TSTP Solution File: LCL156-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL156-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:50:02 EDT 2022
% Result : Unsatisfiable 0.18s 0.47s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 61
% Number of leaves : 93
% Syntax : Number of clauses : 365 ( 184 unt; 0 nHn; 238 RR)
% Number of literals : 628 ( 627 equ; 267 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 : 289 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
implies(truth,X) = X ).
cnf(wajsberg_3,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth ).
cnf(or_definition,axiom,
or(X,Y) = implies(not(X),Y) ).
cnf(or_associativity,axiom,
or(or(X,Y),Z) = or(X,or(Y,Z)) ).
cnf(or_commutativity,axiom,
or(X,Y) = or(Y,X) ).
cnf(and_definition,axiom,
and(X,Y) = not(or(not(X),not(Y))) ).
cnf(and_commutativity,axiom,
and(X,Y) = and(Y,X) ).
cnf(and_star_definition,axiom,
and_star(X,Y) = not(or(not(X),not(Y))) ).
cnf(false_definition,axiom,
not(truth) = falsehood ).
cnf(prove_alternative_wajsberg_axiom,negated_conjecture,
and_star(x,truth) != x ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( and(X,Y) != and(Y,X)
| and(Y,X) = and(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(and(Y,X)))]]) ).
cnf(refute_0_4,plain,
and(Y,X) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),and(Y,X)) )],[and_commutativity,refute_0_3]) ).
cnf(refute_0_5,plain,
and(x,truth) = and(truth,x),
inference(subst,[],[refute_0_4:[bind(X,$fot(truth)),bind(Y,$fot(x))]]) ).
cnf(refute_0_6,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(or(not(X),not(Y)))))]]) ).
cnf(refute_0_7,plain,
not(or(not(X),not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[and_definition,refute_0_6]) ).
cnf(refute_0_8,plain,
( and_star(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) != and(X,Y)
| and_star(X,Y) = and(X,Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and_star(X,Y),and(X,Y)) ),[0],$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_9,plain,
( and_star(X,Y) != not(or(not(X),not(Y)))
| and_star(X,Y) = and(X,Y) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),and(X,Y)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
and_star(X,Y) = and(X,Y),
inference(resolve,[$cnf( $equal(and_star(X,Y),not(or(not(X),not(Y)))) )],[and_star_definition,refute_0_9]) ).
cnf(refute_0_11,plain,
and_star(x,truth) = and(x,truth),
inference(subst,[],[refute_0_10:[bind(X,$fot(x)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_12,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_13,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_12]) ).
cnf(refute_0_14,plain,
( and(x,truth) != and(truth,x)
| and_star(x,truth) != and(x,truth)
| and_star(x,truth) = and(truth,x) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and_star(x,truth))),bind(Y0,$fot(and(x,truth))),bind(Z0,$fot(and(truth,x)))]]) ).
cnf(refute_0_15,plain,
( and(x,truth) != and(truth,x)
| and_star(x,truth) = and(truth,x) ),
inference(resolve,[$cnf( $equal(and_star(x,truth),and(x,truth)) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
and_star(x,truth) = and(truth,x),
inference(resolve,[$cnf( $equal(and(x,truth),and(truth,x)) )],[refute_0_5,refute_0_15]) ).
cnf(refute_0_17,plain,
( and(truth,x) != x
| and_star(x,truth) != and(truth,x)
| and_star(x,truth) = x ),
introduced(tautology,[equality,[$cnf( $equal(and_star(x,truth),and(truth,x)) ),[1],$fot(x)]]) ).
cnf(refute_0_18,plain,
( and(truth,x) != x
| and_star(x,truth) = x ),
inference(resolve,[$cnf( $equal(and_star(x,truth),and(truth,x)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
and(truth,x) != x,
inference(resolve,[$cnf( $equal(and_star(x,truth),x) )],[refute_0_18,prove_alternative_wajsberg_axiom]) ).
cnf(refute_0_20,plain,
and(or(falsehood,and(truth,truth)),Y) = not(or(not(or(falsehood,and(truth,truth))),not(Y))),
inference(subst,[],[and_definition:[bind(X,$fot(or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_21,plain,
and(X_14,truth) = not(or(not(X_14),not(truth))),
inference(subst,[],[and_definition:[bind(X,$fot(X_14)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_22,plain,
( and(X_14,truth) != not(or(not(X_14),not(truth)))
| not(truth) != falsehood
| and(X_14,truth) = not(or(not(X_14),falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_14,truth),not(or(not(X_14),not(truth)))) ),[1,0,1],$fot(falsehood)]]) ).
cnf(refute_0_23,plain,
( and(X_14,truth) != not(or(not(X_14),not(truth)))
| and(X_14,truth) = not(or(not(X_14),falsehood)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_22]) ).
cnf(refute_0_24,plain,
and(X_14,truth) = not(or(not(X_14),falsehood)),
inference(resolve,[$cnf( $equal(and(X_14,truth),not(or(not(X_14),not(truth)))) )],[refute_0_21,refute_0_23]) ).
cnf(refute_0_25,plain,
( or(X,Y) != or(Y,X)
| or(Y,X) = or(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(or(Y,X)))]]) ).
cnf(refute_0_26,plain,
or(Y,X) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),or(Y,X)) )],[or_commutativity,refute_0_25]) ).
cnf(refute_0_27,plain,
or(not(X_14),falsehood) = or(falsehood,not(X_14)),
inference(subst,[],[refute_0_26:[bind(X,$fot(falsehood)),bind(Y,$fot(not(X_14)))]]) ).
cnf(refute_0_28,plain,
not(or(not(X_14),falsehood)) = not(or(not(X_14),falsehood)),
introduced(tautology,[refl,[$fot(not(or(not(X_14),falsehood)))]]) ).
cnf(refute_0_29,plain,
( not(or(not(X_14),falsehood)) != not(or(not(X_14),falsehood))
| or(not(X_14),falsehood) != or(falsehood,not(X_14))
| not(or(not(X_14),falsehood)) = not(or(falsehood,not(X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X_14),falsehood)),not(or(not(X_14),falsehood))) ),[1,0],$fot(or(falsehood,not(X_14)))]]) ).
cnf(refute_0_30,plain,
( or(not(X_14),falsehood) != or(falsehood,not(X_14))
| not(or(not(X_14),falsehood)) = not(or(falsehood,not(X_14))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_14),falsehood)),not(or(not(X_14),falsehood))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
not(or(not(X_14),falsehood)) = not(or(falsehood,not(X_14))),
inference(resolve,[$cnf( $equal(or(not(X_14),falsehood),or(falsehood,not(X_14))) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
( and(X_14,truth) != not(or(not(X_14),falsehood))
| not(or(not(X_14),falsehood)) != not(or(falsehood,not(X_14)))
| and(X_14,truth) = not(or(falsehood,not(X_14))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_14,truth),not(or(falsehood,not(X_14)))) ),[0],$fot(not(or(not(X_14),falsehood)))]]) ).
cnf(refute_0_33,plain,
( and(X_14,truth) != not(or(not(X_14),falsehood))
| and(X_14,truth) = not(or(falsehood,not(X_14))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_14),falsehood)),not(or(falsehood,not(X_14)))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
and(X_14,truth) = not(or(falsehood,not(X_14))),
inference(resolve,[$cnf( $equal(and(X_14,truth),not(or(not(X_14),falsehood))) )],[refute_0_24,refute_0_33]) ).
cnf(refute_0_35,plain,
and(or(falsehood,falsehood),truth) = not(or(falsehood,not(or(falsehood,falsehood)))),
inference(subst,[],[refute_0_34:[bind(X_14,$fot(or(falsehood,falsehood)))]]) ).
cnf(refute_0_36,plain,
and(truth,truth) = not(or(falsehood,not(truth))),
inference(subst,[],[refute_0_34:[bind(X_14,$fot(truth))]]) ).
cnf(refute_0_37,plain,
( and(truth,truth) != not(or(falsehood,not(truth)))
| not(truth) != falsehood
| and(truth,truth) = not(or(falsehood,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,truth),not(or(falsehood,not(truth)))) ),[1,0,1],$fot(falsehood)]]) ).
cnf(refute_0_38,plain,
( and(truth,truth) != not(or(falsehood,not(truth)))
| and(truth,truth) = not(or(falsehood,falsehood)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_37]) ).
cnf(refute_0_39,plain,
and(truth,truth) = not(or(falsehood,falsehood)),
inference(resolve,[$cnf( $equal(and(truth,truth),not(or(falsehood,not(truth)))) )],[refute_0_36,refute_0_38]) ).
cnf(refute_0_40,plain,
( and(truth,truth) != not(or(falsehood,falsehood))
| not(or(falsehood,falsehood)) = and(truth,truth) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,truth))),bind(Y0,$fot(not(or(falsehood,falsehood))))]]) ).
cnf(refute_0_41,plain,
not(or(falsehood,falsehood)) = and(truth,truth),
inference(resolve,[$cnf( $equal(and(truth,truth),not(or(falsehood,falsehood))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( and(or(falsehood,falsehood),truth) != not(or(falsehood,not(or(falsehood,falsehood))))
| not(or(falsehood,falsehood)) != and(truth,truth)
| and(or(falsehood,falsehood),truth) = not(or(falsehood,and(truth,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,not(or(falsehood,falsehood))))) ),[1,0,1],$fot(and(truth,truth))]]) ).
