood,X_19),X_20),implies(falsehood,or(X_19,X_20))) ),[0],$fot(or(truth,or(X_19,X_20)))]]) ).
cnf(refute_0_263,plain,
( or(implies(falsehood,X_19),X_20) != or(truth,or(X_19,X_20))
| or(implies(falsehood,X_19),X_20) = implies(falsehood,or(X_19,X_20)) ),
inference(resolve,[$cnf( $equal(or(truth,or(X_19,X_20)),implies(falsehood,or(X_19,X_20))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
or(implies(falsehood,X_19),X_20) = implies(falsehood,or(X_19,X_20)),
inference(resolve,[$cnf( $equal(or(implies(falsehood,X_19),X_20),or(truth,or(X_19,X_20))) )],[refute_0_260,refute_0_263]) ).
cnf(refute_0_265,plain,
or(implies(falsehood,X_47),not(implies(falsehood,X_47))) = implies(falsehood,or(X_47,not(implies(falsehood,X_47)))),
inference(subst,[],[refute_0_264:[bind(X_19,$fot(X_47)),bind(X_20,$fot(not(implies(falsehood,X_47))))]]) ).
cnf(refute_0_266,plain,
( or(implies(falsehood,X_47),not(implies(falsehood,X_47))) != implies(falsehood,or(X_47,not(implies(falsehood,X_47))))
| or(implies(falsehood,X_47),not(implies(falsehood,X_47))) != truth
| implies(falsehood,or(X_47,not(implies(falsehood,X_47)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(falsehood,X_47),not(implies(falsehood,X_47))),truth) ),[0],$fot(implies(falsehood,or(X_47,not(implies(falsehood,X_47)))))]]) ).
cnf(refute_0_267,plain,
( or(implies(falsehood,X_47),not(implies(falsehood,X_47))) != truth
| implies(falsehood,or(X_47,not(implies(falsehood,X_47)))) = truth ),
inference(resolve,[$cnf( $equal(or(implies(falsehood,X_47),not(implies(falsehood,X_47))),implies(falsehood,or(X_47,not(implies(falsehood,X_47))))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
implies(falsehood,or(X_47,not(implies(falsehood,X_47)))) = truth,
inference(resolve,[$cnf( $equal(or(implies(falsehood,X_47),not(implies(falsehood,X_47))),truth) )],[refute_0_255,refute_0_267]) ).
cnf(refute_0_269,plain,
implies(falsehood,or(truth,not(implies(falsehood,truth)))) = truth,
inference(subst,[],[refute_0_268:[bind(X_47,$fot(truth))]]) ).
cnf(refute_0_270,plain,
or(truth,not(implies(falsehood,truth))) = implies(falsehood,not(implies(falsehood,truth))),
inference(subst,[],[refute_0_83:[bind(X_4,$fot(not(implies(falsehood,truth))))]]) ).
cnf(refute_0_271,plain,
( implies(falsehood,or(truth,not(implies(falsehood,truth)))) != truth
| or(truth,not(implies(falsehood,truth))) != implies(falsehood,not(implies(falsehood,truth)))
| implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(falsehood,or(truth,not(implies(falsehood,truth)))),truth) ),[0,1],$fot(implies(falsehood,not(implies(falsehood,truth))))]]) ).
cnf(refute_0_272,plain,
( implies(falsehood,or(truth,not(implies(falsehood,truth)))) != truth
| implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))) = truth ),
inference(resolve,[$cnf( $equal(or(truth,not(implies(falsehood,truth))),implies(falsehood,not(implies(falsehood,truth)))) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(falsehood,or(truth,not(implies(falsehood,truth)))),truth) )],[refute_0_269,refute_0_272]) ).
cnf(refute_0_274,plain,
or(not(X),not(Y)) = not(not(or(not(X),not(Y)))),
inference(subst,[],[refute_0_228:[bind(Y,$fot(or(not(X),not(Y))))]]) ).
cnf(refute_0_275,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_276,plain,
not(or(not(X),not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[and_definition,refute_0_275]) ).
cnf(refute_0_277,plain,
( not(or(not(X),not(Y))) != and(X,Y)
| or(not(X),not(Y)) != not(not(or(not(X),not(Y))))
| or(not(X),not(Y)) = not(and(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X),not(Y)),not(not(or(not(X),not(Y))))) ),[1,0],$fot(and(X,Y))]]) ).
cnf(refute_0_278,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( $equal(not(or(not(X),not(Y))),and(X,Y)) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
or(not(X),not(Y)) = not(and(X,Y)),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),not(not(or(not(X),not(Y))))) )],[refute_0_274,refute_0_278]) ).
cnf(refute_0_280,plain,
or(not(X),not(Y)) = implies(X,not(Y)),
inference(subst,[],[refute_0_248:[bind(Y,$fot(not(Y))),bind(X_45,$fot(X))]]) ).
cnf(refute_0_281,plain,
( or(not(X),not(Y)) != implies(X,not(Y))
| or(not(X),not(Y)) != not(and(X,Y))
| implies(X,not(Y)) = not(and(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X),not(Y)),not(and(X,Y))) ),[0],$fot(implies(X,not(Y)))]]) ).
cnf(refute_0_282,plain,
( or(not(X),not(Y)) != not(and(X,Y))
| implies(X,not(Y)) = not(and(X,Y)) ),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),implies(X,not(Y))) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
implies(X,not(Y)) = not(and(X,Y)),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),not(and(X,Y))) )],[refute_0_279,refute_0_282]) ).
cnf(refute_0_284,plain,
implies(falsehood,not(and(falsehood,implies(falsehood,truth)))) = not(and(falsehood,and(falsehood,implies(falsehood,truth)))),
inference(subst,[],[refute_0_283:[bind(X,$fot(falsehood)),bind(Y,$fot(and(falsehood,implies(falsehood,truth))))]]) ).
cnf(refute_0_285,plain,
implies(falsehood,not(implies(falsehood,truth))) = not(and(falsehood,implies(falsehood,truth))),
inference(subst,[],[refute_0_283:[bind(X,$fot(falsehood)),bind(Y,$fot(implies(falsehood,truth)))]]) ).
cnf(refute_0_286,plain,
implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))) = implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))),
introduced(tautology,[refl,[$fot(implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))))]]) ).
cnf(refute_0_287,plain,
( implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))) != implies(falsehood,implies(falsehood,not(implies(falsehood,truth))))
| implies(falsehood,not(implies(falsehood,truth))) != not(and(falsehood,implies(falsehood,truth)))
| implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))) = implies(falsehood,not(and(falsehood,implies(falsehood,truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))),implies(falsehood,implies(falsehood,not(implies(falsehood,truth))))) ),[1,1],$fot(not(and(falsehood,implies(falsehood,truth))))]]) ).
cnf(refute_0_288,plain,
( implies(falsehood,not(implies(falsehood,truth))) != not(and(falsehood,implies(falsehood,truth)))
| implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))) = implies(falsehood,not(and(falsehood,implies(falsehood,truth)))) ),
inference(resolve,[$cnf( $equal(implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))),implies(falsehood,implies(falsehood,not(implies(falsehood,truth))))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))) = implies(falsehood,not(and(falsehood,implies(falsehood,truth)))),
inference(resolve,[$cnf( $equal(implies(falsehood,not(implies(falsehood,truth))),not(and(falsehood,implies(falsehood,truth)))) )],[refute_0_285,refute_0_288]) ).
cnf(refute_0_290,plain,
( implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))) != implies(falsehood,not(and(falsehood,implies(falsehood,truth))))
| implies(falsehood,not(and(falsehood,implies(falsehood,truth)))) != not(and(falsehood,and(falsehood,implies(falsehood,truth))))
| implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))) = not(and(falsehood,and(falsehood,implies(falsehood,truth)))) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))))),bind(Y0,$fot(implies(falsehood,not(and(falsehood,implies(falsehood,truth)))))),bind(Z0,$fot(not(and(falsehood,and(falsehood,implies(falsehood,truth))))))]]) ).
cnf(refute_0_291,plain,
( implies(falsehood,not(and(falsehood,implies(falsehood,truth)))) != not(and(falsehood,and(falsehood,implies(falsehood,truth))))
| implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))) = not(and(falsehood,and(falsehood,implies(falsehood,truth)))) ),
inference(resolve,[$cnf( $equal(implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))),implies(falsehood,not(and(falsehood,implies(falsehood,truth))))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))) = not(and(falsehood,and(falsehood,implies(falsehood,truth)))),
inference(resolve,[$cnf( $equal(implies(falsehood,not(and(falsehood,implies(falsehood,truth)))),not(and(falsehood,and(falsehood,implies(falsehood,truth))))) )],[refute_0_284,refute_0_291]) ).
cnf(refute_0_293,plain,
( implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))) != not(and(falsehood,and(falsehood,implies(falsehood,truth))))
| implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))) != truth
| not(and(falsehood,and(falsehood,implies(falsehood,truth)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))),truth) ),[0],$fot(not(and(falsehood,and(falsehood,implies(falsehood,truth)))))]]) ).
cnf(refute_0_294,plain,
( implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))) != truth
| not(and(falsehood,and(falsehood,implies(falsehood,truth)))) = truth ),
inference(resolve,[$cnf( $equal(implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))),not(and(falsehood,and(falsehood,implies(falsehood,truth))))) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
not(and(falsehood,and(falsehood,implies(falsehood,truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(falsehood,implies(falsehood,not(implies(falsehood,truth)))),truth) )],[refute_0_273,refute_0_294]) ).
cnf(refute_0_296,plain,
( and(falsehood,and(falsehood,implies(falsehood,truth))) != not(not(and(falsehood,and(falsehood,implies(falsehood,truth)))))
| not(and(falsehood,and(falsehood,implies(falsehood,truth)))) != truth
| and(falsehood,and(falsehood,implies(falsehood,truth))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(and(falsehood,and(falsehood,implies(falsehood,truth))),not(not(and(falsehood,and(falsehood,implies(falsehood,truth)))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_297,plain,
( and(falsehood,and(falsehood,implies(falsehood,truth))) != not(not(and(falsehood,and(falsehood,implies(falsehood,truth)))))
| and(falsehood,and(falsehood,implies(falsehood,truth))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(and(falsehood,and(falsehood,implies(falsehood,truth)))),truth) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
and(falsehood,and(falsehood,implies(falsehood,truth))) = not(truth),
inference(resolve,[$cnf( $equal(and(falsehood,and(falsehood,implies(falsehood,truth))),not(not(and(falsehood,and(falsehood,implies(falsehood,truth)))))) )],[refute_0_254,refute_0_297]) ).
cnf(refute_0_299,plain,
( and(falsehood,and(falsehood,implies(falsehood,truth))) != not(truth)
| not(truth) != falsehood
| and(falsehood,and(falsehood,implies(falsehood,truth))) = falsehood ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(falsehood,and(falsehood,implies(falsehood,truth))),falsehood) ),[0],$fot(not(truth))]]) ).
cnf(refute_0_300,plain,
( and(falsehood,and(falsehood,implies(falsehood,truth))) != not(truth)
| and(falsehood,and(falsehood,implies(falsehood,truth))) = falsehood ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_299]) ).
cnf(refute_0_301,plain,
and(falsehood,and(falsehood,implies(falsehood,truth))) = falsehood,
inference(resolve,[$cnf( $equal(and(falsehood,and(falsehood,implies(falsehood,truth))),not(truth)) )],[refute_0_298,refute_0_300]) ).
cnf(refute_0_302,plain,
implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood) = implies(implies(falsehood,and(falsehood,implies(X_56,truth))),and(falsehood,implies(X_56,truth))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(and(falsehood,implies(X_56,truth)))),bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_303,plain,
implies(or(truth,not(implies(X_25,truth))),implies(implies(X_25,truth),truth)) = truth,
inference(subst,[],[refute_0_54:[bind(X,$fot(truth)),bind(Y,$fot(implies(X_25,truth)))]]) ).
cnf(refute_0_304,plain,
( implies(X_25,X_25) != implies(implies(X_25,truth),truth)
| implies(implies(X_25,truth),truth) = implies(X_25,X_25) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_25,X_25))),bind(Y0,$fot(implies(implies(X_25,truth),truth)))]]) ).
cnf(refute_0_305,plain,
implies(implies(X_25,truth),truth) = implies(X_25,X_25),
inference(resolve,[$cnf( $equal(implies(X_25,X_25),implies(implies(X_25,truth),truth)) )],[refute_0_93,refute_0_304]) ).
cnf(refute_0_306,plain,
( implies(implies(X_25,truth),truth) != implies(X_25,X_25)
| implies(or(truth,not(implies(X_25,truth))),implies(implies(X_25,truth),truth)) != truth
| implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(truth,not(implies(X_25,truth))),implies(implies(X_25,truth),truth)),truth) ),[0,1],$fot(implies(X_25,X_25))]]) ).
cnf(refute_0_307,plain,
( implies(or(truth,not(implies(X_25,truth))),implies(implies(X_25,truth),truth)) != truth
| implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_25,truth),truth),implies(X_25,X_25)) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)) = truth,
inference(resolve,[$cnf( $equal(implies(or(truth,not(implies(X_25,truth))),implies(implies(X_25,truth),truth)),truth) )],[refute_0_303,refute_0_307]) ).
cnf(refute_0_309,plain,
or(truth,not(implies(X_25,truth))) = implies(falsehood,not(implies(X_25,truth))),
inference(subst,[],[refute_0_83:[bind(X_4,$fot(not(implies(X_25,truth))))]]) ).
cnf(refute_0_310,plain,
implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)) = implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)),
introduced(tautology,[refl,[$fot(implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)))]]) ).
cnf(refute_0_311,plain,
( implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)) != implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25))
| or(truth,not(implies(X_25,truth))) != implies(falsehood,not(implies(X_25,truth)))
| implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)) = implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)),implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25))) ),[1,0],$fot(implies(falsehood,not(implies(X_25,truth))))]]) ).
cnf(refute_0_312,plain,
( or(truth,not(implies(X_25,truth))) != implies(falsehood,not(implies(X_25,truth)))
| implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)) = implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) ),
inference(resolve,[$cnf( $equal(implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)),implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25))) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)) = implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)),
inference(resolve,[$cnf( $equal(or(truth,not(implies(X_25,truth))),implies(falsehood,not(implies(X_25,truth)))) )],[refute_0_309,refute_0_312]) ).
cnf(refute_0_314,plain,
( implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)) != implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25))
| implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)) != truth
| implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)),truth) ),[0],$fot(implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)))]]) ).
cnf(refute_0_315,plain,
( implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)) != truth
| implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) = truth ),
inference(resolve,[$cnf( $equal(implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)),implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) = truth,
inference(resolve,[$cnf( $equal(implies(or(truth,not(implies(X_25,truth))),implies(X_25,X_25)),truth) )],[refute_0_308,refute_0_315]) ).
cnf(refute_0_317,plain,
or(and(falsehood,implies(X_25,truth)),truth) = implies(falsehood,and(falsehood,implies(X_25,truth))),
inference(subst,[],[refute_0_102:[bind(X,$fot(and(falsehood,implies(X_25,truth))))]]) ).
cnf(refute_0_318,plain,
implies(not(and(falsehood,implies(X_25,truth))),truth) = or(and(falsehood,implies(X_25,truth)),truth),
inference(subst,[],[refute_0_46:[bind(X,$fot(and(falsehood,implies(X_25,truth)))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_319,plain,
( implies(not(and(falsehood,implies(X_25,truth))),truth) != or(and(falsehood,implies(X_25,truth)),truth)
| or(and(falsehood,implies(X_25,truth)),truth) != implies(falsehood,and(falsehood,implies(X_25,truth)))
| implies(not(and(falsehood,implies(X_25,truth))),truth) = implies(falsehood,and(falsehood,implies(X_25,truth))) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(implies(not(and(falsehood,implies(X_25,truth))),truth))),bind(Y0,$fot(or(and(falsehood,implies(X_25,truth)),truth))),bind(Z0,$fot(implies(falsehood,and(falsehood,implies(X_25,truth)))))]]) ).
cnf(refute_0_320,plain,
( or(and(falsehood,implies(X_25,truth)),truth) != implies(falsehood,and(falsehood,implies(X_25,truth)))
| implies(not(and(falsehood,implies(X_25,truth))),truth) = implies(falsehood,and(falsehood,implies(X_25,truth))) ),
inference(resolve,[$cnf( $equal(implies(not(and(falsehood,implies(X_25,truth))),truth),or(and(falsehood,implies(X_25,truth)),truth)) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
implies(not(and(falsehood,implies(X_25,truth))),truth) = implies(falsehood,and(falsehood,implies(X_25,truth))),
inference(resolve,[$cnf( $equal(or(and(falsehood,implies(X_25,truth)),truth),implies(falsehood,and(falsehood,implies(X_25,truth)))) )],[refute_0_317,refute_0_320]) ).
cnf(refute_0_322,plain,
implies(X_25,X_25) = truth,
inference(subst,[],[refute_0_189:[bind(X_30,$fot(X_25))]]) ).
cnf(refute_0_323,plain,
implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25)) = implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25)),
introduced(tautology,[refl,[$fot(implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25)))]]) ).
cnf(refute_0_324,plain,
( implies(X_25,X_25) != truth
| implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25)) != implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25))
| implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25)) = implies(not(and(falsehood,implies(X_25,truth))),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25)),implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_325,plain,
( implies(X_25,X_25) != truth
| implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25)) = implies(not(and(falsehood,implies(X_25,truth))),truth) ),
inference(resolve,[$cnf( $equal(implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25)),implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25))) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25)) = implies(not(and(falsehood,implies(X_25,truth))),truth),
inference(resolve,[$cnf( $equal(implies(X_25,X_25),truth) )],[refute_0_322,refute_0_325]) ).
cnf(refute_0_327,plain,
implies(falsehood,not(implies(X_25,truth))) = not(and(falsehood,implies(X_25,truth))),
inference(subst,[],[refute_0_283:[bind(X,$fot(falsehood)),bind(Y,$fot(implies(X_25,truth)))]]) ).
cnf(refute_0_328,plain,
implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) = implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)),
introduced(tautology,[refl,[$fot(implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)))]]) ).
cnf(refute_0_329,plain,
( implies(falsehood,not(implies(X_25,truth))) != not(and(falsehood,implies(X_25,truth)))
| implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) != implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25))
| implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) = implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)),implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25))) ),[1,0],$fot(not(and(falsehood,implies(X_25,truth))))]]) ).
cnf(refute_0_330,plain,
( implies(falsehood,not(implies(X_25,truth))) != not(and(falsehood,implies(X_25,truth)))
| implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) = implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25)) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)),implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25))) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) = implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25)),
inference(resolve,[$cnf( $equal(implies(falsehood,not(implies(X_25,truth))),not(and(falsehood,implies(X_25,truth)))) )],[refute_0_327,refute_0_330]) ).