cnf(refute_0_43,plain,
( and(or(falsehood,falsehood),truth) != not(or(falsehood,not(or(falsehood,falsehood))))
| and(or(falsehood,falsehood),truth) = not(or(falsehood,and(truth,truth))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,falsehood)),and(truth,truth)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
and(or(falsehood,falsehood),truth) = not(or(falsehood,and(truth,truth))),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,not(or(falsehood,falsehood))))) )],[refute_0_35,refute_0_43]) ).
cnf(refute_0_45,plain,
and(or(falsehood,falsehood),truth) = and(truth,or(falsehood,falsehood)),
inference(subst,[],[refute_0_4:[bind(X,$fot(truth)),bind(Y,$fot(or(falsehood,falsehood)))]]) ).
cnf(refute_0_46,plain,
( and(or(falsehood,falsehood),truth) != and(truth,or(falsehood,falsehood))
| and(or(falsehood,falsehood),truth) != not(or(falsehood,and(truth,truth)))
| and(truth,or(falsehood,falsehood)) = not(or(falsehood,and(truth,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,and(truth,truth)))) ),[0],$fot(and(truth,or(falsehood,falsehood)))]]) ).
cnf(refute_0_47,plain,
( and(or(falsehood,falsehood),truth) != not(or(falsehood,and(truth,truth)))
| and(truth,or(falsehood,falsehood)) = not(or(falsehood,and(truth,truth))) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),truth),and(truth,or(falsehood,falsehood))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
and(truth,or(falsehood,falsehood)) = not(or(falsehood,and(truth,truth))),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,and(truth,truth)))) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
( and(truth,or(falsehood,falsehood)) != not(or(falsehood,and(truth,truth)))
| not(or(falsehood,and(truth,truth))) = and(truth,or(falsehood,falsehood)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,or(falsehood,falsehood)))),bind(Y0,$fot(not(or(falsehood,and(truth,truth)))))]]) ).
cnf(refute_0_50,plain,
not(or(falsehood,and(truth,truth))) = and(truth,or(falsehood,falsehood)),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),not(or(falsehood,and(truth,truth)))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( and(or(falsehood,and(truth,truth)),Y) != not(or(not(or(falsehood,and(truth,truth))),not(Y)))
| not(or(falsehood,and(truth,truth))) != and(truth,or(falsehood,falsehood))
| and(or(falsehood,and(truth,truth)),Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),not(or(not(or(falsehood,and(truth,truth))),not(Y)))) ),[1,0,0],$fot(and(truth,or(falsehood,falsehood)))]]) ).
cnf(refute_0_52,plain,
( and(or(falsehood,and(truth,truth)),Y) != not(or(not(or(falsehood,and(truth,truth))),not(Y)))
| and(or(falsehood,and(truth,truth)),Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,truth))),and(truth,or(falsehood,falsehood))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
and(or(falsehood,and(truth,truth)),Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),not(or(not(or(falsehood,and(truth,truth))),not(Y)))) )],[refute_0_20,refute_0_52]) ).
cnf(refute_0_54,plain,
implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = implies(implies(and(truth,truth),not(falsehood)),not(falsehood)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(falsehood))),bind(Y,$fot(and(truth,truth)))]]) ).
cnf(refute_0_55,plain,
or(or(falsehood,falsehood),X_19) = implies(not(or(falsehood,falsehood)),X_19),
inference(subst,[],[or_definition:[bind(X,$fot(or(falsehood,falsehood))),bind(Y,$fot(X_19))]]) ).
cnf(refute_0_56,plain,
( not(or(falsehood,falsehood)) != and(truth,truth)
| or(or(falsehood,falsehood),X_19) != implies(not(or(falsehood,falsehood)),X_19)
| or(or(falsehood,falsehood),X_19) = implies(and(truth,truth),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(falsehood,falsehood),X_19),implies(not(or(falsehood,falsehood)),X_19)) ),[1,0],$fot(and(truth,truth))]]) ).
cnf(refute_0_57,plain,
( or(or(falsehood,falsehood),X_19) != implies(not(or(falsehood,falsehood)),X_19)
| or(or(falsehood,falsehood),X_19) = implies(and(truth,truth),X_19) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,falsehood)),and(truth,truth)) )],[refute_0_41,refute_0_56]) ).
cnf(refute_0_58,plain,
or(or(falsehood,falsehood),X_19) = implies(and(truth,truth),X_19),
inference(resolve,[$cnf( $equal(or(or(falsehood,falsehood),X_19),implies(not(or(falsehood,falsehood)),X_19)) )],[refute_0_55,refute_0_57]) ).
cnf(refute_0_59,plain,
or(or(falsehood,falsehood),X_19) = or(falsehood,or(falsehood,X_19)),
inference(subst,[],[or_associativity:[bind(X,$fot(falsehood)),bind(Y,$fot(falsehood)),bind(Z,$fot(X_19))]]) ).
cnf(refute_0_60,plain,
( or(or(falsehood,falsehood),X_19) != implies(and(truth,truth),X_19)
| or(or(falsehood,falsehood),X_19) != or(falsehood,or(falsehood,X_19))
| or(falsehood,or(falsehood,X_19)) = implies(and(truth,truth),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(falsehood,falsehood),X_19),implies(and(truth,truth),X_19)) ),[0],$fot(or(falsehood,or(falsehood,X_19)))]]) ).
cnf(refute_0_61,plain,
( or(or(falsehood,falsehood),X_19) != implies(and(truth,truth),X_19)
| or(falsehood,or(falsehood,X_19)) = implies(and(truth,truth),X_19) ),
inference(resolve,[$cnf( $equal(or(or(falsehood,falsehood),X_19),or(falsehood,or(falsehood,X_19))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
or(falsehood,or(falsehood,X_19)) = implies(and(truth,truth),X_19),
inference(resolve,[$cnf( $equal(or(or(falsehood,falsehood),X_19),implies(and(truth,truth),X_19)) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
or(falsehood,or(falsehood,not(falsehood))) = implies(and(truth,truth),not(falsehood)),
inference(subst,[],[refute_0_62:[bind(X_19,$fot(not(falsehood)))]]) ).
cnf(refute_0_64,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_65,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[or_definition,refute_0_64]) ).
cnf(refute_0_66,plain,
implies(not(X),not(Y)) = or(X,not(Y)),
inference(subst,[],[refute_0_65:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_67,plain,
implies(implies(not(X),not(Y)),implies(Y,X)) = implies(implies(not(X),not(Y)),implies(Y,X)),
introduced(tautology,[refl,[$fot(implies(implies(not(X),not(Y)),implies(Y,X)))]]) ).
cnf(refute_0_68,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != implies(implies(not(X),not(Y)),implies(Y,X))
| implies(not(X),not(Y)) != or(X,not(Y))
| implies(implies(not(X),not(Y)),implies(Y,X)) = implies(or(X,not(Y)),implies(Y,X)) ),
introduced(tautology,[equality,[$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_69,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( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(not(X),not(Y)),implies(Y,X))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
implies(implies(not(X),not(Y)),implies(Y,X)) = implies(or(X,not(Y)),implies(Y,X)),
inference(resolve,[$cnf( $equal(implies(not(X),not(Y)),or(X,not(Y))) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != implies(or(X,not(Y)),implies(Y,X))
| implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(or(X,not(Y)),implies(Y,X)) = truth ),
introduced(tautology,[equality,[$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_72,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(or(X,not(Y)),implies(Y,X)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(or(X,not(Y)),implies(Y,X))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
implies(or(X,not(Y)),implies(Y,X)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[wajsberg_4,refute_0_72]) ).
cnf(refute_0_74,plain,
implies(or(X_26,not(truth)),implies(truth,X_26)) = truth,
inference(subst,[],[refute_0_73:[bind(X,$fot(X_26)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_75,plain,
implies(truth,X_26) = X_26,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_26))]]) ).
cnf(refute_0_76,plain,
( implies(or(X_26,not(truth)),implies(truth,X_26)) != truth
| implies(truth,X_26) != X_26
| implies(or(X_26,not(truth)),X_26) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_26,not(truth)),implies(truth,X_26)),truth) ),[0,1],$fot(X_26)]]) ).
cnf(refute_0_77,plain,
( implies(or(X_26,not(truth)),implies(truth,X_26)) != truth
| implies(or(X_26,not(truth)),X_26) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_26),X_26) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
implies(or(X_26,not(truth)),X_26) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_26,not(truth)),implies(truth,X_26)),truth) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
or(X_26,not(truth)) = or(X_26,not(truth)),
introduced(tautology,[refl,[$fot(or(X_26,not(truth)))]]) ).
cnf(refute_0_80,plain,
( not(truth) != falsehood
| or(X_26,not(truth)) != or(X_26,not(truth))
| or(X_26,not(truth)) = or(X_26,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_26,not(truth)),or(X_26,not(truth))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_81,plain,
( not(truth) != falsehood
| or(X_26,not(truth)) = or(X_26,falsehood) ),
inference(resolve,[$cnf( $equal(or(X_26,not(truth)),or(X_26,not(truth))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
or(X_26,not(truth)) = or(X_26,falsehood),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_81]) ).
cnf(refute_0_83,plain,
implies(or(X_26,not(truth)),X_26) = implies(or(X_26,not(truth)),X_26),
introduced(tautology,[refl,[$fot(implies(or(X_26,not(truth)),X_26))]]) ).
cnf(refute_0_84,plain,
( implies(or(X_26,not(truth)),X_26) != implies(or(X_26,not(truth)),X_26)
| or(X_26,not(truth)) != or(X_26,falsehood)
| implies(or(X_26,not(truth)),X_26) = implies(or(X_26,falsehood),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_26,not(truth)),X_26),implies(or(X_26,not(truth)),X_26)) ),[1,0],$fot(or(X_26,falsehood))]]) ).
cnf(refute_0_85,plain,
( or(X_26,not(truth)) != or(X_26,falsehood)
| implies(or(X_26,not(truth)),X_26) = implies(or(X_26,falsehood),X_26) ),
inference(resolve,[$cnf( $equal(implies(or(X_26,not(truth)),X_26),implies(or(X_26,not(truth)),X_26)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
implies(or(X_26,not(truth)),X_26) = implies(or(X_26,falsehood),X_26),
inference(resolve,[$cnf( $equal(or(X_26,not(truth)),or(X_26,falsehood)) )],[refute_0_82,refute_0_85]) ).
cnf(refute_0_87,plain,
( implies(or(X_26,not(truth)),X_26) != implies(or(X_26,falsehood),X_26)
| implies(or(X_26,not(truth)),X_26) != truth
| implies(or(X_26,falsehood),X_26) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_26,not(truth)),X_26),truth) ),[0],$fot(implies(or(X_26,falsehood),X_26))]]) ).
cnf(refute_0_88,plain,
( implies(or(X_26,not(truth)),X_26) != truth
| implies(or(X_26,falsehood),X_26) = truth ),
inference(resolve,[$cnf( $equal(implies(or(X_26,not(truth)),X_26),implies(or(X_26,falsehood),X_26)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
implies(or(X_26,falsehood),X_26) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_26,not(truth)),X_26),truth) )],[refute_0_78,refute_0_88]) ).
cnf(refute_0_90,plain,
implies(or(truth,falsehood),truth) = truth,
inference(subst,[],[refute_0_89:[bind(X_26,$fot(truth))]]) ).
cnf(refute_0_91,plain,
or(truth,X_19) = implies(not(truth),X_19),
inference(subst,[],[or_definition:[bind(X,$fot(truth)),bind(Y,$fot(X_19))]]) ).
cnf(refute_0_92,plain,
( not(truth) != falsehood
| or(truth,X_19) != implies(not(truth),X_19)
| or(truth,X_19) = implies(falsehood,X_19) ),
introduced(tautology,[equality,[$cnf( $equal(or(truth,X_19),implies(not(truth),X_19)) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_93,plain,
( or(truth,X_19) != implies(not(truth),X_19)
| or(truth,X_19) = implies(falsehood,X_19) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_92]) ).
cnf(refute_0_94,plain,
or(truth,X_19) = implies(falsehood,X_19),
inference(resolve,[$cnf( $equal(or(truth,X_19),implies(not(truth),X_19)) )],[refute_0_91,refute_0_93]) ).
cnf(refute_0_95,plain,
or(truth,falsehood) = implies(falsehood,falsehood),
inference(subst,[],[refute_0_94:[bind(X_19,$fot(falsehood))]]) ).
cnf(refute_0_96,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_97,plain,
( implies(or(truth,falsehood),truth) != truth
| implies(implies(falsehood,falsehood),truth) = truth ),
inference(resolve,[$cnf( $equal(or(truth,falsehood),implies(falsehood,falsehood)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
implies(implies(falsehood,falsehood),truth) = truth,
inference(resolve,[$cnf( $equal(implies(or(truth,falsehood),truth),truth) )],[refute_0_90,refute_0_97]) ).
cnf(refute_0_99,plain,
implies(implies(truth,X_8),X_8) = implies(implies(X_8,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_100,plain,
implies(truth,X_8) = X_8,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_8))]]) ).
cnf(refute_0_101,plain,
( implies(implies(truth,X_8),X_8) != implies(implies(X_8,truth),truth)
| implies(truth,X_8) != X_8
| implies(X_8,X_8) = implies(implies(X_8,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_8),X_8),implies(implies(X_8,truth),truth)) ),[0,0],$fot(X_8)]]) ).
cnf(refute_0_102,plain,
( implies(implies(truth,X_8),X_8) != implies(implies(X_8,truth),truth)
| implies(X_8,X_8) = implies(implies(X_8,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(truth,X_8),X_8) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
implies(X_8,X_8) = implies(implies(X_8,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_8),X_8),implies(implies(X_8,truth),truth)) )],[refute_0_99,refute_0_102]) ).
cnf(refute_0_104,plain,
implies(not(X_18),not(X_18)) = implies(implies(not(X_18),truth),truth),
inference(subst,[],[refute_0_103:[bind(X_8,$fot(not(X_18)))]]) ).
cnf(refute_0_105,plain,
or(X_18,truth) = implies(not(X_18),truth),
inference(subst,[],[or_definition:[bind(X,$fot(X_18)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_106,plain,
( or(X_18,truth) != implies(not(X_18),truth)
| implies(not(X_18),truth) = or(X_18,truth) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X_18,truth))),bind(Y0,$fot(implies(not(X_18),truth)))]]) ).
cnf(refute_0_107,plain,
implies(not(X_18),truth) = or(X_18,truth),
inference(resolve,[$cnf( $equal(or(X_18,truth),implies(not(X_18),truth)) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
( implies(not(X_18),not(X_18)) != implies(implies(not(X_18),truth),truth)
| implies(not(X_18),truth) != or(X_18,truth)
| implies(not(X_18),not(X_18)) = implies(or(X_18,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_18),not(X_18)),implies(implies(not(X_18),truth),truth)) ),[1,0],$fot(or(X_18,truth))]]) ).
cnf(refute_0_109,plain,
( implies(not(X_18),not(X_18)) != implies(implies(not(X_18),truth),truth)
| implies(not(X_18),not(X_18)) = implies(or(X_18,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(not(X_18),truth),or(X_18,truth)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
implies(not(X_18),not(X_18)) = implies(or(X_18,truth),truth),
inference(resolve,[$cnf( $equal(implies(not(X_18),not(X_18)),implies(implies(not(X_18),truth),truth)) )],[refute_0_104,refute_0_109]) ).
cnf(refute_0_111,plain,
implies(not(X_18),not(X_18)) = or(X_18,not(X_18)),
inference(subst,[],[refute_0_65:[bind(X,$fot(X_18)),bind(Y,$fot(not(X_18)))]]) ).
cnf(refute_0_112,plain,
( implies(not(X_18),not(X_18)) != implies(or(X_18,truth),truth)
| implies(not(X_18),not(X_18)) != or(X_18,not(X_18))
| or(X_18,not(X_18)) = implies(or(X_18,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_18),not(X_18)),implies(or(X_18,truth),truth)) ),[0],$fot(or(X_18,not(X_18)))]]) ).
cnf(refute_0_113,plain,
( implies(not(X_18),not(X_18)) != implies(or(X_18,truth),truth)
| or(X_18,not(X_18)) = implies(or(X_18,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(not(X_18),not(X_18)),or(X_18,not(X_18))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
or(X_18,not(X_18)) = implies(or(X_18,truth),truth),
inference(resolve,[$cnf( $equal(implies(not(X_18),not(X_18)),implies(or(X_18,truth),truth)) )],[refute_0_110,refute_0_113]) ).
cnf(refute_0_115,plain,
or(X,truth) = or(truth,X),
inference(subst,[],[or_commutativity:[bind(Y,$fot(truth))]]) ).
cnf(refute_0_116,plain,
or(truth,X) = implies(falsehood,X),
inference(subst,[],[refute_0_94:[bind(X_19,$fot(X))]]) ).
cnf(refute_0_117,plain,
( or(X,truth) != or(truth,X)
| or(truth,X) != implies(falsehood,X)
| or(X,truth) = implies(falsehood,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(or(X,truth),implies(falsehood,X)) ),[0],$fot(or(truth,X))]]) ).
cnf(refute_0_118,plain,
( or(X,truth) != or(truth,X)
| or(X,truth) = implies(falsehood,X) ),
inference(resolve,[$cnf( $equal(or(truth,X),implies(falsehood,X)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
or(X,truth) = implies(falsehood,X),
inference(resolve,[$cnf( $equal(or(X,truth),or(truth,X)) )],[refute_0_115,refute_0_118]) ).
cnf(refute_0_120,plain,
or(X_18,truth) = implies(falsehood,X_18),
inference(subst,[],[refute_0_119:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_121,plain,
implies(or(X_18,truth),truth) = implies(or(X_18,truth),truth),
introduced(tautology,[refl,[$fot(implies(or(X_18,truth),truth))]]) ).
cnf(refute_0_122,plain,
( implies(or(X_18,truth),truth) != implies(or(X_18,truth),truth)
| or(X_18,truth) != implies(falsehood,X_18)
| implies(or(X_18,truth),truth) = implies(implies(falsehood,X_18),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_18,truth),truth),implies(or(X_18,truth),truth)) ),[1,0],$fot(implies(falsehood,X_18))]]) ).
cnf(refute_0_123,plain,
( or(X_18,truth) != implies(falsehood,X_18)
| implies(or(X_18,truth),truth) = implies(implies(falsehood,X_18),truth) ),
inference(resolve,[$cnf( $equal(implies(or(X_18,truth),truth),implies(or(X_18,truth),truth)) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
implies(or(X_18,truth),truth) = implies(implies(falsehood,X_18),truth),
inference(resolve,[$cnf( $equal(or(X_18,truth),implies(falsehood,X_18)) )],[refute_0_120,refute_0_123]) ).
cnf(refute_0_125,plain,
( implies(or(X_18,truth),truth) != implies(implies(falsehood,X_18),truth)
| or(X_18,not(X_18)) != implies(or(X_18,truth),truth)
| or(X_18,not(X_18)) = implies(implies(falsehood,X_18),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_18,not(X_18)),implies(or(X_18,truth),truth)) ),[1],$fot(implies(implies(falsehood,X_18),truth))]]) ).