cnf(refute_0_332,plain,
( implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) != implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25))
| implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25)) != implies(not(and(falsehood,implies(X_25,truth))),truth)
| implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) = implies(not(and(falsehood,implies(X_25,truth))),truth) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)))),bind(Y0,$fot(implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25)))),bind(Z0,$fot(implies(not(and(falsehood,implies(X_25,truth))),truth)))]]) ).
cnf(refute_0_333,plain,
( implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25)) != implies(not(and(falsehood,implies(X_25,truth))),truth)
| implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) = implies(not(and(falsehood,implies(X_25,truth))),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)),implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25))) )],[refute_0_331,refute_0_332]) ).
cnf(refute_0_334,plain,
implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) = implies(not(and(falsehood,implies(X_25,truth))),truth),
inference(resolve,[$cnf( $equal(implies(not(and(falsehood,implies(X_25,truth))),implies(X_25,X_25)),implies(not(and(falsehood,implies(X_25,truth))),truth)) )],[refute_0_326,refute_0_333]) ).
cnf(refute_0_335,plain,
( implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) != implies(not(and(falsehood,implies(X_25,truth))),truth)
| implies(not(and(falsehood,implies(X_25,truth))),truth) != implies(falsehood,and(falsehood,implies(X_25,truth)))
| implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) = implies(falsehood,and(falsehood,implies(X_25,truth))) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)))),bind(Y0,$fot(implies(not(and(falsehood,implies(X_25,truth))),truth))),bind(Z0,$fot(implies(falsehood,and(falsehood,implies(X_25,truth)))))]]) ).
cnf(refute_0_336,plain,
( implies(not(and(falsehood,implies(X_25,truth))),truth) != implies(falsehood,and(falsehood,implies(X_25,truth)))
| implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) = implies(falsehood,and(falsehood,implies(X_25,truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)),implies(not(and(falsehood,implies(X_25,truth))),truth)) )],[refute_0_334,refute_0_335]) ).
cnf(refute_0_337,plain,
implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) = implies(falsehood,and(falsehood,implies(X_25,truth))),
inference(resolve,[$cnf( $equal(implies(not(and(falsehood,implies(X_25,truth))),truth),implies(falsehood,and(falsehood,implies(X_25,truth)))) )],[refute_0_321,refute_0_336]) ).
cnf(refute_0_338,plain,
( implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) != implies(falsehood,and(falsehood,implies(X_25,truth)))
| implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) != truth
| implies(falsehood,and(falsehood,implies(X_25,truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)),truth) ),[0],$fot(implies(falsehood,and(falsehood,implies(X_25,truth))))]]) ).
cnf(refute_0_339,plain,
( implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)) != truth
| implies(falsehood,and(falsehood,implies(X_25,truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)),implies(falsehood,and(falsehood,implies(X_25,truth)))) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
implies(falsehood,and(falsehood,implies(X_25,truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,not(implies(X_25,truth))),implies(X_25,X_25)),truth) )],[refute_0_316,refute_0_339]) ).
cnf(refute_0_341,plain,
implies(falsehood,and(falsehood,implies(X_56,truth))) = truth,
inference(subst,[],[refute_0_340:[bind(X_25,$fot(X_56))]]) ).
cnf(refute_0_342,plain,
( implies(falsehood,and(falsehood,implies(X_56,truth))) != truth
| implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood) != implies(implies(falsehood,and(falsehood,implies(X_56,truth))),and(falsehood,implies(X_56,truth)))
| implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood) = implies(truth,and(falsehood,implies(X_56,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood),implies(implies(falsehood,and(falsehood,implies(X_56,truth))),and(falsehood,implies(X_56,truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_343,plain,
( implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood) != implies(implies(falsehood,and(falsehood,implies(X_56,truth))),and(falsehood,implies(X_56,truth)))
| implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood) = implies(truth,and(falsehood,implies(X_56,truth))) ),
inference(resolve,[$cnf( $equal(implies(falsehood,and(falsehood,implies(X_56,truth))),truth) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood) = implies(truth,and(falsehood,implies(X_56,truth))),
inference(resolve,[$cnf( $equal(implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood),implies(implies(falsehood,and(falsehood,implies(X_56,truth))),and(falsehood,implies(X_56,truth)))) )],[refute_0_302,refute_0_343]) ).
cnf(refute_0_345,plain,
or(or(not(X_21),not(X_22)),Y) = implies(not(or(not(X_21),not(X_22))),Y),
inference(subst,[],[or_definition:[bind(X,$fot(or(not(X_21),not(X_22))))]]) ).
cnf(refute_0_346,plain,
and(X_21,X_22) = not(or(not(X_21),not(X_22))),
inference(subst,[],[and_definition:[bind(X,$fot(X_21)),bind(Y,$fot(X_22))]]) ).
cnf(refute_0_347,plain,
( and(X_21,X_22) != not(or(not(X_21),not(X_22)))
| not(or(not(X_21),not(X_22))) = and(X_21,X_22) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_21,X_22))),bind(Y0,$fot(not(or(not(X_21),not(X_22)))))]]) ).
cnf(refute_0_348,plain,
not(or(not(X_21),not(X_22))) = and(X_21,X_22),
inference(resolve,[$cnf( $equal(and(X_21,X_22),not(or(not(X_21),not(X_22)))) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
( not(or(not(X_21),not(X_22))) != and(X_21,X_22)
| or(or(not(X_21),not(X_22)),Y) != implies(not(or(not(X_21),not(X_22))),Y)
| or(or(not(X_21),not(X_22)),Y) = implies(and(X_21,X_22),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(not(X_21),not(X_22)),Y),implies(not(or(not(X_21),not(X_22))),Y)) ),[1,0],$fot(and(X_21,X_22))]]) ).
cnf(refute_0_350,plain,
( or(or(not(X_21),not(X_22)),Y) != implies(not(or(not(X_21),not(X_22))),Y)
| or(or(not(X_21),not(X_22)),Y) = implies(and(X_21,X_22),Y) ),
inference(resolve,[$cnf( $equal(not(or(not(X_21),not(X_22))),and(X_21,X_22)) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
or(or(not(X_21),not(X_22)),Y) = implies(and(X_21,X_22),Y),
inference(resolve,[$cnf( $equal(or(or(not(X_21),not(X_22)),Y),implies(not(or(not(X_21),not(X_22))),Y)) )],[refute_0_345,refute_0_350]) ).
cnf(refute_0_352,plain,
or(or(not(X_21),not(X_22)),Y) = or(not(X_21),or(not(X_22),Y)),
inference(subst,[],[or_associativity:[bind(X,$fot(not(X_21))),bind(Y,$fot(not(X_22))),bind(Z,$fot(Y))]]) ).
cnf(refute_0_353,plain,
( or(or(not(X_21),not(X_22)),Y) != implies(and(X_21,X_22),Y)
| or(or(not(X_21),not(X_22)),Y) != or(not(X_21),or(not(X_22),Y))
| or(not(X_21),or(not(X_22),Y)) = implies(and(X_21,X_22),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(not(X_21),not(X_22)),Y),implies(and(X_21,X_22),Y)) ),[0],$fot(or(not(X_21),or(not(X_22),Y)))]]) ).
cnf(refute_0_354,plain,
( or(or(not(X_21),not(X_22)),Y) != implies(and(X_21,X_22),Y)
| or(not(X_21),or(not(X_22),Y)) = implies(and(X_21,X_22),Y) ),
inference(resolve,[$cnf( $equal(or(or(not(X_21),not(X_22)),Y),or(not(X_21),or(not(X_22),Y))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
or(not(X_21),or(not(X_22),Y)) = implies(and(X_21,X_22),Y),
inference(resolve,[$cnf( $equal(or(or(not(X_21),not(X_22)),Y),implies(and(X_21,X_22),Y)) )],[refute_0_351,refute_0_354]) ).
cnf(refute_0_356,plain,
or(not(X_22),Y) = implies(X_22,Y),
inference(subst,[],[refute_0_248:[bind(X_45,$fot(X_22))]]) ).
cnf(refute_0_357,plain,
implies(X_21,or(not(X_22),Y)) = implies(X_21,or(not(X_22),Y)),
introduced(tautology,[refl,[$fot(implies(X_21,or(not(X_22),Y)))]]) ).
cnf(refute_0_358,plain,
( implies(X_21,or(not(X_22),Y)) != implies(X_21,or(not(X_22),Y))
| or(not(X_22),Y) != implies(X_22,Y)
| implies(X_21,or(not(X_22),Y)) = implies(X_21,implies(X_22,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_21,or(not(X_22),Y)),implies(X_21,or(not(X_22),Y))) ),[1,1],$fot(implies(X_22,Y))]]) ).
cnf(refute_0_359,plain,
( or(not(X_22),Y) != implies(X_22,Y)
| implies(X_21,or(not(X_22),Y)) = implies(X_21,implies(X_22,Y)) ),
inference(resolve,[$cnf( $equal(implies(X_21,or(not(X_22),Y)),implies(X_21,or(not(X_22),Y))) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
implies(X_21,or(not(X_22),Y)) = implies(X_21,implies(X_22,Y)),
inference(resolve,[$cnf( $equal(or(not(X_22),Y),implies(X_22,Y)) )],[refute_0_356,refute_0_359]) ).
cnf(refute_0_361,plain,
or(not(X_21),or(not(X_22),Y)) = implies(X_21,or(not(X_22),Y)),
inference(subst,[],[refute_0_248:[bind(Y,$fot(or(not(X_22),Y))),bind(X_45,$fot(X_21))]]) ).
cnf(refute_0_362,plain,
( implies(X_21,or(not(X_22),Y)) != implies(X_21,implies(X_22,Y))
| or(not(X_21),or(not(X_22),Y)) != implies(X_21,or(not(X_22),Y))
| or(not(X_21),or(not(X_22),Y)) = implies(X_21,implies(X_22,Y)) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(or(not(X_21),or(not(X_22),Y)))),bind(Y0,$fot(implies(X_21,or(not(X_22),Y)))),bind(Z0,$fot(implies(X_21,implies(X_22,Y))))]]) ).
cnf(refute_0_363,plain,
( implies(X_21,or(not(X_22),Y)) != implies(X_21,implies(X_22,Y))
| or(not(X_21),or(not(X_22),Y)) = implies(X_21,implies(X_22,Y)) ),
inference(resolve,[$cnf( $equal(or(not(X_21),or(not(X_22),Y)),implies(X_21,or(not(X_22),Y))) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
or(not(X_21),or(not(X_22),Y)) = implies(X_21,implies(X_22,Y)),
inference(resolve,[$cnf( $equal(implies(X_21,or(not(X_22),Y)),implies(X_21,implies(X_22,Y))) )],[refute_0_360,refute_0_363]) ).
cnf(refute_0_365,plain,
( or(not(X_21),or(not(X_22),Y)) != implies(X_21,implies(X_22,Y))
| or(not(X_21),or(not(X_22),Y)) != implies(and(X_21,X_22),Y)
| implies(X_21,implies(X_22,Y)) = implies(and(X_21,X_22),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X_21),or(not(X_22),Y)),implies(and(X_21,X_22),Y)) ),[0],$fot(implies(X_21,implies(X_22,Y)))]]) ).
cnf(refute_0_366,plain,
( or(not(X_21),or(not(X_22),Y)) != implies(and(X_21,X_22),Y)
| implies(X_21,implies(X_22,Y)) = implies(and(X_21,X_22),Y) ),
inference(resolve,[$cnf( $equal(or(not(X_21),or(not(X_22),Y)),implies(X_21,implies(X_22,Y))) )],[refute_0_364,refute_0_365]) ).
cnf(refute_0_367,plain,
implies(X_21,implies(X_22,Y)) = implies(and(X_21,X_22),Y),
inference(resolve,[$cnf( $equal(or(not(X_21),or(not(X_22),Y)),implies(and(X_21,X_22),Y)) )],[refute_0_355,refute_0_366]) ).
cnf(refute_0_368,plain,
( implies(X_21,implies(X_22,Y)) != implies(and(X_21,X_22),Y)
| implies(and(X_21,X_22),Y) = implies(X_21,implies(X_22,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_21,implies(X_22,Y)))),bind(Y0,$fot(implies(and(X_21,X_22),Y)))]]) ).
cnf(refute_0_369,plain,
implies(and(X_21,X_22),Y) = implies(X_21,implies(X_22,Y)),
inference(resolve,[$cnf( $equal(implies(X_21,implies(X_22,Y)),implies(and(X_21,X_22),Y)) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
implies(and(falsehood,implies(X_56,truth)),falsehood) = implies(falsehood,implies(implies(X_56,truth),falsehood)),
inference(subst,[],[refute_0_369:[bind(Y,$fot(falsehood)),bind(X_21,$fot(falsehood)),bind(X_22,$fot(implies(X_56,truth)))]]) ).
cnf(refute_0_371,plain,
implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood) = implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood),
introduced(tautology,[refl,[$fot(implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood))]]) ).
cnf(refute_0_372,plain,
( implies(and(falsehood,implies(X_56,truth)),falsehood) != implies(falsehood,implies(implies(X_56,truth),falsehood))
| implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood) != implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood)
| implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood) = implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood),implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood)) ),[1,0],$fot(implies(falsehood,implies(implies(X_56,truth),falsehood)))]]) ).
cnf(refute_0_373,plain,
( implies(and(falsehood,implies(X_56,truth)),falsehood) != implies(falsehood,implies(implies(X_56,truth),falsehood))
| implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood) = implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) ),
inference(resolve,[$cnf( $equal(implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood),implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood)) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood) = implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood),
inference(resolve,[$cnf( $equal(implies(and(falsehood,implies(X_56,truth)),falsehood),implies(falsehood,implies(implies(X_56,truth),falsehood))) )],[refute_0_370,refute_0_373]) ).
cnf(refute_0_375,plain,
( implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood) != implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood)
| implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood) != implies(truth,and(falsehood,implies(X_56,truth)))
| implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) = implies(truth,and(falsehood,implies(X_56,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood),implies(truth,and(falsehood,implies(X_56,truth)))) ),[0],$fot(implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood))]]) ).
cnf(refute_0_376,plain,
( implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood) != implies(truth,and(falsehood,implies(X_56,truth)))
| implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) = implies(truth,and(falsehood,implies(X_56,truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood),implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood)) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
implies(truth,and(falsehood,implies(X_56,truth))) = and(falsehood,implies(X_56,truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(and(falsehood,implies(X_56,truth))))]]) ).
cnf(refute_0_378,plain,
( implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) != implies(truth,and(falsehood,implies(X_56,truth)))
| implies(truth,and(falsehood,implies(X_56,truth))) != and(falsehood,implies(X_56,truth))
| implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) = and(falsehood,implies(X_56,truth)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood),and(falsehood,implies(X_56,truth))) ),[0],$fot(implies(truth,and(falsehood,implies(X_56,truth))))]]) ).
cnf(refute_0_379,plain,
( implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) != implies(truth,and(falsehood,implies(X_56,truth)))
| implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) = and(falsehood,implies(X_56,truth)) ),
inference(resolve,[$cnf( $equal(implies(truth,and(falsehood,implies(X_56,truth))),and(falsehood,implies(X_56,truth))) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
( implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood) != implies(truth,and(falsehood,implies(X_56,truth)))
| implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) = and(falsehood,implies(X_56,truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood),implies(truth,and(falsehood,implies(X_56,truth)))) )],[refute_0_376,refute_0_379]) ).
cnf(refute_0_381,plain,
implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) = and(falsehood,implies(X_56,truth)),
inference(resolve,[$cnf( $equal(implies(implies(and(falsehood,implies(X_56,truth)),falsehood),falsehood),implies(truth,and(falsehood,implies(X_56,truth)))) )],[refute_0_344,refute_0_380]) ).
cnf(refute_0_382,plain,
implies(truth,falsehood) = falsehood,
inference(subst,[],[wajsberg_1:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_383,plain,
implies(or(X_28,not(not(X))),implies(not(X),X_28)) = truth,
inference(subst,[],[refute_0_54:[bind(X,$fot(X_28)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_384,plain,
or(X,X_28) = implies(not(X),X_28),
inference(subst,[],[or_definition:[bind(Y,$fot(X_28))]]) ).
cnf(refute_0_385,plain,
( or(X,X_28) != implies(not(X),X_28)
| implies(not(X),X_28) = or(X,X_28) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,X_28))),bind(Y0,$fot(implies(not(X),X_28)))]]) ).
cnf(refute_0_386,plain,
implies(not(X),X_28) = or(X,X_28),
inference(resolve,[$cnf( $equal(or(X,X_28),implies(not(X),X_28)) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
( implies(not(X),X_28) != or(X,X_28)
| implies(or(X_28,not(not(X))),implies(not(X),X_28)) != truth
| implies(or(X_28,not(not(X))),or(X,X_28)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_28,not(not(X))),implies(not(X),X_28)),truth) ),[0,1],$fot(or(X,X_28))]]) ).
cnf(refute_0_388,plain,
( implies(or(X_28,not(not(X))),implies(not(X),X_28)) != truth
| implies(or(X_28,not(not(X))),or(X,X_28)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X),X_28),or(X,X_28)) )],[refute_0_386,refute_0_387]) ).
cnf(refute_0_389,plain,
implies(or(X_28,not(not(X))),or(X,X_28)) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_28,not(not(X))),implies(not(X),X_28)),truth) )],[refute_0_383,refute_0_388]) ).
cnf(refute_0_390,plain,
not(not(X)) = X,
inference(subst,[],[refute_0_230:[bind(Y,$fot(X))]]) ).
cnf(refute_0_391,plain,
or(X_28,not(not(X))) = or(X_28,not(not(X))),
introduced(tautology,[refl,[$fot(or(X_28,not(not(X))))]]) ).
cnf(refute_0_392,plain,
( not(not(X)) != X
| or(X_28,not(not(X))) != or(X_28,not(not(X)))
| or(X_28,not(not(X))) = or(X_28,X) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_28,not(not(X))),or(X_28,not(not(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_393,plain,
( not(not(X)) != X
| or(X_28,not(not(X))) = or(X_28,X) ),
inference(resolve,[$cnf( $equal(or(X_28,not(not(X))),or(X_28,not(not(X)))) )],[refute_0_391,refute_0_392]) ).
cnf(refute_0_394,plain,
or(X_28,not(not(X))) = or(X_28,X),
inference(resolve,[$cnf( $equal(not(not(X)),X) )],[refute_0_390,refute_0_393]) ).
cnf(refute_0_395,plain,
implies(or(X_28,not(not(X))),or(X,X_28)) = implies(or(X_28,not(not(X))),or(X,X_28)),
introduced(tautology,[refl,[$fot(implies(or(X_28,not(not(X))),or(X,X_28)))]]) ).