cnf(refute_0_126,plain,
( or(X_18,not(X_18)) != implies(or(X_18,truth),truth)
| or(X_18,not(X_18)) = implies(implies(falsehood,X_18),truth) ),
inference(resolve,[$cnf( $equal(implies(or(X_18,truth),truth),implies(implies(falsehood,X_18),truth)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
or(X_18,not(X_18)) = implies(implies(falsehood,X_18),truth),
inference(resolve,[$cnf( $equal(or(X_18,not(X_18)),implies(or(X_18,truth),truth)) )],[refute_0_114,refute_0_126]) ).
cnf(refute_0_128,plain,
( or(X_18,not(X_18)) != implies(implies(falsehood,X_18),truth)
| implies(implies(falsehood,X_18),truth) = or(X_18,not(X_18)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X_18,not(X_18)))),bind(Y0,$fot(implies(implies(falsehood,X_18),truth)))]]) ).
cnf(refute_0_129,plain,
implies(implies(falsehood,X_18),truth) = or(X_18,not(X_18)),
inference(resolve,[$cnf( $equal(or(X_18,not(X_18)),implies(implies(falsehood,X_18),truth)) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
implies(implies(falsehood,falsehood),truth) = or(falsehood,not(falsehood)),
inference(subst,[],[refute_0_129:[bind(X_18,$fot(falsehood))]]) ).
cnf(refute_0_131,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_132,plain,
( implies(implies(falsehood,falsehood),truth) != truth
| or(falsehood,not(falsehood)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,falsehood),truth),or(falsehood,not(falsehood))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
or(falsehood,not(falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,falsehood),truth),truth) )],[refute_0_98,refute_0_132]) ).
cnf(refute_0_134,plain,
( or(falsehood,not(falsehood)) != truth
| or(falsehood,or(falsehood,not(falsehood))) != implies(and(truth,truth),not(falsehood))
| or(falsehood,truth) = implies(and(truth,truth),not(falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(falsehood,not(falsehood))),implies(and(truth,truth),not(falsehood))) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_135,plain,
( or(falsehood,or(falsehood,not(falsehood))) != implies(and(truth,truth),not(falsehood))
| or(falsehood,truth) = implies(and(truth,truth),not(falsehood)) ),
inference(resolve,[$cnf( $equal(or(falsehood,not(falsehood)),truth) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
or(falsehood,truth) = implies(and(truth,truth),not(falsehood)),
inference(resolve,[$cnf( $equal(or(falsehood,or(falsehood,not(falsehood))),implies(and(truth,truth),not(falsehood))) )],[refute_0_63,refute_0_135]) ).
cnf(refute_0_137,plain,
implies(or(falsehood,not(falsehood)),implies(falsehood,falsehood)) = truth,
inference(subst,[],[refute_0_73:[bind(X,$fot(falsehood)),bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_138,plain,
( implies(or(falsehood,not(falsehood)),implies(falsehood,falsehood)) != truth
| or(falsehood,not(falsehood)) != truth
| implies(truth,implies(falsehood,falsehood)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,not(falsehood)),implies(falsehood,falsehood)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_139,plain,
( implies(or(falsehood,not(falsehood)),implies(falsehood,falsehood)) != truth
| implies(truth,implies(falsehood,falsehood)) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,not(falsehood)),truth) )],[refute_0_133,refute_0_138]) ).
cnf(refute_0_140,plain,
implies(truth,implies(falsehood,falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,not(falsehood)),implies(falsehood,falsehood)),truth) )],[refute_0_137,refute_0_139]) ).
cnf(refute_0_141,plain,
implies(truth,implies(falsehood,falsehood)) = implies(falsehood,falsehood),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(falsehood,falsehood)))]]) ).
cnf(refute_0_142,plain,
( implies(truth,implies(falsehood,falsehood)) != implies(falsehood,falsehood)
| implies(truth,implies(falsehood,falsehood)) != truth
| implies(falsehood,falsehood) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(falsehood,falsehood)),truth) ),[0],$fot(implies(falsehood,falsehood))]]) ).
cnf(refute_0_143,plain,
( implies(truth,implies(falsehood,falsehood)) != truth
| implies(falsehood,falsehood) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(falsehood,falsehood)),implies(falsehood,falsehood)) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
implies(falsehood,falsehood) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(falsehood,falsehood)),truth) )],[refute_0_140,refute_0_143]) ).
cnf(refute_0_145,plain,
or(falsehood,truth) = implies(falsehood,falsehood),
inference(subst,[],[refute_0_119:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_146,plain,
( implies(falsehood,falsehood) != truth
| or(falsehood,truth) != implies(falsehood,falsehood)
| or(falsehood,truth) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(falsehood,truth))),bind(Y0,$fot(implies(falsehood,falsehood))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_147,plain,
( implies(falsehood,falsehood) != truth
| or(falsehood,truth) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,truth),implies(falsehood,falsehood)) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
or(falsehood,truth) = truth,
inference(resolve,[$cnf( $equal(implies(falsehood,falsehood),truth) )],[refute_0_144,refute_0_147]) ).
cnf(refute_0_149,plain,
( or(falsehood,truth) != implies(and(truth,truth),not(falsehood))
| or(falsehood,truth) != truth
| truth = implies(and(truth,truth),not(falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,truth),implies(and(truth,truth),not(falsehood))) ),[0],$fot(truth)]]) ).
cnf(refute_0_150,plain,
( or(falsehood,truth) != implies(and(truth,truth),not(falsehood))
| truth = implies(and(truth,truth),not(falsehood)) ),
inference(resolve,[$cnf( $equal(or(falsehood,truth),truth) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
truth = implies(and(truth,truth),not(falsehood)),
inference(resolve,[$cnf( $equal(or(falsehood,truth),implies(and(truth,truth),not(falsehood))) )],[refute_0_136,refute_0_150]) ).
cnf(refute_0_152,plain,
( truth != implies(and(truth,truth),not(falsehood))
| implies(and(truth,truth),not(falsehood)) = truth ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(and(truth,truth),not(falsehood))))]]) ).
cnf(refute_0_153,plain,
implies(and(truth,truth),not(falsehood)) = truth,
inference(resolve,[$cnf( $equal(truth,implies(and(truth,truth),not(falsehood))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
( implies(and(truth,truth),not(falsehood)) != truth
| implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) != implies(implies(and(truth,truth),not(falsehood)),not(falsehood))
| implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = implies(truth,not(falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)),implies(implies(and(truth,truth),not(falsehood)),not(falsehood))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_155,plain,
( implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) != implies(implies(and(truth,truth),not(falsehood)),not(falsehood))
| implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = implies(truth,not(falsehood)) ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),not(falsehood)),truth) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = implies(truth,not(falsehood)),
inference(resolve,[$cnf( $equal(implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)),implies(implies(and(truth,truth),not(falsehood)),not(falsehood))) )],[refute_0_54,refute_0_155]) ).
cnf(refute_0_157,plain,
implies(or(X_28,falsehood),X_28) = truth,
inference(subst,[],[refute_0_89:[bind(X_26,$fot(X_28))]]) ).
cnf(refute_0_158,plain,
or(falsehood,X_28) = or(X_28,falsehood),
inference(subst,[],[or_commutativity:[bind(X,$fot(falsehood)),bind(Y,$fot(X_28))]]) ).
cnf(refute_0_159,plain,
( or(falsehood,X_28) != or(X_28,falsehood)
| or(X_28,falsehood) = or(falsehood,X_28) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(falsehood,X_28))),bind(Y0,$fot(or(X_28,falsehood)))]]) ).
cnf(refute_0_160,plain,
or(X_28,falsehood) = or(falsehood,X_28),
inference(resolve,[$cnf( $equal(or(falsehood,X_28),or(X_28,falsehood)) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
( implies(or(X_28,falsehood),X_28) != truth
| or(X_28,falsehood) != or(falsehood,X_28)
| implies(or(falsehood,X_28),X_28) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_28,falsehood),X_28),truth) ),[0,0],$fot(or(falsehood,X_28))]]) ).
cnf(refute_0_162,plain,
( implies(or(X_28,falsehood),X_28) != truth
| implies(or(falsehood,X_28),X_28) = truth ),
inference(resolve,[$cnf( $equal(or(X_28,falsehood),or(falsehood,X_28)) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
implies(or(falsehood,X_28),X_28) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_28,falsehood),X_28),truth) )],[refute_0_157,refute_0_162]) ).
cnf(refute_0_164,plain,
implies(or(falsehood,and(truth,truth)),and(truth,truth)) = truth,
inference(subst,[],[refute_0_163:[bind(X_28,$fot(and(truth,truth)))]]) ).
cnf(refute_0_165,plain,
implies(implies(X,not(X_18)),not(X_18)) = implies(implies(not(X_18),X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(not(X_18)))]]) ).
cnf(refute_0_166,plain,
or(X_18,X) = implies(not(X_18),X),
inference(subst,[],[or_definition:[bind(X,$fot(X_18)),bind(Y,$fot(X))]]) ).
cnf(refute_0_167,plain,
( or(X_18,X) != implies(not(X_18),X)
| implies(not(X_18),X) = or(X_18,X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X_18,X))),bind(Y0,$fot(implies(not(X_18),X)))]]) ).
cnf(refute_0_168,plain,
implies(not(X_18),X) = or(X_18,X),
inference(resolve,[$cnf( $equal(or(X_18,X),implies(not(X_18),X)) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
( implies(implies(X,not(X_18)),not(X_18)) != implies(implies(not(X_18),X),X)
| implies(not(X_18),X) != or(X_18,X)
| implies(implies(X,not(X_18)),not(X_18)) = implies(or(X_18,X),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(X_18)),not(X_18)),implies(implies(not(X_18),X),X)) ),[1,0],$fot(or(X_18,X))]]) ).
cnf(refute_0_170,plain,
( implies(implies(X,not(X_18)),not(X_18)) != implies(implies(not(X_18),X),X)
| implies(implies(X,not(X_18)),not(X_18)) = implies(or(X_18,X),X) ),
inference(resolve,[$cnf( $equal(implies(not(X_18),X),or(X_18,X)) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
implies(implies(X,not(X_18)),not(X_18)) = implies(or(X_18,X),X),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X_18)),not(X_18)),implies(implies(not(X_18),X),X)) )],[refute_0_165,refute_0_170]) ).
cnf(refute_0_172,plain,
implies(implies(and(truth,truth),not(falsehood)),not(falsehood)) = implies(or(falsehood,and(truth,truth)),and(truth,truth)),
inference(subst,[],[refute_0_171:[bind(X,$fot(and(truth,truth))),bind(X_18,$fot(falsehood))]]) ).
cnf(refute_0_173,plain,
( implies(implies(and(truth,truth),not(falsehood)),not(falsehood)) != implies(or(falsehood,and(truth,truth)),and(truth,truth))
| implies(or(falsehood,and(truth,truth)),and(truth,truth)) != truth
| implies(implies(and(truth,truth),not(falsehood)),not(falsehood)) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(implies(and(truth,truth),not(falsehood)),not(falsehood)))),bind(Y0,$fot(implies(or(falsehood,and(truth,truth)),and(truth,truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_174,plain,
( implies(or(falsehood,and(truth,truth)),and(truth,truth)) != truth
| implies(implies(and(truth,truth),not(falsehood)),not(falsehood)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,truth),not(falsehood)),not(falsehood)),implies(or(falsehood,and(truth,truth)),and(truth,truth))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
implies(implies(and(truth,truth),not(falsehood)),not(falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,and(truth,truth)),and(truth,truth)),truth) )],[refute_0_164,refute_0_174]) ).
cnf(refute_0_176,plain,
( implies(implies(and(truth,truth),not(falsehood)),not(falsehood)) != truth
| implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) != implies(implies(and(truth,truth),not(falsehood)),not(falsehood))
| implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)))),bind(Y0,$fot(implies(implies(and(truth,truth),not(falsehood)),not(falsehood)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_177,plain,
( implies(implies(and(truth,truth),not(falsehood)),not(falsehood)) != truth
| implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)),implies(implies(and(truth,truth),not(falsehood)),not(falsehood))) )],[refute_0_54,refute_0_176]) ).
cnf(refute_0_178,plain,
implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(and(truth,truth),not(falsehood)),not(falsehood)),truth) )],[refute_0_175,refute_0_177]) ).
cnf(refute_0_179,plain,
( implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) != implies(truth,not(falsehood))
| implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) != truth
| truth = implies(truth,not(falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)),implies(truth,not(falsehood))) ),[0],$fot(truth)]]) ).
cnf(refute_0_180,plain,
( implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) != implies(truth,not(falsehood))
| truth = implies(truth,not(falsehood)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)),truth) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
implies(truth,not(falsehood)) = not(falsehood),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(falsehood)))]]) ).
cnf(refute_0_182,plain,
( implies(truth,not(falsehood)) != not(falsehood)
| truth != implies(truth,not(falsehood))
| truth = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(truth,implies(truth,not(falsehood))) ),[1],$fot(not(falsehood))]]) ).
cnf(refute_0_183,plain,
( truth != implies(truth,not(falsehood))
| truth = not(falsehood) ),
inference(resolve,[$cnf( $equal(implies(truth,not(falsehood)),not(falsehood)) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
( implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) != implies(truth,not(falsehood))
| truth = not(falsehood) ),
inference(resolve,[$cnf( $equal(truth,implies(truth,not(falsehood))) )],[refute_0_180,refute_0_183]) ).
cnf(refute_0_185,plain,
truth = not(falsehood),
inference(resolve,[$cnf( $equal(implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)),implies(truth,not(falsehood))) )],[refute_0_156,refute_0_184]) ).
cnf(refute_0_186,plain,
( truth != not(falsehood)
| not(falsehood) = truth ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(truth)),bind(Y0,$fot(not(falsehood)))]]) ).
cnf(refute_0_187,plain,
not(falsehood) = truth,
inference(resolve,[$cnf( $equal(truth,not(falsehood)) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
not(not(truth)) = not(not(truth)),
introduced(tautology,[refl,[$fot(not(not(truth)))]]) ).
cnf(refute_0_189,plain,
( not(not(truth)) != not(not(truth))
| not(truth) != falsehood
| not(not(truth)) = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(truth)),not(not(truth))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_190,plain,
( not(truth) != falsehood
| not(not(truth)) = not(falsehood) ),
inference(resolve,[$cnf( $equal(not(not(truth)),not(not(truth))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
not(not(truth)) = not(falsehood),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_190]) ).
cnf(refute_0_192,plain,
( not(falsehood) != truth
| not(not(truth)) != not(falsehood)
| not(not(truth)) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(not(not(truth)))),bind(Y0,$fot(not(falsehood))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_193,plain,
( not(falsehood) != truth
| not(not(truth)) = truth ),
inference(resolve,[$cnf( $equal(not(not(truth)),not(falsehood)) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
not(not(truth)) = truth,
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_187,refute_0_193]) ).
cnf(refute_0_195,plain,
or(falsehood,Y) = implies(not(falsehood),Y),
inference(subst,[],[or_definition:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_196,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_197,plain,
( or(falsehood,Y) != implies(not(falsehood),Y)
| or(falsehood,Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_187,refute_0_196]) ).
cnf(refute_0_198,plain,
or(falsehood,Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(or(falsehood,Y),implies(not(falsehood),Y)) )],[refute_0_195,refute_0_197]) ).
cnf(refute_0_199,plain,
implies(truth,Y) = Y,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_200,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_201,plain,
( or(falsehood,Y) != implies(truth,Y)
| or(falsehood,Y) = Y ),
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
or(falsehood,Y) = Y,
inference(resolve,[$cnf( $equal(or(falsehood,Y),implies(truth,Y)) )],[refute_0_198,refute_0_201]) ).
cnf(refute_0_203,plain,
or(falsehood,not(X_14)) = not(X_14),
inference(subst,[],[refute_0_202:[bind(Y,$fot(not(X_14)))]]) ).
cnf(refute_0_204,plain,
not(or(falsehood,not(X_14))) = not(or(falsehood,not(X_14))),
introduced(tautology,[refl,[$fot(not(or(falsehood,not(X_14))))]]) ).
cnf(refute_0_205,plain,
( not(or(falsehood,not(X_14))) != not(or(falsehood,not(X_14)))
| or(falsehood,not(X_14)) != not(X_14)
| not(or(falsehood,not(X_14))) = not(not(X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,not(X_14))),not(or(falsehood,not(X_14)))) ),[1,0],$fot(not(X_14))]]) ).
cnf(refute_0_206,plain,
( or(falsehood,not(X_14)) != not(X_14)
| not(or(falsehood,not(X_14))) = not(not(X_14)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_14))),not(or(falsehood,not(X_14)))) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
not(or(falsehood,not(X_14))) = not(not(X_14)),
inference(resolve,[$cnf( $equal(or(falsehood,not(X_14)),not(X_14)) )],[refute_0_203,refute_0_206]) ).
cnf(refute_0_208,plain,
( and(X_14,truth) != not(or(falsehood,not(X_14)))
| not(or(falsehood,not(X_14))) != not(not(X_14))
| and(X_14,truth) = not(not(X_14)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_14,truth),not(not(X_14))) ),[0],$fot(not(or(falsehood,not(X_14))))]]) ).
cnf(refute_0_209,plain,
( and(X_14,truth) != not(or(falsehood,not(X_14)))
| and(X_14,truth) = not(not(X_14)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_14))),not(not(X_14))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
and(X_14,truth) = not(not(X_14)),
inference(resolve,[$cnf( $equal(and(X_14,truth),not(or(falsehood,not(X_14)))) )],[refute_0_34,refute_0_209]) ).
cnf(refute_0_211,plain,
and(truth,truth) = not(not(truth)),
inference(subst,[],[refute_0_210:[bind(X_14,$fot(truth))]]) ).
cnf(refute_0_212,plain,
or(falsehood,and(truth,truth)) = and(truth,truth),
inference(subst,[],[refute_0_202:[bind(Y,$fot(and(truth,truth)))]]) ).
cnf(refute_0_213,plain,
( and(truth,truth) != not(not(truth))
| or(falsehood,and(truth,truth)) != and(truth,truth)
| or(falsehood,and(truth,truth)) = not(not(truth)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(falsehood,and(truth,truth)))),bind(Y0,$fot(and(truth,truth))),bind(Z0,$fot(not(not(truth))))]]) ).
cnf(refute_0_214,plain,
( and(truth,truth) != not(not(truth))
| or(falsehood,and(truth,truth)) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),and(truth,truth)) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
or(falsehood,and(truth,truth)) = not(not(truth)),
inference(resolve,[$cnf( $equal(and(truth,truth),not(not(truth))) )],[refute_0_211,refute_0_214]) ).