cnf(refute_0_396,plain,
( implies(or(X_28,not(not(X))),or(X,X_28)) != implies(or(X_28,not(not(X))),or(X,X_28))
| or(X_28,not(not(X))) != or(X_28,X)
| implies(or(X_28,not(not(X))),or(X,X_28)) = implies(or(X_28,X),or(X,X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_28,not(not(X))),or(X,X_28)),implies(or(X_28,not(not(X))),or(X,X_28))) ),[1,0],$fot(or(X_28,X))]]) ).
cnf(refute_0_397,plain,
( or(X_28,not(not(X))) != or(X_28,X)
| implies(or(X_28,not(not(X))),or(X,X_28)) = implies(or(X_28,X),or(X,X_28)) ),
inference(resolve,[$cnf( $equal(implies(or(X_28,not(not(X))),or(X,X_28)),implies(or(X_28,not(not(X))),or(X,X_28))) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
implies(or(X_28,not(not(X))),or(X,X_28)) = implies(or(X_28,X),or(X,X_28)),
inference(resolve,[$cnf( $equal(or(X_28,not(not(X))),or(X_28,X)) )],[refute_0_394,refute_0_397]) ).
cnf(refute_0_399,plain,
( implies(or(X_28,not(not(X))),or(X,X_28)) != implies(or(X_28,X),or(X,X_28))
| implies(or(X_28,not(not(X))),or(X,X_28)) != truth
| implies(or(X_28,X),or(X,X_28)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_28,not(not(X))),or(X,X_28)),truth) ),[0],$fot(implies(or(X_28,X),or(X,X_28)))]]) ).
cnf(refute_0_400,plain,
( implies(or(X_28,not(not(X))),or(X,X_28)) != truth
| implies(or(X_28,X),or(X,X_28)) = truth ),
inference(resolve,[$cnf( $equal(implies(or(X_28,not(not(X))),or(X,X_28)),implies(or(X_28,X),or(X,X_28))) )],[refute_0_398,refute_0_399]) ).
cnf(refute_0_401,plain,
implies(or(X_28,X),or(X,X_28)) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_28,not(not(X))),or(X,X_28)),truth) )],[refute_0_389,refute_0_400]) ).
cnf(refute_0_402,plain,
implies(or(falsehood,X_58),or(X_58,falsehood)) = truth,
inference(subst,[],[refute_0_401:[bind(X,$fot(X_58)),bind(X_28,$fot(falsehood))]]) ).
cnf(refute_0_403,plain,
or(X,falsehood) = or(falsehood,X),
inference(subst,[],[or_commutativity:[bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_404,plain,
or(falsehood,X) = X,
inference(subst,[],[refute_0_135:[bind(Y,$fot(X))]]) ).
cnf(refute_0_405,plain,
( or(X,falsehood) != or(falsehood,X)
| or(falsehood,X) != X
| or(X,falsehood) = X ),
introduced(tautology,[equality,[$cnf( ~ $equal(or(X,falsehood),X) ),[0],$fot(or(falsehood,X))]]) ).
cnf(refute_0_406,plain,
( or(X,falsehood) != or(falsehood,X)
| or(X,falsehood) = X ),
inference(resolve,[$cnf( $equal(or(falsehood,X),X) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
or(X,falsehood) = X,
inference(resolve,[$cnf( $equal(or(X,falsehood),or(falsehood,X)) )],[refute_0_403,refute_0_406]) ).
cnf(refute_0_408,plain,
or(X_58,falsehood) = X_58,
inference(subst,[],[refute_0_407:[bind(X,$fot(X_58))]]) ).
cnf(refute_0_409,plain,
( implies(or(falsehood,X_58),or(X_58,falsehood)) != truth
| or(X_58,falsehood) != X_58
| implies(or(falsehood,X_58),X_58) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,X_58),or(X_58,falsehood)),truth) ),[0,1],$fot(X_58)]]) ).
cnf(refute_0_410,plain,
( implies(or(falsehood,X_58),or(X_58,falsehood)) != truth
| implies(or(falsehood,X_58),X_58) = truth ),
inference(resolve,[$cnf( $equal(or(X_58,falsehood),X_58) )],[refute_0_408,refute_0_409]) ).
cnf(refute_0_411,plain,
implies(or(falsehood,X_58),X_58) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,X_58),or(X_58,falsehood)),truth) )],[refute_0_402,refute_0_410]) ).
cnf(refute_0_412,plain,
implies(implies(not(X),X_25),X_25) = implies(implies(X_25,not(X)),not(X)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(X))),bind(Y,$fot(X_25))]]) ).
cnf(refute_0_413,plain,
or(X,X_25) = implies(not(X),X_25),
inference(subst,[],[or_definition:[bind(Y,$fot(X_25))]]) ).
cnf(refute_0_414,plain,
( or(X,X_25) != implies(not(X),X_25)
| implies(not(X),X_25) = or(X,X_25) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,X_25))),bind(Y0,$fot(implies(not(X),X_25)))]]) ).
cnf(refute_0_415,plain,
implies(not(X),X_25) = or(X,X_25),
inference(resolve,[$cnf( $equal(or(X,X_25),implies(not(X),X_25)) )],[refute_0_413,refute_0_414]) ).
cnf(refute_0_416,plain,
( implies(implies(not(X),X_25),X_25) != implies(implies(X_25,not(X)),not(X))
| implies(not(X),X_25) != or(X,X_25)
| implies(or(X,X_25),X_25) = implies(implies(X_25,not(X)),not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),X_25),X_25),implies(implies(X_25,not(X)),not(X))) ),[0,0],$fot(or(X,X_25))]]) ).
cnf(refute_0_417,plain,
( implies(implies(not(X),X_25),X_25) != implies(implies(X_25,not(X)),not(X))
| implies(or(X,X_25),X_25) = implies(implies(X_25,not(X)),not(X)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_25),or(X,X_25)) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
implies(or(X,X_25),X_25) = implies(implies(X_25,not(X)),not(X)),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_25),X_25),implies(implies(X_25,not(X)),not(X))) )],[refute_0_412,refute_0_417]) ).
cnf(refute_0_419,plain,
not(not(implies(X,and(X_25,X)))) = implies(X,and(X_25,X)),
inference(subst,[],[refute_0_230:[bind(Y,$fot(implies(X,and(X_25,X))))]]) ).
cnf(refute_0_420,plain,
and(X,not(X_45)) = not(or(not(X),not(not(X_45)))),
inference(subst,[],[and_definition:[bind(Y,$fot(not(X_45)))]]) ).
cnf(refute_0_421,plain,
( and(X,not(X_45)) != not(or(not(X),not(not(X_45))))
| not(not(X_45)) != X_45
| and(X,not(X_45)) = not(or(not(X),X_45)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,not(X_45)),not(or(not(X),not(not(X_45))))) ),[1,0,1],$fot(X_45)]]) ).
cnf(refute_0_422,plain,
( and(X,not(X_45)) != not(or(not(X),not(not(X_45))))
| and(X,not(X_45)) = not(or(not(X),X_45)) ),
inference(resolve,[$cnf( $equal(not(not(X_45)),X_45) )],[refute_0_245,refute_0_421]) ).
cnf(refute_0_423,plain,
and(X,not(X_45)) = not(or(not(X),X_45)),
inference(resolve,[$cnf( $equal(and(X,not(X_45)),not(or(not(X),not(not(X_45))))) )],[refute_0_420,refute_0_422]) ).
cnf(refute_0_424,plain,
or(not(X),X_45) = implies(X,X_45),
inference(subst,[],[refute_0_248:[bind(Y,$fot(X_45)),bind(X_45,$fot(X))]]) ).
cnf(refute_0_425,plain,
not(or(not(X),X_45)) = not(or(not(X),X_45)),
introduced(tautology,[refl,[$fot(not(or(not(X),X_45)))]]) ).
cnf(refute_0_426,plain,
( not(or(not(X),X_45)) != not(or(not(X),X_45))
| or(not(X),X_45) != implies(X,X_45)
| not(or(not(X),X_45)) = not(implies(X,X_45)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),X_45)),not(or(not(X),X_45))) ),[1,0],$fot(implies(X,X_45))]]) ).
cnf(refute_0_427,plain,
( or(not(X),X_45) != implies(X,X_45)
| not(or(not(X),X_45)) = not(implies(X,X_45)) ),
inference(resolve,[$cnf( $equal(not(or(not(X),X_45)),not(or(not(X),X_45))) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
not(or(not(X),X_45)) = not(implies(X,X_45)),
inference(resolve,[$cnf( $equal(or(not(X),X_45),implies(X,X_45)) )],[refute_0_424,refute_0_427]) ).
cnf(refute_0_429,plain,
( and(X,not(X_45)) != not(or(not(X),X_45))
| not(or(not(X),X_45)) != not(implies(X,X_45))
| and(X,not(X_45)) = not(implies(X,X_45)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,not(X_45)),not(implies(X,X_45))) ),[0],$fot(not(or(not(X),X_45)))]]) ).
cnf(refute_0_430,plain,
( and(X,not(X_45)) != not(or(not(X),X_45))
| and(X,not(X_45)) = not(implies(X,X_45)) ),
inference(resolve,[$cnf( $equal(not(or(not(X),X_45)),not(implies(X,X_45))) )],[refute_0_428,refute_0_429]) ).
cnf(refute_0_431,plain,
and(X,not(X_45)) = not(implies(X,X_45)),
inference(resolve,[$cnf( $equal(and(X,not(X_45)),not(or(not(X),X_45))) )],[refute_0_423,refute_0_430]) ).
cnf(refute_0_432,plain,
and(X,not(and(X_25,X))) = not(implies(X,and(X_25,X))),
inference(subst,[],[refute_0_431:[bind(X_45,$fot(and(X_25,X)))]]) ).
cnf(refute_0_433,plain,
implies(X_25,not(X)) = not(and(X_25,X)),
inference(subst,[],[refute_0_283:[bind(X,$fot(X_25)),bind(Y,$fot(X))]]) ).
cnf(refute_0_434,plain,
and(X,implies(X_25,not(X))) = and(X,implies(X_25,not(X))),
introduced(tautology,[refl,[$fot(and(X,implies(X_25,not(X))))]]) ).
cnf(refute_0_435,plain,
( and(X,implies(X_25,not(X))) != and(X,implies(X_25,not(X)))
| implies(X_25,not(X)) != not(and(X_25,X))
| and(X,implies(X_25,not(X))) = and(X,not(and(X_25,X))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,implies(X_25,not(X))),and(X,implies(X_25,not(X)))) ),[1,1],$fot(not(and(X_25,X)))]]) ).
cnf(refute_0_436,plain,
( implies(X_25,not(X)) != not(and(X_25,X))
| and(X,implies(X_25,not(X))) = and(X,not(and(X_25,X))) ),
inference(resolve,[$cnf( $equal(and(X,implies(X_25,not(X))),and(X,implies(X_25,not(X)))) )],[refute_0_434,refute_0_435]) ).
cnf(refute_0_437,plain,
and(X,implies(X_25,not(X))) = and(X,not(and(X_25,X))),
inference(resolve,[$cnf( $equal(implies(X_25,not(X)),not(and(X_25,X))) )],[refute_0_433,refute_0_436]) ).
cnf(refute_0_438,plain,
( and(X,implies(X_25,not(X))) != and(X,not(and(X_25,X)))
| and(X,not(and(X_25,X))) != not(implies(X,and(X_25,X)))
| and(X,implies(X_25,not(X))) = not(implies(X,and(X_25,X))) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(and(X,implies(X_25,not(X))))),bind(Y0,$fot(and(X,not(and(X_25,X))))),bind(Z0,$fot(not(implies(X,and(X_25,X)))))]]) ).
cnf(refute_0_439,plain,
( and(X,not(and(X_25,X))) != not(implies(X,and(X_25,X)))
| and(X,implies(X_25,not(X))) = not(implies(X,and(X_25,X))) ),
inference(resolve,[$cnf( $equal(and(X,implies(X_25,not(X))),and(X,not(and(X_25,X)))) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
and(X,implies(X_25,not(X))) = not(implies(X,and(X_25,X))),
inference(resolve,[$cnf( $equal(and(X,not(and(X_25,X))),not(implies(X,and(X_25,X)))) )],[refute_0_432,refute_0_439]) ).
cnf(refute_0_441,plain,
and(implies(X_25,not(X)),X) = and(X,implies(X_25,not(X))),
inference(subst,[],[refute_0_39:[bind(Y,$fot(implies(X_25,not(X))))]]) ).
cnf(refute_0_442,plain,
( and(X,implies(X_25,not(X))) != not(implies(X,and(X_25,X)))
| and(implies(X_25,not(X)),X) != and(X,implies(X_25,not(X)))
| and(implies(X_25,not(X)),X) = not(implies(X,and(X_25,X))) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(and(implies(X_25,not(X)),X))),bind(Y0,$fot(and(X,implies(X_25,not(X))))),bind(Z0,$fot(not(implies(X,and(X_25,X)))))]]) ).
cnf(refute_0_443,plain,
( and(X,implies(X_25,not(X))) != not(implies(X,and(X_25,X)))
| and(implies(X_25,not(X)),X) = not(implies(X,and(X_25,X))) ),
inference(resolve,[$cnf( $equal(and(implies(X_25,not(X)),X),and(X,implies(X_25,not(X)))) )],[refute_0_441,refute_0_442]) ).
cnf(refute_0_444,plain,
and(implies(X_25,not(X)),X) = not(implies(X,and(X_25,X))),
inference(resolve,[$cnf( $equal(and(X,implies(X_25,not(X))),not(implies(X,and(X_25,X)))) )],[refute_0_440,refute_0_443]) ).
cnf(refute_0_445,plain,
not(and(implies(X_25,not(X)),X)) = not(and(implies(X_25,not(X)),X)),
introduced(tautology,[refl,[$fot(not(and(implies(X_25,not(X)),X)))]]) ).
cnf(refute_0_446,plain,
( and(implies(X_25,not(X)),X) != not(implies(X,and(X_25,X)))
| not(and(implies(X_25,not(X)),X)) != not(and(implies(X_25,not(X)),X))
| not(and(implies(X_25,not(X)),X)) = not(not(implies(X,and(X_25,X)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(implies(X_25,not(X)),X)),not(and(implies(X_25,not(X)),X))) ),[1,0],$fot(not(implies(X,and(X_25,X))))]]) ).
cnf(refute_0_447,plain,
( and(implies(X_25,not(X)),X) != not(implies(X,and(X_25,X)))
| not(and(implies(X_25,not(X)),X)) = not(not(implies(X,and(X_25,X)))) ),
inference(resolve,[$cnf( $equal(not(and(implies(X_25,not(X)),X)),not(and(implies(X_25,not(X)),X))) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
not(and(implies(X_25,not(X)),X)) = not(not(implies(X,and(X_25,X)))),
inference(resolve,[$cnf( $equal(and(implies(X_25,not(X)),X),not(implies(X,and(X_25,X)))) )],[refute_0_444,refute_0_447]) ).
cnf(refute_0_449,plain,
( not(and(implies(X_25,not(X)),X)) != not(not(implies(X,and(X_25,X))))
| not(not(implies(X,and(X_25,X)))) != implies(X,and(X_25,X))
| not(and(implies(X_25,not(X)),X)) = implies(X,and(X_25,X)) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(not(and(implies(X_25,not(X)),X)))),bind(Y0,$fot(not(not(implies(X,and(X_25,X)))))),bind(Z0,$fot(implies(X,and(X_25,X))))]]) ).
cnf(refute_0_450,plain,
( not(not(implies(X,and(X_25,X)))) != implies(X,and(X_25,X))
| not(and(implies(X_25,not(X)),X)) = implies(X,and(X_25,X)) ),
inference(resolve,[$cnf( $equal(not(and(implies(X_25,not(X)),X)),not(not(implies(X,and(X_25,X))))) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
not(and(implies(X_25,not(X)),X)) = implies(X,and(X_25,X)),
inference(resolve,[$cnf( $equal(not(not(implies(X,and(X_25,X)))),implies(X,and(X_25,X))) )],[refute_0_419,refute_0_450]) ).
cnf(refute_0_452,plain,
implies(implies(X_25,not(X)),not(X)) = not(and(implies(X_25,not(X)),X)),
inference(subst,[],[refute_0_283:[bind(X,$fot(implies(X_25,not(X)))),bind(Y,$fot(X))]]) ).
cnf(refute_0_453,plain,
( implies(implies(X_25,not(X)),not(X)) != not(and(implies(X_25,not(X)),X))
| not(and(implies(X_25,not(X)),X)) != implies(X,and(X_25,X))
| implies(implies(X_25,not(X)),not(X)) = implies(X,and(X_25,X)) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(implies(implies(X_25,not(X)),not(X)))),bind(Y0,$fot(not(and(implies(X_25,not(X)),X)))),bind(Z0,$fot(implies(X,and(X_25,X))))]]) ).
cnf(refute_0_454,plain,
( not(and(implies(X_25,not(X)),X)) != implies(X,and(X_25,X))
| implies(implies(X_25,not(X)),not(X)) = implies(X,and(X_25,X)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_25,not(X)),not(X)),not(and(implies(X_25,not(X)),X))) )],[refute_0_452,refute_0_453]) ).
cnf(refute_0_455,plain,
implies(implies(X_25,not(X)),not(X)) = implies(X,and(X_25,X)),
inference(resolve,[$cnf( $equal(not(and(implies(X_25,not(X)),X)),implies(X,and(X_25,X))) )],[refute_0_451,refute_0_454]) ).
cnf(refute_0_456,plain,
( implies(implies(X_25,not(X)),not(X)) != implies(X,and(X_25,X))
| implies(or(X,X_25),X_25) != implies(implies(X_25,not(X)),not(X))
| implies(or(X,X_25),X_25) = implies(X,and(X_25,X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X,X_25),X_25),implies(implies(X_25,not(X)),not(X))) ),[1],$fot(implies(X,and(X_25,X)))]]) ).
cnf(refute_0_457,plain,
( implies(or(X,X_25),X_25) != implies(implies(X_25,not(X)),not(X))
| implies(or(X,X_25),X_25) = implies(X,and(X_25,X)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_25,not(X)),not(X)),implies(X,and(X_25,X))) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
implies(or(X,X_25),X_25) = implies(X,and(X_25,X)),
inference(resolve,[$cnf( $equal(implies(or(X,X_25),X_25),implies(implies(X_25,not(X)),not(X))) )],[refute_0_418,refute_0_457]) ).
cnf(refute_0_459,plain,
implies(or(falsehood,X_58),X_58) = implies(falsehood,and(X_58,falsehood)),
inference(subst,[],[refute_0_458:[bind(X,$fot(falsehood)),bind(X_25,$fot(X_58))]]) ).
cnf(refute_0_460,plain,
( implies(or(falsehood,X_58),X_58) != implies(falsehood,and(X_58,falsehood))
| implies(or(falsehood,X_58),X_58) != truth
| implies(falsehood,and(X_58,falsehood)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,X_58),X_58),truth) ),[0],$fot(implies(falsehood,and(X_58,falsehood)))]]) ).
cnf(refute_0_461,plain,
( implies(or(falsehood,X_58),X_58) != truth
| implies(falsehood,and(X_58,falsehood)) = truth ),
inference(resolve,[$cnf( $equal(implies(or(falsehood,X_58),X_58),implies(falsehood,and(X_58,falsehood))) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
implies(falsehood,and(X_58,falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,X_58),X_58),truth) )],[refute_0_411,refute_0_461]) ).
cnf(refute_0_463,plain,
implies(falsehood,and(X_56,falsehood)) = truth,
inference(subst,[],[refute_0_462:[bind(X_58,$fot(X_56))]]) ).
cnf(refute_0_464,plain,
implies(implies(and(X_60,falsehood),falsehood),falsehood) = implies(implies(falsehood,and(X_60,falsehood)),and(X_60,falsehood)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(and(X_60,falsehood))),bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_465,plain,
implies(falsehood,and(X_60,falsehood)) = truth,
inference(subst,[],[refute_0_462:[bind(X_58,$fot(X_60))]]) ).
cnf(refute_0_466,plain,
( implies(falsehood,and(X_60,falsehood)) != truth
| implies(implies(and(X_60,falsehood),falsehood),falsehood) != implies(implies(falsehood,and(X_60,falsehood)),and(X_60,falsehood))
| implies(implies(and(X_60,falsehood),falsehood),falsehood) = implies(truth,and(X_60,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(X_60,falsehood),falsehood),falsehood),implies(implies(falsehood,and(X_60,falsehood)),and(X_60,falsehood))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_467,plain,
( implies(implies(and(X_60,falsehood),falsehood),falsehood) != implies(implies(falsehood,and(X_60,falsehood)),and(X_60,falsehood))
| implies(implies(and(X_60,falsehood),falsehood),falsehood) = implies(truth,and(X_60,falsehood)) ),
inference(resolve,[$cnf( $equal(implies(falsehood,and(X_60,falsehood)),truth) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
implies(implies(and(X_60,falsehood),falsehood),falsehood) = implies(truth,and(X_60,falsehood)),
inference(resolve,[$cnf( $equal(implies(implies(and(X_60,falsehood),falsehood),falsehood),implies(implies(falsehood,and(X_60,falsehood)),and(X_60,falsehood))) )],[refute_0_464,refute_0_467]) ).
cnf(refute_0_469,plain,
implies(falsehood,falsehood) = truth,
inference(subst,[],[refute_0_189:[bind(X_30,$fot(falsehood))]]) ).
cnf(refute_0_470,plain,
implies(X_60,implies(falsehood,falsehood)) = implies(X_60,implies(falsehood,falsehood)),
introduced(tautology,[refl,[$fot(implies(X_60,implies(falsehood,falsehood)))]]) ).
cnf(refute_0_471,plain,
( implies(X_60,implies(falsehood,falsehood)) != implies(X_60,implies(falsehood,falsehood))
| implies(falsehood,falsehood) != truth
| implies(X_60,implies(falsehood,falsehood)) = implies(X_60,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_60,implies(falsehood,falsehood)),implies(X_60,implies(falsehood,falsehood))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_472,plain,
( implies(falsehood,falsehood) != truth
| implies(X_60,implies(falsehood,falsehood)) = implies(X_60,truth) ),
inference(resolve,[$cnf( $equal(implies(X_60,implies(falsehood,falsehood)),implies(X_60,implies(falsehood,falsehood))) )],[refute_0_470,refute_0_471]) ).
cnf(refute_0_473,plain,
implies(X_60,implies(falsehood,falsehood)) = implies(X_60,truth),
inference(resolve,[$cnf( $equal(implies(falsehood,falsehood),truth) )],[refute_0_469,refute_0_472]) ).
cnf(refute_0_474,plain,
implies(and(X_60,falsehood),falsehood) = implies(X_60,implies(falsehood,falsehood)),
inference(subst,[],[refute_0_369:[bind(Y,$fot(falsehood)),bind(X_21,$fot(X_60)),bind(X_22,$fot(falsehood))]]) ).
cnf(refute_0_475,plain,
( implies(X_60,implies(falsehood,falsehood)) != implies(X_60,truth)
| implies(and(X_60,falsehood),falsehood) != implies(X_60,implies(falsehood,falsehood))
| implies(and(X_60,falsehood),falsehood) = implies(X_60,truth) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(implies(and(X_60,falsehood),falsehood))),bind(Y0,$fot(implies(X_60,implies(falsehood,falsehood)))),bind(Z0,$fot(implies(X_60,truth)))]]) ).
cnf(refute_0_476,plain,
( implies(X_60,implies(falsehood,falsehood)) != implies(X_60,truth)
| implies(and(X_60,falsehood),falsehood) = implies(X_60,truth) ),
inference(resolve,[$cnf( $equal(implies(and(X_60,falsehood),falsehood),implies(X_60,implies(falsehood,falsehood))) )],[refute_0_474,refute_0_475]) ).
cnf(refute_0_477,plain,
implies(and(X_60,falsehood),falsehood) = implies(X_60,truth),
inference(resolve,[$cnf( $equal(implies(X_60,implies(falsehood,falsehood)),implies(X_60,truth)) )],[refute_0_473,refute_0_476]) ).
cnf(refute_0_478,plain,
implies(implies(and(X_60,falsehood),falsehood),falsehood) = implies(implies(and(X_60,falsehood),falsehood),falsehood),
introduced(tautology,[refl,[$fot(implies(implies(and(X_60,falsehood),falsehood),falsehood))]]) ).
cnf(refute_0_479,plain,
( implies(and(X_60,falsehood),falsehood) != implies(X_60,truth)
| implies(implies(and(X_60,falsehood),falsehood),falsehood) != implies(implies(and(X_60,falsehood),falsehood),falsehood)
| implies(implies(and(X_60,falsehood),falsehood),falsehood) = implies(implies(X_60,truth),falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(X_60,falsehood),falsehood),falsehood),implies(implies(and(X_60,falsehood),falsehood),falsehood)) ),[1,0],$fot(implies(X_60,truth))]]) ).
cnf(refute_0_480,plain,
( implies(and(X_60,falsehood),falsehood) != implies(X_60,truth)
| implies(implies(and(X_60,falsehood),falsehood),falsehood) = implies(implies(X_60,truth),falsehood) ),
inference(resolve,[$cnf( $equal(implies(implies(and(X_60,falsehood),falsehood),falsehood),implies(implies(and(X_60,falsehood),falsehood),falsehood)) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
implies(implies(and(X_60,falsehood),falsehood),falsehood) = implies(implies(X_60,truth),falsehood),
inference(resolve,[$cnf( $equal(implies(and(X_60,falsehood),falsehood),implies(X_60,truth)) )],[refute_0_477,refute_0_480]) ).
cnf(refute_0_482,plain,
( implies(implies(and(X_60,falsehood),falsehood),falsehood) != implies(implies(X_60,truth),falsehood)
| implies(implies(and(X_60,falsehood),falsehood),falsehood) != implies(truth,and(X_60,falsehood))
| implies(implies(X_60,truth),falsehood) = implies(truth,and(X_60,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(X_60,falsehood),falsehood),falsehood),implies(truth,and(X_60,falsehood))) ),[0],$fot(implies(implies(X_60,truth),falsehood))]]) ).
cnf(refute_0_483,plain,
( implies(implies(and(X_60,falsehood),falsehood),falsehood) != implies(truth,and(X_60,falsehood))
| implies(implies(X_60,truth),falsehood) = implies(truth,and(X_60,falsehood)) ),
inference(resolve,[$cnf( $equal(implies(implies(and(X_60,falsehood),falsehood),falsehood),implies(implies(X_60,truth),falsehood)) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
implies(truth,and(X_60,falsehood)) = and(X_60,falsehood),
inference(subst,[],[wajsberg_1:[bind(X,$fot(and(X_60,falsehood)))]]) ).
cnf(refute_0_485,plain,
( implies(implies(X_60,truth),falsehood) != implies(truth,and(X_60,falsehood))
| implies(truth,and(X_60,falsehood)) != and(X_60,falsehood)
| implies(implies(X_60,truth),falsehood) = and(X_60,falsehood) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X_60,truth),falsehood),and(X_60,falsehood)) ),[0],$fot(implies(truth,and(X_60,falsehood)))]]) ).
cnf(refute_0_486,plain,
( implies(implies(X_60,truth),falsehood) != implies(truth,and(X_60,falsehood))
| implies(implies(X_60,truth),falsehood) = and(X_60,falsehood) ),
inference(resolve,[$cnf( $equal(implies(truth,and(X_60,falsehood)),and(X_60,falsehood)) )],[refute_0_484,refute_0_485]) ).
cnf(refute_0_487,plain,
( implies(implies(and(X_60,falsehood),falsehood),falsehood) != implies(truth,and(X_60,falsehood))
| implies(implies(X_60,truth),falsehood) = and(X_60,falsehood) ),
inference(resolve,[$cnf( $equal(implies(implies(X_60,truth),falsehood),implies(truth,and(X_60,falsehood))) )],[refute_0_483,refute_0_486]) ).
cnf(refute_0_488,plain,
implies(implies(X_60,truth),falsehood) = and(X_60,falsehood),
inference(resolve,[$cnf( $equal(implies(implies(and(X_60,falsehood),falsehood),falsehood),implies(truth,and(X_60,falsehood))) )],[refute_0_468,refute_0_487]) ).
cnf(refute_0_489,plain,
implies(implies(X_56,truth),falsehood) = and(X_56,falsehood),
inference(subst,[],[refute_0_488:[bind(X_60,$fot(X_56))]]) ).
cnf(refute_0_490,plain,
implies(falsehood,implies(implies(X_56,truth),falsehood)) = implies(falsehood,implies(implies(X_56,truth),falsehood)),
introduced(tautology,[refl,[$fot(implies(falsehood,implies(implies(X_56,truth),falsehood)))]]) ).
cnf(refute_0_491,plain,
( implies(falsehood,implies(implies(X_56,truth),falsehood)) != implies(falsehood,implies(implies(X_56,truth),falsehood))
| implies(implies(X_56,truth),falsehood) != and(X_56,falsehood)
| implies(falsehood,implies(implies(X_56,truth),falsehood)) = implies(falsehood,and(X_56,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(falsehood,implies(implies(X_56,truth),falsehood)),implies(falsehood,implies(implies(X_56,truth),falsehood))) ),[1,1],$fot(and(X_56,falsehood))]]) ).
cnf(refute_0_492,plain,
( implies(implies(X_56,truth),falsehood) != and(X_56,falsehood)
| implies(falsehood,implies(implies(X_56,truth),falsehood)) = implies(falsehood,and(X_56,falsehood)) ),
inference(resolve,[$cnf( $equal(implies(falsehood,implies(implies(X_56,truth),falsehood)),implies(falsehood,implies(implies(X_56,truth),falsehood))) )],[refute_0_490,refute_0_491]) ).
cnf(refute_0_493,plain,
implies(falsehood,implies(implies(X_56,truth),falsehood)) = implies(falsehood,and(X_56,falsehood)),
inference(resolve,[$cnf( $equal(implies(implies(X_56,truth),falsehood),and(X_56,falsehood)) )],[refute_0_489,refute_0_492]) ).
cnf(refute_0_494,plain,
( implies(falsehood,and(X_56,falsehood)) != truth
| implies(falsehood,implies(implies(X_56,truth),falsehood)) != implies(falsehood,and(X_56,falsehood))
| implies(falsehood,implies(implies(X_56,truth),falsehood)) = truth ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(implies(falsehood,implies(implies(X_56,truth),falsehood)))),bind(Y0,$fot(implies(falsehood,and(X_56,falsehood)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_495,plain,
( implies(falsehood,and(X_56,falsehood)) != truth
| implies(falsehood,implies(implies(X_56,truth),falsehood)) = truth ),
inference(resolve,[$cnf( $equal(implies(falsehood,implies(implies(X_56,truth),falsehood)),implies(falsehood,and(X_56,falsehood))) )],[refute_0_493,refute_0_494]) ).
cnf(refute_0_496,plain,
implies(falsehood,implies(implies(X_56,truth),falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(falsehood,and(X_56,falsehood)),truth) )],[refute_0_463,refute_0_495]) ).
cnf(refute_0_497,plain,
implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) = implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood),
introduced(tautology,[refl,[$fot(implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood))]]) ).
cnf(refute_0_498,plain,
( implies(falsehood,implies(implies(X_56,truth),falsehood)) != truth
| implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) != implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood)
| implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) = implies(truth,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood),implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_499,plain,
( implies(falsehood,implies(implies(X_56,truth),falsehood)) != truth
| implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) = implies(truth,falsehood) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood),implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood)) )],[refute_0_497,refute_0_498]) ).
cnf(refute_0_500,plain,
implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) = implies(truth,falsehood),
inference(resolve,[$cnf( $equal(implies(falsehood,implies(implies(X_56,truth),falsehood)),truth) )],[refute_0_496,refute_0_499]) ).
cnf(refute_0_501,plain,
( implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) != implies(truth,falsehood)
| implies(truth,falsehood) != falsehood
| implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) = falsehood ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood))),bind(Y0,$fot(implies(truth,falsehood))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_502,plain,
( implies(truth,falsehood) != falsehood
| implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) = falsehood ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood),implies(truth,falsehood)) )],[refute_0_500,refute_0_501]) ).
cnf(refute_0_503,plain,
implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) = falsehood,
inference(resolve,[$cnf( $equal(implies(truth,falsehood),falsehood) )],[refute_0_382,refute_0_502]) ).
cnf(refute_0_504,plain,
( implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) != and(falsehood,implies(X_56,truth))
| implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) != falsehood
| falsehood = and(falsehood,implies(X_56,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood),and(falsehood,implies(X_56,truth))) ),[0],$fot(falsehood)]]) ).
cnf(refute_0_505,plain,
( implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood) != and(falsehood,implies(X_56,truth))
| falsehood = and(falsehood,implies(X_56,truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood),falsehood) )],[refute_0_503,refute_0_504]) ).
cnf(refute_0_506,plain,
falsehood = and(falsehood,implies(X_56,truth)),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,implies(implies(X_56,truth),falsehood)),falsehood),and(falsehood,implies(X_56,truth))) )],[refute_0_381,refute_0_505]) ).
cnf(refute_0_507,plain,
( falsehood != and(falsehood,implies(X_56,truth))
| and(falsehood,implies(X_56,truth)) = falsehood ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(falsehood)),bind(Y0,$fot(and(falsehood,implies(X_56,truth))))]]) ).
cnf(refute_0_508,plain,
and(falsehood,implies(X_56,truth)) = falsehood,
inference(resolve,[$cnf( $equal(falsehood,and(falsehood,implies(X_56,truth))) )],[refute_0_506,refute_0_507]) ).
cnf(refute_0_509,plain,
and(falsehood,implies(falsehood,truth)) = falsehood,
inference(subst,[],[refute_0_508:[bind(X_56,$fot(falsehood))]]) ).
cnf(refute_0_510,plain,
and(falsehood,and(falsehood,implies(falsehood,truth))) = and(falsehood,and(falsehood,implies(falsehood,truth))),
introduced(tautology,[refl,[$fot(and(falsehood,and(falsehood,implies(falsehood,truth))))]]) ).
cnf(refute_0_511,plain,
( and(falsehood,and(falsehood,implies(falsehood,truth))) != and(falsehood,and(falsehood,implies(falsehood,truth)))
| and(falsehood,implies(falsehood,truth)) != falsehood
| and(falsehood,and(falsehood,implies(falsehood,truth))) = and(falsehood,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(and(falsehood,and(falsehood,implies(falsehood,truth))),and(falsehood,and(falsehood,implies(falsehood,truth)))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_512,plain,
( and(falsehood,implies(falsehood,truth)) != falsehood
| and(falsehood,and(falsehood,implies(falsehood,truth))) = and(falsehood,falsehood) ),
inference(resolve,[$cnf( $equal(and(falsehood,and(falsehood,implies(falsehood,truth))),and(falsehood,and(falsehood,implies(falsehood,truth)))) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
and(falsehood,and(falsehood,implies(falsehood,truth))) = and(falsehood,falsehood),
inference(resolve,[$cnf( $equal(and(falsehood,implies(falsehood,truth)),falsehood) )],[refute_0_509,refute_0_512]) ).
cnf(refute_0_514,plain,
( and(falsehood,and(falsehood,implies(falsehood,truth))) != and(falsehood,falsehood)
| and(falsehood,and(falsehood,implies(falsehood,truth))) != falsehood
| and(falsehood,falsehood) = falsehood ),
introduced(tautology,[equality,[$cnf( $equal(and(falsehood,and(falsehood,implies(falsehood,truth))),falsehood) ),[0],$fot(and(falsehood,falsehood))]]) ).
cnf(refute_0_515,plain,
( and(falsehood,and(falsehood,implies(falsehood,truth))) != falsehood
| and(falsehood,falsehood) = falsehood ),
inference(resolve,[$cnf( $equal(and(falsehood,and(falsehood,implies(falsehood,truth))),and(falsehood,falsehood)) )],[refute_0_513,refute_0_514]) ).
cnf(refute_0_516,plain,
and(falsehood,falsehood) = falsehood,
inference(resolve,[$cnf( $equal(and(falsehood,and(falsehood,implies(falsehood,truth))),falsehood) )],[refute_0_301,refute_0_515]) ).
cnf(refute_0_517,plain,
( and(and(falsehood,falsehood),Z) != and(falsehood,and(falsehood,Z))
| and(falsehood,falsehood) != falsehood
| and(falsehood,Z) = and(falsehood,and(falsehood,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(falsehood,falsehood),Z),and(falsehood,and(falsehood,Z))) ),[0,0],$fot(falsehood)]]) ).
cnf(refute_0_518,plain,
( and(and(falsehood,falsehood),Z) != and(falsehood,and(falsehood,Z))
| and(falsehood,Z) = and(falsehood,and(falsehood,Z)) ),
inference(resolve,[$cnf( $equal(and(falsehood,falsehood),falsehood) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
and(falsehood,Z) = and(falsehood,and(falsehood,Z)),
inference(resolve,[$cnf( $equal(and(and(falsehood,falsehood),Z),and(falsehood,and(falsehood,Z))) )],[refute_0_253,refute_0_518]) ).
cnf(refute_0_520,plain,
and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))) = and(X_50,and(falsehood,and(falsehood,implies(falsehood,truth)))),
inference(subst,[],[and_associativity:[bind(X,$fot(X_50)),bind(Y,$fot(falsehood)),bind(Z,$fot(and(falsehood,implies(falsehood,truth))))]]) ).