cnf(refute_0_216,plain,
( not(not(truth)) != truth
| or(falsehood,and(truth,truth)) != not(not(truth))
| or(falsehood,and(truth,truth)) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(falsehood,and(truth,truth)))),bind(Y0,$fot(not(not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_217,plain,
( not(not(truth)) != truth
| or(falsehood,and(truth,truth)) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),not(not(truth))) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
or(falsehood,and(truth,truth)) = truth,
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_194,refute_0_217]) ).
cnf(refute_0_219,plain,
and(or(falsehood,and(truth,truth)),Y) = and(or(falsehood,and(truth,truth)),Y),
introduced(tautology,[refl,[$fot(and(or(falsehood,and(truth,truth)),Y))]]) ).
cnf(refute_0_220,plain,
( and(or(falsehood,and(truth,truth)),Y) != and(or(falsehood,and(truth,truth)),Y)
| or(falsehood,and(truth,truth)) != truth
| and(or(falsehood,and(truth,truth)),Y) = and(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),and(or(falsehood,and(truth,truth)),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_221,plain,
( or(falsehood,and(truth,truth)) != truth
| and(or(falsehood,and(truth,truth)),Y) = and(truth,Y) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),and(or(falsehood,and(truth,truth)),Y)) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
and(or(falsehood,and(truth,truth)),Y) = and(truth,Y),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),truth) )],[refute_0_218,refute_0_221]) ).
cnf(refute_0_223,plain,
( and(or(falsehood,and(truth,truth)),Y) != and(truth,Y)
| and(or(falsehood,and(truth,truth)),Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) ),[0],$fot(and(truth,Y))]]) ).
cnf(refute_0_224,plain,
( and(or(falsehood,and(truth,truth)),Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),and(truth,Y)) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
or(falsehood,not(Y)) = not(Y),
inference(subst,[],[refute_0_202:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_226,plain,
and(falsehood,truth) = not(or(falsehood,not(falsehood))),
inference(subst,[],[refute_0_34:[bind(X_14,$fot(falsehood))]]) ).
cnf(refute_0_227,plain,
( and(falsehood,truth) != not(or(falsehood,not(falsehood)))
| or(falsehood,not(falsehood)) != truth
| and(falsehood,truth) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(and(falsehood,truth),not(or(falsehood,not(falsehood)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_228,plain,
( and(falsehood,truth) != not(or(falsehood,not(falsehood)))
| and(falsehood,truth) = not(truth) ),
inference(resolve,[$cnf( $equal(or(falsehood,not(falsehood)),truth) )],[refute_0_133,refute_0_227]) ).
cnf(refute_0_229,plain,
and(falsehood,truth) = not(truth),
inference(resolve,[$cnf( $equal(and(falsehood,truth),not(or(falsehood,not(falsehood)))) )],[refute_0_226,refute_0_228]) ).
cnf(refute_0_230,plain,
( and(falsehood,truth) != not(truth)
| not(truth) != falsehood
| and(falsehood,truth) = falsehood ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(falsehood,truth),falsehood) ),[0],$fot(not(truth))]]) ).
cnf(refute_0_231,plain,
( and(falsehood,truth) != not(truth)
| and(falsehood,truth) = falsehood ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_230]) ).
cnf(refute_0_232,plain,
and(falsehood,truth) = falsehood,
inference(resolve,[$cnf( $equal(and(falsehood,truth),not(truth)) )],[refute_0_229,refute_0_231]) ).
cnf(refute_0_233,plain,
and(truth,falsehood) = and(falsehood,truth),
inference(subst,[],[refute_0_4:[bind(X,$fot(falsehood)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_234,plain,
( and(falsehood,truth) != falsehood
| and(truth,falsehood) != and(falsehood,truth)
| and(truth,falsehood) = falsehood ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(truth,falsehood))),bind(Y0,$fot(and(falsehood,truth))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_235,plain,
( and(falsehood,truth) != falsehood
| and(truth,falsehood) = falsehood ),
inference(resolve,[$cnf( $equal(and(truth,falsehood),and(falsehood,truth)) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
and(truth,falsehood) = falsehood,
inference(resolve,[$cnf( $equal(and(falsehood,truth),falsehood) )],[refute_0_232,refute_0_235]) ).
cnf(refute_0_237,plain,
or(falsehood,falsehood) = falsehood,
inference(subst,[],[refute_0_202:[bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_238,plain,
and(truth,or(falsehood,falsehood)) = and(truth,or(falsehood,falsehood)),
introduced(tautology,[refl,[$fot(and(truth,or(falsehood,falsehood)))]]) ).
cnf(refute_0_239,plain,
( and(truth,or(falsehood,falsehood)) != and(truth,or(falsehood,falsehood))
| or(falsehood,falsehood) != falsehood
| and(truth,or(falsehood,falsehood)) = and(truth,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,or(falsehood,falsehood)),and(truth,or(falsehood,falsehood))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_240,plain,
( or(falsehood,falsehood) != falsehood
| and(truth,or(falsehood,falsehood)) = and(truth,falsehood) ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),and(truth,or(falsehood,falsehood))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
and(truth,or(falsehood,falsehood)) = and(truth,falsehood),
inference(resolve,[$cnf( $equal(or(falsehood,falsehood),falsehood) )],[refute_0_237,refute_0_240]) ).
cnf(refute_0_242,plain,
( and(truth,falsehood) != falsehood
| and(truth,or(falsehood,falsehood)) != and(truth,falsehood)
| and(truth,or(falsehood,falsehood)) = falsehood ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(truth,or(falsehood,falsehood)))),bind(Y0,$fot(and(truth,falsehood))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_243,plain,
( and(truth,falsehood) != falsehood
| and(truth,or(falsehood,falsehood)) = falsehood ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),and(truth,falsehood)) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
and(truth,or(falsehood,falsehood)) = falsehood,
inference(resolve,[$cnf( $equal(and(truth,falsehood),falsehood) )],[refute_0_236,refute_0_243]) ).
cnf(refute_0_245,plain,
or(and(truth,or(falsehood,falsehood)),not(Y)) = or(and(truth,or(falsehood,falsehood)),not(Y)),
introduced(tautology,[refl,[$fot(or(and(truth,or(falsehood,falsehood)),not(Y)))]]) ).
cnf(refute_0_246,plain,
( and(truth,or(falsehood,falsehood)) != falsehood
| or(and(truth,or(falsehood,falsehood)),not(Y)) != or(and(truth,or(falsehood,falsehood)),not(Y))
| or(and(truth,or(falsehood,falsehood)),not(Y)) = or(falsehood,not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(truth,or(falsehood,falsehood)),not(Y)),or(and(truth,or(falsehood,falsehood)),not(Y))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_247,plain,
( and(truth,or(falsehood,falsehood)) != falsehood
| or(and(truth,or(falsehood,falsehood)),not(Y)) = or(falsehood,not(Y)) ),
inference(resolve,[$cnf( $equal(or(and(truth,or(falsehood,falsehood)),not(Y)),or(and(truth,or(falsehood,falsehood)),not(Y))) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
or(and(truth,or(falsehood,falsehood)),not(Y)) = or(falsehood,not(Y)),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),falsehood) )],[refute_0_244,refute_0_247]) ).
cnf(refute_0_249,plain,
( or(and(truth,or(falsehood,falsehood)),not(Y)) != or(falsehood,not(Y))
| or(falsehood,not(Y)) != not(Y)
| or(and(truth,or(falsehood,falsehood)),not(Y)) = not(Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(and(truth,or(falsehood,falsehood)),not(Y)))),bind(Y0,$fot(or(falsehood,not(Y)))),bind(Z0,$fot(not(Y)))]]) ).
cnf(refute_0_250,plain,
( or(falsehood,not(Y)) != not(Y)
| or(and(truth,or(falsehood,falsehood)),not(Y)) = not(Y) ),
inference(resolve,[$cnf( $equal(or(and(truth,or(falsehood,falsehood)),not(Y)),or(falsehood,not(Y))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
or(and(truth,or(falsehood,falsehood)),not(Y)) = not(Y),
inference(resolve,[$cnf( $equal(or(falsehood,not(Y)),not(Y)) )],[refute_0_225,refute_0_250]) ).
cnf(refute_0_252,plain,
not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(or(and(truth,or(falsehood,falsehood)),not(Y))),
introduced(tautology,[refl,[$fot(not(or(and(truth,or(falsehood,falsehood)),not(Y))))]]) ).
cnf(refute_0_253,plain,
( not(or(and(truth,or(falsehood,falsehood)),not(Y))) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| or(and(truth,or(falsehood,falsehood)),not(Y)) != not(Y)
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(and(truth,or(falsehood,falsehood)),not(Y))),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) ),[1,0],$fot(not(Y))]]) ).
cnf(refute_0_254,plain,
( or(and(truth,or(falsehood,falsehood)),not(Y)) != not(Y)
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(not(or(and(truth,or(falsehood,falsehood)),not(Y))),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(not(Y)),
inference(resolve,[$cnf( $equal(or(and(truth,or(falsehood,falsehood)),not(Y)),not(Y)) )],[refute_0_251,refute_0_254]) ).
cnf(refute_0_256,plain,
( and(truth,Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) != not(not(Y))
| and(truth,Y) = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(truth,Y),not(not(Y))) ),[0],$fot(not(or(and(truth,or(falsehood,falsehood)),not(Y))))]]) ).
cnf(refute_0_257,plain,
( and(truth,Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(not(or(and(truth,or(falsehood,falsehood)),not(Y))),not(not(Y))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
( and(or(falsehood,and(truth,truth)),Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(and(truth,Y),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) )],[refute_0_224,refute_0_257]) ).