cnf(refute_0_521,plain,
( and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))) != and(X_50,and(falsehood,and(falsehood,implies(falsehood,truth))))
| and(falsehood,and(falsehood,implies(falsehood,truth))) != falsehood
| and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))) = and(X_50,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))),and(X_50,and(falsehood,and(falsehood,implies(falsehood,truth))))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_522,plain,
( and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))) != and(X_50,and(falsehood,and(falsehood,implies(falsehood,truth))))
| and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))) = and(X_50,falsehood) ),
inference(resolve,[$cnf( $equal(and(falsehood,and(falsehood,implies(falsehood,truth))),falsehood) )],[refute_0_301,refute_0_521]) ).
cnf(refute_0_523,plain,
and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))) = and(X_50,falsehood),
inference(resolve,[$cnf( $equal(and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))),and(X_50,and(falsehood,and(falsehood,implies(falsehood,truth))))) )],[refute_0_520,refute_0_522]) ).
cnf(refute_0_524,plain,
and(and(X_50,falsehood),implies(falsehood,truth)) = and(X_50,and(falsehood,implies(falsehood,truth))),
inference(subst,[],[and_associativity:[bind(X,$fot(X_50)),bind(Y,$fot(falsehood)),bind(Z,$fot(implies(falsehood,truth)))]]) ).
cnf(refute_0_525,plain,
and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth))) = and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth))),
introduced(tautology,[refl,[$fot(and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth))))]]) ).
cnf(refute_0_526,plain,
( and(and(X_50,falsehood),implies(falsehood,truth)) != and(X_50,and(falsehood,implies(falsehood,truth)))
| and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth))) != and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth)))
| and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth))) = and(falsehood,and(X_50,and(falsehood,implies(falsehood,truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth))),and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth)))) ),[1,1],$fot(and(X_50,and(falsehood,implies(falsehood,truth))))]]) ).
cnf(refute_0_527,plain,
( and(and(X_50,falsehood),implies(falsehood,truth)) != and(X_50,and(falsehood,implies(falsehood,truth)))
| and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth))) = and(falsehood,and(X_50,and(falsehood,implies(falsehood,truth)))) ),
inference(resolve,[$cnf( $equal(and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth))),and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth)))) )],[refute_0_525,refute_0_526]) ).
cnf(refute_0_528,plain,
and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth))) = and(falsehood,and(X_50,and(falsehood,implies(falsehood,truth)))),
inference(resolve,[$cnf( $equal(and(and(X_50,falsehood),implies(falsehood,truth)),and(X_50,and(falsehood,implies(falsehood,truth)))) )],[refute_0_524,refute_0_527]) ).
cnf(refute_0_529,plain,
and(and(X_50,X_51),X_52) = and(X_50,and(X_51,X_52)),
inference(subst,[],[and_associativity:[bind(X,$fot(X_50)),bind(Y,$fot(X_51)),bind(Z,$fot(X_52))]]) ).
cnf(refute_0_530,plain,
and(X_51,X_50) = and(X_50,X_51),
inference(subst,[],[and_commutativity:[bind(X,$fot(X_51)),bind(Y,$fot(X_50))]]) ).
cnf(refute_0_531,plain,
( and(X_51,X_50) != and(X_50,X_51)
| and(X_50,X_51) = and(X_51,X_50) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_51,X_50))),bind(Y0,$fot(and(X_50,X_51)))]]) ).
cnf(refute_0_532,plain,
and(X_50,X_51) = and(X_51,X_50),
inference(resolve,[$cnf( $equal(and(X_51,X_50),and(X_50,X_51)) )],[refute_0_530,refute_0_531]) ).
cnf(refute_0_533,plain,
( and(X_50,X_51) != and(X_51,X_50)
| and(and(X_50,X_51),X_52) != and(X_50,and(X_51,X_52))
| and(and(X_51,X_50),X_52) = and(X_50,and(X_51,X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(X_50,X_51),X_52),and(X_50,and(X_51,X_52))) ),[0,0],$fot(and(X_51,X_50))]]) ).
cnf(refute_0_534,plain,
( and(and(X_50,X_51),X_52) != and(X_50,and(X_51,X_52))
| and(and(X_51,X_50),X_52) = and(X_50,and(X_51,X_52)) ),
inference(resolve,[$cnf( $equal(and(X_50,X_51),and(X_51,X_50)) )],[refute_0_532,refute_0_533]) ).
cnf(refute_0_535,plain,
and(and(X_51,X_50),X_52) = and(X_50,and(X_51,X_52)),
inference(resolve,[$cnf( $equal(and(and(X_50,X_51),X_52),and(X_50,and(X_51,X_52))) )],[refute_0_529,refute_0_534]) ).
cnf(refute_0_536,plain,
and(and(X_51,X_50),X_52) = and(X_51,and(X_50,X_52)),
inference(subst,[],[and_associativity:[bind(X,$fot(X_51)),bind(Y,$fot(X_50)),bind(Z,$fot(X_52))]]) ).
cnf(refute_0_537,plain,
( and(and(X_51,X_50),X_52) != and(X_50,and(X_51,X_52))
| and(and(X_51,X_50),X_52) != and(X_51,and(X_50,X_52))
| and(X_51,and(X_50,X_52)) = and(X_50,and(X_51,X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(X_51,X_50),X_52),and(X_50,and(X_51,X_52))) ),[0],$fot(and(X_51,and(X_50,X_52)))]]) ).
cnf(refute_0_538,plain,
( and(and(X_51,X_50),X_52) != and(X_50,and(X_51,X_52))
| and(X_51,and(X_50,X_52)) = and(X_50,and(X_51,X_52)) ),
inference(resolve,[$cnf( $equal(and(and(X_51,X_50),X_52),and(X_51,and(X_50,X_52))) )],[refute_0_536,refute_0_537]) ).
cnf(refute_0_539,plain,
and(X_51,and(X_50,X_52)) = and(X_50,and(X_51,X_52)),
inference(resolve,[$cnf( $equal(and(and(X_51,X_50),X_52),and(X_50,and(X_51,X_52))) )],[refute_0_535,refute_0_538]) ).
cnf(refute_0_540,plain,
( and(X_51,and(X_50,X_52)) != and(X_50,and(X_51,X_52))
| and(X_50,and(X_51,X_52)) = and(X_51,and(X_50,X_52)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_51,and(X_50,X_52)))),bind(Y0,$fot(and(X_50,and(X_51,X_52))))]]) ).
cnf(refute_0_541,plain,
and(X_50,and(X_51,X_52)) = and(X_51,and(X_50,X_52)),
inference(resolve,[$cnf( $equal(and(X_51,and(X_50,X_52)),and(X_50,and(X_51,X_52))) )],[refute_0_539,refute_0_540]) ).
cnf(refute_0_542,plain,
and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))) = and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth))),
inference(subst,[],[refute_0_541:[bind(X_50,$fot(and(X_50,falsehood))),bind(X_51,$fot(falsehood)),bind(X_52,$fot(implies(falsehood,truth)))]]) ).
cnf(refute_0_543,plain,
( and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))) != and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth)))
| and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth))) != and(falsehood,and(X_50,and(falsehood,implies(falsehood,truth))))
| and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))) = and(falsehood,and(X_50,and(falsehood,implies(falsehood,truth)))) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))))),bind(Y0,$fot(and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth))))),bind(Z0,$fot(and(falsehood,and(X_50,and(falsehood,implies(falsehood,truth))))))]]) ).
cnf(refute_0_544,plain,
( and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth))) != and(falsehood,and(X_50,and(falsehood,implies(falsehood,truth))))
| and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))) = and(falsehood,and(X_50,and(falsehood,implies(falsehood,truth)))) ),
inference(resolve,[$cnf( $equal(and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))),and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth)))) )],[refute_0_542,refute_0_543]) ).
cnf(refute_0_545,plain,
and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))) = and(falsehood,and(X_50,and(falsehood,implies(falsehood,truth)))),
inference(resolve,[$cnf( $equal(and(falsehood,and(and(X_50,falsehood),implies(falsehood,truth))),and(falsehood,and(X_50,and(falsehood,implies(falsehood,truth))))) )],[refute_0_528,refute_0_544]) ).
cnf(refute_0_546,plain,
( and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))) != and(X_50,falsehood)
| and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))) != and(falsehood,and(X_50,and(falsehood,implies(falsehood,truth))))
| and(falsehood,and(X_50,and(falsehood,implies(falsehood,truth)))) = and(X_50,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))),and(X_50,falsehood)) ),[0],$fot(and(falsehood,and(X_50,and(falsehood,implies(falsehood,truth)))))]]) ).
cnf(refute_0_547,plain,
( and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))) != and(X_50,falsehood)
| and(falsehood,and(X_50,and(falsehood,implies(falsehood,truth)))) = and(X_50,falsehood) ),
inference(resolve,[$cnf( $equal(and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))),and(falsehood,and(X_50,and(falsehood,implies(falsehood,truth))))) )],[refute_0_545,refute_0_546]) ).
cnf(refute_0_548,plain,
and(falsehood,and(X_50,and(falsehood,implies(falsehood,truth)))) = and(X_50,falsehood),
inference(resolve,[$cnf( $equal(and(and(X_50,falsehood),and(falsehood,implies(falsehood,truth))),and(X_50,falsehood)) )],[refute_0_523,refute_0_547]) ).
cnf(refute_0_549,plain,
and(falsehood,and(and(X,Y),and(falsehood,implies(falsehood,truth)))) = and(and(X,Y),falsehood),
inference(subst,[],[refute_0_548:[bind(X_50,$fot(and(X,Y)))]]) ).
cnf(refute_0_550,plain,
and(and(X,Y),and(falsehood,implies(falsehood,truth))) = and(X,and(Y,and(falsehood,implies(falsehood,truth)))),
inference(subst,[],[and_associativity:[bind(Z,$fot(and(falsehood,implies(falsehood,truth))))]]) ).
cnf(refute_0_551,plain,
( and(and(X,Y),and(falsehood,implies(falsehood,truth))) != and(X,and(Y,and(falsehood,implies(falsehood,truth))))
| and(falsehood,and(and(X,Y),and(falsehood,implies(falsehood,truth)))) != and(and(X,Y),falsehood)
| and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))) = and(and(X,Y),falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(and(falsehood,and(and(X,Y),and(falsehood,implies(falsehood,truth)))),and(and(X,Y),falsehood)) ),[0,1],$fot(and(X,and(Y,and(falsehood,implies(falsehood,truth)))))]]) ).
cnf(refute_0_552,plain,
( and(falsehood,and(and(X,Y),and(falsehood,implies(falsehood,truth)))) != and(and(X,Y),falsehood)
| and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))) = and(and(X,Y),falsehood) ),
inference(resolve,[$cnf( $equal(and(and(X,Y),and(falsehood,implies(falsehood,truth))),and(X,and(Y,and(falsehood,implies(falsehood,truth))))) )],[refute_0_550,refute_0_551]) ).
cnf(refute_0_553,plain,
and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))) = and(and(X,Y),falsehood),
inference(resolve,[$cnf( $equal(and(falsehood,and(and(X,Y),and(falsehood,implies(falsehood,truth)))),and(and(X,Y),falsehood)) )],[refute_0_549,refute_0_552]) ).
cnf(refute_0_554,plain,
and(and(X,Y),falsehood) = and(falsehood,and(X,Y)),
inference(subst,[],[refute_0_39:[bind(X,$fot(falsehood)),bind(Y,$fot(and(X,Y)))]]) ).
cnf(refute_0_555,plain,
( and(and(X,Y),falsehood) != and(falsehood,and(X,Y))
| and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))) != and(and(X,Y),falsehood)
| and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))) = and(falsehood,and(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))),and(and(X,Y),falsehood)) ),[1],$fot(and(falsehood,and(X,Y)))]]) ).
cnf(refute_0_556,plain,
( and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))) != and(and(X,Y),falsehood)
| and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))) = and(falsehood,and(X,Y)) ),
inference(resolve,[$cnf( $equal(and(and(X,Y),falsehood),and(falsehood,and(X,Y))) )],[refute_0_554,refute_0_555]) ).
cnf(refute_0_557,plain,
and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))) = and(falsehood,and(X,Y)),
inference(resolve,[$cnf( $equal(and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))),and(and(X,Y),falsehood)) )],[refute_0_553,refute_0_556]) ).
cnf(refute_0_558,plain,
and(Y,and(falsehood,implies(falsehood,truth))) = and(Y,and(falsehood,implies(falsehood,truth))),
introduced(tautology,[refl,[$fot(and(Y,and(falsehood,implies(falsehood,truth))))]]) ).
cnf(refute_0_559,plain,
( and(Y,and(falsehood,implies(falsehood,truth))) != and(Y,and(falsehood,implies(falsehood,truth)))
| and(falsehood,implies(falsehood,truth)) != falsehood
| and(Y,and(falsehood,implies(falsehood,truth))) = and(Y,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(and(Y,and(falsehood,implies(falsehood,truth))),and(Y,and(falsehood,implies(falsehood,truth)))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_560,plain,
( and(falsehood,implies(falsehood,truth)) != falsehood
| and(Y,and(falsehood,implies(falsehood,truth))) = and(Y,falsehood) ),
inference(resolve,[$cnf( $equal(and(Y,and(falsehood,implies(falsehood,truth))),and(Y,and(falsehood,implies(falsehood,truth)))) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
and(Y,and(falsehood,implies(falsehood,truth))) = and(Y,falsehood),
inference(resolve,[$cnf( $equal(and(falsehood,implies(falsehood,truth)),falsehood) )],[refute_0_509,refute_0_560]) ).
cnf(refute_0_562,plain,
and(X,and(Y,and(falsehood,implies(falsehood,truth)))) = and(X,and(Y,and(falsehood,implies(falsehood,truth)))),
introduced(tautology,[refl,[$fot(and(X,and(Y,and(falsehood,implies(falsehood,truth)))))]]) ).
cnf(refute_0_563,plain,
( and(X,and(Y,and(falsehood,implies(falsehood,truth)))) != and(X,and(Y,and(falsehood,implies(falsehood,truth))))
| and(Y,and(falsehood,implies(falsehood,truth))) != and(Y,falsehood)
| and(X,and(Y,and(falsehood,implies(falsehood,truth)))) = and(X,and(Y,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,and(Y,and(falsehood,implies(falsehood,truth)))),and(X,and(Y,and(falsehood,implies(falsehood,truth))))) ),[1,1],$fot(and(Y,falsehood))]]) ).
cnf(refute_0_564,plain,
( and(Y,and(falsehood,implies(falsehood,truth))) != and(Y,falsehood)
| and(X,and(Y,and(falsehood,implies(falsehood,truth)))) = and(X,and(Y,falsehood)) ),
inference(resolve,[$cnf( $equal(and(X,and(Y,and(falsehood,implies(falsehood,truth)))),and(X,and(Y,and(falsehood,implies(falsehood,truth))))) )],[refute_0_562,refute_0_563]) ).
cnf(refute_0_565,plain,
and(X,and(Y,and(falsehood,implies(falsehood,truth)))) = and(X,and(Y,falsehood)),
inference(resolve,[$cnf( $equal(and(Y,and(falsehood,implies(falsehood,truth))),and(Y,falsehood)) )],[refute_0_561,refute_0_564]) ).
cnf(refute_0_566,plain,
and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))) = and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))),
introduced(tautology,[refl,[$fot(and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))))]]) ).
cnf(refute_0_567,plain,
( and(X,and(Y,and(falsehood,implies(falsehood,truth)))) != and(X,and(Y,falsehood))
| and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))) != and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth)))))
| and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))) = and(falsehood,and(X,and(Y,falsehood))) ),
introduced(tautology,[equality,[$cnf( $equal(and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))),and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth)))))) ),[1,1],$fot(and(X,and(Y,falsehood)))]]) ).
cnf(refute_0_568,plain,
( and(X,and(Y,and(falsehood,implies(falsehood,truth)))) != and(X,and(Y,falsehood))
| and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))) = and(falsehood,and(X,and(Y,falsehood))) ),
inference(resolve,[$cnf( $equal(and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))),and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth)))))) )],[refute_0_566,refute_0_567]) ).
cnf(refute_0_569,plain,
and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))) = and(falsehood,and(X,and(Y,falsehood))),
inference(resolve,[$cnf( $equal(and(X,and(Y,and(falsehood,implies(falsehood,truth)))),and(X,and(Y,falsehood))) )],[refute_0_565,refute_0_568]) ).
cnf(refute_0_570,plain,
( and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))) != and(falsehood,and(X,Y))
| and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))) != and(falsehood,and(X,and(Y,falsehood)))
| and(falsehood,and(X,and(Y,falsehood))) = and(falsehood,and(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))),and(falsehood,and(X,Y))) ),[0],$fot(and(falsehood,and(X,and(Y,falsehood))))]]) ).
cnf(refute_0_571,plain,
( and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))) != and(falsehood,and(X,Y))
| and(falsehood,and(X,and(Y,falsehood))) = and(falsehood,and(X,Y)) ),
inference(resolve,[$cnf( $equal(and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))),and(falsehood,and(X,and(Y,falsehood)))) )],[refute_0_569,refute_0_570]) ).
cnf(refute_0_572,plain,
and(falsehood,and(X,and(Y,falsehood))) = and(falsehood,and(X,Y)),
inference(resolve,[$cnf( $equal(and(falsehood,and(X,and(Y,and(falsehood,implies(falsehood,truth))))),and(falsehood,and(X,Y))) )],[refute_0_557,refute_0_571]) ).
cnf(refute_0_573,plain,
implies(implies(X_37,truth),implies(implies(truth,X_39),implies(X_37,X_39))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_37)),bind(Y,$fot(truth)),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_574,plain,
implies(truth,X_39) = X_39,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_39))]]) ).
cnf(refute_0_575,plain,
( implies(implies(X_37,truth),implies(implies(truth,X_39),implies(X_37,X_39))) != truth
| implies(truth,X_39) != X_39
| implies(implies(X_37,truth),implies(X_39,implies(X_37,X_39))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_37,truth),implies(implies(truth,X_39),implies(X_37,X_39))),truth) ),[0,1,0],$fot(X_39)]]) ).
cnf(refute_0_576,plain,
( implies(implies(X_37,truth),implies(implies(truth,X_39),implies(X_37,X_39))) != truth
| implies(implies(X_37,truth),implies(X_39,implies(X_37,X_39))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_39),X_39) )],[refute_0_574,refute_0_575]) ).
cnf(refute_0_577,plain,
implies(implies(X_37,truth),implies(X_39,implies(X_37,X_39))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_37,truth),implies(implies(truth,X_39),implies(X_37,X_39))),truth) )],[refute_0_573,refute_0_576]) ).
cnf(refute_0_578,plain,
implies(implies(falsehood,truth),implies(and(X_58,falsehood),implies(falsehood,and(X_58,falsehood)))) = truth,
inference(subst,[],[refute_0_577:[bind(X_37,$fot(falsehood)),bind(X_39,$fot(and(X_58,falsehood)))]]) ).
cnf(refute_0_579,plain,
( implies(falsehood,and(X_58,falsehood)) != truth
| implies(implies(falsehood,truth),implies(and(X_58,falsehood),implies(falsehood,and(X_58,falsehood)))) != truth
| implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,truth),implies(and(X_58,falsehood),implies(falsehood,and(X_58,falsehood)))),truth) ),[0,1,1],$fot(truth)]]) ).