cnf(refute_0_259,plain,
and(truth,Y) = not(not(Y)),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) )],[refute_0_53,refute_0_258]) ).
cnf(refute_0_260,plain,
and(truth,x) = not(not(x)),
inference(subst,[],[refute_0_259:[bind(Y,$fot(x))]]) ).
cnf(refute_0_261,plain,
( and(truth,x) != not(not(x))
| not(not(x)) != x
| and(truth,x) = x ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(truth,x),x) ),[0],$fot(not(not(x)))]]) ).
cnf(refute_0_262,plain,
( not(not(x)) != x
| and(truth,x) = x ),
inference(resolve,[$cnf( $equal(and(truth,x),not(not(x))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
not(not(x)) != x,
inference(resolve,[$cnf( $equal(and(truth,x),x) )],[refute_0_262,refute_0_19]) ).
cnf(refute_0_264,plain,
implies(implies(not(not(Y)),Y),Y) = implies(implies(Y,not(not(Y))),not(not(Y))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_265,plain,
implies(or(X_26,not(X_27)),implies(X_27,X_26)) = truth,
inference(subst,[],[refute_0_73:[bind(X,$fot(X_26)),bind(Y,$fot(X_27))]]) ).
cnf(refute_0_266,plain,
or(not(X_27),X_26) = or(X_26,not(X_27)),
inference(subst,[],[or_commutativity:[bind(X,$fot(not(X_27))),bind(Y,$fot(X_26))]]) ).
cnf(refute_0_267,plain,
( or(not(X_27),X_26) != or(X_26,not(X_27))
| or(X_26,not(X_27)) = or(not(X_27),X_26) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(not(X_27),X_26))),bind(Y0,$fot(or(X_26,not(X_27))))]]) ).
cnf(refute_0_268,plain,
or(X_26,not(X_27)) = or(not(X_27),X_26),
inference(resolve,[$cnf( $equal(or(not(X_27),X_26),or(X_26,not(X_27))) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
( implies(or(X_26,not(X_27)),implies(X_27,X_26)) != truth
| or(X_26,not(X_27)) != or(not(X_27),X_26)
| implies(or(not(X_27),X_26),implies(X_27,X_26)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_26,not(X_27)),implies(X_27,X_26)),truth) ),[0,0],$fot(or(not(X_27),X_26))]]) ).
cnf(refute_0_270,plain,
( implies(or(X_26,not(X_27)),implies(X_27,X_26)) != truth
| implies(or(not(X_27),X_26),implies(X_27,X_26)) = truth ),
inference(resolve,[$cnf( $equal(or(X_26,not(X_27)),or(not(X_27),X_26)) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
implies(or(not(X_27),X_26),implies(X_27,X_26)) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_26,not(X_27)),implies(X_27,X_26)),truth) )],[refute_0_265,refute_0_270]) ).
cnf(refute_0_272,plain,
implies(or(not(X_50),not(not(X_50))),implies(X_50,not(not(X_50)))) = truth,
inference(subst,[],[refute_0_271:[bind(X_26,$fot(not(not(X_50)))),bind(X_27,$fot(X_50))]]) ).
cnf(refute_0_273,plain,
or(X,not(X)) = implies(not(X),not(X)),
inference(subst,[],[or_definition:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_274,plain,
or(falsehood,or(falsehood,X_22)) = implies(and(truth,truth),X_22),
inference(subst,[],[refute_0_62:[bind(X_19,$fot(X_22))]]) ).
cnf(refute_0_275,plain,
or(X_22,falsehood) = or(falsehood,X_22),
inference(subst,[],[or_commutativity:[bind(X,$fot(X_22)),bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_276,plain,
( or(X_22,falsehood) != or(falsehood,X_22)
| or(falsehood,X_22) = or(X_22,falsehood) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X_22,falsehood))),bind(Y0,$fot(or(falsehood,X_22)))]]) ).
cnf(refute_0_277,plain,
or(falsehood,X_22) = or(X_22,falsehood),
inference(resolve,[$cnf( $equal(or(X_22,falsehood),or(falsehood,X_22)) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
( or(falsehood,X_22) != or(X_22,falsehood)
| or(falsehood,or(falsehood,X_22)) != implies(and(truth,truth),X_22)
| or(falsehood,or(X_22,falsehood)) = implies(and(truth,truth),X_22) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(falsehood,X_22)),implies(and(truth,truth),X_22)) ),[0,1],$fot(or(X_22,falsehood))]]) ).
cnf(refute_0_279,plain,
( or(falsehood,or(falsehood,X_22)) != implies(and(truth,truth),X_22)
| or(falsehood,or(X_22,falsehood)) = implies(and(truth,truth),X_22) ),
inference(resolve,[$cnf( $equal(or(falsehood,X_22),or(X_22,falsehood)) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
or(falsehood,or(X_22,falsehood)) = implies(and(truth,truth),X_22),
inference(resolve,[$cnf( $equal(or(falsehood,or(falsehood,X_22)),implies(and(truth,truth),X_22)) )],[refute_0_274,refute_0_279]) ).
cnf(refute_0_281,plain,
or(falsehood,or(X_22,falsehood)) = or(X_22,falsehood),
inference(subst,[],[refute_0_202:[bind(Y,$fot(or(X_22,falsehood)))]]) ).
cnf(refute_0_282,plain,
( or(falsehood,or(X_22,falsehood)) != implies(and(truth,truth),X_22)
| or(falsehood,or(X_22,falsehood)) != or(X_22,falsehood)
| or(X_22,falsehood) = implies(and(truth,truth),X_22) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(X_22,falsehood)),implies(and(truth,truth),X_22)) ),[0],$fot(or(X_22,falsehood))]]) ).
cnf(refute_0_283,plain,
( or(falsehood,or(X_22,falsehood)) != implies(and(truth,truth),X_22)
| or(X_22,falsehood) = implies(and(truth,truth),X_22) ),
inference(resolve,[$cnf( $equal(or(falsehood,or(X_22,falsehood)),or(X_22,falsehood)) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
implies(truth,X_22) = X_22,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_22))]]) ).
cnf(refute_0_285,plain,
( and(truth,truth) != not(not(truth))
| not(not(truth)) != truth
| and(truth,truth) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(truth,truth))),bind(Y0,$fot(not(not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_286,plain,
( not(not(truth)) != truth
| and(truth,truth) = truth ),
inference(resolve,[$cnf( $equal(and(truth,truth),not(not(truth))) )],[refute_0_211,refute_0_285]) ).
cnf(refute_0_287,plain,
and(truth,truth) = truth,
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_194,refute_0_286]) ).
cnf(refute_0_288,plain,
implies(and(truth,truth),X_22) = implies(and(truth,truth),X_22),
introduced(tautology,[refl,[$fot(implies(and(truth,truth),X_22))]]) ).
cnf(refute_0_289,plain,
( and(truth,truth) != truth
| implies(and(truth,truth),X_22) != implies(and(truth,truth),X_22)
| implies(and(truth,truth),X_22) = implies(truth,X_22) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(truth,truth),X_22),implies(and(truth,truth),X_22)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_290,plain,
( and(truth,truth) != truth
| implies(and(truth,truth),X_22) = implies(truth,X_22) ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),X_22),implies(and(truth,truth),X_22)) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
implies(and(truth,truth),X_22) = implies(truth,X_22),
inference(resolve,[$cnf( $equal(and(truth,truth),truth) )],[refute_0_287,refute_0_290]) ).
cnf(refute_0_292,plain,
( implies(and(truth,truth),X_22) != implies(truth,X_22)
| implies(truth,X_22) != X_22
| implies(and(truth,truth),X_22) = X_22 ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(and(truth,truth),X_22))),bind(Y0,$fot(implies(truth,X_22))),bind(Z0,$fot(X_22))]]) ).
cnf(refute_0_293,plain,
( implies(truth,X_22) != X_22
| implies(and(truth,truth),X_22) = X_22 ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),X_22),implies(truth,X_22)) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
implies(and(truth,truth),X_22) = X_22,
inference(resolve,[$cnf( $equal(implies(truth,X_22),X_22) )],[refute_0_284,refute_0_293]) ).
cnf(refute_0_295,plain,
( implies(and(truth,truth),X_22) != X_22
| or(X_22,falsehood) != implies(and(truth,truth),X_22)
| or(X_22,falsehood) = X_22 ),
introduced(tautology,[equality,[$cnf( $equal(or(X_22,falsehood),implies(and(truth,truth),X_22)) ),[1],$fot(X_22)]]) ).
cnf(refute_0_296,plain,
( or(X_22,falsehood) != implies(and(truth,truth),X_22)
| or(X_22,falsehood) = X_22 ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),X_22),X_22) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
( or(falsehood,or(X_22,falsehood)) != implies(and(truth,truth),X_22)
| or(X_22,falsehood) = X_22 ),
inference(resolve,[$cnf( $equal(or(X_22,falsehood),implies(and(truth,truth),X_22)) )],[refute_0_283,refute_0_296]) ).
cnf(refute_0_298,plain,
or(X_22,falsehood) = X_22,
inference(resolve,[$cnf( $equal(or(falsehood,or(X_22,falsehood)),implies(and(truth,truth),X_22)) )],[refute_0_280,refute_0_297]) ).
cnf(refute_0_299,plain,
or(X_26,falsehood) = X_26,
inference(subst,[],[refute_0_298:[bind(X_22,$fot(X_26))]]) ).