cnf(refute_0_580,plain,
( implies(implies(falsehood,truth),implies(and(X_58,falsehood),implies(falsehood,and(X_58,falsehood)))) != truth
| implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(falsehood,and(X_58,falsehood)),truth) )],[refute_0_462,refute_0_579]) ).
cnf(refute_0_581,plain,
implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,truth),implies(and(X_58,falsehood),implies(falsehood,and(X_58,falsehood)))),truth) )],[refute_0_578,refute_0_580]) ).
cnf(refute_0_582,plain,
implies(and(X_58,falsehood),truth) = implies(X_58,implies(falsehood,truth)),
inference(subst,[],[refute_0_369:[bind(Y,$fot(truth)),bind(X_21,$fot(X_58)),bind(X_22,$fot(falsehood))]]) ).
cnf(refute_0_583,plain,
implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)) = implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)),
introduced(tautology,[refl,[$fot(implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)))]]) ).
cnf(refute_0_584,plain,
( implies(and(X_58,falsehood),truth) != implies(X_58,implies(falsehood,truth))
| implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)) != implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth))
| implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)) = implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)),implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth))) ),[1,1],$fot(implies(X_58,implies(falsehood,truth)))]]) ).
cnf(refute_0_585,plain,
( implies(and(X_58,falsehood),truth) != implies(X_58,implies(falsehood,truth))
| implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)) = implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)),implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth))) )],[refute_0_583,refute_0_584]) ).
cnf(refute_0_586,plain,
implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)) = implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))),
inference(resolve,[$cnf( $equal(implies(and(X_58,falsehood),truth),implies(X_58,implies(falsehood,truth))) )],[refute_0_582,refute_0_585]) ).
cnf(refute_0_587,plain,
( implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)) != implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth)))
| implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)) != truth
| implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)),truth) ),[0],$fot(implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))))]]) ).
cnf(refute_0_588,plain,
( implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)) != truth
| implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)),implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth)))) )],[refute_0_586,refute_0_587]) ).
cnf(refute_0_589,plain,
implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,truth),implies(and(X_58,falsehood),truth)),truth) )],[refute_0_581,refute_0_588]) ).
cnf(refute_0_590,plain,
implies(truth,implies(X_58,truth)) = implies(X_58,truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_58,truth)))]]) ).
cnf(refute_0_591,plain,
implies(implies(implies(falsehood,implies(X_64,truth)),implies(falsehood,truth)),implies(falsehood,truth)) = implies(implies(implies(falsehood,truth),implies(falsehood,implies(X_64,truth))),implies(falsehood,implies(X_64,truth))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(falsehood,implies(X_64,truth)))),bind(Y,$fot(implies(falsehood,truth)))]]) ).
cnf(refute_0_592,plain,
implies(implies(falsehood,truth),implies(and(falsehood,X_60),implies(falsehood,and(falsehood,X_60)))) = truth,
inference(subst,[],[refute_0_577:[bind(X_37,$fot(falsehood)),bind(X_39,$fot(and(falsehood,X_60)))]]) ).
cnf(refute_0_593,plain,
and(falsehood,X_60) = and(X_60,falsehood),
inference(subst,[],[and_commutativity:[bind(X,$fot(falsehood)),bind(Y,$fot(X_60))]]) ).
cnf(refute_0_594,plain,
( and(falsehood,X_60) != and(X_60,falsehood)
| and(X_60,falsehood) = and(falsehood,X_60) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(falsehood,X_60))),bind(Y0,$fot(and(X_60,falsehood)))]]) ).
cnf(refute_0_595,plain,
and(X_60,falsehood) = and(falsehood,X_60),
inference(resolve,[$cnf( $equal(and(falsehood,X_60),and(X_60,falsehood)) )],[refute_0_593,refute_0_594]) ).
cnf(refute_0_596,plain,
( and(X_60,falsehood) != and(falsehood,X_60)
| implies(falsehood,and(X_60,falsehood)) != truth
| implies(falsehood,and(falsehood,X_60)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(falsehood,and(X_60,falsehood)),truth) ),[0,1],$fot(and(falsehood,X_60))]]) ).
cnf(refute_0_597,plain,
( implies(falsehood,and(X_60,falsehood)) != truth
| implies(falsehood,and(falsehood,X_60)) = truth ),
inference(resolve,[$cnf( $equal(and(X_60,falsehood),and(falsehood,X_60)) )],[refute_0_595,refute_0_596]) ).
cnf(refute_0_598,plain,
implies(falsehood,and(falsehood,X_60)) = truth,
inference(resolve,[$cnf( $equal(implies(falsehood,and(X_60,falsehood)),truth) )],[refute_0_465,refute_0_597]) ).
cnf(refute_0_599,plain,
( implies(falsehood,and(falsehood,X_60)) != truth
| implies(implies(falsehood,truth),implies(and(falsehood,X_60),implies(falsehood,and(falsehood,X_60)))) != truth
| implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,truth),implies(and(falsehood,X_60),implies(falsehood,and(falsehood,X_60)))),truth) ),[0,1,1],$fot(truth)]]) ).
cnf(refute_0_600,plain,
( implies(implies(falsehood,truth),implies(and(falsehood,X_60),implies(falsehood,and(falsehood,X_60)))) != truth
| implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(falsehood,and(falsehood,X_60)),truth) )],[refute_0_598,refute_0_599]) ).
cnf(refute_0_601,plain,
implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,truth),implies(and(falsehood,X_60),implies(falsehood,and(falsehood,X_60)))),truth) )],[refute_0_592,refute_0_600]) ).
cnf(refute_0_602,plain,
implies(and(falsehood,X_60),truth) = implies(falsehood,implies(X_60,truth)),
inference(subst,[],[refute_0_369:[bind(Y,$fot(truth)),bind(X_21,$fot(falsehood)),bind(X_22,$fot(X_60))]]) ).
cnf(refute_0_603,plain,
implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)) = implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)),
introduced(tautology,[refl,[$fot(implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)))]]) ).
cnf(refute_0_604,plain,
( implies(and(falsehood,X_60),truth) != implies(falsehood,implies(X_60,truth))
| implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)) != implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth))
| implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)) = implies(implies(falsehood,truth),implies(falsehood,implies(X_60,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)),implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth))) ),[1,1],$fot(implies(falsehood,implies(X_60,truth)))]]) ).
cnf(refute_0_605,plain,
( implies(and(falsehood,X_60),truth) != implies(falsehood,implies(X_60,truth))
| implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)) = implies(implies(falsehood,truth),implies(falsehood,implies(X_60,truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)),implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth))) )],[refute_0_603,refute_0_604]) ).
cnf(refute_0_606,plain,
implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)) = implies(implies(falsehood,truth),implies(falsehood,implies(X_60,truth))),
inference(resolve,[$cnf( $equal(implies(and(falsehood,X_60),truth),implies(falsehood,implies(X_60,truth))) )],[refute_0_602,refute_0_605]) ).
cnf(refute_0_607,plain,
( implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)) != implies(implies(falsehood,truth),implies(falsehood,implies(X_60,truth)))
| implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)) != truth
| implies(implies(falsehood,truth),implies(falsehood,implies(X_60,truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)),truth) ),[0],$fot(implies(implies(falsehood,truth),implies(falsehood,implies(X_60,truth))))]]) ).
cnf(refute_0_608,plain,
( implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)) != truth
| implies(implies(falsehood,truth),implies(falsehood,implies(X_60,truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)),implies(implies(falsehood,truth),implies(falsehood,implies(X_60,truth)))) )],[refute_0_606,refute_0_607]) ).
cnf(refute_0_609,plain,
implies(implies(falsehood,truth),implies(falsehood,implies(X_60,truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,truth),implies(and(falsehood,X_60),truth)),truth) )],[refute_0_601,refute_0_608]) ).
cnf(refute_0_610,plain,
implies(implies(falsehood,truth),implies(falsehood,implies(X_64,truth))) = truth,
inference(subst,[],[refute_0_609:[bind(X_60,$fot(X_64))]]) ).
cnf(refute_0_611,plain,
( implies(implies(falsehood,truth),implies(falsehood,implies(X_64,truth))) != truth
| implies(implies(implies(falsehood,implies(X_64,truth)),implies(falsehood,truth)),implies(falsehood,truth)) != implies(implies(implies(falsehood,truth),implies(falsehood,implies(X_64,truth))),implies(falsehood,implies(X_64,truth)))
| implies(implies(implies(falsehood,implies(X_64,truth)),implies(falsehood,truth)),implies(falsehood,truth)) = implies(truth,implies(falsehood,implies(X_64,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(falsehood,implies(X_64,truth)),implies(falsehood,truth)),implies(falsehood,truth)),implies(implies(implies(falsehood,truth),implies(falsehood,implies(X_64,truth))),implies(falsehood,implies(X_64,truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_612,plain,
( implies(implies(implies(falsehood,implies(X_64,truth)),implies(falsehood,truth)),implies(falsehood,truth)) != implies(implies(implies(falsehood,truth),implies(falsehood,implies(X_64,truth))),implies(falsehood,implies(X_64,truth)))
| implies(implies(implies(falsehood,implies(X_64,truth)),implies(falsehood,truth)),implies(falsehood,truth)) = implies(truth,implies(falsehood,implies(X_64,truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,truth),implies(falsehood,implies(X_64,truth))),truth) )],[refute_0_610,refute_0_611]) ).
cnf(refute_0_613,plain,
implies(implies(implies(falsehood,implies(X_64,truth)),implies(falsehood,truth)),implies(falsehood,truth)) = implies(truth,implies(falsehood,implies(X_64,truth))),
inference(resolve,[$cnf( $equal(implies(implies(implies(falsehood,implies(X_64,truth)),implies(falsehood,truth)),implies(falsehood,truth)),implies(implies(implies(falsehood,truth),implies(falsehood,implies(X_64,truth))),implies(falsehood,implies(X_64,truth)))) )],[refute_0_591,refute_0_612]) ).
cnf(refute_0_614,plain,
implies(implies(falsehood,and(X_60,falsehood)),implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(falsehood)),bind(Y,$fot(and(X_60,falsehood)))]]) ).
cnf(refute_0_615,plain,
( implies(falsehood,and(X_60,falsehood)) != truth
| implies(implies(falsehood,and(X_60,falsehood)),implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) != truth
| implies(truth,implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,and(X_60,falsehood)),implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_616,plain,
( implies(implies(falsehood,and(X_60,falsehood)),implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) != truth
| implies(truth,implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(falsehood,and(X_60,falsehood)),truth) )],[refute_0_465,refute_0_615]) ).
cnf(refute_0_617,plain,
implies(truth,implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,and(X_60,falsehood)),implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))),truth) )],[refute_0_614,refute_0_616]) ).
cnf(refute_0_618,plain,
implies(and(X_60,falsehood),Z) = implies(X_60,implies(falsehood,Z)),
inference(subst,[],[refute_0_369:[bind(Y,$fot(Z)),bind(X_21,$fot(X_60)),bind(X_22,$fot(falsehood))]]) ).
cnf(refute_0_619,plain,
implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z)) = implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z)),
introduced(tautology,[refl,[$fot(implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z)))]]) ).
cnf(refute_0_620,plain,
( implies(and(X_60,falsehood),Z) != implies(X_60,implies(falsehood,Z))
| implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z)) != implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))
| implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z)) = implies(implies(X_60,implies(falsehood,Z)),implies(falsehood,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z)),implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) ),[1,0],$fot(implies(X_60,implies(falsehood,Z)))]]) ).
cnf(refute_0_621,plain,
( implies(and(X_60,falsehood),Z) != implies(X_60,implies(falsehood,Z))
| implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z)) = implies(implies(X_60,implies(falsehood,Z)),implies(falsehood,Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z)),implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) )],[refute_0_619,refute_0_620]) ).
cnf(refute_0_622,plain,
implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z)) = implies(implies(X_60,implies(falsehood,Z)),implies(falsehood,Z)),
inference(resolve,[$cnf( $equal(implies(and(X_60,falsehood),Z),implies(X_60,implies(falsehood,Z))) )],[refute_0_618,refute_0_621]) ).
cnf(refute_0_623,plain,
implies(truth,implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) = implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))))]]) ).
cnf(refute_0_624,plain,
( implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z)) != implies(implies(X_60,implies(falsehood,Z)),implies(falsehood,Z))
| implies(truth,implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) != implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))
| implies(truth,implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) = implies(implies(X_60,implies(falsehood,Z)),implies(falsehood,Z)) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(implies(truth,implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))))),bind(Y0,$fot(implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z)))),bind(Z0,$fot(implies(implies(X_60,implies(falsehood,Z)),implies(falsehood,Z))))]]) ).
cnf(refute_0_625,plain,
( implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z)) != implies(implies(X_60,implies(falsehood,Z)),implies(falsehood,Z))
| implies(truth,implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) = implies(implies(X_60,implies(falsehood,Z)),implies(falsehood,Z)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))),implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) )],[refute_0_623,refute_0_624]) ).
cnf(refute_0_626,plain,
implies(truth,implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) = implies(implies(X_60,implies(falsehood,Z)),implies(falsehood,Z)),
inference(resolve,[$cnf( $equal(implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z)),implies(implies(X_60,implies(falsehood,Z)),implies(falsehood,Z))) )],[refute_0_622,refute_0_625]) ).
cnf(refute_0_627,plain,
( implies(truth,implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) != implies(implies(X_60,implies(falsehood,Z)),implies(falsehood,Z))
| implies(truth,implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) != truth
| implies(implies(X_60,implies(falsehood,Z)),implies(falsehood,Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))),truth) ),[0],$fot(implies(implies(X_60,implies(falsehood,Z)),implies(falsehood,Z)))]]) ).
cnf(refute_0_628,plain,
( implies(truth,implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))) != truth
| implies(implies(X_60,implies(falsehood,Z)),implies(falsehood,Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))),implies(implies(X_60,implies(falsehood,Z)),implies(falsehood,Z))) )],[refute_0_626,refute_0_627]) ).
cnf(refute_0_629,plain,
implies(implies(X_60,implies(falsehood,Z)),implies(falsehood,Z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(and(X_60,falsehood),Z),implies(falsehood,Z))),truth) )],[refute_0_617,refute_0_628]) ).
cnf(refute_0_630,plain,
implies(implies(implies(falsehood,implies(X_64,truth)),implies(falsehood,truth)),implies(falsehood,truth)) = truth,
inference(subst,[],[refute_0_629:[bind(Z,$fot(truth)),bind(X_60,$fot(implies(falsehood,implies(X_64,truth))))]]) ).
cnf(refute_0_631,plain,
( implies(implies(implies(falsehood,implies(X_64,truth)),implies(falsehood,truth)),implies(falsehood,truth)) != implies(truth,implies(falsehood,implies(X_64,truth)))
| implies(implies(implies(falsehood,implies(X_64,truth)),implies(falsehood,truth)),implies(falsehood,truth)) != truth
| truth = implies(truth,implies(falsehood,implies(X_64,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(falsehood,implies(X_64,truth)),implies(falsehood,truth)),implies(falsehood,truth)),implies(truth,implies(falsehood,implies(X_64,truth)))) ),[0],$fot(truth)]]) ).
cnf(refute_0_632,plain,
( implies(implies(implies(falsehood,implies(X_64,truth)),implies(falsehood,truth)),implies(falsehood,truth)) != implies(truth,implies(falsehood,implies(X_64,truth)))
| truth = implies(truth,implies(falsehood,implies(X_64,truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(falsehood,implies(X_64,truth)),implies(falsehood,truth)),implies(falsehood,truth)),truth) )],[refute_0_630,refute_0_631]) ).
cnf(refute_0_633,plain,
implies(truth,implies(falsehood,implies(X_64,truth))) = implies(falsehood,implies(X_64,truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(falsehood,implies(X_64,truth))))]]) ).
cnf(refute_0_634,plain,
( implies(truth,implies(falsehood,implies(X_64,truth))) != implies(falsehood,implies(X_64,truth))
| truth != implies(truth,implies(falsehood,implies(X_64,truth)))
| truth = implies(falsehood,implies(X_64,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(truth,implies(truth,implies(falsehood,implies(X_64,truth)))) ),[1],$fot(implies(falsehood,implies(X_64,truth)))]]) ).
cnf(refute_0_635,plain,
( truth != implies(truth,implies(falsehood,implies(X_64,truth)))
| truth = implies(falsehood,implies(X_64,truth)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(falsehood,implies(X_64,truth))),implies(falsehood,implies(X_64,truth))) )],[refute_0_633,refute_0_634]) ).
cnf(refute_0_636,plain,
( implies(implies(implies(falsehood,implies(X_64,truth)),implies(falsehood,truth)),implies(falsehood,truth)) != implies(truth,implies(falsehood,implies(X_64,truth)))
| truth = implies(falsehood,implies(X_64,truth)) ),
inference(resolve,[$cnf( $equal(truth,implies(truth,implies(falsehood,implies(X_64,truth)))) )],[refute_0_632,refute_0_635]) ).
cnf(refute_0_637,plain,
truth = implies(falsehood,implies(X_64,truth)),
inference(resolve,[$cnf( $equal(implies(implies(implies(falsehood,implies(X_64,truth)),implies(falsehood,truth)),implies(falsehood,truth)),implies(truth,implies(falsehood,implies(X_64,truth)))) )],[refute_0_613,refute_0_636]) ).
cnf(refute_0_638,plain,
truth = implies(falsehood,implies(implies(Y,truth),truth)),
inference(subst,[],[refute_0_637:[bind(X_64,$fot(implies(Y,truth)))]]) ).
cnf(refute_0_639,plain,
implies(implies(truth,Y),Y) = implies(implies(Y,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth))]]) ).
cnf(refute_0_640,plain,
( implies(implies(truth,Y),Y) != implies(implies(Y,truth),truth)
| implies(implies(Y,truth),truth) = implies(implies(truth,Y),Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(truth,Y),Y))),bind(Y0,$fot(implies(implies(Y,truth),truth)))]]) ).
cnf(refute_0_641,plain,
implies(implies(Y,truth),truth) = implies(implies(truth,Y),Y),
inference(resolve,[$cnf( $equal(implies(implies(truth,Y),Y),implies(implies(Y,truth),truth)) )],[refute_0_639,refute_0_640]) ).
cnf(refute_0_642,plain,
( implies(implies(Y,truth),truth) != implies(implies(truth,Y),Y)
| truth != implies(falsehood,implies(implies(Y,truth),truth))
| truth = implies(falsehood,implies(implies(truth,Y),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(truth,implies(falsehood,implies(implies(Y,truth),truth))) ),[1,1],$fot(implies(implies(truth,Y),Y))]]) ).