cnf(refute_0_300,plain,
implies(or(X_26,falsehood),X_26) = implies(or(X_26,falsehood),X_26),
introduced(tautology,[refl,[$fot(implies(or(X_26,falsehood),X_26))]]) ).
cnf(refute_0_301,plain,
( implies(or(X_26,falsehood),X_26) != implies(or(X_26,falsehood),X_26)
| or(X_26,falsehood) != X_26
| implies(or(X_26,falsehood),X_26) = implies(X_26,X_26) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_26,falsehood),X_26),implies(or(X_26,falsehood),X_26)) ),[1,0],$fot(X_26)]]) ).
cnf(refute_0_302,plain,
( or(X_26,falsehood) != X_26
| implies(or(X_26,falsehood),X_26) = implies(X_26,X_26) ),
inference(resolve,[$cnf( $equal(implies(or(X_26,falsehood),X_26),implies(or(X_26,falsehood),X_26)) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
implies(or(X_26,falsehood),X_26) = implies(X_26,X_26),
inference(resolve,[$cnf( $equal(or(X_26,falsehood),X_26) )],[refute_0_299,refute_0_302]) ).
cnf(refute_0_304,plain,
( implies(or(X_26,falsehood),X_26) != implies(X_26,X_26)
| implies(or(X_26,falsehood),X_26) != truth
| implies(X_26,X_26) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_26,falsehood),X_26),truth) ),[0],$fot(implies(X_26,X_26))]]) ).
cnf(refute_0_305,plain,
( implies(or(X_26,falsehood),X_26) != truth
| implies(X_26,X_26) = truth ),
inference(resolve,[$cnf( $equal(implies(or(X_26,falsehood),X_26),implies(X_26,X_26)) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
implies(X_26,X_26) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_26,falsehood),X_26),truth) )],[refute_0_89,refute_0_305]) ).
cnf(refute_0_307,plain,
implies(not(X),not(X)) = truth,
inference(subst,[],[refute_0_306:[bind(X_26,$fot(not(X)))]]) ).
cnf(refute_0_308,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_309,plain,
( or(X,not(X)) != implies(not(X),not(X))
| or(X,not(X)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X)),truth) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
or(X,not(X)) = truth,
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(not(X),not(X))) )],[refute_0_273,refute_0_309]) ).
cnf(refute_0_311,plain,
or(not(X_50),not(not(X_50))) = truth,
inference(subst,[],[refute_0_310:[bind(X,$fot(not(X_50)))]]) ).
cnf(refute_0_312,plain,
( implies(or(not(X_50),not(not(X_50))),implies(X_50,not(not(X_50)))) != truth
| or(not(X_50),not(not(X_50))) != truth
| implies(truth,implies(X_50,not(not(X_50)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X_50),not(not(X_50))),implies(X_50,not(not(X_50)))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_313,plain,
( implies(or(not(X_50),not(not(X_50))),implies(X_50,not(not(X_50)))) != truth
| implies(truth,implies(X_50,not(not(X_50)))) = truth ),
inference(resolve,[$cnf( $equal(or(not(X_50),not(not(X_50))),truth) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
implies(truth,implies(X_50,not(not(X_50)))) = truth,
inference(resolve,[$cnf( $equal(implies(or(not(X_50),not(not(X_50))),implies(X_50,not(not(X_50)))),truth) )],[refute_0_272,refute_0_313]) ).
cnf(refute_0_315,plain,
implies(truth,implies(X_50,not(not(X_50)))) = implies(X_50,not(not(X_50))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_50,not(not(X_50)))))]]) ).
cnf(refute_0_316,plain,
( implies(truth,implies(X_50,not(not(X_50)))) != implies(X_50,not(not(X_50)))
| implies(truth,implies(X_50,not(not(X_50)))) != truth
| implies(X_50,not(not(X_50))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(X_50,not(not(X_50)))),truth) ),[0],$fot(implies(X_50,not(not(X_50))))]]) ).
cnf(refute_0_317,plain,
( implies(truth,implies(X_50,not(not(X_50)))) != truth
| implies(X_50,not(not(X_50))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_50,not(not(X_50)))),implies(X_50,not(not(X_50)))) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
implies(X_50,not(not(X_50))) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(X_50,not(not(X_50)))),truth) )],[refute_0_314,refute_0_317]) ).
cnf(refute_0_319,plain,
implies(Y,not(not(Y))) = truth,
inference(subst,[],[refute_0_318:[bind(X_50,$fot(Y))]]) ).
cnf(refute_0_320,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_321,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( $equal(implies(Y,not(not(Y))),truth) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
implies(implies(not(not(Y)),Y),Y) = implies(truth,not(not(Y))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(Y,not(not(Y))),not(not(Y)))) )],[refute_0_264,refute_0_321]) ).
cnf(refute_0_323,plain,
or(Y,not(Y)) = truth,
inference(subst,[],[refute_0_310:[bind(X,$fot(Y))]]) ).
cnf(refute_0_324,plain,
or(not(Y),Y) = or(Y,not(Y)),
inference(subst,[],[refute_0_26:[bind(X,$fot(Y)),bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_325,plain,
( or(Y,not(Y)) != truth
| or(not(Y),Y) != or(Y,not(Y))
| or(not(Y),Y) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(not(Y),Y))),bind(Y0,$fot(or(Y,not(Y)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_326,plain,
( or(Y,not(Y)) != truth
| or(not(Y),Y) = truth ),
inference(resolve,[$cnf( $equal(or(not(Y),Y),or(Y,not(Y))) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
or(not(Y),Y) = truth,
inference(resolve,[$cnf( $equal(or(Y,not(Y)),truth) )],[refute_0_323,refute_0_326]) ).
cnf(refute_0_328,plain,
implies(not(not(Y)),Y) = or(not(Y),Y),
inference(subst,[],[refute_0_65:[bind(X,$fot(not(Y)))]]) ).
cnf(refute_0_329,plain,
( implies(not(not(Y)),Y) != or(not(Y),Y)
| or(not(Y),Y) != truth
| implies(not(not(Y)),Y) = truth ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(not(not(Y)),Y))),bind(Y0,$fot(or(not(Y),Y))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_330,plain,
( or(not(Y),Y) != truth
| implies(not(not(Y)),Y) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),Y),or(not(Y),Y)) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
implies(not(not(Y)),Y) = truth,
inference(resolve,[$cnf( $equal(or(not(Y),Y),truth) )],[refute_0_327,refute_0_330]) ).
cnf(refute_0_332,plain,
implies(implies(not(not(Y)),Y),Y) = implies(implies(not(not(Y)),Y),Y),
introduced(tautology,[refl,[$fot(implies(implies(not(not(Y)),Y),Y))]]) ).
cnf(refute_0_333,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_334,plain,
( implies(not(not(Y)),Y) != truth
| implies(implies(not(not(Y)),Y),Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(not(not(Y)),Y),Y)) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
implies(implies(not(not(Y)),Y),Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),Y),truth) )],[refute_0_331,refute_0_334]) ).
cnf(refute_0_336,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(truth,Y)
| implies(truth,Y) != Y
| implies(implies(not(not(Y)),Y),Y) = Y ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(implies(not(not(Y)),Y),Y))),bind(Y0,$fot(implies(truth,Y))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_337,plain,
( implies(truth,Y) != Y
| implies(implies(not(not(Y)),Y),Y) = Y ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,Y)) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
implies(implies(not(not(Y)),Y),Y) = Y,
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_199,refute_0_337]) ).
cnf(refute_0_339,plain,
( implies(implies(not(not(Y)),Y),Y) != Y
| implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
| Y = implies(truth,not(not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,not(not(Y)))) ),[0],$fot(Y)]]) ).
cnf(refute_0_340,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
| Y = implies(truth,not(not(Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),Y) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
implies(truth,not(not(Y))) = not(not(Y)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_342,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_343,plain,
( Y != implies(truth,not(not(Y)))
| Y = not(not(Y)) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(Y))),not(not(Y))) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
| Y = not(not(Y)) ),
inference(resolve,[$cnf( $equal(Y,implies(truth,not(not(Y)))) )],[refute_0_340,refute_0_343]) ).
cnf(refute_0_345,plain,
Y = not(not(Y)),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,not(not(Y)))) )],[refute_0_322,refute_0_344]) ).
cnf(refute_0_346,plain,
( Y != not(not(Y))
| not(not(Y)) = Y ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(Y)),bind(Y0,$fot(not(not(Y))))]]) ).
cnf(refute_0_347,plain,
not(not(Y)) = Y,
inference(resolve,[$cnf( $equal(Y,not(not(Y))) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
not(not(x)) = x,
inference(subst,[],[refute_0_347:[bind(Y,$fot(x))]]) ).
cnf(refute_0_349,plain,
( not(not(x)) != x
| x != x
| not(not(x)) = x ),
introduced(tautology,[equality,[$cnf( ~ $equal(not(not(x)),x) ),[0],$fot(x)]]) ).
cnf(refute_0_350,plain,
( x != x
| not(not(x)) = x ),
inference(resolve,[$cnf( $equal(not(not(x)),x) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
x != x,
inference(resolve,[$cnf( $equal(not(not(x)),x) )],[refute_0_350,refute_0_263]) ).
cnf(refute_0_352,plain,
x = x,
introduced(tautology,[refl,[$fot(x)]]) ).
cnf(refute_0_353,plain,
$false,
inference(resolve,[$cnf( $equal(x,x) )],[refute_0_352,refute_0_351]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL156-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 11:14:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.47
% 0.18/0.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.33/0.51
%------------------------------------------------------------------------------