cnf(refute_0_643,plain,
( truth != implies(falsehood,implies(implies(Y,truth),truth))
| truth = implies(falsehood,implies(implies(truth,Y),Y)) ),
inference(resolve,[$cnf( $equal(implies(implies(Y,truth),truth),implies(implies(truth,Y),Y)) )],[refute_0_641,refute_0_642]) ).
cnf(refute_0_644,plain,
truth = implies(falsehood,implies(implies(truth,Y),Y)),
inference(resolve,[$cnf( $equal(truth,implies(falsehood,implies(implies(Y,truth),truth))) )],[refute_0_638,refute_0_643]) ).
cnf(refute_0_645,plain,
implies(Y,Y) = truth,
inference(subst,[],[refute_0_189:[bind(X_30,$fot(Y))]]) ).
cnf(refute_0_646,plain,
implies(implies(truth,Y),Y) = implies(implies(truth,Y),Y),
introduced(tautology,[refl,[$fot(implies(implies(truth,Y),Y))]]) ).
cnf(refute_0_647,plain,
( implies(implies(truth,Y),Y) != implies(implies(truth,Y),Y)
| implies(truth,Y) != Y
| implies(implies(truth,Y),Y) = implies(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,Y),Y),implies(implies(truth,Y),Y)) ),[1,0],$fot(Y)]]) ).
cnf(refute_0_648,plain,
( implies(truth,Y) != Y
| implies(implies(truth,Y),Y) = implies(Y,Y) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,Y),Y),implies(implies(truth,Y),Y)) )],[refute_0_646,refute_0_647]) ).
cnf(refute_0_649,plain,
implies(implies(truth,Y),Y) = implies(Y,Y),
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_132,refute_0_648]) ).
cnf(refute_0_650,plain,
( implies(Y,Y) != truth
| implies(implies(truth,Y),Y) != implies(Y,Y)
| implies(implies(truth,Y),Y) = truth ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(implies(implies(truth,Y),Y))),bind(Y0,$fot(implies(Y,Y))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_651,plain,
( implies(Y,Y) != truth
| implies(implies(truth,Y),Y) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,Y),Y),implies(Y,Y)) )],[refute_0_649,refute_0_650]) ).
cnf(refute_0_652,plain,
implies(implies(truth,Y),Y) = truth,
inference(resolve,[$cnf( $equal(implies(Y,Y),truth) )],[refute_0_645,refute_0_651]) ).
cnf(refute_0_653,plain,
implies(falsehood,implies(implies(truth,Y),Y)) = implies(falsehood,implies(implies(truth,Y),Y)),
introduced(tautology,[refl,[$fot(implies(falsehood,implies(implies(truth,Y),Y)))]]) ).
cnf(refute_0_654,plain,
( implies(falsehood,implies(implies(truth,Y),Y)) != implies(falsehood,implies(implies(truth,Y),Y))
| implies(implies(truth,Y),Y) != truth
| implies(falsehood,implies(implies(truth,Y),Y)) = implies(falsehood,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(falsehood,implies(implies(truth,Y),Y)),implies(falsehood,implies(implies(truth,Y),Y))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_655,plain,
( implies(implies(truth,Y),Y) != truth
| implies(falsehood,implies(implies(truth,Y),Y)) = implies(falsehood,truth) ),
inference(resolve,[$cnf( $equal(implies(falsehood,implies(implies(truth,Y),Y)),implies(falsehood,implies(implies(truth,Y),Y))) )],[refute_0_653,refute_0_654]) ).
cnf(refute_0_656,plain,
implies(falsehood,implies(implies(truth,Y),Y)) = implies(falsehood,truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,Y),Y),truth) )],[refute_0_652,refute_0_655]) ).
cnf(refute_0_657,plain,
( implies(falsehood,implies(implies(truth,Y),Y)) != implies(falsehood,truth)
| truth != implies(falsehood,implies(implies(truth,Y),Y))
| truth = implies(falsehood,truth) ),
introduced(tautology,[equality,[$cnf( $equal(truth,implies(falsehood,implies(implies(truth,Y),Y))) ),[1],$fot(implies(falsehood,truth))]]) ).
cnf(refute_0_658,plain,
( truth != implies(falsehood,implies(implies(truth,Y),Y))
| truth = implies(falsehood,truth) ),
inference(resolve,[$cnf( $equal(implies(falsehood,implies(implies(truth,Y),Y)),implies(falsehood,truth)) )],[refute_0_656,refute_0_657]) ).
cnf(refute_0_659,plain,
truth = implies(falsehood,truth),
inference(resolve,[$cnf( $equal(truth,implies(falsehood,implies(implies(truth,Y),Y))) )],[refute_0_644,refute_0_658]) ).
cnf(refute_0_660,plain,
( truth != implies(falsehood,truth)
| implies(falsehood,truth) = truth ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(falsehood,truth)))]]) ).
cnf(refute_0_661,plain,
implies(falsehood,truth) = truth,
inference(resolve,[$cnf( $equal(truth,implies(falsehood,truth)) )],[refute_0_659,refute_0_660]) ).
cnf(refute_0_662,plain,
implies(X_58,implies(falsehood,truth)) = implies(X_58,implies(falsehood,truth)),
introduced(tautology,[refl,[$fot(implies(X_58,implies(falsehood,truth)))]]) ).
cnf(refute_0_663,plain,
( implies(X_58,implies(falsehood,truth)) != implies(X_58,implies(falsehood,truth))
| implies(falsehood,truth) != truth
| implies(X_58,implies(falsehood,truth)) = implies(X_58,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_58,implies(falsehood,truth)),implies(X_58,implies(falsehood,truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_664,plain,
( implies(falsehood,truth) != truth
| implies(X_58,implies(falsehood,truth)) = implies(X_58,truth) ),
inference(resolve,[$cnf( $equal(implies(X_58,implies(falsehood,truth)),implies(X_58,implies(falsehood,truth))) )],[refute_0_662,refute_0_663]) ).
cnf(refute_0_665,plain,
implies(X_58,implies(falsehood,truth)) = implies(X_58,truth),
inference(resolve,[$cnf( $equal(implies(falsehood,truth),truth) )],[refute_0_661,refute_0_664]) ).
cnf(refute_0_666,plain,
implies(truth,implies(X_58,implies(falsehood,truth))) = implies(truth,implies(X_58,implies(falsehood,truth))),
introduced(tautology,[refl,[$fot(implies(truth,implies(X_58,implies(falsehood,truth))))]]) ).
cnf(refute_0_667,plain,
( implies(X_58,implies(falsehood,truth)) != implies(X_58,truth)
| implies(truth,implies(X_58,implies(falsehood,truth))) != implies(truth,implies(X_58,implies(falsehood,truth)))
| implies(truth,implies(X_58,implies(falsehood,truth))) = implies(truth,implies(X_58,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(X_58,implies(falsehood,truth))),implies(truth,implies(X_58,implies(falsehood,truth)))) ),[1,1],$fot(implies(X_58,truth))]]) ).
cnf(refute_0_668,plain,
( implies(X_58,implies(falsehood,truth)) != implies(X_58,truth)
| implies(truth,implies(X_58,implies(falsehood,truth))) = implies(truth,implies(X_58,truth)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_58,implies(falsehood,truth))),implies(truth,implies(X_58,implies(falsehood,truth)))) )],[refute_0_666,refute_0_667]) ).
cnf(refute_0_669,plain,
implies(truth,implies(X_58,implies(falsehood,truth))) = implies(truth,implies(X_58,truth)),
inference(resolve,[$cnf( $equal(implies(X_58,implies(falsehood,truth)),implies(X_58,truth)) )],[refute_0_665,refute_0_668]) ).
cnf(refute_0_670,plain,
implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) = implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))),
introduced(tautology,[refl,[$fot(implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))))]]) ).
cnf(refute_0_671,plain,
( implies(falsehood,truth) != truth
| implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) != implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth)))
| implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) = implies(truth,implies(X_58,implies(falsehood,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))),implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_672,plain,
( implies(falsehood,truth) != truth
| implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) = implies(truth,implies(X_58,implies(falsehood,truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))),implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth)))) )],[refute_0_670,refute_0_671]) ).
cnf(refute_0_673,plain,
implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) = implies(truth,implies(X_58,implies(falsehood,truth))),
inference(resolve,[$cnf( $equal(implies(falsehood,truth),truth) )],[refute_0_661,refute_0_672]) ).
cnf(refute_0_674,plain,
( implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) != implies(truth,implies(X_58,implies(falsehood,truth)))
| implies(truth,implies(X_58,implies(falsehood,truth))) != implies(truth,implies(X_58,truth))
| implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) = implies(truth,implies(X_58,truth)) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))))),bind(Y0,$fot(implies(truth,implies(X_58,implies(falsehood,truth))))),bind(Z0,$fot(implies(truth,implies(X_58,truth))))]]) ).
cnf(refute_0_675,plain,
( implies(truth,implies(X_58,implies(falsehood,truth))) != implies(truth,implies(X_58,truth))
| implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) = implies(truth,implies(X_58,truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))),implies(truth,implies(X_58,implies(falsehood,truth)))) )],[refute_0_673,refute_0_674]) ).
cnf(refute_0_676,plain,
implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) = implies(truth,implies(X_58,truth)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_58,implies(falsehood,truth))),implies(truth,implies(X_58,truth))) )],[refute_0_669,refute_0_675]) ).
cnf(refute_0_677,plain,
( implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) != implies(truth,implies(X_58,truth))
| implies(truth,implies(X_58,truth)) != implies(X_58,truth)
| implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) = implies(X_58,truth) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))))),bind(Y0,$fot(implies(truth,implies(X_58,truth)))),bind(Z0,$fot(implies(X_58,truth)))]]) ).
cnf(refute_0_678,plain,
( implies(truth,implies(X_58,truth)) != implies(X_58,truth)
| implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) = implies(X_58,truth) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))),implies(truth,implies(X_58,truth))) )],[refute_0_676,refute_0_677]) ).
cnf(refute_0_679,plain,
implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) = implies(X_58,truth),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_58,truth)),implies(X_58,truth)) )],[refute_0_590,refute_0_678]) ).
cnf(refute_0_680,plain,
( implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) != implies(X_58,truth)
| implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) != truth
| implies(X_58,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))),truth) ),[0],$fot(implies(X_58,truth))]]) ).
cnf(refute_0_681,plain,
( implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))) != truth
| implies(X_58,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))),implies(X_58,truth)) )],[refute_0_679,refute_0_680]) ).
cnf(refute_0_682,plain,
implies(X_58,truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,truth),implies(X_58,implies(falsehood,truth))),truth) )],[refute_0_589,refute_0_681]) ).
cnf(refute_0_683,plain,
implies(X_60,truth) = truth,
inference(subst,[],[refute_0_682:[bind(X_58,$fot(X_60))]]) ).
cnf(refute_0_684,plain,
implies(implies(X_60,truth),falsehood) = implies(implies(X_60,truth),falsehood),
introduced(tautology,[refl,[$fot(implies(implies(X_60,truth),falsehood))]]) ).
cnf(refute_0_685,plain,
( implies(X_60,truth) != truth
| implies(implies(X_60,truth),falsehood) != implies(implies(X_60,truth),falsehood)
| implies(implies(X_60,truth),falsehood) = implies(truth,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_60,truth),falsehood),implies(implies(X_60,truth),falsehood)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_686,plain,
( implies(X_60,truth) != truth
| implies(implies(X_60,truth),falsehood) = implies(truth,falsehood) ),
inference(resolve,[$cnf( $equal(implies(implies(X_60,truth),falsehood),implies(implies(X_60,truth),falsehood)) )],[refute_0_684,refute_0_685]) ).
cnf(refute_0_687,plain,
implies(implies(X_60,truth),falsehood) = implies(truth,falsehood),
inference(resolve,[$cnf( $equal(implies(X_60,truth),truth) )],[refute_0_683,refute_0_686]) ).
cnf(refute_0_688,plain,
( implies(implies(X_60,truth),falsehood) != implies(truth,falsehood)
| implies(truth,falsehood) != falsehood
| implies(implies(X_60,truth),falsehood) = falsehood ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(implies(implies(X_60,truth),falsehood))),bind(Y0,$fot(implies(truth,falsehood))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_689,plain,
( implies(truth,falsehood) != falsehood
| implies(implies(X_60,truth),falsehood) = falsehood ),
inference(resolve,[$cnf( $equal(implies(implies(X_60,truth),falsehood),implies(truth,falsehood)) )],[refute_0_687,refute_0_688]) ).
cnf(refute_0_690,plain,
implies(implies(X_60,truth),falsehood) = falsehood,
inference(resolve,[$cnf( $equal(implies(truth,falsehood),falsehood) )],[refute_0_382,refute_0_689]) ).
cnf(refute_0_691,plain,
( implies(implies(X_60,truth),falsehood) != and(X_60,falsehood)
| implies(implies(X_60,truth),falsehood) != falsehood
| falsehood = and(X_60,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_60,truth),falsehood),and(X_60,falsehood)) ),[0],$fot(falsehood)]]) ).
cnf(refute_0_692,plain,
( implies(implies(X_60,truth),falsehood) != and(X_60,falsehood)
| falsehood = and(X_60,falsehood) ),
inference(resolve,[$cnf( $equal(implies(implies(X_60,truth),falsehood),falsehood) )],[refute_0_690,refute_0_691]) ).
cnf(refute_0_693,plain,
falsehood = and(X_60,falsehood),
inference(resolve,[$cnf( $equal(implies(implies(X_60,truth),falsehood),and(X_60,falsehood)) )],[refute_0_488,refute_0_692]) ).
cnf(refute_0_694,plain,
( falsehood != and(X_60,falsehood)
| and(X_60,falsehood) = falsehood ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(falsehood)),bind(Y0,$fot(and(X_60,falsehood)))]]) ).
cnf(refute_0_695,plain,
and(X_60,falsehood) = falsehood,
inference(resolve,[$cnf( $equal(falsehood,and(X_60,falsehood)) )],[refute_0_693,refute_0_694]) ).
cnf(refute_0_696,plain,
and(X,falsehood) = falsehood,
inference(subst,[],[refute_0_695:[bind(X_60,$fot(X))]]) ).
cnf(refute_0_697,plain,
and(Y,falsehood) = falsehood,
inference(subst,[],[refute_0_695:[bind(X_60,$fot(Y))]]) ).
cnf(refute_0_698,plain,
and(X,and(Y,falsehood)) = and(X,and(Y,falsehood)),
introduced(tautology,[refl,[$fot(and(X,and(Y,falsehood)))]]) ).
cnf(refute_0_699,plain,
( and(X,and(Y,falsehood)) != and(X,and(Y,falsehood))
| and(Y,falsehood) != falsehood
| and(X,and(Y,falsehood)) = and(X,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,and(Y,falsehood)),and(X,and(Y,falsehood))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_700,plain,
( and(Y,falsehood) != falsehood
| and(X,and(Y,falsehood)) = and(X,falsehood) ),
inference(resolve,[$cnf( $equal(and(X,and(Y,falsehood)),and(X,and(Y,falsehood))) )],[refute_0_698,refute_0_699]) ).
cnf(refute_0_701,plain,
and(X,and(Y,falsehood)) = and(X,falsehood),
inference(resolve,[$cnf( $equal(and(Y,falsehood),falsehood) )],[refute_0_697,refute_0_700]) ).
cnf(refute_0_702,plain,
( and(X,and(Y,falsehood)) != and(X,falsehood)
| and(X,falsehood) != falsehood
| and(X,and(Y,falsehood)) = falsehood ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(and(X,and(Y,falsehood)))),bind(Y0,$fot(and(X,falsehood))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_703,plain,
( and(X,falsehood) != falsehood
| and(X,and(Y,falsehood)) = falsehood ),
inference(resolve,[$cnf( $equal(and(X,and(Y,falsehood)),and(X,falsehood)) )],[refute_0_701,refute_0_702]) ).
cnf(refute_0_704,plain,
and(X,and(Y,falsehood)) = falsehood,
inference(resolve,[$cnf( $equal(and(X,falsehood),falsehood) )],[refute_0_696,refute_0_703]) ).
cnf(refute_0_705,plain,
and(falsehood,and(X,and(Y,falsehood))) = and(falsehood,and(X,and(Y,falsehood))),
introduced(tautology,[refl,[$fot(and(falsehood,and(X,and(Y,falsehood))))]]) ).
cnf(refute_0_706,plain,
( and(X,and(Y,falsehood)) != falsehood
| and(falsehood,and(X,and(Y,falsehood))) != and(falsehood,and(X,and(Y,falsehood)))
| and(falsehood,and(X,and(Y,falsehood))) = and(falsehood,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(and(falsehood,and(X,and(Y,falsehood))),and(falsehood,and(X,and(Y,falsehood)))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_707,plain,
( and(X,and(Y,falsehood)) != falsehood
| and(falsehood,and(X,and(Y,falsehood))) = and(falsehood,falsehood) ),
inference(resolve,[$cnf( $equal(and(falsehood,and(X,and(Y,falsehood))),and(falsehood,and(X,and(Y,falsehood)))) )],[refute_0_705,refute_0_706]) ).
cnf(refute_0_708,plain,
and(falsehood,and(X,and(Y,falsehood))) = and(falsehood,falsehood),
inference(resolve,[$cnf( $equal(and(X,and(Y,falsehood)),falsehood) )],[refute_0_704,refute_0_707]) ).
cnf(refute_0_709,plain,
( and(falsehood,and(X,and(Y,falsehood))) != and(falsehood,falsehood)
| and(falsehood,falsehood) != falsehood
| and(falsehood,and(X,and(Y,falsehood))) = falsehood ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(and(falsehood,and(X,and(Y,falsehood))))),bind(Y0,$fot(and(falsehood,falsehood))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_710,plain,
( and(falsehood,falsehood) != falsehood
| and(falsehood,and(X,and(Y,falsehood))) = falsehood ),
inference(resolve,[$cnf( $equal(and(falsehood,and(X,and(Y,falsehood))),and(falsehood,falsehood)) )],[refute_0_708,refute_0_709]) ).
cnf(refute_0_711,plain,
and(falsehood,and(X,and(Y,falsehood))) = falsehood,
inference(resolve,[$cnf( $equal(and(falsehood,falsehood),falsehood) )],[refute_0_516,refute_0_710]) ).
cnf(refute_0_712,plain,
( and(falsehood,and(X,and(Y,falsehood))) != and(falsehood,and(X,Y))
| and(falsehood,and(X,and(Y,falsehood))) != falsehood
| falsehood = and(falsehood,and(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and(falsehood,and(X,and(Y,falsehood))),and(falsehood,and(X,Y))) ),[0],$fot(falsehood)]]) ).
cnf(refute_0_713,plain,
( and(falsehood,and(X,and(Y,falsehood))) != and(falsehood,and(X,Y))
| falsehood = and(falsehood,and(X,Y)) ),
inference(resolve,[$cnf( $equal(and(falsehood,and(X,and(Y,falsehood))),falsehood) )],[refute_0_711,refute_0_712]) ).
cnf(refute_0_714,plain,
falsehood = and(falsehood,and(X,Y)),
inference(resolve,[$cnf( $equal(and(falsehood,and(X,and(Y,falsehood))),and(falsehood,and(X,Y))) )],[refute_0_572,refute_0_713]) ).
cnf(refute_0_715,plain,
( falsehood != and(falsehood,and(X,Y))
| and(falsehood,and(X,Y)) = falsehood ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(falsehood)),bind(Y0,$fot(and(falsehood,and(X,Y))))]]) ).
cnf(refute_0_716,plain,
and(falsehood,and(X,Y)) = falsehood,
inference(resolve,[$cnf( $equal(falsehood,and(falsehood,and(X,Y))) )],[refute_0_714,refute_0_715]) ).
cnf(refute_0_717,plain,
and(falsehood,and(falsehood,Z)) = falsehood,
inference(subst,[],[refute_0_716:[bind(X,$fot(falsehood)),bind(Y,$fot(Z))]]) ).
cnf(refute_0_718,plain,
( and(falsehood,Z) != and(falsehood,and(falsehood,Z))
| and(falsehood,and(falsehood,Z)) != falsehood
| and(falsehood,Z) = falsehood ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(falsehood,Z),falsehood) ),[0],$fot(and(falsehood,and(falsehood,Z)))]]) ).
cnf(refute_0_719,plain,
( and(falsehood,Z) != and(falsehood,and(falsehood,Z))
| and(falsehood,Z) = falsehood ),
inference(resolve,[$cnf( $equal(and(falsehood,and(falsehood,Z)),falsehood) )],[refute_0_717,refute_0_718]) ).
cnf(refute_0_720,plain,
and(falsehood,Z) = falsehood,
inference(resolve,[$cnf( $equal(and(falsehood,Z),and(falsehood,and(falsehood,Z))) )],[refute_0_519,refute_0_719]) ).
cnf(refute_0_721,plain,
and(falsehood,X_8) = falsehood,
inference(subst,[],[refute_0_720:[bind(Z,$fot(X_8))]]) ).
cnf(refute_0_722,plain,
implies(X_8,and(falsehood,X_8)) = implies(X_8,and(falsehood,X_8)),
introduced(tautology,[refl,[$fot(implies(X_8,and(falsehood,X_8)))]]) ).
cnf(refute_0_723,plain,
( and(falsehood,X_8) != falsehood
| implies(X_8,and(falsehood,X_8)) != implies(X_8,and(falsehood,X_8))
| implies(X_8,and(falsehood,X_8)) = implies(X_8,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_8,and(falsehood,X_8)),implies(X_8,and(falsehood,X_8))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_724,plain,
( and(falsehood,X_8) != falsehood
| implies(X_8,and(falsehood,X_8)) = implies(X_8,falsehood) ),
inference(resolve,[$cnf( $equal(implies(X_8,and(falsehood,X_8)),implies(X_8,and(falsehood,X_8))) )],[refute_0_722,refute_0_723]) ).
cnf(refute_0_725,plain,
implies(X_8,and(falsehood,X_8)) = implies(X_8,falsehood),
inference(resolve,[$cnf( $equal(and(falsehood,X_8),falsehood) )],[refute_0_721,refute_0_724]) ).
cnf(refute_0_726,plain,
( implies(X_8,and(falsehood,X_8)) != implies(X_8,falsehood)
| xor(truth,X_8) != implies(X_8,and(falsehood,X_8))
| xor(truth,X_8) = implies(X_8,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_8),implies(X_8,and(falsehood,X_8))) ),[1],$fot(implies(X_8,falsehood))]]) ).
cnf(refute_0_727,plain,
( xor(truth,X_8) != implies(X_8,and(falsehood,X_8))
| xor(truth,X_8) = implies(X_8,falsehood) ),
inference(resolve,[$cnf( $equal(implies(X_8,and(falsehood,X_8)),implies(X_8,falsehood)) )],[refute_0_725,refute_0_726]) ).
cnf(refute_0_728,plain,
xor(truth,X_8) = implies(X_8,falsehood),
inference(resolve,[$cnf( $equal(xor(truth,X_8),implies(X_8,and(falsehood,X_8))) )],[refute_0_252,refute_0_727]) ).
cnf(refute_0_729,plain,
xor(truth,x) = implies(x,falsehood),
inference(subst,[],[refute_0_728:[bind(X_8,$fot(x))]]) ).
cnf(refute_0_730,plain,
( not(x) != implies(x,falsehood)
| xor(truth,x) != implies(x,falsehood)
| not(x) = xor(truth,x) ),
introduced(tautology,[equality,[$cnf( ~ $equal(not(x),xor(truth,x)) ),[1],$fot(implies(x,falsehood))]]) ).
cnf(refute_0_731,plain,
( not(x) != implies(x,falsehood)
| not(x) = xor(truth,x) ),
inference(resolve,[$cnf( $equal(xor(truth,x),implies(x,falsehood)) )],[refute_0_729,refute_0_730]) ).
cnf(refute_0_732,plain,
not(x) != implies(x,falsehood),
inference(resolve,[$cnf( $equal(not(x),xor(truth,x)) )],[refute_0_731,refute_0_8]) ).
cnf(refute_0_733,plain,
and(X,not(Y)) = and(not(Y),X),
inference(subst,[],[and_commutativity:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_734,plain,
( and(X,not(Y)) != and(not(Y),X)
| xor(X,Y) != or(and(X,not(Y)),and(not(X),Y))
| xor(X,Y) = or(and(not(Y),X),and(not(X),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X,Y),or(and(X,not(Y)),and(not(X),Y))) ),[1,0],$fot(and(not(Y),X))]]) ).
cnf(refute_0_735,plain,
( xor(X,Y) != or(and(X,not(Y)),and(not(X),Y))
| xor(X,Y) = or(and(not(Y),X),and(not(X),Y)) ),
inference(resolve,[$cnf( $equal(and(X,not(Y)),and(not(Y),X)) )],[refute_0_733,refute_0_734]) ).
cnf(refute_0_736,plain,
xor(X,Y) = or(and(not(Y),X),and(not(X),Y)),
inference(resolve,[$cnf( $equal(xor(X,Y),or(and(X,not(Y)),and(not(X),Y))) )],[xor_definition,refute_0_735]) ).
cnf(refute_0_737,plain,
xor(truth,X_82) = or(and(not(X_82),truth),and(not(truth),X_82)),
inference(subst,[],[refute_0_736:[bind(X,$fot(truth)),bind(Y,$fot(X_82))]]) ).
cnf(refute_0_738,plain,
( not(truth) != falsehood
| xor(truth,X_82) != or(and(not(X_82),truth),and(not(truth),X_82))
| xor(truth,X_82) = or(and(not(X_82),truth),and(falsehood,X_82)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_82),or(and(not(X_82),truth),and(not(truth),X_82))) ),[1,1,0],$fot(falsehood)]]) ).
cnf(refute_0_739,plain,
( xor(truth,X_82) != or(and(not(X_82),truth),and(not(truth),X_82))
| xor(truth,X_82) = or(and(not(X_82),truth),and(falsehood,X_82)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_738]) ).
cnf(refute_0_740,plain,
xor(truth,X_82) = or(and(not(X_82),truth),and(falsehood,X_82)),
inference(resolve,[$cnf( $equal(xor(truth,X_82),or(and(not(X_82),truth),and(not(truth),X_82))) )],[refute_0_737,refute_0_739]) ).
cnf(refute_0_741,plain,
xor(truth,X_82) = implies(X_82,falsehood),
inference(subst,[],[refute_0_728:[bind(X_8,$fot(X_82))]]) ).
cnf(refute_0_742,plain,
( xor(truth,X_82) != implies(X_82,falsehood)
| xor(truth,X_82) != or(and(not(X_82),truth),and(falsehood,X_82))
| implies(X_82,falsehood) = or(and(not(X_82),truth),and(falsehood,X_82)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(truth,X_82),or(and(not(X_82),truth),and(falsehood,X_82))) ),[0],$fot(implies(X_82,falsehood))]]) ).
cnf(refute_0_743,plain,
( xor(truth,X_82) != or(and(not(X_82),truth),and(falsehood,X_82))
| implies(X_82,falsehood) = or(and(not(X_82),truth),and(falsehood,X_82)) ),
inference(resolve,[$cnf( $equal(xor(truth,X_82),implies(X_82,falsehood)) )],[refute_0_741,refute_0_742]) ).
cnf(refute_0_744,plain,
or(falsehood,not(X_82)) = not(X_82),
inference(subst,[],[refute_0_135:[bind(Y,$fot(not(X_82)))]]) ).
cnf(refute_0_745,plain,
not(not(X_21)) = X_21,
inference(subst,[],[refute_0_230:[bind(Y,$fot(X_21))]]) ).
cnf(refute_0_746,plain,
( and(X_21,truth) != not(not(X_21))
| not(not(X_21)) != X_21
| and(X_21,truth) = X_21 ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_21,truth),X_21) ),[0],$fot(not(not(X_21)))]]) ).
cnf(refute_0_747,plain,
( and(X_21,truth) != not(not(X_21))
| and(X_21,truth) = X_21 ),
inference(resolve,[$cnf( $equal(not(not(X_21)),X_21) )],[refute_0_745,refute_0_746]) ).
cnf(refute_0_748,plain,
and(X_21,truth) = X_21,
inference(resolve,[$cnf( $equal(and(X_21,truth),not(not(X_21))) )],[refute_0_150,refute_0_747]) ).
cnf(refute_0_749,plain,
and(not(X_82),truth) = not(X_82),
inference(subst,[],[refute_0_748:[bind(X_21,$fot(not(X_82)))]]) ).
cnf(refute_0_750,plain,
or(falsehood,and(not(X_82),truth)) = or(falsehood,and(not(X_82),truth)),
introduced(tautology,[refl,[$fot(or(falsehood,and(not(X_82),truth)))]]) ).
cnf(refute_0_751,plain,
( and(not(X_82),truth) != not(X_82)
| or(falsehood,and(not(X_82),truth)) != or(falsehood,and(not(X_82),truth))
| or(falsehood,and(not(X_82),truth)) = or(falsehood,not(X_82)) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,and(not(X_82),truth)),or(falsehood,and(not(X_82),truth))) ),[1,1],$fot(not(X_82))]]) ).
cnf(refute_0_752,plain,
( and(not(X_82),truth) != not(X_82)
| or(falsehood,and(not(X_82),truth)) = or(falsehood,not(X_82)) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(not(X_82),truth)),or(falsehood,and(not(X_82),truth))) )],[refute_0_750,refute_0_751]) ).
cnf(refute_0_753,plain,
or(falsehood,and(not(X_82),truth)) = or(falsehood,not(X_82)),
inference(resolve,[$cnf( $equal(and(not(X_82),truth),not(X_82)) )],[refute_0_749,refute_0_752]) ).
cnf(refute_0_754,plain,
and(falsehood,X_82) = falsehood,
inference(subst,[],[refute_0_720:[bind(Z,$fot(X_82))]]) ).
cnf(refute_0_755,plain,
or(and(falsehood,X_82),and(not(X_82),truth)) = or(and(falsehood,X_82),and(not(X_82),truth)),
introduced(tautology,[refl,[$fot(or(and(falsehood,X_82),and(not(X_82),truth)))]]) ).
cnf(refute_0_756,plain,
( and(falsehood,X_82) != falsehood
| or(and(falsehood,X_82),and(not(X_82),truth)) != or(and(falsehood,X_82),and(not(X_82),truth))
| or(and(falsehood,X_82),and(not(X_82),truth)) = or(falsehood,and(not(X_82),truth)) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(falsehood,X_82),and(not(X_82),truth)),or(and(falsehood,X_82),and(not(X_82),truth))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_757,plain,
( and(falsehood,X_82) != falsehood
| or(and(falsehood,X_82),and(not(X_82),truth)) = or(falsehood,and(not(X_82),truth)) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,X_82),and(not(X_82),truth)),or(and(falsehood,X_82),and(not(X_82),truth))) )],[refute_0_755,refute_0_756]) ).
cnf(refute_0_758,plain,
or(and(falsehood,X_82),and(not(X_82),truth)) = or(falsehood,and(not(X_82),truth)),
inference(resolve,[$cnf( $equal(and(falsehood,X_82),falsehood) )],[refute_0_754,refute_0_757]) ).
cnf(refute_0_759,plain,
( or(and(falsehood,X_82),and(not(X_82),truth)) != or(falsehood,and(not(X_82),truth))
| or(falsehood,and(not(X_82),truth)) != or(falsehood,not(X_82))
| or(and(falsehood,X_82),and(not(X_82),truth)) = or(falsehood,not(X_82)) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(or(and(falsehood,X_82),and(not(X_82),truth)))),bind(Y0,$fot(or(falsehood,and(not(X_82),truth)))),bind(Z0,$fot(or(falsehood,not(X_82))))]]) ).
cnf(refute_0_760,plain,
( or(falsehood,and(not(X_82),truth)) != or(falsehood,not(X_82))
| or(and(falsehood,X_82),and(not(X_82),truth)) = or(falsehood,not(X_82)) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,X_82),and(not(X_82),truth)),or(falsehood,and(not(X_82),truth))) )],[refute_0_758,refute_0_759]) ).
cnf(refute_0_761,plain,
or(and(falsehood,X_82),and(not(X_82),truth)) = or(falsehood,not(X_82)),
inference(resolve,[$cnf( $equal(or(falsehood,and(not(X_82),truth)),or(falsehood,not(X_82))) )],[refute_0_753,refute_0_760]) ).
cnf(refute_0_762,plain,
( or(and(falsehood,X_82),and(not(X_82),truth)) != or(falsehood,not(X_82))
| or(falsehood,not(X_82)) != not(X_82)
| or(and(falsehood,X_82),and(not(X_82),truth)) = not(X_82) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(or(and(falsehood,X_82),and(not(X_82),truth)))),bind(Y0,$fot(or(falsehood,not(X_82)))),bind(Z0,$fot(not(X_82)))]]) ).
cnf(refute_0_763,plain,
( or(falsehood,not(X_82)) != not(X_82)
| or(and(falsehood,X_82),and(not(X_82),truth)) = not(X_82) ),
inference(resolve,[$cnf( $equal(or(and(falsehood,X_82),and(not(X_82),truth)),or(falsehood,not(X_82))) )],[refute_0_761,refute_0_762]) ).
cnf(refute_0_764,plain,
or(and(falsehood,X_82),and(not(X_82),truth)) = not(X_82),
inference(resolve,[$cnf( $equal(or(falsehood,not(X_82)),not(X_82)) )],[refute_0_744,refute_0_763]) ).
cnf(refute_0_765,plain,
or(and(not(X_82),truth),and(falsehood,X_82)) = or(and(falsehood,X_82),and(not(X_82),truth)),
inference(subst,[],[refute_0_14:[bind(X,$fot(and(falsehood,X_82))),bind(Y,$fot(and(not(X_82),truth)))]]) ).
cnf(refute_0_766,plain,
( or(and(falsehood,X_82),and(not(X_82),truth)) != not(X_82)
| or(and(not(X_82),truth),and(falsehood,X_82)) != or(and(falsehood,X_82),and(not(X_82),truth))
| or(and(not(X_82),truth),and(falsehood,X_82)) = not(X_82) ),
inference(subst,[],[refute_0_105:[bind(X0,$fot(or(and(not(X_82),truth),and(falsehood,X_82)))),bind(Y0,$fot(or(and(falsehood,X_82),and(not(X_82),truth)))),bind(Z0,$fot(not(X_82)))]]) ).
cnf(refute_0_767,plain,
( or(and(falsehood,X_82),and(not(X_82),truth)) != not(X_82)
| or(and(not(X_82),truth),and(falsehood,X_82)) = not(X_82) ),
inference(resolve,[$cnf( $equal(or(and(not(X_82),truth),and(falsehood,X_82)),or(and(falsehood,X_82),and(not(X_82),truth))) )],[refute_0_765,refute_0_766]) ).
cnf(refute_0_768,plain,
or(and(not(X_82),truth),and(falsehood,X_82)) = not(X_82),
inference(resolve,[$cnf( $equal(or(and(falsehood,X_82),and(not(X_82),truth)),not(X_82)) )],[refute_0_764,refute_0_767]) ).
cnf(refute_0_769,plain,
( implies(X_82,falsehood) != or(and(not(X_82),truth),and(falsehood,X_82))
| or(and(not(X_82),truth),and(falsehood,X_82)) != not(X_82)
| implies(X_82,falsehood) = not(X_82) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_82,falsehood),not(X_82)) ),[0],$fot(or(and(not(X_82),truth),and(falsehood,X_82)))]]) ).
cnf(refute_0_770,plain,
( implies(X_82,falsehood) != or(and(not(X_82),truth),and(falsehood,X_82))
| implies(X_82,falsehood) = not(X_82) ),
inference(resolve,[$cnf( $equal(or(and(not(X_82),truth),and(falsehood,X_82)),not(X_82)) )],[refute_0_768,refute_0_769]) ).
cnf(refute_0_771,plain,
( xor(truth,X_82) != or(and(not(X_82),truth),and(falsehood,X_82))
| implies(X_82,falsehood) = not(X_82) ),
inference(resolve,[$cnf( $equal(implies(X_82,falsehood),or(and(not(X_82),truth),and(falsehood,X_82))) )],[refute_0_743,refute_0_770]) ).
cnf(refute_0_772,plain,
implies(X_82,falsehood) = not(X_82),
inference(resolve,[$cnf( $equal(xor(truth,X_82),or(and(not(X_82),truth),and(falsehood,X_82))) )],[refute_0_740,refute_0_771]) ).
cnf(refute_0_773,plain,
implies(x,falsehood) = not(x),
inference(subst,[],[refute_0_772:[bind(X_82,$fot(x))]]) ).
cnf(refute_0_774,plain,
( implies(x,falsehood) != not(x)
| not(x) != not(x)
| not(x) = implies(x,falsehood) ),
introduced(tautology,[equality,[$cnf( ~ $equal(not(x),implies(x,falsehood)) ),[1],$fot(not(x))]]) ).
cnf(refute_0_775,plain,
( not(x) != not(x)
| not(x) = implies(x,falsehood) ),
inference(resolve,[$cnf( $equal(implies(x,falsehood),not(x)) )],[refute_0_773,refute_0_774]) ).
cnf(refute_0_776,plain,
not(x) != not(x),
inference(resolve,[$cnf( $equal(not(x),implies(x,falsehood)) )],[refute_0_775,refute_0_732]) ).
cnf(refute_0_777,plain,
not(x) = not(x),
introduced(tautology,[refl,[$fot(not(x))]]) ).
cnf(refute_0_778,plain,
$false,
inference(resolve,[$cnf( $equal(not(x),not(x)) )],[refute_0_777,refute_0_776]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL153-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 21:14:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.47/0.65 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.65
% 0.47/0.65 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.54/0.74
%------------------------------------------------------------------------------